The length of a rectangle is twice the width. The area is 162 yd? Find the length and the width.
The length is yd.
(SimplifyJyour answer.)

The volume of the flower box is 7560 cubic inches

The given parameters in the question are:

Length = 5 ft

Upper and lower bases = 18 inches and 10 inches

Height  = 9 inches

The volume of the box can be calculated using the following volume equation

Volume = 0.5 * Height * Length * (Sum of the bases)

Substitute the known values in the above equation So, we have the following equation

Volume = 0.5 * 9 inches * 5 feet * (18 inches + 10 inches)

Convert feet to inches

Volume = 0.5 * 9 inches * 60 inches * (18 inches + 10 inches)

Evaluate

Volume = 7560 cubic inches

Hence, the volume is 7560 cubic inches

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Answer:

B. (2x+4y)(4x2-8xy+16y2)

Step-by-step explanation:

hope this helps!

a) The formula that describes the geometric sequence is of:

\(a_n = 20\left(\frac{7}{9}\right)^{n - 1}\)

b) The maximum height on the 6th bounce is of: 5.69 feet.

The definition of a geometric sequence is given by the equation presented as follows:

\(a_n = a_1(r)^{n - 1}\)

Which is used to calculate the nth term of the sequence.

In which the parameters of the equation are given as follows:

From the description in the text, the first term and the common ratio of the sequence are given as follows:

\(a_1 = 20, r = \frac{7}{9}\)

Then the formula that defines the sequence is given as follows:

\(a_n = 20\left(\frac{7}{9}\right)^{n - 1}\)

The maximum height, in feet, after the 6th bounce is given as follows:

\(a_6 = 20\left(\frac{7}{9}\right)^{6 - 1} = 5.69\)

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Answer:

x^2

Step-by-step explanation:

1^2=1

2^2=4

3^2=9

Answer:

Daniel gained 30 dollars.

Step-by-step explanation:

-10 + 20 = 10

10 - 30 = -20

-20 + 50 = 30

Hope this helps :)

Given that y = x + 3

Find the value of y when x = 1, 2, 3, 4, 5, and 6

For x = 1

y = 1 + 3

y = 4

For x = 2

y = 2 + 3

y = 5

For x = 3

y = 3 + 3

y = 6

For x = 4

y = 4 + 3

y = 7

For x = 5

y = 5 + 3

y = 8

For x = 6

y = 6 + 3

y = 9

Hence, the table can be filled as follows

x y

1 4

2 5

3 6

4 7

5 8

6 9

The next thing is to graph it on a graph

Given the following five-number summary: 2.9, 5.7, 10.0, 13.2, 21.1, so Q₁ = 5.7. This can be solved using the concept of quartile.

A kind of percentile is a quartile. The first quartile (Q₁, or the lowest quartile), which corresponds to the 25th percentile of the data, is below which 25% of the data are found. The second quartile (Q₂, or the median), which represents the 50th percentile, indicates that 50% of the data are below this quartile.

There are 5 data points, and the middle value of the lower half of the data set will represent the first quartile. So the second data value is the first quartile. So, Q₁ = 5.7

There are 5 data points, and the middle value of the upper half of the data set will represent the third quartile. The fourth data value is the third quartile. So,

Q₃ = 13.2

SO IQR will be:

= Q₃ - Q₁

= 13.7 - 5.1

= 7.5

Thus, Q₁ = 5.7

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Answer:

\(\huge\boxed{x=\dfrac{5}{4}}\)

Step-by-step explanation:

\(\left(\dfrac{1}{2}\right)^{x-1}=2^{3x-4}\qquad\text{use}\ a^{-1}=\dfrac{1}{a}\\\\\left(2^{-1}\right)^{x-1}=2^{3x-4}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\2^{(-1)(x-1)}=2^{3x-4}\qquad\text{use the distributive property}:\ a(b+c)=ab+ac\\\\2^{(-1)(x)+(-1)(-1)}=2^{3x-4}\\\\2^{-x+1}=2^{3x-4}\iff-x+1=3x-4\qquad\text{subtract 1 from both sides}\\\\-x+1-1=3x-4-1\\\\-x=3x-5\qquad\text{subtract}\ 3x\ \text{from both sides}\\\\-x-3x=3x-3x-5\\\\-4x=-5\qquad\text{divide both sides by (-4)}\)

\(\dfrac{-4x}{-4}=\dfrac{-5}{-4}\\\\x=\dfrac{5}{4}\)

Answer:

The answer is 390 × pi.

