If f(x) equals 4^x- 8 and g(x) equals 5times + 6, find (f-g)(x)

Answer:

For a volume of 60 ounces, the appropriate price is $16

Step-by-step explanation:

Firstly, we need to determine the relationship between volume of popcorn and the price of bag.

Let us try and see if there is a linear relationship

A linear model is of the form ;

y = mx + b

where m is the slope and b is the y intercept

While the price represents the y axis values, the volume represents the x axis values

For the slope;

m = (y2-y1)/(x2-x1)

m = (13.6-11)/(48-35) = 2.6/13 = 0.2

So we have the slope value as 0.2

the equation is;

y = 0.2x + b

to get b, substitute any value of (x,y)

6 = 0.2(10) + b

6 = 2 + b

b = 6-2 = 4

If we had substituted (20,8)

8 = 0.2(20) + b

8 = 4 + b

b = 4

if (48,13.6)

13.6 = 48(0.2) + b

13.6 = 9.6 + b

b = 13.6-9.6

b = 4

Hence we have established linear relationship between the volume in ounces and the price in $

So we have this as

Price = 0.2(volume) + 4

So for volume of 60 ounces;

Price = 0.2(60) + 4

price = 12 + 4

price = $16

The reason why this is appropriate is because it follows the rule of the established linear relationship

Answer:

$16

Step-by-step explanation:

Answer:

8.6

Step-by-step explanation:

Use the pythagorean therom for this

(5.9)^2 + (6.3)^2 = c

c= 74.5

square root of 74.5 is 8.631 or 8.6

hope this helps

Answer:

The mean is 19.33

Step-by-step explanation:

How to Find the Mean. The mean is the average of the numbers. It is easy to calculate: add up all the numbers, then divide by how many numbers there are. In other words it is the sum divided by the count.

Answer:

x=32°

Step-by-step explanation:

ABC+BCA+CDE=180

Substitute

61+57+2x=180

118+2x=180

2x=62

x=32

Answer:

30.5 i think

Step-by-step explanation:

plz let me know if wrong!

Answer:

Step-by-step explanation:

the angles are equivalent, so set them equal to each other

4x + 2 = 124

    - 2      - 2

4x = 122

/ 4     / 4

x = 30.5

Answer:

6

Step-by-step explanation:

Answer:

Yes, because each input (number of bagels) has a single output (cost).

Step-by-step explanation:

Answer:

C D anf F

Step-by-step explanation:

c : by expanding and canceling 4^x .

d : its the expanded form.

f : its just another way of expressing the expression

Answer:

41

Step-by-step explanation:

In order to find the measure of angle C we must find the value of x

Remember the measures of the angles in a triangle add up to equal 180

that being said we use this equation to solve for x

180 = (sum of angles) 63 + 2x + 8 + x + 7

now we solve

step 1 combine like terms

63 + 7 + 8 = 78

2x + x = 3x

now we have 180 = 78 + 3x

step 2 subtract 78 from each side

180 - 78 = 102

78 - 78 cancels out

now we have 102 = 3x

step 3 divide each side by 3x

102/3=34

3x/3=x

we're left with x = 34

Now to find the measure of angle C

We plug in the value of x in the expression (x + 7)

so c = 34 + 7

34 + 7 =  41

therefore your answer is 41

Answer:

She can make :

5 3/5 pies

Algebraic equation =

1 1/4 p = (9 - 2)

Step-by-step explanation:

Clara has 9 pounds of apples. If she saves 2 pounds for applesauce, how many pies, p, can she make?

Total number of pounds of apples = 9 pounds

She saves 2 pounds for apple sauce

The number of pounds of apples left =

9 pounds - 2 pounds

= 7 pounds

She needs 1 1/4 pounds to make one apple pie.

