A rectangle has sides of 4 and 6 units. Which expression could you use to find the volume (in
cubic units) of the three-dimensional object formed by continuously rotating the rectangle about
the shorter side?

Answer: he invested $120000 at 6% and $281000 at 9%

Step-by-step explanation:

Let x represent the amount invested at 6%

Let y represent the amount invested at 9%

The Actor invest some money at 6% and $41000 more than twice the amount at 9%. This means that

y = 2x + 41000- - - - - - - - - 1

The interest gotten from x is

6/100 × x = 0.06x

The interest gotten from y is

9/100 × y = 0.09y

The total annual interest earned from the investment is $32490. It means that

0.06x + 0.09y = 32490- - - - - - - - -2

Substituting equation 1 into equation 2, it becomes

0.06x + 0.09(2x + 41000) = 32490

0.06x + 0.18x + 3690 = 32490

0.06x + 0.18x = 32490 - 3690

0.24x = 28800

x = 28800/0.24

x = 120000

Substituting x = 120000 into equation 1, it becomes

y = 2(120000) + 41000

y = 281000

Answer:

$ 21

Step-by-step explanation:

Money spent = (2/5) * 60 + (1/4) * 60

                      = 2*12 + 1*15

                      = 24 + 15

                      = $ 39

Money save = 60 - 39 = $ 21

Answer:

A=(1/2)(b)(h)

Step-by-step explanation:

The area of a triangle is 1/2(b)(h), so in this case, A=(1/2)(24)(16)=192

Answer:

It is 3.

Step-by-step explanation:

By looking at the sentences, you can translate the sentences to equations.

The sum of two numbers is 90, so this involves addition because the sum is the answer of an addition problem. x+y=90.

x is the larger number

y is the smaller number

The larger number is 14 more than or addition sign 3 times or multiplying the smaller number (y).

The equation would be x=14+3y because it is 3 times the smaller number.

Hope this helps!

Answer:

1. $3.85 per gallon

2. $1.59

3. 7/12

Step-by-step explanation:

1. Jayden spent $46.20 on 12 gallons of gasoline. The price per gallon can be gotten by dividing the total price paid by the total number of gallons bought:

46.20 / 12 = $3.85 per gallon

The price per gallon is $3.85

2. Jayla buys 1.2 pounds of bananas and they cost $1.29 per pound. The total amount paid for the bananas is:

1.2 * 1.29 = $1.59

3. Billy ate 1/4 of a pizza, and Wi ate 1/3 of the same pizza. The total fraction of the pizza ate is:

1/4 + 1/3 = 7/12

They ate 7/12 of the pizza

Answer: See bolded below

Step-by-step explanation:

Average rate of change is the slope. To find that, we would need the equation [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex].

Reminder: The scale fo the graph goes by 2. You need to make sure you are looking at the right coordinates.

1. The coordinate points are (1, 2) and (2, 4).

[tex]m=\frac{4-2}{2-1}=\frac{2}{1} =2[/tex]

The average rate of change is 2.

2. The coordinate points are (2, 4) and (3, 8).

[tex]m=\frac{8-4}{3-2} =\frac{4}{1} =4[/tex]

The average rate of change is 4.

3. The coordinates are (3, 8) and (4, 16).

[tex]m=\frac{16-8}{4-3} =\frac{8}{1} =8[/tex]

The average rate of change is 8.

Answer:

150

Step-by-step explanation:

Step 1: Plug in what we know

5x + 10(5) = 800

Step 2: Solve for x (smaller cars)

5x + 50 = 800

5x = 750

x = 150

Answer:

150

Step-by-step explanation:

:)

Answer: (9 - 2) ⋅ 180 ° = 7 ⋅ 180 ° = 126 0 °

Step-by-step explanation:

Answer:

Step-by-step explanation:

20 x 15%

is equal too...

20 x 0.15

and that is equal to

...

3

Answer:

0.40x=1900

Step-by-step explanation:

Answer:

(-1,1)

Step-by-step explanation:

The solution to the system of equations is where the two lines cross

They cross at x=-1 y=1

(-1,1)

Answer:

The answer is (-1,1)

Step-by-step explanation:

First of all, you can see where the two lines intersect.

Also, if there was no graph, then you could solve by substitution:

1. Substitute y from y = 2x + 3 to -x

2. Then simplify

-x = 2x + 3

subtract 2x from each side

-3x = 3

divide -3 from each side

x = -1

3. To solve for the value of y, you can plug -1 for x and solve.

y = -(-1)

y = 1

Answer:

A) inside the circle

Step-by-step explanation:

equation of the circle is:

[tex](x-a)^{2} + (y-b)^{2} = r^{2}[/tex]

where (a,b) is center of the circle and r is radius so

[tex]x^{2} + y^{2} = r^{2}[/tex] now plug in given point to find the radius

[tex](6)^{2} + (-4)^{2} = r^{2}[/tex]

36 +16 = 52 so

r = [tex]\sqrt{52}[/tex]  ≈ 7.2 or  [tex]r^{2} =52[/tex]

when you plug point (√2 , -7) into equation of the circle

(√2)^2 + (-7)^2 = 2 +49 =51

51 is less than 52 so this is inside of the circle

Answer:

49

Step-by-step explanation:

Add then subtract

Answer:

-44

Step-by-step explanation:

(-4+1)+(10-51)

-4+1+10-51

-3-41

-44

Answer:

[tex]9^{-7}, 9^{-2}[/tex]

Step-by-step explanation:

[tex]\frac{9^5\times9^{-9}}{9^3}\\\frac{9^{-4}}{9^3}\\ 9^{-7}[/tex]

When you multiply like terms, you add their powers. When dividing like terms, you subtract their powers (subtract the power in the denominator from the one in the numerator).

