What value of x would make KM ∥ JN?Triangle J L N is cut by line segment K M. Line segment K M goes from side J L to side L N. The length of J K is x minus 5, the length of K L is x, the length of L M is x + 4, and the length of M N is x minus 3.
Complete the statements to solve for x.
By the converse of the side-splitter theorem, if JK/KL = , then KM ∥ JN.
Substitute the expressions into the proportion: StartFraction x minus 5 Over x EndFraction = StartFraction x minus 3 Over x + 4 EndFraction.
Cross-multiply: (x – 5)() = x(x – 3).
Distribute: x(x) + x(4) – 5(x) – 5(4) = x(x) + x(–3).
Multiply and simplify: x2 – x – = x2 – 3x.
Solve for x: x = .
Answers
Answer:
x = 10
Step-by-step explanation:
By the converse of the side-splitter theorem, if , then KM ∥ JN.
Substitute the expressions into the proportion:
Cross-multiply:
(x – 5)(x+4) = x(x – 3).
Distribute:
Multiply and simplify:
Solve for x: x = 10
Therefore, the value of x that would make KM parallel to JN is 10.
Answer:
What value of x would make KM ∥ JN?
Triangle J L N is cut by line segment K M. Line segment K M goes from side J L to side L N. The length of J K is x minus 5, the length of K L is x, the length of L M is x + 4, and the length of M N is x minus 3.
Complete the statements to solve for x.
By the converse of the side-splitter theorem, if JK/KL =
✔ NM/ML
, then KM ∥ JN.
Substitute the expressions into the proportion: StartFraction x minus 5 Over x EndFraction = StartFraction x minus 3 Over x + 4 EndFraction.
Cross-multiply: (x – 5)(
✔ x + 4
) = x(x – 3).
Distribute: x(x) + x(4) – 5(x) – 5(4) = x(x) + x(–3).
Multiply and simplify: x2 – x –
✔ 20
= x2 – 3x.
Solve for x: x =
✔ 10
.Step-by-step explanation:
Related Questions
Write a formula that will compute the final grade for the course, using G to represent the final grade, H to represent the homework average, Q to represent the quiz average, P to represent the project grade, T to represent the test average, and F to represent the final exam grade. Note: Keep in mind how you must write the percentages that show the weighting of each category when doing computations!
A recent study conducted by the state government attempts to determine whether the voting public supports a further increase in cigarette taxes to help the public schools. The opinion poll recently sampled 1500 voting age citizens. 622 of the sampled citizens were in favor of an increase in taxes. The state government would like to decide if there is enough evidence to establish whether the proportion of citizens supporting an increase in cigarette taxes is significantly greater than 66%. At what level of significance will the null hypothesis not be rejected?
-3-[(6+3)+(-5-18)]
6(2x-5y)-2(x+9y) simplified
Answers
The conditional probability that a degree is earned by a person whose race is White, given that it is an associate's degree, is 57.14%.
Given that of all postsecondary degrees awarded in the United States, including master's and doctorate degrees, 21% are associate's degrees, 58% are earned by people whose race is White, and 12% are associate's degrees earned by Whites, to determine what is the conditional probability that a degree is earned by a person whose race is White, given that it is an associate's degree, the following calculation should be performed:
- A cross multiplication must be applied to obtain the percentage of whites who have obtained an associate degree.
- 21 = 100
- 12 = X
- 12 x 100/21 = X
- 1200/21 = X
- 57.14 = X
Therefore, the conditional probability that a degree is earned by a person whose race is White, given that it is an associate's degree, is 57.14%.
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Final answer:
The conditional probability that a degree is earned by a person whose race is White, given that it is an associate's degree, is 57 %.
Explanation:
The question asks us to compute the conditional probability that a degree is earned by a person whose race is White, given that it is an associate's degree. The definition of conditional probability P(A|B) is the probability of event A given that event B has happened. In your case, event A is 'degree is earned by a person whose race is White' and event B is 'the degree is an associate's degree'.
The probability P(A|B) can be calculated using the formula: P(A|B) = P(A ∩ B) / P(B).
Applying this information to your question, P(A ∩ B) is the probability that the degree is an associate's degree earned by a person whose race is white, which is 12 %. P(B) is the probability that the degree is an associate's degree, which is 21 %. Therefore, P(A|B) = 12/21 = 0.57 or 57 %.
So the conditional probability that a degree is earned by a person whose race is White, given that it is an associate's degree is 57 %.
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f(x)= 11x + 10 ; shifts 3 units up.
Answers
The 3 units vertical shift graph of f(x) = 11x + 10 is g(x) = 11x + 13.
What is vertical shift?
A vertical shift is just a change in the y-value of each function. It is literally picking up the entire function or graph and moving the entire thing up or down. If it is moved up, we add to the y-value, if it is moved down, we subtract from the y-value.
A shift of 3 units up, implies adding 3 to the y value.
New function becomes,
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Answer:
f(x)= 11x +10 +3 or 11x +13
Step-by-step explanation:
Answers
2.357 divided by 21= 17
3. 1215 divided by 15= 81
4.360 divided by 24= 15
Answer:
51.111, 17, 81, 15
Step-by-step explanation:
Answers
Answer:
Step-by-step explanation:
In parallelogram adjacent angles are supplementary
∠U +∠V = 180
9x + 15 + 6x + 15 = 180
Combine like terms
9x + 6x + 15 + 15 = 180
15x + 30 = 180
Subtract 30 from both sides
15x = 180 - 30
15x = 150
Divide both sides by 15
x = 150/15
x = 10
∠U = 9x + 15
= 9*10 + 15
= 90 + 15
∠U = 105
∠V = 6x + 15
= 6*10 + 15
= 60 + 15
∠V = 75
Answer:
Equation:
x = 10°
∠U = 105°
∠V = 75°
Step-by-step explanation:
Hello!
The sum of angles in a parallelogram is 360°. The oppositeangles of a parallelogram are congruent.
Part A
Equation: %20%3D%20360)
Solve
The value of x is 10°.
Part B
To find the measures of each angle, simply plug in 10° for x in each equation.
∠U
Angle U is 105°.
∠V
Angle V is 75°.
1 year?
Answers
Answer:
Steven ears $565 more in one year.
Step-by-step explanation:
Giving the following information:
Mark:
PV= $45,000
n= 1
i= 0.032
Steven:
PV= $45,000
n= 1
i= 0.045
To calculate the Future Value of each investment, we need to use the following formula:
FV= PV*(1+i)^n
Mark:
FV= 45,000*1.032= $46,440
Steven:
FV= 45,000*1.045= $47,025
Difference= 47,025 - 46,440= $565
Steven ears $565 more in one year.
Final answer:
After investing their inheritance for one year, Steven has $585 more than Mark due to the higher interest rate of his investment.
Explanation:
After one year, the amount of money Mark and Steven have can be calculated using the formula for compound interest, which is P(1 + r) to the power of n, where P is the principal amount, r is the annual interest rate, and n is the time in years. So, Mark's future value would be $45000(1 + 0.032) = $46440. In contrast, Steven's future value would be $45000(1 + 0.045) = $47025. Therefore, Steven has $47025 - $46440 = $585 more than Mark after 1 year.
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Please help ☝
Answers
Answer:
-2x - 12
Step-by-step explanation:
-5(4x)+6(3x - 2)
-20x +18x - 12
-2x - 12