PLEASE HELP ASAP Us the screenshot below

4) The equation of a line in the slope intercept form is expressed as

y = mx + b

where

m represents slope

b represents y intercept. This is also the point where the line cuts across the y axis.

The formula for determining slope is expressed as

m = (y2 - y1)/(x2 - x1)

y2 and y1 are final and initial values of y corresponding to given points on the line and on the vertical axis.

x2 and x1 are final and initial values of y corresponding to given points on the line and on the horizontal axis. From the graph,

when x1 = - 1, y1 = - 4

when x2 = 1, y2 = 2

m = (2 - - 4)/(1 - - 1) = 6/2

m = 3

Slope of the line = 3

y intercept, b = - 1

Thus, equation of the line is

y = 3x - 1

Answer:

5.7 liters of 5% solution and 4.3 liters of 40% solution is needed to be mixed to get 10 liters of a 20% acid solution

Step-by-step explanation:

Let

x = Amount of 5% solution needed

(10 - x) = Amount of 40% solution needed

Equation:

5% of x + 40% of (10-x) = 20% of 10

0.05x + 0.40(10-x) = 0.20 * 10

Open parenthesis

0.05x + 4.0 - 0.40x = 0.20 * 10

Collect like terms

4.0 - 0.35x = 2.0

Add 0.35x to both sides of the equation

4.0 = 2.0 + 0.35x

Subtract 2.0 from both sides of the equation

2.0 = 0.35x

Divide both sides by 0.35

2.0 / 0.35 =x

5.7 = x

5.7 liter of the 5% solution is needed

Next is to find the amount of 40% solution needed

(10 - x) = Amount of 40% solution used

Amount of 40% solution used = 10 - 5.7

= 4.3

4.3 liters of 40% solution is needed

Answer:

x < 10

set builder notation: (-∞ , 10)

Step-by-step explanation:

2(x - 4) < 12

multiply left side out:

2x - 8 < 12

add 8 to both sides:

2x - 8 + 8 < 12 + 8

2x < 20

divide both sides by 2:

2x/2 < 20/2

x < 10

in set builder notation: (-∞ , 10)

Therefore, there are 24,387,120 different line-ups permutation that can be made with 17 players for 9 positions.

The number of different line-ups that can be made with 17 players for 9 positions can be calculated using the permutation formula:

P(17, 9) = 17! / (17 - 9)!

where "!" represents the factorial function.

P(17, 9) = 17! / 8!

= (17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 9) / (1 x 2 x 3 x 4 x 5 x 6 x 7 x 8)

= 24,387,120

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Answer:

b/c

Step-by-step explanation:

a/b is the equivalent of b/c, sorry if this is incorrect.

Answer: 6 ft

Step-by-step explanation:

20/25 = 5/x

multiply using butterfly then divide

sry if i’m wrong

Answer:

(0,0)

(2,2)

(0,1)

Step-by-step explanation:

All of these points lie inside

Answer:

Answer:

B

Step-by-step explanation:

This is just -10³, so it is -1,000. Hope this helps!

Answer:

Below.

Step-by-step explanation:

What we know: 4 Shaded. 12 in total.

That means,

12 divided by 4=3.

1/3 of the shape is shaded.

Answer:

picture of answer on edge 2023.

Step-by-step explanation:

Answer:

C. x > 15

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer: The nth term is \(a_n = n^2 - 6\)

n is any positive integer (1,2,3,...)

===================================================

Work Shown:

The jump from -5 to -2 is +3

The jump from -2 to 3 is +5

The jump from 3 to 10 is +7

The jump from 10 to 19 is +9

Focusing on the increases we see: 3, 5, 7, 9

This is an arithmetic sequence of its own. It steadily increases by 2 each time. Because of this, we can say that the original sequence is a quadratic one.

