Terry sold 30 cans of paint at a total cost of $425. A can of paint holding one quart cost $10 each. A can of paint holding one gallon cost $15 each. The equations and graph below can be used to determine the number of cans of paint Terry sold, where x represents the number of quarts of paint, and y represents the number of gallons of paint.

Number of cans: x + y = 30
Total cost of cans: 10x + 15y = 425

A. 42 quarts, 28 gallons

B. 25 quarts, 5 gallons

C. 5 quarts, 25 gallons

D. 15 quarts, 15 gallons

Answer:

minimum value of 7

Step-by-step explanation:

It is open up so it has a minimum

The minimum value is the lowest y

So we first must find the x that the point happens at which is -b/(2a)

So -(-8)/(2*1)=8/2=4

Now to find the y use y=x^2-8x+23

y=4^2-8(4)+23

y=16-32+23

y=-16+23

y=7  (lowest y-minimum value is 7)

Answer:

The rate of simple interest is 9%

Step-by-step explanation:

* Lets talk about the simple interest

- The simple Interest Equation (Principal + Interest)  is:

  A = P(1 + rt)  , Where

# A = Total amount (principal + interest)

# P = Principal amount

# I = Interest amount

# r = Rate of Interest per year in decimal r = R/100

# R = Rate of Interest per year as a percent R = r * 100

# t = Time period involved in months or years

- The rule of the simple interest is I = Prt

* lets solve the problem

- Charles deposited $12,000

∴ P = $12,000

- He withdrew $5,000 from his account after one year

- He receives a total amount of $9,340 after 3 years

∴ A = $9340 and t = 3

- Lets find the inetrest after 1 year

∵ I = Prt

∵ P = 12000

∵ t = 1

∴ I = 12000(r)(1) = 12000r

- Lets subtract the money that he withdrew

∵ He withdrew $5000

∵ He deposit at first 12000

∴ He has after the withdrew 12000 - 5000 = 7000

- The new P for the next 2 years is 7000

- This amount will take the same rate r for another two years

- The total money is $9340

∵ I = A - P

∵ A = 9340

∵ P = 7000

∴ The amount of interest = 9340 - 7000 = 2340

- The amount of interest after 3 years is 2340

- Lets find the amount of interest in the two years

∴ I = 7000(r × 2) = 14000r

- The amount of interest after the 3 years is the sum of the interest in

  the 1st year and the other 2 years

∴ 2340 = 14000r + 12000r

∴ 2340 = 26000r ⇒ divide both sides bu 2340

∴ r = 2340 ÷ 26000 = 0.09

∵ The rate R in percentage = r × 100

∴ R = 0.09 × 100 = 9%

∴ The rate of simple interest is 9%

Answer:

We can easily simplify the expression by using a computational tool

The expression is

"6 x squared minus 54 x plus 84 over quantity 8 x squared minus 40 x plus 48 divided by quantity x squared plus x minus "

Please, see attached images below, for a full explanation

Answer:

38

Step-by-step explanation:

The 38-deg angle and and angle 6 are vertical angles, so they are congruent.

m<6 = 38 deg

Angles 6 and 4 are corresponding angles of parallel lines cut by a transversal, so they are congruent.

m<4 = m<6 = 38 deg

Answer:

38

Step-by-step explanation:

< 6 = 38  vertical angles

< 6 = <2  alternate interior angles

<2 = <4  vertical angles

<4 = 38

Hello There!

32% of 300 is 96

Work shown in image attached.

Answer:

96

Step-by-step explanation:

To get the solution, we are looking for, we need to point out what we know.

1. We assume, that the number 300 is 100% - because it's the output value of the task.

2. We assume, that x is the value we are looking for.

3. If 300 is 100%, so we can write it down as 300=100%.

4. We know, that x is 32% of the output value, so we can write it down as x=32%.

5. Now we have two simple equations:

1) 300=100%

2) x=32%

where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:

300/x=100%/32%

6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for what is 32% of 300

300/x=100/32

(300/x)*x=(100/32)*x       - we multiply both sides of the equation by x

300=3.125*x       - we divide both sides of the equation by (3.125) to get x

300/3.125=x

96=x

x=96

now we have:

32% of 300=96

Answer:

[tex]\large\boxed{(f+g)(x)=2x^2+\dfrac{3}{2}x-5}[/tex]

Step-by-step explanation:

[tex](f+g)(x)=f(x)+g(x)\\\\f(x)=\dfrac{x}{2}-2=\dfrac{1}{2}x-2\\\\g(x)=2x^2+x-3\\\\(f+g)(x)=\left(\dfrac{1}{2}x-2\right)+(2x^2+x-3)\\\\=\dfrac{1}{2}x-2+2x^2+x-3\qquad\text{combine like terms}\\\\=2x^2+\left(\dfrac{1}{2}x+x\right)+(-2-3)\\\\=2x^2+1\dfrac{1}{2}x-5\\\\=2x^2+\dfrac{3}{2}x-5[/tex]

4x-22=62+2x

4x-2x=62+22

2x=84

x=84/2= 42

x= 42 is the answer

[tex]x=42[/tex]

Move the variables to one side and the constants to the other. [tex]4x-2x=62+22[/tex]

Combine the variables. [tex]2x=62+22[/tex]

Combine the constants. [tex]2x=84[/tex]

Divide both sides by 2. [tex]x=42[/tex]

Answer:

D

Step-by-step explanation:

8x-5x<21-6

x<15÷3

x<5

Answer:

D) { x | x < 5}

Step-by-step explanation:

2(4 x + 3) < 5 x + 21

Distribute

8x +6 < 5x+21

Subtract 5x from each side

8x-5x+6 < 5x-5x+21

3x+6 < 21

Subtract 6 from each side

3x+6-6<21-6

3x <15

Divide each side by 3

3x/3 <15/3

x < 5

Answer:

y=3

Step-by-step explanation:

3 (3y - 9) = 0

Divide each side by 3

3/3 (3y - 9) = 0/3

3y -9 = 0

Add 9 to each side

3y -9+9 = 0+9

3y =9

Divide by 3

3y/3 = 9/3

y =3

Hello

Good Luck

Goodbye ♥

Answer:

-2 = m

Step-by-step explanation:

y = -2x + 2; your y-intercept is [0, 2] and your x-intercept is [1, 0] (not all the time your x-intercept will be an endpoint). Simply do rise\run until you hit another endpoint. As you can see, you go two blocks south then go one block over east. Do you understand?

Answer:

d= 9.032 units

Step-by-step explanation:

Given

[tex]Circumference = 28.36[/tex]

We will use the formula for circumference of a circle to find it's radius and then diameter will be found using radius.

So,

[tex]C=2\pi r\\Putting\ the\ value\ of\ \pi and \C\\28.36 = 2 * 3.14 *r\\28.36=6.28* r\\r=\frac{28.36}{6.28}\\ r=4.516\ units[/tex]

Now to find the diameter:

d = r*2

d = 4.516*2

d= 9.032 units

Answer:

The diameter of the circle is 9.03 units

Step-by-step explanation:

The formula for calculating the circumference of a circle is [tex]C=\pi d[/tex].

From the question, the diameter of the circle is 28.36 units.

Since the circumference is rounded to the nearest hundredth, we substitute [tex]\pi=3.14[/tex]  and [tex]C=28.36[/tex] into the formula and solve for d.

[tex]\implies 28.36=3.14d[/tex]

Divide both sides by 3.14

[tex]\implies \frac{28.36}{3.14}=\frac{3.14d}{3.14}[/tex]

[tex]\implies 9.03=d[/tex].

Hence the diameter of the circle is 9.03 units to the nearest hundredths

Answer:

12

Step-by-step explanation:

First, multiply the length by two then, subtract the total by the sum, last divide by two.

(25 * 2)

(74 - 50)

(24/2)

Answer = 12

Answer:

w>/=12

Step-by-step explanation:

2(25)+2w>/= 74

50+2w>/=74

-50          -50

2w>/=24/2

w>/=12

Answer:

[tex]\boxed{\text{A. \$1.25; B. September by 4.7 \%}}[/tex]

Step-by-step explanation:

Part A. Price of flowers in September

Let x = price of flowers in September.

Then 1.2x = price of flowers in October

1.2x = $1.50

[tex]x = \dfrac{\$1.50 }{1.20} = \$1.25\\\\\text{The price of flowers in September was }\boxed{\textbf{\$1.25}}[/tex]

Part B. Seventh-grade class

40 % of September price = 0.40 × $1.25 = $0.50

    40 % of October price = 0.40 × $1.50 = $0.60

In September

[tex]\text{Earnings} = \text{900 flowers} \times \dfrac{\$0.50}{\text{1 flower} } = \$450[/tex]

In October,

[tex]\text{Earnings} = \text{700 flowers} \times \dfrac{\$0.60}{\text{1 flower} } = \$430\\\\\text{Difference} = \$450 - \$430 = \$20[/tex]

The class earned $20 more in September.

