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2 years ago

Find the value of x.(Image)Find the value of x so that f || g(Image)

Mathematics

1 answer:

Helga [31]2 years ago

7 0

Answer:

x = 13 , x = 9

Step-by-step explanation:

for the lines to be parallel then 9x + 2 and 119 are alternate angles and are congruent , so

9x + 2 = 119 ( subtract 2 from both sides )

9x = 117 ( divide both sides by 9 )

x = 13

-------------------------------------------------------

For f and g to be parallel then 18x - 44 and 8x - 10 are same- side interior angles and sum to 180° , then

18x - 44 + 8x - 10 = 180 , that is

26x - 54 = 180 ( add 54 to both sides )

26x = 234 ( divide both sides by 26 )

x = 9

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What are all of the values?

Arada [10]

(i) x = 3

(ii) y = 6

Explanation:

The two polygons are similar.

The congruent angles are:

∠J ≅ ∠G

∠R ≅ ∠M

∠I ≅ ∠A

∠C ≅ ∠T

∠E ≅ ∠H

Proportional sides are:

$\frac{JR}{GM} = \frac{RI}{MA} = \frac{IC}{AT} = \frac{CE}{TH} = \frac{EJ}{HG}$

(i) Value of x = ?

$\frac{JR}{GM} = \frac{RI}{MA}$

Putting the values from the figure

$\frac{6}{12} = \frac{2x + 1}{3x + 5} \\\\6 ( 3x + 5) = 12 ( 2x + 1)\\\\18x + 30 = 24x + 12\\\\30 - 12 = 24x - 18x\\\\18 = 6x\\\\x = 3$

(ii) Value of y = ?

$\frac{JR}{GM} = \frac{IC}{AT}$

On putting the value we get:

$\frac{6}{12} = \frac{x^2-4}{y+4} \\\\6(y+4) = 12(x^2 - 4)\\\\6y + 24 = 12[(3)^2 - 4]\\\\6y + 24 = 12[ 9 - 4]\\\\6y + 24 = 60\\\\6y = 36\\\\y = 6$

4 0

3 years ago

X + 2y = 10 3x + 4y = 8

REY [17]

Answer:

x + 2y = 10 - x= 10−2y

3x + 4y = 8 - x=8/3 - 4y/3

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Evelyn went shopping with half of her monthly allowance. She spent $39.95 on a dress and 3/7 of the remainder on some accessorie

Gnoma [55]

Answer:

Evelyn monthly allowance is $187.

Step-by-step explanation:

Let the monthly allowance be 'x'.

Given:

Money taken with for shopping = $\frac{x}{2}$

Money spent of dress = $39.95

Also Given:

3/7 of the remainder on some accessories.

Money spent on accessories is equal to $\frac{3}{7}$ times Difference of monthly allowance and Money spent of dress.

framing in equation form we get;

Money spent on accessories = $\frac{3}{7}\times(\frac{x}{2}-39.95)$

Also Given:

Money left after shopping = $30.60

Now we know that;

Money taken with for shopping is equal to sum of Money spent of dress and Money spent on accessories and Money left after shopping.

framing in equation form we get;

$\frac{x}{2}=39.95+\frac{3}{7}(\frac{x}{2}-39.95)+30.60\\\\\frac{x}{2}=39.95+\frac{3x}{14}- 17.12 +30.60$

Combining like terms we get;

$\frac{x}{2}-\frac{3x}{14}=39.95-17.12+30.60\\\\\frac{x}{2}-\frac{3x}{14}= 53.43$

Now we will make denominator common using L.C.M

$\frac{x\times 7}{2\times7}-\frac{3x\times1}{14\times1}= 53.43\\\\\frac{7x}{14}-\frac{3x}{14}= 53.43\\\\\frac{7x-3x}{14}=53.43\\\\\frac{4x}{14}=53.43\\\\4x=53.43\times14\\\\x= \frac{53.43\times14}{4} = \$187$

Hence Evelyn monthly allowance is $187.

3 0

4 years ago

Anne, Scott and Beth won $300 in a lottery. The jackpot will be divided among them based on their money they put towards the tic

Shkiper50 [21]

Answer: Beth should get $135

Step-by-step explanation:

Money won in the lottery by Anne, Scott and Beth =$300

Amount necessary for Anne = 30% X 300

=$90

Amount necessary to Scott =1/4 X 300

=$75

Therefore Beth should get the remainder=Total money won -(Amount necessary to Anne and Scott)

=$300-(90+75)

=$300-$165

=$135

8 0

3 years ago

I need answers ASAP

AURORKA [14]

Answer:

Simplifying

6r + r + -5r = 0

Combine like terms: 6r + r = 7r

7r + -5r = 0

Combine like terms: 7r + -5r = 2r

2r = 0

Solving

2r = 0

Solving for variable 'r'.

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

Divide each side by '2'.

r = 0

Simplifying

r = 0

8 0

3 years ago

Read 2 more answers