Answer:
U=8
Step-by-step explanation:
48<5U+8
-5U<8-48
-5U<-40
-5U/-5<-40/+5
U>8
(3x+1)^2=3(x+1). Solve for X
Answer:
Step-by-step explanation:
(3x+1)^2 = 3x+3
9x^2 +6x +1=3x+3
9x^2+3x-2=0
finally we got a trinomial quadratic equation solve by factorizing
9x^2 -6x+3x-2=0
3x(3x-2)+(3x-2)=0
3x-2 = 0 or 3x+1=0
x= 2/3 or x= -1/3
Consider the function f (x, y) = xy - 7y - 49x + 343 on the region on or above y = x^2 and on or below y = 50. Find the absolute minimum value: -7 Find the points at which the absolute minimum value is attained. List your answer sas points in the form (a, b). (0, 50) Find the absolute maximum value: 343 Find the points at which the absolute maximum value is attained. List your answers as points in the form (a, b) (0, 0).
The absolute maximum value is attained: (0, 0)
The given function is, f(x, y) = xy - 7y - 49x + 343The region is on or above y = x^2 and on or below y = 50. To find the absolute minimum and absolute maximum value of the function, f(x, y), first we will find the critical points of the function.f(x, y) = xy - 7y - 49x + 343 ⇒ ∂f/∂x = y - 49 = 0 ⇒ y = 49 ⇒ ∂f/∂y = x - 7 = 0 ⇒ x = 7Thus, the critical point is (7, 49).Next, we will check for the boundary points. The boundary of the region is y = x^2 and y = 50. The points of intersection are:x^2 = 50 ⇒ x = ±√50 (not in the region)x = ±1.58 ⇒ y = x^2 = 2.50 (not in the region)Also, x = 0 ⇒ y = 0, and x = 0 ⇒ y = 50Thus, the critical points are (7, 49) and (0, 0).f(7, 49) = 7(49) - 7(49) - 49(7) + 343 = -7f(0, 0) = 0 - 7(0) - 49(0) + 343 = 343f(0, 50) = 0 - 7(50) - 49(0) + 343 = -357f(±1.58, 2.50) = ±1.58(2.50) - 7(2.50) - 49(±1.58) + 343 = ∓36.97The absolute minimum value is -7. The points at which the absolute minimum value is attained are (7, 49) and (0, 50).The absolute maximum value is 343. The point at which the absolute maximum value is attained is (0, 0).Hence, the required points are as follows:Points at which the absolute minimum value is attained: (7, 49) and (0, 50)Points at which the absolute maximum value is attained: (0, 0)
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Translate Into a equation!
The sum of 7 times a number and 6 is 3
Step-by-step explanation:
x is the number.
the equation is
7x + 6 = 3
Which of the following are the first four nonzero terms of the Maclaurin series for the function g defined by g (x) = (1+x)e-* ? A 1 + 2x + 3x2 + x3 + ... B 1+ 2x + 3 x2 + x3 + ... с 1-222 + x3 – 124 + ... D 1 - 3x2 + 3x3 – 6:24 + ...
Let x₁ and x₂ be two independent random variabIes, each with a mean of 10 and a variance of 5.y has a mean of 203 and a variance of 85.
What is function ?A function, in mathematics, is a reIationship between a set of possibIe inputs and an equaIIy IikeIy set of outputs, where each input is associated to exactIy one outcome. Functions are commonIy represented as equations or graphs, and they are used to modeI many reaI-worId processes in domains such as physics, engineering, and economics.
Function types incIude Iinear, quadratic, trigonometric, and exponentiaI functions, among others. CaIcuIus, a fieId of mathematics that investigates how quantities change over time or space, heaviIy reIies on functions.
given
The foIIowing is the MacIaurin series for the function g(x) = (1+x)e(-x):
g(x) = ∑[n=0 to ∞] ((-1)ⁿ*xⁿ) / n!
