Vocabulary Is every relation also a function? Explain.

A. No. A relation is a special type of function where each input maps to exactly one output. In a function, an input can have one or more outputs.

B. Yes. A function is a special type of relation where each input maps to exactly one output. In a relation, an input can have one or more outputs.

C. Yes. A relation is a special type of function where each input maps to exactly one output. In a function, an input can have one or more outputs.

d. No. A function is a special type of relation where each input maps to exactly one output. In a relation, an input can have one or more outputs.

i can help, but you need to write the whole question..

Answer:

[tex]y = \frac{1}{2}x + 3[/tex]

Answer:

3

Step-by-step explanation:

1+1=2

Answer:

Range: {-12, -8, 0, 8}

Step-by-step explanation:

To find the range of [tex] f(x) = -2x + 6 [/tex], plug in the value of each domain into the equation of the function to get the corresponding range value.

Given that the domain is {-1,3,7,9}, therefore:

✅[tex] f(-1) = -2(-1) + 6 = 2 + 6 [/tex]

[tex] f(-1) = 8 [/tex]

✅[tex] f(3) = -2(3) + 6 = -6 + 6 [/tex]

[tex] f(3) = 0 [/tex]

✅[tex] f(7) = -2(7) + 6 = -14 + 6 [/tex]

[tex] f(7) = -8 [/tex]

✅[tex] f(9) = -2(9) + 6 = -18 + 6 [/tex]

[tex] f(9) = -12 [/tex]

Range would be: {-12, -8, 0, 8}

x  =  3  − log  565/  log  2  =  −  6.142107057

Step-by-step explanation:

2^3-x =565

Log 2^3-x =  log  565

(3-x) times log 2 = log 565

3 −  x  =  log  565 / log  2

3  −  log  565 / log  2  =  x

x  =  3  − log  565/  log  2  =  −  6.142107057

Answer:

x = -557

Step-by-step explanation:

2^3 is 2x2x2 which equals 8. 8 - x = 565. Move the constant to the right-hand side and change its sign. -x = 565 - 8. This is 557. Now change the negative sign on the x to a positive and the positive sign on the 557 to a negative. x= -557.

Complete Question

The diagram of the barn is shown on the first uploaded image

Answer:

The cost is [tex]C = \$ 530[/tex]

Step-by-step explanation:

From the question we are told that

   The  cost of one gallon of paint is  [tex]c = \$35[/tex]

    The area the one gallon of paint covers is  [tex]A = 550 \ square\ feet[/tex]

Generally from the diagram  the region of the barn which can be painted is mathematically represented as

       [tex]A =80 * 35 + 38 * 35 + 2( \frac{1}{2} * 38 * 2 )[/tex]

=>    [tex]A = 8336 \ ft^2[/tex]

From the question

     1 gallon  covers  500 square feet

     x gallon will cover  8336  square feet

So

       [tex]x = \frac{8336}{550}[/tex]

=>    [tex]x =15 \ gallons[/tex]

Generally the cost of 15 gallons of paint is mathematically represented as

       [tex]C = c * x[/tex]

=>     [tex]C = 15 * 35[/tex]

=>     [tex]C = \$ 530[/tex]

Answer:

A

Step-by-step explanation:

12x 5/2= 60/2= 30

3x5/2=15/2=7.5

7.5 by 30

Answer:

The actual answer is 7 units.

Step-by-step explanation:

Distance between two bodies=

root under[(x2-x1)^2+(y2-y1)^2]

=root under[(-3-4)^2+(5-5)^2]

= root under (49)

=7 units.

Answer:

2. 30 × 700 = 21,000 Over

3. 200 × 700 = 140,000 under

4. 40 × 100 = 4,000 under

5. 400 × 700 = 280,000 over

Answer:

10

Step-by-step explanation:

20x – 2y = 6

y=10x-3

Parallel line have same slope

Answer: 32

Step-by-step explanation: 45wheeej5t

Answer: 21 1/2

Step-by-step explanation:

12 9/10 + 8 3/5 = 21 1/2

hope this helps!

