ΔABC has three sides with these lengths: AB = 9, BC = 40, and CA = 41. What is the value of cos C?

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.

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:

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]

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

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

Final answer:

To find the simplified form of the quadratic equation at² + bt + c = 0 with constants a = 4.90, b = -14.3, and c = -20.0, we use the quadratic formula to calculate the discriminant and then the two possible solutions for t.

Explanation:

The original expression provided: [tex](m^3/4c^5)-4[/tex] does not match the information given about quadratic equations. Instead, here's how we would solve a quadratic equation using the provided constants:

A quadratic equation is of the form at² + bt + c = 0. Given constants a = 4.90, b = -14.3, and c = -20.0, the solutions to the quadratic equation can be found using the quadratic formula, which is t = (-b ± √(b²-4ac)) / (2a).

To find the solutions for the given quadratic equation, plug in the values for a, b, and c into the quadratic formula:

The simplified form of the quadratic equation will be two solution values of t.

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.

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.

Answer:

A = (1/2)(16 cm)(12 cm) = 96 cm^2

Step-by-step explanation:

Because this is a right triangle, we know that the leg lengths are 12 cm and 16 cm respectively, and that these legs are at right angles to one another.

We can assume that the base of this triangle is 16 cm and that the height is 12 cm.  Then, according to the area-of-a-triangle formula, A = (1/2)(base)(height), the area of this particular triangle is

A = (1/2)(16 cm)(12 cm) = 96 cm^2.

Answer:

A

Step-by-step explanation:

The hypotenuse is the longest side of a triangle, meaning the hypotenuse is 20 cm. The equation for the area of a triangle is base multiplied by height multiplied by one half. (1/2bh) 12 × 16 = 192. 192 × 1/2 = 96. The area of this triangle is 96 cm^2.

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:

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

To know more about Fractions here

https://brainly.com/question/5565347

#SPJ2

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 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.

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:

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)

Answer:

(4, 11)

Step-by-step explanation:

Given the 2 equations

y = 5x - 9 → (1)

y = x² - 3x + 7 → (2)

Substitute y = x² - 3x + 7 = 5x - 9 ( subtract 5x - 9 from both sides )

x² - 8x + 16 = 0 ← quadratic equation in standard form

(x - 4)² = 0 ← in factored form as a perfect square, so

x - 4 = 0 ⇒ x = 4

Substitute x = 4 into (1) for corresponding value of y

y = 20 - 9 = 11

Solution (x, y) → (4, 11)

Answer:

Slope

Step-by-step explanation:

Slope is the gradient or steepness of a line.

The term slope defines steepness of a line

Steepness of a line is the the inclination of the line.

Steepness of the line can be defined by the term slope.

Slope is the inclination of the line towards x-axis.

Find more about "Slope " here: https://brainly.com/question/3493733

#SPJ2

Answer:

A. a) 24

A. b) 4

B. a) 40320

B. b) 576

Step-by-step explanation:

General formula for Permutations:

[tex]P(n,r) = \frac{n!}{(n - r)!}[/tex]

A. Concert seats:  2 couple --- total of 4 persons.

a) without restrictions

Since there are no restrictions, but that the order is important (John, Mary, Paul, Michelle isn't the  same as Michelle, Mary, Paul, John), it's a permutation calculation.

Then we calculate the permutations of 4, out of 4, so...

[tex]P(4,4) = \frac{4!}{(4 - 4)!} = 4! = 24[/tex]

24 different ways for them to sit.

b) couples together

Now, we can see the problem as having 2 levels of permutations, first the couples, then inside the couples.

There are 2 ways for the first level or order... couples AB or BA, so 2 possibilities.

Inside each couple, man then woman (MW) or woman then man (WM), so 2 possibilities there too on 2nd level.

Overall 2 * 2 = 4 ways to sit by couple.

B) Single file

a) without restrictions

Again, order is important, so another permutation, not a combination.  And since we have no restriction, it can be any sequence.

We then have to calculate the number of permutations of 8 out of 8...

[tex]P(8,8) = \frac{8!}{(8 - 8)!} = 8! = 40320[/tex]

There are 40,320 ways these 8 kids can pass the door.

b) girls first.

So, the four girls have to enter first.... and these four girls can be in any order.. how many permutations? P(4,4)... so 24 as calculated above.

For the four boys, how many permutations?  Yes, again P(4,4)... so 24 again.

Overall, we need to multiply the two... 24 x 24 = 576 ways if the girls enter first, followed by the boys.

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.

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.

https://brainly.com/question/14412941

#SPJ2

Answer:

(c)  9x^2.

Step-by-step explanation:

(a) and (b) are correct.

(c)  (3x)^2 = 3^2 * x^2

= 9x^2.

Answer:

$1803

Step-by-step explanation:

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

The answer will be B

Arranging the given data in ascending order:

1, 2, 2, 3, 3, 4, 7, 7, 7, 9

Meadian is the middle-most observation.

i.e. The Median here is average of 3 and 4.

= (3+4)/2

= 7/2

=3.5

Hope it helps...

Regards;

Leukonov/Olegion

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

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?

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:

(2,3)

Step-by-step explanation:

The given equations  are:

[tex]y=-4x+11[/tex]

and

[tex]y=\frac{1}{2}x+2[/tex]

Equate both equations:

[tex]\frac{1}{2}x+2=-4x+11[/tex]

Multiply through by 2:

[tex]x+4=-8x+22[/tex]

[tex]x+8x=22-4[/tex]

[tex]9x=18[/tex]

x=2

Put x=2 into the first equation:

[tex]y=-4(2)+11[/tex]

[tex]y=-8+11[/tex]

y=3

The solution is (2,3)

Answer:

C. (2, 3)

Step-by-step explanation:

A system of linear equations is a set of (linear) equations that have more than one unknown. The unknowns appear in several of the equations, but not necessarily in all of them. What these equations do is relate the unknowns to each other.

Solve a system of equations is to find the value of each unknown so that all the equations of the system are met.

Ordering both equations

First equation

[tex]y=-4y+11[/tex]

[tex]4x+y=11[/tex]

Second equation

[tex]y=\frac{1}{2} x+2[/tex]

[tex]-\frac{1}{2}x+y=2[/tex]

Ordering in a system of equations

[tex]\left \{ {{4x+y=11} \atop {-\frac{1}{2}x+y=2}} \right.[/tex]

Using the reduction method which consists of operating between the equations, such as adding or subtracting both equations, so that one of the unknowns disappears. Thus, we obtain an equation with a single unknown.

We're going to subtract the second equation from the first to eliminate the unknown y.

           4x + y = 11

   -  ((-1/2)x + y = 2)

       (9/2)x       =  9 ------>    x= [(2)(9)]/9 ----->  x = 2

Substituing the value x = 2 in [tex]y=\frac{1}{2} x+2[/tex]

y = (1/2)x + 2 ---------> y = (1/2)(2) + 2 -------> y = (2/2) + 2

y = 1 + 2 --------> y = 3

The solution of the system of equations is (2, 3).

Check the picture below.

using the 30-60-90 rule.

Answer:

The correct answer is y = cos (x - π)

Step-by-step explanation:

2. The answer after that is y = sin x + π

3. Zero, minimum, zero, maximum, zero

4. Graph C

5. The answer is 4

Hope this saved some time for some people

The equation of the translation y = cos x, shifted π units to the right is y = cos (x − π).

A translation is a slide from one location to another, without any change in size or orientation.

The given equation is;

y = cosx

We want to translate the graph in the x-direction, so our final equation should look like:

y = cos(x-b)

Where b is the number of units translated.

We are translating the graph π units to the right, so b should be equal to π. Therefore, our final equation should look like:

[tex]\rm y = cos(x-b)\\\\y = cos(x-\pi )[/tex]

Hence, the equation of the translation y = cos x, shifted π units to the right is y = cos (x − π).

Learn more about translation here;

https://brainly.com/question/22280094

#SPJ2