The price of a mathematics book is $50.00, but you have only $35.00with you. If you get a discount of 20%, how much money do youneed to borrow from a friend so that you can buy the book?

Answer:

I Believe the answer is 20

Here you go enjoy

Have a good rest of your night

Answer:

3/13

Step-by-step explanation:

We put this equation into slope-intercept form by adding 13y to both sides. Then we divide both sides by 13. Lastly, the number we multiply x by equals our slope.

Answer:

a) 15 000 litres

b) 1/3

Step-by-step explanation:

a) Since the pool has 7500 litres when half full, it must have double that when full.

7500 * 2 = 15 000

b) Since the full pool is 15000, when the pool has 5000 litres it has 5000 out of 15000, hence the fraction 5000/15000 which simplifies to 1/3.

Simplification: divide the numerator and denominator by 5000.

Answer:

a) 15000

b) 1/3

Step-by-step explanation:

Answer:

4.5

Step-by-step explanation:

3/2+ 1/2 = 4/2 = 2

2(2)+1/2

4 + 1/2

4 1/2 or 4.5 in decimal form

Answer:

B) Convergent infinite geometric series sum to a single value

Step-by-step explanation:

An infinite geometric series of the form [tex]\[ \sum_{r=1}^{\infty} ar^{n-1}[/tex] converges if [tex]|r|<1[/tex], so the summation of the series will result in a single value if that is true.

The sequence of numbers when x₁ = 1 of the given series [tex]x_{n+1}[/tex] =  [tex]{x_{n}}^2[/tex] + xₙ will be 1,  2,  6,  42,...

A sequence's series is the total number of terms in the sequence.

A series follows some pattern for example if you take data set of natural numbers then there will be a sequence of that data and something will be due to that we can form that series.

As per the given series,

[tex]x_{n+1}[/tex] =  [tex]{x_{n}}^2[/tex] + xₙ

Substitute,n = 1 into

x₂ = x₁² + x₁

x₂ = (1)² + 1 = 2

Substitute,n = 2

x₃ = x₂² + x₂

x₃ = 2² + 2

x₃ = 6

Substitute,n = 3

x₄ = x₃² + x₃

x₃ = 6² + 6

x₃ = 42

Hence "The sequence of numbers when x₁ = 1 of the given series [tex]x_{n+1}[/tex] =  [tex]{x_{n}}^2[/tex] + xₙ will be 1,  2,  6,  42,...".

For more information about the series,

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The given question is incorrect,correct question is,

A sequence of numbers is formed by the iterative process xn+1=(xn)^2+xn Describe the sequence of numbers when x1=1

Show your working to justify your answer

If your teacher wants you to find a positive integer for n that will make [tex]n^3+2n[/tex] not divisible by 3, then you'll be searching for quite a while.

This is because Rehan is correct in the statement that [tex]n^3+2n[/tex] is divisible by 3 for any positive integer n.

n = {1,2,3,...}

For example, if n = 5, then

[tex]n^3+2n = 5^3+2(5) = 125+10 = 135[/tex]

That is divisible by 3 because 135/3 = 45 is a whole number result without any decimal or fractional extras.

---------------

Here's the proof that Rehan probably used or set up.

Base case: Plug in n = 1 to find that [tex]n^3+2n = 1^3+2(1) = 3[/tex] which is definitely divisible by 3.

Inductive step:

Assume that [tex]k^3+2k[/tex] is divisible by 3 for some integer k > 1.

The goal is to then show it leads to [tex](k+1)^3+2(k+1)[/tex] is also divisible by 3.

Skipping a bunch of steps, you should find that [tex](k+1)^3+2(k+1) = (k^3+2k) + 3(k^2+k+1)[/tex]

The first part k^3+2k is already assumed to be a multiple of 3, so we don't need to worry about it. The second part 3(k^2+k+1) is also a multiple of 3 because 3 is a factor.

Summing any two multiples of 3 gets us another multiple of 3.

Therefore, this concludes the proof that Rehan would have done. There are probably alternative proof methods he could have used, but he likely followed these steps or similar when doing the induction proof.

---------------

Long story short, the fact that the statement [tex]n^3+2n \text{ is divisible by } 3[/tex] is proven to work with any integer n from the set {1,2,3,...} means that we cannot find a counterexample.