We may simpIify and pIug in the first few vaIues of n to determine the first four nonzero terms of this series:
n = 0: ((-1)⁰*x⁰) / 0! = 1
n = 1: ((-1)¹*x¹) / 1! = -x
n = 2: ((-1)²*x²) / 2! = x²/2
n = 3: ((-1)³*x³) / 3! = -x³/6
The MacIaurin series for g(x) therefore has the foIIowing first four nonzero terms:
1 - x + x²/2 - x³/6
Let x₁ and x₂ be two independent random variabIes, each with a mean of 10 and a variance of 5. y has a mean of 203 and a variance of 85.
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Solve the given differential equation by undetermined coefficients.y" - 8y' +16y = 24x +2
The solution to the differential equation y" - 8y' + 16y = 24x + 2 is y = (c1 + c2 x) e^(4x) - 3x + 1 plus any constants determined by initial or boundary conditions.
To solve the given differential equation y" - 8y' + 16y = 24x + 2 using the method of undetermined coefficients, we first find the complementary solution of the homogeneous equation y" - 8y' + 16y = 0:
The characteristic equation is r^2 - 8r + 16 = 0, which has a double root of r = 4. Therefore, the complementary solution is y_c = (c1 + c2 x) e^(4x).
Next, we need to find a particular solution for the non-homogeneous equation. Since the right-hand side has two terms, we can try a particular solution of the form y_p = Ax + B for the homogeneous term and y_p = C for the constant term.
Substituting this form into the differential equation, we get:
y_p" - 8y_p' + 16y_p = 24x + 2
Taking the derivatives and plugging them back into the equation, we get:
-8A + 16B + 16C = 2
0 + 0 + 16C = 24
Solving for A, B, and C, we get A = -3, B = -1/2, and C = 3/2.
Therefore, the particular solution is y_p = -3x - 1/2 + 3/2 = -3x + 1.
The general solution is then y = y_c + y_p = (c1 + c2 x) e^(4x) - 3x + 1.
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the number of bacteria in a second study is modeled by the function . what is the growth rate, r, for this equation?
The number of bacteria in a second study is modeled by the function, the growth rate r for the equation is 0.017, since the equation is [tex]A(t) = 2500e^{(0.017t)}[/tex].
How to determine the growth rate r of an exponential function?To find the growth rate r of an exponential function, use the following formula:[tex]A = Pe^{(rt)}[/tex] Where:
A represents the final amountP represents the initial amountr represents the growth ratet represents timeTo determine r, divide both sides by P and take the natural logarithm of both sides. It yields: ln(A/P) = rt Therefore: r = ln(A/P) / tNow, given that the number of bacteria in a second study is modeled by the equation: [tex]A(t) = 2500e^{(0.017t)}[/tex] Compare the given equation with [tex]A = Pe^{(rt)}[/tex]. The initial amount (P) is 2500, since that is the starting amount. The final amount (A) is [tex]2500e^{(0.017t)}[/tex], since that is the amount after a certain period of time (t).Thus, [tex]r = ln(A/P) / t= ln(2500e^{(0.017t)} / 2500) / t= ln(e^{(0.017t))} / t= 0.017[/tex] (rounded to 3 decimal places)Therefore, the growth rate r for the equation is 0.017.
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using the net below find the area of the triangular prism
10 cm
7 cm
6 cm
4 cm
4 cm
10 cm
6 cm
4 cm
Answer:51
Step-by-step explanation:
Suppose that the speed at which cars go on the freeway is normally distributed with a mean of 66 miles per hour (mph) and standard deviation 10 mph. Letxxbe the speed for a randomly selected car. Round all answers to 4 decimal places where possible.What is the z-score for a car that is caught going 60 mph? The z-score =What is the probability of randomly choosing a car on the freeway and it going below 60 mph?P(x≤60)=P(x≤60)=What is the z-score for a car that is caught going 86 mph? The z-score =What is the probability of randomly choosing a car on the freeway and it going above 86 mph?P(x≥86)=P(x≥86)=If a highway patrol woman only wants to catch the top 1% of all cars on the freeway , then what speed does the car on the freeway need to be going in order for her want to catch the speeder? mph
To catch the top 1% of all cars on the freeway, the speed of the car needs to be greater than 99 mph. This is because 99 mph is three standard deviations above the mean, which would put it in the top 1% of speeds.
