chapter 8
Find the area of each. Use your calculator's value of [pi]. Round your answer to the nearest tenth.

Step-by-step explanation:

h(-4) = 5(-4) - 1

= -20 - 1

= -21.

Answer:

-21 is correct

Step-by-step explanation:

The slope of the line that is parallel to the given equation is 4

From the question, we are to determine the slope of the equation that is parallel to the given line

The given line is

y = 4x + 4

First, we will determine the slope of the given line

By comparing with the slope-intercept form of the equation of a straight line,

y = mx + b

Where m is the slope

and b is the y-intercept

By comparison,

m = 4

Thus,

The slope of the line is 4

NOTE: If two lines are parallel, their slopes are equal

Hence, the slope is 4

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Answer:

24, 48

Step-by-step explanation:

The 4th common multiple is 6(4)=24.

The 8th common multiple is 6(8)=48.

The percentage of batteries that last between 1.25 and 5.75 years will be 99.73%.

The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.

The z-score is given as

z = (x - μ) / σ

Where μ is the mean, σ is the standard deviation, and x is the sample.

One significant manufacturer's batteries are known to have a shelf life that is regularly distributed, with an average life of 3.5 years and a standard deviation of 0.75 years.

The value of the z-score will be

z = (1.25 - 3.5) / 0.75, (5.75 - 3.5) / 0.75

z = -3, 3

The percentage of batteries that last between 1.25 and 5.75 years will be

P(1.25 < x < 5.75) = P(- 3 < z < 3) x 100

P(1.25 < x < 5.75) = 0.9973 x 100

P(1.25 < x < 5.75) = 99.73%

The percentage of batteries that last between 1.25 and 5.75 years will be 99.73%.

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Answer:

Jade Howey

Step-by-step explanation:

Answer:

Maria

Step-by-step explanation:

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The value of x from the triangle is 12

Given the sides as;

Using the Pythagorean theorem

Hypotenuse square = opposite square + adjacent square

Substitute the value, we have;

15² = x ² + 9²²

Find the squares

225= x² + 81

collect like terms

225 - 81 = x²

144 = x²

Take the square root of both sides

x √144

x = 12

Thus, the value of x from the triangle is 12

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If the height and volume of the prism are 6 inches and 30 cubic inches. Then the base area of the prism is 5 square inches.

What is a rectangular prism?

A rectangular prism is a closed solid that has two parallel rectangular bases connected by a rectangle surface.

The volume of a right rectangular prism is found by multiplying the length of the base by the width of the base by the height of the prism.

A right rectangular prism has a volume of 30 cubic inches.

If the height of the prism is 6 inches. Then the base area of the prism will be

The volume is given as

Volume = Base area × Height

We know

Volume = 30

Height = 6

Then the base area will be

  30 = Area × 6

Area = 5

Answer:

1

5

3

in order

Step-by-step explanation:

First, note that the degree of a polynomial is the value of the highest exponent in the polynomial

There will be as many solutions as there are degrees

1.  - 6x − 9y = 2 has degree 1 since x == x¹ so 1 solution

2. [tex]2x^5-x^4+2x^3-6x^2+2x\:+\:4=0[/tex] has degree 5 so 5 solutions

3. [tex]-4x^3 - 10x^2+7x+5[/tex] has degree 3 so 3 solutions

Answer:

Step-by-step explanation:

each side of square=10/4=2.5

because all the vertices are in quarter |||

so all the coordinates are negative.

x coordinate=-0.5-2.5=-3

y coordinate=-2-2.5=-4.5

all the coordinates are (-3,-2) ,(-0.5,-2)

and (-3,-4.5),(-0.5,-4.5)

Answer:

there are 7 green apples to 8 red apples, or it can be said as 7/8.

Step-by-step explanation:

15 - 7 = 8. This leaves 8 apples left, making these ones red.

Answer:

The system consists

Step-by-step explanation:

The length of rectangular room is 9.5 meter.

The width of rectangular room is 5 meter.

What is Perimeter of rectangular?

The perimeter of a rectangle is two time the sum of length and width of rectangle.

Given that;

The perimeter of rectangular room = 29 meter

The length of rectangular room is 1.9 times as long as it is wide.

Now, Let the width of rectangular room = x

Then Length of rectangular room = 1.9x

Since, Perimeter of rectangular room = 2 ( length + width)

⇒ 29 =  2 (1.9x + x)

⇒ 29 = 2 * 2.9x

⇒ x = 5

Hence, The length of rectangular room = 1.9x

                                                             = 1.9 * 5

                                                             = 9.5 meter

The width of rectangular room is = x

                                                    = 5 meter.