It is of the form an^2 + bn + c

-----------

Plug in n = 1 to get

an^2 + bn + c = a(1)^2 + b(1) + c = a+b+c

This is set equal to -5 as this is the first term; meaning we have a+b+c = -5

-----------

Now plug in n = 2

an^2 + bn + c = a(2)^2 + b(2) + c = 4a+2b+c

Set this equal to -2, as this is the second term, getting 4a+2b+c = -2

-----------

Plug in n = 3 and follow the same basic steps as before

an^2 + bn + c = a(3)^2 + b(3) + c = 9a+3b+c

We get 9a+3b+c = 3 due to 3 being the third term

-----------

The system of equations we end up with are

\(\begin{cases}a+b+c = -5\\4a+2b+c = -2\\9a+3b+c = 3\end{cases}\)

Solve this system however you like. One option is to use a matrix (either inverse or RREF), or you could use elimination. Graphing is not really feasible here. Whichever method you pick, you should end up with the solution (a,b,c) = (1,0,-6)

Meaning, a = 1, b = 0, c = -6

Therefore, an^2 + bn + c would update to 1n^2+0n+(-6) which is the same as n^2 - 6 which is the nth term we're after

-----------

As a check, plug in n = 1 and see what happens. We should get -5 as a result

n^2 - 6 = 1^2 - 6 = -5

Checks out. Let's try n = 2

n^2 - 6 = 2^2 - 6 = -2

That works as well. I'll let you check the others.

Answer:  I believe it's (x-1) 2+(y-1) 2=13

Answer:

a number or placement number

Step-by-step explanation:

Answer:

"m" refer to the gradient

The measure of DE is 8x. This was found by using the distance formula to calculate the length of the side.

Measurements are the process of comparing an unknown quantity to a known reference value in order to estimate the size, quantity, distance, weight, or other characteristics of that unknown quantity. Measurements are used in science and engineering to quantify the properties of objects, or to compare objects to each other. Measurements are also used in everyday life to help make decisions and assess the impact of changes.

To find the measure of DE, we must first calculate the length of the side. We can do this by using the distance formula. The distance formula is used to calculate the length of a line between two points in a plane. The formula is given as d = √(x2 - x1)2 + (y2 - y1)2.

For the side DE, we can use the coordinates (2x+7, 4(x-3)). The first point is (2x+7, 4(x-3)) and the second point is (2x+7, 4(x+3)). We can substitute these points into the distance formula to calculate the length of DE.

The formula becomes d = √[(2x+7 - 2x+7)2 + (4(x+3) - 4(x-3))2]

Simplifying, we get d = √[(0)2 + (8x)2]

d = √[64x2]
d = 8x

Therefore, the measure of DE is 8x.

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Answer:

1. y= 2/5x+11

2. y=3x-15

2y-5x=9

Step-by-step explanation:

I did this already

Answer:

The sign would be turned into an equal sign

Step-by-step explanation:

4(-3)= -12

A negative times a positive is a negative.

-12 = -12

Answer:

x=7

Step-by-step explanation:

expand -2(2x-3): -4x+6

expand 4-(3x-5): -3x-1

it's now -4x+6=-3x-1

subtract 6 from both sides

-4x+6-6=-3x-1-6

simplify

-4x=-3x-7

add 3x to both sides

-4x+3x=-3x-7+3x

simplify

-x=-7

divide both sides by -1

\(\frac{-x}{-1}\)=\ \(\frac{-7}{-1}\)

simplify

x=7

sorry for the lengthy explanation hope this helps :) have a nice day !!

The statement is proven true by induction: for any positive integer n, the sum of (2i - 1)³ from i = 1 to n is equal to n²(2n² - 1).

To prove the statement using mathematical induction, we need to establish two conditions: the base case and the inductive step.

Base Case:

Let's start with the base case, where n = 1.

When n = 1, we have p₁ ∑ (2i - 1)³ = 1³ = 1.

On the right-hand side, we have 1 * (2 * 1² - 1) = 1.

Since the statement holds true for n = 1, the base case is satisfied.

Inductive Step:

Next, we assume that the statement holds true for some positive integer k, i.e., pₖ ∑ (2i - 1)³ = k²(2k² - 1).

Now, we need to prove that the statement also holds for n = k + 1, i.e., pₖ₊₁ ∑ (2i - 1)³ = (k + 1)²(2(k + 1)² - 1).

Starting with the left-hand side:

pₖ₊₁ ∑ (2i - 1)³ = (pₖ ∑ (2i - 1)³) + (2(k + 1) - 1)³

                 = k²(2k² - 1) + (2k + 1)³ (using the inductive hypothesis)

                 = 2k⁴ - k² + 8k³ + 12k² + 6k + 1

Simplifying the right-hand side:

(k + 1)²(2(k + 1)² - 1) = (k² + 2k + 1)(2k² + 4k + 2 - 1)

                         = 2k⁴ + 4k³ + 2k² + 4k³ + 8k² + 4k + 2k² + 4k + 2 - k² - 2k - 1

                         = 2k⁴ + 8k³ + 12k² + 6k + 1

Comparing the left-hand side and right-hand side, we can see that they are equal.

Therefore, by the principle of mathematical induction, the statement is proven true for all positive integers n.

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Answer:

Step-by-step explanation:

The answer is Samples. A sample is a random selection of members of a population. It is a smaller group drawn from the people with the entire population's characteristics.

I hope I have helped.

Answer:

D. 29

Step-by-step explanation:

just did the test and got it correct. Edmentum, Plato.

Answer:

y=2

Step-by-step explanation:

Answer:

step 1 is commutative property of addition

step 2 is commutative property of multiplication

step 3 is distributive property

Answer:

Step 1- commutative property of addition

Step 2- distributive property

Step 3- associative property of addition

:)

The maximum abundance of species 1 if 250 of species 2 coexists with it is B. 500.

Determine the carrying capacity ratio between species 1 and 2.
Carrying capacity of species 1 = 1000
Carrying capacity of species 2 = 500
Ratio = 1000 / 500 = 2

Calculate the abundance of species 1 considering the presence of species 2.
Abundance of species 2 = 250
Abundance of species 1 = 2 * 250 = 500

So, the maximum abundance of species 1 if 250 of species 2 coexists with it is 500 (Option B).

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Polynomial \(-4x^2y\) is called a monomial of degree 3 and a polynomial \(3x^4 - 2x^3 - 5x^2 + 6x - 12\) is a quintic polynomial.

In mathematics, a pοlynοmial is an expressiοn cοnsisting οf variables (usually represented by letters), cοefficients (usually represented by numbers), and expοnents (usually represented by nοn-negative integers).

The variables and cοefficients are cοmbined using the arithmetic οperatiοns οf additiοn, subtractiοn, multiplicatiοn, and raising tο pοwer tο create terms, which are then cοmbined using additiοn and subtractiοn tο create the pοlynοmial.

1) The polynomial \(-4x^2y\) has a degree of 3 and a single term, so it is called a monomial of degree 3.

2) The polynomial \(3x^4 - 2x^3 - 5x^2 + 6x - 12\) has a degree of 4 and five terms, so it is called a polynomial of degree 4 and five terms, or simply a quintic polynomial.

3) The polynomial \(x^2 + 5x - 4\) has a degree of 2 and three terms, so it is called a polynomial of degree 2 and three terms, or simply a quadratic polynomial.

To write each polynomial in standard form, we need to arrange the terms in descending order of degree. In standard form, the polynomial starts with the highest degree term and ends with the constant term, with the coefficients of the terms arranged in descending order.

4) \(x^3 + 3x^2 - 5x - 4\)

5) \(-x^5 + 4x^4 + 2x^3 + 2x - 7\)

6) \(-x^2 + 5x + 9\)

To combine like terms and write each expression in standard form, we need to simplify the coefficients of each variable to obtain the sum of the like terms:

7)  \(-5y + 3y^2 + 2y - 2y^2 - 9\)

=\((3y^2 - 2y^2) + (-5y + 2y) - 9\)

=\(y^2 - 3y - 9\)

8)  \(-2x^2 + x + 5x^3 + 4x + 2x^2\)

= \(5x^3 + 3x\)

9) \(x^2 - 5 + 2x + x^2\)

= \(2x^2 + 2x - 5\)

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The equation of the tangent line to the curve y = ln(x^2 - 2x + 1) at the point (2, 0) is y = 2x - 4.

