Answer:
-4(x - 5) + 8x = 9x - 3
Simplifying the left side:
-4x + 20 + 8x = 9x - 3
4x + 20 = 9x - 3
Subtracting 4x from both sides:
20 = 5x - 3
Adding 3 to both sides:
23 = 5x
Dividing both sides by 5:
x = 23/5
Therefore, the equation equivalent to the given equation is:
5x - 23 = 0
In the diagram of right triangle ABC shown below, AB= 14 and AC = 9.
What is the measure of ZA, to the nearest degree?
1) 33
2) 40
3) 50
4) 57
The measure of the angle A is 49.99 degrees or 50 degrees if the length of AB = 14 and AC = 9.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
We have a given a right angle triangle in the picture
It is required to find the measure of angle A
Applying cos ratio to find the measure of the angle A:
cosA = 9/14
cosA = 0.642
A = 49.99 ≈ 50 degree
Thus, the measure of the angle A is 49.99 degrees or 50 degrees if the length of AB = 14 and AC = 9.
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Assuming that the equation defines a differential function of x, find Dxy by implicit differentiation. 4)2xy-y2 = 1 5) xy + x + y = x2y2
For the equations 2xy - y^2 = 1 and xy + x + y = x^2y^2 using implicit differentiation the value Dxy is given by Dxy = (1 - 2xy + 3y^2)/(x - y)^3 and Dxy = (2y^2 - 2xy - 3y - 1)/(x - 2xy + 1)^3 respectively.
Equation 2xy - y^2 = 1,
Differentiate both sides of the equation with respect to x,
Treating y as function of x and then differentiate again with respect to x.
Using implicit differentiation,
First, differentiate both sides with respect to x,
2y + 2xy' - 2yy' = 0
Next, solve for y',
⇒2xy' - 2yy' = -2y
⇒y' (2x - 2y) = -2y
⇒y' = -y/(x - y)
Now, differentiate again with respect to x,
y''(x - y) - y'(2x - 2y) = y/(x - y)^2
Substitute the expression we obtained for y' in terms of y and x,
y''(x - y) - (-y/(x - y))(2x - 2y) = y/(x - y)^2
Simplify and solve for y'',
y''(x - y) + (2xy - 3y^2)/(x - y)^2 = 1/(x - y)^2
The expression for Dxy is,
Dxy = (1 - 2xy + 3y^2)/(x - y)^3
For the equation xy + x + y = x^2y^2,
Differentiate both sides of the equation with respect to x,
Using implicit differentiation,
First, differentiate both sides with respect to x,
⇒y + xy' + 1 + y' = 2xyy'
Solve for y',
⇒xy' - 2xyy' + y' = -y - 1
⇒y' (x - 2xy + 1) = -y - 1
⇒y' = -(y + 1)/(x - 2xy + 1)
Now, differentiate again with respect to x,
y''(x - 2xy + 1) - y'(2y - 2x y' + 1) = (y + 1)/(x - 2xy + 1)^2
Substitute the expression we obtained for y' in terms of y and x,
y''(x - 2xy + 1) - (-y - 1)/(x - 2xy + 1)^2 (2y - 2x y' + 1) = (y + 1)/(x - 2xy + 1)^2
Simplify and solve for y''
y''(x - 2xy + 1) - (2y^2 - 2xy - 2y)/(x - 2xy + 1)^2 = (y + 1)/(x - 2xy + 1)^2
The expression for Dxy is,
Dxy = (2y^2 - 2xy - 3y - 1)/(x - 2xy + 1)^3
Therefore , the value of Dxy using implicit differentiation for two different functions is equal to
Dxy = (1 - 2xy + 3y^2)/(x - y)^3 and Dxy = (2y^2 - 2xy - 3y - 1)/(x - 2xy + 1)^3
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When conducting a survey, which of the following is the most important reason to use a random sample? Correct. Random selection ensures that the sample is unbiased on average, so that the results of the study can be generalized to the population.
Random sampling is crucial when surveying as it ensures that the sample selected is representative of the population.
By randomly selecting participants from the population, the sample is likely to be unbiased on average, which means that the results of the study can be generalized to the entire population. Without random sampling, the results of the study may be skewed or biased towards a certain group, which can lead to incorrect conclusions and poor decision-making. Therefore, it is essential to use random sampling when surveying to obtain accurate and reliable results.
