The area of a playground is 160 yd2. The width of the playground is 6 yd longer than its length. Find the length and width of the playground.

Answer:

There are 96 liters of oil in both containers originally

Step-by-step explanation:

* Lets change the story problem to mathematics equation

- Let the first container had A liters of oil and the second container

 had B liters of oil

- The quantity of oil B in the second container is twice the quantity

  of oil in A in the first container

∴ B = 2A ⇒ (1)

- After using 13 liters from the quantity of oil A in the first container,

 the container had (A - 13) liters

- After using 7 liters from the quantity of oil B in the second container,

 the container had (B - 7) liters

-  After that the quantity of oil in the second container is 3 times

 more oil than the first one

∴ B - 7 = 3(A - 13) ⇒ simplify

∴ B - 7 = 3A - 39 ⇒ add 7 and subtract 3A from both sides

∴ B - 3A = -39 + 7

∴ B - 3A = -32 ⇒ (2)

- Substitute the value of B from (1) into (2)

∴ 2A - 3A = -32

∴ -A = -32 ⇒ × -1

∴ A = 32 liters

- Find the value of B by substitute value of A in (1)

∴ B = 2(32) = 64 liters

- Now find the total liters of oil in both containers

∴ A + B = 32 + 64 = 96 liters

* There are 96 liters of oil in both containers originally

To calculate the amount of steel needed to construct the oil tank, we need to find the surface area of the cylinder. A cylinder's surface area is composed of two parts: the area of its circular top and bottom (which are identical), and the area of its side.
Let's start by calculating the area of the two circular ends of the cylinder.
1. The area of one circle (either the top or the bottom) is given by the formula:
 \[ A_{\text{circle}} = \pi r^2 \]
  where \( r \) is the radius of the circle.
  Since the diameter is twice the radius, we have:
  \[ d = 12 \ \text{ft} \]
  \[ r = \frac{d}{2} = \frac{12 \ \text{ft}}{2} = 6 \ \text{ft} \]
  Now, we calculate the area of one circle:
  \[ A_{\text{circle}} = \pi (6 \ \text{ft})^2 = \pi \times 36 \ \text{ft}^2 \]
  \[ A_{\text{circle}} = 36\pi \ \text{ft}^2 \]
  Since there are two circles (top and bottom), we double this area:
  \[ A_{\text{circles}} = 2 \times 36\pi \ \text{ft}^2 \]
  \[ A_{\text{circles}} = 72\pi \ \text{ft}^2 \]
2. Next, we calculate the area of the side of the cylinder. The side is essentially a rectangle that is wrapped around the circular ends. The width of this rectangle is the height of the cylinder, and the length is the circumference of the circle.
 The circumference of the base circle is given by:
     \[ C = 2\pi r \]
  Using the radius we found before:
  \[ C = 2\pi \times 6 \ \text{ft} = 12\pi \ \text{ft} \]
 The area of the side is then:
  \[ A_{\text{side}} = C \times \text{height} \]
  \[ A_{\text{side}} = 12\pi \ \text{ft} \times 18 \ \text{ft} \]
  \[ A_{\text{side}} = 216\pi \ \text{ft}^2 \]
3. The total surface area of the steel needed to make the tank is the sum of the areas of the circular ends and the side:
  \[ A_{\text{total}} = A_{\text{circles}} + A_{\text{side}} \]
  Substitute the values found above:
  \[ A_{\text{total}} = 72\pi \ \text{ft}^2 + 216\pi \ \text{ft}^2 \]
  \[ A_{\text{total}} = 288\pi \ \text{ft}^2 \]
  To find a numerical value, we use the approximation \( \pi \approx 3.14159 \) (you can use a more precise value based on your requirements):
  \[ A_{\text{total}} \approx 288 \times 3.14159 \ \text{ft}^2 \]
  \[ A_{\text{total}} \approx 904.77792 \ \text{ft}^2 \]
  So approximately 904.78 square feet of steel are needed to make the tank.

Answer:

A+C=34

10C+20A=570

Answer:

(3, 2)

(−6, −4)

Step-by-step explanation:

Final answer:

To find the missing value so that the two given points have a slope of -2, substitute the values into the slope formula and solve for y. The missing value is y = 5.

Explanation:

To find the missing value for the given points (1, y) and (6, -5) so that the two points have a slope of -2, we can use the formula for finding the slope between two points:

Slope = (y₂ - y₁) / (x₂ - x₁)

Substituting the given values into the formula, we have:

(-5 - y) / (6 - 1) = -2

Simplifying this equation:

-5 - y = -2(6 - 1)

-5 - y = -2(5)

-5 - y = -10

Solving for y:

y = -5 + 10

y = 5

Therefore, the missing value 'y' is 5.

