What is the length of the third side of the window frame below? (Figure is not drawn to scale.)
48 inches
60 inches
70 inches
75 inches

Answer:

(x+1)^2 = 49

x = 6                 x = -8

Step-by-step explanation:

x^2 + 2x – 48 = 0

Add 48 to each side

x^2 + 2x =48

Take the coefficient of x

2

Divide by 2

2/2=1

Square it

1^2 =1

x^2 + 2x +1=48+1

x^2 +2x+1 = 49

(x+1)^2 = 49

Take the square root of each side

sqrt((x+1)^2) =±sqrt( 49)

x+1 = ±7

Subtract 1 from each side

x+1-1 = -1  ±7

x = -1+7          x = -1 -7

x = 6                 x = -8

None of these answers work.  I believe you recorded the equations incorrectly.

Answer:  Open the compass to point D

Step-by-step explanation:  You will draw an arch with a radius BD so it will be able to intersect above and below with another arc of the same radius drawn with the compass point on point D

Answer:

Identity property of multiplication

Step-by-step explanation:

Given

Step 5: 1x = 20

Step 6: x = 20

Required

Property that justifies step 6

It should be noted that step 6 is a result of step 5.

So, basically the question is asking for the property applied on step 5.

Given that step 5 is: 1x = 20

The property applied is the identity property of multiplication.

This is so because this property states that when 1 is multiplied to an equation, the result remains the same.

Hence;

When 1 is multiplied to x (i.e. 1x), the result is still x.

So, 1x = 20 at step 5 gives x = 20 at step 6

Answer: Option B is the correct answer.

The identity property of addition

Answer:

$1788

Step-by-step explanation:

1200 x 0.07 = 84

84 × 7 = 588

588 + 1200 = 1788

The value of the  account after the 10th deposit if no withdraws or additional deposits are made should be $15,093.47.

Since

The initial deposit is $1.200

The rate of interest is 5%

Now the future value be like

[tex]= (1,200 \times (1 + 0.05)^{9} - 1) \div 0.05) \times (1 + 0.05) + 1,200\\\\= 1,200 \times (1.5513 - 1) \div 0.05) \times (1 + 0.05) + 1,200\\\\= (1,200 \times 11.0265) \times (1.05) + 1,200[/tex]

= 13893.4711 + 1,200

= $15,093.47

hence, The value of the  account after the 10th deposit if no withdraws or additional deposits are made should be $15,093.47.

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Answer:

2.94117647

Step-by-step explanation:

17 x 2 = 34

50 -34 = 16

The answer is 2 with a remainder of 16

Answer:

20

Step-by-step explanation:

2 in 529 is in the tens place - 10

So if 2 is in the tens place, we have 20 as the value of 2.

Answer:

the answer to ur question would be 20 B)

Answer:   $1450

The profit that is gained from the production and selling of the jeans is given to be calculated through the the equation,

                         P = 20x - 50

For 75 jeans, we just have to substitute 75 to the x's of the equation. This then becomes,

                       P = 20(75) - 50 = 1450

Thus, the company will make a profit of $1450 by production of 75 jeans. 

Step-by-step explanation:

The company will make a profit of $1450 by the production of 75 jeans.

The profit that is gained from the production and selling of the jeans is modeled by the equation;

P = 20x - 50

If 75 jeans are produced, substitute 75 to represent the value of x in the equation.

P = 20(75) - 50 = 1450

Hence, the company will make a profit of $1450 by the production of 75 jeans.

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Answer:

y = -7

Step-by-step explanation:

A horizontal line has an equation of the form

y = b,

where b = y-intercept

The y-intercept is -7, so the equation is

y = -7

Answer:

Y=-7

Step-by-step explanation:

No matter what x equals, y has to be equal to negative 7. For example i chose 3 to by X, the equation would still be (3,-7).

Answer:

The system of equations that make the definition are;

x + y = 10 •••••••••(i)

6x + 8y = 72 ••••••••(ii)

Where x refer to the number of packages of AA battery bought and y refers to the number of packages of AAA batteries bought

Step-by-step explanation:

Here, we are to write system of equations that can be solved which will help give the number of packages of each type of battery bought.

Let the number of AA batteries bought be x while the number of AAA batteries bought be y;

Since he bought a total of 10 packages,

What this means is that;

x + y = 10 •••••••••(i)

We are also told that the AA batteries are sold in packages of 6, so the total number of AA batteries bought is; 6 * x = 6x

Also, we know that the AAA batteries are sold in packages of 8, so the total number of AAA batteries bought is 8 * y = 8y

We add both to give the total number of packages.

Mathematically, that would be;

6x + 8y = 72 •••••••••(ii)

By solving both equation set, we shall have the number of each types of batteries bought

Answer:

x = 18

A = 110

Step-by-step explanation:

Angles A and B are supplementary angles so they add to 180 degrees

A + B = 180

5x+20 + 9x -92 = 180

Combine like terms

14x -72 = 180

Add 72 to each side

14x-72+72 = 180+72

14x = 252

Divide each side by 14

14x/14 = 252/14

x =18

A = 5x+20

  = 5*18 +20

   =90 +20

   = 110

Answer:

6x¹⁰ - 96x²

6x²(x⁸ - 16)

B) 6x²(x⁸ - 16)

6x²[(x⁴)² - 4²]

6x²[(x⁴ - 4)(x⁴ + 4)]

6x²(x⁴ + 4)[(x²)² - 2²]

6x²(x⁴ + 4)(x² - 2)(x² + 2)

Answer:

Step-by-step explanation:

Part A: The rewritten expression created by factoring out the greatest common factor is 6x2(x8 – 16).

Part B: The completely factored expression is 6x2(x4 + 4) (x2 + 2) (x2 – 2).

My work for Part B:

Step 1: Using the expression from Part A, we just simplify the inside of the parentheses as much as possible by using the difference of two perfect squares pattern:

6x2(x4 + 4) (x2 + 2) (x2 – 2).

Answer:

The volume doubles to 120

Step-by-step explanation:

Volume of Rectangular Prism Formula: V = lwh

Step 1: Find volume of given lengths

V = 3(4)(5) = 60 in²

Step 2: Find volume when we double h

4(2) = 8

V = 3(8)(5) = 120 in²

Step 3: Divide the 2 numbers to find the ratio

120/60 = 2, or double the amount.

Answer:

$49.71

Step-by-step explanation:

Take $54.99 - 20% to get $43.99 add 13% and get $49.71

Answer:

[tex]\boxed{0.06 < 0.0604 < 0.6 < 0.604 < 0.64}[/tex]

Step-by-step explanation:

In ascending order: (starting from the smallest)

[tex]\boxed{0.06 < 0.0604 < 0.6 < 0.604 < 0.64}[/tex]

Answer:

.0604 < .604 < .06< .64 < .6

Step-by-step explanation:

.6= 6/10

.64=.64/100

.06=6/100

.604=604/1000

.0604=604/10000

Step-by-step explanation:

The area of triangle is 53.5m2

Answer: 118.2977 sq. m.

Step-by-step explanation:

Step 1: Calculate "s" (half of the triangles perimeter):

s = a+b+c / 2

s = (13 + 18.2 + 22.3) / 2

s = 26.75

Step 2: Then calculate the Area:

Herons formula

A = √( s(s-a)(s-b)(s-c) )

A = √(26.75 (26.75 - 13)(26.75-18.2)(26.75-22.3)

A = (3√9951535) /80

A = 118.2977 sq. m.

Answer: valu of a

Step-by-step explanation: I Did the test

Answer:

The value of A affects the answer.

Answer:

Abigail was four times faster in the skateboard than when she is walking

Step-by-step explanation:

Let the total distance to travel be d

distance traveled on skateboard = 2/3 * d = 2d/3

distance walked = 1/3 * d = d/3

So let the time taken to skate be t, then time taken to walk home will be 2t since it is 2 times longer.

Now, the speed on both trips is distance/time

For the snowboard trip, speed is 2d/3/t = 2d/3t

For the walking trip, distance would be;

d/3/2t = d/6t

So let’s compare these two speeds.

Obviously the speed on the skateboard is greater than that walking.

So we can equally divide the speed on the skateboard by that while walking to know how many times faster it is.

Thus, mathematically we have

2d/3t divided by d/6t

So that would be;

2d/3t * 6t/d = 4

So this means she was four times faster on the skateboard

Answer:

The factors of the polynomial are:

(x + 1) and (x - 3).

Step-by-step explanation:

Consider the image attached.

The upper tiles shows: (x + 1)

And the left tiles shows: (x - 3)

So, the factors of the polynomial are:

(x + 1) and (x - 3).

Answer:

x+1 and x -3

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given the height h (t )of the sunglasses after t seconds modeled by the polynomial function h(t ) =  -16t²+ 4096

Since the sunglasses hit the ground, the height of the glass on the ground will be 0feet. Substituting h(t)= 0 into the formula to know the time it takes the glass to hit the ground will give;

0 = -16t²+ 4096

0+16t² = 4096

16t² = 4096

Dividing both sides by 16;

16t²/16 = 4096/16

t² = 256

Taking the square root of both sides

√t² = √256

t = 16 seconds

This means that the sunglasses will hit the ground after 16 seconds

Answer:

6x^2 -31x +40

Step-by-step explanation:

2x * 3x + 2x * - 8 + -5 * 3x -5 * -8  Distributive property

6x^2 -16x -15x + 40  Math

6x^2 -31x +40 Answer

Answer:

(0, 2)

Step-by-step explanation:

The graph of g(t)= -(t-1)^2+5 is an inverted parabola with vertex at (1, 5).

Making a table of t and g values would be helpful here:

 t      g(t) = -(t - 1)^2 + 5

------ -----

  2     4

  0     4

 -1      1

  1      5

We're looking for an interval on which the average rate of change is zero.

Note that this is the case on the interval (2, 4); g(0) = g(2) = 4, so the change in g is 4 - 4, or zero (0).

The average rate of change of [tex]g(t)=-(t-1)^2+5[/tex] is 0 in interval [tex]-1\leq t\leq 3[/tex].

Given,

[tex]g(t)=-(t-1)^2+5\\[/tex].

We have to find the interval in which [tex]g(t)=-(t-1)^2+5\\[/tex] have an average rate of change of zero.

We know that, the function [tex]f(x)[/tex] will have average range of 0 when [tex]f(b)=f(a)[/tex].

Now we calculate g(1), g(2),g(3) and g(-1),

[tex]g(1)=-(1-1)^2+5\\g(1)=5[/tex]

[tex]g(2)=-(2-1)^2+5\\g(2)=-1+5\\g(2)=4[/tex]

[tex]g(3)=-(3-1)^2+5\\g(3)=-4+5\\g(3)=1[/tex]

[tex]g(-1)=-(-1-1)^2+5\\g(-1)=-4+5\\g(-1)=1[/tex]

Since,

[tex]g(3)=g(-1)=1[/tex]  so the function [tex]g(t)=-(t-1)^2+5\\[/tex] has an average rate of zero at [tex]-1\leq t\leq 3[/tex].

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Answer:

1/3

Step-by-step explanation:

In math, to find the probability of an event we need to take the total amount of favorable outcomes and divide this number between the total amount of possible outcomes.

In this case Paul has 15 T-shirts and he takes one of his blue T-shirts at random. We can see that he has a total of 3 blue shirts, thus, the total amount of possible outcomes is 3.

Now, we need to find the probability that the T-shirt is light blue, he only has 1 light blue t-shirt so the number of favorable outcomes is 1.