Step-by-step explanation:

Big cone:

V = 1/3 x pi x r^2 x h

= 1/3 x 3.14 x 9^2 x 15

= 1272.3 cubic inches

Small cone:

V = 1/3 x pi x r^2 x h

= 1/3 x 3.14 x 3^2 x 5

= 47.1 cubic inches  

1272.3 - 47.1 = 1225.2 cubic inches

1272/3.14 ≈ 390

The answer is 390 × pi.

Answer:

6

Step-by-step explanation:

he needs 6 points to score over the last nine holes

Kevin needs to score 8.5 strokes per hole for the last nine holes to get back to an even par.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

We can find the total number of strokes Kevin needs to score over 18 holes to reach an even par.

If the par score for 18 holes is 72,

and Kevin scored 4 over par on the first nine holes

= 9 × 4 = 36 extra strokes.

Now, if the par score for the last nine holes is x, then we have:

4 + x + x + x + x + x + x + x + x = 72

4 + 8x = 72

8x = 68

x = 8.5

Therefore, Kevin needs to score 8.5 strokes per hole for the last nine holes to get back to an even par.

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Answer:

5.

Step-by-step explanation:

15.90 / 3.18 =

Step-by-step explanation:

Let's solve the given questions step by step:

1. Determine the equation of f:

From the given information, we know that the turning point of f is (1, 4). The general form of a quadratic function is f(x) = ax^2 + bx + c. We are given that f(x) = a(x + p)^2 + q, so let's substitute the values:

f(x) = a(x + p)^2 + q

Since the turning point is (1, 4), we can substitute x = 1 and f(x) = 4 into the equation:

4 = a(1 + p)^2 + q

This gives us one equation involving a, p, and q.

2. Determine the equation of g:

The equation of g is given as g(x) = 0.3x + p1.

3. Determine the coordinates of the x-intercept of g:

The x-intercept is the point where the graph of g intersects the x-axis. At this point, the y-coordinate is 0.

Setting g(x) = 0, we can solve for x:

0 = 0.3x + p1

-0.3x = p1

x = -p1/0.3

Therefore, the x-intercept of g is (-p1/0.3, 0).

4. For which values of x will f(x) ≥ g(x)?

To determine the values of x where f(x) is greater than or equal to g(x), we need to compare their expressions.

f(x) = a(x + p)^2 + q

g(x) = 0.3x + p1

We need to find the values of x for which f(x) ≥ g(x):

a(x + p)^2 + q ≥ 0.3x + p1

Simplifying the equation will involve expanding the square and rearranging terms, but since the equation involves variables a, p, and q, we cannot determine the exact values without further information or constraints.

To summarize:

We have determined the equation of f in terms of a, p, and q, and the equation of g in terms of p1. We have also found the coordinates of the x-intercept of g. However, without additional information or constraints, we cannot determine the exact values of a, p, q, or p1, or the values of x for which f(x) ≥ g(x).

500 represents the initial amount of medication, since when t=0, a=500.

Answer: That would be distributive

Step-by-step explanation:

The biconditional statement for the given conditional statement would be:

2x = 18 if and only if x = 9.

The given conditional statement "If 2x = 18, then x = 9" can be represented symbolically as p → q, where p represents the statement "2x = 18" and q represents the statement "x = 9".

To form the biconditional statement, we need to determine if the converse of the conditional statement is also true. The converse of the original statement is "If x = 9, then 2x = 18". Let's evaluate the converse statement.

If x = 9, then substituting this value into the equation 2x = 18 gives us 2(9) = 18, which is indeed true. Therefore, the converse of the original statement is true.

Based on this, we can write the biconditional statement:

2x = 18 if and only if x = 9.

The biconditional statement implies that if 2x is equal to 18, then x must be equal to 9, and conversely, if x is equal to 9, then 2x is equal to 18. The biconditional statement asserts the equivalence between the two statements, indicating that they always hold true together.

