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Use the diagram and given information to answer the questions and prove the statement.

Given: Angle X ≅ Angle Z
XY ≅ ZY
Prove: AZ ≅ BX

Prove AZ ≅ BX using a flow chart proof.

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Work Shown:

area = base*height

area = 16*7

area = 112 square cm

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Extra info (optional section):

The area formula for a parallelogram is the same as the formula for a rectangle. Imagine tilting a rectangle so that it's slanted. The area has not changed.

Or another thing to imagine is that let's say we had a stack of 2 by 4s. If the stack is perfectly vertical, aka forming a rectangle, then we can nudge the beams so that we can form a slanted parallelogram instead. Both configurations involve the same amount of wood, and therefore would lead to the same frontal surface area.

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Explanation:

For now, focus on triangle ABD. This is a right triangle due to BD being an altitude.

Use the pythagorean theorem to find that...

(AD)^2 + (BD)^2 = (AB)^2

(1)^2 + (BD)^2 = (3)^2

1 + (BD)^2 = 9

(BD)^2 = 9-1

(BD)^2 = 8

Normally we would isolate BD itself, but I'll stop short and use that last line instead.

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The triangles ABD and BCD are similar triangles (we can prove this using the AA similarity theorem).

Since we have similar triangles, we can form the proportion shown below

AD/BD = BD/CD

This cross multiplies to

AD*CD = (BD)^2

We know that AD = 1 and (BD)^2 = 8, so,

AD*CD = (BD)^2

1*CD = 8

CD = 8

This then means,

x = CD+DA

x = 8+1

x = 9

AC is 9 units long.

Answer:

$120

$48

Step-by-step explanation:

total amount Jin spent = cost of bicycle + cost of helmet

$149 + $19 = $168

This equation can be derived from the question :

1.4 x t = 168

where t = total cost Stephan spent on the helmet and bicycle

t = 168/1.4 = $120

Profit = selling price - cost price

$168 - $120 = $48

Answer:

[tex]d. \: \: 66[/tex]

Step-by-step explanation:

[tex]r + 63 \div t \times 3[/tex]

[tex]45+63÷9 \times 3[/tex]

[tex]45+7 \times 3[/tex]

[tex]45 + 21[/tex]

[tex]66[/tex]

Answer:

The answer is 37

Step-by-step explanatio

Answer:

b

Step-by-step explanation:

8×19= 152  

1 : 4.5  

152×4.5=684  

Answer:

49 in the first box and 7 in the second one

25 in the 3rd box and 5 in the 4th

Answer:

[tex] \displaystyle 8[/tex]

Step-by-step explanation:

we would like to compute the following limit

[tex] \displaystyle \lim_{x \to 16} \left( \frac{x - 16}{ \sqrt{x} - 4} \right) [/tex]

if we substitute 16 directly we'd end up

[tex] \displaystyle = \frac{16 - 16}{ \sqrt{16} - 4} [/tex]

[tex] \displaystyle = \frac{0}{ 0} [/tex]

which isn't a good answer now notice that we have a square root on the denominator so we can rationalise the denominator to do so multiply the expression by √x+4/√x+4 which yields:

[tex] \displaystyle \lim_{x \to 16} \left( \frac{x - 16}{ \sqrt{x} - 4} \times \frac{ \sqrt{x} + 4 }{ \sqrt{x} + 4 } \right) [/tex]

simplify which yields:

[tex] \displaystyle \lim_{x \to 16} \left( \frac{(x - 16)( \sqrt{x} + 4)}{ x - 16} \right) [/tex]

we can reduce fraction so that yields:

[tex] \displaystyle \lim_{x \to 16} \left( \frac{ \cancel{(x - 16)}( \sqrt{x} + 4)}{ \cancel{x - 16} } \right) [/tex]

[tex] \displaystyle \lim _{x \to 16} \left( \sqrt{x } + 4\right) [/tex]

now it's safe enough to substitute 16 thus

substitute:

[tex] \displaystyle = \sqrt{16} + 4[/tex]

simplify square root:

[tex] \displaystyle = 4 + 4[/tex]

simplify addition:

[tex] \displaystyle = 8[/tex]

hence,

[tex] \displaystyle \lim_{x \to 16} \left( \frac{x - 16}{ \sqrt{x} - 4} \right) = 8[/tex]

Answer:

3(b+2)balls

Step-by-step explanation:

Given data

number of bags of golf balls= 3

number of balls in each bag=b

total number of balls in all three bags= 3b

His friend gave him 6 more= 3b+6

Hence the total balls is = 3b+6

= 3(b+2)balls

Answer:

[tex]482.5\:\mathrm{in^2}[/tex]

Step-by-step explanation:

The area of the figure consists of a rectangle with a triangle removed from the corner of it. Therefore, the area of the composite of the figure can be found by subtracting the area of the triangle from the area of the rectangle.

