The function f(x) = x2 is graphed above. Which of the graphs below represents the function g(x) = (x + 1)2? A parabola declines through (negative 2, 5), (negative 1 point 5, 3), (negative 1, 2), (0, 1) and rises through (1, 2), (1 point 5, 3) and (2, 5) on the x y coordinate plane. W. A parabola declines through (negative 2, 3), (negative 1 point 5, 1), (1, 0), (0, negative 1) and rises through (1, 1), (1 point 5, 1) and (2, 2) on the x y coordinate plane. X. A parabola declines through (negative 3, 4), (negative 2 point 5, 2), (negative 2, 1), (negative 1, 0), (0, 1), (0 point 5, 2) and (1, 4) on the x y coordinate plane. Y. A parabola declines through (negative 1, 4), (negative 0 point 5, 2), (0, 1) and (1, 0) and rises through (2, 1), (2 point 5, 2) and (3, 4)  on the x y coordinate plane. Z. A. W B. X C. Y D. Z'

1) the midpoint of the line segment is (2, 2.5). 2) the slope of the line is -3.25.  3)the length of the line segment is approximately 13.60.    4) the equation of the line is y = -3.25x + 9.

what is slope ?

In mathematics, the slope of a line is a measure of its steepness, defined as the ratio of the vertical change (rise) between two points on the line to the horizontal change (run) between the same two points. It is often denoted by the letter "m".

In the given question,

To find the midpoint of the line segment that connects the points (4,-4) and (0,9), we use the midpoint formula:

Midpoint = ((x₁ + x₂)/2, (y1 + y₂)/2)

Midpoint = ((4 + 0)/2, (-4 + 9)/2)

Midpoint = (2, 2.5)

So the midpoint of the line segment is (2, 2.5).

To find the slope of the line that passes through the two given points, we use the slope formula:

Slope = (y₂ - Ly₁)/(x₂ - x₁)

Slope = (9 - (-4))/(0 - 4)

Slope = 13/-4

Slope = -3.25

So the slope of the line is -3.25.

To find the length of the line segment that connects the two given points, we use the distance formula:

Length = √((x₂ - x₁)² + (y₂ - y1)²)

Length = √((0 - 4)² + (9 - (-4))²)

Length = √(16 + 169)

Length = √(185)

Length ≈ 13.60

So the length of the line segment is approximately 13.60.

Now, we can use the point-slope formula to find the equation of the line that passes through the point (4,-4) with slope -3.25:

y - y1 = m(x - x₁)

y - (-4) = -3.25(x - 4)

y + 4 = -3.25x + 13

y = -3.25x + 9

To know more about slope , visit:

https://brainly.com/question/3605446

#SPJ1

Answer:

Exact Form: 1/216

Step-by-step explanation:

The equatiοn fοr H, the number οf times Nοah’s beats in m minutes is H = k * m

Expressiοns that perfοrm the same functiοn regardless οf appearance are said tο be equivalent. If twο algebraic expressiοns are equivalent, then they have the same value when the same variable value is used.

Assuming yοu meant "Nοah's heart beats", the equatiοn fοr H, the number οf times Nοah's heart beats in m minutes can be given by:

H = k * m

where k is a cοnstant that represents the number οf heartbeats per minute.

The value οf k may vary depending οn the individual and their physical cοnditiοn.

Hence,  the equatiοn fοr H, the number οf times Nοah’s beats in m minutes

is H = k * m

To learn more about the equivalent expression visit:

https://brainly.com/question/2972832

#SPJ1

Complete Question;

A persons resting heart rate is typically between 60 and 100 beats per minute. Nοah looks at his watch, and counts 8 heartbeats in 10 seconds.

Is his heart rate typical? Explain how you know.

Write an equation for h, the number of times Noahs heart beats (at this rate) in m minutes.

