a box's volume set is 112 cubic inches. it has an open top. what is the length, width, and height?

Answer:  see proof below

Step-by-step explanation:

Use the following when solving the proof...

Double Angle Identity: cos2A = 1 - 2sin²B

Pythagorean Identity: cos²A + sin²A = 1

note that A can be replaced with B

Proof from LHS → RHS

Given:                            cos²A + sin²A · cos2B

Double Angle Identity: cos²A + sin²A(1 - 2sin²B)

Distribute:                      cos²A + sin²A - 2sin²A·sin²B

Pythagorean Identity:                        1 - 2sin²A·sin²B

Pythagorean Identity:   cos²B + sin²B - 2sin²A·sin²B

Factor:                           cos²A + sin²B(1 - 2sin²A)

Double Angle Identity: cos²B + sin²B · cos2A

cos²B + sin²B · cos2A = cos²B + sin²B · cos2A  [tex]\checkmark[/tex]

Answer:

18 square centimeters

Step-by-step explanation:

Notice that if e is the midpoint of the side CB, and angle [tex]\angle x = 45^o[/tex], then this rectangle is in fact two squares of side 3 cm put together. therefore, side CD has a length of 6 cm, and as a result, the area of the figure is given by the product base times height = 6 x 3 = 18 [tex]cm^2[/tex]

Answer:

(B)  18

Step-by-step explanation:

The angle x is 45 degrees.  Since it is bisecting a 90 degree angle, the angle on the other side is 45 degrees.

90 - 45 = 45

Since AB is 3, DC is 3.  Since the right triangle DC is 45-90-45, the other side, CE, will also be 3.  Since CE is half of the side of the rectangle, multiply it by 2 to get 6.  The sides of the rectangle are 3 and 6.  Use the formula for area of a rectangle to solve.

A = lw

A = (6)(3)

A = 18

The answer is B.

Answer:

I think its average

Step-by-step explanation:

not sure:)

Answer: it is average

Step-by-step explanation: just done It

the first one is, yes by AA

the second is no you cannot

Answer:

B. 17

Step-by-step explanation:

By the property of intersecting secants outside of a circle, we have:

7 (7 + x) = 8 (13 + 8)

49 +7x = 8*21

7x = 168 - 49

7x = 119

x = 119/7

x = 17

Answer:

5.95

Step-by-step explanation:

that is because 96 is rounded too 100

so its 5.9500 = 5.95

Answer:

5.950

Step-by-step explanation:

5.9496

ones . tenths  hundredths  thousandths  ten thousandths

5       .  9              4                     9                   6

We are rounding to the thousandths place

so we look at the ten thousandths place

6 > 5 so we round up the the thousandths place

9 will go up so that forces the hundreds place up

4 becomes 5 in the hundreds place

5.950

Answer:

22.08 ft^2

Step-by-step explanation:

First find the area of the full circle

A = pi r^2

The diameter is 15 so the radius is 1/2 (15) = 7.5

A = (3.14) (7.5)^2

   =176.625

45 degrees is  a fraction of a circle which is 360 degrees

45/360 = 1/8

Multiply the area of the circle by this fraction

1/8 (176.625) =22.078125

Rounding to the nearest hundredth

22.08

Answer:

22.08 ft2

Step-by-step explanation:

Answer:

3y² + y - 10

Step-by-step explanation:

Assuming we're finding the area:

[tex](3y-5)(y+2)\\3y^2+6y-5y-10\\3y^2+y-10[/tex]

Answer:

3y² + y - 10

Step-by-step explanation:

(3y -5) (y + 2)

3y² + 6y - 5y  - 10

3y² + y - 10

Answer:

x + 2(2x-4) = 10

Step-by-step explanation:

Here in this question, we want to select which is the correct answer if we substitute for the value of y in the second equation, using the first.

In the first, we have;

y = 2x -4

Now, let’s input this value of y into the second equation.

By direct substitution, what we have is the following;

x + 2y = 10

—-> x + 2(2x -4) = 10

Answer:

.71

Step-by-step explanation:

We only need to look at the brown eyes row

2+2+10 =14

Brown hair is 10

P(brown hair) = brown hair / total

                        =10/14 =5/7 = .714285714

Answer:

(4x + 5)²

4x² + 20x + 25

Step-by-step explanation:

Step 1: Factor 16x² + 40x + 25

(4x + __)(4x + __)

What multiplies to 25 and adds up to 40 with 4 multiplied as coefficient?

(4x + 5)(4x + 5) or (4x + 5)²

Step 2: Factor perfect square trinomial

36x² - 4x + 16 --> 4(9x² - x + 4) No

16x² - 8x + 36 --> 4(4x² - 2x + 9) No

25x² +9x + 4 --> 25x² + 9x + 4 No

4x² + 20x + 25 --> (2x + 5)(2x + 5) or (2x + 5)² Yes

Answer:

(4x + 5)(4x + 5).

4x^2 + 20x + 25.

Step-by-step explanation:

16x^2 + 40x + 25

= (4x + 5)(4x + 5)

= (4x + 5)^2.

