A bookshop has an offer. "Buy one book and get one free!" Ria gets 8 books from the shop with that offer. The normal price of each book is £6.99. How much does Ria spend?

Answer:

(3a+4)(9a^2-12a+16)

Step-by-step explanation:

It's a perfect square :)

The factors of the given polynomial are (4+3a)(9a²-12a+16)

A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations.

Given that, a polynomial, 64+27a³

Using identity : a³+b³ = (a+b)(a²-ab+b²)

We get,

= (4+3b)(4²-4x3a+(3a)²)

= (4+3a)(16-12a+9a²)

Hence, the factors of the given polynomial are (4+3a)(9a²-12a+16)

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Answer:

-1/2 is m and 3 is b

Step-by-step explanation:

-1/2 is the slope and 3 is the y-intercept,

Answer:

Step-by-step explanation:

The slope m is -1/2

The y-int b is 3

Since the slope is negative the graph should start from the top left and should go down all the way down to the bottom right. The line should also pass the point (0,3) since 3 is the y-int

Answer:

The equivalent expression is cosec2x

option B

Step-by-step explanation:

The correct question is ;

which expression is equivalent to sec2xcot2x?

Solution

Mathematically;

sec2x = 1/cos2x

cot2x = 1/tan2x

so we have

1/cos2x * 1/tan2x

recall that the product of tan and cos is sin

from the formula;

tan = sin/cos

so we have our final answer as;

1/sin2x

Kindly recall that ;

sin = 1/cosec

so therefore;

1/sin2x = csc2x

Answer:

pipe will empty the tank in 10.5 hours, working alone.

Step-by-step explanation:

Let x be the rate of work of the slower pipe (measured in the tank volume per hour).

Then the rate of work of the faster pipe is 2.5x of the tank volume per hour.

The combined rate of the two pipes is then  x + 2.5x = 3.5x.

We are given

7.5*3.5*x = 1;  hence   x = 1%2F%287.5%2A3.5%29.

Then  2.5x = 2.5%2F%287.5%2A3.5%29 = 1%2F%283%2A3.5%29 = 1%2F10.5.

It means that the faster pipe will empty the tank in 10.5 hours, working alone.

The faster pipe will empty the tank in 10.5 hours, working alone.

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.

Let x be the rate of work of the slower pipe (measured in the tank volume per hour).

Then the rate of work of the faster pipe is 2.5x of the tank volume per hour.

The combined rate of the two pipes is then  x + 2.5x = 3.5x.

We are given

7.5×3.5×x = 1

7.5×3.5 x=1

Divide both sides by 7.5×3.5

x=1/ 7.5×3.5

2.5x=2.5/ 7.5×3.5

x=1/10.5

It means that the faster pipe will empty the tank in 10.5 hours, working alone.

Hence, the faster pipe will empty the tank in 10.5 hours, working alone.

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Answer:

angle j = 98 degrees

angle c = 78 degrees

JK = 16

AD = 32

x=8

y=11

Step-by-step explanation:

Answer:

Step-by-step explanation:

7x - 2(7x - 9) = 2(-6x + 4)                      Remove the brackets on both sides.

7x - 14x + 18 = -12x + 8                         Combine like terms

-7x + 18 = -12x + 8                                Add 12x to both sides

-7x+12x + 18 = 8                                   Combine like terms on the left

5x + 18 = 8                                           Subtract 18 from both sides

5x = 8 - 18

5x = -10                                                Divide by 5

x = - 10/5

x = - 2                                                                                                                                                                                                                                                     Proof

LHS

7*-2 -2(7*-2 - 9)                                                                                                      -14 - 2*(-14 - 9)                                      

-14 -2 (-23)

-14 + 46

32

RHS

2(-6*-2 + 4)

2(12 + 4)

32

QUESTION:

Simplify each expression

ANSWER:

1.) [tex]\green{{- 8n}}[/tex]

2.) [tex]\green{{- 2b - 60}}[/tex]

3.) [tex]\green{{- 10x - 14}}[/tex]

4.) for number 4 study my step-by-step explanation so you can answer that

STEP-BY-STEP EXPLANATION:

1.) First, If the term doesn't have a coefficients, it is considered that the coefficients is 1

WHY?

Learn why:

Why is it considered that the coefficient is 1?