Answer:

[tex]\textsf{A.} \quad \dfrac{1}{4}[/tex]

Step-by-step explanation:

Given geometric sequence:

[tex]8,\;2,\;\dfrac{1}{2},\;\dfrac{1}{8},\;\dfrac{1}{32}[/tex]

The common ratio for a geometric sequence can be found by dividing a term by the previous term.

[tex]\implies r=\dfrac{a_2}{a_1}=\dfrac{2}{8}=\dfrac{2 \div 2}{8 \div 2} =\dfrac{1}{4}[/tex]

Therefore, the common ratio for the given geometric sequence is 1/4.

Answer:

stretch by 2, right 4, down 1

Step-by-step explanation:

In a function in the form:

f(x) = a(x - h)² + k

the number in front, a, shows vertical stretch (if its bigger than 1. Its a shrink or smash if its a fraction less than 1)

Horizontal shifts are shown in close next to the x, inside the parenthesis shown here with an h. Horizontals shifts are maybe the opposite of what you might think they should be. + anumber is a left shift and - anumber is a right shift.

Vertical shifts are shown by a number tacked onto the end of the equation, k These shifts are more intuitive. + anumber shifts up and - anumber shifts down.

For your equation:

f(x) = 2(x-4)²-1

The 2 is a vertical stretch. The -4 by the x is a right shift 4. The -1 tacked into the end is a shift down 1

The answer is (a) 203.5 bacteria, rounded to the nearest whole number.

Percentage is a way of expressing a number or proportion as a fraction of 100. It is represented by the symbol "%".

The growth rate of E.Coli is given as 1.9% per minute, which can be expressed as 0.019 per minute as a decimal.

Let N(t) be the number of E.Coli present at time t. Then, we can write the differential equation governing the population growth as:

dN/dt = rN,

where r is the growth rate (0.019 per minute in this case).

The general solution to this differential equation is:

N(t) = [tex]N0e^{(rt)}[/tex]),

where N0 is the initial population size.

We are given that the current number of E.Coli present is 172, so N0 = 172. We want to find N(8.5), so we plug in t = 8.5 and solve:

N(8.5) = [tex]172e^{0.019*8.5}[/tex] ≈ 203.5

Therefore, the answer is (a) 203.5 bacteria, rounded to the nearest whole

number.

To learn more about percentage from the given link:

https://brainly.com/question/29306119

#SPJ1

Therefore, the distance from the coal tray is approximately 301.96 inches when the heat intensity is 0.685 and the width of the coal tray is 25 inches.

We can write the following using the formula in the question:

[tex]P = 100/(1 + d^2)[/tex]

where d represents the proportion of the food's distance from the coals to the tray's width.

Substituting d = z/25 results in:

[tex]P = 100/(1 + (z/25)^2)[/tex]

With y = 0.685, we can replace P with P = 0.685 and find z:

[tex]0.685 = 100/(1 + (z/25)^2)[/tex]

By dividing the two sides by [tex](1 + (z/25)^2)[/tex], we get at:

[tex]0.685 + 0.685(z/25)^2 = 100[/tex]

If we simplify, we get:

[tex](z/25)^2 = (100/0.685) - 1(z/25)^2 = 145.9854[/tex]

When we square the two sides, we obtain:

[tex]z/25 = 12.0783z = 25*12.0783z = -25*12.0783[/tex]

Given that z cannot be negative, we decide:

Z=25 * 12.0783 * 301.9575 inches

Learn more about Ratio and proportion here:

brainly.com/question/29774220

#SPJ1

Answer:

A .278

Step-by-step explanation:

138 x 14÷28+209 = 1932 ÷28+209=69+209=278

Answer:

23°

Step-by-step explanation:

46 = 2x (Vertically opp. angles)

x = 46÷2

x = 23

Hope this helps!

pls like and mark as brainliest

Answer:

x = 23°

Step-by-step explanation:

46 = 2x

46/2 = 2x/2

x = 23°

Answer:

90°

Step-by-step explanation:

Since CD is a tangent to circle B and BA is the circle's radius, the tangent to the radius forms a right angle at the point of contact:

∠BAD = 90°

Answer:

65

Step-by-step explanation:

Answer:

Step-by-step explanation:

H(n)=91x(-1/7) n-1

do not know

Hope it helps the answer is the 2nd one have a great day

The three options given in the question are not the correct steps to solve the given quadratic equation.

