Recall that the diagonals of a square bisect each other, therefore:
\(BW=DW=6.\)The diagonals are congruent, therefore:
\(AC\cong DB=2DW=2(6)=12.\)To compute DA we use the fact that the figure is a square:
\(DA=DC=8.5.\)Now, we know that the angles at the vertices are right angles, therefore:
\(m\angle ABC=90.\)To determine the measure of angles ABD, and DCA we use the trigonometric function sine:
\(\begin{gathered} sin(\angle ABD)=\frac{DA}{DB}=\frac{\sqrt{287}}{2(12)}, \\ sin(\angle DCA)=\frac{DA}{CA}=\frac{\sqrt{287}}{2(12)}. \end{gathered}\)Therefore:
\(m\angle ABD=m\angle DCA\approx45^{\circ}.\)Finally, to determine the measure of angle DWA, we use the fact that the figure is a square, therefore the diagonals bisect each other at 90° angles.
Answer: \(\begin{gathered} BW=6, \\ AC=12, \\ DA=8.5, \\ m\angle DWA=90^{\circ}, \\ m\angle ABC=90^{\circ}, \\ m\angle ABD=45^{\circ}, \\ m\angle DCA=45^{\circ}. \end{gathered}\)what is the mean of 61, 55, 66, 58, 50, 70
Answer:
Mean: 60
Step-by-step explanation:
First of all, in order to find the mean, one must add all the numbers together (61,55,66,58,50,70), which would give a total of 360.
After that, divide that total by the quantity of numbers (in other words, the total number of numbers, which in this case is 6). So, you would have to divide 360 by 6 leading to an answer of 60(the mean, which in other words is like finding the average).
Look at the system of equations in the box at
the right. Kevin stated that the equations in this system
have the same slope, so there will be infinitely many
solutions. Does Kevin's statement make sense?
Answer:
No.
Step-by-step explanation:
No, Kevin’s statement doesn’t make sense. He is correct that since the two equations have the same slope. Thus, they are parallel to each other.
However, since they are parallel, they will never touch. Therefore, there is no solution.
They will be infinitely many solutions if they are parallel and they have the same y-intercept.
Answer:
No it does not make sense
Step-by-step explanation:
If 2 linear equations have the same slope, then they represent two parallel linesParallel lines never cross, so they cannot have any solutionCan someone please help me with this problem?
Answer: -13
Step-by-step explanation:
c-2y
= -5-2(4)
= -5 - 8
= -13
Answer:
-13
Step-by-step explanation:
\(c=-5\\y=4\\c-2y=\\-5-(4*2)=\\-5-8=\\-13\)
The expression is equal to -13 when \(c=-5\) and \(y=4\).
Use the drop-down menus to identify the method used to collect data for each scenario.
While standing in front of the school, Jace recorded the number of students who walked, rode their bikes, took the bus, and were driven there.
Noah researched statistics online about the percentage of babies born with brown eyes.
Lara knew that she had a 25% chance of winning a contest, so she flipped two coins repeatedly to determine how many times two heads occurred.
The method used to collect data for each scenario is observational study , secondary data , simulation .
What is Data Collection ?The accumulation of data to perform research , experiment or any other study is called data collection
It is done by different methods.
While standing in front of the school, Jace recorded the number of students who walked, rode their bikes, took the bus, and were driven there. :
Because all feasible channels and techniques were investigated in order to get accurate data, this study is known as an observational study.
Noah conducted research to learn the data pertaining to the proportion of newborns having brown eyes. Since he didn't perform this directly, it is referred to as secondary data.
Lara repeatedly flipped two coins to see how many times two heads appeared because she knew she had a 25% chance of winning a contest. This is an example of simulation because she wanted to see if she would come up with the same outcome.
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Answer:
A. observational study
B. published data
C. study
Step-by-step explanation:
Did the question in edge 2022
If f (x)=2x^2+5 square root x-2
The value of f(2) in the given algebraic expression is: 18
How to solve the Algebraic Expression?The algebraic expression we are given is expressed as:
f(x) = 2x² + 5√(x + 2)
Now, we want to find f(2) which means we want to find the range when the domain is x = 2. Therefore we solve it as:
f(2) = 2(2)² + 5√(2 + 2)
f(2) = (2 * 4) + 5√4
f(2) = 8 + 5√4
f(2) = 8 + (5 * 2)
f(2) = 8 + 10
f(2) = 18
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Complete Question is:
If f(x) = 2(x)^2 + 5 square root (x+2), complete the following statement f(2) = ______
Sandy expects a project to take 12.75 hours. She works 4.25 hours on Monday. How many hours should the project take?
