Analyze the diagram below and complete the instructions that follow.
Find the value of x and the value of y.
A.x = 15, y = 10
B.x = 20, y = 50
C.x = 50, y = 10
D.x = 50, y = 20
Answer is C x=50 y=10
Answers
Answer:
C. [tex]x=50[/tex], [tex]y=10[/tex]
Step-by-step explanation:
We have been given an image of two intersecting lines. We are asked to find the value of x and y for our given diagram.
We know that when two line intersect each other, then vertical angles are congruent.
Using vertical angles theorem, we will get a system of equations as sown below:
[tex]3y=x-20...(1)[/tex]
[tex]5x-100=y+140...(2)[/tex]
From equation (1), we will get:
[tex]x=3y+20[/tex]
Upon substituting this value in equation (2), we will get:
[tex]5(3y+20)-100=y+140[/tex]
[tex]5*3y+5*20-100=y+140[/tex]
[tex]15y+100-100=y+140[/tex]
[tex]15y=y+140[/tex]
[tex]15y-y=y-y+140[/tex]
[tex]14y=140[/tex]
[tex]\frac{14y}{14}=\frac{140}{14}[/tex]
[tex]y=10[/tex]
Therefore, the value of y is 10.
To find the value of x, we will substitute [tex]y=10[/tex] in equation (1) as:
[tex]3*10=x-20[/tex]
[tex]30=x-20[/tex]
[tex]30+20=x-20+20[/tex]
[tex]50=x[/tex]
Therefore, the value of x is 50 and option C is the correct choice.
Answer:
Option C) x = 50, y = 10
Step-by-step explanation:
We are given a two pairs of vertically opposite angle in the image.
Vertically opposite angle is formed when two lines intersect anf they are always equal.
Thus, we can write:
[tex]3y = x -20\\\Rightarrow x - 3y = 20\\5x-100 = y +140\\\Rightarrow 5x - y =240[/tex]
Solving the two equations in two variable, we get:
[tex]x - 3y = 20\\5x - y =240\\\text{Multiplying first equation by 5}\\5x - 15y = 100\\\text{Subtracting the equations}\\5x - 15y-(5x-y) = 100-240\\-14y = -140\\y = 10\\ x - 3(10) = 20\\x = 20 + 30\\x =50[/tex]
The value of x is 50 and y is 10.
Related Questions
How do i write 0.624 in expanded form?
Answers
btw not rrly so sure wut expanded form is.
Of the 50 tables in a restaurant, 40% seat 2 people. The remaining tables seat 4 people. How many seats are there in the restaurant?
Answers
Answer: 160 seats
Step-by-step explanation: Got it right on TTM
What value of z divides the standard normal distribution so that half the area is on one side and half is on the other? round your answer to two decimal places?
Answers
The value of [tex]z[/tex] which divides the standard normal distribution so that half the area is on one side and half is on the other is [tex]0.00[/tex].
A normal distribution with a mean of [tex]0[/tex] and a standard deviation of [tex]1[/tex] is known as a standard normal distribution.
The typical normal distribution is divided into two equal halves with 50% on each side when the [tex]z[/tex] value is [tex]0.00[/tex].
Hence, the value of [tex]z[/tex] which divides the standard normal distribution so that half the area is on one side and half is on the other is [tex]0.00[/tex].
Learn more about standard normal distribution here:
https://brainly.com/question/11876263?referrer=searchResults
Emma is scrapbooking she has 9 inches of paper and needs to cut it into 2/5 inch strips of paper how many strips will she be able to make
Answers
Then by using the reciprocal, multiply them both (change 9 to 9/1)
9/1 x 5/5 = 45/2
If you would like to convert it, it would be 22 1/2
Answer:
22 strips.
Step-by-step explanation:
In order to solve this you just have to divide the total inches of paper that she actually has by the size of the strips that she´s going to make:
[tex]9 inches/2/5\\\frac{ 9inches}{\frac{2}{5} } \\\frac{45}{2}\\22\frac{1}{2}[/tex]
So as you can see she can make a total of 22 strips and a half, but the half won´t be useful so she can make 22 strips.
Addison earn $25 Mowing her neighbors lawn. Then she loaned her friend $18, and got $50 from her grandmother for her birthday she now has $86. how much money did Addison have to begin with?
