Why can't you use the product of powers rule to simplify
this expression? Explain.
3^4•2^8

Answer:

The equation of line passes through [tex](4,-1)[/tex] and perpendicular to the graph [tex]y=\frac{7}{2}x-\frac{3}{2}[/tex] is [tex]y=\frac{-2x}{7}+\frac{1}{7}[/tex]

Step-by-step explanation:

Given point is [tex](4,-1)[/tex] and equation of line is [tex]y=\frac{7}{2}x-\frac{3}{2}[/tex]

Let the slope of line that passes through point [tex](4,-1)[/tex] is [tex]m_1[/tex]

And slope of line [tex]y=\frac{7}{2}x-\frac{3}{2}[/tex] is [tex]m_2=\frac{7}{2}[/tex] . As it is in the form of [tex]y=mx+c[/tex]

We know the relation between slope of perpendicular line are given by

[tex]m_1\times m_2=-1\\And\ m_1=\frac{-1}{m_2}[/tex]

So, the slope [tex]m_1=\frac{-1}{\frac{7}{2}}=\frac{-2}{7}[/tex]

Now, we can write the equation of line having point  [tex](4,-1)[/tex] and slope [tex]\frac{-2}{7}[/tex]

[tex](y-y_1)=m(x-x_1)\\\\(y-(-1))=\frac{-2}{7}(x-4)\\\\y+1=\frac{-2x}{7}-(\frac{2\times -4}{7})\\ \\y+1=\frac{-2x}{7}+\frac{8}{7}\\\\y=\frac{-2x}{7}+\frac{8}{7}-1\\\\y=\frac{-2x}{7}+\frac{8-7}{7}\\\\y=\frac{-2x}{7}+\frac{1}{7}[/tex]

So, the equation of line passes through [tex](4,-1)[/tex] and perpendicular to the graph [tex]y=\frac{7}{2}x-\frac{3}{2}[/tex] is [tex]y=\frac{-2x}{7}+\frac{1}{7}[/tex]

Answer:

1. Basically, a ratio is a relation between two values, such that the change of one value will result in the same proportional change in the other (if one value increases 6 times, or decreases 4 times, for example, the same will happen with the other value too.

Since Mrs. Jollie will save $60 for every two panels, then the ratio is:

2 panels: $60

Every ratio can be written in a form of fraction, by simply dividing these values:

2/60  

or, as a reduced fraction:

1/30

2. Now we are given several ratios, which we need to use to find price for 9 panels.

First way:

we can set a proportion because we already said that if we change one value, others will change proportionally as well. So, we take any of these ratios and make a proportion:

2 : $3,000 = 9 : $ x

Solving for x, we get:

x = $3,000 • 9 / 2

x = $13,500

Second way:

From the ratio, we can find the price for a single panel. Then, we simply multiply that with 9 and find the price for nine panels:

one panel costs $3,000 / 2 = $1,500

nine panels cost $1,500 • 9 = $13,500

3. Now, we are again given several ratios and we need to find the price per hour for each company. We can do this by simply dividing:

- ABC Co. 5h : $128

so, price per hour is $128/5 = $25.6

- Solar R' Us 6h : $181

so, price per hour is $181/6 = $30.17

- Light in the Sky 8h: $195

so, price per hour is $195/8 = $24.4

So, the best deal means that the price per hour is the lowest, so the best deal is the Light in the Sky company.

Please show the picture of the box plot otherwise your question is unanswerabe.

Answer:

12

Step-by-step explanation:

This is an example of Addition property between two positive integers (i.e. whole value numbers), which means the result will be positive and larger than the two numbers.

The result of the addition would be:

[tex]5 + 7 = 12[/tex]

Another way to do it if you are struggling a bit you can write the value of [tex]7[/tex] as [tex]7 = 5 +2[/tex] so then you can say:

[tex]5 + (5 + 2) = 5 + 5 + 2 = 10 + 2 = 12[/tex]

Answer:

95-9 (3+7)

95-9 (10)

86 (10)

= 8600

Step-by-step explanation:

Final answer:

By using the elimination method to solve the given system of linear equations, we find that x = 18 and y = 15.

