Answer:
y=-5.5x-52
Step-by-step explanation:
Your input: find the equation of a line given two points P = (-10 , 3) and Q = (-8 , -8). The slope of a line passing through the two pointsP=(x1,y1) and Q=(x2,y2) is given byWe have that x1 = -10 , y1 = 3, x2 = -8 , y2 = -8Step 2:Plug the given values into the formula for slope:Step 3:Now, the y-intercept is b=y1−m⋅x1 (or b=y2−m⋅x2, the result is the same).b = 3 - (-5.5) ⋅ (-10) = -52Step 4:Finally, the equation of the line can be written in the form y=mx+b.y = -5.5x -52The equation of the line in the slope-intercept form is:y = -5.5x -52The equation of the line in the point-slope form is:y - (3) = -5.5 ⋅ ( x - (-10))The equation of the line in the point-slope form is:y - (-8) = -5.5 ⋅ ( x - (-8))The general equation of the line is:-5.5x - y -52 = 0
There are currently 25 frogs in a (large) pond. The frog population grows exponentially, tripling every 10 days.
How long will it take (in days) for there to be 150 frogs in the pond?
Time to 150 frogs: days
The pond's ecosystem can support 1400 frogs. How long until the situation becomes critical?
Time to 1400 frogs: days
There are 21 days for there to be 150 frogs in the pond.
There are 37 days for there to be 1400 frogs in the pond.
What is exponential growth?
Quantity increases over time through a process called exponential growth. When a quantity's instantaneous rate of change with respect to time is proportional to the quantity itself, it happens.
Given:
There are currently 25 frogs in a (large) pond. The frog population grows exponentially, tripling every 10 days.
The exponential equation for the given problem is,
[tex]A(t) = Ar^t^/^1^0[/tex]
To find the number of days for there to be 150 frogs in the pond.
Here,
A(t) = 250, A = 25, r = 3
⇒
[tex]250 = 25(3)^t^/^1^0\\10 = 3^t^/^1^0\\t = 20.97[/tex]
t ≈ 21
Hence, there are 21 days for there to be 150 frogs in the pond.
Now to find how long for there to be 1400 frogs in the pond, we solve:
[tex]1400 = 25(3)^t^/^1^0\\56 = (3)^t^/^1^0\\t = 36.64[/tex]
t ≈ 37
Hence, there are 37 days for there to be 1400 frogs in the pond.
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McDonald's has a leaking drink machine. The manager placed a cup under the leak until he
could get it fixed. After 1 1/4 hours, the manager noticed that the cup had collected 1/3 cups of
soda. What is the rate, in cups per hour, at which the drink machine is leaking?
Answer:
4/15 cups of soda per hour
Step-by-step explanation:
1 1/4 = 5/4 and if 5/4 hours yielded 1/3 cups, you would have to multiply 1/3 by the reciprocal to find the hourly rate
1 4 4
- * - = --
3 5 15
This function vertically stretches y = √x by a factor of 3, then translates it 2 units left.
We get 3y= √(x+2) after vertically stretches by 3 and translated 2 unit left.
What means vertically stretches?If a function is multiplied by a positive value that greater than 1, the graph of function is called vertically stretched graph. Here vertically stretches means the factor 3>1 and we need to multiply the y value by 3.
What means by translate 2 unit left?Translation of a graph means move the graph from one position to another position without changing its size, shape or orientation. Here, the graph is translated 2 units left so we need to add 2 with the x value.
We are given a graph, y= √X
Hence, after transformation the graph became 3y= √(x+2)
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Your iron works has contracted to design and build a 500-ft^3, square-based, open-top, rectangular steel holding tank for a paper company. The tank is made by welding thin stainless steel plates together along their edges. As the production engineer, your job is to find dimensions for the base and height that will make the tank weigh as little as possible. What dimensions do you tell the shop to use?
