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3 years ago

(HELP ASAP!)Which postulate or theorem proves △HJZ∼△WJR ?

Mathematics

1 answer:

Tomtit [17]3 years ago

8 0

Answer:

SAS Similarity Theorem

Step-by-step explanation:

we know that

<u>SAS Similarity Theorem</u>: States that if two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar

In this problem

∠HJZ=∠RJW ----> by vertical angles

and

WJ/HJ=JR/JZ

substitute the values

8/4=6/3

2=2 ----> is true

Two sides of triangle HJZ are proportional with the two corresponding sides of triangle WJR and the included angle is congruent

therefore

Triangles are similar by SAS Similarity Theorem

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Does the system shown always, sometimes, or never have a solution when a >b?

Rama09 [41]

Answer:

sometimes

Step-by-step explanation:when a >b?

ax+y=8

bx + y = 5

always

sometimes

never

5 0

3 years ago

I will give brainliest but you need to explain how you received the answer so i can learn how to do it on my own/// thanks!

Readme [11.4K]

To solve this problem we must know that when any two lines intersect , a pair of opposite angles from the figure Will be equal
so that means that
$4x + 20 = 3x + 55$
we can subtract twenty from each side
$4x + (20 - 20) = 3x + (55 - 20)$
$4x = 3x + 35$
now we can subtract like terms
$4x - 3x = (3x - 3x) + 35$
so we can get the final answer as
$1x = 35$

6 0

3 years ago

iren2701 [21]

Answer:

The distance between points A and B is 13

Step-by-step explanation:

We need to find distance between points A and B

Looking at the graph,

Point A : (2,6) and Point B: (-3,-6)

We need to find the distance between these points.

The formula used is: $Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\$

We have Points A : (2,6) and B: (-3,-6)

So, $x_1=2, y_1=6, x_2=-3, y_2=-6$

Putting values in formula and finding distance

$Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\\\Distance=\sqrt{(-3-2)^2+(-6-6)^2} \\Distance=\sqrt{(-5)^2+(-12)^2} \\Distance=\sqrt{25+144} \\Distance =\sqrt{169}\\Distance = 13$

So, the distance between points A and B is 13

6 0

3 years ago

Choose the best answer:

Oksi-84 [34.3K]

Answer:

The length of the hypotenuse is 2 square root of 13 ⇒ c

Step-by-step explanation:

The rule of the area of the right triangle is A = $\frac{1}{2}$ × leg1 × leg2, where

leg1 and leg2 are the sides of the right angle

∵ The area of a right triangle is 12 in²

∵ The ratio of the length of its legs is 2: 3

→ Let leg1 = 2x and leg2 = 3x

∵ leg1 = 2x and leg2 = 3x

→ Substitute them in the rule of the area above

∴ 12 = $\frac{1}{2}$ × 2x × 3x

∵ 2x × 3x = 6x²

∴ 12 = $\frac{1}{2}$ × 6x²

∴ 12 = 3x²

→ Divide both sides by 3 to find x²

∴ 4 = x²

→ Take √ for both sides

∴ x = 2

→ Substitute x in the expressions of leg1 and leg2 to find them

∴ leg1 = 2(2) = 4 inches

∴ leg2 = 3(2) = 6 inches

∵ hypotenuse = $\sqrt{(leg1)^{2}+(leg2)^{2}}$

∴ hypotenuse = $\sqrt{(4)^{2}+(6)^{2}}=\sqrt{16+36}=\sqrt{52}$

∵ The simplest form of $\sqrt{52}$ = 2 $\sqrt{13}$

∴ The length of the hypotenuse = 2 $\sqrt{13}$ inches

3 0

2 years ago

Ms. Moran has started an investment club at BSS. $8000 is invested, some at 10%

labwork [276]

The answer can be readily calculated using a single variable, x:

Let x = the amount being invested at an annual rate of 10%
Let (8000 - x) = the amount being invested at an annual rate of 12%

The problem is then stated as:

(x * 0.10) + ((8000 - x) * 0.12) = 900
0.10(x) + ((8000 * 0.12) - 0.12(x)) = 900
0.10(x) + 960 - 0.12(x) = 900
0.10(x) - 0.12(x) = 900 - 960
-0.02(x) = -60
-0.02(x) * -100/2 = -60 * -100/2
x = 6000 / 2
x = 3000

Thus, $3,000 is invested at 10% = $300 annually; and $8,000 - $3,000 = $5,000 invested at 12% = $600 annually, which sum to $900 annual investment.

6 0

2 years ago