A family needs to build fencing around their rectangular home and square swimming pool, depicted below.
A rectangle labeled home has its right side labeled (2 + 5 x) yards and its bottom side labeled (3 + 10 x) yards. The square, labeled pool, is smaller than the rectangle. One of its sides is labeled (2x) yards.
The total amount of fencing they need can be written as x + 10.

If x = 5;
The family needs yards of fencing for their home.

The family needs yards of fencing for their pool.

The equation of the parabola graphed is given as follows:

y = a(x + 1)² - 4.

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

Considering the vertex given, we have that h = -1, k = -4, hence the equation is:

y = a(x + 1)² - 4

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Answer:

2700

Step-by-step explanation:

*6*10*9/4!*4*4*6*5/4!

Answer:

69%

Step-by-step explanation:

Overall grade = 0.35*minor grade + 0.65*major grade

major grade: 0.65*61 = 39.65

minor grade: 0.35*84 = 29.4

total: 39.65+29.4 = 69.05

Rounded = 69%

Answer:

Step-by-step explanation:

1 1/6 + (x/3 · 1/4) = 1 3/4

solve for x

1 1/6 + x/12 = 1 3/4

1 1/6 - 1 3/4 = -x/12

-7/12 = -x/12

-7 = -x

x = 7

----------------

check

1 1/6 + (7/12 * 1/4) = 1 3/4

1 1/6 + 7/48 = 1 3/4

1 15/16 = 1 3/4

1 3/4 = 1 3/4

the answer is good

The right triangle whose hypotenuse is the square root of 17 has legs of 1 inch and 4 inches

Step 1 and 2: Create an isosceles right triangle

This is represented by the attached figure in (see figure 1 for this triangle)

The legs of this triangle have a length of 1 inch

Step 3: The hypotenuse

This is calculated using the following Pythagoras theorem

[tex]h^2 = 1^2 + 1^2[/tex]

This gives

[tex]h = \sqrt 2[/tex]

Step 4: Create another isosceles right triangle

This is represented by the attached figure in (see figure 2 for this triangle)

The legs of this triangle are 1 inch and 2 inches, respectively

This hypotenuse is calculated by:

[tex]h^2 = 2^2 + 1^2[/tex]

This gives

[tex]h = \sqrt 5[/tex]

Step 5: Create another isosceles right triangle

This is represented by the attached figure in (see figure 3 for this triangle)

The legs of this triangle are 1 inch and 3 inches, respectively

This hypotenuse is calculated by:

[tex]h^2 = 3^2 + 1^2[/tex]

This gives

[tex]h = \sqrt {10[/tex]

Step 6: Create another isosceles right triangle

This is represented by the attached figure in (see figure 4 for this triangle)

The legs of this triangle are 1 inch and 4 inches, respectively

This hypotenuse is calculated by:

[tex]h^2 = 4^2 + 1^2[/tex]

This gives

[tex]h = \sqrt{[17[/tex]

See that the hypotenuse is the square root of 17

Hence, the right triangle whose hypotenuse is the square root of 17 has legs of 1 inch and 4 inches

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Answer:

This is your answer.

Step-by-step explanation:

There are different kinds of angles:

Angles below 90= Acute

90= Right

91–179= Obtuse

180= Straight Angle

181–359= Reflex Angle

360= Complete Angle or Circle.

Because 80 degrees is less than 90 degrees, Angle ABC is an acute angle.

This question is asking to create 5 of your own questions, so here are mine with the process on how I got each:

Question 1: Given c(x) = 8x + 32, find the range of c for the domain {1, 3, 5}.

Answer w/ Process:

For each equation, I am plugging in each domain value for x in the function, multiplying by 8, and adding by 32.

c(1) = 8(1) + 32 = 8 + 32 = 40

c(3) = 8(3) + 32 = 24 + 32 = 56

c(5) = 8(5) + 32 = 40 + 32 = 72

Range: {40, 56, 72}

Question 2: Given d(x) = x - 7, find the range of d for the domain {-2, 3}.

Answer w/ Process:

For each equation, I am plugging in each domain value for x in the function, and subtracting 7.

d(-2) = -2 - 7 = -9

d(3) = 3 - 7 = -4

Range: {-9. -4}

Question 3: Given f(x) = 7x + 738, find the range of f for the domain {1.5, 11}.

Answer w/ Process:

For each equation, I am plugging in each domain value for x in the function, multiplying by 7, and adding 738.

f(1.5) = 7(1.5) + 738 = 10.5 + 738 = 748.5

f(11) = 7(11) + 738 = 77 + 738 = 815

Range: {748.5, 815}

Question 4: Given g(x) = -2804x + 7268, find the range of g for the domain {50, 75, 256}.

Answer w/ Process:

For each equation, I am plugging in each domain value for x in the function, multiplying by -2804, and adding 7268.

g(50) = -2804(50) + 7268 = -140200 + 7268 = -132932

g(75) = -2804(75) + 7268 = -210300 + 7268 = -203032

g(256) = -2804(256) + 7268 = -717824 + 7268 = -710556

Range: {-132932, -203032, -710556}

Question 5: Given h(x) = -3x - 4, find the range of h for the domain {1, 2, 3}.

Answer w/ Process:

For each equation, I am plugging in each domain value for x in the function, multiplying by -3, and subtracting by 4.

h(1) = -3(1) - 4 = -3 - 4 = -7

h(2) = -3(2) - 4 = -6 - 4 = -10

h(3) - -3(3) - 4 = -9 - 4 = -13

Range: {-13, -10, -7}

b(-3)

b(5)

b(9)

Range

Rest questions

#1

k(x)=2x²-5

Find the range of k for domain {1,2,6}

#2

h(x)=9x³

Find the range of h for domain {9,0,8}

#3

o(x)=6x-7

find the range of o for domain {0,1,9}

#4

p(x)=23x²-5x

Find the range of p for domain {3,4,8}

Yes, the planner has met the minimum height, as the minimum height was 9 feet and the maximum height of the arc is 9.6 feet

As we can see that at the mid value, for x=4, the value of f(x)=9.4

It means that the maximum height occurs at mid of the arc where it is height is 9.6 feet above the ground.

It means that the planner has met the minimum height, as the minimum height was 9 feet and the maximum height of arc is 9.6 feet

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The correct option is the third one:

-1 ≤ y - 3 and y - 3 ≤ 1

Which compound inequality represents the absolute value inequality?

Here we have:

|y - 3| - 4 ≤ -3

We can rewrite it to:

|y - 3| ≤ -3 + 4

|y - 3| ≤ 1

This can be decomposed in two inequalities, which are:

(y - 3) ≤ 1

(y - 3) ≥ -1

Then we can see that the correct option is the third one, as both inequalities must be meet.

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Answer: If the product of any two numbers in the list is equal to 0, you can't conclude that the list is composed only by zeroes. In fact, suppose that you have a list of N numbers which are all zeroes except one. Whenever you multiply two elements of this list, you either multiplies two zeroes, or you multiply the non-zero element by a zero element, and so the result is zero, but the list is not composed by zeroes only.

Step-by-step explanation:

The fraction 16/22 represents the number of problems completed over the total number of problems in the assignment.

According to the question,

There are 22 problems in her assignment and Sabrina finished 8/11 of her math assignment.

In order to find the fraction represents the number of problems completed over the total number of problems in the assignment.

(8/11) * (2/2) = 16/22

Hence, the fraction 16/22 represents the number of problems completed over the total number of problems in the assignment.

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Answer:

112

Step-by-step explanation:

If she takes 1/8 of an hour to complete one then she can finish 8 in 1 hour.

8 x 14 = 112

The average speed is 50 meters per second

The given parameters are:

Laps = 4

Time = 2 minutes

1 lap = 25 meters

Start by calculating the total distance

Distance = Laps * Meters

Distance = 4 * 25 meters

Distance = 100 meters

The average speed is then calculated as:

Speed = Distance/Time

This gives

Speed = 100 meters/2 minutes

Evaluate

Speed = 50 meters per second

Hence, the average speed is 50 meters per second

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Answer: Correct

Step-by-step explanation:

The conclusion is valid. Since [tex]\overline{AB} \parallel \overline{DC}[/tex] and [tex]\overline{AD} \parallel \overline{BC}[/tex], we know that ABCD is a parallelogram because it has two pairs of parallel sides. Also, since [tex]\overline{AB} \cong \overline{BC}[/tex], we know that ABCD is a parallelogram with a pair of consecutive congruent sides, making it a rhombus.

The percentage of great lakes states would we expect the economic impact from fishing to be between $234.5 and $401.5 is 50%.

Given that mean is $318 , standard deviation is $83.5 and confidence interval is $234.5 and $401.5.

We have to calculate the percentage of great  lakes that we would expect the economic impact from fishing to be between $234.5 and $401.5.

Because we have not given the sample size taken so we will use any test.We are using z test.

We know that,

z=X-μ/σ

where μ is population mean and σ is population standard deviation.

We cannot find p value between $234.5 and $401.5. We have to find the p value between $234.5 and $318 and then add the p value between $318 and $401.5 by calculating.

P value between $234.5 and $318:

z=234.5-318/83.5

=-83.5/83.5

=-1

p value of -1 is 0.1587

P value between $318 and $401.5:

z=401.5-318.5/83.5

=83.5/83.5

=1

p value of z=1 is 0.3413

Total p value=0.1587+0.3413

=0.5

Total percentage=0.5*100

=50%

Hence the percentage that we would expect the impact to be between $234.5 and $401.5 is 50%.

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Answer:

  II only

Step-by-step explanation:

The positive leading coefficient and even degree of f(x) tell you its graph is U-shaped and opens upward.

If there is an interval where the function is negative, it must lie between the two x-intercepts. The graph will be above the x-axis (f(x) > 0) for x-values outside that interval.

The only reasonable answer choice is ...

  II  (-1, 4) . . . . only

  [a] x = 175 - 7.5p

For a, we are isolating the x variable to one side of the equation.

        0.4x + 3p = 70

        0.4x = - 3p + 70

        x =  - 7.5p + 175

  [b] x = 115

For b, we are solving for x when p = 8.

        x =  - 7.5p + 175

        x =  - 7.5(8) + 175

        x = 115

Answer:   y = -x + 2

Step-by-step explanation:

Point slope form is y - y = m(x - x)

m = the slope of the line

Slope-intercept form is y = mx + b

m = the slope of the line

b = y-intercept

So because the - is in the m spot in the point-slope form, that means that is the slope of the line meaning it will also be in the m spot in slope-intercept form. The y-intercept of the line is found when x is 0.  When we look at the two coordinates provided you can see that one of them shows when x is 0.  We see that when x is 0, y is 2  which means that the y-intercept is 2.

So when you put the 2 in place of b,  you get   y = -x + 2

Answer:

12  and 3

Step-by-step explanation:

Let  x= length

If you draw a rectangle.  two sides would be the length x.  The other two sides would be (x-9).

(length)(width) = Area

(x)(x-9) = 36

x^2 - 9x = 36 Substitute in x and x-9 for the length and width

x^2 - 9x - 36 =0  Subtract 36 from both sides

(x-12)(x+3) = 0   We are looking for 2 number that add to -9 and mult. to -36

x-12=0 and x+3=0  Set both factors to 0 and solve

x = 12 and x =-3.  It does not make sense that a length could be -3 so we reject that answer.  If the length is 12, then the width is 3

Answer:

width = 9 inches

Step-by-step explanation:

let width be w then length is w + 12

the perimeter ( P) is calculated as

P = 2( width + length )

here P = 60 , then

2(w + w + 12) = 60 ( divide both sides by 2 )

2w + 12 = 30 ( subtract 12 from both sides )

2w = 18 ( divide both sides by 2 )

w = 9

that is the width of the rectangle is 9 inches

The dimensions of the rectangle are: length= 18 in and width =1 in.

There are different types of quadrilaterals, for example, square, rectangle, rhombus, trapezoid, and parallelogram.  Each type is defined accordingly to its length of sides and angles. For example, in a rectangle,  the opposite sides are equal and parallel and their interior angles are equal to 90°.

The area of a rectangle can be found for the formula : l*w, where b = length and w =width. The question gives that the area is 18 in².

For this question, the length exceeds its width by 17 inches - l=w+17. Thus,  from the value of area given, you can find the values of the length and width of the rectangle.

A=l*w

18=(w+17)*w

18=w²+17w

w²+17w-18=0

Next step will be solve the previous equation ( W²+17W-18=0)

[tex]w_{1,\:2}=\frac{-17\pm \sqrt{17^2-4\cdot \:1\cdot \left(-18\right)}}{2\cdot \:1}\\ \\ w_{1,\:2}=\frac{-17\pm \:19}{2\cdot \:1}[/tex]

Therefore,

[tex]w_1=\frac{-17+19}{2\cdot \:1}=1\\ \\ \\ w_2=\frac{-17-19}{2\cdot \:1}=-18[/tex]

For dimensions, only positive numbers must be used. Then, the width is equal to 1 inch.

As, the area (l*w) is 18 in², you have.

18=l*w

18=l*1

l=18 in

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The quotient of the polynomials [tex]2x^{3} +3x^{2} -5x-6[/tex] divided by (x+1) is [tex]2x^{2} -x-6[/tex].

Given two polynomials [tex]2x^{3}+3x^{2} -5x-6[/tex] and (x+1).

We have to determine whether [tex]2x^{3}+3x^{2} -5x-6[/tex] is divisible by (x+1).

Factors are the numbers which are multiplied to get the number whose factors are given. The factor theorem is a theorem which links factors and zeroes of a polynomial.

Polynomial is an expression of more than two algebraic terms may be in addition or subtraction.

We have to first find the factors of polynomial [tex]2x^{3}+3x^{2} -5x-6[/tex].

[tex]2x^{3}+3x^{2} -5x-6[/tex]=[tex]2x^{3}+3x^{2} -4x-x-6[/tex]

=[tex]x^{2}[/tex](2x+3)-2(2x+3)-x

=[tex](x^{2} -x-2)[/tex](2x+3)

=([tex]x^{2}[/tex]-x-2)(2x+3)

=[[tex]x^{2}[/tex]-2x+x-2](2x+3)

=[x(x-2)+1(x-2)](2x+3)

=(x+1)(x-2)(2x+3)

Because (x+1) is a factor of [tex]2x^{3}+3x^{2} -4x-x-6[/tex],so it is divisible by (x+1).

Hence using factor theorem we can say that [tex]2x^{3}+3x^{2} -4x-x-6[/tex]is divisible by (x+1).

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The solutions of the equations x - 5y = 0 and 15x + 10y = 17 at x and y is 1 and 1/5 respectively.

Two algebraic expressions separated by an equal symbol in between them and with the same value of the expression are called equations.

Given that:

The linear equations are:

x - 5y = 0

15x + 10y = 17

Solve the equations using elimination method:

Multiply equation 1 by 2

2(x - 5y) = 0

15x + 10y = 17

This can be solved as:

2x-10y = 0.....(1)

15x + 10y = 17....(2)

On subtracting equation 1 from 2

17x = 17

x = 1

The value of x is 1.

