we want to factor the following expression: (x - 3)^2 - 64y^4 which pattern can we use to factor the expression? u and v are either constant integers or single variable expression.

The value of expression a²-b is 12 and value of equation -a+√-4+b id 10+2i where a is -2 and b is 8.

In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. An expression in mathematics is a collection of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) Expressions and phrases are similar in structure.

Here,

if a = -2 and b = 8

a²-b=(-2)²-8

=-4

-a+√-4+b=-(-2)+2i+8

=10+2i

The equation a²-b has a value of 12 and the expression -a+-4+b has a value of 10+2i, where a is -2 and b is 8.

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We can find the linear equation by using the given graph, the equation is:

y = 4.8*x + 24

On the graph we can see the best fit line, remember that a linear equation is of the form:

y = m*x + b

Where m is the slope and b is the y-intercept.

On the graph we can see that the y-intercept is at y = 24, then:

y = m*x + 24

Now, notice that when x = 5, the value of y is 48, replacing these values we get:

48 = m*5 + 24

48 -24 = m*5

24/5 = m

4.8*m

The linear equation is:

y = 4.8*x + 24

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The slope of the function A which is presented as an equation and the slope of function B presented as a table are presented as follows;

The slope of function A is 4

The slope of function B are;

Between f(0) and f(1), the slope is 1

Between f(1) and f(2), the slope is 3

Between f(2) and f(3), the slope is 5

The slope is found by the ratio of the rise to the run of the graph.

The function A is; y = 4·x - 5

Function A is of the form y = m·x + c

Where;

m = The slope of the function = 4

Therefore;

The slope of function A is 4

The first difference of the values of function B is not a constant.

The value of f(0) in function B is 0

The value of f(1) in function B is 1

The slope between f(0) and f(1) is m = (f(1) - f(0))/(1 - 0)

Which indicates that m = (1 - 0)/(1 - 0) = 1

The slope of function B between f(1) and f(2) is found as follows;

f(2) = 4, f(1) = 1, from which we get;

m = (4 - 1)/(2 - 1) = 3

The slope between f(2) and f(1) is 3

The slope of the function B between f(2) and f(3) is found as follows;

f(2) = 4, f(3) = 9, from which we get;

m = (9 - 4)/(3 - 2) = 5

The slope of the function B between f(2) and f(3) is 5

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The slopes and the y-intercepts of two equations are different.

Mathematically, the slope-intercept form of a line can be calculated by using this equation:

y = mx + c

Where:

From the information provided, we have the following equations:

2x + y = 3       ....equation 1.

−2y = 14 − 6x    ....equation 2.

In slope-intercept form, the first equation can be written by subtracting 2x from both sides as follows:

2x + y - 2x = 3 - 2x

y = 3 - 2x

y = -2x + 3

Therefore, m = -2 and c = 3.

For the second equation, we would divide both sides by -2 as follows:

−2y/-2 = 14/-2 − 6x/-2

y = -7 + 3x

y = 3x - 7

Therefore, m = 3 and c = -7.

In this context, we can reasonably and logically deduce that the slopes and the y-intercepts are quite different.

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Answer:

y = -2x + 3

y = 3x + -7

The slopes and the y-intercepts are different.

The system represents lines that Intersect at one point

Exactly one solution

Step-by-step explanation:

Edge2022

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The polynomial f(c)=4x^3+19x^2-58x+35 as a product of linear factors is f(c)=(x-1)(x+7)(4x-5)

To express the polynomial as a product of linear factors we have to find the zeros of the polynomial.

Here,

We have Given that f(c)=4x^3+19x^2-58x+35 and -7 is a zero of f(k) and we need to find the polynomial f(c)=4x^3+19x^2-58x+35 as a product of linear factor

Now,

-7 is a zero of f(k)

i.e. (x+7) is a linear factor of f(k)

now,

we will find out the linear factor of f(c)

so,

f(c)=4x^3+19x^2-58x+35

f(c)=4x^3-4x^2+23x^2-23x-35x+35

f(c)=(x-1)(4x^2+23x-35)

f(c)=(x-1)(4x^2+28x-5x-35)

f(c)=(x-1)(4x(x+7)-5(x+7))

f(c)=(x-1)(x+7)(4x-5)

Hence,

The polynomial f(c)=4x^3+19x^2-58x+35 as a product of linear factor is f(c)=(x-1)(x+7)(4x-5)

Thus,

the linear factor of given polynomial is (x-1)(x+7)(4x-5)

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The customer have to pay $87.9 for the watch.

A customer at the store wanted to buy a different watch that was listed at $88 but had a 15% discount.

Given the information is

Watch is listed at $88 and had a discount of 15%

The customer had to pay a sales tax of 5%

Than, by reducing the discount from the price listed

= $88 - 15%

= 88 - [tex]\frac{15}{100}[/tex]

= 87.85

Now we have to add 5% tax to the discounted price

= 87.85+5%

= $87.9

Hence the answer is the customer have to pay $87.9 for the watch.

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Step-by-step explanation:

x = price per muffin

21 × x = 30

x = 30/21 = 10/7 = $1.428571429... ≈

≈ $1.43

she needs to charge $1.43 per muffin.

When a quadratic equation is given in the form y = a( x− ℎ )^2 + k the easily seen features are

Equation of a parabola is the equation used to trace the path of a parabola. this equation is a quadratic equation

The quadratic equation in the factored form is written as

y = a ( x − ℎ )^2 + k

This equation shows the coordinates of the vertex which is v(h, k)

The axis of symmetry refers to the axis where the parabolic curve can be bisected. this is in the y axis

"a" helps to determine if the curve opens upwards or downwards. when a is:

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The equation of the given line is y = 2x + 4

The equation y = mx + c is the general equation of any straight line, where m is the slope of the line and c is the y -intercept.

Given a line passing through points (-1, 2) and (-3, -2)

We know (y - y1) = [(y2−y1)/(x2−x1)](x - x1).

Therefore, y - 2 = [(-2-2)/(-3+1)](x+1)

y-2 = 2x + 2

y = 2x + 4

Hence, The equation of the given line is y = 2x + 4

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The dimensions that will minimize the cost, obtained from the cost function are;

Width = [tex]\sqrt[3]{\frac{45}{11} }[/tex] feet

Length = [tex]2\cdot \sqrt[3]{\frac{45}{11} }[/tex] feet

Height = [tex]\dfrac{20}{\left(\sqrt[3]{\frac{45}{11} }\right)^2 }[/tex]

A function is a rule, or law or expression that provides the definition between an input variable and an output variable.

Base length of the box = 2 × The base width of the box

Cost of the material used to build the top and the bottom = $11 per square feet

Cost of the material used to build the sides = $3 per square feet

Volume of the box = 40 cubic feet

Let x represent the width of the base of the box, and let y represent the height of the box

The information from the question indicates;

The length of the base of the box = 2·x

The volume of the box, V = x × 2·x × y = 2·x²·y = 40

V = 2·x²·y = 40

[tex]y = \dfrac{40}{2\cdot x^2} = \dfrac{20}{x^2}[/tex]

The cost of the box which can be obtained from the surface area of the box can be found as follows;

Cost of the top and the bottom = 2 × x × 2·x × 11 = 44·x²

Cost of the material for the sides = (2 × x × y + 2 × 2·x × y) × 3 = 18·x·y

Cost of the box, C = 44·x² + 18·x·y

[tex]C = 44\cdot x^2 + 18\cdot x \times \dfrac{20}{x^2} = \dfrac{44\cdot x^2+360}{x}[/tex]

To minimize the cost of the box, we get;

[tex]C' =\dfrac{d}{dx}\left( \dfrac{44\cdot x^2+360}{x}\right) = 0[/tex]