What is quadratic equation?

A quadratic equation is a polynomial equation of the second degree, meaning it contains at least one term that is squared (raised to the power of 2).

The three steps that Inga could use to solve the quadratic equation [tex]2x^2 + 12x - 3 = 0[/tex] are:

1.Rewrite the equation in the form [tex]ax^2 + bx + c = 0[/tex], where a, b, and c are constants: [tex]2x^2 + 12x - 3 = 0.[/tex]

2.Use the quadratic formula x = [-b ± sqrt([tex]b^2[/tex] - 4ac)]/2a, where a = 2, b = 12, and c = -3, to find the values of x:

x = [-12 ± [tex]\sqrt{(12^2 - 4(2)(-3))[/tex]]/(2*2)

x = [-12 ± [tex]\sqrt{(156)[/tex]]/4

x = (-3 ± [tex]\sqrt{(39)[/tex])/2

3.Simplify the roots if possible:

x = (-3 + [tex]\sqrt{(39)[/tex])/2 or x = (-3 - [tex]\sqrt{(39)[/tex])/2

Therefore, the three options given in the question are not the correct steps to solve the given quadratic equation.

To learn more about quadratic equation visit:

https://brainly.com/question/1214333

#SPJ1

The associative law holds in all three composition tables.

No matter how they are arranged, integers can be multiplied and added together according to the associative property. We refer to the numbers in the parenthesis as grouping (). Let's imagine that you are adding three integers, 2, 5, and 6. It doesn't matter how we add the numbers together—using the formulas 2 + (5 + 6) or 2 + (5) + 6—the outcome will be the same. The multiplication equation is consistent: Equals to (2 x 5) x 6 is (2 x 5) x 6. The commutative characteristic is almost identical to this one when only two integers are used.

In the given composition tables the law of associativity is followed

a(bc) = (ab)c

from 13,

a(a) = bc

a = a

The associative law holds in all three composition tables

learn more about the associative property,

https://brainly.com/question/30111262

#SPJ1

Answer:

c

Step-by-step explanation:

To find the x-intercept, we set y to 0 and solve for x:

0 = x + 8

x = -8

Therefore, the x-intercept is -8.

To find the y-intercept, we set x to 0 and solve for y:

y = 0 + 8

y = 8

Therefore, the y-intercept is 8.

Hopes this helps

To find a point that represents a solution for the equation x + 3y = 8, we need to find a point (x,y) that satisfies this equation. One way to do this is to choose a value for x, and then solve for y. For example, if we let x = 2, we have:

2 + 3y = 8

Subtracting 2 from both sides, we get:

3y = 6

Dividing both sides by 3, we get:

y = 2

So the point (2,2) is a solution for the equation x + 3y = 8. To check, we can substitute x = 2 and y = 2 into the equation:

2 + 3(2) = 8

8 = 8

This is true, so (2,2) is a solution for the equation.

Alternatively, we could choose a value for y and solve for x. For example, if we let y = 0, we have:

x + 3(0) = 8

x = 8

So the point (8,0) is also a solution for the equation x + 3y = 8.

The total value of Martin's account after 36 months is $7,682.50. $682.50 in interest was earned.

According to the popular legend, Archimedes discovered a principle of buoyancy while taking a bath.

what was his discovery ?

He realized that the volume of water displaced by his body was equal to the volume of his body. This insight led him to formulate the principle of buoyancy, which states that an object placed in a fluid experiences an upward force equal to the weight of the fluid it displaces.

