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3 years ago

Use the following functions: yf(x) = 3x - 7

Mathematics

1 answer:

igomit [66]3 years ago

5 0

Answer:

(f + g) (x) = 5x - 11

(f - g) (x) = x + 3

Step-by-step explanation:

f(x) = 3x - 7

g(x) = 2x - 4

to find ; (f + g) (x) and (f - g) (x)

now,

(f + g ) (x) = f (x) + g(x)

= (3x - 7) +( 2x - 4 )

= 3x - 7 + 2x - 4

= 5x - 11

again ,

(f - g ) (x) = f(x) - g(x)

= (3x - 7) - (2x - 4)

= 3x - 7 - 2x + 4

= x + 3

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Use a half-angle identity to find the exact value

Tatiana [17]

Given:

$\cos 15^{\circ}$

To find:

The exact value of cos 15°.

Solution:

$$\cos 15^{\circ}=\cos\frac{ 30^{\circ}}{2}$

Using half-angle identity:

$$\cos \left(\frac{x}{2}\right)=\sqrt{\frac{1+\cos (x)}{2}}$

$$\cos \frac{30^{\circ}}{2}=\sqrt{\frac{1+\cos \left(30^{\circ}\right)}{2}}$

Using the trigonometric identity: $\cos \left(30^{\circ}\right)=\frac{\sqrt{3}}{2}$

$$=\sqrt{\frac{1+\frac{\sqrt{3}}{2}}{2}}$

Let us first solve the fraction in the numerator.

$$=\sqrt{\frac{\frac{2+\sqrt{3}}{2}}{2}}$

Using fraction rule: $\frac{\frac{a}{b} }{c}=\frac{a}{b \cdot c}$

$$=\sqrt{\frac {2+\sqrt{3}}{4}}$

Apply radical rule: $\sqrt[n]{\frac{a}{b}}=\frac{\sqrt[n]{a}}{\sqrt[n]{b}}$

$$=\frac{\sqrt{2+\sqrt{3}}}{\sqrt{4}}$

Using $\sqrt{4} =2$ :

$$=\frac{\sqrt{2+\sqrt{3}}}{2}$

$$\cos 15^\circ=\frac{\sqrt{2+\sqrt{3}}}{2}$

5 0

3 years ago

Every day, Kylie's orange juice stand uses 1/2 of a bag of oranges. How many days will

nordsb [41]

Answer:

9 Days

Step-by-step explanation:

1/2x10=5

1/2x8=4

Logic tells you that 1/2x9=4 1/2

4 1/2 divided by 9= 1/2

So this answer is reasonable!!!

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3 0

3 years ago

Ben said the graph of the inequality

Ksivusya [100]

Answer:

Ben is incorrect

The solutions are x>-3 and x < 3

Step-by-step explanation:

we have

$-x^{2} +9 > 0$

Multiply by -1 both sides

$x^{2} -9 < 0$

Adds 9 both sides

$x^{2} < 9$

The solutions are

$x < 3$

and

$-x < 3$ -----> Multiply by -1 both sides ----> $x > -3$

therefore

The solution is the interval (-3,3)

Ben is incorrect

7 0

3 years ago

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Tasya [4]

Answer:

(-2,-2)

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Find volume with full working out pls asap

ZanzabumX [31]

Answer:

868 m³

Step-by-step explanation:

Volume = Difference of cones

V = ⅓(pi×r²h)

Volume of cone with base Circle O:

h = 8.2+8.2 = 16.4 m

V1 = ⅓(pi×7.6²×16.4)

V1 = 991.97

Volume of cone with base Circle A:

V2 = ⅓(pi×3.8²× 8.2)

V2 = 124 m³

Volume = V1 - V2

991.97 - 124 = 868 m³

6 0

3 years ago