The question asks for the z-scores and probabilities of cars going 60 mph and 86 mph on the freeway. It also asks for the speed at which the highway patrol woman needs to catch the top 1% of cars.
Let xx be the speed for a randomly selected car on the freeway, with a mean of 66 mph and standard deviation of 10 mph.
The z-score for a car that is caught going 60 mph is -2.0000. This means that the car is two standard deviations below the mean. The probability of randomly choosing a car on the freeway and it going below 60 mph is 0.0228.
The z-score for a car that is caught going 86 mph is 2.0000. This means that the car is two standard deviations above the mean. The probability of randomly choosing a car on the freeway and it going above 86 mph is 0.0228.
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Can 3 feet, 3 feet and 7 feet create a triangle explain why or why not
The given lengths of 3 feet, 3 feet, and 7 feet cannot form a triangle because they do not satisfy the Triangle Inequality Theorem, which is the sum of the lengths of any two sides is greater than the length of the third side.
To form a triangle, the sum of the lengths of any two sides of the triangle must be greater than the length of the third side. This is known as the Triangle Inequality Theorem.
Let's apply this theorem to the given lengths of 3 feet, 3 feet, and 7 feet:
The sum of the first two sides is 3 + 3 = 6 feet, which is less than the length of the third side of 7 feet. So, the first two sides cannot form a triangle.
The sum of the first and third sides is 3 + 7 = 10 feet, which is greater than the length of the second side of 3 feet. However, the sum of the second and third sides is 3 + 7 = 10 feet, which is also greater than the length of the first side of 3 feet.
Therefore, neither of the two combinations of sides satisfy the Triangle Inequality Theorem, and so it is impossible to form a triangle with sides of 3 feet, 3 feet, and 7 feet.
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Find the equation of the straight line passing through the point (3,5) which is perpendicular to the line y=3x+2
Answer:
y = -1/3x +6
Step-by-step explanation:
You want the equation of the line through the point (3, 5) and perpendicular to y = 3x +2.
Slope-intercept formThe slope-intercept form of the equation of a line is ...
y = mx +b
where m is the slope, and b is the y-intercept.
Comparing this to the given equation, we see that m=3 for the given line.
Perpendicular linesThe slopes of perpendicular lines are opposite reciprocals of one another. This means the slope of the line we want is ...
desired slope = -1/m = -1/3
Y-interceptThe slope-intercept equation above can be solved for b to give ...
b = y -mx
Then the y-intercept for the line we want is ...
b = 5 -(-1/3)(3) = 5 +1 = 6
The equation of the desired line is y = -1/3x +6.
__
Additional comment
Once you understand how to find the slope of the given line and of the desired line, you can write down the desired equation in point-slope form.
Given slope = 3; perpendicular slope = -1/3
Point-slope equation: y -k = m(x -h) . . . . line through (h, k) with slope m
y -5 = -1/3(x -3) . . . . . line through (3, 5) with slope -1/3
The only "work" required is to rearrange this equation to whatever form you may want. In standard form it is x +3y = 18.
Arrange the steps in the correct order to find an inverse of a modulo m for each of the following pairs of relatively prime integers using the Euclidean algorithm. a = 55, m= 89 Rank the options below. The steps to find gcd(55, 89) using the Euclidean algorithm are listed below. 89 = 1.55 +34 55 = 1.34 +21 34 = 1.21 + 13 21 1 . 13 + 8 13 = 1.8+5 8 = 1.5+ 3 5 = 1.3+2 3 = 1.2+1 2 = 1.2 The Bézout coefficient of 55 is 34, and it is an inverse of 55 modulo 89. The Bézout coefficients of 55 and 89 are 34 and -21, respectively. -21, respectively. The ged in terms of 55 and 89 is written as 1 = 3-1.2 = 3-1. (5-1.3) = 2.3-1.5 = 2. (8-1.5) - 1.5 = 2.8-3.5 = 2.8-3. (13-1-8)= 5.8-3.13 = 5. (21-1.13) - 3.13 = 5.21-8. 13 = 5.21-8. (34-1.21) = 13.21-8.34 = 13. (55 - 1. 34)- 8. 34 = 13.55 - 21 34 = 13.55 - 21 - (89-1. 55) = 34.55 -21.89
The correct order of steps is 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.