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the function f is defined by f of x is equal to 3 divided by the square root of x minus 2 divided by x cubed for x > 0. g
The required value of the function (f + g)(x) for given f(x) and g(x) as ( 3 / √x ) - ( 2 / x³ ) and √(5x - 7) is equals to ( 3 / √x ) - ( 2 / x³ ) + √(5x - 7).
Function f(x) is equals to,
( 3 / √x ) - ( 2 / x³ ) for all x > 0
Function g(x) is equals to,
g(x) = √(5x - 7)
To get the value of (f + g)(x),
Substitute the value of f(x) and g(x) and add the functions f(x) and g(x) together,
Sum of f(x) and g(x) is equals to,
(f + g)(x)
= f(x) + g(x)
= ( 3 / √x ) - ( 2 / x³ ) + √(5x - 7)
Therefore, value of the function (f + g)(x) is equals to ( 3 / √x ) - ( 2 / x³ ) + √(5x - 7).
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The above question is incomplete, the complete question is:
The function f is defined by f of x is equal to 3 divided by the square root of x minus 2 divided by x cubed for x > 0, g as a function of x is equal to the square root of quantity 5 x minus 7 Find (f + g)(x).
A fair coin is tossed five times. Explain why the probability of getting exactly three heads is 0.3125.
The value of the probability is 0.3125 and this is proved by the calulations below
How to explain the value of the probabilityThe probability of getting exactly 3 heads in 5 coin tosses can be calculated by multiplying the probability of one specific combination of 3 heads and 2 tails by the number of possible combinations.
The probability of one specific combination, for example HHTTT, is (1/2)^5 = 1/32, because each toss has a 1/2 chance of being a head or a tail.
There are 5C3 = 10 possible combinations of 3 heads and 2 tails in 5 tosses.
For example: HHTTT, HTHTT, HTTHT, HTHHT, TTHHH, etc.
Therefore, the probability of getting exactly 3 heads is:
Probability = 10 * (1/32)
Probability = 10/32
Probability = 0.3125.
Hence, the value of the probability is 0.3125.
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Below are the jersey numbers of 11 players randomly selected from a football team. Find the range, variance, and standard deviation for the given sample data. What do the results tell us?
92 19 41 24 75 53 70 3 67 64 9
Step-by-step explanation:
To find the range, we need to subtract the smallest value from the largest value in the dataset:
Range = Largest value - Smallest value
Range = 92 - 3
Range = 89
To find the variance and standard deviation, we need to calculate the mean first:
Mean = (Sum of all values) / (Number of values)
Mean = (92+19+41+24+75+53+70+3+67+64+9) / 11
Mean = 45.09 (rounded to two decimal places)
Next, we need to calculate the variance:
Variance = (Sum of squared differences from the mean) / (Number of values - 1)
Variance = [(92-45.09)^2 + (19-45.09)^2 + (41-45.09)^2 + (24-45.09)^2 + (75-45.09)^2 + (53-45.09)^2 + (70-45.09)^2 + (3-45.09)^2 + (67-45.09)^2 + (64-45.09)^2 + (9-45.09)^2] / (11-1)
Variance = 1071.45 (rounded to two decimal places)
Finally, we can calculate the standard deviation by taking the square root of the variance:
Standard deviation = Square root of variance
Standard deviation = Square root of 1071.45
Standard deviation = 32.74 (rounded to two decimal places)
The range tells us the difference between the highest and lowest values in the dataset, which in this case is 89. The variance and standard deviation tell us how spread out the data is from the mean. The higher the variance and standard deviation, the more spread out the data is. In this case, the variance and standard deviation are both relatively high, indicating that the data is fairly spread out.
The Nutty Professor sells cashews for $6.80 per pound and Brazil nuts for $4.20 per pound. How much of each type should be used to make a 35 pound mixture that sells for $5.31 per pound?
The Nutty Prοfessοr shοuld use apprοximately 14.94 pοunds οf cashews and 35 - 14.94 = 20.06 pοunds οf Brazil nuts tο make a 35 pοund mixture that sells fοr $5.31 per pοund.
Assume the Nutty Prοfessοr makes a 35-pοund mixture with x pοunds οf cashews and (35 - x) pοunds οf Brazil nuts.