Answers
what is 2 equivalent ratios for 5/11
Answers
or
25/55
You just have to multiply the numerator and denominator by the same number
i need to know what t is but i don't understand how to get it
Answers
What is the converse of the statement given? "If a triangle is equilateral, then it is isosceles." Question 1 options: A triangle is equilateral if and only if it is isosceles. A triangle is not isosceles then if it is not equilateral. If a triangle is isosceles, then it is equilateral. All equilateral triangles are isosceles.
Answers
"If a triangle is isosceles, then it is equilateral."
For a normal population with a mean of m = 80 and a standard deviation of s = 10, what is the probability of obtaining a sample mean greater than m = 75 for a sample of n = 25 scores? p = 0.0062 p = 0.9938 p = 0.3085 p = 0.6915
Answers
The calculated z-score is -2.5, and the corresponding probability is 0.9938, meaning there is a 99.38% chance of drawing a sample with a mean greater than 75.
To find the probability of obtaining a sample mean greater than m = 75 for a sample of n = 25 scores when the population mean is m = 80 and the standard deviation is s = 10, we will use the concept of sampling distributions and the Central Limit Theorem.
First, we need to calculate the standard error of the mean (SEM), which is the standard deviation of the sampling distribution of the sample mean.
The SEM is calculated using the formula [tex]SEM = s / \sqrt{n[/tex] where s is the population standard deviation and n is the sample size.
Here, SEM = [tex]10 / \sqrt{25[/tex]
= 10 / 5
= 2.
Next, we convert the sample mean to a z-score to find out how many standard errors the sample mean is from the population mean.
The z-score is calculated using the formula z = (M - m) / SEM, with M being the sample mean and m the population mean.
Therefore, z = (75 - 80) / 2 = -5 / 2 = -2.5.
Looking at the standard normal distribution table or using statistical software, we find that the probability associated with a z-score of -2.5 is approximately 0.9938. This means that the probability of obtaining a sample mean greater than 75 is 0.9938.
A students received a score of 50 on his history test. The test had a mean of 69 and a standard deviation of 10. Find the z score and assess whether his score is considered unusual.
Answers
The general rule is that 68% of all scores are within 1 z-score of the mean.
95% are within 2 z-scores of the mean.
99% are within 3 z-scores of the mean.
1.9 is pretty close to 2, so this means approximately only 5% of all scores are more unusual than this students' score.
solve using break apart strategy 132+42=
Answers
2+2=4
170+4=174
What is the place value relationships of 8's in 6,588
Answers
EXAMPLE
9-ones
97- tens
987-hundreds and so on
Evaluate -(4/5) over 8/15
Answers
I need help with simplifying this question
43+a-2a
Thank you!!!!
Answers
(Hope this helps you!)
The correct answer is 43-a. In other words, the result of simplifying algebraic expressions 43 + a - 2a is 43 - a.
To simplify the expression 43 + a - 2a, you can combine like terms.
The expression consists of three terms: 43, a, and -2a.
Starting with the numbers, 43 is a constant term and does not contain any variables. Since there are no other terms with numbers, 43 remains unchanged.
Next, let's simplify the terms with variables. We have a and -2a. To combine these terms, we can group them together as a single term.
The term with a is positive a, and the term with -2a is negative 2a. When we combine them, we subtract 2a from a. This gives us a - 2a, or -a.
Therefore, the simplified expression is 43 - a.
Therefore, the correct answer is 43-a. In other words, the result of simplifying algebraic expressions 43 + a - 2a is 43 - a.
Learn more about simplifying algebraic expressions here:
https://brainly.com/question/30200858
#SPJ6
The area of a regular octagon is 35 cm^2. What is the area of a regular octagon with sides five times as long?
A. 625 cm^2
B. 875 cm^2
C. 175 cm^2
D. 245 cm^2
I'm not very good at this kind of stuff :/
Answers
[tex]\bf \qquad \qquad \textit{ratio relations} \\\\ \begin{array}{ccccllll} &Sides&Area&Volume\\ &-----&-----&-----\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3} \end{array} \\\\ -----------------------------\\\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\\\\ -------------------------------\\\\[/tex]
[tex]\bf \cfrac{small}{large}\quad \stackrel{area~ratio}{\cfrac{s^2}{s^2}}\implies \stackrel{area~ratio}{\cfrac{x^2}{(5x)^2}}\implies \stackrel{area~ratio}{\cfrac{x^2}{5^2x^2}}\implies \stackrel{area~ratio}{\cfrac{\underline{x^2}}{25\underline{x^2}}}=\stackrel{area~ratio}{\cfrac{35}{a}} \\\\\\ \cfrac{1}{25}=\cfrac{35}{a}\implies a=\cfrac{25\cdot 35}{1}[/tex]
Factor the expression using the GCF. 2+8
Answers
8: 1,2,4,8
Greatest common factor is 2.