Remember that any term multiplied by [tex]\blue{{1}}[/tex] remains the same :

[tex]\blue{{1}}[/tex] [tex]{× x = x}[/tex]

Step 1:

The equality can be read in the other way as a well, so any term can be written as a product of [tex]\blue{{1}}[/tex] and itself:

[tex]{x = }[/tex] [tex]\blue{{1}}[/tex] [tex]{× x}[/tex]

Step 2:

Usually, we don't need to write multiplacation sign between the coefficient and variable, so the simple form is:

[tex]{x = 1x}[/tex]

This is why we can write the term without the coefficient as a term with coefficient [tex]{1}[/tex]

Now let's go back to solving as what i said if a term doesn't have a coefficient, it is considered that the coefficient is 1

[tex]{n - 9n}[/tex]

[tex]\red{{1}}[/tex] [tex]{n -9n}[/tex]

Second, Collect like terms by subtracting their coefficients

[tex]\red{{1n - 9n}}[/tex]

[tex]\red{{( 1 - 9)n}}[/tex]

Third, Calculate the difference

how?

Keep the sign of the number with the larger absolute value and subtract the smaller absolute value from larger

[tex]\red{{1 - 9}}[/tex]

[tex]\red{{- (9 - 1)}}[/tex]

Subtract the numbers

- ([tex]\red{{9 - 1}}[/tex])n

- [tex]\red{{8}}[/tex]n

[tex]\green{\boxed{- 8n}}[/tex]

2.) First, Distribute - 6 through the parentheses

how?

Multiply each term in the parentheses by - 6

[tex]\red{{- 6(b + 10)}}[/tex]

[tex]\red{{- 6b - 6 × 10}}[/tex]

Multiply the numbers

- [tex]{6b}[/tex] - [tex]\red{{6 × 10}}[/tex]

- [tex]{6b}[/tex] - [tex]\red{{60}}[/tex]

Second, Collect like term

how?

Collect like terms by calculating the sum or difference of their coefficient

[tex]\red{{- 6b + 4b}}[/tex]

[tex]\red{{(- 6 + 4)b}}[/tex]

Calculate the sum

[tex]\red{{(- 6 + 4)}}[/tex]b

[tex]\red{{-2}}[/tex]b

[tex]\green{\boxed{- 2b - 60}}[/tex]

3.) First, Distribute 2 through parentheses

how?

Multiply each term in the parentheses by 2

[tex]\red{{2(x - 5)}}[/tex]

[tex]\red{{2x - 2 × 5}}[/tex]

Multiply the numbers

[tex]{2x -}[/tex] [tex]\red{{2 × 5}}[/tex]

[tex]{2x -}[/tex] [tex]\red{{10}}[/tex]

Second, Distribute - 4 through the parentheses

how?

Multiply each term in the parentheses by - 4

[tex]\red{{- 4(3x + 1)}}[/tex]

[tex]\red{{- 4 × 3x - 4}}[/tex]

Calculate the product

- [tex]\red{{4 × 3}}[/tex]x - 4

- [tex]\red{{12}}[/tex]x - 4

Third, Collect like terms

how?

Collect like terms by subtracting their coefficient

[tex]\red{{2x - 12x}}[/tex]

[tex]\red{{(2 - 12)x}}[/tex]

Calculate the difference

[tex]\red{{(2 - 12)}}[/tex]x

[tex]\red{{- 10}}[/tex]x

Fourth, Calculate the difference

how?

Factor out the negative sign from the expression

[tex]\red{{- 10 - 4}}[/tex]

[tex]\red{{- (10 + 4)}}[/tex]

Add the numbers

- ([tex]\red{{10 + 4}}[/tex])

- [tex]\red{{14}}[/tex]

[tex]\green{\boxed{- 10x - 14}}[/tex]

That's all I know sorry but I hope it helps :)

Answer: t=3.75

Step-by-step explanation:45=6t×2

6t=22.5

t=3.75

The object will take 3 seconds to fall 54 feet on Mercury according to the given function f(t) = 6t².

A certain kind of relationship called a function binds inputs to essentially one output.

A function can be regarded as a computer, which is helpful.

Given the function,

f(t) = 6t² where t is time in seconds while f(t) is the distance in feet.

At f(t) = 54 feet

6t² = 54

t² = 54/6 = 9

t = 3 seconds

Hence "The object will take 3 seconds to fall 54 feet on Mercury according to the given function f(t) = 6t²".

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Answer:

hi

Step-by-step explanation:

I'm anmol kulkar from India thanks for free points by

Answer:

The correct answer is B,

3/4.

Step-by-step explanation:

choices A and D, you may have incorrectly formed your answer out of the coefficients in the point (2p,5r). If you picked Choice C, you may have confused r and p.

y=2x+b gives:

5r=2(2p)+b

5r=4p+b

b = 5r−4p.

Next, we can set the two equations equal to b equal to each other and simplify:

b=r−p=5r−4p

3p=4r

Finally, to find

r/p

divide both sides of the equation by p and by 4:

3p=4r

3=4r/p

3/4=r/p

Answer:

5 Remainder 2

Answer:

The answer is 5 remainder 2

Step-by-step explanation:

Answer:

5: 15

10: 30

15: 45

20: 60

answer: ? = 60

Step-by-step explanation:

Answer:

The missing value in the ordered pair is 66

Step-by-step explanation:

Given that:

(12,10) and (-2,r)

Slope = m = -4

We have to find the value of r so that the line has a slope of -4.

