Consider functions f and g below.

f(x) = -9x^2 - 7x + 12
g(x) = 3x^2 - 4x - 15

Find f(x) - g(x).

A. -12x^2 - 11x - 3
B. 6x^2 - 11x + 27
C. -6x^2 + 3x - 3
D. -12x^2 - 3x + 27

Answer:

Part 1) Option D [tex]75=10d+5n[/tex]

Part 2) Option B [tex](4, -2), (0, -1), (-4, 0)[/tex]

Part 3) Option A [tex]50=2LW[/tex]

Part 4) Option A Ms. Monti bought [tex]4[/tex] adult tickets and [tex]3[/tex] children’s tickets

Part 5) Option D The kitten weighed [tex]14[/tex] ounces when it was [tex]4[/tex] weeks old

Step-by-step explanation:

Part 1)

we know that

[tex]1\ dime=\$0.10[/tex]

[tex]1\ nickel=\$0.05[/tex]

Let

d-------> the number of dimes

n-----> the number of nickels

so

[tex]0.10d+0.05n=0.75[/tex]

Multiply by [tex]100[/tex] both sides

[tex]10d+5n=75[/tex]

Part 2)

we have

[tex]y=(-\frac{1}{4})x-1[/tex]

To calculate the solutions of the equation for an x value, substitute the value of x in the equation and find the value of y

For [tex]x=4[/tex] -----> [tex]y=(-\frac{1}{4})(4)-1=-2[/tex] ----> [tex](4,-2)[/tex]

For [tex]x=0[/tex] -----> [tex]y=(-\frac{1}{4})(0)-1=-1[/tex] ----> [tex](0,-1)[/tex]

For [tex]x=-4[/tex] -----> [tex]y=(-\frac{1}{-4})(4)-1=0[/tex] ----> [tex](-4,0)[/tex]

Part 3)

we know that

The perimeter of a rectangle is equal to

[tex]P=2(L+W)[/tex]

we have

[tex]P=50\ ft[/tex]

substitute

[tex]50=2(L+W)[/tex] ------> [tex]50/2=(L+W)[/tex] -----> [tex]50=2L+2W[/tex]

Par 4)

Let

x------> the number of adult tickets

y------> the number of children tickets

we have

[tex]25x + 15y = 145[/tex]

The ordered pair [tex](4,3)[/tex] represent

[tex]x=4\ adult\ tickets[/tex]

[tex]y=3\ children\ tickets[/tex]

therefore

Ms. Monti bought [tex]4[/tex] adult tickets and [tex]3[/tex] children’s tickets

Part 5)  

Let

x------> the number of weeks after it was born

y-----> the kitten’s weight in ounces

we have

[tex]y=2.5x+4[/tex]  

The ordered pair [tex](4,14)[/tex] represent

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

[tex]y=14\ ounces[/tex]

therefore

The kitten weighed [tex]14[/tex] ounces when it was [tex]4[/tex] weeks old

Answer:

There are 10,000 1s in Ten Thousand

Hope this helped:)

Step-by-step explanation:

Answer:

J=PM/300

Step-by-step explanation:

300J/P=M

*p              *P

300J=PM

300J/300=PM/300

J=PM/300

Answer:

J=MP/300

Step-by-step explanation:

M=300J/P

now take p to the left hand side of the equation

MP= 300J

MP/300 = J

J= PM/300

If C is the cost and x the amount of cans.

C = 0.5x - 0.8

Answer:

A) 10^2

Step-by-step explanation:

100 is 10 times 10 or 10 to the second power

100 = 10 * 10 = 10 ^2

Answer:

They're equally as important because they are the same thing, but just meant for finding different sides.