The dimensions for the base and height that will make the tank weigh as little as possible are 10 feet and 5 feet, respectively
How to determine the dimensions to use?From the question, we have the following parameters that can be used in our computation:
Volume = 500 cubic feet
Base = square base
This means that the volume can be calculated using
V = b²h
Where
b = base length
h = height
So, we have
b²h = 500
Make h the subject
h = 500/b²
The surface area is calculated as
A = 4bh + b²
Substitute h = 500/b² in A = 4bh + b²
A = 4b(500/b²) + b²
Evaluate
A = 2000/b + b²
Differentiate and set to 0
-2000/b² + 2b = 0
So, we have
2b = 2000/b²
Divide by 2
b = 1000/b²
Multiply by b²
b³ = 1000
So, we have
b = 10
Substitute b = 10 in h = 500/b²
h = 500/10²
Evaluate
h = 5
Hence, the height is 5 feet
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austin is driving to san francisco, suppose that the distance to his destnation in miles is a linear function of total driving time
40 miles will he have after 85 minutes of driving .
Given :
austin is driving to san francisco, suppose that the distance to his destination in miles is a linear function of total driving time. has 67 miles to his destination after 49 minutes of driving . He has 47.5 miles to his destination after 75 minutes of driving .
slope = y2 - y1 / x2 - x1
m = 47.5 - 67 / 75 - 49
= -19.5 / 26
= -3/4
= -0.75
Use the point slope y - y1 = m(x - x1)
y - 67 = -.75 ( x - 49 )
y - 67 = -.75x + 36.75
y = -.75x + 36.75 + 67
y = -.75x + 103.75
x = 85
y = -.75(85) + 103.75
y = -63.75 + 103.75
y = 40 miles
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Full question :
austin is driving to san francisco, suppose that the distance to his destnation in miles is a linear function of total driving time has 67 miles to his destination after 49 minutes of driving . He has 47.5 miles to his destination after 75 minutes of driving . How many miles will he have after 85 minutes of driving ?
Cost of goldfish: $3.45
Markup: 29%
What is the new cost?
After the markup in the price, the new cost of goldfish will be equal to $4.45.
What is the Percentage?The Latin phrase "per centum," which means "by the hundred," is where the English word "percentage" comes from. Percentage segments are those with a numerator of 100. In other words, it is a connection where the whole is always deemed to be valued 100.
As per the given information in the question,
Cost of goldfish = $3.45
Markup = 29%
So, the price increase will be,
(3.45 × 29)/100
= 100.05/100
= 1.0005
So, the new price is,
$3.45 + $1.0005
= $4.4505 ≈ $4.45
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Select the number that completes the equivalent fraction.
3/4=9/?
4
8
10
12
which of the following is not a valid property of circles? a rotateangle b none of these c left d width
There is no property named 'left' for the circle. So the answer is 'c'.
What is Circle?Circle is a two dimensional figure which has a round shape. It is formed by joining all the points which are at an equal distance from a fixed point called the center of the circle.
The line formed by joining the center to any point on the boundary of the circle is called radius. Diameter is double of the radius.
Rotate angle is the term defining the angle of rotation of the circle. Angle of rotation of a complete circle is 2π.
Width is another term for diameter of the circle, although it is not commonly used.
Left is the only term which does not have any role in the properties of circles.
Hence, the term 'left' is not a valid property of circles.
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Use the definition of continuity and the properties of limits to show that the function is continuous at the given number a.
f(x) = 3x^4 − 5x + ^3√(x^2 + 4), a = 2
The function f(x) = 3[tex]x^{4}[/tex] - 5[tex]x^{3}[/tex] + 3 [tex]\sqrt{x^{2} +4}[/tex] is continuous at x = 2.
Given that,
We need to follow the following steps:
The function is:
f(x) = 3x^4 − 5x + ^3√(x^2 + 4)
The function is continuous at point x=2 if:
The function f(x) exists at x=2.
The limit on both sides of 2 exists.
The value of the function at x=2 is the same as the value of the limit of the function at x = 2.
Therefore:
The value of the function at x = 2 is:
f(x) = 3[tex]x^{4}[/tex] - 5[tex]x^{3}[/tex] + 3 [tex]\sqrt{x^{2} +4}[/tex]
f(2) = 3[tex](2^{4} )[/tex] - 5[tex](2^{3} )[/tex] + 3[tex]\sqrt{2^{2} +4}[/tex]
f(2) = 3*16 - 5*8 + 3 [tex]\sqrt{8}[/tex]
f(2) = 48 - 40 + 3*2.82
f(2) = 8 + 8.46
f(2) = 16.46
The limit of the f(x) is the same at both sides of x=2, that is, the evaluation of the limit for values coming below x = 2, or 1,0.5 is the same that the limit for values coming above x = 2, or 3 , 4 , 5 etc.