Slope is the steepness of line which is denoted by m.

Here,

[tex]x_1=12, y_1=10\\x_2=-2, y_2=r[/tex]

Putting the values in slope of line formula,

[tex]-4=\frac{r-10}{-2-12}\\ -4=\frac{10-r}{-14}\\[/tex]

Multiplying both sides by -14

[tex]-4*-14=\frac{r-10}{-14}*-14\\56=r-10\\56+10=r\\66=r\\ r=66[/tex]

The value of r is 66

Hence,

The missing value in the ordered pair is 66

Answer:

B

Step-by-step explanation:

i did the test

Answer:

16.65

Step-by-step explanation:

37 * 0.45 = 16.65

Answer:

is it 16.65????

Step-by-step explanation:

lol i took the testtt

Answer: B 35/4

Step-by-step explanation:

Answer: 144.84

Step-by-step explanation:

Answer:

copper and illuminum

Step-by-step explanation:

i got it right on the test

Step-by-step explanation:

5-1+0.85= -0.666x

4.85/-0.666= -0.666/-0.666x

x= -5.6

Answer:

the answers are bolded below!

Step-by-step explanation:

1. y-y1=m(x-x1)

line one- 14-4/6-1 = 10/5 = 2

so....     y-1=2(x-4)

simplified     y=2x-7

line two- -2-23/1-6 = -25/5 = -5

so.....      y-6=-5(x-23)

simplified         y=-5x+121

b- they will intersect 1 time at (18.2,29.5)

2. No, it the system has infinitely many solutions, then the lines would be on top of each other. But since there are only two solutions, then your answer would not be infinitely many solutions.

3. y=-2x+1. This would not intersect with y=-2x+3 because they are parallel. the slopes are the same so they will each travel at the same rate but they have different y intercepts.

4. y=-2x+7 ------> x=-1/2y-7/2

y=-3(-1/2y+7/2)+8  -----> y=5

y=-2x+7 --->   5=-2x+7  ----> x=1

one solution at (1,5) because f graphed, the lines would only intersect once.

b- x=5

3x-y=5   --->   3(5)-y=5   --->   y=10

one solution at (5,10) because f graphed, the lines would only intersect once.

c- no solutions because if it were to be graphed, the lines would not intersect at all.

d- no solutions because if it were to be graphed, the lines would not intersect at all.

e- no solutions because if it were to be graphed, the lines would not intersect at all.

i am in algebra two so you can trust my answer. If you need more help lmk in the comments. Happy holidays and stay safe!

Given:

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

Divisor = [tex]x+3[/tex]

To find:

The quotient and remainder.

Solution:

On dividing [tex]3x^3-3x^2-4x+3[/tex] by  [tex]x+3[/tex], we get

[tex]x+3\ |\overline{3x^3-3x^2-4x+3} |\ 3x^2-12x+32[/tex]

         [tex]3x^3+9x^2[/tex]

    [tex]\underline{(-)\quad (-)\quad \quad \quad \quad \quad }[/tex]

                [tex]-12x^2-4x+3[/tex]

                [tex]-12x^2-36x[/tex]

               [tex]\underline{(+)\quad (+)\quad \quad \quad }[/tex]

                             [tex]32x+3[/tex]

                            [tex]32x+96[/tex]

                        [tex]\underline{(-)\quad (-)\quad }[/tex]

                               [tex]\underline{\quad -93\quad }[/tex]

Here,

Quotient = [tex]3x^2-12x+32[/tex]

Remainder = [tex]-93[/tex]

Therefore, the correct option is D.

Step-by-step explanation:

-X - 7 > -6

-7 > X - 6

X < -1

Hence the answer in set notation is (-∞, -1).

Answer:

x<-1

x€(-∞,-1)

Step-by-step explanation:

Yes she made mistake

Here's the correction

Answer:

b = 50 - 5m

Step-by-step explanation:

i think this is correct but i didnt put much thought into it

Answer:

b = 6

Step-by-step explanation:

this is because you have to multiply by 3 on both sides then add 9 on both sides. then you get 6

Answer:

.

Step-by-step explanation:

Answer:300

Step-by-step explanation:

25*8 =200

500-200=300

Answer:

$300

Step-by-step explanation:

25 a week for 8 weeks is a total of 25*8 or 200 so he spent $200

500 - 200 is 300 so he has $300 left

Answer:

I think it’s D

Step-by-step explanation:

Answer:

125x=1000

=8 bags of sand

Step-by-step explanation: