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notsponge [240]
1 year ago
8

Suppose that the functions p and q are defined as follows.

Mathematics
1 answer:
inessss [21]1 year ago
7 0

The most appropriate choice for function can be given by

qop(3) =  \sqrt{15}+1

poq(3) =  2\sqrt{3} + 10

What is function?

A function from A to B is a rule that maps to each element of A a unique element of B.

A is called the domain of the function and B is called the co domain of the function.

We can do addition, subtraction, multiplication, division and composition on functions.

Let f and g be two functions

fog(x) = f(g(x)) and gof(x) = g(f(x))

This is known as composition of function.

Here,

p(x) = x^2 + 6\\q(x) = \sqrt{x} +1

qop(x) = q(p(x))

          =q(x^2+6)

          = \sqrt{x^2+6}+1

qop(3) = \sqrt{3^2+6}+1

          = \sqrt{15}+1

poq(x) = p(q(x))

          = p(\sqrt{x}+1)

          = (\sqrt{x}+1)^2+6

          = x + 1 + 2\sqrt{x} + 6

          = x + 2\sqrt{x} +7

poq(3) = 3 + 2\sqrt{3}  +7

               2\sqrt{3} + 10

               2\sqrt{3} + 10

To learn more about functions, refer to the link:

brainly.com/question/10439235

#SPJ9

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Identify sinJ as a fraction and as a decimal rounded to the nearest hundredth.
KiRa [710]

In the given right triangle, the trigonometric ratio, <u>sin J</u> has a fractional value of <u>5/13</u> and a decimal value of <u>0.39</u>.

In trigonometry, for a right triangle, the <u>sine</u> (sin) of any angle θ is given as the ratio of its opposite side to the hypotenuse of the triangle, that is, sin θ = (opposite side)/(hypotenuse).

In the question, we are asked to find the trigonometric ratio, sin J, for the given right triangle JKL.

The side opposite to angle J is KL, which has a value of 3 units.

The hypotenuse of the given right triangle is JK, which has a value of 7.8 units.

Thus, sin J can be calculated as:

sin J = KL/JK = 3/7.8 = 5/13 = 0.39.

Thus, in the given right triangle, the trigonometric ratio, <u>sin J</u> has a fractional value of <u>5/13</u> and a decimal value of <u>0.39</u>.

Learn more about trigonometric ratios at

brainly.com/question/20367642

#SPJ1

8 0
1 year ago
Please help me with this:(
dolphi86 [110]

Answer:

Y = 32.7°

Step-by-step explanation:

We will apply the Cosine law in the given triangle XYZ,

x = 90 ft

y = 55 ft

z = 50 ft

We have to find the measure of angle Y.

y² = x² + z² - 2xzCosY

(55)² = (90)² + (50)² - 2(90)(50)cosY

3025 = 8100 + 2500 - 9000.cosY

9000.cosY = 10600 - 3025

cosY = \frac{7575}{9000}

        = 0.84167

Y = \text{cos}^{-1}(0.84167)

Y = 32.68 ≈ 32.7°

Therefore, measure of angle Y = 32.7°

5 0
3 years ago
What is the range of the graph below?<br>​
torisob [31]

Answer:

B) -4 < y

Step-by-step explanation:

The lowest point on the y axis of the graph is -4 and everything else is higher

6 0
3 years ago
Can someone help me with this, please? I'm not sure how to solve this.
bazaltina [42]

Answer:

11.) 10w^2 + 43w + 21.

12.) -15y^2 - 2y + 8

Check the explanation for details

Step-by-step explanation:

11.) You are meant to multiply each row by both columns. For instance, multiply 5w by 2w and 7 you will get 10 w^2 and 35 w

Also, multiply 3 by both 2w and 7 you will get 6w and 21. Therefore,

Expansion of ( 5w + 3 )( 2w + 7 ) will produce 10w^2 + 37w + 6w + 21

= 10w^2 + 43w + 21.

12.) Repeat the same process by multiplying row by column.

Multiply -3y by 5y and 4 you will get -15y^2 and -12y.

Also, multiply 2 by same 5y and 4. You will get 10y and 8

Therefore, the expansion of

( -3y + 2 )( 5y + 4 ) will be

-15y^2 - 12y + 10y + 8

-15y^2 - 2y + 8

4 0
3 years ago
3x = 8 <br> 3x + y = 15<br><br> ???
fiasKO [112]
3x=8

Solve for x by dividing by 3 on both sides

x=8/3

Now plug 8/3 in for x in second equation

3(8/3)+y=15

This gives you

8+y=15

Subtract by 8 on both sides to find y

y=8

Now write it in ordered pair form (x,y)

So your answer is (8/3,8)
6 0
3 years ago
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