Explanation:

We are looking to solve the system of linear equations:

3x – 2y = 24

x + 2y = 48

To find the values of x and y, we can use substitution or elimination methods. In this case, the elimination method is very straightforward since the y coefficients in the two equations are additive inverses. If we add both equations together, the y terms will cancel out:

3x + x = 24 + 48

4x = 72

Dividing both sides by 4 gives us the value of x:

x = 18

To find y, we can substitute x back into either of the original equations. Let's use the second equation:

18 + 2y = 48

Subtracting 18 from both sides:

2y = 30

Dividing by 2:

y = 15

Thus, the solution to the system of equations is x = 18 and y = 15.

- 2a = - 20 | x (-)

2a = 20

a = 20 : 2

a = 10

Answer:

a=10

Step-by-step explanation:

-2a=-20

Divide -2 on each side. You should get a=10

Answer:

11 hrs

Step-by-step explanation:

so he made 135 for 9 hrs.....thats (135/9) = $ 15 an hr

so if he made 165, he would have to work (165/15) = 11 hrs <==

Answer: its going in straight lines

Step-by-step explanation:

Answer:

Therefore, the variable expression when a=-4, b=2, c=-3, and d =4 is

[tex]\dfrac{b-3a}{bc^{2}-d}=1[/tex]

Step-by-step explanation:

Evaluate:

[tex]\dfrac{b-3a}{bc^{2}-d}[/tex]

When a=-4, b=2, c=-3, and d =4

Solution:

Substitute, a=-4, b=2, c=-3, and d =4 in above expression we get

[tex]\dfrac{b-3a}{bc^{2}-d}=\dfrac{2-3(-4)}{2(-3)^{2}-4}\\\\=\dfrac{2+12}{18-4}\\\\[/tex]

[tex]\dfrac{b-3a}{bc^{2}-d}=\dfrac{14}{14}=1[/tex]

Therefore, the variable expression when a=-4, b=2, c=-3, and d =4 is

[tex]\dfrac{b-3a}{bc^{2}-d}=1[/tex]

Answer:

Step-by-step explanation:

Let the no. Of rye bread = x

Wheat bread = x + 8

The total bread is 32

: x + x + 8 = 32

2x = 32 - 8

2x = 24

x = 24/2

x = 12

No. Of wheat bread = x + 8 = 12+8

No. Of wheat bread = 20

Answer:

Wheat loaves is 20

Step-by-step explanation:

Let wheat loaves be A

And rye loaves be B

A + B = 32

Hence A = B + 8

So, B + B + 8 = 32

2B = 24

B = 12

A = 20

Answer:

X = 5

Y= 12

Step-by-step explanation:

3x + 2y = 39 —> (1)

5x - y = 13 —> (2)

Multiply (2) with 2

10x - 2y = 26 —> (b)

(1) + (b)

This will eliminate the y factor, leaving:

13x = 65

Therefore, x = 65/14

X= 5. Put this value of 5 in equation 1, which gives;

15 + 2y = 39

2y = 39-25

2y = 24

Y = 12

Answer:

x=5

y = 12

Step-by-step explanation:

3x + 2y = 39

2y = 39 - 3x

y = (39 - 3x) / 2

5x - y = 13

5x - ((39 - 3x) / 2) = 13

5x - 39/2 + 3/2x = 13

5x + 3/2x = 13 + 39/2

13/2x = 65/2

x = 65/2 * 2/13

x = 65/13

x = 5

y = (39 - 3x) / 2

y = (39 - 3*5) / 2

y = (39 - 15) / 2

y = 24/2

y = 12

The present age of father is 35 and daughter is 7.

Step-by-step explanation:

Let,

Age of father = x

Age of daughter = y

According to given statement;

A man is 5 times older than his daughter.

x = 5y      Eqn 1

In 7 years, the man is 3 times as old as his daughter.

x+7 = 3(y+7)

[tex]x+7=3y+21\\x=3y+21-7\\x=3y+14\ \ \ Eqn\ 2[/tex]

Putting value of x from Eqn 2 in Eqn 1

[tex]3y+14=5y\\14=5y-3y\\14=2y\\2y=14[/tex]

Dividing both sides by 2

[tex]\frac{2y}{2}=\frac{14}{2}\\y=7[/tex]

Putting y=7 in Eqn 1

[tex]x=5(7)\\x=35[/tex]

The present age of father is 35 and daughter is 7.

Keywords: linear equation, substitution method

Learn more about substitution method at:

#LearnwithBrainly

Final answer:

The present ages of the man and his daughter are 35 years and 7 years, respectively.

Explanation:

The question asks us to find the current ages of a man and his daughter, given that the man is currently five times older than his daughter and that after 7 years, he will be three times as old as her. To solve this, we can set up two equations based on the information provided:

Now, we solve the equation from step 2 to find the daughter's age:

So, the daughter is currently 7 years old. To find the man's age, we multiply the daughter's age by 5:

Man's age = 5 x 7 = 35 years old

Therefore, the man is currently 35 years old and the daughter is 7 years old.

The equation relates the scale drawing of the sculpture room to its actual dimensions using equivalent ratios. By setting the actual length corresponding to 6 cm on the drawing to 30 m, we can solve for the unknown actual length, which is 6 meters. So, the actual length of the sculpture room in the museum is 6 meters.

Completing the equation:

The equation in the image is missing a part: it should be:

1 cm : 5 m = x cm : 30 m

Explanation of the equation:

1 cm: This represents the length of the sculpture room on the scale drawing, as indicated by the scale 1 cm : 5 m.

5 m: This represents the actual length corresponding to every 1 cm on the scale drawing.

x cm: This is the unknown variable we're trying to solve for. It represents the actual length of the sculpture room in the museum.

30 m: This is a constant value, chosen because we want to find the length corresponding to 6 cm on the scale drawing (since the sculpture room in the drawing is 6 cm long).

What each part represents:

The colon (:) separates the two equivalent ratios.

The first ratio (1 cm : 5 m) represents the scale factor, which is the conversion factor between the scale drawing and the actual museum dimensions. It tells us that every 1 cm on the drawing corresponds to an actual length of 5 m.

The second ratio (x cm : 30 m) represents the unknown ratio we want to solve for. It relates the unknown actual length (x cm) to the desired actual length of 30 m (corresponding to 6 cm on the drawing).

Solving for x:

To solve for x, we can cross-multiply the two ratios:

(1 cm) * (30 m) = (5 m) * (x cm)

Simplifying the equation, we get:

30 m = 5x cm

Finally, dividing both sides by 5, we get:

x = 6 m

Therefore, the actual length of the sculpture room in the museum is 6 meters.

Answer:x = -7

Step-by-step explanation:

-2x-10=4

-2x=14

-x=7

X=-7

Answer:

Step-by-step explanation:

[tex]-2(x+5)=4\qquad\text{divide both sides by (-2)}\\\\\dfrac{-2\!\!\!\!\diagup(x+5)}{-2\!\!\!\!\diagup}=\dfrac{4\!\!\!\!\diagup^2}{-2\!\!\!\!\diagup_1}\\\\x+5=-2\qquad\text{subtract 5 from both sides}\\\\x+5-5=-2-5\\\\x=-7[/tex]

Answer: M  = ⁹/₅S

Step-by-step explanation:

 M  ∞ S -------------------------------- 1

M  =  KS ------------------------------ 2

K is a constant and need to be calculated

substitute for M and S in 2 to find K

900 = K500

K      =  ⁹⁰⁰/₅₀₀

       = ⁹/₅

Therefore , the equation that connect / relates M to S will be

M   =  KS

M   = ⁹/₅S

Final answer:

The equation that relates M to S is M = kS, where k is the constant of proportionality.

If M is 900 when S is 500, the equation becomes M = 1.8S.

Explanation:

The equation that relates M to S is M = kS, where k is the constant of proportionality.

To find the value of k, we can use the given values of M and S.

If M = 900 when S = 500, we can substitute these values into the equation to get 900 = k(500).

Solving for k, we divide both sides of the equation by 500, getting k = 1.8.

Therefore, the equation that relates M to S is M = 1.8S.

Answer:

20 - 4×(−6) = 20 + 4×6 = 20 + 24 = 44

Using a calculator, 1200/180 = 6.67 approximately

If you use long division, then you'll get what you see in the diagram below

The 6's go on forever after the decimal point, but if you round to two decimal places, then you'll get that approximate value of 6.67

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

If you want a remainder, then 1200/180 = 6 remainder 120

You can think of it like you having 1200 cookies and 180 friends. Each friend will get 6 whole cookies and there will be 120 left over as the remainder.

[tex]2-11i \text{ is the standard form of given expression }[/tex]

Solution:

The standard form of complex number is: a + bi

where a is the real part and bi is the imaginary part

Given expression is:

[tex](2-i)^3[/tex]

Expand the above expression using algebraic identity

[tex](a-b)^3=a^3-b^3-3ab(a-b)[/tex]

[tex]\text{For } (2-i)^3 \text{ we get, a = 2 and b = i}[/tex]

Thus on expanding using the above algebraic identity we get,

[tex](2-i)^3=(2)^3-(i)^3-3(2)(i)(2-i)[/tex]

Simplify the above expression

[tex](2-i)^3=8 -i^3-6i(2-i)\\\\(2-i)^3=8 -i^3-12i+6i^2[/tex]

We know that,

[tex]i^2 = -1\\\\i^3 = -i[/tex]

Substituting in above simplified expression, we get,

[tex](2-i)^3=8-(-i)-12i+6(-1)\\\\(2-i)^3=8 + i -12i -6\\\\\text{Combine the like terms }\\\\(2-i)^3=8 - 6 + i -12i\\\\(2-i)^3=2-11i[/tex]

Thus the given expression is expressed in standard form

Answer:

$224.88

Step-by-step explanation:

4.99×12= 59.88 for kids

6×25=150 for adults

2.50×6=15 for babies

59.88+150+15= $224.88 collected in total

Answer:

B)  (8x-3)²

Step-by-step explanation:

64x2 - 48x + 9= (8x)² - 2*8x*3 + 3²

Compare with a² - 2ab +b² = (a-b)²;  a = 8x and b =3

=(8x-3)²

Answer:

170

Step-by-step explanation:

A number which rounds to 170 when it is rounded to the nearest ten is 168.

What is the number line ?

A number line is a picture of a graduated straight line that serves as visual representation of the real number.

Since we are trying to round of a number, which rounds to 170 when it is rounded to the nearest ten. Therefore, it should be in the range of 166 to 174 (both included).

Let take example of 168, as it can be seen that it is closest to 170, therefore, when it is rounded it will be closest to 170.

Hence, 168 is a number which rounds to 170 when it is rounded to the nearest ten.

To know more about number line click on the link below:

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Answer:

A 0

Step-by-step explanation:

because the lines are a paraell and they don't touch

A solution is a point that is in both shaded regions at the same time. This is impossible due to the fact the regions do not overlap. This is like saying there is a number larger than 1 and this same number is less than -1 at the same time. This is why there are no solutions to this system of inequalities.

Answer:

The probability distribution for which the value of the median is greater than the value of the mean is - negatively skewed probability distribution.

Step-by-step explanation:

The probability distribution for which the value of the median is greater than the value of the mean is - negatively skewed probability distribution.

Answer:

negative skewed  distribution

Step-by-step explanation:

As can be seen in the figure attached,

Answer:

Original garden: 42 feet

Enlarged garden: 98 feet

Step-by-step explanation:

Perimeter = length (2) + width (2)

Original perimeter:

P = 15(2) + 6(2)

P = 30 + 12

P = 42 feet

In this problem, similar is proportional, so the new garden will be proportional to the old one.

If the original length was 15 and the new length is 35, then 15 would have had to have been multiplied by 2 1/3. That means you need to multiply 6 by 2 1/3, which is 14. That means the dimensions of the enlarged yard is 14 (width) × 35 (length).

Enlarged perimeter

P = 35(2) + 14(2)

P = 70 + 28

P = 98 feet

Final answer:

The perimeter of the original rectangular garden is 42 feet, and the perimeter of the enlarged garden, which is similar in proportion to the original, is 98 feet.

Explanation:

The original garden has a width of 6 feet and a length of 15 feet. The perimeter of a rectangle is calculated by adding the lengths of all its sides. In this case, the perimeter of the original garden is 2(6 feet + 15 feet) = 2(21 feet) = 42 feet.

Since the new garden is similar to the original one, and its length is 35 feet, it means that the width will also increase in the same proportion. The original length to width ratio is 15:6 which simplifies to 5:2. Applying this ratio to the new length of 35 feet will give us the new width:

35 feet / 5 = 7 feet (per unit of the ratio)
7 feet * 2 = 14 feet (new width)

The perimeter of the enlarged garden is then 2(14 feet + 35 feet) = 2(49 feet) = 98 feet. So, the perimeter of the original garden is 42 feet and the perimeter of the enlarged garden is 98 feet.

Answer:

3

Step-by-step explanation:

4x+7=19

4x=19-7

4x=12

x=12/4

x=3

Answer: 26

Step-by-step explanation: In this problem we have 3 consecutive even numbers whose sum is 84 and it asks us to find the smallest number.

Consecutive even numbers can be represented as x, x + 2, and x + 4.

Since the sum of these is 84, our equation reads

x + (x + 2) + (x + 4) = 84.

Simplifying on the left we get 3x + 6 = 84.

Subtract 6 from both sides and we have 3x = 78.

Divide both sides by 3 and x = 26.

So our smallest number is 26.

To find the smallest of three consecutive even numbers that sum up to 84, we set up an equation and solve for 'x', where 'x', 'x+2', and 'x+4' represent the numbers. Solving this gives us the smallest number, which is 26.

If the sum of three consecutive even numbers is 84, we can find the smallest number by setting up an equation. Let's denote the smallest even number as 'x'. The next consecutive even number would be 'x + 2', and the one after that would be 'x + 4'. The sum of these three numbers should equal 84:

x + (x + 2) + (x + 4) = 84

Simplifying this equation, we get:
3x + 6 = 84

Subtracting 6 from both sides, we have:
3x = 78

Now, dividing both sides by 3 gives us:
x = 26

Therefore, the smallest of the three consecutive even numbers is 26.

Answer:

  350

Step-by-step explanation:

We have two points on the demand curve as (10, 450) and (15, 200). Using the two-point form of the equation for the line between them, we can find the "y" value for "x" = 12 as ...

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

  y = (200 -450)/(15 -10)(12 -10) +450

  = (-250/5)(2) +450

  = -100 +450 = 350

We predict the number of tickets sold at $12 will be 350.

_____

Check

The drop in sales of 50 tickets for each $1 increase in price is consistent with other table values.

Answer: 5508

Step-by-step explanation:

all the numbers together equal 72 marbles in total.

(6x2)x (3x3)x (3x17)=

  12       9          51              first multiply the easy numbers 12x9 =108 then

108x51= 5508

Answer:

no

Step-by-step explanation:

16.28 can also be written 16.280 (you could add as many zeros to the end as you want its still the same number)

280 is bigger than 275