First, let's find the derivative of the function

y = ln(x^2 - 2x + 1).

Using the chain rule, the derivative is given by:

dy/dx = (1 / (x^2 - 2x + 1)) * (2x - 2) = (2x - 2) / (x^2 - 2x + 1)

Now, we can find the slope of the tangent line at x = 2 by substituting the x-coordinate of the given point into the derivative:

m = (2(2) - 2) / ((2)^2 - 2(2) + 1) = 2 / 1 = 2

So, the slope of the tangent line at the point (2, 0) is 2.

Next, we can use the point-slope form of the equation of a line to find the equation of the tangent line.

Given the point (2, 0) and the slope m = 2, the equation of the tangent line is:

y - 0 = 2(x - 2)

Simplifying this equation gives us the equation of the tangent line:

y = 2x - 4

Therefore, the equation of the tangent line to the curve y = ln(x^2 - 2x + 1) at the point (2, 0) is y = 2x - 4.

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Answer:

3%

Step-by-step explanation:

percent of two numbers x and y

x as a percent of y is given by x/y * 100

given

Total bill = $11.18

in the bill , tax amount = $0.33

thus,

tax as percent of total bill is =  tax amount /Total bill  * 100

tax as percent of total bill is = 0.33 /11.18  * 100= 2.95 %

Thus,

tax percentage is 2.95%

tax percentage to nearest whole number is 3%

(a) the sample mean is 0.0494 and the sample variance is 0.000016, (b) the upper quartile is 0.04775, and the lower quartile is 0.0510, (c) the sample median is 0.04975, (d) boxplot is attached, and (e) the 5th and 95th percentiles of the inside diameter are 0.03974 and 0.056995 respectively.

(a) The mean = sum of all values divided by the number of values

μ = (x1 + x2 + ..... + xn)/n

n = 20

μ = (0.0395 + 0.0443+ 0.0450 + ... + 0.0550 + 0.0571)/20

μ = 0.9878/20

μ = 0.0494

(b) Variance = sum of squared deviations from the mean divided by n-1

s² = {(x1-μ)² + (x2-μ)² + .... (xn - μ)²)/(n-1)

s² = {(0.0395-0.0494)² + (0.0443-0.0494)² + .... +(0.0571-0.0494)²}/19

s² = 0.000016

(b) The minimum is 0.0395 and the maximum is 0.0571.

since the number of data is even, the median will be the average of two middle values.

M = Q2 = (0.0496+0.0499)/2 = 0.04975

Now, the first quartile is the median of the data values below the median

so Q1 = (0.0470+0.0485)/2 = 0.04775

And third quartile will be the median of the data values above the median

Q3 = (0.0504+0.0516)/2 = 0.0510

(c) Since we know that the number of data values is even, the median will be the average of the two middle values of the data set

so M = (0.0496+0.0499)/2

or M = 0.04975

(d) The boxplot is at maximum and minimum values. It will start in Q1 and end in Q3 and has a vertical line at the median or Q2.

The boxplot is attached.

(e) The 5th percentile means 0.05(n+1)th data value

or = 0.05(20+1) = 1.05th data value

5th percentile = 0.0550 + 0.05(0.0443-0.0395) = 0.03974

similarly,

95th percentile = 0.0550 + 0.95(0.0571-0.0550) = 0.056995

Therefore, (a) the sample mean is 0.0494 and the sample variance is 0.000016, (b) the upper quartile is 0.04775, and the lower quartile is 0.0510, (c) the sample median is 0.04975, and (e) the 5th and 95th percentiles of the inside diameter are 0.03974 and 0.056995 respectively.

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