[tex](9^4)^3\times9^{-14}\\9^{12}\times9^{-14}\\9^{-2}[/tex]

Answer:

8

Step-by-step explanation:

h(t) = -t + 3;

h(-5)

Let t = -5

h(-5) = - -5 +3

       = 5+3

       = 8

Answer:

8

Step-by-step explanation:

h(t) = -t + 3

Put t as -5 in the function.

h(-5) = -(-5) + 3

The negative signs cancel.

h(-5) = 5 + 3

Add both the terms.

h(-5) = 8

Answer:

The answer would be, 2.75

Step-by-step explanation:

Add all the numbers up:

0+1+1+2+3+4+5+6=22

Divide the answer by the amount of numbers:

22÷8=2.75

Answer:

The mean of the following dot plot:

Mean: 3

Step-by-step explanation:

0 x 1 = 0

3 x 1 = 3

6 x 1 = 6

(we only add the numbers that only has a dot on the number in the dot plot)

So:

Mean: 0 + 3 + 6 = 9/3 = 3

Answer:

associative property with respect to addition and subtraction

3+[7+(-4)]=(3+7)+(-4)

3+[7-4]=10+(-4)

3+3=10-4

6=6

Step-by-step explanation:

i hope it will help you

Answer:

x=5

Step-by-step explanation:

2(x+4)+2x+3=3x+16

One solution was found :

                  x = 5

Answer:

2x+8+2x+3=3x+16=

2x+2x-3x=-8-3+16=

4x-3x=-11+16=

x=5

Answer:

First equation: 1/2

Second equation: -1/3

Step-by-step explanation:

We get the following equations:

[tex]\frac{1}{3}x+\frac{1}{6}y=2[/tex]          first equation

[tex]\frac{1}{2}x+\frac{3}{4}y=-3[/tex]       2nd equation

Then, to obtain opposite terms for the x variable, we need to identify the coefficient of the x for the 1st equation and the 2nd equation as:

The coefficient for x in the 1st equation is [tex]\frac{1}{3}[/tex] and the coefficient for x in the 2nd equation is [tex]\frac{1}{2}[/tex]

Finally, we need to multiply 1st equation with the coefficient of the 2nd equation and multiply the 2nd equation with the negative of the coefficient of the 1st equation.

We multiply by the negative of the coefficient of the 1st equation because we need to find opposite terms for x.

So, the first equation is equal to:

[tex](\frac{1}{3}x+\frac{1}{6}y)*\frac{1}{2} =2*\frac{1}{2} \\\frac{1}{6}x+\frac{1}{12}y=1[/tex]        

The second equation is:

[tex](\frac{1}{2}x+\frac{3}{4}y)*\frac{-1}{3} =-3*\frac{-1}{3} \\\frac{-1}{6}x+\frac{-1}{4}y=1[/tex]

Now, the coefficients for x, 1/6 and -1/6, are opposite terms.

Answer:3, -2

Step-by-step explanation:

Answer:

Ratio of sandwiches with white bread and brown bread is 10:3. Of the white sandwiches 2/3 are vegetarian, of the sandwiches that are brown half are vegetarian. What fraction of the sandwiches are vegetarian?

Step-by-step explanation:

Givens

The ratio between white bread and brown bread is 10:3, that is, for every 10 white bread, there are 3 brown bread.

2/3 of white sandwiches are vegetarian.

1/2 of brown sandwiches are vegetarian.

We know that white bread is represented by 10, and brown bread is represents by 3. So, 2/3 of 10 are vegetarians, and 1/2 of 3 are vegetarians. The sum of them is

2/3 of 10 are vegetarians = [tex]\frac{2}{3} \times 10 = \frac{20}{3}[/tex]

1/2 of 3 are vegetarians = [tex]\frac{1}{2} \times 3 = \frac{3}{2}[/tex]

[tex]=\frac{20}{3}+\frac{3}{2}\\\\=\frac{40+9}{6}\\\\=\frac{49}{6}[/tex]

Therefore, 49/6 represents all the sandwiches which are vegetarian.

Answer:

3.1

Step-by-step explanation:

15.7 - 12.6 = 3.1

Pls mark me brainliest !!

Answer:

91.99%

Step-by-step explanation:

To find what percentage of $7599 is $6990, we simply need to divide $7599 by $6990 and multiply by 100:

6990 / 7599 * 100 = 91.99%

Therefore, they paid 91.99% of the original price.

Answer:

The answer is C, 60 degrees.

Step-by-step explanation:

Answer:

B. x-intercept = 2, y-intercept = 4

Step-by-step explanation:

→The y-intercept can be found on the vertical line, while the x-intercept can be found on the horizontal line.

→Looking at the graph, you can see that the line intersects at a point on the vertical line (y-intercept), and this number is 4.

→Looking at the graph, you can see that the line intersects at a point on the horizontal line (x-intercept), and this number is 2.

Answer:

([tex]\frac{13}{5}[/tex] , [tex]\frac{6}{5}[/tex] )

Step-by-step explanation:

Given the 2 equations

2x - y - 4 = 0 → (1)

3x + y - 9 = 0 → (2)

Adding the 2 equations term by term will eliminate the term in y, thus

5x - 13 = 0 ( add 13 to both sides )

5x = 13 ( divide both sides by 5 )

x = [tex]\frac{13}{5}[/tex]

Substitute this value into either of the 2 equations and evaluate for y

Substituting into (2)

[tex]\frac{39}{5}[/tex] + y - 9 = 0

- [tex]\frac{6}{5}[/tex] + y = 0 ( add [tex]\frac{6}{5}[/tex] to both sides )

y = [tex]\frac{6}{5}[/tex]

Solution is

([tex]\frac{13}{5}[/tex] , [tex]\frac{6}{5}[/tex] )