Answer:
if I did the math correctly it should be 8.50 hours.
Fully factorise 27t² + 15t
Answer: 3t(9t + 5)
Step-by-step explanation:
Sure! Factoring involves breaking down an expression into simpler factors that, when multiplied together, give the original expression.
To factor 27t² + 15t, we can look for the greatest common factor (GCF) of the two terms. The GCF of 27t² and 15t is 3t, because both terms can be divided by 3t.
So we start by factoring out the 3t:
27t² + 15t = 3t(9t + 5)
Notice that we can check if the factorization is correct by using the distributive property to multiply the factor 3t by the expression inside the parentheses:
3t(9t + 5) = 3t(9t) + 3t(5) = 27t² + 15t
Therefore, 27t² + 15t can be fully factorized as 3t(9t + 5).
Use factoring to solve the polynomial equation. Check by substitution or by using a graphing utility and identifying
x-intercepts.
8x4-32x² = 0
Rewrite the equation in factored form.
(Blank)=0
Then what is the solution pair?
The solution to the polynomial equation 8x⁴ - 32x² = 0 by factoring are x = 0 or x = -2 or x = 2
Using factoring to solve the polynomial equationTo solve the equation 8x⁴ - 32x² = 0 by factoring, we can factor out the greatest common factor of the terms:
8x²(x² - 4) = 0
Now we can use the difference of squares identity to factor the quadratic expression:
8x²(x + 2)(x - 2) = 0
Using the zero product property, we know that the product of two factors is zero if and only if at least one of the factors is zero.
Therefore, we can set each factor equal to zero and solve for x:
8x² = 0 or x + 2 = 0 or x - 2 = 0
Solving for x, we get:
x = 0 or x = -2 or x = 2
So the solution set for the equation is {0, -2, 2}.
To check the solution, we can substitute each value into the original equation and verify that it equals zero.
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what ratio in the simplest form between the length of a side XYZ and the length of its corresponding side in MPN
A. 2/5
B. 3/2
C. 2/1
D. 5/2
Answer:
D. 5/2
Step-by-step explanation:
Since, you are required to find the ratio of the side of triangle XYZ and triangle MPN in simplest form.
So, it would be XZ/MN = 5/2
Which of the following numbers is included in the graph of 3x +8 > -2x - 16
a) -5
b) -6
c) -4
d) -20
The answer is Option (C) -4.
I NEED HELP ! ill mark brainlist
Answer:(x + 3)(x + 3)
Step-by-step explanation:
½ cup of sugar, and I only have a ¼ cup scoop and a ⅛ cup scoop. I need at least two different ways I can get ½ cup
2 ways to get to 1/2
Way 1:
Use the 1/4 scoop 2 times
1/4 + 1/4 =2/4
2/4 simplified is 1/2
Way 2:
Use the 1/8 scoop 4 titmes
1/8+1/8+1/8+1/8=4/8
4/8 simplified is 1/2
Hope this helps!
Write the quadratic equation whose roots are -6 and -1, and whose leading coefficient is 2.
Answer:
Y= 2x^2+14x+12
Explaination:
When it gives you the roots you can automatically change the sign and put them with the x in factors such as
y = (x+6)(x+1)
Then you put the leading coefficient of 2
y = 2(x+6)(x+1)
Then to get it in standard form you distribute the parenthesis the the 2 to get:
Y= 2x^2+2x+12x+12
Combine like terms and you'll answer will be
Y= 2x^2+14x+12
Find the area of each sector. Leave in terms of pi
Answer:
choice B
Step-by-step explanation:
using the formula:
\(theta \div 360\pi \times r ^{2} \)
Answer:
B
Step-by-step explanation:
Formula
\(\textsf{Area of a sector of a circle}=\left(\dfrac{\theta}{360^{\circ}}\right) \pi r^2\)
Solution
Given:
\(r\) = 9 cm\(\theta\) = 60°\(\begin{aligned}\implies \textsf{Area} & =\left(\dfrac{60^{\circ}}{360^{\circ}}\right) \pi \cdot 9^2\\\\ & = \dfrac16 \cdot \pi \cdot81\\\\ & = \dfrac{81}{6} \pi\\\\ & = \dfrac{27}{2} \pi \: \sf cm^2\end{aligned}\)
Pls help me I'm stuck
The measure of the angle BAM is approximately 40.894°.
What is the angle withing a rectangle?