Answer:

y = 5, 3; x = 171, 155

Step-by-step explanation:

8y - 15 = y^2

y^2-8y+15=0

y^2-3y-5y+15=0

y(y-3)-5(y-3)=0

(y-5)(y-3)=0

y can be 5 or 3.

x = 180 - (8y - 15)

x = 180 - (8(3)-15)

x = 180 - 9

x = 171

OR

x = 180 - (8(5) - 15)

x = 180 - 25

x = 155

Answer:

x

x

are

Step-by-step explanation:

For x ≥ 0, the value of f(g(x)) is x,For x ≥ 0, the value of g(f(x)) will be x and functions f and g are inverse functions.Option a from all the choices is corect.

A connection between independent variables and the dependent variable.is defined by the function.

Functions help to represent graphs and equations. A function is represented by two variables one is dependent and another one is an independent function.

The relation between them is shown as y if dependent and x is the independent variable;

Given function;

f(x) = 16x²

g(x)=(1/4)√x

For x ≥ 0, the value of f(g(x)) is found as;

f(x) = 16x²

[tex]\rm f(g(x)) = 16 (\frac{1}{4} \sqrt x) ^2\\\\ f(g(x)) =\frac{16}{16} x\\\\ f(g(x)) = x[/tex]

For x ≥ 0, the value of g(f(x)) is

g(x)=(1/4)√x

[tex]\rm g(x)=\frac{1}{4}\sqrt x \\\\ g(x ) = \frac{1}{4} \times \sqrt{16 \ x^2}\\\\ g(x) = \frac{4}{4} x \\\\ g(x) = x[/tex]

For x ≥ 0, functions f and g are  inverse functions

Let,

y=F(X)

If,

y= 16x²

x=16y²

y² = x/16

y=(1/4)√x

Hence,For x ≥ 0, the value of f(g(x)),For x ≥ 0, the value of g(f(x)) will be x and x respectively.and For x ≥ 0, functions f and g are inverse functions.

Hence, option a from all the choices is corect.

To learn more about the function refer to the link https://brainly.com/question/12431044.

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Answer:

The only two values that have the same absolute value of 34, is +34 and -34.

Step-by-step explanation:

The expected number of coupons that will be redeemed is 0.96.

Given data:

To find the expected number of coupons that will be redeemed, multiply the probability of redemption for a single coupon by the number of coupons distributed.

Given that 16% of $10-off coupons delivered by mail are redeemed, the probability of redemption for a single coupon is 0.16.

Since six customers are randomly selected and mailed coupons, the number of coupons distributed is 6.

Therefore, the expected number of coupons that will be redeemed is:

Expected number of redeemed coupons = Probability of redemption * Number of coupons distributed

= 0.16 * 6

= 0.96

Hence, the expected number of coupons is 0.96.

To learn more about probability, refer:

https://brainly.com/question/17089724

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Answer:

1/3÷1/2

1/3×2 (reciprocal on dividing)

=2/3

Answer: answer is 2/3

Step-by-step explanation:

Answer:

im pretty sure its a

Step-by-step explanation:

Answer:

..........

Step-by-step explanation:

Answer:

x=14

Step-by-step explanation:

Answer:

x=14

Step-by-step explanation:

Step-1 :

Multiply the coefficient of the first term by the constant   1 • 28 = 28  

Step-2 :Find two factors of  28  whose sum equals the coefficient of the middle term, which is   -16 .

-28 +   -1  =  -29  

-14 +  -2 =  -16  

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -14  and  -2

x2 - 14x - 2x - 28

Step-4 : Add up the first 2 terms, pulling out like factors :

          x • (x-14)

 Add up the last 2 terms, pulling out common factors :

          2 • (x-14)

Step-5 : Add up the four terms of step 4 :

     (x-2)  •  (x-14)

Answer:

x=14

Answer:

30.5

Step-by-step explanation:

hope that helps

Answer: 5 pizzas and 17 sodas were bought

Step-by-step explanation:

I don't have answers for a or b but I have them for c.