Substitute the value of x in equation (1)

2(1)-10y = 0

2=10y

y = 1/5

Thus, the value of x and y is 1 and 1/5 respectively.

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If the sum of an integer and 7 more than the next consecutive integer is 66 then the integers are 29 and 30.

Given that the sum of an integer and 7 more than the next consecutive integer is 66.

Integer is a number that is written without a fraction component. It can be positive as well as negative.

let the first integer be x.

Consecutive integer will be x+1.

Sum of integer and 7 more than the next consecutive integer is 66.

Sum according to the given information=x+x+1+7

=2x+8

2x+8=66

2x=66-8

2x=58

x=58/2

x=29

Next integer=29+1-30.

Hence if the sum of an integer and 7 more than the next consecutive integer is 66 then the integers are 29 and 30.

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Answer:

m=15

Step-by-step explanation:

Oh, I think I answered this question recently, but it's m=15c

The explanation for the question was written in my other response.

Answer:

d.  m = 15c

Step-by-step explanation:

Directly proportional means as one amount increases, another amount increases at the same rate.

Proportionality can be used to set up an equation.

Given variables:

If m is directly proportional to c then:  [tex]m \propto c[/tex]

Convert this to an equation by using a constant of proportionality, k:

[tex]\implies m=kc[/tex]

We are told that Paul washed 8 cars and earned $120.

Substitute these values into the found equation and solve for k:

[tex]\implies 120=8k[/tex]

[tex]\implies k=\dfrac{120}{8}[/tex]

[tex]\implies k=15[/tex]

Finally, substitute the found constant of proportionality (k) into the equation:

[tex]\implies m=15c[/tex]

the necessary steps to predict data not included in a data set using a scatter plot and line of best fit are Options 2, 3, 4

In using the line of best fit also known as the slope, they following steps are involved;

In using scatterplot, they following steps are involved;

This explains that the average of the set of data is found from the scatter plot and line of best fit.

Thus, the necessary steps to predict data not included in a data set using a scatter plot and line of best fit are Options 2, 3, 4

Graph the data in a scatter plot

Extend the line of best fit beyond the data

Find the average of the data

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Profit function : p(x) = 53 x - 12

Cost is the total cost of producing the output.

The cost function consists of two different types of costs:

- Variable costs

- Fixed costs.

Variable costs vary with output (number of units produced). Total variable costs can be

expressed as the product of variable costs per unit and the number of units produced. If there are multiple items

manufactured costs are higher.

Fixed costs usually do not vary with performance.

Revenue is the total payment received from the sale of goods or the provision of a service.

The revenue function R() reflects the revenue from selling “” quantity of output items at price

"p" after item.

() =

Profit functions

The profit function P() is the difference between the revenue function R(x) and the total cost function C()

So P() = R() – C()

=−

Now, Profit = Revenue - Cost

= 60 x - ( 12 + 7 x)

= 60 x -12 -7 x

Profit = 53 x - 12

Hence, Profit function : p(x) = 53 x - 12

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The equation of a trend line that passes through the points (7, 450) and (14, 401) is y = -7x+99.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

More than one variable may be present in a linear equation. An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation.

Points are: (7, 450) and (14, 401)

Slope(m)=(401-450)/(14-7)

              = -49/7

              = -7

Equation of trend line:

(y-450)= -7(x-7)

y-450= -7x+49

y= -7x+49+450

y= -7x+499

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A random samples of ticket prices for concerts and the random samples of Coldplay ticket prices are independent . The answer is True.

According to the questions,

A random samples of ticket prices for concerts by the Rolling Stones was obtained. For comparison purposes another random samples of Coldplay ticket prices was obtained.

The two groups of data are independent samples.

Hence, a random samples of ticket prices for concerts and the random samples of Coldplay ticket prices are independent . The answer is True.

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Part 1: Correct.

Part 2

[tex]\sqrt{(-52)^2 + 48^2} \approx 70.77[/tex]