If f(x) = 10x + 7 and g(x) = x^2 - 7x, find (f - g)(x)

A. (f - g)(x) = x^2 + 3x + 7
B. (f - g)(x) = 10x^3 - 63x^2 - 49x
C. (f - g)(x) = -x^2 + 17x + 7
D. (f - g)(x) = 10x + 7

Answer:

The width of both rectangles are [tex]\frac{36}{l},\frac{21}{L}[/tex].

Step-by-step explanation:

Given : The area of one rectangle is 36 square  feet. The area of a second rectangle is  21 square feet. The rectangles have the  same width and the dimensions are  whole numbers.

To find : What is the width of  both rectangles?

Solution :

According to question, the two rectangles have the same widths but they have different lengths.

Let the width of both rectangle be 'w'

Let the length of one rectangle be 'l'

Let the length of second rectangle be 'L'

The area of the rectangle is [tex]\text{Area}=\text{Length}\times \text{Width}[/tex]

The area of one rectangle,

[tex]36=l\times w[/tex]

[tex]w=\frac{36}{l}[/tex]

The area of second rectangle,

[tex]21=L\times w[/tex]

[tex]w=\frac{21}{L}[/tex]

The width of both rectangles are [tex]\frac{36}{l},\frac{21}{L}[/tex].

Answer:

angle b is 135 degrees

Step-by-step explanation:

lets work backwards to solve this

if angle c is 45, c is vertical to angle a, and we know vertical angles equal each other, we can reduce that angle a equals 45

if angle a is supplementary to angle b, and we know angle a is 45 degrees, we can make the equation 45+b=180. subtracting 45 from 180, we get 135 degrees for angle B

Answer:

A. What is the weight of each type of fruit in decimal form?

Grapes in decimal form = 0.8181 pounds

Bananas in decimal form = 1.75 pounds

Apples in decimal form = 2.8333 pounds

B. Does the weight of each type of fruit in decimal form represent a rational number? Explain.

Of course, each of the weights of the fruits in decimal form represent a rational number. The weights can be expressed as a fraction where both the numerator and the denominator in the fraction are integers, like we checked with 9/11, 1 3/4 and 2 5/6. The denominator in a rational number cannot be zero.

Step-by-step explanation:

1. Let's check the information provided to us to answer the questions correctly:

Janis purchased:

9/11 pounds of grapes

1 3/4 pounds of bananas

2 5/6 pounds of apples

2. What is the weight of each type of fruit in decimal form?

Grapes in decimal form = 0.8181 pounds

Bananas in decimal form = 1.75 pounds

Apples in decimal form = 2.8333 pounds

3. Does the weight of each type of fruit in decimal form represent a rational number? Explain.

Of course, each of the weights of the fruits in decimal form represent a rational number. The weights can be expressed as a fraction where both the numerator and the denominator in the fraction are integers, like we checked with 9/11, 1 3/4 and 2 5/6. The denominator in a rational number cannot be zero.

Answer: gay

Step-by-step explanation: y = mc2

Answer:

80 years old

Step-by-step explanation:

the ratio is 1:10 and their total is 88. Just by looking at it you can see that Geoff's age is 8 and Eathan is 80. The total is 88 and the ratio also matches.

1:10  1 times 10 is 10

8:80 8 times 10 is 80

Answer:

hi there!

The correct answer to this question is: 80 years old

Step-by-step explanation:

you first need to set up to equations:

in this case: I will use the variable "e" for Ethan and "g" for Geoff

e=10g

g + e = 88

since e = 10g, substitute that into the second equation and you get 10g + g = 88

you add the variables and you get 11g=88 then you divide 11 on both sides and you get 8 so geoff is 8

then you plug 8 back into the second equation and you get ethan's age which is 80

Answer:

36.2

Step-by-step explanation:

Answer:

55 minutes :)

Step-by-step explanation:

Rate of drop of temperature = Change in temperature/Rate

=> (165 - 135)/15

=> 30/15

=> 2 ⁰F/min

Now, The time at which the temperature of will be 70⁰F = 70/Rate

=> 70/2

=> 35 min

Time for 110⁰ F

=> 110/2

=> 55 min

Answer:

34 minutes

Step-by-step explanation: I just took the test

Answer:

see explanation

Step-by-step explanation:

(10)

To evaluate f(- 4) substitute x = - 4 into f(x)

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

f(- 4) = 3(- 4) + 3 = - 12 + 3 = - 9

(11)

To evaluate f(- 2) substitute x = - 2 into f(x)

f(- 2) = 2(- 2)² - 8 = 2(4) - 8 = 8 - 8 = 0

(12)