Step-by-step explanation:

Answer:

c ∛ (16)

Step-by-step explanation:

2 ^ (4/3)

We can separate this into 2 pieces using the power of power rule in reverse

x^a ^b = x^ (ab)

(2^4 ) ^ 1/3

2 to the 4th power is

16 ^ (1/3)

We now have the cubed root of 16

∛ (16)

Answer:

The answer is C :)

Answer:

A

Step-by-step explanation:

here's how I got it A and C are similar but C will have a different answer because you will multiply 12*7 then add 91 that will equal 175 but it wants the answer that is 12 larger than 7 + 91. when it is in parenthesis it goes first so then you do 7+91 first and that is 98. then multiply 12*98=1176 and that is the correct answer because it is 12 times the sum of 7 and 91.

The expression that is 12 times as large as the expression 7 plus 91 is A) 12 x (7+91). First, we solve the expression in parentheses, 7+91, to get 98. Then, we multiply 98 by 12 to get the final result of 1176.

The question is asking which expression results in a value that is 12 times as large as the expression 7 plus 91. The expression 7 plus 91 results in a value of 98. In order to find a value that is 12 times as large as 98, we need to multiply 98 by 12. That operation is represented by the expression 12 x (7+91), which is option A.

To break it down step by step:

In conclusion, the expression that is 12 times as large as the expression 7 plus 91 is A) 12 x (7+91).

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Hi there! :) :D

Answer:

A. -9

*The answer must have a negative sign.*

Step-by-step explanation:

Lesson: Dividing integers

First, you divide by the numbers from left to right.

[tex]72/8=9[/tex]

It change positive to negative sign.

[tex]72/9=8[/tex]

Then, you can also multiply by the numbers from left to right.

[tex]9*8=72[/tex]

[tex]8*9=72[/tex]

Final answer is -9

Hope this helps!

Have a nice day! :)

:D

-Charlie

Thank you so much! :)

:D

Answer:

3 3/4 cups

Step-by-step explanation:

We can use ratio's to solve this problem.  we will put flour over sugar

3/4 cup sugar        x cups sugar

---------------------- = -------------------

1/5 cup flour               1 cup flour

Using cross products

3/4 *1 = 1/5 * x

Multiply each side by 5

5 *3/4 = 5 * 1/5 x

15/4 = x

Changing this from an improper fraction to a mixed number

4 goes into 15  3 times with 3 left over

3 3/4 cups

Answer:

the answer is  G. 4/15

Step-by-step explanation:

you take 3/4 and 1/5  and divide them both by 3

that would make 1/4 and 1/15

then it is four cups so it would be four times 1/15

that would be 4/15

Total money Marcus has = $28

Money spent to buy a notebook = $3.75

Money left now = [tex]28-3.75=24.25[/tex]

Money needed to be saved = $11.25

So, the amount of money Marcus can spend = [tex]24.25-11.25=13[/tex]

Cost of a packet of chips = $1.30

The inequality to determine the maximum number of chips he can buy is:

Let the number of chips Marcus can buy = x

As he cannot spend more than $13 to buy chips so equation becomes:

[tex]1.30x\leq 13[/tex]

Solving this we get

[tex]x\leq 10[/tex]

Hence, Marcus can buy a maximum of 10 packs of chips and  save $11.25

Answer:

sqrt(52)

Step-by-step explanation:

Given points P(2,2)  and Q(6,8)

To find distance between points we apply distance formula

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

(x1,y1) is (2,2)  and (x2,y2) is (6,8)

Plug in the values in the formula

[tex]D = \sqrt{(6-2)^2+(8-2)^2}[/tex]

[tex]D = \sqrt{16+36}[/tex]

[tex]D = \sqrt{52}[/tex]

Answer:

answer is B sqrt65

Step-by-step explanation:

Answer:

4 - π

Step-by-step explanation:

(a) Radius of circle

  A = πr²      Substitute value of A

4π = πr²      Divide each side by π

 r² = 4         Take the square root of each side

  r = 2

(b) Area of MON

A = ¼ × area of circle

A = ¼ × 4π

A = π

(c) Area of MONP

 l = r      Substitute the value of r

 l = 2

A = l²      Substitute the value of l

A = 2²

A = 4

(d) Area of MPN

A(MPN) = A(MONP) – A(MON)  

Area(MPN) = 4 - π

Answer:

Percent increase is 17.6%

We still have to pay 7.50 with the coupon

Step-by-step explanation:

Percent increase = (new- original)/original *100%

                             = (10-8.5)/8.5 * 100%

                             = 1.5/8.5 * 100%

                             = 17.6470588%

Round to the nearest tenth

                                 17.6%

This is an increase since the cost went up.

