Amanda is framing her pool for resurfacing. The pool began with 14,340 gallons of water and it is draining at a rate of 880 gallons per hour. How long has the pool been draining if currently there are 8,840 gallons in the pool.

So solutions of the linear quadratic systems are (-5,-3) and (1,3)

Given,

y = x²+5x -3 . . . . . . . . . .. ..1

y-x= 2 . . . . . .. . . . . . . . . . . 2\

From 1 and 2

y=x+2

substitute y=x+2 in 1

x+2= x²+5x -3

x²+5x -x-3-2 = 0

x²+4x -5=0

x²+5x-x -5=0

x(x+5) -1(x+5) = 0

(x+5)(x-1)=0

x= -5 and x=1

at x=-5

y=x+2=-5+2=-3

at x=1

y=x+2=1+2=3

So solutions of the linear quadratic systems are (-5,-3) and (1,3)

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The term, coefficient and constant in the expression are 11q, 11 and 2 respectively.

The parts of an algebraic expression are;

Terms:  A term can be defined as a number, a variable, or the product of two or more variables or that of a product of a number and a variable.

The term is 11q

Coefficients: A coefficient is  defined as an integer multiplied by the variable.

The coefficient is 11

Constants: A constant is a number that do not change.

The constant is 2

Thus, the term, coefficient and constant in the expression are 11q, 11 and 2 respectively.

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The compound inequality is  60 < n < 104.

Let 'x' denote the amount of money saved by Julian.

Then x is between $30 and $52.

I.e., x>30 and x<52.

This can be written as a single inequality by combining the both.

i.e., 30 < x < 52

His friend Daniela saved twice as much as Julian.

Let 'n' denotes the amount of money Daniela saved.

Then n = 2x

We need to write the compound inequality for the money saved by Daniela.

As Daniela saved twice as much as Julian, it will be between 2 x 30 = $60 and 2 x 52 = $104

So the compound inequality is 60 < n < 104.

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For the given parallel ines cut by a transversal line the correct statement is (4). ∠7 and ∠8 are supplementary because they are a pair of adjacent angles that form a straight line.

The intersections of two parallel lines formed by a transversal form several angles. These are referred to as transversal angles. Here are some examples of transversal angles:

Angles are said to be supplementary to each other when two adjacent angles are formed at a point on a line so that the sum of their measures is 180°.

∠7 and ∠8 are supplementary in the attached figure since they represent a pair of adjacent angles which constitute a straight line.

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The correct question:

Please Help! The figure below shows parallel lines cut by a transversal:

Which statement is true about ∠7 and ∠8?

1. ∠7 and ∠8 are supplementary because they are a pair of corresponding angles.

2. ∠7 and ∠8 are complementary because they are a pair of adjacent angles on a straight line.

3. ∠7 and ∠8 are congruent because they are a pair of adjacent angles on a straight line.

4. ∠7 and ∠8 are supplementary because they are a pair of adjacent angles that form a straight line.

Answer:

9 and 3/5 hours or 9 hours and 36 minutes

Step-by-step explanation:

Rate x times = number of jobs

Jemuel's rate is 1 job/ 16 hours.

Lemuels's rate is 1 job/12 hours.

1/16T + 1/14T = 1  Get a common denominator of 48

3/48T + 2/48 t = 1

5/48T = 1  Multiply both sides by 48/5

(45/5)(5/48)T = 1(48/5)

t = 48/5 = 9 3/5 hours.

Plotting the inequalities using online graphing calculator. The graph is attached.

What is the example of inequality?

Given the system of inequalities:

3y > 2x + 12

3y - 2x > 12   (1)

2x + y < -5    (2)

Plotting the inequalities using  online graphing calculator. The graph is attached.

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Answer:

[tex](x + 21)(3x + 9) \\ x(3x + 9) + 21(3x + 9) \\ 3 {x}^{2} + 9x + 63x + 189 \\ 3 {x}^{2} + 72x + 189[/tex]

If the overall percentage of the defective panels from the two plants is 5% then plant B produced 4000 panels in total.