So the factored expression would be 2(2) + 8(2)= 10(2)
The expression '2+8' simplifies to 10. Factoring using the Greatest Common Factor (GCF) is commonly used with expressions that contain variables.
Explanation:The expression you're looking to factor, 2+8, does not really involve any complex mathematical concepts, and there's no variable to enable factoring in its usual way. However, we can simplify it by adding the numbers. So, 2+8 equals to 10. Factoring using the greatest common factor(GCF) is most often used when you're handling expressions that involve variables, for instance, 2x + 8x. In this case, the GCF would be 2x, and the expression would factor to 2x(1 + 4).
Learn more about Factoring Using GCF here:https://brainly.com/question/34359196
#SPJ11
9 1/ 2 gal of gas into his car. Convert this amount to a decimal.
Answers
Initially, a store has 35 train sets. The store sells 3 train sets each month.
What is the explicit rule for the number of train sets the store has after ‘n’ months?
Answers
The explicit rule for the remaining train sets after 'n' months is represented by the formula T(n) = 35 - 3n, where T(n) is the total number of train sets, and 'n' is the number of months.
Explanation:The explicit rule for the number of train sets a store has after ‘n’ months, given that the store starts with 35 train sets and sells 3 each month, can be represented by a linear equation. The initial amount of train sets is the starting point, and the number of sets sold each month is the rate of change.
The explicit rule for the number of train sets the store has after 'n' months can be represented by the linear function:
\[ T(n) = 35 - 3n \]
Here, \( T(n) \) represents the number of train sets after 'n' months, 35 is the initial number of train sets, and 3n represents the number of train sets sold each month. The negative coefficient (-3) indicates the decrease in the number of train sets each month. By plugging in different values for 'n', you can determine the number of train sets the store will have at any given month.
This is reflected in the equation:
T(n) = 35 - 3n
where T(n) represents the total number of train sets after n months, and n is the number of months that have passed.
hat is the solution set of the following equation? -8x + x + 15 = -7x + 12 Ø {} {all reals}
Answers
-7x + 15 = -7x + 12
First of all, we need to put the variables apart and the numbers apart. So we add 7x on both sides:
-7x + 7x + 15 = -7x + 7x + 12
0x + 15 = 0x + 12
15 = 12
This answer is impossible since 15 can never be equal to 12. So there are no values of x that can make the equation true.
Hope this helps! :)
If one of the purple-flowered progeny plants is selected at random and self-fertilized, what is the probability it will breed true? if one of the purple-flowered progeny plants is selected at random and self-fertilized, what is the probability it will breed true? 2/3 3/4 1/4 1/3
Answers
However, I will provide the answer by making biology-related assumptions.
1. The genotype of the purple-flowered progeny is Pp
2. The purple-flower phenotype is recessive.
If self fertilized, both "parents" have genotype Pp
The punnett square is as follows:
P p
P PP Pp
p Pp pp
Since purple-flowers are recessive, only PP will come out purple, hence the probability is 1/4.
Solve the inequality T > L plus D all divided by B for D. (2 points)
Select one:
a. T + B − L > D
b. TB − L > D
c. T divided by B − L > D
d. T times B divided by L > D
Answers
TB > L + D...subtract L from both sides
TB - L > D <==
Catherine walks her dog 3/4 mile everyday. how far does she walk each day?
Answers
A market research firm conducts telephone surveys with a 44% historical response rate. what is the probability that in a new sample of 400 telephone numbers, at least 150 individuals will cooperate and respond to the questions? in other words, what is the probability that the sample proportion will be at least 150/400 = .375? calculate the probability to 4 decimals.
Answers
To calculate the probability that at least 150 individuals will cooperate and respond to the questions in a new sample of 400 telephone numbers with a historical response rate of 44%, we use the binomial distribution formula.
Explanation:To calculate the probability that at least 150 individuals will cooperate and respond to the questions, we need to use the binomial distribution formula. The formula is:
P(X ≥ k) = 1 - P(X
Where n is the sample size, k is the desired number of successes, p is the historical response rate, q = 1 - p is the failure rate.
In this case, n = 400, k = 150, p = 0.44, q = 1 - 0.44 = 0.56. Plugging these values into the formula, we get:
P(X ≥ 150) = 1 - P(X<150)
We can use a software or calculator to evaluate this expression. The probability is approximately 0.9328 to 4 decimal places.