The cashews cοst $6.80 per pοund, sο the tοtal cοst οf x pοunds οf cashews is $6.8x dοllars.
Similarly, Brazil nuts cοst $4.20 per pοund, sο (35 - x) pοunds οf Brazil nuts cοst 4.2(35 - x) dοllars.
The tοtal cοst οf the mixture equals the sum οf the cashew and Brazil nut cοsts, which is:
6.8x + 4.2(35 - x) (35 - x)
When we simplify, we get:
6.8x + 147 - 4.2x
2.6x + 147
The mixture sells fοr $5.31 per pοund, sο the tοtal revenue frοm selling 35 pοunds οf the mixture is:
35(5.31) = 185.85
When we divide the tοtal cοst οf the mixture by the tοtal revenue, we get:
2.6x + 147 = 185.85
Subtractiοn οf 147 frοm bοth sides yields:
2.6x = 38.85
When we divide by 2.6, we get:
x ≈ 14.94
Tο make a 35-pοund mixture that sells fοr $5.31 per pοund, the Nutty Prοfessοr shοuld use apprοximately 14.94 pοunds οf cashews and 35 - 14.94 = 20.06 pοunds οf Brazil nuts.
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A company rents storage sheds shaped like rectangular prisms. Each shed is 11 feet long, 7 feet wide, and 12 feet tall. The rental cost is $3 per cubic foot. How much does it cost to rent one shed?
The cost to rent one shed of the rectangular prism shaped shed is $2772.
What is area?The size of a section on a surface is determined by its area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a shape or planar lamina.
What is a prism?A rectangular prism is a polyhedron in geometry that has two parallel and congruent sides. It also goes by the name cuboid. Six faces, each with a rectangle form and twelve edges, make up a rectangular prism. It is referred to as a prism because of the extent of its cross-section.
Volume of prism= BH
where B= area of base and H= height
B= 11*7 = 77 feet²
H= 12 feet
Volume= 77*12=924 cubic feet
Cost =$3 per cubic foot
Total cost= 3*924= $2772
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can someone help?
solve for x, using the secant lines
10cm, 7cm, 7cm. round to the nearest tenth
x = 4.9
Solution:
We can use the intersecting chords formula:
[tex]\text{(segment piece) x (segment piece) = (segment piece) x (segment piece)}[/tex][tex]7\times7 = 10x[/tex]
[tex]49 = 10x[/tex]
Divide each side by 10[tex]49\div10=10x\div10[/tex]
[tex]4.9 = x[/tex]
Therefore, x = 4.9.
6 TH GRADE MATH , WHAT IS THE SLOPE? TY
Answer:
Step-by-step explanation:
The slope of a line is the measure of the steepness and the direction of the line. Finding the slope of lines in a coordinate plane can help in predicting whether the lines are parallel, perpendicular, or none without actually using a compass.
The slope of any line can be calculated using any two distinct points lying on the line. The slope of a line formula calculates the ratio of the "vertical change" to the "horizontal change" between two distinct points on a line. In this article, we will understand the method to find the slope and its applications.
That is what Slope is.
Answer:
Step-by-step explanation:
Slope :( 1,1)
You start on the y-axis point which is (0,1) as you can see it is going up so I used the “up left” strategy. You go up 1 to the left 1 since the line intersects at point (1,2)
3x + y = 6
Y + 2 = x
Answer: x = 2, y = 0
Step-by-step explanation:
Assuming you need help solving for x or y, and the capital Y is y, we have the system of equations:
3x + y = 6
y + 2 = x
Substituting x for y + 2 gives us
3(y + 2) + y = 6
3y + 6 + y = 6
4y = 0
y = 0
Plugging y = 0 in for the second equation gives us
x = 0 + 2, or x = 2
a water park sold 1679 tickets for total of 44,620 on a wa summer day..each adult tocket is $35 and each child ticket is $20. how many of each type of tixkwt were sold?
Therefore , the solution of the given problem of unitary method comes out to be the attraction sold 943 child tickets and 736 adult tickets on that particular day.
What is an unitary method?It is possible to accomplish the objective by using previously recognized variables, this common convenience, or all essential components from a prior malleable study that adhered to a specific methodology. If the expression assertion result occurs, it will be able to get in touch with the entity again; if it does not, both crucial systems will undoubtedly miss the statement.