To find the inverse of 55 modulo 89 using the Euclidean algorithm, the steps are:
1. 89 = 1.55 +34
2. 55 = 1.34 +21
3. 34 = 1.21 + 13
4. 21 = 1.13 + 8
5. 13 = 1.8 +5
6. 8 = 1.5 +3
7. 5 = 1.3 +2
8. 3 = 1.2 +1
9. 2 = 1.2
10. The Bézout coefficient of 55 is 34, and it is an inverse of 55 modulo 89.
11. The Bézout coefficients of 55 and 89 are 34 and -21, respectively.
12. The gcd in terms of 55 and 89 is written as 1 = 34-21.89 = 34-21. (55-1.34) = 13.34-21.55 = 13. (21-1.13) - 3.13 = 5.21-8. 13 = 5. (8-1.5) - 1.5 = 2.8-3.5 = 2. (3-1.2) = 2.3-1.5 = 2. (2-1) = 3-1.2 = 3-1. (1-0) = 34-21.89
The correct order of steps is 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.
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ratings services measure television audiences. the measurement of the percentage of all households with televisions that are tuned into the same show at the same time is called
Therefore , the solution of the given problem of percentage comes out to be were tuned in to a specific program or show at a given moment.
What is percentage?A number or figure stated as a fraction of 100 is referred to as "a%" in statistics. The versions that begin with "pct," "pct," and "pc" are also uncommon. The common way to indicate it is with the numeral "%," though. Furthermore, there are no indicators and a flat ratio of every single thing to the total number. Percentages are basically integers because they frequently add up to 100.
Here,
The TV ratings, also known as the TV audience share, are a measurement of the proportion of all television-owning households that are watching the same program at the same moment.
Networks and marketers use it as a gauge of a TV show's popularity to decide how successful a program will be and how much to charge for advertising during it.
Companies like Nielsen, which use a sample of homes with televisions to estimate the audience size for a given program or show, are usually in charge of gathering the TV ratings.
TV ratings are expressed as a proportion of all households with televisions that were tuned in to a specific program or show at a given moment.
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One characteristic of all exponential functions is that they change by
One characteristic of all exponential functions is that they change by a constant factor at each step, which means that they exhibit exponential growth or decay.
The constant factor by which an exponential function changes is called the base, which is usually denoted by the symbol "b". If b is greater than 1, the function exhibits exponential growth, and if b is between 0 and 1, the function exhibits exponential decay.
For example, the function f(x) = 2^x is an exponential function with a base of 2. At each step, the function increases by a factor of 2. For instance, f(0) = 1, f(1) = 2, f(2) = 4, f(3) = 8, and so on.
On the other hand, the function g(x) = (1/2)^x is an exponential function with a base of 1/2. At each step, the function decreases by a factor of 1/2. For instance, g(0) = 1, g(1) = 1/2, g(2) = 1/4, g(3) = 1/8, and so on.
Therefore, exponential functions exhibit a characteristic change by a constant factor at each step, which leads to either exponential growth or decay.
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a rectangular prism has a height of 1/5 m and a square base with an area of 7 1/2 m^2. What is the volume of the rectangular prism?
The volume of the rectangular prism is approximately 0.2996 cubic meters.
What is rectangular prism and its volume?Six rectangular faces that are congruent and parallel to one another make up the three-dimensional solid known as a rectangular prism. A rectangular cuboid is another name for it.
By multiplying the prism's length, width, and height, one may get the volume of a rectangular prism, which is the volume of the interior space of the prism.
Given that, area of the square base is 7 1/2 sq. m.
The side of the square base is thus,
√(7 1/2) ≈ 2.7386 m
The volume of the rectangular prism is given as:
Volume = length x width x height
Volume ≈ 2.7386 x 2.7386 x 1/5 m
Volume ≈ 0.2996 cubic meters.
Hence, the volume of the rectangular prism is approximately 0.2996 cubic meters.
