Laura bought some books. She spent a total of $71 after a discount of $5 off of her total purchase. Each book cost $4. How many books did she buy?

Answer:

a) A-B = { 1 , 3, 5 }

b) The remainder is 50

c) f + g)(x) = x⁴+ 5x³

d) [tex]\frac{dy}{dx} = \frac{2x- y^3(3x^2)) }{ 1- x^3 3y^2}[/tex]

Step-by-step explanation:

Step(I):-

1) a)

Let A = { 1, 3, 5, 7 } and B = { 7 , 14 , 21 }

A - B = {1,3,5,7} - { 7,14,21}

A - B  = { 1 , 3, 5}

b)

Given f (x)=3x³−11x−48

    x-1  ) 3 x³ - 11x -48 (- 3x²-3x -2

            -3x³ +3x²

                 3x²-11x-48

                -3x²+9x

                     2x -48

                    -2x +2  

                         50

The remainder is 50

c)  Given f(x) = x³ and g(x) = x + 5

(f. g)(x) = f(x) .g(x) = x³ . (x+5) = x³(x) + 5 x³ = x⁴+ 5x³

d)

 Given function   y = 3 + x²+x³y³  ...(I)

By using derivative formulas

            y = xⁿ

            [tex]\frac{dy}{dx} = n x^{n-1}[/tex]

Apply d/dx ( UV) = U V¹ + V U¹



Differentiating equation (I) with respective to 'x' , we get

                      [tex]\frac{dy}{dx} = 0 + 2x + ( x^3 3y^2(\frac{dy}{dx} )+ y^3(3x^2))[/tex]

                     [tex]\frac{dy}{dx} - ( x^3 3y^2(\frac{dy}{dx} )= 2x- y^3(3x^2))[/tex]

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



Answer:

Not possible

Step-by-step explanation:

Given quadratic polynomial = x² + 2x + 3.

Possible factors of 3 are , 1 & 3 .

And we can get 2 from 3 and 1 in only one way that is 3 - 1 .

=> x² + 2x + 3 .

=> x² + 3x - x + 3 .

=> x ( x + 3 ) - 1 ( x - 3 )

Hence the factorisation is not possible .

Answer:

1.75qt

Step-by-step explanation:

Answer:

The basketball travels in a parabolic route in order to engage in the passage through the net.

Step-by-step explanation:

Answer:

So?

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

where is the functions

Step-by-step explanation:

Answer:

The are 8 dimes and 12 nickels

Step-by-step explanation:

1.We set n+d=20 because 20 is the total number of dimes and nickels in the jar.We have $0.05 n because for ever nickel,we earn $0.05.Adding this to the value of dimes,represented similarly by $0.1,then we set this to the amount of money we have in total,which is $1.40.

2.Subtract d from both sides of the first equation to get it by itself.Substitute-d for n in the second equation.The divide both sides by 0.5 to obtain the answer.

3.Substitute 8 in for d to obtain the value or n.

Answer:

d. nq / q - 1

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define

q = d / (d + n)

Step 2: Solve for d

Answer:

DRFHDFG

Step-by-step explanation:

6=6+4

Answer: A

Step-by-step explanation:y=2x−2 2.00AM 2°c and rises 2°C each hour for x hours

Answer:

the ratio is 1:3 for brown sugar to sugar

Answer:

Step-by-step explanation:

Sorry for the shadow.

Step-by-step explanation:

D. 10 %

hope it helps!

.......

Answer:

normal distribution can be used to model the sample proportions

Step-by-step explanation:

N ( sample size ) = 100

probability of earning high school diploma (p)  = 0.87

probability of not earning high school diploma ( q ) = 0.13

hence ;

∈( P ) = p = 0.87

Var ( p ) = [tex]\frac{pq}{n}[/tex]  = [tex]\frac{0.86 * 0.13 }{100}[/tex]  = 0.001131

therefore ; p ~ N = ( 0.87 , 0.001131 )

Answer:

4.42 is the answer........

Step-by-step explanation:

Im not sure

Answer:

60 of each

Step-by-step explanation:

water          juice

12                10

24               20

36               30

48               40

60               50

                  60

Answer:

Option 2

Step-by-step explanation:

Number of breakdowns of the photocopiers in year 2011,

A1 = 15

A2 = 21

B1 = 34

B2 = 32

B3 = 23

Option (1)

A1 had just under a half the number of breakdowns compared to photocopier B3.

Half of B3 = 12

And A1 = 15

Therefore, A1 > B3

So the statement is False.

Option (2)

A1 had just under 50% of the breakdowns compared to photocopier B2

50% of the breakdowns of B2 = 16

A1 = 15

So, A1 < 50% of B2

Statement (2) is True.

Option (3)

A1 had more than 25 extra breakdowns compared to B1.