This question can be solved by formulating the problem into the form of a linear equation having two variables. Linear equation in two variables can be represented in the form of ax+by+c=0 where a, b and c are real numbers and x, y are variables or the coefficients, and a, b ≠ 0.

Let the production from plant A be x, and according to the question x=10000.

Also, let the production from plant B be y.

Now, as 3% of products are found defective from plant A and 10% of products are found defective from plant B and overall defective products is 5%.

Thus, 0.03x+0.1y=0.05(x+y)

As x=10000 then

0.03×10000+0.1y=0.05(10000+y)

300+0.1y=500+0.05y

0.05y=200

=>y=4000

Thus, the total number of panels produced by plant B is equal to 4000.

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The number of outfits she can buy is 3.

The The first step is to determine the total cost of all the items already bought.

Total cost = cost of new bicycle + (cost of one reflector x number of reflectors) + cost of the gloves

$488.20 + (2 x $11.17) + 19.05

$488.20 + 19.05 + $22.34 = $529.59

Now, determine the amount that is left to buy the outfits :

$660 - $529.59 = $130.41

Here are inequality signs and what they mean:

> means greater than

< means less than

≥ means greater than or equal to

≤ less than or equal to

The inequality sign that would be used is ≤

(cost of one outfit x number of outfits)  ≤ amount left

$37.26x ≤ $130.41

x  ≤ 130.41 / 37.26

x  ≤ 3.5

x = 3

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Answer:

y=-2

Step-by-step explanation:

5(2y-3)=40y

10y-15=40y

-15=30y

-2 = y

y = -2

Answer:

5x - 8y = -2

Step-by-step explanation:

m = 5/8, x = 0, y = 1/4

so y = mx + b

1/4 = 5/8(0) + b

b = 1/4

so y = 5/8x + 1/4

8y = 5x + 2

5x - 8y = -2

a. 55% of the maximum weight is 33 pounds.

b. 114 pounds is 190% of the weight limit.

c. 57 pounds is 95% of the maximum.

Answer to Part a:

Let c be the weight limit percentage for 33 pounds.

Then we have (60 x c)/100 = 33 pounds

This implies 3c/5 = 33

This means that 3c = 33 x 5 = 165.

This means that c = 165 / 3 = 55.

Therefore 55% of the weight limit is 33 pounds.

Answer to Part b:

Let d be the weight limit percentage for 114 pounds.

Then we have (60 x d)/100 = 114 pounds

This implies 3d/5 = 114

This means that 3d = 114 x 5 = 570.

This means that d = 570 / 3 = 190.

Therefore 190% of the weight limit is 114 pounds.

Answer to Part c:

95% of the weight limit is

= 95 x 60 /100

= 95 x 3/5

= 19 x 3

= 57

Therefore, 95% of the weight limit is 57 pounds.

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The two integers which the length of one side is in between are 72 yards and 73 yards

The given parameters are

Area = 5280 square yards

Shape = Square

The area of a shape is calculated using

Area = Length^2

So, we have

Length^2 = 5280 square yards

Take the square root of both sides

Length = 72.66 yards

72.66 yards is between 72 yards and 73 yards

Hence, the two integers which the length of one side is in between are 72 yards and 73 yards

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Answer:

=-2

________________________________________________________

[tex]a-\left(-b\right)=a+b[/tex] <- Apply this rule too -14-(-12)
[tex]-14-\left(-12\right)=-14+12[/tex]
[tex]=-14+12[/tex]
[tex]-14+12=-2[/tex] <- Add the numbers
[tex]=-2[/tex]
________________________________________________________
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Answer:

  translation 3 units up: g(x) = f(x)+3

Step-by-step explanation:

You are given graphs of f(x) and g(x) and want to know the transformation that gives g(x) from f(x).

The sorts of transformations of graphs that we study are translation, scaling (horizontally or vertically), and reflection about an axis.

Here, both graphs have the same shape, but one is in a different place than the other. The applicable transformation is one of translation.

The vertex of f(x) is at (0, -1). The vertex of g(x) is at (0, 2). We note the x-value has not changed, but the y-value has had 3 added to it. (-1 +3 = 2)

  g(x) = f(x) +3 . . . . . . the function f is translated 3 units upward.

