Compare the two linear functions listen below

Distributive Property

Factoring

Functions

Let's organize what is given to us in the problem.

We are given a function f, defined as f(x) = x² + 3x - 10.

We are asked to find the values of b and c in f(x - 2) = x² + bx + c.

In order to solve the question, we first must find the full function of f(x - 2):

[tex]\displaystyle\begin{aligned}f(x - 2) & = (x - 2)^2 + 3(x - 2) - 10 \\& = \underbrace{x^2 - 4x + 4}_{\text{FOIL}} + \underbrace{3x - 6}_{\text{Distribute}} - 10 \\& = \boxed{ x^2 - x - 12 } \\\end{aligned}[/tex]

∴  [tex]\displaystyle \boxed{ f(x - 2) = x^2 - x - 12 }[/tex]

Now, we can correlate our variables to the f(x - 2) function by comparing them side-by-side:

[tex]\displaystyle\begin{aligned}f(x - 2) & = x^2 - x - 12 \\& = x^2 + bx + c \\& \Rightarrow \boxed{ b = -1 ,\ c = -12 }\end{aligned}[/tex]

∴ we have found the values of b and c.

∴ the value of b is equal to -1 and the value of c is equal to -12.

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Topic: Algebra I

Unit: Factoring

a) To write an equation in slope-intercept form to represent the growth of the Magnolia trees over time, we can use the formula y = mx + b, where x represents the number of years, y represents the height of the tree in feet, m represents the slope (or rate of growth) of the tree, and b represents the y-intercept (or the height of the tree at x = 0).

In this case, the slope (m) of the tree is 3/4 feet per year and the y-intercept (b) is 3 feet, as the trees are initially 3 feet tall when they are purchased. Plugging these values into the formula gives us:

y = (3/4)x + 3

This equation represents the growth of the Magnolia trees over time.

b) The y-intercept of an equation in slope-intercept form represents the value of y when x is equal to 0. In this case, the y-intercept of the equation y = (3/4)x + 3 is 3 feet. This means that when x is equal to 0 (when no years have passed), the height of the tree is 3 feet.

c) To determine the height of the tree in 3 years, we can substitute 3 for x in the equation y = (3/4)x + 3 and solve for y. This gives us:

y = (3/4)(3) + 3

= 9/4 + 3

= 21/4

= 5.25 feet

Therefore, the height of the tree in 3 years is approximately 5.25 feet.

The farmer needs to sow 135 acres of corn and wheat, and 45 acres of wheat.

A linear equation is the algebraic expression y=mx+b. B is the y-intercept, and m is the slope. A "linear equation in two variables" is the term used to describe the previous sentence, where y and x are variables. Two variables make up bivariate linear equations. Examples include the linear equations 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is said to be linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.

given

180 acres total land area

The corn acres should be C.

The wheat acres should be W.

A 180-acre property is planted with wheat and corn by a farmer.

Equation 1: C + W = 180

Corn is grown on three times as many acres as wheat:

Equation 2 is created by substituting C = 3W into Equation 1. The result is:

45 acres is W.

For corn, 135 acres equals C.

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Answer:

Step-by-step explanation:

  3 [tex]\frac{1}{6}[/tex]

+  1 [tex]\frac{5}{6}[/tex]

_______

4 [tex]\frac{6}{6}[/tex]   =  5 pounds

[tex]\frac{6 }{6}[/tex]  = 1  add this to the 4 and you have 5 pounds total

Answer:

=4.5

Step-by-step explanation:

the rule is

positive - negative  changes to positive + positive so

3- (-1.5) changes to 3 + 1.5 which equals 4.5

Answer:

The tower is 113 meters.

Step-by-step explanation:

We are given a pole and a tower that both create a shadow.

Hence, the figures made are triangles.

If you draw the figure (attached to this response), you can see the two triangles are similar triangles.

⭐What are similar triangles?

The length of the height of the pole (3.2) corresponds to the length of the height of the tower (x).

The length of the shadow of the pole (1.32) corresponds to the length of the shadow of the tower (46.75).

Therefore, our two ratios are:

[tex]\frac{3.2}{x}[/tex] and [tex]\frac{1.32}{46.75}[/tex]

A proportion is when you set two ratios equal to each other:

[tex]\frac{3.2}{x} = \frac{1.32}{46.75}[/tex]

To solve for x, cross multiply by multiplying the opposite parts of the fraction together.

