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3 years ago

Determine the value of x in the figure.

Mathematics

1 answer:

IgorLugansk [536]3 years ago

8 0

Step-by-step explanation:

Hey there!

Your required answer is option B.

Here,

Given,

The figure is an equilateral triangle with, side (7x+9) and (x+27).

By the defination of equilateral triangle we have,

All sides of equilateral triangle are equal. 

So,

$( 7x+ 9) = x + 27$

Simplify them to get answer.

$7x - x = 27 - 9$

$6x = 18$

$x = \frac{18}{6}$

Therefore the value of x is 3.

Hope it helps...

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3 years ago

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FromTheMoon [43]

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1/2

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2 years ago

Can you please help me

Ket [755]

Answer:

The scale factor for the dilation of rectangle ABCD to rectangle MNOP is $\frac{3}{4}$ ⇒ B

Step-by-step explanation:

In similar rectangles, their corresponding dimensions are proportional, which means $\frac{L_{1} }{L_{2}}$ = $\frac{W_{1} }{W_{2}}$ , where L is the length and W is the width

∵ Rectangle ABCD is similar to rectangle MNOP

∴ Their dimensions are proportional

∵ The dimensions of rectangle ABCD are 6 m, 14 m

∴ L $_{1}$ = 14 and W $_{1}$ = 6

∵ The dimensions of rectangle MNOP are 4.5 m, 10.5 m

∴ L $_{2}$ = 10.5 and W $_{2}$ = 4.5

∵ The rectangle MNOP is the image of rectangle ABCD after dilation

→ To find the scale factor of dilation find the ratio between the

corresponding dimensions in the two rectangles (image/pre-image)

∵ $\frac{L_{2} }{L_{1}}$ = $\frac{10.5}{14}$ = $\frac{3}{4}$

∵ $\frac{W_{2} }{W_{1}}$ = $\frac{4.5}{6}$ = $\frac{3}{4}$

∴ The scale factor for the dilation is $\frac{3}{4}$

The scale factor for the dilation of rectangle ABCD to rectangle MNOP is $\frac{3}{4}$

6 0

3 years ago

The sum of the angle measures of any triangle is 180 degrees. find the angle measures of a triangle if the second angle measures

MissTica

A+b+c= 180
a = ?
b = 2a - 10 (twice a minus 10)
c = b + 25 (25 more than b)
Substitute for b
c = (2a-10) + 25
Now substitute back into a+b+c=180
a + (2a-10) + (2a-10+25) = 180
Eliminate the parentheses
a + 2a - 10 + 2a - 10 + 25 = 180
Combine like terms
5a + 5 = 180
Subtract 5 from both sides
5a = 175
Divide both sides by 5
a = 35
Substitute into the equation for b.
b = 2a -10 = 2*35 - 10 = 70 - 10 = 60
Add 25 to b to get c.
c = 60 + 25 = 85Check by adding them up.
35 + 60 + 85 = 180
Done.

3 0

3 years ago