So, The length of rectangular room is 9.5 meter.

The width of rectangular room is 5 meter.

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The value of the account is $47226.73.

The compound interest formula is equal to  

A = P( 1 + r/n )^{nt}

where  A is the Final Investment Value, P is the Principal amount of money that is to be invested, r is the rate of interest, t is the Number of Time Periods, and n is the number of times interest is compounded per year.

Now, we have:

t = 21 years

Principal amount, P = $9000

Rate, r = 8% = 0.08 and

n = 12 as a year has 12 months.

Substituting these values in the formula,

[tex]A = P( 1 + \frac{r}{n} )^{nt}[/tex]

A = 9000 × ( 1 + 0.08/12)²⁵²

A = 9000 × ( 1 + 0.0066)²⁵²

A = 9000 × ( 1.0066)²⁵²

A = 9000 × 5.247

A = 47226.73

The value of the account will be $47226.73.

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The function that represents the difference, h(x) = f(x) – g(x), between the value of Aleka’s and Helene’s total savings after x years is C. h(x) = 1000(1.025)x – 200x.

It should be noted that Aleka and Helene both opened savings accounts that earn 2.5% interest a year. Aleka puts $2,500 into her account.

The function for Aleka will be:

= 2500 (1.025)^x

The function for Helene will be:

= 1500(1./25)^x + 200x

Therefore, the difference of the function will be 1000(1.025)x – 200x.

In conclusion, the correct option is C.

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In the remaining part of the semester, Zachery wrote an average of 10,000 words per month to complete his final project for the course.

We are given that Zachery has to write a total of 95,234 words.

Total words to be written = 95,234 words.

Words already written in the first month = 35,295 words.

Words already written in the second month = 19,240 words.

Words written in total = 35,295 words + 19,240 words.

= 54,535 words

Words left for writing = 95,234 words - 54,535 words

= 39,699 words

months left = 4

Average Words written in remaining month = 39,699 words / 4

= 9924.75 words.

= 10,000 words.

Therefore, in the remaining part of the semester, Zachery wrote an average of 10,000 words per month to complete his final project for the course.

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Simplification - The process of making something less complicated and therefore easier to do or understand, or the thing that results from this process .

What is the simplification rule?

The general rule to simplify expressions is PEMDAS - stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.

Replace Question mark .

1.) 1/2 = 1× x / 2 ×10

     1/2 = x / 20

     x = 20 / 2

      x = 10.

2.) 3/4 = 3 x 5 / 4× x

     3/4 = 15 / 4x

     12x = 60

x = 60 / 12

x = 5

3.) 7/8 = 7× 3 / x × 3

     7/8 = 21 / 3x

      21x = 21 × 8

        x = 8

4.) 2/3 = x×4 / 3  × 4

2/3 = 4x / 12

12x = 24

x =2 .

5.) 6/12 = (6/6) / (12/x)

1/2 = 1 / (12/x)

1/2 = x/12

2x = 12

x = 6.

6.) 3 / 15 = (3 /x) /(15 / 3)

3/15 = (3/x) / 5

3/15 = 3/5x

15x = 15× 3

x =3.

7.) 175/250 = (x/25) / (250/25)

taking LHS

175/250 = 7/ 10

Solve RHS

(x/25) / (250/25)

(x/25) / (10) = x/250

x/250 = 7/10

x = 175.

8.) 28 /56 = (28/28) / (x/28)

28/56 = 1/ (x/28)

28 / 56 = 28 /x

x =56 .

9.) 14/16 =(14/x) / (x/2)

14/16 = 14/x × 2/x

14 /16 = 28  /x²

1 /16 = 2/ x²

x² =32 .

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Answer: 5 5/8

Step-by-step explanation:

6 5/8=  6*8= 48 48+5=53 53/8

8 5/8= 8*8=64 64+5=69 69/8

5 5/8= 5*8=40 40+5=45 45/8

7 5/8= 7*8=56 56+5=61 61/8

Answer:

  (c)  -19 + x = -21

Step-by-step explanation:

You want the mathematical expression equivalent to the English sentence "a number added to -19 is -21."

Addition is written using the math plus symbol (+).

The English word "is" usually signifies sameness or equality, expressed using the math equal sign (=).

The variable x is often used to represent "a number."

When a number is added to -19, we start with -19, then, using the plus symbol, we add x:

  "a number added to -19"   ⇒   -19 + x

  "is"   ⇒   =

   "-21"   ⇒   -21

So, the translated description is ...

