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avanturin [10]
3 years ago
6

State whether the triangles are similar. If so, write a similarity statement and the postulate or theorem you used.

Mathematics
1 answer:
never [62]3 years ago
8 0

Answer:

Triangles ABC and MNO are similar by SSS

Step-by-step explanation:

we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional

In this problem

If this problem the corresponding sides are

AB and MN

BC and NO

AC and MO

Verify if the corresponding sides are proportional

\frac{AB}{MN}=\frac{BC}{NO}=\frac{AC}{MO}

substitute the given values

\frac{5}{7.5}=\frac{5}{7.5}=\frac{8}{12}

0.67=0.67=0.67 ----- is true

so

When two triangles have corresponding sides with identical ratios , the triangles are similar by SSS Similarity

therefore

Triangles ABC and MNO are similar by SSS

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Determine the axis of symmetry and the vertex of the given function.<br> y = 2x2 - 12x + 21
mestny [16]

Answer:

the vertex is ( 3 , 3)

Symetric axis‘s equation: x = 3

Step-by-step explanation:

Let‘s name the function ” f ”

f(x) = y = 2x² - 12x + 21

the vertex has coordinates of ( -b/2a , f(-b/2a) )

-b/2a = 12/2(2) = 12/4 = 3

f(-b/2a) = f(3) = 2(3)² - 12(3) + 21 = 3

then the vertex is ( 3 , 3)

the symetric axis has the equation :

x = -b/2a

then

4 0
2 years ago
Solve the following system of equations: 5x + y = 9 3x + 2y = 4 (−2, 5) (1, 4) (2, −1) (4, −4)
Mila [183]
Multiply first equation by 2:
10x + 2y = 18
Subtract the second equation from this so that the 2y terms cancel:
10x - 3x = 18 - 4
7x = 14
x = 2
Plug into first equation to find y:
5(2) + y = 9
10 + y = 9
y = -1
The answer is (2,-1)
7 0
3 years ago
Read 2 more answers
Given the following shape with parellel lines, explain why these two triangles are similar.
ohaa [14]

Answer:

All 3 angles are the same, it is simply a dilation. the size is the only difference.

Step-by-step explanation:


3 0
3 years ago
The speed limit sign on the freeway said 110 kilometers per hour, but the speedometer on Cesar's car is calibrated in miles per
Lisa [10]

Answer:

68.2 miles per hour

Step-by-step explanation:

Speed limit = 110 kilometers per hour

1 kilometer = 0.62 miles

110 kilometers = x miles

Cross product

1*x = 0.62*110

x = 68.2 miles

Cesar should drive at 68.2 miles per hour to avoid a speeding ticket

110 kilometers per hour = 68.2 miles per hour

6 0
2 years ago
3. Given: Circle Q<br>&lt;A = 35<br>Find: m AB​
Agata [3.3K]

Answer:  110°

<u>Step-by-step explanation:</u>

∠A ≅ ∠B  

since ∠A = 35° (given), then ∠B = 35°

Use the Triangle Sum Theorem to find ∠C:

∠A + ∠B + ∠Q = 180°

35° + 35° + ∠Q = 180°

     70°    + ∠Q = 180°

                 ∠Q = 110°

The central angle (∠AQB) ≅ arc AB

since ∠AQB = 110° (solved above), then arc AB = 110°

5 0
3 years ago
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