Therefore

1 1/4 pounds = 1 apple pie

7 pounds = p

Cross Multiply

1 1/4 × p = 7 × 1

p = 7 ÷ 1 1/4

p = 7 ÷ 5/4

p = 7 × 4/5

p = 28/5

p = 5 3/5 pies

An Algebraic equation for this situation is:

1 1/4 p = (9 - 2)

Where p = Number of pies

Answer:

the awnser is 30 degrees

Step-by-step explanation:

You have to look at your d ruler between different angles

Answer: it is a

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

Answer:

A=522

Explanation:

Answer:

[tex]\boxed {\boxed {\sf (1, 3) \ or \ x=1 \ and \ y=3}}}[/tex]

Step-by-step explanation:

We are given this system of equations:

[tex]4x+y=7\\4x-2y=-2[/tex]

We use elimination to solve to eliminate one of the variables, so we only have to work with one at a time. We do this by adding and subtracting the equations, and sometimes multiplying the entire equation by a number.

Notice how both equations have a 4x. This means they can easily be eliminated, without multiplying the equations by another number first. Let's subtract the 2 equations.

[tex]\ \ \ 4x+y=7\\ -(4x-2y)=-2[/tex]

The 4x will cancel because 4x-4x=0.

[tex]\ \ \ \ y=7 \\ - (-2y) = -2[/tex]

Since there are back to back negative signs, they become addition signs.

[tex]\ \ \ \ y=7 \\+2y=2[/tex]

[tex]3y=9[/tex]

We are solving for y , so we must isolate the variable. It is being multiplied by 3 and the inverse of multiplication is division. Divide both sides by 3.

[tex]3y/3=9/3\\y=3[/tex]

Now we can substitute 3 in for y in the original equations. Let's use the first one.

[tex]4x+y=7\\4x+3=7[/tex]

3 is being added to 4x. The inverse of addition is subtraction. Subtract 3 from both sides.

[tex]4x+3-3=7-3\\4x=4\\[/tex]

x is being multiplied by 4. The inverse of multiplication is division. Divide both sides by 4.

[tex]4x/4=4/4\\x=1[/tex]

x is equal to 1 and y is equal to 3. Coordinate points are written as (x, y). The solution to this system of equations is (1, 3).

Answer:

Logic

Step-by-step explanation:

3 square = 9

4 square = 16

9+16= 25

5 square = 25

4 square = 16

5 square = 25

16+25= 41

6 square = 36

Answer:

Yes SAS

Step-by-step explanation:

2 sides are the same

1 90 degree angle for each triangle

Hence the Answer Side-Angle-Side

Answer:

d = 7.5

Step-by-step explanation:

Calculate the slope m using the slope formula and equate to - 3

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 3, - 6) and (x₂, y₂ ) = (d, - 5d)

m = [tex]\frac{-5d+6}{d+3}[/tex] = - 3 ( multiply both sides by (d + 3) )

- 5d + 6 = - 3(d + 3)

- 5d + 6 = - 3d - 9 ( add 3d to both sides )

- 2d + 6 = - 9 ( subtract 6 from both sides )

- 2d = - 15 ( divide both sides by - 2 )

d = 7.5

Answer:

a=6

b=-2

Step-by-step explanation:

You can use the hint provided on the mathswatch question page, I've attached it below

step 1

h(4) = ax+b = (ax4)+b = 4a+b

it is given in the question that h(4)=22, therefore 4a+b=22

step 2

work out the equation for inverse g

g^-1(x) = [tex]\frac{x-2}{3}[/tex]

step 3

input 14 into the equation in place of x to find g^-1(x)

[tex]\frac{x-2}{3} =\frac{14-2}{3} =\frac{12}{3} =4[/tex]

so, g(x)^-1=4

step 4

find h(1):

h(1) = (ax1)+b = a+b

so, h(1)=a+b

step 5

a+b=4 (as it is given in the question that g^-1(14) is equal to h(1))

step 6

Now you have two simultaneous equations:

4a+b=22

a+b=4

then, solve for a:

4a+b=22

- a+b=4  

3a=18

a=6

then, input answer for a into either equation (I've gone with the a+b=4 equation):

6+b=4

-6   - 6

b=-2

(p.s i know this is very late but hope it helps someone)

Answer:

d

Step-by-step explanation:

(7,1)

Answer:

[tex] \frac{4}{3} \pi {r}^{3} [/tex]

Step-by-step explanation:

Since,

Basketball is a spherical object.