[tex]\dfrac{d}{dx}\left( \dfrac{44\cdot x^3+360}{x}\right) = \dfrac{x\times 44\times 3 \times x^2 - \left(44\times x^3+360\right)}{x^2} = \dfrac{88\cdot x^3-360}{x^2} =0[/tex]

At the minimum cost, [tex]\dfrac{88\cdot x^3-360}{x^2} =0[/tex]

Therefore; 88·x³ - 360 = 0

88·x³ = 360

[tex]x = \sqrt[3]{\dfrac{360}{88} } =\sqrt[3]{\dfrac{45}{11} }[/tex]

The width of the base of the box that minimizes the cost is; [tex]x =\sqrt[3]{\dfrac{45}{11}}[/tex]

The length of the base of the box that minimizes the cost is; [tex]2\cdot x =2\times \sqrt[3]{\dfrac{45}{11}}[/tex]

The height of the box that minimizes the cost is; [tex]\dfrac{20}{x^2} = \dfrac{20}{\sqrt[3]{\dfrac{45}{11} } }[/tex]

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If no withdrawals were made from the accounts. The total interest earned at the end of 1 year is $230 and the percent interest for the total deposited is 5.75%.

a. Total interest earned  :

Total interest earned  = (0.02)($1000)+(0.07)($3000)

Total interest earned =$20+$210

Total interest earned =$230

b. Percent interest amount deposited

Percent interest amount deposited = Total interest earned / Total amount deposited

Percent interest amount deposited = $230 /( $1,000 + $3,000)

Percent interest amount deposited = $230 / $4000

Percent interest amount deposited = 0.0575 × 100

Percent interest amount deposited =5.75%

Therefore $230 is the interest earned and 5.75 is the percent interest.

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According to the given distance, the dog can run on 22.5 miles

Distance:

Distance refers the the length of the line joining the two points. Here the two points lie on the same horizontal or same vertical line, the distance can be found by subtracting the coordinates that are not the same.

Given,

On his trip to meet Clare, Kiran brought his dog with him.

Here at the same time Kiran and Clare started walking, the dog started running 6 miles per hour.

When they got to Clare it turned around and ran back to Kiran. And when it got to Kiran, it turned around and ran back to Clare, and continued running in this fashion until Kiran and Clare met.

Here we know that they meet after 3.75 hours.

And we know that the dog was running 6 miles per hour

So, for 3.75 hours, it can be calculated as,

=> 3.75 x 6

=> 22.5

Therefore, then the dog can ran 22.5 miles.

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The expected value of your third punch is 5660.

What is probability?

A linear scale from 0 (impossibility) to 1 (certainty) or as a percentage between 0 and 100% expresses the likelihood that a specific event (or series of events) will occur.

Given that,

This is the third and last punch and also there is no removal of prizes after each punch. Hence, the expected value would be equal to the mean of all the possibilities available.

E(third punch) = Σ  x  p(x)

=  100× (5/50) + 250 × (10/50) + 500 × (10/50) + 1000 × (10/50) + 2500 ×(8/50) + 5000 × (4/50)     + 100000 × (2/50) + 25000 × (1/50)

=  5660

Let us find the median of the given possibilities,

5 100's, 10 250's, 10 500's, 10 1000's, 8 2500's, 4 5000's, 2 100000's, 1 25000

There is a total of 50 possibilities and hence the median will be the average of the 25th and 26th terms.

25th term = 500

26th term = 1000

Median = (500 + 1000) / 2 = 750

The next available possibility greater than 750 is 1000.

Probability of getting more than 1000 in third punch = P (x > 1000) = (No. of terms greater than 1000) / Total no. of possible outcomes                                                                                                         = 15 / 50 = 0.3

Probability of getting less than 1000 in third punch = P (x > 1000) = (No. of terms lesser than 1000) / Total no. of possible outcomes                                                                                                                

= 25 / 50 = 0.5

Hence, in the second chance of punch, 1000 or anything greater than 1000 is preferred because the probability of getting more than 1000 in the next chance is less than the probability of getting less than 1000.