For this case:
[tex]lim_{x -2} f(x)[/tex] = 3[tex]x^{4}[/tex] - 5[tex]x^{3}[/tex] + 3 [tex]\sqrt{x^{2} +4}[/tex]
[tex]lim_{x -2} f(x)[/tex] = 16.46
Since
f(2) = 16.46
And
[tex]lim_{x -2} f(x)[/tex] = 16.46
Therefore,
The function f(x) = 3[tex]x^{4}[/tex] - 5[tex]x^{3}[/tex] + 3 [tex]\sqrt{x^{2} +4}[/tex] is continuous at x = 2.
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Which equation is the inverse of y = 2x^2 – 8?
Inverse of the equation y = [tex]2x^2-8[/tex] is [tex]y = \pm \sqrt{\frac{x+8}{2} }[/tex]
What do you mean by inverse function?
Let f and g be two functions. If
f(g(x)) = x and g(f(x)) = x,
g is the reciprocal of f, and f is the reciprocal of g.
Some functions don't have inverses Let f be a function.
If the horizontal line crosses the graph of f more than once, then f has no inverse.
If no horizontal line crosses the graph of f more than once, then f is the inverse.
Given equation:
y = [tex]2x^2-8[/tex]
To find the inverse of the function find the value of the x in terms of y
[tex]2x^2-8=y[/tex]
[tex]2x^2=y+8[/tex]
[tex]x^{2} =\frac{y+8}{2}[/tex]
x = [tex]\pm \sqrt{\frac{y+8}{2} }[/tex]
Therefore, inverse of the equation y = [tex]2x^2-8[/tex] is [tex]y = \pm \sqrt{\frac{x+8}{2} }[/tex]
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Which expressions are equivalent to 20 divided by 1 plus 4
The expression equivalent to "20 divided by 1 plus 4" is 20 ÷ 1 + 4.
What are the rules of PEDMAS?The rules of PEDMAS can be understood by the full form of the name. B stands for bracket, O for of, D for division, M for multiplication, A for addition and S stands for subtraction. For a mathematical expression involving the combination of any of these operators the priority will be given to the letter that comes first.
The given statement for the problem is, " 20 divided by 1 plus 4".
It can be written in the form of expression as follows,
The sign of plus is given as '+'.
And, for divide it is '÷'.
Now, 20 divided by 1 plus 4 can be written as,
20 ÷ 1 + 4
Which is evaluated by BODMAS to give,
20 + 4 = 24.
Hence, the expression for the given case is 20 ÷ 1 + 4 which is equal to 24.
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MP MODELING REAL LIFE You sell instruments at a
Caribbean music festival. You earn $326 by selling 12 sets
of maracas, 6 sets of claves, and x djembe drums. Find the
number of djembe drums you sold.
The number of djembe drums you sold is 8
How to determine the number of djembe drums you sold.From the question, we have the following parameters that can be used in our computation:
Total = 12 sets of maracas, 6 sets of claves, and x djembe drums.
Earning = $326
Also, we have:
The maracas costs $14 per set, the claves costs $5 per set, and the drum cost $16.
So, we have
12 * 14 + 6 * 5 + x * 16 = 326
Evaluate the products
198 + 16x = 326
Evaluate the iike terms
16x = 128
So, we have
x = 8
Hence, the number of djembe drums is 8
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Complete question
You sell instruments at a Caribbean music festival. You earn $326 by selling 12 sets of maracas, 6 sets of claves, and x djembe drums.
The maracas costs $14 per set, the claves costs $5 per set, and the drum cost $16.
Find the number of djembe drums you sold.
a school organized three different trips. 50% of the students went on 1st trip, 80% went on the second trip and 90% went on the third trip. a total of 160 students went on all the three trips. how many students are at the school
Answer:m
Step-by-step explanation:
An air traffic controller is tracking two planes. To start, plane A is at an altitude of 3500 feet and plane B is at an altitude of 2609 feet. Plane A is gaining altitude at 45.5 feet per second and plane B is gaining 65.75 feet per second. How many seconds will pass before the planes are at the same altitude? What will their altitudes be when they’re at the same altitude?
44 seconds will pass before the planes are at the same altitude.
What do you mean by algebraic expression?
An algebraic expression in mathematics is an expression that consists of variables and constants and algebraic operations (addition, subtraction, etc.). Expressions are made up of concepts.
There are three main types of algebraic expressions:
Monomial Expression
Binomial Expression
Polynomial Expression
An algebraic expression with only one term is called a monomial.
It is given that plane A is at an altitude of 3500 feet and plane B is at an altitude of 2609 feet. Plane A is gaining altitude at 45.5 feet per second and plane B is gaining 65.75 feet per second.
Let x seconds will pass before the planes are at the same altitude.
Plane A, 3500 + 45.5x
Plane B, 2609 + 65.75x
x is number of seconds of time
When altitudes equal
3500 + 45.5x = 2609 + 65.75x
3500 - 2609 = 65.75x - 45.5x
891 = 20.25x
891/20.25 = x
44 = x
Therefore, 44 seconds will pass before the planes are at the same altitude.
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Total students in a class are 120. 40% of them are female students. 70 male students passed with 100% pass rate. What is the pass rate of female students at 100 percent rate?
Answer:
Here is the answer
Step-by-step explanation:
If 40% of the students in the class are female, then there are 40/100 * 120 = 48 female students.
If 70 male students passed with a 100% pass rate, then the pass rate for male students is 100%.
If the pass rate for male students is 100%, then the pass rate for female students must also be 100%. This is because the pass rate is calculated as the number of students who pass divided by the total number of students, and if all the male students pass, then the pass rate for male students must be 100%.
Therefore, the pass rate for female students at a 100% rate is also 100%.
Five acres of land were divided into 4 lots of equal size. How many square feet did each lot measure? (1 acre = 43,560 sq ft)
The number of square feet each lot measure is 54, 450 square feet.
How to find the area in square feet of the lot?Five acres of land were divided into 4 lots of equal size. The number of square feet each lot measure can be calculated as follows:
1 acre = 43,560 square ft
5 acres = ?
cross multiply
number of acres = 5 × 43,560
number of acres = 217800 square feet.
Therefore, the lots is divide into 4 equal lots.
Hence,
measure of each lot = 217800 / 4
measure of each lot = 54, 450 square feet.
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find the value of the expression w2 + 1v for v=3 and w=3
Answer: 12
Step-by-step explanation:
Since we are given what v and w are, we can directly plug them in to solve the expression.
w²+1v [plug in v and w]
(3)²+1(3) [exponent]
9+1(3) [multiply]
9+3 [add]
12
The expression is equal to 12.
Evaluate the expression below for s=3 and t=6.
3st² - s²
For s = 3 and t = 6, 3st² - s² =
The value of the expression is 3st² - s² is 315.
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)
Given expression is 3st² - s².
For s = 3 and t = 6, find the value of the expression 3st² - s².
To find the value of the expression, replace s by 3 and t by 6:
3st² - s²
= 3×3×6² - 3²
= (9 × 36) - 9
= 324 - 9
= 315
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If a fair coin is tossed 9 times, what is the probability, rounded to the nearest thousandth, of getting at most 2 tails?
Answer:
Below
Step-by-step explanation:
2^9 possibilities =512
9 possibles with only ONE tails (9 C 1)
36 possibles with TWO tails ( 9 C 2)
45 out of 512 45/512 = .088
Kim decided that she wanted to go bowling. The bowling alley charges $2.75 per game and $10 for shoes. If Kim has $30, how many complete games can she bowl?
Write an equation and solve it.
Answer: 2 complete games
Step-by-step explanation:
add shoes and game charge
$10.00 + 2.75 = 12.75 <— that’s 1 complete game
subtract it from $30.00
$30.00 - 12.75 = 17.25.
A complete game costs 12.75. so, Kim had enough money for one more game.
17.25 - 12.75 = $4.50 remaining after 2 complete games
Answer: 7 games
Step-by-step explanation: if it charges 10 for shoes, then you already subtract 10 from 30. 30-10=20. then, to find out how many games she can play, divide 2.75 from 20. 20/2.75=7.272727.... Since you can't pay for half of a game, it would be 7 games.