Compared with October earnings,

[tex]\text{\% Difference} = \dfrac{\text{Difference}}{\text{October earnings}} \times 100\%\\\\\text{\% Difference} = \dfrac{\$20}{\$430} \times 100\% = 4.7 \%\\\\\text{The class made more money in } \boxed{\textbf{September}} \text{ by } {\boxed{\mathbf{4.7 \%}}[/tex]

The answer above me deserves brainliest !! They did so well!!!

Answer:

SA = 1099 square inches.

Step-by-step explanation:

Just plug into the formula

SA = 2pir^2 + 2pi r h where pi = 3.14, r = 5 and h = 30

SA = 2 (3.14) (5^2) + 2 (3.14)(5)(30)

SA = 157 + 942

SA = 1099 square inches.

Answer:

1099.56 or 1099.6 dependong on what you wanna round to

Step-by-step explanation:

2×pi×5^2+2×pi×5×30

Find the ordered pairs for y = 2ˣ by substituting various values of x into the equation, calculate y, and list the pairs. These can then be plotted on a graph to show the exponential relationship.

To determine the ordered pairs for the given function y = 2ˣ, you will perform substitutions for x with various values and calculate the corresponding y values. Once this is done, you can plot these points on a graph to visualize the function.

Choose a range of x-values (for example, -3, -2, -1, 0, 1, 2, 3).

Calculate the corresponding y-values using the equation y = 2ˣ.

List the ordered pairs (x,y).

Plot each pair on a coordinate graph.

Connect the points to represent the exponential graph.

Remember, shifting an exponential graph parallel to the x-axis can be done by adjusting the exponent's value.

Answer:

1/28

Step-by-step explanation:

Before picking 1st song

Total songs = 8

Rock songs = 2

Probability of picking a rock song as the first song,

= 2 rock songs out of 8 total songs remaining

= 2/8

After picking 1st song

Total songs left over = 7

Rock songs left over = 1

Hence, Probability of picking a rock song as the second song,

= 1 rock song out of 7 total songs remaining

= 1/7

Probability of picking 2 consecutive rock songs,

= [tex]\frac{2}{8}[/tex] x [tex]\frac{1}{7}[/tex]

= [tex]\frac{1}{28}[/tex]

Answer:

(t+p,r)

Step-by-step explanation:

To find midpoint you average the x's and averages the y's of the endpoints.

So x-coordinate (2p+2t)/2 =p+t

So y-coordinate (2r+0)/2=2r/2=r

So midpoint (p+t, r)

Answer:

The correct answer is first option

(t + p, r)

Step-by-step explanation:

Points to remember

midpoint formula

Length of a line segment with end points (x1, y1) and (x2, y2) is given by,

Midpoint= [(x2 + x1)/2 , (y2 + y1)/2]

To find the midpoint of EC

Let   (x1, y1) = E(2t, 0) and  (x2, y2) = C(2p, 2r)

Midpoint = [(2t + 2p)/2 , (0 + 2r)/2]

 = (2(t + p)/2 , 2r/2)

 = (t + p, r)

Therefore midpoint of EC = (t + p, r)

The correct answer is first option

Answer:

[tex]\large\boxed{V=Bh,\ 26x=B(6.5)\to B=4x}[/tex]

Step-by-step explanation:

[tex]\text{The formula of a volume of cylinder:}\\\\V=Bh\\\\\text{We have}\ V=26x\ m^3\ \text{and}\ h=6.5\ m.\\\\\text{Substitute:}\\\\26x=B(6.5)\qquad\text{divide both sides by 6.5}\\\\\dfrac{26x}{6.5}=B\to B=4x[/tex]

Answer:

The diagonal of the base is 4√5 centimeters.

The area of a base is 40 square centimeters.

The area of a lateral side between the bases is about 126.5 square centimeters.

Step-by-step explanation:

Answer:

The simplification of the given expression  (r3s2t)4 is:

r¹²s⁸t⁴

Step-by-step explanation:

Given expression:

(r³s²t)⁴

power of '4' on the whole term will be applied to individual terms after we open the brackets. In this case the power on the whole term will be multiplied to the power of each individual term:

= (r³)⁴(s²)⁴(t1)⁴

= r³ˣ⁴ s²ˣ⁴ t¹ˣ⁴

= r¹²s⁸t⁴

Answer:

1.) 2

Step-by-step explanation:

We have points (3,3) and (5,7) on the line.

Slope of a line = change in y ÷ change in x

i.e Slope = [tex]\frac{7 - 3}{5 - 3}[/tex] = 2

The slope of the line passing through the points (3, 3) and (5, 7) is 2. Therefore, the correct answer is option 1.

The given coordinate points are (3, 3) and (5, 7).