A figure with the same perimeter as the one shown is a rectangle of base 3x and height 2, as given in the end of the question.

The perimeter of a figure is given by the sum of all the outer sides of the figure.

Hence, for this problem, the perimeter is given by:

P = x + 3 + 2x + 1 + 3

P = 6x + 4.

A figure with the same perimeter as the one shown is a rectangle of base 3x and height 2, as given in the end of the question, as:

3x + 3x + 2 + 2 = 6x + 4.

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Product Evaluation Rating for Brand A = 7.5

Product Evaluation Rating for Brand B = 7.4

Product Evaluation Rating for Brand C = 8.3

A product's acceptability for customers or a specific group is determined through the methodical process of product evaluation.

A visual representation of consumer behavior in terms of purchasing choices is a consumer buyer matrix. It also serves as a marketing tool for strengthening and expanding brands.

Given that :

Product Attributes -

Probability = 0.2

Sound projection = 0.5

Warranty = 0.3

Probability of Brand A = 7

Probability of Brand B = 10

Probability of Brand C = 6

Sound projection of Brand A = 8

Sound projection of Brand B = 6

Sound projection of Brand C = 10

Warranty of Brand A = 7

Warranty of Brand B = 8

Warranty of Brand C = 7

Calculation of Product Evaluation Rating :

Brand A = (7 x 0.2) + (8 x 0.5) + (7 x 0.3) = 1.4 + 4 + 2.1 = 7.5

Brand B = (10 x 0.2) + (6 x 0.5) + (8 x 0.3) = 2 + 3 + 2.4 = 7.4

Brand C = (6 x 0.2) + (10 x 0.5) + (7 x 0.3) = 1.2 + 5 + 2.1 = 8.3

Therefore,

Product Evaluation Rating for Brand A = 7.5

Product Evaluation Rating for Brand B = 7.4

Product Evaluation Rating for Brand C = 8.3

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Value for  the 3 straight  lines are 180,28 , 152.

What is a straight line, exactly?

Simply put, a straight line is a line devoid of bends. A straight line is one that does not curve and reaches to infinity on both sides.

CBE = 28 + 90 = so the angle is 118 degrees

ABF = you already got the answer written down, 28

CBA = this is not 180 like you wrote, CBA = ABD - CBD

Straight lines = 180, so ABD = 180

You already found out that CBD = 28

so CBA = 180 - 28 so the answer CBA = 152

So,  answers for the 3 lines are 180,28 , 152

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The factorized form of the quadratic is 2*(x + 2)*(x + 4), and when x = 3m, the walkway area is 52 square meters.

Here we know that the area is given by the expression:

2x^2 + 12x + 16

To factorize this, we need to find the roots of the quadratic equation, these are the solutions of:

2*x^2 + 12x + 16 = 0

The solutions are given by:

x = (-12 ± √(12^2 - 4*2*16))/(2*2)

x =  (-12 ± 4)/4

The two solutions are:

x = (-12 + 4)/4 = -2

x = (-12 - 4)/4 = -4

Then the factored form is:

y = 2x^2 + 12x + 16 = 2*(x^2 + 6x + 8) = 2*(x + 2)*(x + 4)

Now we want to get the area if the walkway if x = 3, the total area of the walkway and the garden will be:

y = 2*(3 + 2)*(3 + 4) = 70

And the garden measures x by 2x, then if x = 3, the area of the garden is:

a = x*2x = 3*(2*3) = 18

Then the area of the walkway alone is:

70 - 18 = 52

The area of the walkway is 52 square meters.

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It's 47. I used a calculator.

Answer: x=21

Step-by-step explanation:

Answer:

Volume is when you are finding the space inside of a 3D figure, and surface area is when you are finding the area of the surface(s) of a figure.

Hope this helps :)

$525

Step-by-step explanation:

Ben bought the house for $78,850 so 78,850 divided by 0.15 equals 525. So the answer is $525.

h: The domain

-5 ≤ x ≤ 5

Answer:

{ 0, 1 , 7}

Step-by-step explanation:

A U B= {1,0,1}. {0,1,7}

={0,1,7}