Area of the rectangle: [tex]25\cdot 20=500\:\mathrm{in^2}[/tex]

Area of the triangle: [tex]\frac{1}{2}\cdot 5\cdot 7=17.5\:\mathrm{in^2}[/tex]

Thus, the area of the figure is [tex]500-17.5=\boxed{482.5\:\mathrm{in^2}}[/tex]

Answer:the one to the left

Step-by-step explanation:

Answer:20.75

Step-by-step explanation:

Trust me gangsta

Answer:

Step-by-step explanation:

Triangles are similar if their corresponding angles are congruent and corresponding sides are proportional.

Answer:

gotta be  answer A

Step-by-step explanation:

you can search up f(x) = square root of x

Answer:

96 cm^2

Step-by-step explanation:

the diagonal bisect in the point of intersection, so their length is 12 cm and 16 cm

Area = (12 * 16)/2 = 96 cm^2

Answer:

24 cm^2

Step-by-step explanation:

rhombus -.-

Given:

Radius of a cylinder = 5 units.

Surface area of the cylinder = [tex]160\pi[/tex]

To find:

The height of the right cylinder.

Solution:

Surface area of a cylinder is:

[tex]A=2\pi rh+2\pi r^2[/tex]

Where, r is radius and h is the height of the cylinder.

Putting [tex]r=5, A=160\pi[/tex] in the above formula, we get

[tex]160\pi =2\pi (5)(h)+2\pi (5)^2[/tex]

[tex]160\pi =10\pi h+2\pi (25)[/tex]

[tex]160\pi =10\pi h+50\pi [/tex]

Subtract [tex]50\pi[/tex] from both sides.

[tex]160\pi -50\pi=10\pi h [/tex]

[tex]110\pi=10\pi h [/tex]

Divide both sides by [tex]10\pi[/tex].

[tex]\dfrac{110\pi}{10\pi}=h[/tex]

[tex]11=h[/tex]

Therefore, the height of the cylinder is 11 units.

Answer:

Step-by-step explanation:

Total hours:

Answer:

360 meters

Step-by-step explanation:

[tex]\sqrt{8100}[/tex] = 90

one edge = 90 meters

90 x 4 = 360

360 meters

Answer:

12/4 i really hope this helps i took the test and got a 100

Step-by-step explanation:

Answer:

0.5

Step-by-step explanation:

From the graph given ;

The vertical distance ; y - axis :

(y2 - y1) ; y2 = 2 ; y1 = 1

y2 - y1 = 2 - 1 = 1

The horizontal distance ; the x - axis :

(x2 - x1) ; x2 = 4 ; x1 = 2

x2 - x1 = 4 - 2 = 2

The slope ; the rate of change :

Change in y / change in x

The rate of change ;

(y2 - y1) / (x2 - x1) = 1 / 2

Answer:

6 friends

Step-by-step explanation:

Take 1/7 multiply by 5/6

9514 1404 393

Answer:

  7 friends

Step-by-step explanation:

3 pizzas will give 3/7 of a pizza to each of ...

  3/(3/7) = 3 · 7/3 = 7 . . . friends

7 friends ate the pizza.

_____

We assume that Sunaina and her 6 friends constitute 7 friends.

Answer:

The value of each T-shirt is $ 3 and the value of each sweatshirt is $ 10.

Step-by-step explanation:

Given that our school is selling T-shirts and sweatshirts as a fundraiser, and one student buys 2 Tt-shirts and 2 sweatshirts for $ 26, while another student buys 1 T-shirt and 3 sweatshirts for $ 33, to determine the value of the T-shirts and sweatshirts the following calculation must be made:

2X + 2Y = 26

X + 3Y = 33

Y - X = 7

2 x 3 + 2 x 10 = X

6 + 20 = X

26 = X

Therefore, the value of each T-shirt is $ 3 and the value of each sweatshirt is $ 10.

Answer:

2

Step-by-step explanation:

add 5/4 and 1/4 to get 6/4 or 3/2

(4^3/2 ÷ 4^1/2)^1/2 = 4^3/4 ÷ 4^1/4

4^3/4 ÷ 4^1/4 = 4^2/4 or 4^1/2

4^1/2 is the square root of 4, which is 2

Answer:

2

Step-by-step explanation:

In first step use the product rule of exponents .

so exponents going to add up.

Then in the second step simplified exponents.

After that Its division rule of exponents. and according to division to the exponents get subtracted.

In the end he would be left with four to the power half. which means square root of 4. which is 2.

Answer:

39

Step-by-step explanation:

Answer:

125 M so that you answer