If we divide the number of favorable outcomes between the number of possible outcomes we have [tex]\frac{1}{3}[/tex]. Thus, the probability that the T-shirt is light blue is 1/3

Answer and Step-by-step explanation:

(i) The solution for equation: 2(3x-3) - 5 = 2(x-3) + 15 is:

2(3x-3) - 5 = 2(x-3) + 15

6x - 6 - 5 = 2x - 6 +15

6x - 2x = - 6 + 15 + 6 + 5

4x = 20

x = 5

The solution x is a real number and equals 5.

(ii) Since the order of hot sauce that goes into the gumbo doesn't matter, use combination:

[tex]C^{10}_{3}[/tex] = [tex]\frac{10!}{3! (10-3)!}[/tex]

[tex]C^{10}_{3}[/tex] =  [tex]\frac{10.9.8.7!}{3.2.1.7!}[/tex]

[tex]C^{10}_{3}[/tex] = 120

There are 120 ways of picking 3 sauces out of 10.

(iii) Interest is calculated as:

interest = principal*rate*time

Principal is the value of the loan;

Rate is how much it will increase;

Time is for how long the loan will be taken. In this case, time is 9/12 since it was for months;

Interest = 3000 * [tex]\frac{11.75}{100}*\frac{9}{12}[/tex]

Interest = 264.37

The interest the student will pay will be: $264.37.

Future Value = principal + interest

future value = 3000 + 264.37

future value = 3264.37

The future value for the student is $3264.37.

(iv) As shown in the image in the attachment, the sum of the equations equals 90:

2x + 30 + 2x + 40 = 90

4x = 20

x = 5

The angles are 40° and 50°

Answer:

y=3x+8

Step-by-step explanation:

Perpendicular to -1/3, is 3.

y-5=3(x+1)

y-5=3x+3

y=3x+8

Answer:

y - 5 = 3(x + 1).

Step-by-step explanation:

y = -1/3x - 6

The slope of this line is -1/3 so the slope of the perpendicular line to it is -1/-1/3

= 3.

Using the point-slope form of a straight line:

y - y1 = m(x - x1)  where m = the slope and (x1, y1) is a point on the line:

Here m = 3 and (x1, y1) is (-1, 5) so we have:

y - 5 = 3(x - (-1))

y - 5 = 3(x + 1).

Answer:

12 and 2100

Step-by-step explanation:

(a)

Divide 4800 by 5 for pens per hour produced by 80 machines.

4800 ÷ 5 = 960 pens per hour

Divide 960 by 80 for pens per hour produced by 1 machine.

960 ÷ 80 = 12

Thus 1 machine produces 12 pens per hour

(b)

Multiply 12 by 7 for pens produce in 7 hours by 1 machine.

12 × 7 = 84 pens per hour

Multiply 84 by 25 for pens produced in 1 hour by 25 machines.

84 × 25 = 2100

Thus 2100 pens are produced by 25 machines in 1 hour

Answer:

$175.

Step-by-step explanation:

There are 100 centimeters in  meter and 1000 metres in a kilometer so we have 100,000 cm in a kilometer.

So the required cost

= 0.07 * 100,000 / 40

= 7000 / 40

= $175.

Answer:

Hello! :) The answer will be under “Explanation”

Step-by-step explanation:

As my answer I got $175

1km would equal to 100,000 cm

1m would be 100cm

That means 1 km = 100 000 cm

Now you have to divide.

100,000 divided by 40 equals to 2,500($0.07)

=$175

If we do the math correctly we can now see that the answer should be $175

Hope this helps! :)

By:BrainlyMember ^-^

Good luck!

Answer:

its 60-15(pie) sq inches

Step-by-step explanation:

Answer:

B.   y = 6x^2 - 24x + 16.

Step-by-step explanation:

y = 6(x - 2)^2 - 8

y = 6(x^2 -4x + 4) - 8

y = 6x^2 - 24x + 24 - 8

y = 6x^2 - 24x + 16.