To evaluate g(- 3) substitute x = - 3 into g(x)

g(- 3) = - 2(- 3)² + 3(- 3) = - 2(9) - 9 = - 18 - 9 = - 27

Answer:

g^-1 (x)=1/2x+3/2

Step-by-step explanation:

y=2x-3

x=2y-3

2y=x+3

y=1/2x+3/2

Answer:

Step-by-step explanation:

A = L * W

A = 42

W = 3.5

now sub

42 = 3.5L <=== ur equation

Answer:

A

Step-by-step explanation:

Note that (f - g)(x) = f(x) - g(x)

f(x) - g(x)

= 6x² - 4 - (2x + 2) ← distribute parenthesis by - 1

= 6x² - 4 - 2x - 2 ← collect like terms

= 6x² - 2x - 6 → A

Answer:

A.  6x^2 - 2x - 6.

Step-by-step explanation:

( f - g)(x)

= 6x^2 - 4 - (2x + 2)

= 6x^2 - 4 - 2x - 2

= 6x^2 - 2x - 6.

Answer:

a. 1200          f. 900

b. 600           g. 5700

c. 900           h. 4800

d. 300           i. 8300

e. 800           j. 8500

Step-by-step explanation:

First of all, you need to compute the sums. I find a calculator handy for this.

To round to hundreds, you can examine the digit in the next place to the right of the hundreds place. That digit in the tens place needs to be compared to 5. If it is 5 or greater, add 1 to the digit in the hundreds place. After you have done that, set the digits to the right of the hundreds place to zero.

__

Alternatively, you can add 1/2 of 100 to the sum, then set the digits to the right of the 100s place to zero. (Adding 50 will only change the 100's place digit if the 10's place digit is 5 or more.) This method doesn't require you do any thinking about the size of the digit; it is purely mechanical.

The sums and their rounded values are ...

a. 1221 ⇒ 1200

b. 568 ⇒ 600

c. 931 ⇒ 900

d. 347 ⇒ 300

e. 798 ⇒ 800

f. 911 ⇒ 900

g. 5681 ⇒ 5700

h. 4766 ⇒ 4800

i. 8328 ⇒ 8300

j. 8507 ⇒ 8500

Answer:

14.06=703/50

Step-by-step explanation:

14.06=703/50

Answer:

what is the number in the word problem

Step-by-step explanation:

Answer:

The area of the region inside the circumcircle of the triangle but outside the triangle is

[tex]A=\frac{27}{4}[\pi-3\sqrt{3}]\ units^2[/tex]

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

Find the area of triangle

we have an equilateral triangle

Applying the law of sines

[tex]A_t=\frac{1}{2}(b^2)sin(60^o)[/tex]

where b is the length side of the equilateral triangle

we have

[tex]b=9\ units[/tex]

[tex]A_t=\frac{1}{2}(81)sin(60^o)[/tex]

[tex]A_t=\frac{1}{2}(81)\frac{\sqrt{3}}{2}[/tex]

[tex]A_t=81\frac{\sqrt{3}}{4}\ units^2[/tex]

step 2

Find the area of circle

The area of the circle is equal to

[tex]A_c=\pi r^{2}[/tex]

The formula to calculate the radius of the circumcircle of the triangle equilateral is equal to

[tex]r=b\frac{\sqrt{3}}{6}[/tex]

where b is the length side of the equilateral triangle

we have

[tex]b=9\ units[/tex]

substitute

[tex]r=(9)\frac{\sqrt{3}}{6}[/tex]

[tex]r=3\frac{\sqrt{3}}{2}\ units[/tex]

Find the area

[tex]A_c=\pi (3\frac{\sqrt{3}}{2})^{2}[/tex]

[tex]A_c=\frac{27}{4} \pi\ units^2[/tex]

step 3

Find the area of the shaded region

we know that

The area of the region inside the circumcircle of the triangle but outside the triangle is equal to the area pf the circle minus the area of triangle

so

[tex]A=(\frac{27}{4} \pi-81\frac{\sqrt{3}}{4})\ units^2[/tex]

Simplify

[tex]A=\frac{27}{4}[\pi-3\sqrt{3}]\ units^2[/tex]

Answer:

x=2 1/4

Step-by-step explanation:

Let's swap it around so its 1/3(8x+3)=7

Now you multiply both sides by 3 to make it 1(8x+3)=21

That means its 8x+3= 21

Subtract both sides by 3 to get rid of it

Now you have 8x=18

Which equals to x= 18/8

Which equals 2 1/4

Answer:

Volume of the rectangular prism is given by,

[tex]\frac {15}{2x}[/tex] unit .