In summary, the biconditional statement is a concise way of expressing that 2x = 18 if and only if x = 9, capturing the mutual implication between the two statements.

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The height of the pentagonal prism is approximately 2.94 units

The formula for the volume of a pentagonal prism is;

V = (1/2) × base_area × height × (1 + √(5))

where base_area is the area of the base of the prism, height is the height of the prism, and sqrt(5) is the square root of 5.

In this problem, we are given that the base area is 36 units and the volume is 237.6 units. We can use this information to set up an equation and solve for the height;

237.6 = (1/2) × 36 × height × (1 + √(5))

Dividing both sides by (1/2) × 36 × (1 + √(5)), we get;

height = 237.6 / [18 × (1 + √(5))]

Simplifying this expression, we get;

height = 4.8 / (1 + √(5))

Rationalizing the denominator by multiplying both the numerator and denominator by (√(5) - 1), we get;

height = [4.8 × (√(5) - 1)] / [4]

Simplifying further, we get;

height = 1.2 × √(5) - 1)

height = 2.94 units

Therefore, the height is 2.94 units

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There are 4 cups of brown sugar are required for every 12 cups of white sugar.

A recipe calls for 2 cups of brown sugar for every 6 cups of white sugar. We can set up a proportion to find the relationship between the two quantities:

2 cups brown sugar / 6 cups white sugar = x cups brown sugar / 12 cups white sugar

To find the number of cups of brown sugar required for 12 cups of white sugar, we can cross-multiply and then solve for x:

2 cups brown sugar × 12 cups white sugar = 6 cups white sugar × x cups brown sugar

24 cups brown sugar = 6x cups brown sugar

x = 24/6

x = 4

So, 4 cups of brown sugar are required for every 12 cups of white sugar.

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Assuming that:

There are a total of 52 cards in a deck.

Numbers 2 through 10

Face card: jack, queen and king.

P(odd number card or king):

Odd number = 4

King = 4

P(odd number card or king)= 0.15

P(red card or face card):

Red card = 13 X 2 = 26

Face card ( jacks, queens, and kings) = 4 + 4 + 4 = 16

P(red card or face card) = 0.81

Answer:

oaw2 232 acre is 468688$

Step-by-step explanation:

O MEASUREMENT Unit conversions involving acres and hectares After she retired, a corporate executive moved to wine country and bought a 326.7 acre (ac) vineyard. Use the facts to find the area of the vineyard in square feet (ft²). OA² X Conversion facts for area 1 acre (ac) = 43,560 square feet (t²) 1 square mile (mi²) = 640 acres (ac) 1 hectare (ha) 2.5 acres (ac) Note that means "is For this problem, treat as if it were =. approximately equal to".​

Answer:

9.1 is answer or 91/10 or 9 1/10

Answer:

C. 5 inches

Step-by-step explanation:

I’m area you have to multiply L • W

But since we don’t know the width we can divide the length by the area.

40/8 = 5

So the answer would be 5.

Another way to solve this problem is with using guess and check.

I hope it helps! Have a great day!

Anygays~

Answer:

C. 5 inches

Step-by-step explanation:

Use the numbers we have in the word problem, so you´d divide 40 by 8 since you´re trying to find the width. 40 is the area and 8 is the length so divide it tofind the width.

40/8 = 5

ANSWER: 5 inches

I hope it helps! Have a great day!

Length is 33.33 feet and width is 25 feet are dimensions should

be used so that the enclosed area will be a maximum.

The area of Rectangle is length times of width

Given that, a rancher has 200 feet of fencing to enclose two adjacent rectangular corrals of the same dimensions.

Here, the dimensions of the rectangles are the same.

The width of the two rectangles is W=2W+2W=4W

The length of the two rectangles is L=L+L+L=3L

Because the adjacent side has a common length.

3L+4W=200

3L=200-4W

Divide both sides by 3

L=(200-4W)/3

Let us form an equation using the area of rectangle formula:

A=2LW

=2(200-4W)/3.W

A=400-8W²/3

Let us differentiate to get the area to be maximized dA/dW=0

1/3×(400-8W²)=0

1/3(400-16W)=0

400-16W=0

400=16W

Divide both sides by 16

W=25

The width is 25 feet.