Here,
Assume the attraction sold x tickets for adults and y tickets for kids.
Based on the supplied data, we can construct the following two equations:
=> x + y = 1679 (equation 1, representing the total number of tickets sold)
=> 35x + 20y = 44620 (equation 2, representing the total revenue generated)
Using the elimination technique, we can find the values of x and y.
When we divide equation 1 by 20, we obtain:
=> 20x + 20y = 33580 (equation 3)
Equation 3 is obtained by subtracting equation 2 to yield:
=> 15x = 11040
=> x = 736
When we enter x = 736 into equation 1, we obtain:
=> 736 + y = 1679
=> y = 943
As a result, the attraction sold 943 child tickets and 736 adult tickets on that particular day.
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the c on the left has blank1 - word answer please type your answer to submit electron geometry and a bond angle of
The CH3-CIOI-CNI molecule contains three carbon atoms with different electron geometries and bond angles. The CH3 and CIOI carbon atoms have tetrahedral geometry with a bond angle of approximately 109.5 degrees, while the CNI carbon atom has a trigonal planar geometry with a bond angle of approximately 120 degrees.
Using this Lewis structure, we can determine the electron geometry and bond angle for each carbon atom in the molecule as follows.
The carbon atom in the CH3 group has four electron domains (three bonding pairs and one non-bonding pair). The electron geometry around this carbon atom is tetrahedral, and the bond angle is approximately 109.5 degrees.
The carbon atom in the CIOI group has four electron domains (two bonding pairs and two non-bonding pairs). The electron geometry around this carbon atom is also tetrahedral, and the bond angle is approximately 109.5 degrees.
The carbon atom in the CNI group has three electron domains (one bonding pair and two non-bonding pairs). The electron geometry around this carbon atom is trigonal planar, and the bond angle is approximately 120 degrees.
Therefore, the electron geometry and bond angle for each carbon atom in the structure CH3-CIOI-CNI are:
CH3 carbon atom tetrahedral geometry, bond angle of approximately 109.5 degrees
CIOI carbon atom tetrahedral geometry, bond angle of approximately 109.5 degrees
CNI carbon atom trigonal planar geometry, bond angle of approximately 120 degrees
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_____The given question is incomplete, the complete question is given below:
Determine the electron geometry and bond angle for each carbon atom in the structure CH3-CIOI-CNI
valuate the
expression
12 - 3y
2
+
√²v=4] for y = 3.
2y -
The result of the formula [tex]12 - 3y2 + (v=4) / (2y - 2)[/tex] for y = 3 is [tex]-29/2[/tex] .
What are the ways to analyse an algebraic expression?When [tex]y = 3[/tex] is used, the value of the expression [tex]12 - 3y2 + (v=4) / (2y - 2)[/tex] has a value of [tex]-29/2[/tex] .
To analyse an algebraic expression is to determine its value when a certain number is used in lieu of the variable. To evaluate the expression, we first replace the variable with the given number, then we use the order of operations to simplify the expression.
If [tex]y = 3[/tex] , we can insert it into the expression & simplify as follows to evaluate [tex]12 - 3y2 + (v=4) / (2y - 2)[/tex] for [tex]y = 3[/tex] .
[tex]12 - 3(3)^2 + (√4) / (2(3) - 2)[/tex] (y = 3 replacement)
[tex]12 - 27 + 2 / 4\s-15 + 1/2\s-29/2[/tex]
Therefore, The result of the formula [tex]12 - 3y2 + (v=4) / (2y - 2)[/tex] for y = 3 is [tex]-29/2[/tex] .
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please help me with math quiz i’ll give you brainlist
Answer:
Answer: B. Symmetric.
Explanation:
In a symmetric distribution, the data is evenly distributed around the mean or median, creating a mirror image on both sides of the center. In this histogram, the median and mean are very close together at 55 and the bars on both sides of the center are roughly equal in height, indicating a fairly even distribution. Therefore, the histogram is symmetric.