A line passes through (3, -2) and is perpendicular to 3x - 2y = 7.
Answer:
y=-2x/3
Step-by-step explanation:
Perpendicular lines have opposite reciprocal slopes.
An example of opposite reciprocals: -1/2 and 2
-1*2=-2
The reciprocal of -2 is -1/2.
In order to solve for slope, isolate y:
3x - 2y = 7 ==> solve for y
3x = 7 + 2y ==> add 2y on both sides to make y positive
3x - 7 = 2y ==> isolate y by subtracting 7 on both sides
y = (3x - 7)/2 ==> divide both sides by 2 in order to isolate y
y = 3x/2 - 7/2 ==> distribution
Hence, the slope is 3/2 <== 3x/2.
Now, find the perpendicular slope:
-1*3/2=-3/2
The reciprocal of -3/2 is -2/3 ==> the slope of the perpendicular equation
Now, find the equation of the line that passes through (3, -2):
y=mx+b ==> slope-intercept equation
-2=-2/3 * (3) + b ==> plugin (x=3, y=-2) and m=-2/3 which is the slope.
-2 = 3 * (-2/3) + b ==> solve for b
-2 = -6/3 + b
-2 = -2 + b
b = 0 ==> -2 + 0 = -2
y=-2x/3+0 ==> plugin the slope -2/3 and b=0.
y=-2x/3+0 ==> y=-2x/3
Hence, the equation is y=-2x/3.
Help me! Can someone please
Answer:
13
Step-by-step explanation:
Divide both sides of the equation by 4.
x = 1/4. y = 2/3. z = 4*1/5
Work out the value of X x y x z
Give your answer as a fraction in its simplest form.
Answer:
[tex]\frac{7}{10}[/tex]
Step-by-step explanation:
The numbers on two consecutively numbered gym lockers have a sum of 149. What are the locker numbers?
Answer:
The two locker numbers are 80 and 69.
Hope it helps!
Milan is driving to San Francisco. Suppose that the distance to his destination (in miles) is a linear function of his total driving time (in minutes). Milan has 68
milles to his destination after 37 minutes of driving, and he has 45.6 miles to his destination after 65 minutes of driving. How many miles will he have to his
destination after 81 minutes of driving?
After 81 minutes of driving the distance to destination is 32.8 miles.
What is linear function?Th function that has two variables with first order term is called linear function. While plotting on the XY coordinate system we get a straight line.
Why do we use linear equation in this problem?
as per question, distance to destination is a linear function of total driving time so we use the equation of straight-line having slope m and y intercept b for determining unknown values.
given, distance to destination in miles is a linear function of total driving time in minutes.
y=mx+b
in the equation, y denotes the distance to destination in miles
x is the total driving time in minutes
m is the slope of linear equation
b is the y intercept
Milan has 68 miles to his destination after 37 minutes of driving
68 = mx37+b
he has 45.6 miles to destination after 65 minutes of driving
45.6=mX65+b
solving the two equations by addition method
slope, m= -0.8
from the above two equation
we get b=97.6
now, after 81 minutes of driving the distance to destination, y=mx+b
y= -0.8x81+97.6
distance = 32.8 miles
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Find the equation of a line that contains the points (−7,2) and (2,−2). Write the equation in slope-intercept form using fraction if necessary.
The required equation of the line which contains the points (−7,2) and (2,−2) is y = -4/9x - 8/9.
What is the equation of the line?A straight line's general equation is y = MX + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept.
The equation of the line's general form is:
y = MX + c
Where, m = slope, c = y-intercept and slope = ( y₂ - y₁ ) / ( x₂ - x₁ ).
Determine the line's slope:
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope = ( -2-2) / (2+7 )
Slope= -4/9
The y-intercept is determined as follows:
y = MX + c
2 = -4/9x 2+c
c = -8/9
The lines' equation:
y = MX + c
y = -4/9x - 8/9
Therefore, the required equation of the line which contains the points (−7,2) and (2,−2) is y = -4/9x - 8/9.