Hence,

It's volume would be,

[tex] \frac{4}{3} \pi {r}^{3} [/tex]

Answer ^

Answer:

C)  V= 4/3 pie r 3

Step-by-step explanation:

edge 2022

Answer:

9) 0.46

10) 0.666

11) 18%

12) 2.3%

13) 0.7/ 70%

14) 0.56/ 56%

15) 0.0035/ 0.35%

16) 1.13/113%

Step-by-step explanation:

Answer:

Then the midpoint is (2, -2)

Step-by-step explanation:

We treat the x- and y-coordinates separately, first finding the average (mean) of the x-coordinates and then the average of the y-coordinates:

xm = (-1 + 5)/2 = 2

ym = (1 - 5)/2 = -2

Then the midpoint is (2, -2)

Answer:

(2,-2)

Step-by-step explanation:

Two points are given to us and we need to find the midpoint of those two points. The points are

(-1,1) and (5,-5) . Let us say we have two points ( x1,y1) and ( x2 , y2) . The midpoint will be ,

[tex]\implies Midpoint =\bigg( \dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2} \bigg) \\\\\implies Midpoint = \bigg( \dfrac{-1+5}{2},\dfrac{1-5}{2}\bigg)\\\\\implies Midpoint = \bigg( \dfrac{4}{2},\dfrac{-4}{2}\bigg)\\\\\implies \red{Midpoint = ( 2 , -2) }[/tex]

9514 1404 393

Answer:

  p is proportional to q, r, t, and inversely proportional to s

Step-by-step explanation:

Assuming k is a "constant of proportionality," the value of p is directly proportional to each of the numerator variables: q, r, t. P is inversely proportional to the denominator variable, s.

Answer:

25.9%

Step-by-step explanation:

Since, the actual dimensions of the cylinder is not given we can assume the some dimension to explain the problem

Let us assume the dimension of the cylinder be

radius= 3in

height= 5 in

The expression for the total surface area of a cylinder is

T. S. A. =2πrh+2πr^2

Let us plug in the values to to find TSA

T. S. A. =2×3.14×3×5+2×3.14×3^2

Solving we get

T. S. A. =94.26+56.556

T. S. A. =150.816 in^2

Now let us find the error

we know that error % is calculated as

%error= [actual value-expected value/expected value]×100

%error= [190 -150.816/150.816]×100

%error= [39.184/150.816]×100

%error= 0.259×100

%error= 25.9%

Answer:

R to S

Step-by-step explanation:

Answer: Scale Factor: [tex]\frac{7}{4}[/tex] or 1.75

x= 24[tex]\frac{1}{2}[/tex] or 24.5

Step-by-step explanation:

12+16=28

12+9=21

x=14([tex]\frac{7}{4}[/tex]) =[tex]\frac{98}{4}[/tex]=24[tex]\frac{2}{4}[/tex]=24[tex]\frac{1}{2}[/tex]

x= 14(17.75)=24.5

ΔACD/ΔBE : [tex]\frac{AD}{AE}[/tex]=[tex]\frac{21}{12}[/tex][tex]\frac{/3}{/3}[/tex]=[tex]\frac{7}{4}[/tex]

ΔACD/ΔBE: [tex]\frac{AC}{AB}[/tex]= [tex]\frac{28}{16}[/tex] [tex]\frac{/4}{/4}[/tex] =[tex]\frac{7}{4}[/tex]

Answer:

1.) 12m = d

2.) 120

Answer:

d=12m

$120

Explained

part 1:

d=12m (dollars = $12 times the m (the number of mows))

part 2:

m=10

d=12 (10)

d=$120

Answer:

8 units

Step-by-step explanation:

Find the distance along the y-axis. For the example points (3,2) and (7,8), in which (3,2) is Point 1 and (7,8) is Point 2: (y2 - y1) = 8 - 2 = 6. This means that there are six units of distance on the y-axis between these two points. Find the distance along the x-axis. Learn how to find the distance between two points by using the distance formula, which is an application of the Pythagorean theorem. We can rewrite the Pythagorean theorem as d=√((x_2-x_1)²+(y_2-y_1)²) to find the distance between any two points.