alg 1 adding/subtracting with rational expression

The series is a geometric series and the sum of the first 8 terms of the series 48, 60, 75 is 952.32

The series is given as:

48, 60, 75

The above series is a geometric series with the following parameters:

First term, a = 48

Common ratio, r = 1.25

The sum of n terms is:

[tex]S_n = \frac{a(r^n - 1)}{r -1}[/tex]

So, we have:

[tex]S_8 = \frac{48 * (1.25^8 - 1)}{1.25 -1}[/tex]

Evaluate

[tex]S_8 = 952.32[/tex]

Hence, the sum of the first 8 terms of the series is 952.32

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Answer:

Step-by-step explanation:

4 boxes should do

[tex]\Huge{\mathcal{\color{black}{Hey \: there!}}}[/tex]

[tex] \large\underline{ \boxed{ \sf{✰Important\: points }}}[/tex]

through this we can easily value of another variable by computing value of one variable

[tex]\rule{70mm}{2.9pt}[/tex]

[tex] \underline{ \boxed{ \sf{✰Given\: function }}}[/tex]

⇒y=2+5x

★ if x=3 then y =17

★ if x=4 then y= 22

★ if x=5 then y=27

★ if x=10 then y=52

[tex]\rule{70mm}{2.9pt}[/tex]

Hope it helps!

The standard equation of the circle in the graph is (x - 2)² + (y - 5)² = 16

From the graph, we have the following parameters:

The equation of the circle is then calculated using:

(x - a)² + (y - b)² = r²

So, we have:

(x - 2)² + (y - 5)² = 4²

Evaluate

(x - 2)² + (y - 5)² = 16

Hence, the standard equation of the circle in the graph is (x - 2)² + (y - 5)² = 16

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Answer:

114 sq ft

Step-by-step explanation:

Find out the area of the end triangle;

2x3=6

6x0.5 (1/2) = 12

Find the perimeter of the end triangle;

3+3+3=9

Find the area of the rectangle;

9x10=90

Find the total surface area;

2x12=24

24+90=114 sq ft

Answer:

3

Step-by-step explanation:

the surface area is the base

you will know what the base is based on the name

since it's a triangular prism, the base is a triangle

the triangle in the picture is 2 in hight and and 3 on the ground

2 x 3/2

6/2

3

Answer:

B)  $19,865.03

Step-by-step explanation:

Continuous Compounding Formula

[tex]\large \text{$ \sf A=Pe^{rt} $}[/tex]

where:

Given:

Substituting given values into the formula and solving for A:

[tex]\large \implies \text{$ \sf 8540e^{0.0603 \times 14}=19865.03215 $}[/tex]

Answer:

x> 7/3

Step-by-step explanation:

expand:

4x-2 >12-2x

4x>-2x+14

6x>14

x>14/6

x>7/3

Answer:

C. 31 units

Step-by-step explanation:

Circumference of a circle is the distance around the circle and is given by C = pi•d

Your circle with a point and center given has a radius of 5 because from (2,1) to (7,1) is 5 units. Radius 5 means the diameter is 10.

C = pi•10

= 3.14•10

= 31.4 using 3.14 as an approximation for pi.

Circumference is approximately 31 units.

The Length of ladder is 17.73 feet.

The angle formed by the line of sight and the horizontal plane for an object above the horizontal.

distance of the foot of the ladder =  5 feet

Using trigonometry,

cos [tex]\theta\\[/tex] = B/H

cos 73.61= 5/H

0.282 = 5/H

H = 5/0.282

H = 17.73 feet

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Answer:

24

Step-by-step explanation:

first you have to add 2 and 4; 6. then multiply it by 4; 24

The equation of the line which is perpendicular to 3x - y = 10 is y = -(1/3) x + c. Then the correct option is B.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

The line that is perpendicular to 3x - y = 10.

The equation can be written as

y = 3x - 10

Then the slope of the line will be

m₁ = 3

Let m₂ be the slope of the second line.

The product of the slope of the perpendicular lines is a negative one.

m₁m₂ = -1

 3m₂ = -1

   m₂ = -1/3

Then the equation of the perpendicular line will be

       y = - (1/3)x + c

     3y = -x + c

x + 3y = c

where c is the constant.

Thus, the correct option is B.

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Answer: 1/4.

Step-by-step explanation: Too pass you need to get a least 13 right.

Answer:

Okay so your numbers are:

0, 2, 2, 4, 5, 1, 3, 4, 2, 4, 5, 0, 0, 1, 3, 4

You have to put them in order first:

0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5

Now that its all in order you have to pull out the middle number.

Since there are 16 numbers its an even pile so you have to get the 2 middle numbers:

2, 3

Add them both together:

2 + 3 = 5

Then divide by 2:

5 ÷ 2

= 2.5

Step-by-step explanation:

Hope this helps!

From your neighborhood sofite.

Answer: Median is 78

Step-by-step explanation: What you have to do in this stem and leaf plot is for example 6|0 is 60, 9|4 is 94, etc. To find the median height, ignore the stem (the number by itself) and do the median how you usually do it.  Sorry if its a bit complicated

Answer:

(3x+12)+X=180

Step-by-step explanation:

Supplementary angles always equal 180

Answer:

C. (3x + 12) + x = 180 is the correct answer.

Step-by-step explanation:

The angle of any straight line is 180*, and since thats a sraight line, then the acute angle (x) plus the obtise angle (3x + 12) must equal 180*.

Hope this helps!

Also x = 42* for reference.

Answer:

members is about

✔ –2.843

, which means that the number of choir members this year is

✔ 2.843

standard deviations

✔ below

the mean number of choir members. Therefore, there are

✔ fewer

choir members this year than

Step-by-step explanation:

Answer:

The z-score for 46 choir members is about

✔ –2.843

, which means that the number of choir members this year is

✔ 2.843

standard deviations

✔ below

the mean number of choir members. Therefore, there are

✔ fewer

choir members this year than the average.

Step-by-step explanation:

edge 2023

Based on the information given, the area that will be left uncovered will be 450ft².

= 30 × 30 = 900ft²

The area viewed by the camera = 112.5ft²

Therefore, the number of cameras needed will be:

= 900/112.5 = 8

When he places the cameras in the corners of the store, he area covered will be:

= 4 × 112.5 = 450ft²

Therefore, the area left uncovered will be:

= 900 - 450

= 450 ft²

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Answer:

9 cups

Step-by-step explanation:

Because 1 cup is 8 ounces, and we need to find how many cups we need to have 72 ounces.

You have to divide 72/8 and the answer will be 9

Answer:

{5, -3} {0, -1/3}

Step-by-step explanation:

For the first problem, they all have a GCF of 2, so you divide it all by 2 to get x^2-2x-15=0. Now, we need two factors of -15 that equal -2. Those are -5 and 3. Our new equation is x^2-5x+3x-15. To factor, the GCF of x^2 and 5x is x, so divide by x and you get x(x-5). The GCF of 3x and 15 is 3, so divide by 3 and you get 3(x-5). Now, put the numbers outside of the parenthesis into their own, and you get (x+3)(x-5). To get to 0, for the first one x has to be -3, and for the second, x has to be 5.

For the second, 12x^2 and 4x have a GCF of 4x. Since this we don't have a c value, we just divide and factor like this: 4x(3x+1). Since 4x is outside the parenthesis but we don't have any other terms outside, x=0 because 4(0) is 0. To cancel out 1, our x value inside has to be -1/3, because -1/3*3=-1.

Hope this helped!

Answer:

The answer is B.

Step-by-step explanation:

f(6) = 146 & g(6) = 731 /// The difference of the two is 585.

Answer:

10x - 15 + 5x = 180

Step-by-step explanation:

Solve for x

Answer:

(Second Option) = g of x equals the quantity x squared minus 5x plus 7 end quantity divided by the quantity x minus 3 end quantity

Step-by-step explanation:

A rational function contains a polynomial in both the numerator and the denominator. This answer fits that requirement.

Answer:

=−40y+33

Step-by-step explanation:

√14y2−20y+48−√14y2−20y−15

Simplifies to:

−40y+33

=−40y+33

The relative frequencies of this data by row is

          150 cc    180 cc

Black 0.43         0.57

Blue   0.47         0.53

Red   0.55          0.45

The table of values is given as:

          150 cc    180 cc

Black 18              24

Blue   15              17

Red   26              21

Calculate the row total.

          150 cc    180 cc    Total

Black 18              24          42

Blue   15              17           32

Red   26              21           47

Divide each element by the row total

          150 cc    180 cc

Black 0.43         0.57

Blue   0.47         0.53

Red   0.55          0.45

Hence, the relative frequencies of this data by row is

          150 cc    180 cc

Black 0.43         0.57

Blue   0.47         0.53

Red   0.55          0.45

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Answer:

[tex]x = 13 \\ y = 13 \sqrt{2} [/tex]

Step-by-step explanation:

[tex] \cos(45) = \frac{13}{y} = \frac{ \sqrt{2} }{2} \\ y = \frac{26}{ \sqrt{2} } = 13 \sqrt{2} \\ x = 13 \\ because \: angles \: are \: equally \: 45[/tex]

Answer:

Step-by-step explanation:

According to the box plot we have

The IQR is the difference of the two numbers above

Answer:

IQR = 3.5

Step-by-step explanation:

Explanation of the given box plot:

Therefore, the Five-number summary of the given box plot is:

[tex]\begin{aligned}\textsf{Interquartile range (IQR)} & = \sf Q_3-Q_1\\& = \sf 8 - 4.5\\&= \sf 3.5\end{aligned}[/tex]

Answer:

A=2(wl+hl+hw)

Step-by-step explanation:

To find the surface area of a rectangular prism, measure the length, width, and height of the prism. Find the area of the top and bottom faces by multiplying the length and width of the prism. Then, calculate the area of the left and right faces by multiplying the width and height.

Answer: B, 7

Step-by-step explanation: Mean is adding all numbers then dividing so 4 + 6 + 6 + 7 + 7 + 8 + 8 + 8 + 9 is 63 and then divide it by the total numbers (9)

63 divided by 9 is 7

7 is the mean, or B