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PLEASE HELP
Given that x is a normal variable with mean = 47 and standard deviation = 6.4, find the following probabilities. (Round your answers to four decimal places.)
(a) P(x ≤ 60)
(b) P(x ≥ 50)
(c) P(50 ≤ x ≤ 60)
Given that x is a normal variable with mean = 47 and standard deviation = 6.4, find the following probabilities.
(a) P(x ≤ 60) = 0.9356 (b) P(x ≥ 50) = 0.6744 (c) P(50 ≤ x ≤ 60) = 0.2612What are the probabilities?Generally, To solve these problems, we can use the standard normal distribution table or a computer program to find the desired probabilities.
First, we need to standardize the given values of x by subtracting the mean and dividing by the standard deviation. This gives us a standard normal random variable, denoted by Z, with a mean of 0 and a standard deviation of 1.
(a) P(x ≤ 60) = P(Z ≤ (60 - 47)/6.4) = P(Z ≤ 1.5625). From the standard normal distribution table or a computer program, we find that P(Z ≤ 1.5625) = 0.9356.
(b) P(x ≥ 50) = P(Z ≥ (50 - 47)/6.4) = P(Z ≥ 0.46875). From the standard normal distribution table or a computer program, we find that P(Z ≥ 0.46875) = 0.6744.
(c) P(50 ≤ x ≤ 60) = P(0.46875 ≤ Z ≤ 1.5625) = P(Z ≤ 1.5625) - P(Z ≤ 0.46875) = 0.9356 - 0.6744 = 0.2612.
Therefore, the probabilities are as follows:
(a) P(x ≤ 60) = 0.9356 (b) P(x ≥ 50) = 0.6744 (c) P(50 ≤ x ≤ 60) = 0.2612
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ez question pls help tho x/7 - 2 = 8 x=?
Answer: x = 70
Step-by-step explanation:
You can simply solve for x by simplifying both sides of the equation, then isolating the variable
Solve, x/7 - 2 = 8, for x.
x/7 = 10, added the value of 2 to both sides of the equation.
x=70, multiplied the value of 7 to both sides of the equation.
Thus the value of x is equal to 70.
What is an equation of the parabola
Answer:
(c) x = -1/11(y -3)²
Step-by-step explanation:
You want an equation of the parabola with directrix x = 11/4 and vertex (0, 3).
EquationThe directrix is a vertical line to the right of the vertex. This means the parabola opens to the left.
The vertex form of the equation is ...
x = 1/(4p)(y -k)² +h . . . . . . . . where (h, k) is the vertex, and p is the distance from the directrix to the vertex (also, the distance from the vertex to the focus)
ApplicationHere, we have ...
p = 0 -11/4 = -11/4 . . . . negative because the vertex is left of the directrix
and
(h, k) = (0, 3)
so the equation is ...
x = 1/(4(-11/4))(y -3)² +0
x = -1/11(y -3)²
Solve 0=sin1/2x+cosx−1
The value of x = 2nπ, (n ∈ Z) and
[tex]x=2(n\pi+(-1)^{n} \pi /6)[/tex], (n ∈ Z)
What are Trigonometric Identities?
Trigonometric Identities are useful whenever trigonometric functions are involved in an expression or an equation. Trigonometric Identities are true for every value of variables being on both sides of an equation. Geometrically, these identities involve certain trigonometric functions( similar as sine, cosine, tangent ) of one or further angles.
According to question
⇒ sin(x/2) + cos(x) - 1 = 0
⇒ sin(x/2) + cos(x) - 1 = 0
{ cos(2x) = 1 - 2sin²(x) }
cos(x) = 1 - 2sin²(x/2)
⇒ sin(x/2) + cos(x) - 1 = 0
⇒ sin(x/2) + 1 - 2sin²(x/2) - 1 = 0
⇒ - 2sin²(x/2) + sin(x/2) + 1 - 1 = 0
⇒ - 2sin²(x/2) + sin(x/2) = 0
⇒ sin(x/2)(- 2sin(x/2) + 1) = 0
⇒ sin(x/2) = 0 , x = 2nπ (n ∈ Z)
and
⇒ sin(x/2) = 1/2 , [tex]x=2(n\pi+(-1)^{n} \pi /6)[/tex] (n ∈ Z)
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