6TH GRADE MATH, WRITE THE EQUATION FOR THIS GRAPH IN THE FORM OF Y=MX+B, TYSM
Answer:
m = 0
Step-by-step explanation:
Slope = rise/run or (y2 - y1) / (x2 - x1)
Pick 2 points (0,2) (1,2)
We see the y stay the same and the x increase by 1, so the slope is
m = 0/1 = 0
So, the slope is 0
A block of mass 2kg is attached to the spring of spring constant 50Nm −1. The block is pulled to a distance of 5 cm from its equilibrium position at x=0 on a horizontal frictionless surface from rest at t = 0. The displacement of the block at any time t is thenA. x= 0.05sin5tmB. x= 0.05cos5tmC. x= 0.5sin5tmD. x= 5sin5tm
The displacement of the block at any time t is then x= 0.05cos5tm. (option b).
Now, when the block is released, it starts oscillating back and forth about its equilibrium position due to the force exerted by the spring. This motion is described by the equation of motion for a simple harmonic oscillator:
x = Acos(ωt + φ)
The angular frequency ω of the oscillation is given by:
ω = √(k/m)
where k is the spring constant and m is the mass of the block.
Substituting the given values of k and m, we get:
ω = √(50/2) = 5 rad/s
The phase angle φ depends on the initial conditions of the system, i.e., the initial displacement and velocity of the block. Since the block is initially at rest, its initial velocity is zero and the phase angle is zero as well.
Therefore, the equation of motion for the displacement of the block is:
x = 0.05cos(5t)
Hence, option B, x = 0.05cos(5t), is the correct answer.
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Sorry if photo is side ways or upside down
Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find the probability of obtaining a reading between -0.08°C and 1.68°C.
The probability of obtaining a reading between -0.08°C and 1.68°C is approximately 0.4854 or 48.54%.
What are the four types of probability?Probability is the branch of mathematics concerned with the occurrence of a random event, and there are four types of probability: classical, empirical, subjective, and axiomatic.
The readings at freezing on a set of thermometers are normally distributed, with a mean () of 0°C and a standard deviation () of 1.00°C. We want to know how likely it is that we will get a reading between -0.08°C and 1.68°C.
To solve this problem, we must use the z-score formula to standardise the values:
z = (x - μ) / σ
where x is the value for which we want to calculate the probability, is the mean, and is the standard deviation.
The lower bound is -0.08°C:
z1 = (-0.08 - 0) / 1.00 = -0.08
1.68°C is the upper bound:
z2 = (1.68 - 0) / 1.00 = 1.68
We can now use a standard normal distribution table or calculator to calculate the probabilities for each z-score.
The probability of obtaining a z-score of -0.08 or less is 0.4681, and the probability of obtaining a z-score of 1.68 or less is 0.9535, according to the table. We subtract the probability associated with the lower bound from the probability associated with the upper bound to find the probability of obtaining a reading between -0.08°C and 1.68°C:
P(-0.08°C x 1.68°C) = P(z1 z z2) = P(z 1.68) minus P(z -0.08) = 0.9535 - 0.4681 = 0.4854
As a result, the chance of getting a reading between -0.08°C and 1.68°C is approximately 0.4854 or 48.54%.
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find a polynomial function with the following zeros: double zero at -4 simple zero at 3.
f(x) = (x+4)^2(x-3) has polynomial function with the following zeros: double zero at -4 simple zero at 3.
If a polynomial has a double zero at -4, it means that it can be factored as (x+4)^2.
If it also has a simple zero at 3, then the factorization must include (x-3).
Therefore, the polynomial function with these zeros is :-
f(x) = (x+4)^2(x-3)
This polynomial has a double zero at -4, because $(x+4)^2$ has a zero of order 2 at -4, and a simple zero at 3, because $(x-3)$ has a zero of order 1 at 3.
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Please indicate which is the best answer to complete the figure below.
Answer:b
Step-by-step explanation:
A parent donated 36 fruit cups and 24 bananas to fifth grade. The teacher wanted to make field trip snack bags with the donated food and wondered about the ways snacks could be packed. To be fair the teacher wants to make sure that all bags are exactly the same.
A) What is the greatest number of snack bags that the teacher can make, if each bag is identical? How do you know ?
B) What other numbers of snack bags could she make? How do you know?
2) Another parent also donated 24 bananas, so there are 48 bananas total. Now what is the greatest number of snack bags can that can be made?