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Binomial Problem:A jury has 12 jurors. A vote of at least 10 out of 12 for "guilty" is necessary for a defendant to be convicted of a crime. Assume that each juror acts independently of the others and that the probability that any one juror makes the correct decision on a defendant is .80. If the defendeant is guitly, what is the probability that the jury makes the correct decision?
The probability that the jury makes the correct decision is approximately 0.7063.
To solve this problem, we need to find the probability that the jury makes the correct decision if the defendant is guilty. Let's break down the problem into smaller steps.
We know that the probability of a single juror making the correct decision is 0.80. If the defendant is guilty, then the probability of a juror making the correct decision is still 0.80. Therefore, the probability that a single juror makes the correct decision if the defendant is guilty is 0.80.
We can use the binomial distribution formula to determine the probability of at least 10 out of 12 jurors making the correct decision. The formula is:
P(X ≥ k) = 1 - Σ(i=0 to k-1) [n!/(i!(n-i)!) x [tex]p^i \times (1-p)^{(n-i)}[/tex] ]
where:
P(X ≥ k) is the probability of at least k successes
n is the total number of trials (in this case, 12 jurors)
p is the probability of success in a single trial (in this case, 0.80)
k is the number of successes we want to find the probability of (in this case, 10)
Plugging in the values, we get:
P(X ≥ 10) = 1 - Σ(i=0 to 9) [12!/(i!(12-i)!) x [tex]0.80^i \times (1-0.80)^{(12-i)}[/tex]]
Using a calculator or software, we can calculate this to be approximately 0.7063.
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if you flipped a fair coin 40 times, what is the heoretical proportion of heads? in other words, what percent do you expect to come up heads> based on your confidence interval, do yuou think thje copi used was fair? wy or why not
A fair coin is flipped 40 times. The probability of getting a head when the coin is tossed is 0.5. If the same coin is flipped 40 times, the probability will remain 0.5. That is, there are equal chances of getting heads and tails when a fair coin is flipped.
Based on the confidence interval, if the actual proportion of heads falls within the range of the confidence interval, it can be said that the coin used was fair. If the actual proportion is outside the confidence interval, it may be an indication that the coin was not fair.
The level of confidence is typically 95% or 99%. If a confidence interval is constructed for the proportion of heads based on a sample of 40 flips and the interval includes the expected proportion of 50%, it can be said that the coin used was fair. If the interval does not include 50%, there is evidence that the coin may not be fair.
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Identifying and naming congruent angles 
In response to the stated question, we may state that As a result, the figure's pairs of congruent angles are: ∠BAC ≅ ∠EDF; ∠ABC ≅ ∠DEF; ∠ACB ≅ ∠DFE
What are angles?An angle is a form in Euclidean geometry that is constructed from two rays, known as the tone's sides, that connect at a central location known as angle's vertex.
Two beams may combine to generate an inclination in the plane in which they are located. They are known as dihedral angles. In plane geometry, an angle is a potential arrangement of two rays or planes that meet a termination.
The English term “angle” derives from the Latin phrase "angulus," which means "horn." The vertex is the point at where the twin rays, also termed as the angle's sides, converge.
The congruent angles in the illustration are:
BAC and EDF are vertically opposed angles with the same measurement.
ABC and DEF are equivalent angles with the same measure.
ACB and DFE are equivalent angles with the same measure.
Therefore, the figure's pairs of congruent angles are:
∠BAC ≅ ∠EDF
∠ABC ≅ ∠DEF
∠ACB ≅ ∠DFE
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Need help with b, please show work
Step-by-step explanation:
remember, the sum of all angles in a triangle is always 180°.
the law of sine :
a/sin(A) = b/sin(B) = c/sin(C)
with a, b, c being the sides, and A, B, C being the three corresponding opposite angles.
so, the angle at Q is
180 = 48 + 48 + angle Q = 96 + angle Q
84° = angle Q
5mm/sin(48) = PR/sin(84)
PR = 5×sin(84)/sin(48) = 6.691306064... mm
The length of PR is approximately 10.33 mm.
what is isosceles triangle ?
An isosceles triangle is a triangle with at least two sides that have equal length, and thus two corresponding angles that are also equal in measure. The third side and angle of an isosceles triangle may or may not be of different length or measure. The two sides that are equal in length are called the legs, and the third side is called the base. The angle opposite the base is called the vertex angle, while the angles adjacent to the legs are called the base angles. In an isosceles triangle, the two base angles are equal in measure.