If we have 25% off, we still have to pay (100%-25%) = 75%

10 *.75 = 7.50

We still have to pay 7.50 with the coupon

Answer:

The areas are equal.

Step-by-step explanation:

Let the first rectangle be R and

the second rectangle be R'.

Sine R and R' are identical, their lengths are equal and their breadths are equal.

So, if Inga divided each into equal parts, then each part of both rectangles are equal.

Hence, the colored parts of both rectangles are equal.

Answer:

0.0225 dekameters

hope it helps

Step-by-step explanation:

1 millimeter = 0.0001 dekameters

0.0001 x 225 = 0.0225

The number of dekameters that are in the given millimetres would be =0.0225 dekameters.

To determine the number of dekameters found in the given millimetres the following steps should be taken as follows:

For 1 dekameters = 10,000 millimetres

X dekameters = 225 millimeters

Make X the subject of formula;

X = 225/10000

= 0.0225 dekameters.

Learn more about length here:

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Answer:

x=4 °

z = 77°

Step-by-step explanation:

We know vertically opposite angles are equal

HEre (5x+83)  and 103  are vertically opposite angles . so they are equal'

Set them equal and solve for x

5x+83= 103

subtract 83 on both sides

5x = 20

Divide both sides by 5

x= 4

103  and angle z  are in a straight line

Sum of angles in a straight line is 180 degrees

So 103 + z = 180

subtract 180 on both sides

z = 77°

Answer:

Coordinate of Q (3,4)

Step-by-step explanation:

Let to points S(-2,-6) and T(5,8)  

Le Q(x,y) be the point in which it divide the ST in the ratio 5:2

If a point (x,y)cut the line in the ratio a : b where the end coordinate are( x1,y1) and (x2,y2)

x = x1 + p/w(x2 - x1) and y = y1 + p/w(y2 - y1)  

where p = a and w = a+b

To find the coordinate of Q

x  = x1 + p/w(x2 - x1 )

x = -2 + 5/7(5 - -2) = -2 + 5=3

y = y1 + p/w(y2 - y1)  

y = -6 + 5/7(8 - -6) = -6 + 10 = 4

Therefore the coordinate of Q is (3,4)

Answer: (-2-2i)(-4+6i) = 20 - 4i

Step-by-step explanation:

We have the expression:

(-2 - 2i)*(-4 + 6i)

the rule we need to know here is that i*i = -1

now, the first step is distribute the parentheses.

(-2 - 2i)*(-4 + 6i) = -2*-4 -2*6i - 2i*-4 - 2i*6i = 8 -12i + 8i -12*(i*i)

= 8 + (8 - 12)i +12 = 20 - 4i

Answer:

E = 216 joules

Step-by-step explanation:

The given equation is

E = [tex]\frac{m*v^{2} }{2}[/tex]                ............(i)

Here

m = 3 kg

v = 12 m/s

Putting the given values in equation (i)

E = [tex]\frac{3*12^{2} }{2}[/tex]

E = [tex]\frac{3*144}{2}[/tex]

E = [tex]\frac{432}{2}[/tex]

E = 216 kg m² /s²

or

E = 216 joules

Answer:

4

Step-by-step explanation:

To figure out how many times the population of India  is as compared to the US, we take the population of India and divide by the population of the US

Population of India/population of US

1.2*10^9 /300000000

I will change 300000000  into scientific notation by moving the decimal 8 places to the left, so it becomes 3 *10^8

1.2*10^9 /3* 10^8

Now we divide the numerals and subtract the exponents

1.2/ 3  * 10^(9-8)

.4 * 10^1

.4*10

4

Answer:

Interest (I) = $ 900

Step-by-step explanation:

Formula for interest is given by:

Interest(I) = [tex]\frac{P \times R \times T}{100}[/tex]

where

P represents principal

R represents rate of interest

T represents the time in year.

