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tia_tia [17]
3 years ago
10

Given ƒ(x) = 3x + 9, find x when ƒ(x) = 21.

Mathematics
2 answers:
Dima020 [189]3 years ago
7 0
3x + 9 = 21
3x = 12
x = 4
maksim [4K]3 years ago
6 0

Answer:

4

Step-by-step explanation:

ƒ(x) = 3x + 9; Substitute 21 for ƒ(x).

21 = 3x + 9

21 − 9 = 3x

12 = 3x → x = 4

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3 years ago
If P is the orthocenter of △ABC, AB = 13, BF = 9,and FC = 5.6, find each measure & the perimeter of triangle ABC.
harina [27]

Answer:

Perimeter = 38.6

Step-by-step explanation:

Given

A\ B = 13

B\ F = 9

F\ C = 5.6

Required

Calculate the perimeter of A B C

To calculate the perimeter of A B C, we sum up the sides of the triangle

i.e.

Perimeter = A B + B\ C + A\ C

AB is given in the question already.

So, we need to calculate B F and F C

To solve for BF, we consider triangle B F C

Using Pythagoras Theorem, we have:

B\ C^2 = B\ F^2 + F\ C^2

Substitute values for BF and FC;

B\ C^2 = 9^2 + 5.6^2

B\ C^2 = 81 + 31.36

B\ C^2 = 112.36

B\ C^2= \sqrt{112.36

B\ C = 10.6

Next, we calculate A C.

To calculate A C, we need to calculate A F, considering triangle B F A

Using Pythagoras Theorem, we have:

A\ B^2 = B\ F^2 + A\ F^2

Substitute values for B F and A B;

13^2 = 9^2 + A\ F^2

169= 81 + A\ F^2

A\ F^2 = 169 - 81

A\ F^2 = 88

A\ F = \sqrt{88

A\ F = 9.4

Since F lies on line A C:

A\ C = A\ F + F\ C

A\ C = 9.4 + 5.6

A\ C = 15.0

Recall that:

Perimeter = A\ B + B\ C + A\ C

Perimeter = 13 + 10.6 + 15.0

Perimeter = 38.6

<em>Hence, the perimeter is 38.6</em>

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3 years ago
A rectangular prism has a volume of 160 cm. The height of the prism is 5 cm. The length is twice the width. What are the dimensi
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61 is the prime number.

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