Since the sum of the angles in a triangle is 180 degrees, we can find the measure of angle PQR as follows:
PQR = 180 - QPR - QRP
PQR = 180 - 48 - 48
PQR = 84 degrees
Since angles QRP and QPR have the same measure, we know that sides OP and OR have equal length (they are opposite those angles). Therefore, triangle POR is an isosceles triangle.
To find the length of PR, we can use the Law of Cosines:
PR^2 = OP^2 + OR^2 - 2(OP)(OR)cos(POR)
Since OP and OR are equal in length, we can simplify this equation to:
PR^2 = 2(OP^2) - 2(OP^2)cos(POR)
We know that POR is 180 - PQR = 96 degrees. We also know that OP = OR, and that QP = 5 mm. Using the Law of Cosines, we can find the length of OP:
OP^2 = QP^2 + OR^2 - 2(QP)(OR)cos(QPR)
OP^2 = 5^2 + OR^2 - 2(5)(OR)cos(48)
OP^2 = OR^2 - 5ORcos(48) + 25
Since OP = OR, we can substitute OP for OR in the above equation:
OP^2 = OP^2 - 5OPcos(48) + 25
5OPcos(48) = 25
OP = 25/(5cos(48))
OP ≈ 6.25 mm
Now we can substitute this value into the equation we derived earlier to find PR:
PR^2 = 2(OP^2) - 2(OP^2)cos(POR)
PR^2 = 2(6.25^2) - 2(6.25^2)cos(96)
PR ≈ 10.33 mm
Therefore, the length of PR is approximately 10.33 mm.
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Each section of the graphic organizer contains a vocabulary term or the possible
solution type for the system shown. Use the list below to complete the graphic
organizer. Some terms may be used more than once.
slope y-intercept linear equations
infinitely many solutions no solution one solution
System of
y= 3x+ 2
y= - 4x+ 2
Different
y= 2x+ 7
y= 2x- 4
Same
y= 6x+ 3
y= - x- 4
Number of solutions:
y= 4x+ 3
y= 4x- 1
Different
y= 3x+ 6
y= 3x+ 6
Same
y= 4x+ 3
y= 4x- 1
Number of solutions:
y= 3x+ 6
y= 3x+ 6
Number of solutions:
For the first equation with y = 3x + 2 and y = -4x + 2, the lines have the same slope, but a different y-intercept. This means that the lines are parallel and they will never intersect. Therefore, the system of equations has no solution.
For the second equation with y = 2x + 7 and y = 2x - 4, the lines have the same slope and the same y-intercept. This means that the lines are coincident and they will intersect at one point. Therefore, the system of equations has one solution.
For the third equation with y = 6x + 3 and y = -x - 4, the lines have a different slope and a different y-intercept. This means that the lines are not parallel and they will intersect at one point. Therefore, the system of equations has one solution.
For the fourth equation with y = 4x + 3 and y = 4x - 1, the lines have the same slope and the same y-intercept. This means that the lines are coincident and they will intersect at one point. Therefore, the system of equations has one solution.
For the fifth equation with y = 3x + 6 and y = 3x + 6, the lines have the same slope and the same y-intercept. This means that the lines are coincident and they will intersect at one point. Therefore, the system of equations
What value of x would make the denominator of the rational expression x2+2x+5/
x+5 equal to 0?
Answer:
The Answer is -5 (negative five)
please ive been on this question for a week
NEED HELP DUE TODAY!!!! GIVE GOOD ANSWERS PLEASE!!!!
2. How do the sizes of the circles compare?
3. Are triangles ABC and DEF similar? Explain your reasoning.
4. How can you use the coordinates of A to find the coordinates of D?
When the radius of circle 2 is twice the radius of circle 1, the size of circle 2 is larger than circle 1.