Step-by-step explanation:

According to the question,

height of the prism = [tex]\frac {5}{2x + 8}[/tex] unit = h (say)

depth of the prism = [tex]\frac {x + 4}{4}[/tex] unit = w (say)

length of the prism = [tex]\frac {12}{x}[/tex] unit = l (say)

So,

the volume of the rectangular prism,

V = lwh

   = [tex]\frac {5}{2x + 8} \times \frac {x + 4}{4} \times \frac {12}{x}[/tex] unit

   =  [tex]\frac {15}{2x}[/tex] unit

Answer:

A

Step-by-step explanation:

The larger number is 30 and smaller number is 10.

Step-by-step explanation:

Let,

Larger number = x

Smaller number = y

According to given statement;

The larger number is 20 more than the smaller.

x = y+20    Eqn 1

Four times the larger is 70 more then 5 times the smaller.

4x = 5y+70    Eqn 2

Putting value of x from Eqn 1 in Eqn 2

[tex]4(y+20)=5y+70\\4y+80=5y+70\\80-70=5y-4y\\10=y\\y=10[/tex]

Putting y=10 in Eqn 1

[tex]x=10+20\\x=30[/tex]

The larger number is 30 and smaller number is 10.

Keywords: linear equation, substitution method

Learn more about substitution method at:

#LearnwithBrainly

The weight of wrestler was 80 kg before the special diet

Step-by-step explanation:

Given function is:

[tex]W=80+5.4t[/tex]

We can substitute the values of t to find the weight after t number of months

When we have to find the initial weight , t has to be put equal to zero

So,

[tex]W = 80+5.4t\\t = 0\\W = 80 + 5.4(0)\\W = 80+0\\W = 80[/tex]

Hence,

The weight of wrestler was 80 kg before the special diet

Keywords: Functions, variables

Learn more about functions at:

#LearnwithBrainly

Answer:

80

Step-by-step explanation:

i'm not sure but the answer for people on khan

Option B

Profit earned in the entire month is $ 31486

Solution:

Given that At the start of the month, Jodie had sold 885 copies of her new book

At the end of the month, she had sold 1,364 copies of her book

Each book profits $13.97, approximately

To find: profit earned in entire month

Total books earned = 885 + 1364 = 2249

Profit earned from 1 book = $ 13.97 ≈ 14

Therefore profit earned from 2249 books is found by multiplying profit earned from 1 book by 2249

profit earned from 2249 books = Profit earned from 1 book x 2249

profit earned from 2249 books = 14 x 2249 = 31486

Therefore profit earned in the entire month is $ 31486

Answer:

The System of equation are [tex]\left \{ {{3x+4y=44.50} \atop {4x+8y=84.00}} \right.[/tex]

Step-by-step explanation:

Let the Cost of bags of popcorn be 'x'.

Let the Cost of drinks be 'y'.

Given:

Kevin spends a total of $44.50 on 3 bags of popcorn and 4 drinks.

Now Total Money Spend by Kevin is equal to sum of Number of bags of popcorn multiplied by Cost of bags of popcorn and number of drinks multiplied by Cost of drinks.

framing in equation form with given details we get;

[tex]3x+4y=44.50[/tex]

Also Given:

Levi spends a total of $84.00 on 4 bags of popcorn and 8 drinks.

Now Total Money Spend by Levi is equal to sum of Number of bags of popcorn multiplied by Cost of bags of popcorn and number of drinks multiplied by Cost of drinks.

framing in equation form with given details we get;

[tex]4x+8y=84.00[/tex]

Hence The System of equation are [tex]\left \{ {{3x+4y=44.50} \atop {4x+8y=84.00}} \right.[/tex]

Answer:

Step-by-step explanation:

first we find the slope using the slope formula : (y2 - y1) / (x2 - x1)

(2,-2)....x = 2 and y = -2

(4,1)...x = 4 and y = 1

now sub

slope = (1 - (-2) / (4 - 2) = (1 + 2) / 2 = 3/2

y = mx + b

slope(m) = 3/2

(4,1)...x = 4 and y = 1

now sub and find b, the y int

1 = 3/2(4) + b

1 = 6 + b

1 - 6 = b

-5 = b

so ur equation is : y = 3/2x - 5 <===

Answer: Third option.

Step-by-step explanation:

It is important to know the following:

1. The Slope-Intercept form of a Linear function is:

[tex]y=mx+b[/tex]

Where "m" is the slope of the line and "b" is the y-intercept.

Notice  that the highest exponent of the variable "x" is 1.

2. The General form of a Quadratic function is:

[tex]y=ax^2 + bx + c[/tex]

Where "a", "b" and "c" are known values ([tex]a\neq 0[/tex])

Notice that that the highest exponent of the variable "x" is 2.

The equation given in the exercise  is:

[tex]y= -3x^2+4[/tex]

Observe that highest exponent of the variable "x" is 2. Therefore, it is a Quadratic equation.

Therefore, making an exponent 1 instead of the exponent 2 would turn the given equation into a Linear function.