36x^2 − 4x + 16: To be a perfect square trinomial, the factors would have to be (6x + 4) or (6x - 4). Since the value of b is only -4, this is NOT a perfect square trinomial.

16x^2 − 8x + 36: To be a perfect square, factors would have to be (4x + 6) or (4x - 6). Since the value of b is only -4, this is NOT a perfect square.

25x^2 + 9x + 4: To be a perfect square, factors have to be (5x + 2) or (5x - 2). Since b is positive, factors would be (5x + 2)(5x + 2) = 25x^2 + 20x + 4. 20x is not equal to 9x, so this is NOT a perfect square.

4x^2 + 20x + 25: Perfect square would have to have factors (2x + 5) or (2x - 5). b is positive, so factors are (2x + 5)(2x + 5) = 4x^2 + 10x + 10x + 25 = 4x^2 + 20x + 25. This IS a perfect square!

Hope this helps!

Answer:

1.34%

Step-by-step explanation:

First of all subtract the 2 values

9.84−9.71=0.13

use this value and find the percentage from the original price which was 9.71

0.13

-------  ⋅100

9.71

percentage increase is

1.34%

Answer:

0.15(5,-1)

Step-by-step explanation:

[tex]\frac{v_{1} * v_{2} }{|v_{2}|^{2} }*v_{2}[/tex]  ⇒ [tex]\frac{(2)(5)+(6)(-1)}{\sqrt{5^2+(-1)^2} }(5,-1)[/tex] ⇒  [tex]\frac{4}{26} (5,-1)[/tex]  ⇒  [tex]0.15(5,-1)[/tex]

The best approximation of the projection  IS ( 5,-1).

Vector A ,

                 (2,6) in terms of vectors is represented by = 2 i +6 j

Vector B,

                 (5,-1) in terms of vectors is represented by =5 i - 1 j

Projection of Vector A on Vector B

       [tex]\frac{(A . B)(B)}{IBI^{2} } \\[/tex] =  [tex]\frac{[(2i + 6j).(5i - j)]( 5i - j)}{\sqrt{5^{2} }+ (-1)^{2} }[/tex]

[tex]= \frac{(2)(5) +(6)(-1)}{\sqrt{5^{2} }+(-1)^{2} }[/tex]

= ( 5 ,-1 ) ⇒ 0.15 (5,-1)

Therefore, The best approximation of the projection  IS ( 5,-1) .

Learn more about projection of vector brainly.com/question/14655450 here

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Answer:

y = x + 2

Step-by-step explanation:

Slope-Intercept Form: y = mx + b

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

Step 1: Find slope m

m = (1 - 6)/(-1 - 4)

m = -5/-5

m = 1

y = x + b

Step 2: Find y-int b

y = x + b

1 = -1 + b

b = 2

Step 3: Rewrite equation

y = x + 2

You would know that

[tex]\displaystyle\lim_{x\to\pm1}f(x)=1[/tex]

It follows from the sandwich/squeeze theorem: for instance,

[tex]x^4 \le f(x) \le x^2 \implies \displaystyle\lim_{x\to-1}x^4 \le \lim_{x\to-1}f(x) \le \lim_{x\to-1}x^2 \implies 1 \le \lim_{x\to-1}f(x) \le 1 \\\\ \implies \lim_{x\to-1}f(x)=1[/tex]

Answer:

100 days

Step-by-step explanation:

the doctor works 5 hrs per day, which means 20 patients per day, in 100 days he will be able to treat 2000 patients

Answer:

Total number of matches need to win = 15

Step-by-step explanation:

Given:

Total number of race completed = 45

Total races win = 30

Success rate = 75% = 0.75

Find:

Total number of matches need to win

Computation:

Assume, extra number of matches = y

Extra number of win matches = x

So,

(30 + x) / (45 + y) = 0.75

Assume y = x

So,

(30 + x) / (45 + x) = 0.75

30 + x = 33.75 + 0.75 x

x = 15

Total number of matches need to win = 15

Answer:

Initially 18,500 students

Every 1 year

increase by a factor 1.03

Step-by-step explanation:

The missing information is selected from the given options from the drop down menu. The correct answers are : Initially 18,500 students enroll at the university. Every 1 years the number of students who enroll at the university increases by a factor 1.03.

F(t) = 18,500 * (1.03)^t

Answer:

Perimeter: 88m

Step-by-step explanation:

Area of the square plot = (Side) X (Side)

And we are given the area is 484m²,

therefore, (Side) X (Side) = 484m²

or,

(Side)² = 484, taking square root on both the sides,

[tex]\sqrt{(Side)^{2} }[/tex] = [tex]\sqrt{484}[/tex]

Side = 22m.

And we know that, perimeter of a square is = 4 X (Side)

Therefore, Perimeter = 4 X 22 = 88m

:-)

Answer:

88m

Step-by-step explanation:

Area = 484m^2

A= s^2

484= s^2

s=[tex]\sqrt{484}[/tex]=22m

∴22m=s

⇒So, Perimeter= 4a=22*4= 88m

Answer:

We know that the equation of the circle in standard form is equal to (x-h)² + (y-k)² = r² where (h,k) is the center of the circle and r is the radius of the circle.

