The explicit rule for an arithmetic sequence is an=20/3+1/3(n-1). What is the value of the 89th term?

46 pullups in 2 minutes>

46/2=23

23 pullups per minute

23, 46, 69, 92 ect.

The rate of the pullups would be 23 pullups per minute.

Suppose that we have to measure the rate of change of y as x changes, then we have:

[tex]Rate = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]

Known that we divide by the change in the independent variable so that we get some idea of how much the dependent quantity changes as we change the independent quantity by 1 unit.

Given that Duane can do 46 pullups in two minutes.

46 pullups in 2 minutes

46/2=23

23 pullups per minute

23, 46, 69, 92 etc.

Hence, the rate of the pullups would be 23 pullups per minute.

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Answer:

150 dollhairs

Step-by-step explanation:

Answer:

Refrigerator’s original price = 1000 $

Step-by-step explanation:

Let the original price of refrigerator be r.

Store A advertises that the refrigerator is on sale for 15% off the original price.

[tex]\texttt{Price of  refrigerator in store A = }r-\frac{15}{100}r=0.85r[/tex]

Store B advertises that it is reducing the refrigerator’s price by $150.

              Price of  refrigerator in store B =  r - 150

Stephanie compares the sale prices of the refrigerator in both stores, she concludes that the sale prices are equal

That is

             0.85r = r - 150

                   0.15r = 150

                         r = 1000$

Refrigerator’s original price = 1000 $

To write 2.6666 as a fraction, write 2.6666 as the numerator with 1 as the denominator.

2.6666/1

Now you multiply numerator and denominator by 10000 to make the numerator a whole number ( no decimals)

26666/10000

Both numbers are even and can be divided by 2:

The fraction becomes: 13333/5000

Answer is 525.

Hope this helps!

Answer:

768 square inches

Step-by-step explanation:

see attached

The width and height of the 40 inch television with a 4:3 aspect ratio are 32 inches and 24 inches respectively. The area of the screen is 768 square inches.

To find the width and height of an older 40 inch television with an aspect ratio of 4:3, we can use the formula:
Width = aspect ratio * height
Since the aspect ratio is 4:3, we divide the width by 4 and multiply by 3 to find the height.
Therefore, the width of the television is 32 inches and the height is 24 inches.

To find the area of the screen, we use the formula:
Area = width * height
Substituting the values, we get:
Area = 32 inches * 24 inches
Therefore, the area of the screen is 768 square inches.

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Answer:

total pay for his work is $1704

Step-by-step explanation:

given data

Zenin earns =  $142 per shift

total shifty = 12

to find out

What would his pay for 12  shift

solution

we have given per shift charge and total shift

so

total pay for his work = total shift × per shift charge    ................1

put here value

total pay for his work = 12 × $142

total pay for his work = $1704

Your Answer is x = −2

Hope this Helps.

Answer: if your question here is if they are the same since it says equivalent then yes

Step-by-step explanation: 2/3 = 8/12

Answer:

Width = 11 yards

Length = 17 yards

Step-by-step explanation:

First of all, the length of the rectangle is 6 yards longer than the width, this means, length = width + 6 yards. This dimensions can be represented on figure 1, where w is width, and l, for length.

We know the area of a rectangle is A = width x length

For our case 187 = w . (w + 6)

Using the Distributive Property for the multiplication we obtain

[tex]187 = w^{2} +6w[/tex]

[tex]w^{2} +6w-187 =0,[/tex]

Using the quadratic formula [tex]w=\frac{-b\±\sqrt{b^{2}-4ac } }{2a}[/tex] where a = 1, b = 6, c = - 187 and replacing into the formula, we will have:

[tex]w=\frac{-6\±\sqrt{6^2-4(1)(-187)} }{2(1)}[/tex]

[tex]w=\frac{-6\±\sqrt{36+748} }{2}=\frac{-6\±\sqrt{784} }{2}=\frac{-6\±28}{2}[/tex]

We have two options: [tex]w=\frac{-6+28}{2}=\frac{22}{2}=11  yards[/tex]

Or

[tex]w=\frac{-6-28}{2}=\frac{-34}{2}=-17 yards[/tex] But a distance (width) can not be negative so, this answer for w must be discarded.

The answer must be width = 11 yards.

To find the length [tex]l =\frac{187}{11}=17 yards[/tex]

Answer:

[tex]y = \frac{1}{3} x -1[/tex]

Step-by-step explanation:

1. find the slope that includes the points (-3,-2) and (3,0)

[tex]\frac{y2-y1}{x2-x1} =m[/tex] ->slope

0-(-2)/3-(-3) = [tex]\frac{2}{6} (simplify) = \frac{1}{3}[/tex]

2. find the y-intercept

[tex]y = mx +b[/tex] -> slope-intercept form

plug in the y-coord. and the x-coord along with the slope you found (or rather I found) and solve. It could be from either coordinate given.

[tex]0=\frac{1}{3} (3)+b[/tex]

3. solve.

[tex]0 = 1 +b[/tex]

[tex]-1 = b[/tex]

4. write the equation with the slope and y-int you found and voila!

Answer:

[tex]N=2Z-11[/tex]

[tex]\begin{array}{cc}\text{Zac's score}&\text{Natan's score}\\ 6&1\\7&3\\8&5\\9&7\end{array}[/tex]

Step-by-step explanation:

Nathan's score is 11 less than 2 times Zac's score.

Let Z points be Zac's score and N points be Natan's score. then

2 times Zac's score = 2Z

11 less than 2 times Zac's score = 2Z -11

So, N = 2Z - 11

1. If Z=6, then [tex]N=2\cdot 6-11=12-11=1[/tex]

2. If Z=7, then [tex]N=2\cdot 7-11=14-11=3[/tex]

3. If Z=8, then [tex]N=2\cdot 8-11=16-11=5[/tex]

4. If Z=9, then [tex]N=2\cdot 9-11=18-11=7[/tex]

Thus, four other possibilities are

[tex]\begin{array}{cc}\text{Zac's score}&\text{Natan's score}\\ 6&1\\7&3\\8&5\\9&7\end{array}[/tex]

Answer:

x=12 or x= -12   (answer A)

Step-by-step explanation:

|x| – 5 = 7

|x|  = 12

x=12 or x= -12   (answer A)

it is 11 students in the bus

Answer: w = a/l

Step-by-step explanation:

If a = lw, then w = a/l

W = a/l is an equation to find the width if you already know both the a and l

Answer:

-14°

Step-by-step explanation:

-9 - 5

-9 + (-5)

-14

Hey!

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

Solution:

If the temperature is -9 degrees now and it drops 5 degrees in two hours you just want to subtract.

-9 - 5 = -14 degrees

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

Answer:

-14 degrees

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

Hope This Helped! Good Luck!

Answer:

[tex]- \frac{1}{2}[/tex]

Step-by-step explanation:

6x+7=4

6x+7-7=4-7

6x=-3

[tex]\frac{6x}{6}[/tex]=[tex]\frac{-3}{6}[/tex]

x=[tex]-\frac{1}{2}[/tex]

To solve the inequalities, isolate x in each. The solution for -9x + 5 < 17 is x > -4/3 and the solution for 13x + 25 < -1 is x < -2. The intersection of these solutions, and thus the solution to the compound inequality, is x < -2.

We can solve the inequalities separately, then find the intersection of their solution sets. First, let's solve the inequality -9x + 5 < 17. To do this, we subtract 5 from both sides to isolate the term with x which gives -9x < 12. Finally, we divide both sides by -9, remembering to flip the inequality sign since we divided by a negative. This gives x > -4/3.

The second inequality 13x + 25 < -1 can be solved similarly. Subtracting 25 from both sides will get 13x < -26. Divide both sides by 13 to find that x < -2.

The final answer will be the intersection of the two solutions. Since x < -2 is a stricter condition than x > -4/3, the solution to the compound inequality is x < -2.

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To find Sn for the given arithmetic series with a1 = 22, d = –8, and n = 21, you can use the formula Sn = (n/2)(2a1 + (n - 1)d). Substituting the values into the formula gives Sn = -2418.

To find the sum of an arithmetic series, you can use the formula:

Sn = (n/2)(2a1 + (n - 1)d)

where Sn represents the sum of the series, a1 is the first term, d is the common difference, and n is the number of terms.

In this case, a1 = 22, d = -8, and n = 21. Substituting these values into the formula gives:

S21 = (21/2)(2(22) + (21 - 1)(-8)) = (21/2)(44 + 20(-8)) = (21/2)(44 - 160) = (21/2)(-116) = -2418

Therefore, the sum of the arithmetic series is -2418.

Final answer:

The sum of the first 21 terms (Sn) of the arithmetic series with a first term of 22 and a common difference of -8 is -1222.

Explanation:

To find Sn for the given arithmetic series where the first term a1 = 22, the common difference d = –8, and the number of terms n = 21, we can use the formula for the sum of the first n terms of an arithmetic series:

Sn = ½ n (2a1 + (n - 1)d)

Plugging in the given values:

Sn = ½ × 21 (2 × 22 + (21 - 1)× (–8))

Simplify further to find:

Sn = ½ × 21 (44 – 160)

Sn = ½ × 21 × (–116)

Sn = 10.5 × (–116)

Sn = –1222

Thus, the sum of the first 21 terms of the series is –1222.

Answer:

x = 6

Step-by-step explanation:

-2x + 8 = -3x + 14

Add 3x to both sides.

x + 8 = 14

Subtract 8 from both sides.

x = 6

Both sides of the equation are equal, the solution [tex]x = 6[/tex] is correct.

To solve the equation [tex]-2x + 8 = -3x + 14[/tex], you can follow these steps:

Move the variables to one side of the equation:

Add 3x to both sides of the equation to get the variables on one side:

[tex]-2x + 8 + 3x = -3x + 14 + 3x[/tex]

Simplify:

[tex]x + 8 = 14[/tex]

Isolate the variable:

Subtract 8 from both sides to isolate [tex]x[/tex]:

[tex]x + 8 - 8 = 14 - 8[/tex]

Simplify:

[tex]x = 6[/tex]

Check your solution:

Substitute [tex]x = 6[/tex] back into the original equation to ensure it satisfies the equation:

[tex]-2(6) + 8 = -3(6) + 14[/tex]

Simplify both sides:

[tex]-12 + 8 = -18 + 14[/tex]

[tex]-4 = -4[/tex]

Step-by-step explanation:

B 100

Answer:

B

Step-by-step explanation:

Step-by-step explanation:Step 1: Simplify both sides of the equation.

8(2x+3x+2)=−4x+148

(8)(2x)+(8)(3x)+(8)(2)=−4x+148(Distribute)

16x+24x+16=−4x+148

(16x+24x)+(16)=−4x+148(Combine Like Terms)

40x+16=−4x+148

40x+16=−4x+148

Step 2: Add 4x to both sides.

40x+16+4x=−4x+148+4x

44x+16=148

Step 3: Subtract 16 from both sides.

44x+16−16=148−16

44x=132

Step 4: Divide both sides by 44.

44x

44

=

132

44

x=3

answer: x=3

The solution to the equation 8(2x+3x+2) = -4x + 148 is x = 3.

To solve the given equation, let's start by simplifying both sides. First, we distribute the 8 to each term within the parentheses on the left hand side of the equation: 8(2x + 3x + 2) = 16x + 24x + 16 = 40x + 16. The equation then reads:

40x + 16 = -4x + 148.

Next, let's bring all terms involving x together on one side of the equation and constants on the other. We have:

40x + 4x = 148 - 16,

which gives us:

44x = 132.

Finally, to isolate x we divide both sides of the equation by 44 and we get:

x = 3

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Answer:

300

Step-by-step explanation:

All you do is multiply 10 by 30 [3 tens] to get three hundred.

I am joyous to assist you anytime.

Answer: [tex]m\angle 1=109\°\\m\angle 2=71\°[/tex]

Step-by-step explanation:

It is important to remember the definition of "Linear pair angles".

By definitiion "Linear pair angles" are two angles which are adjacents and supplementary.

Based on this, we know that the angles [tex]\angle1[/tex] and [tex]\angle2[/tex] are supplementary, which means that they add up to 180 degrees.

So, knowing that:

[tex]m\angle 1=5x+9\\m\angle 2=3x+11[/tex]

We can write the following expression and solve for "x":

[tex](5x+9)+(3x+11)=180\\\\8x=180-20\\\\x=\frac{160}{8}\\\\x=20[/tex]

Therefore, substituting, we get that the measures of the angles [tex]\angle1[/tex] and [tex]\angle2[/tex] are:

 [tex]m\angle 1=5(20)+9=109\°\\\\\\m\angle 2=3(20)+11=71\°[/tex]

Measures of both the angles are 109° and 71°. We found the measures of two angles forming a linear pair, then solving the equation 8x + 20 = 180, which gives x = 20. Substituting x finds the angles.

If angle 1 (∡1) and angle 2 (∡2) form a linear pair, their measures add up to 180° because linear pairs are supplementary angles. Given that the measures are m∡1 = 5x + 9 and  m∡2 = 3x + 11, we can set up the equation:

Combine like terms:

Subtract 20 from both sides:

Divide both sides by 8:

Now, substitute x back into the expressions for
∡1 and ∡2:

Therefore, the measures of the angles are :
∡1 = 109° and ∡2 = 71°.

The width of the rectangle will be equal to 12 units.

Perimeter is defined as the sum of all the sides of the given shape. The rectangle has four sides then the perimeter of the rectangle will be the sum of all the sides of the rectangle.

Given that length of a rectangle is 10 units longer than its width. The total perimeter of the rectangle is 44 units.

The width of the rectangle will be calculated as below:-

2l + 2w = P

2(10) + 2w = 44

20 + 2w = 44

2w = 24

w = 12

Therefore, the width of the rectangle will be equal to 12 units.

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Answer:

$3.10 per gallon

Step-by-step explanation:

You are trying to find how many dollars per one gallon.

You divide $68.30 by 22 so you can get dollars per one gallon.

68.30 ÷ 22 = 3.10

Therefore it cost $3.10 per gallon you spend.

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Final answer:

You spent $3.10 per gallon of gas.

Explanation:

To determine how many dollars per gallon of gas was spent, we can divide the total cost by the number of gallons. The question states that the total cost for 22 gallons of gas is $68.30.

So we perform the following calculation:

Cost per gallon = Total cost / Number of gallons

Cost per gallon = $68.30 / 22 gallons

Now, dividing $68.30 by 22 gives us:

Cost per gallon = $3.10

Therefore, the cost was $3.10 per gallon.

Final answer:

To find the dimensions of the rectangle, we used the perimeter formula and set up equations to solve for the width (21 inches) and length (27 inches), given that the length is 6 inches longer than its width and the perimeter is 96 inches.

Explanation:

To solve for the dimensions of the rectangle when the length is 6 inches longer than its width and the perimeter is 96 inches, we need to set up two equations based on the perimeter formula for a rectangle, which is P = 2l + 2w, where P is the perimeter, l is the length, and w is the width.

Let w represent the width of the rectangle. Then, the length of the rectangle is w + 6 inches. By substituting these into the perimeter formula, we get:

Now that we know the width is 21 inches, we can find the length by adding 6 inches to the width:

Therefore, the dimensions of the rectangle are 27 inches in length and 21 inches in width.

Final answer:

To find the dimensions of the rectangle, we used the perimeter formula and set up equations to solve for the width (21 inches) and length (27 inches), given that the length is 6 inches longer than its width and the perimeter is 96 inches.

Explanation:

To solve for the dimensions of the rectangle when the length is 6 inches longer than its width and the perimeter is 96 inches, we need to set up two equations based on the perimeter formula for a rectangle, which is P = 2l + 2w, where P is the perimeter, l is the length, and w is the width.

Let w represent the width of the rectangle. Then, the length of the rectangle is w + 6 inches. By substituting these into the perimeter formula, we get:

96 = 2(w + 6) + 2w

96 = 2w + 12 + 2w

96 = 4w + 12

84 = 4w

w = 21

Now that we know the width is 21 inches, we can find the length by adding 6 inches to the width:

Length = Width + 6 = 21 + 6 = 27 inches

Therefore, the dimensions of the rectangle are 27 inches in length and 21 inches in width.

Answer:

15 = -x/5

 -x/5 = 15

  x    = - 75

Step-by-step explanation:

Answer:

Reduced fraction: 2/3

Answer: 2/3

Step-by-step explanation:

Find the GCD (or HCF) of numerator and denominator

GCD of 108 and 162 is 54

Divide both the numerator and denominator by the GCD

108 ÷ 54

162 ÷ 54

Reduced fraction:

2

3

Therefore, 108/162 simplified to lowest terms is 2/3.

[tex]\bf (\stackrel{x_1}{1}~,~\stackrel{y_1}{-5})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{(-5)}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{1}}}\implies \cfrac{1+5}{3}\implies \cfrac{6}{3}\implies 2[/tex]