Final answer:

To turn the quadratic equation y = [tex]-3x^2[/tex] + 4 into a linear function, the exponent on the x term must be changed from 2 to 1.

Explanation:

The equation y =[tex]-3x^2[/tex] + 4 is a quadratic function due to the exponent 2 on the x term. To turn this equation into a linear function, we need to have the highest exponent of x equal to 1 since linear functions are of the form y = mx + b, where m and b are constants, and x is raised to the first power.

Therefore, the adjustment that would turn the equation into a linear function is to make the exponent 1 instead of 2.

Answer:

The number of items are being purchased is 4 .

Step-by-step explanation:

Given as :

The time taken to process the payment = 27 seconds

The time taken to scan each items = 4 seconds

The total time taken to ring up a customer = 43 seconds

Let The number of items being purchased = n

Now, According to question

The total time taken to ring up a customer = The time taken to process the payment + The time taken to scan each items × The number of items being purchased

i.e 43 =  27 + 4 × n

Or, 4 × n = 43 - 27

Or,  4 × n = 16

∴ n = [tex]\dfrac{16}{4}[/tex]

I.e n = 4

So, The number of items being purchased = n = 4

Hence, The number of items are being purchased is 4 . Answer

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}x=y-2&(1)\\-3x+3y=6&(2)\end{array}\right\qquad\text{substitute (1) to (2)}\\\\-3(y-2)+3y=6\qquad\text{use the distributive property}\\-3y+6+3y=6\qquad\text{combine like terms}\\(-3y+3y)+6=6\\6=6\qquad\bold{TRUE}\\\\\text{That is why the system of equations has infinitely many solutions.}[/tex]

Option D

Money earned by Marty is $ 16.72

Solution:

Given that, Marty started a lawn mowing business

He kept track of his expenses and earnings in a table

Lawn Mower = - $49.99

Gasoline = - $8.79

Moyer's yard = $ 40

Griffen's yard = $ 35.50

To find: Money earned by Marty

Total money earned = lawn mower + gasoline + moyers yard + griffens yard

Total money earned = -49.99 - 8.79 + 40 + 35.50

Total money earned = -58.78 + 40 + 35.50

Total money earned = -18.78 + 35.50 = 16.72

Thus money earned by Marty is $ 16.72

Answer:

109 square feet.

Step-by-step explanation:

109 in: = 109/12 = 9.0833333.... = 9 5/60 = (540+5)/60 = 545/60

Area = L*w

L = 545/60 feet

W = 12 feet

Area = 545/60 *  12

Area = 545*12/60

Area = 545 /5 = 109 square feet.  

Answer:

109

Step-by-step explanation:

Option B

When you roll two number cubes, the odds in simplest form against getting two numbers greater than 3 is 1 : 4

The probability of an event is given as:

[tex]\text {probability of an event }=\frac{\text { number of favorable outcomes }}{\text { total number of possible outcomes }}[/tex]

Given that,

Tow number cubes are rolled

To find: Probability of getting two numbers greater than 3

On a number cube there are 6 numbers {1, 2, 3, 4, 5, 6} Out of which 3 numbers are greater than 3 {4, 5, 6}

So, total number of possible outcomes = 6

Favourable outcomes = number greater than 3 = 3

When you roll one number cube, probability of getting number greater than 3:

[tex]\text { Probability (number greater than } 3 \text { ) }=\frac{3}{6}[/tex]

When you roll two number cubes, probabilty is given as:

[tex]\text { Probability (number greater than }3)= \frac{3}{6} \times \frac{3}{6}=\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}[/tex]

[tex]Probability = \frac{1}{4}[/tex]

In ratio form we can write as 1 : 4

Option B is correct

Answer:

Actually... It's A

Step-by-step explanation:

Odd against is not 1:4, it's most likely 4:1

1:4 is odds in favor, not odds against.

Answer:

[tex]\large\boxed{C=2\pi r}[/tex]

Step-by-step explanation:

A linear equation is an equation in which a variable is in the first power.

The formula of a Circumference of a circle

[tex]C=2\pi r\\\\2,\ \pi-\text{numbers}\\r-\text{variable}\\\\\boxed{\bold{YES}}[/tex]

The formula of an Area of a circle

[tex]A=\pi r^2\\\\\pi-\text{number}\\r^2-\text{variable in the second power}\\\\\boxed{\bold{NO}}[/tex]

The formula of a volume of a sphere

[tex]V=\dfrac{4}{3}\pi r^3\\\\\dfrac{4}{3},\ \pi-\text{numbers}\\r^3-\text{variable in the third power}\\\\\boxed{\bold{NO}}[/tex]

Answer:

39 degrees

Step-by-step explanation:

The square indicates a right angle, or 90 degrees. 90-51=39.