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3 years ago

What is the value of x? Enter your answer in the box.

Mathematics

1 answer:

PIT_PIT [208]3 years ago

6 0

We will use the angle bisector theorem here for $\angle GEH$ . ED being the angle bisector.

Thus, from the diagram we will have:

$\frac{HD}{DG} =\frac{EH}{EG}$

We will now plug in the values given in the diagram.

$\frac{35}{x+4} =\frac{56}{44.8}$

$x+4=\frac{35\times 44.8}{56}$

$x+4=28$

$x=24$

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Three students, Matthew, Thompson and Amos shared #15000 in the ratio of 5:2:x respectively. If Matthew's share is 7500, calcula

jasenka [17]

Answer:

The value of x is 3.

Step-by-step explanation:

Matthew earned 7500 of 15000, which is exactly half the total amount, meaning that the fraction corresponding to his earnings is 1/2.

Rate of 5:2:x, with number 5 corresponding to Matthew, mean that his fraction of the earnings, in function of x is given by:

$\frac{5}{5 + 2 + x} = \frac{5}{7 + x}$

Both fractions are equal, so:

$\frac{5}{7 + x} = \frac{1}{2}$

Applying cross multiplication:

$7 + x = 10$

$x = 10 - 7$

$x = 3$

The value of x is 3.

5 0

2 years ago

Variable termes X-12-3X+22

adell [148]

Answer: x + 12 = 3x + -22

12 + x = 3x + -22

Reorder the terms:

12 + x = -22 + 3x

Solving

12 + x = -22 + 3x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3x' to each side of the equation.

12 + x + -3x = -22 + 3x + -3x

Combine like terms: x + -3x = -2x

12 + -2x = -22 + 3x + -3x

Combine like terms: 3x + -3x = 0

12 + -2x = -22 + 0

12 + -2x = -22

Add '-12' to each side of the equation.

12 + -12 + -2x = -22 + -12

Combine like terms: 12 + -12 = 0

0 + -2x = -22 + -12

-2x = -22 + -12

Combine like terms: -22 + -12 = -34

-2x = -34

Divide each side by '-2'.

x = 17

Simplifying

x = 17

7 0

2 years ago

A truck was carrying 2 and 1/8 tons of sand. When it arrived, only 1 and 1/2 ton of sand were left. How much sand was lost along

erica [24]

I'm pretty sure it's 1 5/8

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3 years ago

If ANQZ - ACBK, find BK. * O BK = 39 O BK = 16 O BK = 65 O BK = 27

patriot [66]

9514 1404 393

Answer:

Step-by-step explanation:

Corresponding sides are proportional in similar triangles, so ...

ZT/ZQ = KF/KB

27/(2x +7) = 45/(4x+1)

27(4x+1) = 45(2x +7) . . . cross-multiply

3(4x +1) = 5(2x +7) . . . . divide by 9

12x +3 = 10x +35 . . . . . eliminate parentheses

2x = 32 . . . . . . . . . . . . . subtract 10x+3

x = 16 . . . . . divide by 2

Then the length of BK is ...

BK = 4x+1 = 4·16 +1

BK = 65

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2 years ago

3/8 is 4 & 3/5 % of what number? (Round to the nearest hundredth.)

Harman [31]

Answer:

n = 8.15

Step-by-step explanation:

3/8 is 4 & 3/5 % of what number?

Rewrite this as: 3/8 is (4 3/5)% of what number?

Convert 4 3/5% into a decimal: 0.046

Then write out and solve the equation 3/8 = 0.046n, where n is the unknown number.

Dividing both sides by 0.046, we get n = 8.15

4 0

3 years ago