Given : P = $ 12,000 , R =2.5% and  T = 3 years.

Interest(I) = [tex]\frac{12000 \times 2.5 \times 3}{100}[/tex]

On simplify:

[tex]I = \$ 900[/tex]

Therefore, the interest is , $ 900

Answer: The option B. 1.9 is correct

Explanation:

We are given the below information:

x               Probability P(x)

0                      0.2

1                       0.1

2                      0.4

3                       0.2

4                       0.1

The expected value of x is given below:

[tex]E(x)=\sum x P(x)[/tex]

         [tex]=(0 \times 0.2)+(1 \times 0.1)+(2 \times 0.4)+(3 \times 0.2)+(4 \times 0.1)[/tex]

        [tex]=0+0.1+0.8+0.6+0.4[/tex]

        [tex]=1.9[/tex]

Therefore, the expected value of x is 1.9      

Answer:

0

Step-by-step explanation:

23/40 - 11/30

We are using the benchmarks 0, 1/2 ,1 to approximate our values

23/40 is close to 1/2

11/30 is close to 1/2

1/2 - 1/2 = 0

Answer:

1. a= -1

2. k=5

3. x= 10

4. y= -1/5

Step-by-step explanation:

1. 2+1/6a= -4

6= -1/6a

a=6*-1/6

a= -1

2. 7k-3=32

7k=32+3

7k=35

k=5

3. 2x-5=15

2x=20

x=10

4. 3y+2:5= -1:5

-3y=3/5

y= 3/5: -3

y= -1/5

Answer:

A: -1

K: 5

X: 10

Y: -1/5

HOPE THIS HELPS! :)

Answer:

=110.8 percent

Step-by-step explanation:

We can use this formula to find the percent increase

percent increase = (new - original)/ original * 100

new = 363,844,490

original =172,602,624

Substitute these values in

percent increase = (363,844,490 - 172,602,624)/ 172,602,624 * 100

percent increase = 191241866/172602624 *100

                             = 1.107989332

                            =110.8 percent

Answer:

A and B.

Step-by-step explanation:

To get to know the graph with least slope, we have to write all equations in the form y=mx + c.

where m is the slope and c is the the y-intercept.

A. y = x + 6

For this equation m = 1

B. y = -x - 9

For equation B, m = -1

C. y = 2x + 1

In this equation, m = 2

D. y = -7x - 2

In equation D, m = -7

The equation with the highest slope is D while the one with the least slope/steep is A and B.

Answer:

The Science Center charge less than the Dino Discovery museum for more then 10 students

Step-by-step explanation:

Let us assume that the number of students are x .

Let us assume that the total charge for x students be y.

As given

Mrs. Williams is deciding between two field trips for her class.

The Science Center charges $120 plus $5 per student.

Than the equations becomes

y = 120 + 5x

The Dino Discovery Museum simply charges $7 per student.

y = 7x

Than

[tex]120 + 5x < 7x[/tex]

[tex]120 < 7x - 5x[/tex]

[tex]120 < 2x[/tex]

[tex]\frac{120}{12} < x[/tex]

[tex]10 < x[/tex]

Therefore the Science Center charge less than the Dino Discovery museum for more then 10 students.

Answer: D

Step-by-step explanation:

D contains both (2,2) and (2,1), and fails the definition. D(2) would have to be 2 and 1 at the same time.

Set S is a function if and only if

x ∈ S implies x is an ordered pair,

and

(a,b) and (a,c) ∈ S implies b = c.

Answer:

set D

Step-by-step explanation:

For a function we need to have for evety x value, only one value of y.

in set D, we have the points (2, 2) and (2, 1)

this two points have one value of x: x=2

but for the same x we have two values of y: 2 and 1

so this does not obey the requirements to be a functios wich is that for every x, we cannot have more than one value of y.