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2 years ago

If triangle VWZ is congruent to triangle XWY, find the length of YX.

Mathematics

1 answer:

valkas [14]2 years ago

8 0

Answer:

Measure of side YX is 22 units.

Step-by-step explanation:

Since ΔVWZ ~ ΔXWY, their corresponding sides will be in the same ratio.

$\frac{VW}{XW}=\frac{VZ}{XY}=\frac{WZ}{WY}$

By substituting the values given in the picture in the ratio,

$\frac{45}{30}=\frac{(3x-9)}{(x+8)}=\frac{36}{24}$

$\frac{(3x-9)}{(x+8)}=\frac{3}{2}$

By cross multiplication,

2(3x - 9) = 3(x + 8)

6x - 18 = 3x + 24

(6x -18) + 18 = 3x + 24 + 18

6x - 3x = (3x + 42) - 3x

6x - 3x = 42

3x = 42

x = $\frac{42}{3}$

x = 14

m(YX) = x + 8

= 14 + 8

= 22

Therefore, measure of side YX is 22 units.

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Ming used the calculations shown to find out how much he would spend on 6 pounds of ground beef if 10 pounds of ground beef cost

Angelina_Jolie [31]

Answer:

He determined pounds per dollar by dividing 10 by 25 but wrote the unit rate as a dollar value.

Step-by-step explanation:

Given

$\frac{10\ pounds}{\$25} = \frac{10\ pounds}{25} / \frac{\$25}{25} = \frac{0.4}{1}$

$Unit\ Price = 40\ cents$

$40\ cents * 6 = \$2.40$

Required

Determine Ming's error

Ming's error is from here

$\frac{10\ pounds}{\$25} = \frac{10\ pounds}{25} / \frac{\$25}{25} = \frac{0.4}{1}$

He calculated the unit rate as pound per dollar.

So, after calculating the unit rate, the unit should be:

$Unit\ Rate = 0.4\ pound/\$$

But instead, he solved as:

$Unit\ Rate = \$0.4/ pound$

<em>Hence, (a) is correct</em>

5 0

2 years ago

Read 2 more answers

Find the coefficient of x2 in (3x2 – 5) (4 + 4x2), expand using algebraic expressions and answer

Scilla [17]

Answer:

- 8

Step-by-step explanation:

Given

(3x² - 5)(4 + 4x²)

Each term in the second factor is multiplied by each term in the first factor, that is

3x²(4 + 4x²) - 5 (4 + 4x²) ← distribute both parenthesis

= 12x² + 12 $x^{4}$ - 20 - 20x² ← collect like terms

= 12 $x^{4}$ - 8x² - 20

The coefficient of the x² term is - 8

7 0

2 years ago

The substitution property of equality allows you to say that if 7j + 14k = 28 And j = 2 then

sergey [27]

$7 \times (2) + 14k = 2 \\ \\ k = -\frac{7}{6}$

6 0

2 years ago

Read 2 more answers

Sanjay bought a basket of oranges, a basket of apples,a basket of mangoes and a basket of peaches.He paid a total of Rs 790 for

Margarita [4]

Let a the price of a basket of oranges be O, that of a basket of apples A, a basket of mangoes M and a basket of peaches P, then
O + A + M + P = 790 . . . (1)
M - 4 = P + 7 = 3O = A/2 . . . (2)
From (2), we have:
M = P + 11
O = (P + 7)/3
A = 2P + 14

Substituting for M, O and A into (1), gives:
(P + 7)/3 + 2P + 14 + P + 11 + P = 790
P + 7 + 6P + 42 + 3P + 33 + 3P = 2370
13P + 82 = 2370
13P = 2288
P = 176

Therefore, the price of a basket of peaches is Rs176.

7 0

2 years ago

A rectangular portrait measures 50cm by 70cm. It is surrounded by a rectangular frame of uniform width. If the area of the frame

snow_tiger [21]

Let us assume uniform width = x cm wide.

Length of rectangular portrait = 50cm and width of rectangular portrait = 70cm.

Therefore, length of rectangle made by frame = 50 + x+x = (2x+50) cm.

And width of rectangle made by frame = 70+x+x = (2x+70) cm.

We know, the area of rectangular portrait = 50 × 70 = 3500 cm^2.

Total area of the rectangle made by frame would be = (2x+50) * (2x+70)

We know,

Actual area of frame = Area of rectangle made by frame - area of rectangular portrait.

We also given "the area of the frame is the same as the area of the portrait."

We can setup an equation now,

3500 = (2x+50) * (2x+70) - 3500.

Subtracting 3500 from both sides, we get

3500-3500 = (2x+50) * (2x+70) - 3500-3500.

0 = (2x+50) * (2x+70) -7000.

FOIL (2x+50) * (2x+70), we get

0 = 2x*2x +2x*70 + 50*2x +50*70 - 7000.

0 = 4x^2 +140x +100x +3500 -7000.

4x^2 +240x -3500 = 0.

Dividing whole equation by 4, we get

x^2 +60x - 875 =0

Applying quadratic formula $=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ , we get

$=\frac{-60\pm \sqrt{60^2-4\cdot \:1\left(-875\right)}}{2\cdot \:1}$

$x=\frac{-60+\sqrt{60^2-4\cdot \:1\left(-875\right)}}{2\cdot \:1}=5\left(\sqrt{71}-6\right)$

$x=\frac{-60-\sqrt{60^2-4\cdot \:1\left(-875\right)}}{2\cdot \:1}:\quad -5\left(6+\sqrt{71}\right)$

We cant take negative value.

So, $x=5\left(\sqrt{71}-6\right)=12.13$

We could take approximately 12 cm.

7 0

2 years ago