Please look at picture! thank you!

we have

x2 + 9x + 8

Find the factors

Complete the square

(x^2+9x+81/4)-81/4+8=0

Rewrite as perfect squares

(x+9/2)^2=81/4-8

(x+9/2)^2=49/4

square root both sides

(x+9/2)=(+/-)7/2

x=-9/2(+/-)7/2

so

x1=-9/2+7/2=-1

x2=-9/2-7/2=-8

therefore

x2 + 9x + 8=(x+1)(x+8)

answer is

The factors are

(x+1) and (x+8)

Answer:

134.375

Step-by-step explanation:

43 is 32% of what number

32% = 0.32

43/0.32 = 134.375

Answer:factor of x³ + 343

Step-by-step explanation: Option D is correct. A factor of an expression is usually referred to as a number or an algebraic expression that divides the known expression. The above algebraic expression needs to be expanded to determine its factor; Mathematically; x³ + 343 = (x + 7) (x² - 7x + 49) Therefore, we can conclude that the factors are (x + 7) (x² - 7x + 49)

a) Tyler ran 0.07 miles farther than Elena in 10 minutes.

b) The paces of each runner are given as follows:

c) Due to the lower measure of minutes per mile, Tyler ran faster during the run.

For this situation, the input and the output are given as follows:

This situation is represented by a proportional relationship, in this following format:

t = dv.

In which v is the pace in minutes per mile.

From the graph, Tyler runs 1 mile in 8 minutes, hence:

Elena's equation is:

y = 8.5x.

Hence her pace is of 8.5 minutes per mile, meaning that she is slower than Tyler, as she takes more time to run a mile.

The distances in 10 minutes are given as follows:

Hence Tyler ran 0.07 miles farther.

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Mode

2 x 5 = 10

6 x 5 = 30

5 x 5 = 25

3 x 5 = 15

7 x 5 = 35

8 x 5 = 40

9 x 5 = 45

2 x 5 = 10

4 x 5 = 20

7 x 5 = 35

4 x 5 = 20

7 x 5 = 35

The mode is 35 because it is repeated 3 times.

Using Two point formula in getting the equation of the line.

x1 = -6

y1 = -3

x2 = 2

y2 = -5

Substitute to the formula :

The answer is :

y = -1/4 x - 9/2

Answer:

it is half of volume of tube.

tube volume = area of circle (πr)× height of tube (h)

volume of tube = π × r × t

1/2 tube volume = 1/2 × π × r × h

╭┄┈┄────────❥

Answer:

↣ A.) Third person limited

Explanation:

A story told from a third person limited point-of-view, or POV, is defined as a narration that describes the thoughts, feelings, and actions of one character.

. . • ☆ . ° . • °: . * ₊ ° . ☆

I hope this helps!

peachtea ^-^

╰┄┈┄──❥

Answer:

$104.14

Step-by-step explanation:

5.2% of $98.99

= $5.15

Price of the shoes + tax

= $98.99 + $5.15

= $104.14

Answer: y = 2

Good luck!

The value of k in this exponential decaying situation of radioactive material is  - 0.0069.

One of the key mathematical operations is the exponential function we allow the exponent to be the independent variable to create an exponential function.

Given, An equation of the form y = y₀e^(kt) models a situation of decaying radioactive material.

y₀ = 10mg, half-life = 100 days.

So, in 100 days the left-out radioactive material will be 5mg.

∴ 5 = 10.e^(100k).

e^(100k) = 1/2.

lne^(100k) = ln(1/2).

100k = - 0.69

k = - 0.69/100.

k = - 0.0069.

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The dimension of the rectangle that has the maximum area is 7.5 by 7.5 feet.

Let the length of the rectangular field be x and the width be y

Now the perimeter is 30

Therefore 2(x + y)=30

or, x + y = 15

or, y = 15 - x

Area of the rectangle = xy

Now we substitute the value of y

area = x ( 15 - x ) = 15x - x²

Now for the maximum area we have to differentiate the area function.

f(x) = 15x - x²

f'(x) = 15-2x

Now the differentiated function is equated to 0 to get the value of x for which the area is  maximum.

15-2x = 0

or, x =7.5

therefore y -= 15 - x = 1 5 - 7.5 = 7.5 feet.

Hence for the area to be maximum the dimension of the field should be 7.5feet by 7.5 feet .

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Answer: 19.6 feet

Step-by-step explanation:

Using the Pythagorean theorem,

[tex]x^2 +(x+6)^2 =48^2\\\\x^2 +x^2 +12x+36=2304\\\\2x^2 +12x-2268=0\\\\x^2 +6x-1134=0\\\\x=\frac{-6 \pm \sqrt{6^2 -4(1)(-1134)}}{2(1)}\\\\x \approx 30.8 \text{ } (x > 0)\\\\\implies x+(x+6) \approx 67.6\\\\\therefore (x+(x+6))-48 \approx 19.6[/tex]

Given the building that can be modeled as a

right rectangular prism with dimentions

8 * 2 3/4 * 2 3/4

Volume is given by

since we have 850 bricks

the volume occupied by 850 bricks is therefore

then

the cost of the 850 bricks is

cost of bricks is $3085.50

The answer of the given fraction after simplification is 2.11.

