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2 years ago

Which congruence theorems can be used to prove ΔABR ≅ ΔACR? Select three options

Mathematics

2 answers:

Mashcka [7]2 years ago

8 0

Answer:

SAS , ASA, SSS

Step-by-step explanation:

SAS , side A= side A . Angle B= Angle C, side R= side R

ASA, Angle A= Angle A . Side B= side C, Angle R= Angle R

SSS

side A= side A . Side B= side c, side R= side R

Leokris [45]2 years ago

7 0

Answer:

<h2>They are congruent by SAS postulate.</h2>

Step-by-step explanation:

Choice for this question are

In the image attached, you can observe the pairs of triangles we are talking about. Notice that they are right triangles, which means the congruence postulates we could use are Hypothenuse-Leg, Leg-Leg, Leg-Angle and Hypothenuse Angle, however, this choices are not useful.

We know by given that

$AC \cong AB$ and $RC \cong RB$

We also know that $\angle B \cong \angle C$

So, we have two corresponding sides congruent, and the pair of corresponding angle formed by those sides are also congruent.

Therefore, by Side-Angle-Side

$\triangle ABR \cong \triangle ACR$

So, the right answer is SAS.

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If f(x) = 3^(x + 4), find f(2).<br><br> A. 729<br> B. 243<br> C. 81<br> D. 18

Umnica [9.8K]

Answer:

f(2) = 729

Step-by-step explanation:

f(x) = 3^(x + 4)

Let x =2

f(2) = 3^(2 + 4)

f(2) = 3^(6)

f(2) = 729

4 0

3 years ago

A 20% solution of fertilizer is to be mixed with a 50% solution of fertilizer in order to get 180 gallons of a 40% solution. How

anyanavicka [17]

Answer: 60 gallons of the 20% solution and 120 gallons of the 50% solution should be mixed.

Step-by-step explanation:

Let x represent the number of gallons of 20% solution that should be mixed.

Let y represent the number of gallons of 50% solution that should be mixed.

A 20% solution of fertilizer is to be mixed with a 50% solution of fertilizer in order to get 180 gallons of a 40% solution. This means that

0.2x + 0.5y = 0.4×180

0.2x + 0.5y = 72- - - - - - - - - - - -1

Since the total number of gallons is 180, it means that

x + y = 180

Substituting x = 180 - y into equation 1, it becomes

0.2(180 - y) + 0.5y = 72

36 - 0.2y + 0.5y = 72

- 0.2y + 0.5y = 72 - 36

0.3y = 36

y = 36/0.3

y = 120

x = 180 - y = 180 - 120

x = 60

4 0

3 years ago

2. Find the volume of the cylinder pictured below. Use 3.14 for pi. Give your answer to the nearest tenth. Show your work to rec

Blababa [14]

Question 2

------------------------------------------------------------------------------------------
Formula
------------------------------------------------------------------------------------------
Volume of the cylinder = πr²h

------------------------------------------------------------------------------------------
Find Radius
------------------------------------------------------------------------------------------
Radius = Diameter ÷ 2
Radius = 10 ÷ 2
Radius = 5 ft

------------------------------------------------------------------------------------------
Find Volume
------------------------------------------------------------------------------------------
Volume = πr²h
Volume = 3.14 x 5² x 21
Volume = 1648.5 ft³

------------------------------------------------------------------------------------------
Answer: Volume = 1648.5 ft³
------------------------------------------------------------------------------------------

Question 3

------------------------------------------------------------------------------------------
Formula
-----------------------------------------------------------------------------------------
Volume of a sphere = 4/3πr³

------------------------------------------------------------------------------------------
Find Volume
------------------------------------------------------------------------------------------
Volume = 4/3 x 3.14 x 20³
Volume = 33493.3 ft³ (nearest tenth)

------------------------------------------------------------------------------------------
Answer: Volume = 33493.3 ft³
------------------------------------------------------------------------------------------

7 0

3 years ago

Natasha_Volkova [10]

Answer:

x = 2, y = -1.

Step-by-step explanation:

2x + y = 3

x - y = 3

Adding the 2 equations eliminates y:

3x = 6

x = 2.

Substitute for x in the first equation: