A fish tank is filled with water.The tank holds 150 gallons.Each cubic foot of water contains about 7.5 gallons.The rank is 5 feet long and 3 feet high.what is the width of the tank

Answer:

(c)  9x^2.

Step-by-step explanation:

(a) and (b) are correct.

(c)  (3x)^2 = 3^2 * x^2

= 9x^2.

Answer:

Step-by-step explanation:

I assume you want to rotate each point about the origin.

To rotate a point (x, y) 90° clockwise about the origin:

(x, y) → (y, -x)

For point A:

(-5, 0) → (0, 5)

For point B:

(-5, 3) → (3, 5)

For point C:

(0, 4) → (4, 0)

Rahm spent 2 1/2 hours writing an essay and 4 times longer on his science project, totaling 12.5 hours for both.

Rahm spent 2 1/2 hours writing an essay. Since it took him 4 times as long to finish his science project, we calculate the time spent on the science project by multiplying 2.5 (which is the decimal equivalent of 2 1/2 hours) by 4. This gives us 10 hours for the science project. To determine how long it took him to complete both the essay and the science project, we add the time spent on both activities:

The total time Rahm spent on both the essay and the science project is 12.5 hours.

Answer:

x = 40

Step-by-step explanation:

According to the Supplementary Angles Theorem, set 4x - 20 and x equal to 180. Once done, combine like-terms to get 5x - 20 = 180. So, straight off the bat, we know that 5x has to equal 200 [bringing 20 over to the right side of the equivalence symbol], therefore 40 is equal to x.

I am joyous to assist you anytime.

Check the picture below.

using the 30-60-90 rule.

Answer:

14/5

Step-by-step explanation:

So first i manipulated a/b= 2/5. i multiplied both sides by 5 making it 5a/b=2. Then i multiplied both sides by b making it 5a=2b. Then i substituted 2b into 5a+3b=35. Making it 2b+3b=35. then i simplified it making it 5b=35. Then i solved for b making it b=7. Then i substituted b into 5a+3b=35. So that it looked like this 5a+3*7=35. then it became 5a+21=35. Then you subtract 21 making it 5a=14. You then divide by 5 making it a=14/5

Answer:

[tex]a = \frac{14}{5} [/tex]

Step-by-step explanation:

[tex]5a + 3b = 35 \\ 3b = 35 - 5a \\ b = \frac{35}{3} - \frac{5}{3} a \\ put \: b\: = \frac{35}{3} - \frac{5}{3} a \: into \: \frac{a}{b} = \frac{2}{5} \\ \frac{a}{ \frac{35}{3} - \frac{5}{3} a} = \frac{2}{5} \\ \frac{a}{ \frac{35 - 5a}{3} } = \frac{2}{5} \\ \frac{3a}{35 - 5a} = \frac{2}{5} \\ 5(3a) = 2(35 - 5a) \\ 15a = 70 - 10a \\ 15a + 10a = 70 \\ 25a = 70 \\ a = \frac{70}{25} \\ a = \frac{14}{5} [/tex]

Answer:

10 minutes

Step-by-step explanation:

The question is on volume/capacity

Volume of the tank is given by = l×w× d where l is length, w is width and d is the depth

l=16 in  w= 24 in and d=15in

v=16×24×15 =5760 in³

Time to fill tank

Given that 600 in³= 1 min

                  5760 in³=?

=(5760×1) /600 = 9.6 min

Final answer:

To fill the tank to a depth of 15 inches with a flow rate of 600 cubic inches per minute, it will take approximately 10 minutes, rounded to the nearest minute.

Explanation:

The student asks how long it will take to fill a fish tank to a depth of 15 inches using a hose with a flow rate of 600 cubic inches per minute. The dimensions of the tank's base are 16 inches by 24 inches, and the desired fill height is 15 inches. First, we calculate the volume of water needed to fill the tank to the desired depth by multiplying the base and the height (Volume = length × width × depth).

Volume needed = 16 inches × 24 inches × 15 inches = 5760 cubic inches.

Now, we divide the total volume by the flow rate to find out how long it will take to fill the tank.

Time = Volume needed / Flow rate = 5760 cubic inches / 600 cubic inches per minute = 9.6 minutes.

To provide an answer to the nearest minute, we round 9.6 to 10 minutes.

For this case we have that by definition, the distance between two points is given by:

[tex]d = \sqrt {(x_ {2} -x_ {1}) ^ 2+ (y_ {2} -y_ {1}) ^ 2}[/tex]

We have to:

[tex](x_ {1}, y_ {1}) = (0,0)\\(x_ {2}, y_ {2}) = (7,3)[/tex]

Substituting:

[tex]d = \sqrt {(7-0) ^ 2 + (3-0) ^ 2}\\d = \sqrt {(7) ^ 2 + (3) ^ 2}\\d = \sqrt {49 + 9}[/tex]

[tex]d = \sqrt {58}\\d = 7.62[/tex]

ANswer:

[tex]d = 7.62[/tex]

Answer:

The Answer Is 10.

Step-by-step explanation:

| x2-x1 | + | y2-y1 | = taxidistance.

(0, x1), (0, y1), (7, x2), (3, y2)

Substitute.

| 7-0| + | 3-0 | = 10

7.

(2b^2+7b^2+b)+(2b^2-4b-12)

(9b^2+b)+(2b^2-4b-12)

9b^2+b+2b^2-4b-12

11b^2+b-4b-12

11b^2-3b-12

8.

(7g^3+4g-1)+(2g^2-6g+2)

7g^3+4g-1+2g^2-6g+2

7g^3-2g-1+2g^2+2

7g^3-2g+1+2g^2

7g^3+2g^2-2g+1

Hope this helps!

Problem 7:

(2b² + 7b² + b) + (2b² - 4b - 12)

= 11b²-3b-12

Problem 8:

(7g³ + 4g - 1) + (2g² - 6g + 2)

= 7g³ + 2g² - 2g + 1

Answer:

Is the 5 separate or to gather like 45

Justin and his dog walked at approximately 0.093 miles per hour.

To find the number of miles per hour, Justin and his dog walked, we need to divide the total distance walked (5 miles) by the total time taken (54 hours). So, 5 miles / 54 hours = 0.093 miles per hour.To find out how many miles per hour Justin and his dog walked, we need to divide the total distance walked by the total time spent. In this case, Justin walked 5 miles in 54 hours. Therefore, the speed is calculated as follows: 5 miles ÷ (54) hours = 4 miles per hour. This means Justin and his dog walked at a speed of 4 miles per hour.

Therefore, Justin and his dog walked at approximately 0.093 miles per hour.

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Answer:

3rd Option is correct.

Step-by-step explanation:

Given Equation:

x² - 16x + 12 = 0

First We need to find solution of the given equation.

x² - 16x + 12 = 0

here, a = 1   , b = -16  &  c = 12

[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

[tex]x=\frac{-(-16)\pm\sqrt{(-16)^2-4(12)}}{2}[/tex]

[tex]x=\frac{16\pm\sqrt{256-48}}{2}[/tex]

[tex]x=\frac{16\pm\sqrt{208}}{2}[/tex]

[tex]x=\frac{16\pm4\sqrt{13}}{2}[/tex]

[tex]x=8+2\sqrt{13}\:\:andx=8-2\sqrt{13}[/tex]

Now,

Option 1).

( x - 8 )² = 144

x - 8 = ±√144

x - 8 = ±12

x = 8 + 12 = 20   and x = 8 - 12 = -4

Thus, This is not correct Option.

Option 2).

( x - 4 )² = 4

x - 4 = ±√4

x - 4 = ±2

x = 4 + 2 = 6   and x = 4 - 2 = 2

Thus, This is not correct Option.

Option 3).

( x - 8 )² = 52

x - 8 = ±√52

x - 8 = ±2√13

x  = 8 + 2√13   and x = 8 - 2√13

Thus, This is correct Option.

Option 4).

( x - 4 )² = 16

x - 4 = ±√116

x - 4 = ±4

x = 4 + 4 = 8  and x = 4 - 4 = 0

Thus, This is not correct Option.

Therefore, 3rd Option is correct.

Answer:

The solutions of the equation is 0 , π , 2π

Step-by-step explanation:

* Lets revise some identities in the trigonometry

- tan²x + 1 = sec²x

- tan²x = sec²x - 1

* Now lets solve the equation

∵ tan²x sec²x + 2sec²x - tan²x = 2

* Lets replace tan²x by sec²x - 1

∴ (sec²x - 1) sec²x + 2sec²x - (sec²x - 1) = 2 ⇒ open the brackets

∴ sec^4 x - sec²x + 2sec²x - sec²x + 1 = 2 ⇒ add the like terms

∴ sec^4 x -2sec²x + 2sec²x + 1 = 2 ⇒ cancel -2sec²x with +2sec²x

∴ sec^4 x + 1 = 2 ⇒ subtract 1 from both sides

∴ sec^4 x = 1 ⇒ take root four to both sides

∴ sec x = ± 1 ⇒ x is on the axes

∵ sec x = 1/cos x

∵ sec x = 1 , then cos x = 1

∵ sec x = -1 , then cos x = -1

∵ 0 ≤ x ≤ 2π

∵ x = cos^-1 (1)

∴ x = 0 , 2π ⇒ x is on the positive part of x-axis

∵ x = cos^-1 (-1)

∴ x = π ⇒ x is on the negative part of x-axis

* The solutions of the equation is 0 , π , 2π

Answer:

Scale factor: 4/7

perimeter ratio: 4:7

area: I don't know the height of the two

Step-by-step explanation:

In all cases, if [tex]f[/tex] has real coefficients, then any complex roots occur in conjugate pairs, so if [tex]a+bi[/tex] is a root, then so is [tex]a-bi[/tex]. Also, by the fundamental theorem of algebra, if [tex]r_1,\ldots,r_n[/tex] are roots to [tex]f[/tex], then for some constant [tex]a\in\mathbb R[/tex],

[tex]f(x)=a(x-r_1)\cdots(x-r_n)[/tex]

1. If [tex]n=3[/tex] and [tex]f(3)=f(2i)=0[/tex], then

[tex]f(x)=a(x-3)(x-2i)(x+2i)=ax^3-3ax^2+4ax-12a[/tex]

Given that [tex]f(-1)=50[/tex], we have

[tex]f(-1)=a(-1-3)(-1-2i)(-1+2i)=-20a=50\implies a=-\dfrac52[/tex]

[tex]\implies\boxed{f(x)=-\dfrac52x^3+\dfrac{15}2x^2-10x+30}[/tex]

2.

[tex]f(x)=a(x-4)(x-(-5+2i))(x-(-5-2i))=a x^3 + 6 a x^2 - 11 a x - 116 a[/tex]

With [tex]f(2)=-636[/tex], we have

[tex]f(2)=a(2-4)(2+5-2i)(2+5+2i)=-106a=-636\implies a=6[/tex]

[tex]\implies\boxed{f(x)=6x^3+36x^2-66x-696}[/tex]

The rest are done in the same exact way.

It takes about 20 years

It will take approximately 13 years for the account value to reach $15,000.

To find the time it takes for the account value to reach $15,000, we used the formula for compound interest and rearranged it to solve for [tex]\(t\).[/tex] Then, we substituted the given values into the formula and calculated the time to be approximately 12.82 years. Rounding to the nearest year gives us 13 years.

To calculate the time it takes for the account value to reach $15,000 with an annual interest rate of 8.5%, we can use the formula for compound interest:

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

Where:

- [tex]\(A\)[/tex] is the future value of the investment/loan, including interest.

- [tex]\(P\)[/tex] is the principal investment amount (the initial deposit or loan amount).

- [tex]\(r\)[/tex] is the annual interest rate (in decimal).

- [tex]\(n\)[/tex] is the number of times that interest is compounded per year.

- [tex]\(t\)[/tex] is the time the money is invested for, in years.

In this case, [tex]\(P = 5600\)[/tex], [tex]\(A = 15000\)[/tex], [tex]\(r = 0.085\)[/tex] (8.5% expressed as a decimal), and [tex]\(n = 1\)[/tex] (compounded annually).

We need to solve for [tex]\(t\)[/tex], so rearranging the formula:

[tex]\[t = \frac{\log(A/P)}{n \cdot \log(1 + r/n)}\][/tex]

Substituting the given values:

[tex]\[t = \frac{\log(15000/5600)}{1 \cdot \log(1 + 0.085/1)}\][/tex]

[tex]\[t[/tex] ≈ [tex]\frac{\log(2.6786)}{\log(1.085)}[/tex]

[tex]\[t[/tex] ≈ [tex]\frac{0.4285}{0.0334}[/tex]

[tex]\[t[/tex]  ≈ [tex]12.82[/tex]

To the nearest year, it will take approximately 13 years for the account value to reach $15,000.

To find the time it takes for the account value to reach $15,000, we used the formula for compound interest and rearranged it to solve for \(t\). Then, we substituted the given values into the formula and calculated the time to be approximately 12.82 years. Rounding to the nearest year gives us 13 years.

Complete question

5600 dollars is placed in an account with an annual interest rate of 8.5%. To the nearest year, how long will it take for the account value to reach 15000 dollars?

Answer:

60

Step-by-step explanation:

Use the formula for the surface area and plug in the given numbers. See work for more.

Answer:

The length of NP is 2 units.

Step-by-step explanation:

Given the radius of 5 units and the length of MP is 4 units in the circle

we have to find the length of NP    

OL=OM=5 units  ( ∵ Radii of same circle)

In ΔOMP, by Pythagoras theorem

[tex]OM^2=MP^2+OP^2[/tex]

[tex]5^2=4^2+OP^2[/tex]

[tex]OP^2=25-16=9[/tex]

[tex]OP=3 units[/tex]

As we see

[tex]ON=OP+NP[/tex]

[tex]5=3+NP[/tex]

[tex]NP=5-3=2\thinspace units[/tex]

Hence, the length of NP is 2 units.

Option D is correct.

The correct equation to find the original price of the shoes that Iola bought is [tex]\frac{x}{2}[/tex] + 6 + 32 = 75, where x represents the regular price of the shoes.

The student is looking for an equation to find the regular price of the shoes that Iola bought. Since Iola has $32 left after buying the shoes and socks, and the socks cost $6, we can state that she spent $75 - $32 - $6 on the shoes on sale. If we represent the regular price of the shoes as x, then the sale price is [tex]\frac{x}{2}[/tex]. The equation that represents this scenario is:

[tex]\frac{x}{2}[/tex] + 6 + 32 = 75

Final answer:

Using the Pythagorean theorem, we solved for the missing sides of a right triangle in three scenarios, finding b approximately as 5.20, c approximately as 7.21, and a approximately as 2.24.

Explanation:

To solve for the missing sides of a right triangle, we use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). The theorem is mathematically represented as a² + b² = c². Let's use this to solve the given problems.

For a = 3 and c = 6, to find b, we use the equation 3² + b² = 6². After calculation, b = √(36 - 9), which simplifies to b = √27 or approximately 5.20.

If a = 4 and b = 6, to find c, the equation is 4² + 6² = c². Solving for c gives us c = √(16 + 36), which is c = √52 or approximately 7.21.

For b = 2 and c = 3, to find a, we apply the formula a² + 2² = 3². This leads to a² = 9 - 4, so a = √5 or about 2.24.

Answer:

$1803

Step-by-step explanation:

850 + 45(4) + 300(2) + 17(4) + 105 = 1803

The two lines with the equations are the same length.

Set the two equations to equal and solve:

3x +3 = 6x - 57

Add 57 to each side:

3x +60 = 6x

Subtract 3x from each side:

60 = 3x

Divide both sides by 3:

x = 20

Answer:

x= 20

Step-by-step explanation:

Jane had 10 Beanie Babies in the beginning.

The number of Beanie Babies Jane had in the beginning.

- She gave 8 to her friend, leaving her with [tex]\( x - 8 \)[/tex] Beanie Babies.

- Her grandma bought her 5 more, so she then had [tex]\( x + 5 \)[/tex] Beanie Babies.

- Combining the Beanie Babies she had at the beginning, the ones she gave away, and the ones her grandma bought her, the total is 27.

- Solving the equation [tex]\( x - 8 + (x + 5) = 27 \)[/tex], we find [tex]\( x = 10 \)[/tex], the number of Beanie Babies Jane had in the beginning.

Jane had 20 Beanie Babies in the beginning.

To calculate:

1. Let's denote the number of Beanie Babies Jane had in the beginning as [tex]\( x \).[/tex]

2. She gave 8 of them to her friend, leaving her with [tex]\( x - 8 \)[/tex] Beanie Babies.

3. Her grandma bought her 5 more Beanie Babies than she had in the beginning, so she now has [tex]\( x + 5 \)[/tex] Beanie Babies.

4. Given that she now has 27 Beanie Babies, we can set up the equation:

[tex]\[ x - 8 + (x + 5) = 27 \][/tex]

Now, let's solve for [tex]\( x \):[/tex]

[tex]\[ 2x - 3 = 27 \][/tex]

[tex]\[ 2x = 30 \][/tex]

[tex]\[ x = 15 \][/tex]

However, this is the number of Beanie Babies Jane had after her grandma bought her 5 more. To find out how many she had in the beginning, we need to subtract 5 from [tex]\( x \):[/tex]

[tex]\[ x = 15 - 5 = 10 \][/tex]

So, Jane had 10 Beanie Babies in the beginning.

- Let [tex]\( x \)[/tex] be the number of Beanie Babies Jane had in the beginning.

- She gave 8 to her friend, leaving her with [tex]\( x - 8 \)[/tex] Beanie Babies.

- Her grandma bought her 5 more, so she then had [tex]\( x + 5 \)[/tex] Beanie Babies.

- Combining the Beanie Babies she had at the beginning, the ones she gave away, and the ones her grandma bought her, the total is 27.

- Solving the equation [tex]\( x - 8 + (x + 5) = 27 \)[/tex], we find [tex]\( x = 10 \)[/tex], the number of Beanie Babies Jane had in the beginning.

Complete question

Jane had R Beanie Babies. She gave 8 of them to her friend. Later her grandma bought her 5 more Beanie Babies than she had in the beginning. How many Beanie Babies did Jane have in the beginning, if now she has 27 of them?

Answer:

see explanation

Step-by-step explanation:

A recursive formula allows us to calculate any term in the sequence from the previous term.

These are the terms of a geometric sequence with r being the common ratio between consecutive terms.

r = 4 ÷ - 2 = - 8 ÷ 4 = 16 ÷ - 8 = - 2

Multiplying a particular term by - 2 gives the next term in the sequence.

Hence recursive formula is

[tex]a_{n+1}[/tex] = - 2 [tex]a_{n}[/tex] with a₁ = - 2

-2,4,-8,16,...

a₁ = -2

a₂ = -2a₁

a₃ = -2a₂

..................

=> aₙ₊₁ = -2•aₙ, with a₁ = -2

Answer:

First subtract the number of students who take both subjects from the number of students who take Consumer Education

22-4=18

Then,

subtract the number of students who take both subjects from the number of students who take French

20-4=16

Now,

Add 18,16 and 4 and subtract the sum from the total number of students in the class

=80-(18+16+4)

=80-38

=42

Step-by-step explanation:

Answer: P= 11/40 + 1/4 + 1/20

Answer:

there are 2.25 one-thirds in a three-fourth.

Hope this helps you out!

In the given Fractions there are 2 and 1/4 (or 2.25) one-thirds in three-fourths.

To find out how many one-thirds are in three-fourths, we need to represent both fractions using a common denominator. In this case, we can see that the smallest common denominator is 12.

So, we can convert both fractions to twelfths by multiplying the numerator and denominator of one-third by 4, and the numerator and denominator of three-fourths by 3. This gives us:

1/3 = 4/12

3/4 = 9/12

Now, we can simply divide the numerator of three-fourths by the numerator of one-third to get our answer:

(9/12) ÷ (4/12) = (9/12) × (12/4) = 27/4 = 2.25

Therefore, there are 2 and 1/4 (or 2.25) one-thirds in three-fourths.

In conclusion, determining how many one-thirds are there in three-fourths requires us to represent both fractions using a common denominator and then dividing the numerator of three-fourths by the numerator of one-third. The answer is 2.25

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Answer:

-1/3

Step-by-step explanation:

You can do rise over run, and, in this case is going to be 1\3.

The slope of the line is 1.

To do this, we'll use the coordinates of two points on the line: Point 1 at (0,6) and Point 2 at (-6,0).

The slope of a line is given by the formula:

[tex]\[ m = \frac{{y_2 - y_1}}{{x_2 - x_1}} \][/tex]

1. Identify the coordinates:

  - Point 1: [tex]\( (x_1, y_1) = (0, 6) \)[/tex]

  - Point 2: [tex]\( (x_2, y_2) = (-6, 0) \)[/tex]

2.Calculate the change in x and change in y:

  - Change in x: [tex]\( x_2 - x_1 = -6 - 0 = -6 \)[/tex]

  - Change in y:[tex]\( y_2 - y_1 = 0 - 6 = -6 \)[/tex]

3. Apply the slope formula:

[tex]\[ m = \frac{{y_2 - y_1}}{{x_2 - x_1}} = \frac{{-6}}{{-6}} = 1 \][/tex]

Therefore, the slope of the line is 1.

Answer:

760 attendees

Step-by-step explanation:

40% of the attendees is 304. That means you can add 304 to 304 (304 x 2) to get 608. To get the last 20%, divide 304 by 2, because 40(%) divided by 2 is 20(%). The answer to that is 152. Now, add it all up. 608 + 152 = 760.

In conclusion, there were 760 attendees at the carnival.

Answer:

The volume of shape Q is [tex]25,600\ cm^{3}[/tex]

Step-by-step explanation:

step 1

Find the scale factor

we know that

If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared

Let

z----> the scale factor

x----> surface area of shape Q

y----> surface area of shape P

[tex]z^{2}=\frac{x}{y}[/tex]

we have

[tex]x=2,880\ cm^{2}[/tex]

[tex]y=720\ cm^{2}[/tex]

substitute

[tex]z^{2}=\frac{2,880}{720}[/tex]

[tex]z=2[/tex]

step 2

Find the volume of shape Q

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

Let

z----> the scale factor

x----> volume of shape Q

y----> volume of shape P

[tex]z^{3}=\frac{x}{y}[/tex]

we have

[tex]z=2[/tex]

[tex]y=3,200\ cm^{3}[/tex]

substitute

[tex]2^{3}=\frac{x}{3,200}[/tex]

[tex]x=(8)(3,200)=25,600\ cm^{3}[/tex]

Answer:

B. 144^12

Step-by-step explanation:

[tex]{144}^{14} \div {144}^{2} \\ = {144}^{14 - 2} \\ = {144}^{12} [/tex]

The simplified exponent form of the given expression 144^14/144^2 would be 144^12.

When the expression of function is such that it involves the input to be present as an exponent (power) of some constant, then such function is called exponential function. There usual form is specified below. They are written in several such equivalent forms.

The given expression can be solved by exponentially

[tex]\dfrac{144^{14}}{144^2}\\\\144^{14} \times144^{-2}}\\\\144^{14-2} \\\\144^{12}[/tex]

Therefore the simplified exponent form of the given expression would be 144^12.

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Answer: they are all being subtracted by 3

Step-by-step explanation:

35-3=32

32-3=29

29-3=26

The common difference in the arithmetic sequence 35, 32, 29, 26... is 3.

To find the common difference in an arithmetic sequence, you subtract one term from the following term. In this case, the sequence is 35, 32, 29, 26... To find the common difference, subtract 32 from 35, which equals 3. Therefore, the common difference in this sequence is 3.