In this problem we proceed to draw the figure representing the entire figure and labeling all known lengths, both from statement and derived from Pythagorean theorem. Since the angle BAM is part of a right triangle, then we can apply the following trigonometric function:
\(\tan \theta = \frac{BM}{AB}\)
\(\tan \theta = \frac{\frac{\sqrt{3}}{2}\cdot x }{x}\)
\(\tan \theta = \frac{\sqrt{3}}{2}\)
θ ≈ 40.894°
The measure of the angle BAM is approximately 40.894°.
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Both numbers have three significant figures. How many significant figures should be recorded for the answer to the division problem below?
\(43.6 \div 21.2\)
= [?] significant figures
Answer:
8 significant figures should be provided.
Step-by-step explanation:
I believe I am correct, but check your answer anyways.
A triangle has a base that is increasing at a rate of 18 mm per minute with the height being held constant. What is the rate of change of the area of the triangle if the height is 7 mm
Answer:
63mm/minStep-by-step explanation:
Area of a triangle = 1/2 * base * height
A = 1/2bh
Rate of change of area is expresssed as dA/dt = dA/db * db/bt
db/dt is the rate at which the base is increasing.
Given db/dt = 18mm/min
A = 1/2*7b
A = 7b/2
dA/db = 7/2
The rate at which the area is changing dA/dt = dA/db * db/bt
dA/dt = 7/2 * 18
dA/dt = 7*9
dA/dt = 63mm/min
Hence the rate at which the area of the triangle is changing is 63mm/min
Select the correct answer.
How do you express a gain of yards in a football game as a rational number?
A.
yards
B.
yards
C.
yards
D.
yards
E.
yards
Answer:
the answer is all yards
Step-by-step explanation:
option are yards
Answer:
b yards
Step-by-step explanation:
i took the test
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Answer:aaaaaaa
Step-by-step explanation:
AAAAAAAAAA
Kinsley went rock climbing at red river gorge at noon she was at an elevation of 76 feet then she climbed 28 feet higher to reach the peak what was kinsley elevation at the peak
Answer:
104 feet
Step-by-step explanation:
Answer:
104
Step-by-step explanation:
Find the length of the arc.arc circle 2A. 45π8 inB. 1890π inC. 21π4 inD. 18π in
Provided the following data:
\(\theta=135º=2.36\text{ }rad\)and r = 7 inches, then we can calculate the length of the arc using the following equation:
\(s=\theta\times r\)Where s represents the length of the arc. Thus:
\(s=\theta\times r=2.36\times7\text{ }in=16.49\text{ }in=\frac{21\pi}{4}in\)So the answer is option c.
A bag contains 5 blue balls, 4 red balls, and 3 orange balls. If a ball is picked from the bag at random, what is the probability that it is a blue ball? Answers have been rounded to the tenths place
Answer:
There is a 41.7% chance that you got a blue ball.Step-by-step explanation:
Total number of blue balls/Total number of balls x 100 = Chance of getting a blue ball
=> 5/12 x 100=> 5/6 x 50=> 5/3 x 25=> 125/3=> 41.7Hence, there is a 41.7% chance that you got a blue ball.
Hoped this helped.
\(BrainiacUser1357\)
where RS = 6y + 2, ST = 2y + 7, and RT = 13y - 21.
Answer:
See Explanation
Step-by-step explanation:
The question is incomplete but a possibility is that the given parameters are points on a straight line.
I'll answer base on that assumption.
\(RS = 6y + 2\)
\(ST =2y + 7\)
\(RT =13y -21\)
To solve for y, we have that:
\(RT = RS + ST\)
This gives:
\(13y - 21 = 6y + 2 + 2y + 7\)
Collect Like Terms
\(13y - 6y - 2y = 21 +2+7\)
\(5y = 30\)
Divide both sides by 5
\(y = 6\)
To get the measure of each line. Substitute 6 for y in
\(RS = 6y + 2\)
\(ST =2y + 7\)
\(RT =13y -21\)
\(RS = 6 * 6 + 2 = 36 + 2 = 38\)
\(ST = 2*6 + 7 = 12 +7 = 19\)
\(RT = 13*6 - 21 = 78 - 21 = 57\)
Find the value of (f o g)' at the given value.
To find the value of (f o g)' at a given value, you first need to understand the concept of composite functions and the chain rule of differentiation. Let's break it down step by step.
To find the value of (f o g)' at a given value, you need to evaluate g(x) and f(x), find their derivatives, and use the chain rule to find the derivative of (f o g) at the given value. It is important to understand the concepts of composite functions and the chain rule to be able to solve problems involving these concepts.