Answer:

-2

Step-by-step explanation:

its a geometric sequence where every term is being divided by -3

Answer:

-2

Step-by-step explanation:

This is a geometric sequence.  We need to find the common ratio

Take the second term and divide by the first

-18/54 = -1/3

Take the third term and divide by the second

-18/6 = -1/3

The common ratio is -1/3

The next term is the third term times the common ratio

6 * -1/3 = -2

The fourth term  is -2

Answer:

y=110x-2... I might be wrong...

Step-by-step explanation:

Answer:

y=114x-6

Step-by-step explanation:

i got a 100 on ed2021 good luck yall

Answer:

The answer is 5x^2+32x-21

Step-by-step explanation:

To find the area of a rectangle, you have to multiply the length by the width. Then, you will get the equation of (5x-3)(x+7). Then, multiply these two together, therefore getting 5x^2+32x-21.

Answer:

88cm^2

Step-by-step explanation:

Answer:

3 * pi

B

Step-by-step explanation:

The diameter is 3 inches.

radius = diameter / 2

radius = 3 / 2 = 1.5 inches.

The circumference of a circle = 2*pi*r where r is the radius, and pi = 3.14

C = 2 * pi * 1.5

C = 3 * pi

B

First, we need to isolate the variable x.

To isolate x, we simply need to multiply both sides by 9, which would result in x = 9

[tex] \frac{x}{9} = 1 \\ \\ 1. \: x = 1 \times 9 \\ \\ 2. \: x = 9[/tex]

Hei there!

Let's start by letting x be the number of children in the 2nd group. So we can make an equation:

(50+x)+x=300

Next, open parenthesis and combine like terms. Then solve for x.

50+x+x=300

2x=300-50

2x=250

x=125

So, there are 125 kinds in the 2nd group.

Hope I helped, sorry if I'm wrong ouo.

~Potato.

Copyright Potato 2019.

Answer: 125 children

We have an unknown amount of children in the second group, so let us call this x. The number of children in the first class must be x + 50. In other words, the total number of children in both classes would be x + x + 50, which equals to 2x+50, and you have a total of 300 children. Let us start with this equation:

2x + 50 = 300

Subtract 50 from both sides

2x + 50 - 50 = 300 - 50

Simplify

2x = 250

Divide both sides by 2

2x / 2  =  250 / 2

Simplify

x = 125

Again, we said, x is an unknown amount of children in the second group. As you can see, x = 125, so there are 125 children in the second group.

125 + 50 = 175

Since, there are 50 more children in the first group, you would add 50 to 125, and that will give us a total of 175 children in the first group.

Answer:

see explanation

Step-by-step explanation:

Using the trigonometric identity

tanx = [tex]\frac{1}{cotx}[/tex], then

tanx = [tex]\frac{1}{\sqrt{3} }[/tex]

x = [tex]tan^{-1}[/tex]( [tex]\frac{1}{\sqrt{3} }[/tex]) = [tex]\frac{\pi }{6}[/tex]

Hence x = [tex]\frac{\pi }{6}[/tex] + kπ ( k ∈ Z )

Answer:

[tex]\large\boxed{b=\sqrt{95}}[/tex]

Step-by-step explanation:

Use the Pyhagorean theorem:

[tex]leg^2+leg^2=hypotenuse^2[/tex]

We have

[tex]leg=b,\ leg=7,\ hypotenuse=12[/tex]

Substitute:

[tex]b^2+7^2=12^2[/tex]

[tex]b^2+49=144[/tex]       subtract 49 from both sides

[tex]b^2=95\to b=\sqrt{95}[/tex]

Answer:

slope= -4/5

y intercept= - 9/5

Step-by-step explanation:

Answer:

if i did my math right then the answer is 244

Step-by-step explanation:

Answer:

92

Step-by-step explanation:

Substitute the given values for a and b into the expression

2a² + 5b²

= 2(- 6)² + 5(2)²

= (2 × 36) + (5 × 4)

= 72 + 20

= 92

First you need to replace all of the letter A's with -6 and all of the B's with 2.

The equation would look like this

2(-6)^2+5(2)^2

Second, you solve what in is the parenthesis 2(-6)=-12         5(2)= 10

Third, you rewrite the problem.   -12^2+10^2

Fourth, you need to figure out what the final answer would be.    

-12^2=-144 and 10^2=100

The answer would be -144+100=-44

Sorry!!! This is probably Wrong, I didn't use an algebra calculator or anything to check the answer. I didn't remember if I needed to bring the number in parenthesis to the power before or after multiplying.

Answer:

15/32 cup

Step-by-step explanation:

Apparently, you're to assume that flour used on the countertop does not end up in the muffins. If that is the case, then the amount of flour in the 8 muffins is ...