Bailey writes the expression g2 + 14g + 40 to represent the area of a planned school garden in square feet. If g = 5, what are the dimensions of the school garden? 20 feet by 2 feet 10 feet by 4 feet 12 feet by 7 feet 15 feet by 9 feet
Answers
g² + 14g + 40
5² + 14(5) + 40
25 + 70 + 40
So, your area would be 135.
Out of your 4 options, you need to find out which dimensions create 130.
20 × 2 = 40
4 × 12 = 48
12 × 7 = 84
15 × 9 = 135
Your dimensions are 15ft by 9ft :)
Hope this helps!
g^2 14g+40
replace g with 5
5^2 +14(5) +40 = 25 + 70 +40 = 135 square feet
Area =L x W
using your choices multiply 15 x 9 = 135
so answer is 15 feet by 9 feet
After you prove that two triangles are congruent, what would CPCTC be useful for?
Answers
Answer with explanation:
When we prove two triangles are congruent, either by following four congruent Axioms
1. S AS
2. SSS
3. A AS
4. A SA
Then C P CT C stands for Corresponding part of Congruent Triangles.
So, C P C TC is useful for proving , those corresponding parts of triangle that is side and Angles equal which are not used while proving Congruency of two triangles.
Which of the following is irrational?
A.7.51... * (-4)
B.sqrt of 16 + 3/4
C. sqrt of 3 + 8.486
D. 8 2/3 x 17.75
Answers
Answer:
c
Step-by-step explanation:
Option (C) √3 + 8.486 is an irrational number.
What is an irrational number?An irrational number is a type of real number which cannot be represented as a simple fraction. It cannot be expressed in the form of a ratio. Those real numbers that are not rational numbers are known as irrational numbers.
For the given situation,
We need to check the options, that is irrational.
Option A: 7.51... x -4
⇒ 7.51 (-4)
We can express this as fraction. So it is not an irrational number.
Option B: root 16 + 3/4
⇒ √16 + 3/4
⇒ 4 + 3/4
We can express this as fraction. So it is not an irrational number.
Option C: root 3 + 8.486
⇒ √3 + 8.486
⇒ √3 is an irrational number, so the sum is also an irrational number.
Option D: 8 2/3 × 17.75
⇒ 8 2/3 × 17.75
We can express this as fraction. So it is not an irrational number.
Hence, we can conclude that option (C) √3 + 8.486 an irrational number.
Learn more about irrational number here
brainly.com/question/3386568
#SPJ7
A swimming pool is circular with a 30-ft diameter. the depth is constant along east-west lines and increases linearly from 1 ft at the south end to 6 ft at the north end. find the volume of water in the pool. (round your answer to the nearest whole number.
Answers
?
How can I find the exact distance between the points(√7,-√2)and (4√7,5√2)
Answers
[tex]\bf d=\sqrt{[4\sqrt{7}-\sqrt{7}]^2~+~[5\sqrt{2}-(-\sqrt{2})]^2} \\\\\\ d=\sqrt{(4\sqrt{7}-\sqrt{7})^2~+~(5\sqrt{2}+\sqrt{2})^2}\implies d=\sqrt{(3\sqrt{7})^2~+~(6\sqrt{2})^2} \\\\\\ d=\sqrt{3^2\cdot 7~~+~~6^2\cdot 2}\implies d=\sqrt{63+72}\implies d=\sqrt{135} \\\\\\ \begin{cases} 135=5\cdot 3\cdot 3\cdot 3\\ \qquad 5\cdot 3^2\cdot 3\\ \qquad 15\cdot 3^2 \end{cases}\implies d=\sqrt{15\cdot 3^2}\implies d=3\sqrt{15}[/tex]
three adults and four children must pay $107. two adults and three children must pay $76. find the price of the adult ticks and the price of a childs ticket
Answers
3a + 4c = 107
2a + 3c = 76
elimination method
2(3a + 4c = 107)
-3(2a + 3c = 76)
6a + 8c = 214
-6a - 9c = -228
----------------------
0 - c = - 14
c = 14
Then 2a + 3(14) = 76
2a = 76 - 42
2a = 34
a = 34/2
a = 17
Help please!! :// don't understand!!!
Answers
The mathematical sum is ³/₄ ÷ ¹/₃
The method for dividing fractions is to flip the second fraction then multiply the two fraction
³/₄ × ³/₁ = ⁹/₄ = 2 ¹/₄ cuts
The greatest number can be cut are 2 pieces with 0.25 meter left over