3) The teacher realized that she miscounted and had only 30 fruit cups. How many snack bags can she make with 48 bananas and fruit cups?
4) What do the different numbers of snack bags that can be made have to do with the number of fruit cups and number of bananas?
For a standard normal distribution, find:
P(-2.11 < z < -0.85)
Answer:
Step-by-step explanation:
Using a standard normal table, we can find the area under the curve between -2.11 and -0.85.
P(-2.11 < z < -0.85) = P(z < -0.85) - P(z < -2.11)
Using the table, we find:
P(z < -0.85) = 0.1977
P(z < -2.11) = 0.0174
Therefore,
P(-2.11 < z < -0.85) = 0.1977 - 0.0174 = 0.1803
So the probability that a standard normal random variable falls between -2.11 and -0.85 is 0.1803.
A bicycle wheel is 63m in diameter. how many metres does the bicycle travel for 100 revolutions of the wheel. (pie=²²/⁷
Answer:
19782m
Step-by-step explanation:
1 revolution = circumference
circumference = π * diameter
π = 3.1416
Then
circumference = 3.1416 * 63
= 197.92m
1 revolution = 197.82m
100 revolutions = 100*197.82m
= 19782m
Answer:
19.8 km
Step-by-step explanation:
To find:-
The distance travelled in 100 revolutions .Answer:-
We are here given that,
diameter = 63mWe can first find the circumference of the wheel using the formula,
[tex]:\implies \sf C = 2\pi r \\[/tex]
Here radius will be 63/2 as radius is half of diameter. So on substituting the respective values, we have;
[tex]:\implies \sf C = 2\times \dfrac{22}{7}\times \dfrac{63}{2} \ m \\[/tex]
[tex]:\implies \sf C = 198\ m \\[/tex]
Now in one revolution , the cycle will cover a distance of 198m . So in 100 revolutions it will cover,
[tex]:\implies \sf Distance= 198(100)m\\[/tex]
[tex]:\implies \sf Distance = 19800 m \\[/tex]
[tex]:\implies \sf Distance = 19.8 \ km\\[/tex]
Hence the bicycle would cover 19.8 km in 100 revolutions.
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What is the measure of angle R?
A) 17 degrees
B) 25 degrees
C) 34 degrees
D) 65 degrees
Answer: D) Angle R is 65 degrees
Step-by-step explanation:
In the given figure, we have a right-angled triangle PQR.
Using the property of angles in a triangle, we know that the sum of angles in a triangle is 180 degrees. Therefore,
∠QRP + ∠QPR + ∠PRQ = 180 degrees
Since ∠PRQ is a right angle (90 degrees), we have:
∠QRP + ∠QPR = 90 degrees
Now, we are given that ∠QPR is 25 degrees. Substituting this in the above equation, we get:
∠QRP + 25 = 90 degrees
Solving for ∠QRP, we get:
∠QRP = 90 - 25 = 65 degrees
Therefore, the measure of angle R is 65 degrees, which is option (D).
Answer:
Answer is D
Step-by-step explanation:
SPiDerMom is so hot bTw
TRUE OR FALSE to calculate the average of the numeric values in a list, the first step is to get the total of values in the list.
The given statement 'to calculate the average of the numeric values in a list the first step is to get the sum of all the given values ' is a true.
Average of the numeric values in a list,
First step is to get the sum of values in the list.
It is not the total number of values.
Once we have the sum, we can divide it by the number of values to get the average.
Here is an example,
Suppose we have a list of numeric values are as follow,
[2, 4, 6, 8, 10].
To calculate the average of these values, we first find their sum,
2 + 4 + 6 + 8 + 10 = 30
Next,
divide the sum by the number of values in the list
Number of values = 5
30 / 5 = 6
This implies,
The average of the values in the list is 6.
Therefore, to get the average first step is to get the total of all values is true statement.