4 cups - 1/4 cup = 3 3/4 cups

When that is divided evenly among 8 muffins, the amount in each is ...

(1/8)·(3 3/4 cups) = (1/8)·(15/4 cups) = 15/32 cup

Answer: 15/32

Step-by-step explanation: Because she uses 1/4 to flour the counter you need to subtract 1/4 from four which gives you 3 3/4. 3 3/4 divided by eight equals 15/32

Answer:

Option B

Step-by-step explanation:

Given are three tables in x and y and we have to find which table shows a linear relation.

We know in  a linear relation between x and y the graph would be a straight line and also the slope would be constant

i.e. change of y/change of x for any pair in the table would be a constant.

Out of three tables given, only second table satisfies this.

Hence B is the answer

Answer:

Step-by-step explanation:

<, > - open circle

≤, ≥ - solid circle

<, ≤ - draw to the left

>, ≥ - draw to the right

[tex]3-x\geq2\qquad\text{subtract 3 from both sides}\\\\-x\geq-1\qquad\text{change the signs}\\\\\boxed{x\leq1}\\\\4x+2\geq10\qquad\text{subtract 2 from both sides}\\\\4x\geq8\qquad\text{divide both sides by 4}\\\\\boxed{x\geq2}[/tex]

Well convert all of them into fourths. 3 1/2 = 3 2/4. Add all the whole numbers 2 + 4 + 3 = 9 and then add the fractions 1/4 + 3/4 + 2/4 = 6/4 = 1 2/4.  Finally add the whole number and fraction together, 10 2/4 or 10 1/2.

10 1/2 cases of popcorn.

The total number of cases of popcorn sold by Emily, Brenda, and Shannon is 10 1/2 cases. We arrived at this number by converting their sales to improper fractions, finding a common denominator, and then adding the fractions together.

The question asks us to calculate the total number of cases of popcorn sold by three girls: Emily, Brenda, and Shannon. Emily sold 2 3/4 cases, Brenda sold 4 1/4 cases, and Shannon sold 3 1/2 cases. To find the total, we need to add these amounts together.

To perform the addition, convert any mixed numbers to improper fractions:

Emily: 2 3/4 = 11/4 cases

Brenda: 4 1/4 = 17/4 cases

Shannon: 3 1/2 = 7/2 cases

Now, add these improper fractions together:

(11/4) + (17/4) + (7/2)

To add these fractions, we need a common denominator, which is 4 in this case. So, we need to multiply the numerator and denominator of Shannon's sales by 2 to get 14/4.

Now we have:

(11/4) + (17/4) + (14/4) = 42/4

After adding the fractions, we get 42/4, simplifying to 10 1/2 cases. Therefore, the girls sold a total of 10 1/2 cases of popcorn in all.

ANSWER

[tex]f(x) = {x}^{3} + 6 {x}^{2} - 19 - 24[/tex]

EXPLANATION

The polynomial function has zeros at:

-8,-1 and 3

This means the polynomial can be factored as:

[tex]f(x) = (x + 8)(x + 1)(x - 3)[/tex]

We expand the last two factors:

[tex]f(x) = (x + 8)( {x}^{2} - 2x - 3)[/tex]

We expand further to get:

[tex]f(x) = {x}^{3} - 2 {x}^{2} - 3x + 8 {x}^{2} - 16x - 24[/tex]

[tex]f(x) = {x}^{3} + 6 {x}^{2} - 19 - 24[/tex]

The polynomial in descending powers of x is said to be in standard form.

____________________________________________________

Answer:

Your answer would be D). Since -2 is to the left of 1, -2 < 1.

____________________________________________________

Step-by-step explanation:

The reason why this would be the correct answer is because it numerically makes sense, and the statement said in the answer choice is correct on the number line.

The numbers that are on the left side of the number line, the negatives, are a lower value than the numbers on the right. To sum it up, the numbers that are more to the left are less value than the ones more to the right.

In the answer choice D, it says, "Since -2 is to the left of 1, -2 < 1."

This is correct because -2 is less than 1, so when you use the the less than sign, it makes sense since -2 is less than 1. To sum it uyp, 1 is greater than -2.

D should be your FINAL answer.

____________________________________________________

Why the other answer choices are incorrect:

The reason why answer choice "A" is incorrect because:

-2 is actually not greater than -1. Remember, The numbers that are more to the right are greater than the numbers on the left. -2 is to the left of -1, which means that -1 would be greater than -2. This statement would be incorrect. This is the reason why this answer choice would be wrong.

