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3 years ago

Which expressions are equivalent to 12x - 6?

Mathematics

1 answer:

iren2701 [21]3 years ago

8 0

<h3>Answer</h3>

B and E

<h3>Explanation</h3>

A) It's wrong because

$- 6 \times (2x - 1) = - 12x + 6$

B) It's right because

$6 \times (2x - 1) = 12x - 6$

C) It's wrong because

$6x \times (2 - 1) = 6x \times 1 = 6x$

D) It's wrong because

$- 6x \times (2x - 1) = - 12 {x}^{2} + 6$

E) It's right because

$- 6 \times ( - 2x + 1) = 12x - 6$

F) It's wrong because

$6 \times ( - 2x + 1) = - 12x + 6$

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3. Given ABCD ≅ FGHJ and mC = 9x - 7, mH = 5x + 13, find the value of x and the measures of angle C and angle H. Show all work

kondor19780726 [428]

Answers:

x = 5

m∠C = m∠H = 38 degrees

WORKINGS

Given that ABCD ≅ FGHJ

We know that corresponding angles of two congruent quadrilaterals are equal

Therefore,

m∠A = m∠F

m∠B = m∠G

m∠C = m∠H

m∠D = m∠I

Given,

m∠C = 9x – 7

m∠H = 5x + 13

Since m∠C = m∠H

9x – 7 = 5x + 13

Add 7 to both sides of the equation

9x – 7 + 7 = 5x + 13 + 7

9x = 5x + 20

Subtract 5x from both sides of the equation

9x – 5x = 5x – 5x + 20

4x = 20

Divide both sides of the equation by 4

4x/4 = 20/4

x = 5

To determine the measures of angle C and angle H

m∠C = m∠H

We know that m∠C = 9x – 7

Since x = 5

m∠C = 9(5) – 7

m∠C = 45 – 7

m∠C = 38

Therefore, m∠C = m∠H = 38 degrees

4 0

3 years ago

Solve 7.8e^((x/3)ln(5))=14. What are the exact and approximate solutions?

Dimas [21]

$\bold{\text{Answer}:\quad x=3\bigg(\dfrac{ln\frac{14}{7.8}}{ln(5)}\bigg)=1.09}$

<u>Step-by-step explanation:</u>

$7.8e^{\frac{x}{3}\cdot ln(5)}=14\\\\\\e^{\frac{x}{3}\cdot ln(5)}=\dfrac{14}{7.8}\\\\\\ln\bigg(e^{\frac{x}{3}\cdot ln(5)}\bigg)=ln\bigg(\dfrac{14}{7.8}\bigg)\\\\\\\frac{x}{3}}\cdot ln(5)=ln\bigg(\dfrac{14}{7.8}\bigg)\\\\\\\large\boxed{x=3\bigg(\dfrac{ln\frac{14}{7.8}}{ln(5)}\bigg)}\\$