Answer:

24 1/4

Step-by-step explanation:

Multiply the 17 and 2/4 by 2 and then subtract.

Answer:

y = -3x + 2.5

Step-by-step explanation:

3x + 2y = 5

-3x              -3x

2y = 5 -3x

/2     /2

y = -3x + 2.5

Answer:

40+4.5p=112, and 16

Step-by-step explanation:

Roger always starts off with the same $40. Then, he gets $4.5 for every pair of shoes he sells. So, if the number of shoes sold is p, we then have the equation:

40+4.5p=112

The next part of the question asks for us to solve this equation, basically. We subtract 40 from both sides:

4.5p=72

p=72/4.5 (Divide both sides by 4.5)

p=16

Answer:

396 in

Step-by-step explanation:

Circumference of circle = [tex]\pi[/tex]d

(where d is the diameter)

Therefore, using [tex]\pi[/tex] = 22/7:

circumference = (22/7) x 126 = 396 in

Answer:

[tex]x=\frac{2\pm i\sqrt{6}}{2}[/tex]

Step-by-step explanation:

[tex]-2x^2+4x=5\\\\-2x^2+4x-5=0\\\\x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\ \\x=\frac{-4\pm\sqrt{(4)^2-4(-2)(-5)}}{2(-2)}\\\\x=\frac{-4\pm\sqrt{16-40}}{-4}\\\\x=\frac{-4\pm\sqrt{-24}}{-4}\\ \\x=\frac{-4\pm2i\sqrt{6}}{-4}\\ \\x=\frac{2\pm i\sqrt{6}}{2}[/tex]

Answer:

∠C and ∠R

Step-by-step explanation:

1. ∠C and ∠T don't match

- One slanted, One Straight

2. ∠D and ∠T don't match

- One slanted, One Straight

3. ∠C and ∠R both match

- Both Straight

4. ∠D and ∠U don't match

- One slanted, One Straight

Answer:

D

Step-by-step explanation:

out of the choices

A) 2x-y=-2

3x+2y=-10

B) x+4y=3

2x+5y=3

C) 2x+3y=5

x-4y=-14

D) 3x+4y=15

x+y=5

only the system in D has a solution of x=5 and y=0

solve by substitution x+y=5 so x=5-y

plug into the other equation so 3(5-y)+4y=15

distribute 15-3y+4y=15 then minus 15 on both sides and combine like terms

so y=0 then put that value back into the other equation

so x+y=5 equals x+0=5 so x=5 this means the solution to the system of equations is the point (5,0)

Hope this helps! :)

Answer:

2m + 4n

Step-by-step explanation:

What's distributive property?

Given the information above, let's distribute 2 to m and 2n.

Therefore, the answer is 2m + 4n.

Have a lovely rest of your day/night, and good luck with your assignments! ♡

Answer:

284.6 cm^2

Step-by-step explanation:

if the radii of inner circles are 3 and 7 respectively, then radius of big circle is 10

100×3.14 = 314 cm^2

Answer: M∠2 just mean measure of angle 2,

Step-by-step explanation: So I worked it out and the awnser is B.

3 numbers/the degrees of all 3 sides always add up to 180 degrees.

Side 1 is 60 degrees and the left side is 20, so 20 + 60 + 3 (unkown    number) = 180

60 - 20 = 100,

Answer:

[tex]\frac{2x+4}{x^{2}-x-6 } \\\frac{2x+4}{x^{2} +2x-3x-6} \\\frac{2x+4}{x(x+2)-3(x+2)} \\\frac{2x+4}{(x-3)(x+2)}[/tex]

Step-by-step explanation:

Answer:

B. 8(2-y)

Step-by-step explanation:

22-10y+2(y-3)

22-10y+2y-6

22-6-10y+2y

16-8y

Using factorisation method

8(2-y)

Using the binomial distribution, it is found that there is a 0.985 = 98.5% probability that you will need to "walk" a guest tonight.

For each guest, there are only two possible outcomes, either they arrive, or they do not. The probability of a guest arriving is independent of any other guest, hence, the binomial distribution is used to solve this question.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

In this problem:

If at least one shows up, you will need to "walk" a guest tonight, hence the probability is:

[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]

In which:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{4,0}.(0.65)^{0}.(0.35)^{4} = 0.015[/tex]

Then:

[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.015 = 0.985[/tex]

0.985 = 98.5% probability that you will need to "walk" a guest tonight.