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The overall weighted average grade for this student in the class is 83.5%.

The weighted average grade is a function of the multiplication of each rate by the average score for each grading category.

The class grades are added to obtain the total grade that the student received for the different categories, involving class participation, classwork/homework, and tests/projects.

                                      Grade   Average    Class Grade

Participation                    10%        100          10% (10% x 100%)

Classwork/Homework   30%         95          28.5% (30% x 95%)

Test/projects                  60%         75          45% (60% x 75%)

Total grade in class                                      83.5%

Thus, from the student's participation, classwork/homework, and tests/projects, we can summarize that they scored an average weighted grade of 83.5%.

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Answer:

1,200 pennies

Step-by-step explanation:

Answer:

7.1032,7.209,7.23,7.3.

so we can not put the dot and imagine like 71032 72090 we not put the 0 but it's can not be with no 0 72300 and we not put 0 73000 it most greatest so

i write answer on the top!

Answer:

The costs are equal at 3 miles.  It coest $8 for either company

At 8 miles the green cost 13 and the red cost 18.

My advice would be to use the Red compnay if traveling less than 3 miles and the green company is traveling more than 3 miels.  At 3 miles the costs are the same.

Step-by-step explanation:

The previous population of the city is 62500

Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. For example, below are some simultaneous equations: 3x + 4y = 14, 5x − 4y = 4.

if the previous population is represented by x and the increment by y, then

y= x×28/100

y = 28x/100 equation 1

the new population = previous population+ increment

therefore x+y= 80,000

represent 28x/100 for y in equation 2

x+28x/100= 80000

making the LHS a single fraction

(100x+28x)/100= 80000

128x= 80000×100

divide both sides by 128

x= 8000000/128

x= 62500

therefore the previous population is 62500

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Answer:

[tex]-1.7f+-25[/tex]

Step-by-step explanation:

1 ) To simplify combine like terms...

[tex]=-2.5f+0.8f+-16+-9[/tex]

[tex]=(-2.5f+0.8f)+(-16+-9)[/tex]

[tex]=-1.7f+-25[/tex]

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The most equitable way to share the coin between Mai and Jeff is ratio 5:3. Mai will have 5 coins and Jeff 3 coins

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity. The general form of representing a ratio of between two quantities say 'a' and 'b' is a: b.

Mai dropped 5 loaves and Jeff 3 loaves. This means that the ratio of brad dropped by Mia and Jeff is 5:3.

The stranger dropped 8coins. the most equitable way to share the coin is to share it in ratio 5:8

Using this ratio, the total ratio is 8

therefore Mia will have 5/8×8=5coins

Jeff will have 3/8×8= 3coins

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Answer: unit rate

Step-by-step explanation:

its obvious

Answer:

I believe it is a unit rate

Answer:

12 pints

Step-by-step explanation:

[tex]\frac{1}{8}[/tex] = [tex]\frac{8}{96}[/tex]

8 ounces is equal to 1 pint.  8 x 12 = 96, so 1 x 12 is 12

Extreme values that significantly deviate from the dataset's or graph's normal distribution are known as outliers.

An outlier, to put it simply, is a data point in a data graph or dataset you're dealing with that is abnormally high or abnormally low in comparison to the nearest data point and the rest of the nearby coexisting values.

The vocabulary term is explained as,

1.Outlier - Extreme values that significantly deviate from the dataset's or graph's normal distribution are known as outliers.

2. Cluster - An identifiable cluster of values in a numerical variable's distribution that is close to one another and appears notably more frequently than values on either side of them.

3. Positive linear association - When the variable on the x-axis grows as the variable on the y-axis increases, a positive linear connection exists. An upward-sloping linear regression line demonstrates this.\

4. Negative linear association - A negative linear correlation exists when one variable rises while the other falls. An upwardly sloping straight regression line illustrates this.

