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uranmaximum [27]
2 years ago
13

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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Tems11 [23]

Answer:

100x+120y = z

z= $ 63000

Step-by-step explanation:

Product               Welding          Assembly       Painting                Cont. to profit

X                              2x hours            3x hours          1xhour         =        $100x

Y                              3y hours            2y hours           1y hour        =       $120y

<u>                                                                                                 </u>

Total hours          1500 hours        1500 hours     550 hours

available

Let X represent product X

Let Y represent Product Y

2x + 3y = 1500

x + y = 550

y= 550-x

2x + 3(550-x) = 1500

2x + 1650- 3x = 1500

150 = x

y = 550-150

y = 400

Objective Function Z = 100x + 120y

Z = 100(150) + 120( 400)

Z = 15000+48000

Z = $63000

7 0
2 years ago
Noor brought 212121 sheets of stickers. She gave \dfrac{1}{3} 3 1 ​ start fraction, 1, divided by, 3, end fraction of a sheet to
My name is Ann [436]

Answer:

12 teachers will get 1/2 sheets each

Step-by-step explanation:

Noor bought 21 sheets of stickers

She gave 1/3 sheets to each 45 students

She wants to give teachers 1/2 of sheets

The question should be: how many teachers will she give

Total sheets=21

Students gets= 1/3 × 45

=45/3

=15 sheets

Remaining sheet= total sheets - students sheets

=21-15

=6 sheets

There are 6 sheets remaining for teachers

She wants to give 1/2 to each teacher

Then,

The number of teachers that will get =Remaining sheets ÷ each teacher's share

=6 ÷1/2

=6 × 2/1

=12 teachers

12 teachers will get 1/2 sheets each

5 0
1 year ago
Look at Andrea’s running journal.
german

First align the decimal points and the numbers,  then add the extra 0's if needed. Lastly, add and the total answer is 14.225.

7 0
1 year ago
Read 2 more answers
Given the first type of plot indicated in each pair: which of the second plots could not always be generated from it? a. dot plo
Elenna [48]

Answer:

C

Step-by-step explanation:

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For (a) dot plot and box plot, dot plot presents all the data while box plot presents only the five-num statistics, namely:

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For (d). Even though dot plot shoots up and down like the histogram, the content is different. In dot plot, it is the actual value represented in dots. But in histogram, it is the frequency distribution of the class intervals.

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Masja [62]
A = L * W
A = 357
W = 17

357 = 17L
357 / 17 = L
21 = L <== length is 21 inches

8 0
1 year ago
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