What are composite functions? Composite functions are functions that are formed by composing two or more functions. The notation used to denote composite functions is (f o g)(x), which means that the output of function g is used as the input for function f. In other words, we first evaluate g(x), and then use the result as the input for f(x).
What is the chain rule of differentiation? The chain rule of differentiation is a method used to find the derivative of composite functions. It states that if a function is composed of two or more functions, then its derivative can be found by taking the derivative of the outer function and multiplying it by the derivative of the inner function.
To find the value of (f o g)' at a given value, we need to follow these steps:1. Find g(x) and f(x)2. Find g'(x) and f'(x)3. Evaluate g(x) at the given value4. Use the chain rule to find (f o g)' at the given value
step 1: Find g(x) and f(x)Let's say that we have two functions: g(x) = x^2 + 3x + 1 and f(x) = sqrt(x). To find (f o g)(x), we first need to evaluate g(x) and then use the result as the input for f(x). Therefore, (f o g)(x) = f(g(x)) = sqrt(x^2 + 3x + 1)
Step 2: Find g'(x) and f'(x)To find g'(x), we need to take the derivative of g(x) using the power rule and the sum rule. Therefore, g'(x) = 2x + 3To find f'(x), we need to take the derivative of f(x) using the power rule and the chain rule. Therefore, f'(x) = 1/2(x)^(-1/2)
Step 3: Evaluate g(x) at the given valueSuppose we want to find (f o g)' at x = 2. To do this, we need to first evaluate g(x) at x = 2. Therefore, g(2) = 2^2 + 3(2) + 1 = 11
Step 4: Use the chain rule to find (f o g)' at the given value now we can use the chain rule to find (f o g)' at x = 2. Therefore, (f o g)'(2) = f'(g(2)) * g'(2) = 1/2(11)^(-1/2) * (2)(3) = 3/sqrt(11)
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What integer is closest to 13/3 divided 2/11 I have been looking at this for while and my brain is going (⊙_◎)
Answer:
24
Step-by-step explanation:
13/3 / 2/11 = 13/3 * 11/2 = 143/6 = 23 and 5/6
23 and 5/6 is closest to 24.
Answer:
23 5/6
Step-by-step explanation:
Joseph's cab company charges a one-time pickup fee of $1.50 for every ride, as well as
a $2.70 charge for each mile traveled. Find the rate of change.
From the equation computed, the rate of change will be 1.50 + 2.7m.
How to solve the equationFrom the information given, it was stated that Joseph's cab company charges a one-time pickup fee of $1.50 for every ride, as well as a $2.70 charge for each mile traveled.
Therefore, the rate of change will be:
= 1.5 + (2.70 × m)
= 1.50 + 2.7m
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Find the circumference in the area of a circle with a diameter of 8 yards
Answer:
C = pi x diameter
Circumference = pi x 8 = 8pi yards
A = pi x radius^2
2 Radius = Diameter = 8 --> Radius = 4 yards
A = pi x 4^2
Area = 16 pi yards^2
Jo has a 10 GB monthly cell phone plan. Jo has used 8 GB in the first 10 days of the month. At that rate, how many GB will Jo use after a month of 30 days?
Answer:
Step-by-step explanation:
1st 10 days - 8 GB
2nd 10 days - 8 GB
3rd 10 days - 8 GB
________________
30 days - 24 GB
A and B are vertical angles. If mA = (3x +22)° and m/B= (7x – 22)°,
then find the value of x.
Answer:
x = 11
Step-by-step explanation:
If given angles m∠A = (3x +22)° and m∠B= (7x – 22)°, the value of x is 11.
Vertical angles are formed by the intersection of two lines. They are opposite to each other and have equal measures. In this case, we have two vertical angles, ∠A and ∠B.
Given that m∠A = (3x + 22)° and m∠B = (7x - 22)°, we can set up an equation based on the fact that vertical angles are equal.
(3x + 22)° = (7x - 22)°
To solve for x, we can simplify the equation:
3x + 22 = 7x - 22
Next, we can isolate the variable x by moving the terms containing x to one side of the equation:
3x - 7x = -22 - 22
-4x = -44
Finally, we divide both sides of the equation by -4 to solve for x:
x = -44 / -4
x = 11
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What should be subtracted from minus 3 / 4 so has to get 5 / 6 ?
Answer:
Step-by-step explanation:
Step 1:First Make 3/4 and 5/6 into like fractions.Find the L.C.M of 4 and
6,which is 12.
3*3/4*3=9/12
5*2/6*2=10/12
Step 2:Subtract 9/12 from 10/12,which is 1/12.