  -19 + x = -21

Answer:

14 girls divided by their percentage 0.4 the result will be

35 students

Answer:$195.70

Step-by-step explanation:

Starting price is : $248.50

Price with 25% off :

$248.50 x ( 1 - 0.25 ) = $248.50 x 0.75 = $186.375

After that she has to pay 5 % sales tax:

$186.375  x 1.05 = $195.70

Answer:

The total cost of the items is $195.70.

The extra calories that you are consuming per year is 182,500 calories.

The number of miles that you should walk to burn the extra calories is 1,825 miles.

You are consuming 20 oz of Dr. Pepper each meal. You take Dr. Pepper twice in a day. To determine the total extra calories that is being consumed, multiply the calories consumed per month by the number of times in a day you consume Dr. Pepper and by the number of days in a week.

Multiplication is the mathematical operation that is used to determine the product of two or more numbers. The sign used to represent multiplication is ×.

Extra calories consumed in a year = calories per meal x 2 x number of days in a year

250 x 2 x 365 = 182,500 calories

In order to determine the number of miles you have to walk to lose the extra calories, divide the extra calories by the calories lost per mile

Number of miles to walk = 182,500 / 100 = 1825 miles

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Answer: [tex]y=x^2 +6x-16[/tex]

Step-by-step explanation:

From the roots, the equation in factored form is [tex]y=a(x-2)(x+8)[/tex]. Substituting in the coordinates (-6, -16),

[tex]-16=a(-6-2)(-6+8)\\\\-16=-16a\\\\a=1[/tex]

So, the equation is [tex]y=(x-2)(x+8)[/tex], which expands to [tex]x^2 +6x-16[/tex].

The amount he put into the first account at 2% interest will be $8,000 and into the second account at 7% interest will be $42,000.

Given that,

Amount invested by Alex = $50,000,

Total interest earned = 6.2%,

Now,

Let,

Amount invested at 2% = x,

So,

Amount invested at 7% = (50,000 - x),

So,

According to the question,

7%(50000 - x) + 2%(x) = 6.2% * 50,000

we get,

0.07(50000 - x) + 0.02(x) = 0.062 * 50,000

3500 - 0.07x + 0.02x = 3100

3500 - 0.05x = 3100

We  get,

0.05x = 3500 - 3100

0.05x = 400

x = 8000,

So,

Amount invested at 2% = $8000,

So,

Amount invested at 7% = (50,000 - 8000) = $42,000,

Hence we can say that the amount he put into the first account at 2% interest will be $8,000 and into the second account at 7% interest will be $42,000.

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Answer:

A

Step-by-step explanation:

1 kilogram is equal to 1000 grams, so 40000 grams is 40 kilos.

Answer:

49

Step-by-step explanation:

You first simplify (1/7)^2 which is 7^2 then you get 49.

Answer:

49

Step-by-step explanation:

did it

The graph that correctly plots the line y=3−2x is option B which is:

Four plotted points on a coordinate plane.

A coordinate plane has a horizontal x-axis and a vertical y-axis. Four points are plotted at left-parenthesis negative 1 comma 5 right-parenthesis, left-parenthesis 0 comma 3 right-parenthesis, left-parenthesis 1 comma 1 right-parenthesis, and left-parenthesis 2 comma negative 1 right-parenthesis.

we use the given equation to get the points by substituting the values of x given, to get the values of y as follows

y = 3 - 2x

for x = -1

y = 3 - 2 ( -1 )

y = 3 - ( -2 )

y = 3 + 2

y = 5

( -1, 5 )

y = 3 - 2x

for x = 0

y = 3 - 2 (0 )

y = 3 - 0

y = 3

( 0, 3 )

y = 3 - 2x

for x = 1

y = 3 - 2 ( 1 )

y = 3 - ( 2 )

y = 3 - 2

y = 1

( 1, 1 )

y = 3 - 2x

for x = 2

y = 3 - 2 ( 2 )

y = 3 - ( 4 )

y = 3 - 4

y = -1

( 2, -1 )

( -1, 5 ), ( 0, 3 ), ( 1, 1 ), and ( 2, -1 ) These represents the points in the second option hence the correct answer.

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Answer:4

Step-by-step explanation:

dilation

In a plane, a transformation in which each point on the image lies on the same line as the corresponding point on the preimage and a fixed point called the center of dilation; the ratio between the distance from the center of dilation to a point on the image and the distance from the center of dilation to the corresponding point on the preimage remains constant.