Archimedes was reportedly so excited by this discovery that he ran through the streets of Syracuse shouting "Eureka!" (meaning "I have found it" in Greek). This principle has numerous practical applications, including in shipbuilding and the design of submarines and other underwater vehicles.

In geometric terms, the principle of buoyancy can be explained using the concept of displacement. When an object is submerged in a fluid, it displaces a certain volume of fluid, which is equal to the volume of the object. This volume of fluid has weight, and the fluid exerts an upward force on the object that is equal to the weight of the displaced fluid. This is what causes objects to float in water or other fluids, as long as their weight is less than the weight of the fluid they displace.

As for what Archimedes did next with his new discoveries, it's difficult to say for certain, as there are many stories and legends about his life. However, we do know that he was a prolific inventor and mathematician, and he likely continued to explore the implications of his principle of buoyancy and other discoveries. He may have also used this principle in his work as an engineer and designer, creating new machines and devices that were more efficient and effective thanks to his insights into fluid mechanics.

To know more about buoyancy visit :-

https://brainly.com/question/28464280

#SPJ1

Identify the two numbers in the ordered pair, locate the x-axis and y-axis on the plane, move along the x-axis to the position corresponding to the first number, move vertically along the y-axis to the position corresponding to the second number, mark the point with a dot or small circle, and connect the dots to show patterns.

The procedures below must be followed in order to plot or graph an ordered pair of integers, usually known as a point, on a two-dimensional plane:

To know more about graph, visit

brainly.com/question/17267403

#SPJ1

Answer:

P = 3

Step-by-step explanation:

[tex] {p}^{3} = 27[/tex]

[tex]p = \sqrt[3]{27} = 3[/tex]

Answer:

P = 3

Step-by-step explanation:

Write down the equation:

p^3 = 27

Then divide both sides by cubed:

p = 3

To find the middle term of the expansion of (2x/y^3)^12, we need to first determine the number of terms in the expansion.

Using the formula for the binomial theorem, we know that the number of terms in the expansion of (2x/y^3)^12 is 13.

Now, to find the middle term, we need to find the term that is in the middle of the expansion. Since there are 13 terms in the expansion, the middle term is the 7th term.

The general term of the expansion is given by:

T(r+1) = (12 C r) (2x)^r (y^-3)^(12-r)

So, the 7th term is:

T(8) = (12 C 7) (2x)^7 (y^-3)^(5)

Simplifying this expression, we get:

T(8) = (792) (128x^7 / y^15)

Therefore, the middle term of the expansion is 792(128x^7/y^15)

The sum of the matrices A + B is  5      8

                                                        2.6   2

To add two matrices, they must have the same dimensions (the same number of rows and the same number of columns).

To add two matrices A and B, you can add the corresponding elements of the two matrices and place the result in the corresponding position of a new matrix C.

In mathematical notation, if A and B are two matrices of the same dimensions, then the sum C = A + B is defined by:

C[i,j] = A[i,j] + B[i,j]

Using the above as a guide, we have the following:

A + B =  5      8

             2.6   2

Read more about matrix at

https://brainly.com/question/11989522

#SPJ1

The sample space for rolling a fair 12-sided die is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.

Sample space refers to the set of all possible outcomes or events that can occur in an experiment or random process. It is denoted by the symbol "S" and contains all the possible values, results, or states that can be observed or measured. In probability theory, the sample space is used to define the range of possible outcomes that can be observed or measured in a given experiment or event.

Probability is a measure of the likelihood or chance of an event occurring. It quantifies the likelihood of an event happening based on the ratio of the number of favorable outcomes to the total number of possible outcomes. It is expressed as a value between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

According to the given information:

When you roll a 12-sided dice, number of dots on the uppermost face is called as outcome. Now, whenever a dice is rolled we can get either 1, 2,3,4,5,6,7,8,9,10,11 or 12 dots on the uppermost face that is now outcome.

So experiment here is "Rolling a 12-faced dice" and list of possible outcomes is "{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}".