You can learn more about the binomial distribution at https://brainly.com/question/24863377

Answer:

p(t) = 0 for t = 1

p(t) = 1 for t = 1/8 = 8^-1

Step-by-step explanation:

the graph you will have to do yourself.

just go there and type in

[tex] - log_{8}(x) [/tex]

well, don't type "log" in letters.

you start by typing the "-" sign, and then you need to look up the functions by clicking on the "funcs" button and look for the log functions .

pick the

[tex] log_{a}[/tex]

option. and then simply enter 8 as the first parameter in the {} brackets and x as the second in the () brackets.

and then you see.

any logarithm is 0 for x (or t) = 1.

because any a⁰ = 1.

and the logarithm gives you that exponent of the base number that leads to the given x value.

in other words : a logarithm is the inverse function of an exponential function.

the exponential function is

y = a^x

and the logarithm then determines

[tex]x = log_{a}(y) [/tex]

that is all.

and

[tex] - log_{8}(x) = 1[/tex]

means that the logarithm itself delivered -1.

and 8^-1 = 1/8

so, p(t) = 1 for t = 1/8

The area of the polygon JKLMNO is 68.5 square units

The coordinates of the triangle are:

M = (-1, -5)

N = (-8, -6)

O = (-5, -2)

Calculate the base and the height of the triangle using:

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

So, we have:

[tex]ON = \sqrt{(-5+ 8)^2 +(-2 + 6)^2[/tex]

ON = 5

[tex]OM = \sqrt{(-5+ 1)^2 +(-2 + 5)^2[/tex]

OM = 5

The area is:

Area = 0.5 * ON * OM

This gives

Area = 0.5 * 5 * 5

Evaluate

Area = 12.5

Hence, the area of the triangle MNO is 12.5 square units

The coordinates of the rectangle are:

J = (1, 6)

L = (5, 3)

M = (-1, -5)

O = (-5, -2)

Calculate the length and the width of the rectangle using:

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

So, we have:

[tex]OM = \sqrt{(-5+ 1)^2 +(-2 + 5)^2[/tex]

OM = 5

[tex]ML = \sqrt{(-1 - 5)^2 + (-5 - 3)^2[/tex]

ML = 10

The perimeter is:

Perimeter = 2 * (OM + ML)

This gives

Perimeter = 2 * (5 + 10)

Evaluate

Perimeter = 30

Hence, the perimeter of the rectangle JLMO is 30 units

In (a), we have:

The area of the triangle MNO is 12.5 square units

The area of the rectangle JKMO is:

Area = OM * ML

This gives

Area = 5 * 10 = 50

The coordinates of triangle JKL are:

J = (1, 6)

K = (5, 6)

L = (5, 3)

Calculate the base and the height of the triangle using:

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

So, we have:

[tex]KL = \sqrt{(5- 5)^2 +(3 - 6)^2[/tex]

KL = 3

[tex]JK = \sqrt{(1- 5)^2 +(6 - 6)^2[/tex]

JK = 4

The area of JKL is

Area = 0.5 * KL * JK

This gives

Area = 0.5 * 3 * 4

Area = 6

Add the three areas

Total area = 6 + 12.5 + 50

Evaluate

Total area = 68.5

Hence, the area of the polygon JKLMNO is 68.5 square units

Read more about area and perimeter at:

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Answer:

y = (slope) + (y-intercept)

Step-by-step explanation:

You put them both together.

Answer:

Solution,

[tex]5x+12=6x-10\\12+10=6x-5x\\22=x\\x=22[/tex]

Step-by-step explanation: They are equal because they are vertically opposite angles.

Hope it will help you.

Answer : 4/7

Here it's given that Brad's family travelled 2/7 of the total distance to his uncle's house on Saturday . So if we assume the total distance to be 1 , then the remaining distance will be ,

[tex]\sf\longrightarrow 1 - \dfrac{2}{7}=\dfrac{7-2}{7}=\boxed{\dfrac{5}{7}}[/tex]

Again it's given that they travelled 4/5 of the remaining distance on Sunday . So , the distance travelled would be ,

[tex]\sf\longrightarrow \dfrac{4}{5}\times \dfrac{5}{7}=\boxed{\sf \dfrac{4}{7}} [/tex]

Therefore Brad's family travelled 4/7 of the total distance on Sunday .