The reason why answer choice "B" is incorrect because:

-1 is not equal to 1. -1 is more to the left than 1, and since the negative sign is there, they wouldn't be the same. Even though they have the same number, they don't have the same value. If the equation said 1 =1, it would be true, but that's not the case in this answer choice, which would make it incorrect. This is the reason why this answer choice would be wrong.

The reason why answer choice "C" is incorrect because:

-2 is not  greater than 1/3. -2 is negative, while 1/3 is positive, therefore making the 1/3 greater than -2. In the answer choice, it's saying that -2 is greater than positive 1/3, which is incorrect. This is the reason why this answer choice would be wrong.

____________________________________________________

Answer:

D

Step-by-step explanation:

Answer:

It should be D if that is an option.

Step-by-step explanation:

The equation is y= -3/2 x + 3

The slope is -3/2. It goes down 3 and over 2 to the right.

The y-intercept is positive 3. It intersects with the y-axis at the point (3,0).

Answer:

y = -3/2x + 3

Step-by-step explanation:

To find the equation for the graph, first you must find the slope. Pick 2 random points on the line, [for example (2,0) and (0,3)] You can find the slope by using the formula rise/run [rise over run]. To get from point (2,0) to point (0,3) you have to go up 3 and left 2 [resulting in the negative infront of 3/2. if you went right, ti would've been positive.] Then you have your slope, -3/2x

Next find the y-intercept [the point where the line hits the y-axis]

The line hits the y-axis at (0,3), so your y-intercept s 3.

Therefore, the equation is -3/2x+3

The population growth of the ants represents a non-linear function or exponential growth. After one year, the ant farm will contain 384 ants.

Exponential growth is evident in this situation as the number of ants in the farm doubles every three months. This doubling is characteristics of exponential functions, therefore, this population growth is a non-linear function, not a linear function. In terms of how many ants will be in the farm after a year, there will be four 3-month periods in a year. So, the ants double four times. Using the formula of exponential growth 2n (where 'n' is the number of cycles), we can precisely calculate the final number of ants. Therefore, the total number of ants after one year, or four 3-month cycles, would be 24 ants * 24 = 24 ants * 16 = 384 ants.

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[tex]c)x^{2/3}[/tex]

5??? Not 100% Sure If Im Correct.

Answer:

statement A

Step-by-step explanation:

If the ratio

[tex]\frac{QT}{TR}[/tex] = [tex]\frac{QU}{US}[/tex]

then TU is parallel to RS

[tex]\frac{QT}{TR}[/tex] = [tex]\frac{32}{36}[/tex] = [tex]\frac{8}{9}[/tex]

[tex]\frac{QU}{US }[/tex] = [tex]\frac{40}{45}[/tex] = [tex]\frac{8}{9}[/tex]

Since the ratios are equal then line segment TU is parallel to line segment RS

Answer:

x=3

Step-by-step explanation:

First we will distribute the 4 into the (x+7) and 9 into (x-1).

You should then got

4x+28=9x-9+22

Afterwards we combine like-terms

4x+28=9x+13

Then, we put all the alike values on the same side together.

4x+28=9x+13

-4x           -4x

___________

28=5x+13

-13        -13

____________

15=5x

You then divide both sides by 5 to isolate x

15/5= 3

x=3

Arlo rented a car, and after accounting for the base price of the rental, it is determined he drove 175 miles

Arlo's total cost for car rental is the base price plus the cost per mile driven. To find out how many miles Arlo drove, we use the equation total cost = base price + (cost per mile  imes number of miles). Arlo paid $75.49, which includes the base price of $29.99 and $0.26 per mile.

We first subtract the base price from the total cost to find out how much was spent on the mileage:
$75.49 - $29.99 = $45.50 spent on mileage

Now, we divide the amount spent on mileage by the cost per mile to get the number of miles driven:
$45.50 / $0.26 per mile = 175 miles driven

Arlo drove 175 miles with his rented car.

The student asked how many miles Arlo drove when he rented a car, given that the total cost was $75.49, with an initial fee of $29.99 and an additional charge of $0.26 per mile. To calculate the number of miles driven, we first subtract the initial fee from the total cost:

Total cost - Initial fee = Cost for miles
$75.49 - $29.99 = $45.50

Next, we divide the remaining cost for the miles by the per-mile charge to find the distance driven:

Cost for miles / Charge per mile = Number of miles
$45.50 / $0.26 = 175 miles

Therefore, Arlo drove 175 miles with the car he rented.

Answer:

Step-by-step explanation:

let:  x , x+1 , x+2 ,x+3 , x+4 ....( 5 consecutive integers is 110)

x+x+1 +x+2 +x+3+x+4=110

5x +10 = 110

5x =100

x=100/5

x=20

the fourth number in this sequenceis : x+3  so : 23