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3 years ago

If k(x) = 5x - 6, which expression is equivalent to (k + k)(4)?

Mathematics

2 answers:

ycow [4]3 years ago

5 0

$\large \boxed{(k + k)(4) = k(4) + k(4)}$

First, we find the value of k(4). We can find the value of k(4) by substituting x = 4 in k(x).

$\large{k(x) = 5x - 6 \longrightarrow k(4) = 5(4) - 6} \\ \large{k(4) = 20 - 6 \longrightarrow 14}$

Therefore the value of k(4) is 14. Next we find k(4)+k(4) which is equivalent to 14+14. Hence, the value of (k+k)(4) is 28. There's also another method.

$\large \boxed{(k + k)(4) = 2k(4)}$

As we know k(4) is 14. Therefore 2k(4) is 2×14 = 28.

Answer

(k+k)(4) = 28

kogti [31]3 years ago

3 0

28! hope this helps, you just plug in 4 for x, and then multiply by two.

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3 years ago

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Find sin(a)&cos(B), tan(a)&cot(B), and sec(a)&csc(B).

Reil [10]

Answer:

Part A) $sin(\alpha)=\frac{4}{7},\ cos(\beta)=\frac{4}{7}$

Part B) $tan(\alpha)=\frac{4}{\sqrt{33}},\ tan(\beta)=\frac{4}{\sqrt{33}}$

Part C) $sec(\alpha)=\frac{7}{\sqrt{33}},\ csc(\beta)=\frac{7}{\sqrt{33}}$

Step-by-step explanation:

Part A) Find $sin(\alpha)\ and\ cos(\beta)$

we know that

If two angles are complementary, then the value of sine of one angle is equal to the cosine of the other angle

In this problem

$\alpha+\beta=90^o$ ---> by complementary angles

$sin(\alpha)=cos(\beta)$

Find the value of $sin(\alpha)$ in the right triangle of the figure

$sin(\alpha)=\frac{8}{14}$ ---> opposite side divided by the hypotenuse

simplify

$sin(\alpha)=\frac{4}{7}$

therefore

$sin(\alpha)=\frac{4}{7}$

$cos(\beta)=\frac{4}{7}$

Part B) Find $tan(\alpha)\ and\ cot(\beta)$

we know that

If two angles are complementary, then the value of tangent of one angle is equal to the cotangent of the other angle

In this problem

$\alpha+\beta=90^o$ ---> by complementary angles

$tan(\alpha)=cot(\beta)$

<em>Find the value of the length side adjacent to the angle alpha</em>

Applying the Pythagorean Theorem

Let

x ----> length side adjacent to angle alpha

$14^2=x^2+8^2\\x^2=14^2-8^2\\x^2=132$

$x=\sqrt{132}\ units$

simplify

$x=2\sqrt{33}\ units$

Find the value of $tan(\alpha)$ in the right triangle of the figure

$tan(\alpha)=\frac{8}{2\sqrt{33}}$ ---> opposite side divided by the adjacent side angle alpha

simplify

$tan(\alpha)=\frac{4}{\sqrt{33}}$

therefore

$tan(\alpha)=\frac{4}{\sqrt{33}}$

$tan(\beta)=\frac{4}{\sqrt{33}}$

Part C) Find $sec(\alpha)\ and\ csc(\beta)$

we know that

If two angles are complementary, then the value of secant of one angle is equal to the cosecant of the other angle

In this problem

$\alpha+\beta=90^o$ ---> by complementary angles

$sec(\alpha)=csc(\beta)$

Find the value of $sec(\alpha)$ in the right triangle of the figure

$sec(\alpha)=\frac{1}{cos(\alpha)}$

Find the value of $cos(\alpha)$

$cos(\alpha)=\frac{2\sqrt{33}}{14}$ ---> adjacent side divided by the hypotenuse

simplify

$cos(\alpha)=\frac{\sqrt{33}}{7}$

therefore

$sec(\alpha)=\frac{7}{\sqrt{33}}$

$csc(\beta)=\frac{7}{\sqrt{33}}$

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3 years ago

Please help solve the problem below.

ivann1987 [24]

Answer:

1. x = 2

2. x = 5

3. x = 8

4. x = 28

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6. x = 11

7. x = 0

8. x = 72

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10. x = 38

Step-by-step explanation:

hope that helps!

1. subtract 6 on both sides

2. add 3 on both sides

3. divide both sides by 2

4. multiply both sides by 2

5. add 8 on both sides

6. subtract 9 on both sides

7. add 5 on both sides

8. multiply both sides by 6

9. divide both sides by 4

10. add 18 on both sides

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a=6700(1.033)^16

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