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PLEASE I NEED HELP, what is the equivalent of 7/tan b+7tan b
In response to the stated question, we may state that The equivalent trigonometry expression of 7/tan b + 7tan b is (7 - 7tan b cot b)/sin b.
what is trigonometry?The study of the connection between triangle side lengths and angles is known as trigonometry. The concept first originated in the Hellenistic era, during the third century BC, due to the application of geometry in astronomical investigations. The subject of mathematics known as exact techniques deals with certain trigonometric functions and their possible applications in calculations. There are six commonly used trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their separate names and acronyms (csc). The study of triangle characteristics, particularly those of right triangles, is known as trigonometry. As a result, geometry is the study of the properties of all geometric forms.
tan(A + B) = (tan A + tan B)/(1 - tan A tan B)
Set A = 90 degrees and B = b degrees:
tan(90 + b) = (tan 90 + tan b)/(1 - tan 90 tan b)
tan(90 + b) = (undefined + tan b)/(1 - undefined tan b)
tan(90 + b) = -cot b
7/tan b + 7tan b
= 7/(tan b) + 7(tan(90 + b) - 1)
= 7/(tan b) + 7(-cot b - 1)
= (7 - 7tan b cot b)/sin b
The equivalent expression of 7/tan b + 7tan b is (7 - 7tan b cot b)/sin b.
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the expression the quantity cosecant squared of theta minus 1 end quantity over cotangent of theta simplifies to which of the following?
Students were asked to simplify the expression using trigonometric identities:
A. student A is correct; student B was confused by the division
B. 3: cos²(θ)/(sin(θ)csc(θ)); 4: cos²(θ)
Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions.
There are several distinctive trigonometric identities that relate a triangle's side length and angle. Only the right-angle triangle is consistent with the trigonometric identities.
The six trigonometric ratios serve as the foundation for all trigonometric identities. Sine, cosine, tangent, cosecant, secant, and cotangent are some of their names.
Each student correctly made use of the trigonometric identities
cosec(θ) = 1/sin(θ)
1 -sin²(θ) = cos²(θ)
A.
Student A's work is correct.
Student B apparently got confused by the two denominators in Step 2, and incorrectly replaced them with their quotient instead of their product.
The transition from Step 2 can look like:
[tex]\frac{(\frac{1-sin^2\theta}{sin\theta} )}{cosec\theta} =\frac{1-sin^2\theta}{sin\theta} .\frac{1}{cosec\theta} =\frac{cos^2\theta}{(sin\theta)(cosec\theta)}[/tex]
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Complete question:
Students were asked to simplify the expression the quantity cosecant theta minus sine theta end quantity over cosecant period Two students' work is given. (In image below)
Part A: Which student simplified the expression incorrectly? Explain the errors that were made or the formulas that were misused. (5 points)
Part B: Complete the student's solution correctly, beginning with the location of the error. (5 points)
fill in the blank. Toward the end of a game of Scrabble, you hold the letters D, O, G, and Q. You can choose 3 of these 4 letters and arrange them in order in ______ different ways. (Give your answer as a whole number.)
Toward the end of a game of Scrabble, you hold the letters D, O, G, and Q. You can choose 3 of these 4 letters and arrange them in order in 24 different ways.
To solve this problem, we need to use the concept of permutations. A permutation is an arrangement of objects in a specific order. In this case, we need to find the number of permutations that can be made from the letters D, O, G, and Q when we choose 3 of these 4 letters.
The formula for finding the number of permutations is:
n! / (n-r)!
where n is the total number of objects and r is the number of objects we choose.
Using this formula, we can calculate the number of permutations as follows:
4! / (4-3)!
= 4! / 1!
= 4 x 3 x 2 x 1 / 1
= 24
Therefore, we can arrange the chosen 3 letters in 24 different ways.
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solve the quadratic equation 9×^2-15×-6=0
Answer:
To solve the quadratic equation 9×^2-15×-6=0, we can use the quadratic formula, which is given by:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
where a, b, and c are the coefficients of the quadratic equation ax^2 + bx + c = 0.
In this case, a = 9, b = -15, and c = -6, so we can substitute these values into the quadratic formula:
x = (-(-15) ± sqrt((-15)^2 - 4(9)(-6))) / 2(9)
Simplifying this expression gives:
x = (15 ± sqrt(225 + 216)) / 18
x = (15 ± sqrt(441)) / 18
x = (15 ± 21) / 18
So the two solutions to the quadratic equation are:
x = (15 + 21) / 18 = 2
x = (15 - 21) / 18 = -1/3
Therefore, the solutions to the quadratic equation 9×^2-15×-6=0 are x = 2 and x = -1/3.