To simplify simply means to make anything easier. Simplifying an equation, fraction, or issue in mathematics entails taking something complex and making it simpler. Calculations and problem-solving techniques simplify the issue. By eliminating all common components from the numerator and the denominator and putting the fraction in its simplest/lowest form, we can simplify fractions.

Given fraction is:

= 3 * 3/9 + 2 * 10/18

By simplifying the given fraction, we get

=  3 * 1/3 + 10/9

= 1 + 1.11

= 2.11

The answer of the given fraction after simplification is 2.11.

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The product of (− 7) ( 14 ) multiplied by ( −6 ) will be C. 588.

A product simply means the value that's gotten when the numbers are multiplied together. Addition, subtraction, multiplication, and division are all possible mathematical operations.

It should be noted that minus × minus = plus

minus × plus = minus

Therefore, the value of ( −7 ) ( 14 ) • ( −6 ) will be:

= ( -7 ) × 14 × ( -6 )

= 588

Therefore, the value of the product is 588 and this implies that the correct option is C.

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Answer:

4 shots were scored

Answer: 9/20 or 0.45 as a decimal :)

The inequality represented by the graph attached is y > -3x + 6

An equation is an expression showing the relationship between two or more numbers and variables.

An inequality is used to show that two numbers or variables are non equal to each other.

The graph attached shows a straight line inequality. It passes through the point (0, 6) and (2, 0). Hence, the straight line has the equation:

y - 6 = [(0 - 6)/(2 - 0)](x - 0)

y - 6 = -3(x)

y = -3x + 6

Based on the dotted line and the shaded region, the inequality is y > -3x + 6

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We fail to reject the null hypothesis and there is no significant evidence for the manager to conclude that the standard deviation has decreased at the α = 0.01

What is standard deviation?

The standard deviation is a statistic that expresses the degree of variation or dispersion among a group of data. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the mean of the collection.

The null and alternative hypotheses are:

[tex]H_{0} :[/tex] α = 0.004

[tex]H_{a} :[/tex] α < 0.004

Under null hypothesis, the test statistic is:

[tex]x^{2} = \frac{(n-1)s^{2} }{\alpha ^{2} }[/tex]

   = (29 - 1)0.0036² / 0.004²

   = 22.68

Now the critical value of x² at 0.01 level of significance for

df = n-1

  = 29 - 1

 = 28

[tex]x_{critical} ^{2}[/tex] = 48.278

Since the test statics

x² = 22.68 is less than the critical value

[tex]x_{critical} ^{2}[/tex] = 48.278

∴ we fail to reject the null hypothesis and there is not significant evidence for the manager to conclude that standard deviation has decreased at α = 0.01

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x=-6

Explanation

to solve this, let´s complete the tables and then compare

Step 1

complete the table:

to do that we need to input the x value and evaluate to obtain f(x)

so

a) for

i)when x=-12

ii) when x= -9

iii) when x=-6

iv) when x= -3

hence

Step 2

Now , for equation(2) g(x)

a) when x=-12

b) when x=-9

c) when x=-6

d)when x=-3

so

Step 3

finally, compare and check wich input value produces the same out put

therefore, the answer is

x=-6

I hope this helps you

Answer:

x=-6

Step-by-step explanation:

exam

Answer: 19/24

Explanation:

From the information given,

Number of green marbles = 15

Number of red marbles = 9

Total number of marbles = 15 + 9 = 24

Probability is expressed as

number of favorable outcomes/number of total outcomes

Probability f selecting a greeen marble = 15/24

Even numbers divide 2 without a remainder. The even numbered marbles are

red = 2, 4, 6, 8

green = 2, 4, , 68, 10, 12, 14

Total number of even numbered marbles = 11

Probability of selecing an oevennumber = 10124

The events are not mutually exclusive becuse they can occur together. For two ebvents, A and B that are not mutually exclusive,

P(A U B) = P(A) + P(B) - P(A and B)

Thus,

the probability that the marble is green or even numbered = Probability of selecting a green marble + Probability of selecting an even number - Probability of selecting a green and even numbered marble

Number of green even numbere marble s = 7

Probability of selecting a green and even numbered marble = 7/24

Thus,

the probability that the marble is green or even numbered = 15/24 + 11/24 - 7/24

the probability that the marble is green or even numbered = 19/24

Let  p be the function that gives the cost , in dollars, of producing 1 watt of solar energy years after 1977. Here is a table showing the values of  from 1977 to 1987.

t         p(t)                       p(10)-p(0)

0 80                          p(10)

1 60                          p(10)- p(0)/10-0

2 45                            p(10-0)

3 33.75

4 25.31

5 18.98

6 14.24

7 10.68

8 8.01

9 6.01

10 4.51

Which phrase best captures the average rate of change in the price of solar energy between 1977 and 1987?