The formula to find the slope of a line is slope = (y₂-y₁)/(x₂-x₁).

Here, slope = (7-3)/(5-3)

= 4/2

= 2

So, the slope is 2.

Therefore, the correct answer is option 1.

To learn more about the slope of a line visit:

https://brainly.com/question/14511992.

#SPJ2

Final answer:

The labor charge for a car repair job that takes 3.5 hours is $267.50. The difference in labor charges between a job that takes 2.4 hours and one that takes 6.3 hours is $214.50. Choosing between two similarly priced used cars requires additional information beyond the asking price.

Explanation:

The question asks for different computations related to the costs of car maintenance and repairs. Here is a solution to one of the calculations:

Labor Charge Calculation

The independent variable is the number of hours worked, and the dependent variable is the total labor charge. The equation to represent this situation is:

Labor Charge = $75 + ($55 × number of hours)

The slope is $55 as it represents the increase in charge per hour, and the y-intercept is $75 since it's the flat fee charged regardless of the hours worked.

For a job taking 3.5 hours:

Labor Charge = $75 + ($55 × 3.5) = $75 + $192.50 = $267.50

Difference in labor costs for two jobs (2.4 and 6.3 hours):

Labor Charge for 2.4 hours = $75 + ($55 × 2.4) = $75 + $132 = $207

Labor Charge for 6.3 hours = $75 + ($55 × 6.3) = $75 + $346.50 = $421.50

Difference = $421.50 - $207 = $214.50

In the context of Marvin shopping for a used car, it is not possible to provide a suggestion on which car to buy (the $4,000 or the $4,600 one) without additional information. Factors such as overall condition, future maintenance costs, and personal budget would need to be considered.

[tex]|\Omega|=20+16+4=40\\|A|16+4=20\\\\P(A)=\dfrac{20}{40}=\dfrac{1}{2}[/tex]

Answer:

1/2

Step-by-step explanation:

16+4 =20 red and white marbles

40 marbles in all

20/40= 1/2

A transversal is a line that passes through two lines (as shown above) on the same plane.

N is the transversal since it passes through line L and M at two distinct points.

Answer:

A transversal is a line that passes through two lines (as shown above) on the same plane.

N is the transversal since it passes through line L and M at two distinct points.

Step-by-step explanation:

Answer:

An  equilateral triangle has all sides equal.  

If perimeter = 18y -6 then one side = (18y -6) / 3 =

6y -2

Step-by-step explanation:

Answer:

54

Step-by-step explanation:

18y-6

y=18/6

y=3

18*3=54

Answer:

3a/4b and 9a/12b are equivalent

Step-by-step explanation:

3a/4b is multiplied by 3/3 to get 9a/12b

Answer:

equivilent

Step-by-step explanation:

it is equivalent because if divide 9a and 12b both by 3, it equals 3a/4b.  Both fractions have the same lowest common denominator.

Hope this helps!

Answer:

P = (8, 0) and Q = (0, 6)

Step-by-step explanation:

To find where the line crosses the x- axis, substitute y = 0 into the equation and solve for x

3x + 4(0) = 24

3x = 24 ( divide both sides by 3 )

x = 8 ⇒ P = 8 ⇒ (8, 0 )

To find where the line crosses the y- axis substitute x = 0 into the equation and solve for y

3(0) + 4y = 24

4y = 24 ( divide both sides by 4 )

y = 6 ⇒ Q = 6 ⇒ (0, 6 )

Hello There!

First we have to see how much does Gigi earns per hour.

For gardening, we are going to divide.

65 ÷ 5 ≈ 13

Gigi earns $13 for gardening for only 1 hour.

Second, we have to see how much Gigi earns per hour for office work.

We will divide

90 ÷ 9 ≈ 10

Now, we can see that Gigi earned $3 more per hour for gardening than for office work.

Final answer:

By using the principle of inclusion-exclusion, we can find that 50 people have both a DVD player and a CD player in a group of 100 people.

Explanation:

To find out how many people have both a DVD player and a CD player, we can use the principle of inclusion-exclusion.

According to the problem, there are 100 people in the group. Out of these, 70 have a DVD player, 60 have a CD player, and 20 have neither.

We can begin by subtracting those who have neither from the total to find out how many people have at least one of the devices:

100 - 20 = 80 people have at least one device.

Now, if we add the number of people who have a DVD player to the number of people who have a CD player, we would double count those who have both. So, we subtract the total number who have at least one device from this sum:

70 (DVD owners) + 60 (CD owners) - 80 (at least one device) = 50 people who have both a DVD and CD player.