[tex]\frac{3.2}{x} = \frac{1.32}{46.75}\\46.75(3.2) = 1.32x\\149.6 = 1.32x\\\\113 = x[/tex]

∴ The tower is 113 meters tall!

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The value for the blanks after calculating the as per the given data is found to be as 4 and 9 respectively.

On solving the question we will get the answer of the final blank as 0.

The question can be rephrased as ,

__x 9 - __ x 4 = ___ - ___ = ___.

Now if we will place 4 in first blank and 9 in second blank we will get the result as follows,

4 x 9 - 9 x 4 = 36 - 36 = 0

Therefore , we will get our desired answer.

A relationship between two quantities or, more broadly, two mathematical expressions that asserts that the quantities have the same value or that the expressions reflect the same mathematical object is referred to as equality.

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Over the course of the three hours, 41.25 gallons of water passed through the pipe in total.

We know that the rate of flow for the first hour was 50% slower than the rate of flow for the second hour. So, if the rate of flow in the second hour was 15 gallons per hour, the rate of flow in the first hour would be:

15 gallons/hour * (100% - 50%) = 15 gallons/hour * 50% = 7.5 gallons/hour

We also know that 25% more water flowed through the pipe in the third hour than in the second. So the rate of flow in the third hour would be:

15 gallons/hour * (1 + 25%) = 15 gallons/hour * 1.25 = 18.75 gallons/hour

To find the total number of gallons of water that flowed through the pipe during the entire three hours, we can multiply the rate of flow for each hour by the number of hours:

First hour: 7.5 gallons/hour * 1 hour = 7.5 gallons

Second hour: 15 gallons/hour * 1 hour = 15 gallons

Third hour: 18.75 gallons/hour * 1 hour = 18.75 gallons

Adding these values we can find the total amount of water that flowed through the pipe during the entire three hours

7.5 gallons + 15 gallons + 18.75 gallons = 41.25 gallons

So, in total 41.25 gallons of water flowed through the pipe during the entire three hours.

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The maximum time (in seconds) that she can take on her last lap and still make the team will be 52 seconds.

From the information, to be eligible for the swim team, the mean pace a student needs to achieve on 5 laps of the pool is 60 seconds (s). The student swims a lap in 63 s, 62 s, 65 s, and 58 s on her first four laps.

The maximum time (in seconds) that she can take on her last lap and still make the team will be:

= (60 × 5) - (63 + 62 + 65 + 58)

= 300 - 248

= 52

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One cannot add themselves directly to Wikipedia as this can cause harm to the platform and community in a later run. As one can start adding content and details on the page based on their personal opinions.

Therefore we can say that  the answer is that we cannot edit or create our own Wikipedia page, because that would be a conflict of interest ,more on this later.

But the thing which one can do is to add themselves in the line ,to list themselves on Wikipedia’s repository of articles which are out there looking for creators who can help maintain the site.

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A power of 3 equation is called as cubic equation.

The term equation in math is known as a mathematical statement with an 'equal to' symbol between two expressions that have equal values.

Here we need to find the term that has been used for power of 3 equation.

Here we have to know that the power of 3 equation is known as cubic equation.

in other terms the polynomial equation which has a degree of three is called a cubic polynomial equation or trinomial polynomial equation.

As we all know that the power of the variable is the maximum up to 3, therefore, we get three values for a variable, say x.

The general form of the power of 3 equation is written as

=> ax³ + bx² + cx + d = 0

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The angle of elevation of the ramp is 28.6 degrees.

Tan = (Change in Height) / (Length of Ramp)

Therefore, using the given information, the angle of elevation of the 23-foot ramp is:

Tan = (6 feet) / (23 feet)

Tan = 0.26

= 14.5° (to the nearest tenth of a degree)

Therefore, the angle of elevation of the 23-foot ramp is 14.5°.

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A) Amaire have more money than Jermaine after 10 years.

B) By [tex]5.387*10^{11}[/tex]% Amaire has more money than Jermaine.

What is compound interest?

The interest charged on a loan or deposit is known as compound interest. It is the idea that we employ the most frequently on a daily basis. Compound interest is calculated for an amount based on both the principal and cumulative interest.

Amare and Jermaine has initial amount = $1000

Amare spend his money that pays 2.25% compounded daily.

where are Jermain invest his money that pays 2.25% compounded annually.

Formula of Compound interest that compounded daily

final amount = [tex]A(1+\frac{r}{365})^{365t}[/tex]

where A is initial amount and t is time in years .

final amount after 10 years

final amount = [tex]1000(1+\frac{2.25}{365})^{365*10}[/tex]

final amount = 1000×[tex]1.00616^{3650}[/tex]

final amount = 1000×5.51×[tex]10^{9}[/tex]

final amount  = $5.51 ×[tex]10^{12}[/tex]

Formula of Compound interest that compounded annually

final amount = [tex]A(1+\frac{r}{100})^{t}[/tex]

where A is initial amount and t is time in years .

final amount after 10 years

final amount = [tex]1000(1+\frac{2.25}{1000})^{10}[/tex]

final amount = 1000×[tex]1.00225^{10}[/tex]

final amount = 1000×1.0227

final amount  = $1022.7

Part A :

Amare has more money after 10 years.

part B :

percent more money = [($5.51 ×[tex]10^{12}[/tex] - 1022.7)/1022.7]*100=[tex]5.387*10^{11}[/tex]%

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The smaller sample's margin of error will be almost twice as great as the larger sample's margin of error.

Calculating the margin of error for a given sample from a population:

Let the level of significance be   and the standard deviation of the population be σ and the sample size be n, then we have:

MOE(Margin of Error)=  [tex]z_{a/2}\times\frac{\sigma}{\sqrt n}[/tex]

Using the above formula to calculate the margin of errors for two specified samples

For first sample:

Sample size = n(1) = 1000

MOE(1) = [tex]z_{a/2}\times\frac{\sigma}{\sqrt {1000}}[/tex]

For second sample:

Sample size = n(2) = 4000

MOE(2) = [tex]z_{a/2}\times\frac{\sigma}{\sqrt {4000}}[/tex]

(since it was given that they have same point estimates, so same standard deviation)

Their ratios are given by

MOE(2)/MOE(1) = [tex]\frac{z_{a/2}\times\frac{\sigma}{\sqrt {4000}}}{z_{a/2}\times\frac{\sigma}{\sqrt {1000}}}[/tex]

MOE(2)/MOE(1) = [tex]\sqrt{\frac{1000}{4000}}[/tex]

MOE(2)/MOE(1) = 1/2

MOE(1) = 2*MOE(2)

Thus, the margin of error from the smaller sample will be about double of the margin of error from the larger sample.

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The left shift required to translate from D to D" is 6 units and scale factor for dilation of D" from D' is 2.5.

The scale factor is a type of measurement which is used to increase or decrease the size of an object keeping its shape as the same. It can be determined by taking the ratio of the new and the original dimension of the object.

Compare the corresponding vertex of the given figures.

It is given as,

(-5, 0) → (1, 0)

It can be concluded that the graph of D is shifted (1 - (-5)) = 6 units towards left.

The scale factor is given as,

Length of side of D" ÷ Length of side of D'

⇒ 10 ÷ 4 = 2.5

Hence, the required shift and the scale factor are obtained as 6 units and 2.5 respectively.

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Answer:

Step-by-step explanation:

a.4 hours drive 240 miles, so the speed is 240÷4=60 miles per hour

b.1 days have 24 hours, then, it will go 60 ×24 = 1440 miles in 1 days

Answer:

1440

Step-by-step explanation:

240+4= 60

distance = rt

r= rate

t = time

IN ONE DAY

60 times 24= 1440

(24 for 24 hours)

The equation of the linear function after a translation down 9 units is given as follows:

f(x) = x - 11.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The graph of the function crosses the y-axis at y = -2, hence the intercept b is given as follows:

b = -2.

When x increases by 2 units, from x = 0 to x = 2, y increases by 2 units, from y = -2 to y = 0, hence the slope is calculated as follows:

m = 2/2.

Then the function is of:

y = x - 2.

After the translation down 9 units, 9 is subtracted from the function, hence:

f(x) = x - 2 - 9

f(x) = x - 11.

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The true statement is 6 less than 10

From the question, we have the following parameters that can be used in our computation:

(-2) (-3) less greater than equal than 8- (-2)

We start by evaluating each expression

So, we have the following representation

(-2) (-3) = 6

8- (-2) = 10

Substitute the known values in the above equation, so, we have the following representation

6 less greater than equal than 10

6 is less than 10

So, we have

6 less than 10

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There is a 0.0001 percent chance that the average amount of cereal in these boxes is less than 9.65 ounces.

Given that,

Mean µ = 9.70

Sample size = n = 5

standard deviation = σ = 0.03

Its distribution is normal, therefore

σx = σ/

σx = 0.03

σx = 0.0134

We must now determine the z value in order to use the table.

z = (x - µ) ÷ σ

z = (9.65 - 9,70) ÷ 0.0134

z = -3.73

Now

From the probability index tables

So P (z ≤ - 3.73) = 0.0001

Hence, the correct option is e) 0.0001

The complete question is:

A company’s cereal boxes advertise that each box contains 9.65 ounces of cereal. In fact, the amount of cereal in a randomly selected box follows a Normal distribution with mean μ = 9.70 ounces and standard deviation σ = 0.03 ounce. Now take an SRS of 5 boxes. What is the probability that the mean amount of cereal in these boxes is less than 9.65 ounces?

a. 0.4525

b. 0.9522

c. 0.9999

d. 0.0478

e. 0.0001

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Each friend of Arya will receive 0.625 cupcakes.

To divide 5 cupcakes equally among 8 friends, we can use simple division. We would divide the total number of cupcakes (5) by the total number of friends (8) to find the number of cupcakes each friend would receive. In this case, 5 divided by 8 is equal to 0.625. This means that each friend will receive 0.625 cupcakes. However, since cupcakes are not divisible it is not possible to divide 5 cupcakes equally among 8 friends. In this case, either Arya will have to make more cupcakes or they will have to decide on a different way to divide the cupcakes.

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To find the equation of a vector given a point and direction, you need to find the components of the vector and plug them into the equation: v = (x, y, z).

The equation of a vector is typically written like this:

v = (x, y, z)

To find the equation of a vector given a point and direction, you need to find the components of the vector and plug them into the equation. For example, let's say you are given the point (1,2,3) and the direction of the vector is (2,3,4). The components of the vector, v, would be x = 2, y = 3, and z = 4, so the equation for that vector would be:

v = (2, 3, 4)

To find the equation of a vector given a point and direction, you need to find the components of the vector and plug them into the equation: v = (x, y, z).

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Answer:

70% Decrease

Step-by-step explanation:

70% Decrease

The percentage decrease in price of an item is 30 %

Step by step solution:

The percentage decrease in price = [(original value - decreased value)/original value]*100

percentage decrease[tex]=\frac{(original value - decreased value}{original value} * 100[/tex]

percentage decrease=[tex]=\frac{60 - 42}{60} *100[/tex]

[tex]=\frac{18}{60} *100[/tex]

[tex]=0.3 *100[/tex]

30 %

Therefore, the percentage decrease in price of an item is 30 %

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$98 is the final price of the sneaker be after the discount is taken off

percentage, a relative value indicating hundredth parts of any quantity.

Given that in macy's department store, every item has a 30% discount or markdown.

The original price of a pair of Adidas sneakers cost $140

We need to find the final price of the sneaker be after the discount is taken off

Let us find 30% of 140

Convert 30% to decimal value by dividing with 100

30/100×140

0.3×140=42

So 30% of 140 is 42.

After removing discount the amount will be 140-42=98

Hence, $98 is the final price of the sneaker be after the discount is taken off

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Answer:

The ratio of the new area to the old area will be 16:1

Step-by-step explanation:

I remember learning this in class. The radius is quadrupled, which means the radius is 4 times bigger. This will make the new area 16 times bigger than the old area.

Let's check

Area of circle: 3.14 x r^2

Area of the circle when radius 6:

3.14 (6)^2 = 113.04 ft^2

Area of the new circle when the radius is quadrupled:

3.14 (24)^2 = 1808.64 ft^2

1808.64 divided by 113.04 = 16

So, the ratio of the new area to the old area will be 16:1

Answer:

x ≈ 70.6°

Step-by-step explanation:

using the tangent ratio in the right triangle

tan x = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{17}{6}[/tex] , then

x = [tex]tan^{-1}[/tex] ( [tex]\frac{17}{6}[/tex] ) ≈ 70.6° ( to the nearest tenth )

If we chosen the one year subscription we have to pay  7.49 per each month.