What is triangle?In geometry, a triangle is a polygon with three sides and three angles. The sum of the angles in a triangle is always 180 degrees. Triangles are one of the most basic and fundamental shapes in geometry and are used in many mathematical and real-world applications, such as in architecture, engineering, and physics. There are different types of triangles based on the length of their sides and the measures of their angles, such as equilateral triangles, isosceles triangles, scalene triangles, acute triangles, obtuse triangles, and right triangles.
Here,
2. This is because the circumference and area of a circle are directly proportional to the radius.
3. To determine if triangles ABC and DEF are similar, we need to check if their corresponding angles are congruent and if their corresponding sides are in proportion. From the diagram, we can see that angle A is congruent to angle D, angle B is congruent to angle E, and angle C is congruent to angle F. This satisfies the angle-angle (AA) similarity criterion. Additionally, we can use the side-side-side (SSS) similarity criterion to determine if the corresponding sides are in proportion. From the diagram, we can see that side AB is parallel to side DE, side AC is parallel to side DF, and side BC is parallel to side EF. Therefore, we can conclude that triangles ABC and DEF are similar.
4. To find the coordinates of D using the coordinates of A, we need to determine the translation from A to D. From the diagram, we can see that A is translated two units to the right and three units down to get to D. Therefore, we can find the coordinates of D by adding two to the x-coordinate of A and subtracting three from the y-coordinate of A. If the coordinates of A are (x1, y1), then the coordinates of D would be (x1 + 2, y1 - 3).
A= (-0.87,0.5)
D=(-0.87 + 2, 0.5 - 3)
D=(1.13,-2.5)
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Imagine that 3 committee members arrive late. The other 5 memebers have already shaken hands. How many handshakes will there be when the 3 late members arrive?
There will be a total of 28 handshakes when the 3 late members arrive.
What is sum of n positive integers?The first n-1 positive integers are added together using the formula n(n-1)/2, where n is the total number of terms being added together.
The number of combinations or arrangements of a given collection of items may be determined using this formula, which can be obtained using the process of mathematical induction. It is often used in combinatorics and discrete mathematics. For instance, the formula was used to determine how many times a group of individuals shook hands in the scenario above. It might also be used to determine the number of pathways in a network of nodes or vertices or the number of ways to choose a portion of an object set from a bigger set in other settings.
Given that, 3 members arrive late, and 5 members are already present.
The total members are 5 + 3 = 8.
Now, using the sum of positive integer formula:
n(n-1)/2
We can determine the number of handshakes.
8(8-1)/2 = 28
Hence, there will be a total of 28 handshakes when the 3 late members arrive.
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you are dealt one card from a standard 52-card deck. playing cards find the probability of being dealt a three and an ace. the probability of being dealt a three and an ace is . (type an integer or a fraction.)
The probability of getting an ace and a three is (4/52) × (3/51) = 12/2652 which simplifies to 1/221.
There are 4 aces and 4 threes in a deck of 52 standard cards.
The probability of getting an ace on your first draw is 4/52.
Once you have the ace, there are 51 cards left in the deck, 3 of which are threes.
Therefore, the probability of drawing a three is 3/51.
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Please help it is due tomorrow
Answer: 30
Step-by-step explanation: So what you do is,
1) Add the 25 to the 8
2) Find the sum
3) Subtract 3 from the sum
4) Done!
I hope this helps!
Best,
Abigail H
8th Grade
Thabang save money by putting coins in a money box. The money box has 600 coins that consist of 20 cents and 50 cents
So calculate how many 50 cents pieces are in the container if there are 220 pieces of 20 cents
The number of 50 cents in the container is 380 fifty cents
How to find the number of 50 cents in the container?Since Thabang save money by putting coins in a money box. The money box has 600 coins that consist of 20 cents and 50 cents
To calculate how many 50 cents pieces are in the container if there are 220 pieces of 20 cents, we proceed as follows.
Let
x = number of 20 cents and y = number of 50 centsSince the total number of cents in the container is 600, we have that
x + y = 600
So, making y subject of the formula, we have that
y = 600 - x
Since x = 220
y = 600 - 220
= 380
So, there are 380 fifty cents
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PLS HELP WITH SOME ONE THE ANSWER (50 points!)
How does cellular respiration help maintain homeostasis in animals?
Explain why cells separate and expel waste.
Why do cells in organisms such as animals reproduce?