Substitute W value in equation to get L value:

L=200-4×25/3

=200-100/3

=100/3

=33.33

The length is 33.33 feet.

Now let us find the maximum area

A=2LW

=2×33.33×25

=1666.66

Hence, length is 33.33 feet and width is 25 feet are dimensions should

be used so that the enclosed area will be a maximum.

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Answer:

x= 17/8

Step-by-step explanation:

6x− 5/2=2x+6

Step 1: Simplify both sides of the equation.

6x+−5/2=2x+6

Step 2: Subtract 2x from both sides.

6x+−5/2−2x=2x+6−2x

4x+−5/2=6

Step 3: Add 5/2 to both sides.

4x+−5/2+5/2=6+5/2

4x=17/2

Step 4: Divide both sides by 4.

4x/4=17/2/4

x=17/8

Answer:

10 pints is equal to 5 quarts

Step-by-step explanation:

Step-by-step explanation:

Average daily balance: Add all balances up and divide by the number of days.

157.63*9+239.98*1+239.98*4+180.38*1+180.38*9+190.57*1+190.57*6 gives us our total of 5756.36, and there were 9+1+4+1+9+1+6=31 days, so 5756.36/31 gives us our average of 185.69, or the fourth option

Daily interest rate: 24.99/365, as a percent, which is the first option

Finance charge: This is the cost of borrowing, and does not seem to be given, so we can take it to be the lowest amount, or the third value

New account balance: Again, this does not seem to be given, but the only option remaining is the second one

Answer:

Average daily balance: Add all balances up and divide by the number of days.

157.63*9+239.98*1+239.98*4+180.38*1+180.38*9+190.57*1+190.57*6 gives us our total of 5756.36, and there were 9+1+4+1+9+1+6=31 days, so 5756.36/31 gives us our average of 185.69, or the fourth option

Daily interest rate: 24.99/365, as a percent, which is the first option

Finance charge: This is the cost of borrowing, and does not seem to be given, so we can take it to be the lowest amount, or the third value

New account balance: Again, this does not seem to be given, but the only option remaining is the second one

m

Step-by-step explanation:

By evaluating the quadratic equation, we will see that the values of the expressions are:

f(-1) + f(4) = 27

f(-1) - f(4) =  -35

Here we need to work with the quadratic function:

f(x) = x^2 + 6x + 1

First, we want to find the value of the expression:

f(-1) + f(4)

To get that, we need to evaluate the quadratic equation:

f(-1) = (-1)^2 + 6*(-1) + 1

f(-1) = 1 - 6 + 1 = -4

f(4) = 4^2 + 6*4 + 1

f(4) = 16 + 24 + 1 = 31

Then the first expression is:

f(-1) + f(4) = -4 + 31 = 27

The second expression is:

f(-1) - f(4)

We already know these values, we can replace these to get:

f(-1) - f(4) = -4 - 31 = -35

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Answer:

V = 3/8 * 1/8 * 5/8 cm^3 = 15 / 512 cm^3

Since all sides are evenly divisible by 1/8 and v = (1 / 8)^3 = 1 / 512 cm^3

N = V / v = (15 / 512) / (1 / 512) = 15 blocks

Example: cut 1/8 by 5/8 into 5 blocks

Cutting 1/8 by 5/8 could be done 3 times for a total  of 15 blocj\ks

2 cos 35 sin 67 can be expressed as the sum of sin(102) and -sin(32).

To express 2 cos 35 sin 67 as a sum, we can use the trigonometric identity for the product of two sine or cosine functions.

Specifically, the identity states that 2 cos A sin B can be written as

sin(A + B) + sin(A - B).

Applying this identity, we have:

2 cos 35 sin 67 = sin(35 + 67) + sin(35 - 67)

Simplifying the expressions inside the sine functions:

sin(102) + sin(-32)

Since the sine function is an odd function,

sin(-x) = -sin(x),

so we can rewrite the equation as:

sin(102) - sin(32)

Therefore, 2 cos 35 sin 67 can be expressed as the sum of sin(102) and -sin(32).

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