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2 years ago

ΔABC and ΔXYZ are similar triangles. If BC = x + 7, AC = x + 6, YZ = 4 − x, and XZ = 3 − x, find the value of x.

Mathematics

2 answers:

Margarita [4]2 years ago

7 0

Given ΔABC and ΔXYZ are similar triangles. BC = x + 7, AC = x + 6, YZ = 4 − x, and XZ = 3 − x.

Similar triangles have sides in proportion.

$\frac{BC}{YZ} =\frac{AC}{XZ}$

Substituting the given values :

$\frac{x+7}{4-x} =\frac{x+6}{3-x}$

To solve for x we cross multiply

(x+7)(3-x)=(4-x)(x+6)

Using FOIL to multiply

$3x-x^{2} +21-7x =4x+24-x^{2} -6x$

Simplifying like terms

-4x+21=-2x+24

To solve for x we isolate the x term

Adding 2x both sides:

-4x+2x+21=24

-2x+21=24

Subtracting 24 both sides

-2x=24-21

-2x=3

Dividing by -2 we have x= $-\frac{3}{2}$

Option B is the right answer.

Montano1993 [528]2 years ago

3 0

I believe the answer is B) -3/2 or -1.5.

Please give a heart and rating if this is right!

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Answer:

Step-by-step explanation:

Given is a function in x as

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1 year ago

In three hours, Company ABC can make X ball bearings. Company DEF can make X ball bearings in 4 hours. Company GHI can make X ba

amm1812

Answer:

<em>X ball bearings will be made in 1 hour and 20 minutes</em>

Step-by-step explanation:

<u>Proportions </u>

The proportions give us an important tool to easily solve common problems of any type. We know that:

Company ABC can make X ball bearings in 3 hours.

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1 year ago

Decrease £19064.67 by 9.5%<br>Give your answer rounded to 2 DP.<br>

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Answer:

£17253.53 to the nearest hundredth.

Step-by-step explanation:

Decreasing by 9,5% is equivalent to multiplying by 1 - 0.095 = 0.905.

19064.67 * 0.905

= £17253.52635.

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1 year ago

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2 years ago

Find two complex numbers that have a sum of i10 a different of -4and a product of -29

lianna [129]

Step-by-step explanation:

Let the complex numbers be $a+ib\textrm{ and }c+id$ .

Given, sum is $10i$ , difference is $-4$ and product is $-29$ .

$(a+c)+i(b+d)=10i$ ⇒ $a+c=0,b+d=10$

$(a-c)+i(b-d)=-4$ ⇒ $a-c=-4,b-d=0$

$a=-2,c=2,b=5,d=5$

$(a+ib)(c+id)=(-2+5i)(2+5i)=-4-25=-29$

Hence, all three equations are consistent yielding the complex numbers $-2+5i\textrm{ and }2+5i$ .

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1 year ago