how do u compare rate of change and slope help plz

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

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

Answer:

36

Step-by-step explanation:

To obtain the required number, multiply 27 by the inverse of [tex]\frac{3}{4}[/tex]

The inverse of [tex]\frac{3}{4}[/tex] is [tex]\frac{4}{3}[/tex] ( fraction turned upside down ), thus

[tex]\frac{4}{3}[/tex] × 27 ← divide 3 and 27 by 3

= 4 × 9 = 36

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:

16,055/16 = 1003

The remainder would be 7

Step-by-step explanation:

Answer: x = 67

Step-by-step explanation:

60+53+x = 180

The degrees of a triangle always equal 180

113+x = 180

Subtract the 113 from the 180

x= 67

Answer:113

explanation: hope it helps☺

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:

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.

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

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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.

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:

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

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.

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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]

[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: its going in straight lines

Step-by-step explanation:

Answer:

7j+7

Step-by-step explanation:

2j+4j+j+7

combine like terms

7j+7

Sorry I don't really know how to explain it, but you just have to combine terms with the same unit

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:

95-9 (3+7)

95-9 (10)

86 (10)

= 8600

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:

15

Count down from 21 and count up from 9 till you have the same number.

21 9

20 10

19 11

18 12

17 13

16 14

15 15

Now they are the same height.

Step-by-step explanation:

When a seesaw is level, the height of both ends above the ground is the average of the heights when one end is lifted. In this case, both ends are 15 inches above the ground when the seesaw is level.

The question is asking for the height of the ends of a seesaw when it is in a level or balanced position. A seesaw balances when it is level, and both ends are at the same height. Considering the given details, one end is 9 inches and the other is 21 inches above ground, when they switch positions due to the seesaw's pendulum-like movement. But when the seesaw is level, both ends are at the same height. Therefore, the height of both ends of the seesaw when it is level is the average of 9 inches and 21 inches. You calculate this average by adding the two given distances and dividing by 2. So:

((9 inches + 21 inches) / 2) = 15 inches

So, when the seesaw is level, both ends are 15 inches above the ground.

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Answer:

Therefore,

[tex]Discriminant=-3[/tex]

Step-by-step explanation:

Given:

[tex]7x^{2}-5x+1=0[/tex]

To Find:

Discriminant = ?

Solution:

For a Quadratic Equation ax²+bx+c=0

The Discriminant is given as

[tex]Discriminant=b^{2}-4ac[/tex]

On comparing we get

[tex]a=7\\b=-5\\c=1[/tex]

Substituting the values we get

[tex]Discriminant=(-5)^{2}-4\times 7\times 1\\Discriminant=25-28\\Discriminant=-3[/tex]

Therefore,

[tex]Discriminant=-3[/tex]

Answer:

3

Step-by-step explanation:

4x+7=19

4x=19-7

4x=12

x=12/4

x=3

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:

The Inequality that shows number of hours Tabitha will need to work to have enough money to buy the tablet is [tex]75+8.5x\geq 306.34[/tex].

Tabitha needs to work at least 28 hours to buy the tablet.

Step-by-step explanation:

Amount earn per hour = $8.50

Amount already saved = $75

Cost of tablet = $289

Sales tax = 6%

We to write and solve the inequality number of hours Tabitha will need to work to have enough money to buy the tablet.

Solution:

Let the number of hours she need to work be 'x'.

First we will find the total amount required to buy tablet.

Amount of sales tax = [tex]\frac{6}{100}\times289 = \$17.34[/tex]

Now Total cost to buy tablet will be equal to sum of Cost of tablet and Amount of sales tax.

framing in equation form we get;

Total cost to buy tablet = [tex]289+17.34 = \$306.34[/tex]

Now we can say that;

Amount already saved plus Amount earn per hour multiplied by Amount earn per hour should be greater than or equal to Total cost to buy tablet.

framing in equation form we get;

[tex]75+8.5x\geq 306.34[/tex]

hence The Inequality that shows number of hours Tabitha will need to work to have enough money to buy the tablet is [tex]75+8.5x\geq 306.34[/tex].

On solving the above Inequality we get;

First we will subtract both side by 75 we get;

[tex]75+8.5x-75\geq 306.34-75\\\\8.5x\geq 231.34[/tex]

Dividing both side by 8.5 we get;

[tex]\frac{8.5x}{8.5}\geq \frac{231.34}{8.5}\\\\x\geq 27.21[/tex]

Hence Tabitha needs to work at least 28 hours to buy the tablet.

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:

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

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:

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: 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.