A1= 15

B1 = 34

A1 < B1

Therefore, statement is False.

Option (4)

A1 had 6% less breakdowns than photocopier A2.

A1 = 15

A2 = 21

A2 - A1 = 21 - 15 = 6

Percentage less breakdowns = [tex]\frac{6}{21}\times 100[/tex] = 28.6%

So this Option is False.

Therefore, Option (2) is the correct option.

Answer:

25% off

Step-by-step explanation:

$32 is 100%. 8 dollars was taken away, and since 8 is 1/4 of 32, we can divide 100% by 4 to get 25%. 25% is $8

Answer:

25%

Step-by-step explanation:

24/32=0.75

100-0.75= 0.25

So 25% off.

Hope that helped! (ﾉ◕ヮ◕)ﾉ*:･ﾟ✧

( ﾟдﾟ)つ Bye

Answer:

What is the question?? The question is not there

Answer:

129870 did not vote or voted for someone else.

Step-by-step explanation:

I don't know what your asking

Answer:

area = 4π-8 cm²

Answer:

2^4 x 5^3 x 70289

Step-by-step explanation:

16 x 125 x 70289=140,578,000

Answer:

A) 2.5

Step-by-step explanation:

20/8 = 2.5

Answer:

Step-by-step explanation:

99 + 99x = 0

Subtract 99 from both sides:

99x = -99

Divide both sides by 99

X = -1

Answer:

[tex]x = - 1[/tex]

Step-by-step explanation:

[tex]99 + 99x = 0 \\ collecting \: like \: terms \\ 99x = - 99 \\ divide \: by \: 99 \: on \: both \: sides \\ \frac{99x}{99} = \frac{ - 99}{99} \\ x = - 1[/tex]

15

Step-by-step explanation:

4t + 2u²- u³

4×2=8

2×1=2²=8

1³=1

8+8-1

16-1=15

Answer:

0.2 cups of sugar

Step-by-step explanation:

Make a proportion:

5 cups / 25 cookies = x cups / 1 cookie ---> 0.2

Answer:

I'm verrry sorry if i get it wrong plz forgive me if it is but here is my hypothesis.

Step-by-step explanation:

You just divide 5 by 25 which would be 0.2 and so it would be 0.2:1 or 0.2 per cookie

plz mark me brainliest!

514.8 your welcome

All you have to do is multiply 19.8 x 26

The slope intercep equation of the following points  (0,5) (3,4) will be y = (-1/3)x + 5.

A slope-intercept equation is the equation of the two variables x and y in which the form of the equation should be in such a way that it should contain the slope of the given equation.

For example, in the equation, y = mx + c here m will be the slope of the equation and this is the slope-intercept equation.

Another example is y = 3x + 7 here 3 will be the slope of that equation.

Slope m = difference in y coordinate/ difference in x coordinate.

Let's suppose our equation is y =mx + c

now m = (4 - 5)/(3 - 0)

m = -1/3 now for c put both point in the equation we get as 5.

So y = (-1/3)x + 5 will be correct slope intercept form.

For more information about slope intercept form

https://brainly.com/question/9682526

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Method 1: A pure algebraic approach

The unknown in this problem is the percent of decrease. A percent of decrease is the percentage of the original price that was deducted from the original price to obtain the sale price. We could write a "word equation" for this process like this:

original price - (percent of decrease)(original price) = sale price

Since the percent of decrease is the unknown in this problem, we'll call the percent of decrease x%.

Here's what we know so far:

The original price was $200

The sale price was $170

The percent of increase was x%

Putting this information in our word equation gives us an algebraic equation:

200 - (x%)(200) = 170

What do we do with the percent sign in this equation? "Percent" means "out of 100", so x% means x out of 100, or . Now we have this:

200 - (200) = 170

Now we'll solve our equation:

200 - (200) = 170

200 - 2x = 170

-2x = -30

x = 15

So the percent of decrease is 15%

Method 2: A method involving pure arithmetic.

If we know the original price and the sale price, we can find the percent of decrease in two steps:

Find the amount of decrease

Divide the amount of decrease by the original amount

This will give us the percent of decrease (written as a decimal number). We can then write the decimal as an equivalent percent to find our final answer.

Let's use method 2 on the same problem:

Frank bought a new television set on sale. If the TV's original price was $200 and Frank paid $170 for the TV, what was the percent of decrease?

First, let's find the amount of decrease:

Amount of decrease = 200 - 170 = 30

So the price decreased by $30.

Next, we'll find the percent of decrease, and rewrite the decimal answer as a percent:

Percent of decrease =  = = .15 = 15%

So the percent of decrease is 15%

Before we leave the problem, let's check our answer:

Original price = $200

Price reduced by 15% of original price = 200(.15) = $30

Sale price would then be = $200 - $30 = $170

Our answer checks. We're done!    Me not know if correct.