5.No association - There is a "negative correlation" when one variable rises while the other one falls. The points in the scatterplot have no connection if there is no correlation between the variables.

6. Non-linear association - When two variables have a nonlinear relationship, the slope of the curve illustrating the relationship alters when the value of one of the variables varies. Any curve whose slope alters when one of the variables' values changes is said to be nonlinear.

Thus, extreme values that significantly deviate from the dataset's or graph's normal distribution are known as outliers.

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The polynomial function with -3 as a zero of multiplicity 3 and 0 as a zero of multiplicity 1 will be x³+9x²+16x.

Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]

It is given that the polynomial is given with -3 as a zero of multiplicity 3 and 0 as a zero of multiplicity 1.

Each zero, such as a, corresponds to a linear factor, such as (x a). The repeating of such components is corresponding to multiplicity. The following polynomial thus meets the requirements in our example:

= (x-(-3))³(x-0)¹

=(x³-3x²(-3)+3x(-3)²-(-3)²)(x)

=x³+9x²+27x-9x

=x³+9x²+16x

Thus, the polynomial function with -3 as a zero of multiplicity 3 and 0 as a zero of multiplicity 1 will be x³+9x²+16x.

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115.5  is the total amount of interest paid by this investment at the end of 5 years

What is the Percentage?

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

Given,

Samantha invested $660 into an account that paid 3.5% interest compounded annually.

We need to find the total amount of interest paid by this investment at the end of 5 years

A=P(1+rt)

A is the final amount

P is the principal amount

r is the rate of interest

t is time

A=?,P=660,r=3.5%=0.035, t=5

A=660(1+0.035(5))

=660(1+0.175)

=660(1.175)

A=775.5

To check the total amount of interest paid by this investment at the end of 5 years

We need to find the difference between the initial amount and the final amount

775.5-660 =115.5

Hence 115.5  is the total amount of interest paid by this investment at the end of 5 years

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The linear equation in the slope intercept form that models this situation is y = 9x + 15 .

In the question ,

it is given that ,

a member of hiking club paid $51 for 4 months ,

let the number of months be represented on x coordinate , and

the amount paid be represented on y coordinate .

So , the point becomes (4 , 51).

also given that you pay a total of $105 after 10 months ,

the second point becomes (10 , 105).

to find the equation in slope intercept form , we need slope ,

So , Slope = (105-51)/(10-4)

= 54/6

= 9

So , the equation having the point (4,51) and slope as 9 , in slope intercept form is

(y - 51) = 9(x - 4)

y - 51 = 9x - 36

y = 9x - 36 + 51

y = 9x + 15

Therefore , The linear equation in the slope intercept form that models this situation is y = 9x + 15 .

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The observation I can make of the pattern is that the sequence always increase by 10.

The sequence above shows an arithmetic pattern. Therefore, the arithmetic formula can be used to solve the next sequence.

7, 17, 27, 37, 47, 57..

Therefore,

aₙ = a + (n - 1)d

where

Therefore,

a = 7

d = 17 - 7 = 10

Hence, the arithmetic formula is as follows:

aₙ = 7 + (n - 1)10

aₙ = 7 + 10n - 10

aₙ = 10n - 3

The sequence always increase by 10.

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Answer:

Step-by-step explanation:

The price of the car before tax was $18,560.3

Let the price of the car be x. Then,

x + 6% of x = $19,674

106x/100 = $19,674

x = $ 19,673*100/106

with BODMAS, we get

x= $18560.3

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Answer: (3, 1)

Step-by-step explanation:

Plug in each coordinate and see if the equation holds true:   

[tex](13, 2)\\13+2(7)=13+14=27\neq 10[/tex]

[tex](2, 1)\\2+7(1)=2+7=9\neq 10[/tex]

[tex](4, 1)\\4+7(1)=4+7=11\neq 10[/tex]

[tex]3+7(1)=3+7=10[/tex]