What is Linear Equation ?

Linear Equation can be defined as the equation in which the highest degree of the variable is one.

Given,

The cost of an online newspaper is 7.99

And if we bought the one year subscription the cost is 89.88

Let the the cost of the each month if we bought the one year subscription be x .

for one year the cost is 89.88

for one month could be

that is, x = 89.88/12

x = 7.49

Hence , If we chosen the one year subscription we have to pay  7.49 per each month.

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The factorization of the polynomial x² + 3x + 2 gives (x + 1)(x + 2)

An equation is an expression that shows how numbers and variables relate with each other.

A polynomial is an expression consisting of variables and their exponents with operations of addition and subtraction. Polynomials are classified based on degree as linear, quadratic and cubic.

The standard form of a quadratic equation is:

y = ax² + bx + c

where a, b and c are constants.

Given the polynomial:

x² + 3x + 2

Factorizing the polynomial:

x² + 2x + x + 2

= x(x + 2) + 1(x + 2)

= (x + 1)(x + 2)

The factorization gives (x + 1)(x + 2)

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According to the given bar chart options A, B and C are the correct.

Relative frequency can be defined as the number of times an event occurs divided by the total number of events occurring in a given scenario.

Given that, the bar chart shows the relative frequencies of students from grades 6 to 12 who participate in the community service activity.

Relative Frequency = Subgroup frequency/ Total frequency.

Relative Frequency = f/ n.

From the given bar chart we can see that

The maximum number of participating students was in grade 9.

The number of participating students in grade 6 was equal to the number of participating students in grade 7.

The relative frequency of all participating students in grades 6 and 7 combined was 0.60.  

Therefore, options A, B and C are the correct answers.

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Complete question is in attachment:

By using the conversion factor: 1 km/h = 0.277778 m/s, we get 12 meter per second is equal to 43.2 km/h.

Velocity is a vector quantity that represents the rate of change of an object's position. It is defined as the displacement of an object divided by the time it takes for that displacement to occur. In other words, velocity tells you how fast an object is moving in a certain direction.

The standard unit for velocity is meters per second (m/s) or kilometers per hour (km/h) in the International System of Units (SI). In imperial system of units, it is expressed in feet per second (ft/s) or miles per hour (mph).

The formula for velocity is:

velocity = displacement / time

To convert 12 m/s to km/h, you can multiply 12 by the conversion factor:

12 m/s * (1 km/h / 0.277778 m/s) = 43.2 km/h

So 12 meters per second is equal to 43.2 kilometers per hour.

Another way to do the conversion is by applying the formula :

Speed (km/h) = Speed (m/s) x 3.6

12 x 3.6 = 43.2

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Answer:

Sine                                                                                                                                                                                                                                         AB is perpendicular to sides AE and BC/                                                                                                                                                  

Step-by-step explanation:

The slope is the change in y over the change in x.

Line segment AE has a slope of 3/4

(0,4)(4,7)

The y values are 7 and 4.

The x values are 4 and 0.  

You find the change by subtracting

[tex]\frac{7-4}{4-0}[/tex] = [tex]\frac{3}{4}[/tex]

Line segment BC has the same slope

((3,0)(7,3)

The y values are 3 and 0.

The x values are 7 a d 3.  

You find the change by subtracting

[tex]\frac{3-0}{7-3}[/tex] = [tex]\frac{3}{4}[/tex]

Since line segments Ae and BC has the same slope.  They are parallel.

Line segments that are perpendicular will have opposite reciprocals slopes.  In this case the slope should be  - [tex]\frac{4}{3}[/tex].

Let's look at line segment AB

(0,4)(3,0)

The y values are 0 and 4.

The x values are 3 and 0.

You find the change by subtracting  

[tex]\frac{0-4}{3-0}[/tex] = [tex]\frac{-4}{3}[/tex]

Since the slopes are opposite reciprocals, side AB is perpendicular to sides AE and BC