Which phrase best captures the average rate of change in the price of solar energy between 1977 and 1987?

Which equation best captures the yearly average increase rate of solar prices between 1977 and 1987?

This discussion aims to help students remember what average rate of change for a function means and how it is computed. Select students to explain what each expression's value in this context means. For instance, the cost difference for a solar cell between 1977 and 1987 is represented by the formula p(10)- p(0), whereas the percent change between 1977 and 1987 may be calculated as p(10)/p(0). The fact that the real phrase for the average rate of change, p(10)-p(0)/10-0=-7.55, reveals that the price declined by -$7.55 on average per year since the expression considers the whole difference in price between the 1977 and 1987 divided by the total number of years that passed.

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The given expression is

Terms are the expressions separated by negative or positive signs. In this case, there are 4 terms.

Coefficients are the number multiplying the variable. IN this case, the coefficients are -2, 3, and -1.

The variable is just x because it's the only letter present in the expression.

The powers are x'8 and x'2.

functionWe have:

The functions f and g have the same y-intercept, this is (0,4).

And the behavior as x approaches infinity is:

In the function f, value of the function approaches - 1.

In the function g, value of the function approaches - 1, too.

Therefore, they have the same behavior.

Answer: they have the same y-intercept and the same behavior as x approaches infinity.

The perimeter of the Garden is 76 meters. and the length is 32m.

Area= L × B

(L×6) = 16 × 12

L = [tex]\frac{288}{6}[/tex] = 32m

Therefore L works out to 32 meters.

Perimeter of Garden = 2 × (32+6) = 76 meter.

The area is the quantity that expresses the extent of a place on the plane or on a curved floor. The area of an aircraft area or aircraft location refers to the region of a shape or planar lamina, at the same time as floor vicinity refers back to the region of an open surface or the boundary of a three-dimensional object. the vicinity may be understood as the quantity of cloth with a given thickness that would be essential to fashion a version of the form, or the amount of paint necessary to cover the floor with an unmarried coat. it's miles the two-dimensional analog of the period of a curve (a one-dimensional idea) or the volume of a strong (a three-dimensional concept).

vicinity of a form may be measured by evaluating the form to squares of a fixed size. inside the international system of devices (SI), the usual unit of the region is the rectangular meter (written as m²), which is the region of a square whose facets are one meter lengthy. A shape with a place of three square meters would have the same place as 3 such squares. In arithmetic, the unit rectangular is defined to have region one, and the place of any other shape or floor is a dimensionless actual wide variety.

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a. The images coincide because rotations preserve rays.

b. Transformations preserve distances, so the image of point A and point E are the same distance along the same ray from C and they have to coincide.

c. The rotation would also make the image of B equal with D. So there is a rigid motion that takes CBA onto CDE.

Transformations are classified into rigid and non-rigid, according to the definitions presented as follows:

In this problem, the transformation was a rotation of triangle BAC over vertex C, generating triangle EDC.

A rotation is a rigid transformation, hence the distances are preserved.

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The equation which represents total pay P and the number of copies sold N is P = 2300 + 90N and the total pay for 22 copies sells will be $4280.

How to form an equation?

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

Total pay = base salary + additional

Total pay = base salary + number of copies × per copy price

P = 2300 + N × 90

P = 2300 + 90N

Now for 22 copies

P = 2300 + 90(22) = $4280

Hence, the equation which represents total pay P and the number of copies sold N is P = 2300 + 90N and the total pay for 22 copies sells will be $4280.

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The focus of a parabola does not lie on it. Hence, the equation of parabola is given as y² = 2y - x².

The parabola can be defined as a conic section curve, all of whose points are equidistant from a fixed point called as focus and a fixed line called as directrix.

Given that,

The focus of parabola is (0, 1).

The vertex of parabola is (0, 0).

Suppose, there is one more point on parabola as (x, y).

Since focus of a parabola is equidistant from all the points on parabola.

Use distance formula to find the distance between two points (x₁, y₁) and (x₂, y₂) as √((x₂ - x₁)² + (y₂ - y₁)²) to find the equation of parabola as,

√((x - 0)² + (y - 1)²) = √((0- 0)² + (0 - 1)²)

=> x² + (y - 1)² = 1

=>  (y - 1)² = 1 - x²

=> y² - 2y + 1 = 1 - x²

=> y² = 2y - x²

Hence, the equation of the parabola having vertex at origin and focus at  (0, 1) is  y² = 2y - x².

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