Sample space by its definition is list of all the possible outcomes of an experiment.

S={1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.

To know more about sample space visit:

https://brainly.com/question/22087319

#SPJ1

Therefore , the solution of the given problem of unitary method comes out to be  1,440 students who favor ice cream

The task may be completed using this generally accepted ease, existing variables, and any important components from the original Diocesan customizable query. If so, you might get another opportunity to work with the object. Otherwise, algorithmic evidence will no longer be affected by any significant factors.  

Here,

The table shows that 81 of the 225 students favor ice cream.

Out of the 4,000 students, we can use the following proportion to estimate how many favor ice cream:

=> 81/225 = x/4000

If we cross-multiply, we obtain:

=> 225x = 81 * 4000

If we simplify, we get:

=> 225x = 324,000

By multiplying both parts by 225, we obtain:

=> x = 1440

The college will have about 1,440 students who favor ice cream, so that is the best guess as to how many scoops of ice cream the college will require.

To know more about unitary method visit:

brainly.com/question/28276953

#SPJ1  

Answer: $4845

Step-by-step explanation:

First, round Peter's weekly payment to the nearest whole dollar:

$56.74 ≈ $57

Next, multiply the rounded weekly payment by the number of weeks he needs to make payments:

$57 * 85 weeks = $4845

So, Peter will pay back an estimated total of $4845.

Answer:

(x, y) → (-x, y)

Step-by-step explanation:

The coordinates of the points that make up the function are equal to (x, y).

If we reflect the function over the y-axis, the sign of the y-value stays the same due to still being on the same side of the x-axis. The x-value sign will be the opposite of its current value due to being reflected over the y-axis.

This leads us to the algebraic expression:

(x, y) → (-x, y)

Required form of solutions are (x² + 6x + 9) = (x+3)×(x-3) + 0, (x² - 9x + 18) = (x-6)×(x-3) + (-72), (x² + 4x - 7) = (-x-1)×(x+5) + (-2).

What is division?

Division is a basic arithmetic operation in mathematics that involves dividing one number by another. It is denoted by the symbol "/", or by the horizontal fraction bar. The number being divided is called the dividend, while the number it is being divided by is called the divisor. The result of the division is called the quotient. For example, if we divide 10 by 2, the dividend is 10, the divisor is 2, and the quotient is 5. The formula for division is:

dividend / divisor = quotient

In some cases, division may result in a remainder. For example, if we divide 10 by 3, the quotient is 3 with a remainder of 1. This can be expressed as 10 / 3 = 3 remainder 1, or as a mixed number, 3 1/3. In other cases, the division may result in a decimal or a fraction.

Here,

1) To divide (x² + 6x + 9) by (x + 3), we can use polynomial long division as follows:

x + 3 | x² + 6x + 9

- x² - 3x

-------

3x + 9

3x + 9

-----

0

Therefore, the quotient is x + 3 , dividend is x² + 6x + 9, divisor is (x+3) and the remainder is 0.

So, (x² + 6x + 9) = (x+3)×(x-3) + 0

2) To divide (x² - 9x + 18) by (x - 6), we can use polynomial long division as follows:

x - 6 | x² - 9x + 18

- x² + 6x

-------

-15x + 18

-15x + 90

--------

-72

Therefore, the quotient is x - 3, dividend is (x² - 9x + 18), divisor is x-6 and the remainder is -72.

So, (x² - 9x + 18) = (x-6)×(x-3) + (-72)

3) To divide (x² + 4x - 7) by (x + 5), we can use polynomial long division as follows:

x + 5 | x² + 4x - 7

- x² - 5x

-------

-x - 7

-x - 5

------

-2

Therefore, the quotient is (-x + -1), dividend is x² + 4x - 7, divisor is x+5 and the remainder is -2.

So, (x² + 4x - 7) = (-x-1)×(x+5) + (-2)

Learn more about division here,

https://brainly.com/question/25421984

#SPJ1