          Number of pizzas

      9.50n+1.25(3n+2)=68.75

         9.50+3.75n+2.50=68.75

           combine like terms

         13.25+2.5= 68.75

      subtract from both sides

     13.25=68.75-2.5

         13.35=66.25

            Divide

             n=5

         Number of sodas

        3n+2=3(5)+2=15+2=17

Answer: 25

               2

Step-by-step explanation:

900 - 400 = 500 = 25

  50 - 10 =     40=    2        

Answer:

Gianna is the faster texter. She types 42 wpm, while Victor types 41 wpm.

Step-by-step explanation:

Calculate the unit rates. Time is usually on the bottom. For example, to calculate how many words Gianna types in a minute, use the expression 168/4.

Answer:

Gianna is the faster texter

Step-by-step explanation:

168/4 = 42 wpm for Gianna

246/6 = 41 wpm for Victor

Answer:

1/26

Step-by-step explanation:

1 out of 13 would be equal to the amount of cards that would be a jack.

But you also have to take into regards the coin flip 50%chance so you would just could what the number is divided by to get the right answer. Since out come could be tails or head instead of just being one for sure for example.

Answer:

5.38516480713

Step-by-step explanation:

a^2+b^2=c^2

5^2+2^2=c^2

25+4=c^2

c^2=square root of 29

c=5.38516480713

Answer:

The matrixes are in the explanation box.

1. A mapping of (x,y,z) to (x,y,0)

2. Is a mapping of (x,y,z) to (-x,-y,z)

Step-by-step explanation:

We have the orthogonal projection onto the cy-plane to be a mapping of (x,y,z) to (x,y,0). Then we will have a transformation matrix that has the form below.

[1 0 0]

[0 1 0]

[0 0 1]

For the reflection in the z-axis,it is a reflection of (x,y,z) to (-x,-y,z). Our matrix will then have the form below

[-1 0 0]

[0 -1 0]

[0 0  1]

The matrix that projects into the XY plane is:

[tex]\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&0\end{array}\right][/tex]

The matrix that reflects in the z-axis is:

[tex]\left[\begin{array}{ccc}-1&0&0\\0&-1&0\\0&0&1\end{array}\right][/tex]

First, we want to find the transformation that goes from (x, y, z) to (x, y, 0).

Remember that:

[tex](x, y, z)*\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right] = (x, y, z)[/tex]

That matrix is the identity matrix.

Then, if we want to remove the z component, then we just need to make the last row-column equal to zero, we will get:

[tex](x, y, z)*\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&0\end{array}\right] = (x, y, 0)[/tex]

Now we want to make a reflection over the z-axis, this is a rotation of 180° around the z-axis, so it changes the sign of the x and y components:

(x, y, z) to (-x, -y, z)

From this, we conclude that the matrix will be:

[tex](x, y, z)*\left[\begin{array}{ccc}-1&0&0\\0&-1&0\\0&0&1\end{array}\right] = (-x, -y, z)[/tex]

If you want to learn more about matrices, you can read:

https://brainly.com/question/11989522

Answer:

y = -3x + 1

Step-by-step explanation:

Perpendicular lines have opposite reciprocal slopes, so the slope will be -3.

Plug in the slope and given point into y = mx + b

y = mx + b

-5 = -3(2) + b

-5 = -6 + b

1 = b

Then, plug in the slope and y intercept into y = mx + b again:

y = -3x + 1 will be the equation of the line

Answer:

0.72

Step-by-step explanation:

it doesn't exist

Answer: 5 1/4

Step-by-step explanation:

Answer:

Step-by-step explanation:

Its D