Explain how plant cells use photosynthesis to maintain homeostasis?
How does cellular respiration help maintain homeostasis in animals?
Answer: Cellular respiration helps animals maintain homeostasis by breaking down glucose to produce ATP, which is the energy currency of the cell. ATP is necessary for many cellular processes that help maintain homeostasis such as active transport and protein synthesis.
Explain why cells separate and expel waste.
Answer: Cells separate and expel waste to prevent the accumulation of toxic substances that can disrupt cellular function and lead to disease. The waste products are transported out of the cell and into the bloodstream where they are filtered and excreted by organs such as the kidneys.
Why do cells in organisms such as animals reproduce?
Answer: Cells in organisms such as animals reproduce to replace damaged or dying cells, and to enable growth and development. Reproduction ensures that the organism maintains the proper balance of cells and that there is enough tissue to perform necessary functions.
Explain how plant cells use photosynthesis to maintain homeostasis?
Answer: Plant cells use photosynthesis to maintain homeostasis by converting light energy into chemical energy in the form of glucose. This glucose is then used to produce ATP, which is necessary for cellular processes such as active transport and protein synthesis. Additionally, plants use photosynthesis to produce oxygen, which is necessary for respiration.
I hope this helps :)
the number of students using the cafeteria's healthy lunch line can be found by solving the inequality 1/5s - 51 < 20. How many students use this lunch line?
Select the answers from the drop-down list to correctly complete the sentence
There are ___ students ___ that use this lunch line
1. 142
2. 62
3. 36
4.35
1. or more
2. or fewer
PLEASE HELP NEEDED!!!
The answer of the given question based on the the number of students using the cafeteria's healthy lunch line can be found by solving the inequality 1/5s - 51 < 20, the correct answer is (1) 142 , (1) or more.
What is Equation?An equation is mathematical statement that shows equality of two expressions, typically separated by equal sign. Equations are used to express relationships between variables and to solve problems in various fields of mathematics, science, and engineering. In essence, an equation is representation of real-world scenario or problem in mathematical terms.
The variables in equation can take on different values, and equation remains true regardless of the values chosen for variables. Solving equation means finding values of the variables that make equation true.
Equations can be linear, quadratic, polynomial, exponential, logarithmic, or trigonometric, among other types. They are fundamental tool in mathematics and have numerous applications in fields like physics, engineering, economics, and finance.
There are 155 students or more students that use this lunch line.
The correct answer is 1. or more.
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What is the value of x? X = X-38° O X X-33°
Answer:
Step-by-step explanation:
A company finds that if it charges x dollars for a cell phone, it can expect to sell 1,000−2x phones. The company uses the function r defined by r(x)=x⋅(1,000−2x) to model the expected revenue, in dollars, from selling cell phones at x dollars each. At what price should the company sell their phones to get the maximum revenue? x i tercept
The company should sell their phones for $250 each to get the maximum revenue.
What do you mean by maximum revenue?
Maximum revenue refers to the highest possible amount of income that can be generated from a particular product or service. In the context of the given problem, it means finding the price at which the company can sell its cell phones to earn the highest amount of revenue.
Finding the price at which the company should sell their phones to get the maximum revenue:
We need to find the vertex of the parabolic function [tex]r(x)=x(1,000-2x)[/tex], which represents the revenue as a function of the selling price.
To find the vertex of the function r(x), we need to first rewrite it in standard form by expanding the product:
[tex]r(x) = 1000x - 2x^2[/tex]
Now we can see that the function is a quadratic polynomial in standard form, with [tex]a=-2, b=1000[/tex], and [tex]c=0[/tex]. To find the x-coordinate of the vertex, we can use the formula:
[tex]x = -b / (2a)[/tex]
Substituting the values of a and b, we get:
[tex]x = -1000 / (2\times(-2)) = 250[/tex]
Therefore, the company should sell their phones for $250 each to get the maximum revenue. To find the maximum revenue, we can substitute this value of x into the function r(x):
[tex]r(250) = 250\times(1000-2\times250) = $125,000[/tex]
So the maximum revenue the company can expect to earn is $125,000 if they sell their phones for $250 each.
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