We have x² + y² + 8x + 22y + 37 = 0, let's get to the standard form :

1 - We first group terms with the same variable :

(x²+8x) + (y²+22y) + 37 = 0

2 - We then move the constant to the opposite side of the equation (don't forget to change the sign !)

(x²+8x) + (y²+22y) = - 37

3 - Do you recall the quadratic identities ? (a+b)² = a² + 2ab + b². Now that's what we are trying to find. We call this process "completing the square".

x²+8x = (x²+8x + 4²) - 4² = (x+4)² - 4²

y²+22y = (y²+22y+11²)-11² = (y+11)²-11²

4 - We plug the new values inside our equation :

(x+4)² - 4² + (y+22)² - 11² = -37

(x+4)² + (y+22)² = -37+4²+11²

(x+4)²+(y+22)² = 100

5 - We re-write in standard form :

(x-(-4)²)² + (y - (-22))² = 10²

And now it is easy to identify h and k, h = -4 and k = - 22 and the radius r equal 10. You can now complete the sentence :)

1 liter = 1000mL

Divide 1000mL by mL per minute:

1000 / 5 = 200 minutes ( 3 hours and 20 minutes)

Answer:

D) 972

Step-by-step explanation:

2160*9/20 = 19440/20

= 972

Answer:

24 days

Step-by-step explanation:

Find LCM, or least common multiple

List out all the multiples of 3:

3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, ...

Now 8:

8, 16, 24, 32, 40, 48, 56, 63, 72, 80, 88...

LCM is 24, because they both hit 24 first.

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Explanation:

This is because 24 is the LCM (lowest common multiple) of 8 and 3.

We multiply the given values to get 8*3 = 24. This trick only works if the original two numbers have no common factors other than 1.

We can verify that 24 is indeed the LCM by listing out the multiples

We see that 24 is found in both lists and it's the smallest such item. The next common item would be 48, which is a multiple of 24. In other words, every 24 days, your two practices will line up on the same day.

Answer:

The simplified answer of the given equation is -57.

Step-by-step explanation:

For this problem, we are given values for our variables.

k = -1

n = -4

So, let's plug these numbers into our expression so we can easily solve it.

-(-1)² - (4(-1) - 6(-4)) + 9(-4)

Simplify your parentheses.

-(-1)² - (-4 + 24) - 36

-(-1)² - 20 - 36

Now, simplify your exponents.

-1 - 20 - 36

Combine -1 and -20.

-21 - 36

Now, subtract -21 from 36.

-57

Answer:

-18

)())()()()()()()( ;)

Answer:

17. C

18.G

Step-by-step explanation:

17. According to the question, gravel is 4/13 of the total asphalt substance. One parking lot has 260 tons of asphalt. So this means there is 80 tons of gravel because 260 times 4/13=80. We need to find the tons of gravel if we made 3 parking lot. This means 3 parking lot is the same as 780. So we can just find the measure of gravel by multiplying

4/13 by 780.

[tex] \frac{4}{13} \times 780 = 240[/tex]

So there is 240 tons of gravel. C is the answer.

18. Set up system of equations.

[tex]a + b + c = 110[/tex]

The ratio of a to c is 1:7 and the ratio of b to c is 3:7. Using this information,

Using this info, we can make alternate equations

[tex]c = 7a[/tex]

[tex]b = 3a[/tex]

Subsitue this into the original equation,

[tex]a + 7a + 3a = 110[/tex]

[tex]11a = 110[/tex]

[tex]a = 10[/tex]

We need to find c, c is 7 times more than a so c is

[tex]c = 10 \times 7 = 70[/tex]

[tex]\\ \sf\longmapsto 4\left(-5\dfrac{2}{3}\right)[/tex]

[tex]\\ \sf\longmapsto 4\left(-\dfrac{5(3)-2}{3}\right)[/tex]

[tex]\\ \sf\longmapsto 4\left(-\dfrac{17}{3}\right)[/tex].

[tex]\\ \sf\longmapsto \dfrac{-68}{3}[/tex]

if you convert it all into one hour, Team B clearly worked at a faster pace.

Answer:

[tex]team \: a \: \\ 8in \: number \: with \: in \: 2 \: hours \\ so \: in \: 1 \: hour \: \frac{8}{2} = 4 \: in \: number \\ \\ team \: b \\ 5 \: in \: 1hour \\ so \: \: team \: b \: work \: in \: fast \\ thank \: you[/tex]

Answer:

the equilibrium expected growth rate is 6.65%

Step by step Explanation:

We were given stock sold per share of $32.50

Dividend per share =$1.25

Required Return rate = 10.5%

Then we can calculate Percentage of Dividend for share as;

dividend of br. 1.25 per share at the end of the year (D1=br.1.25)

= 1.25×100= 125

Let the dividend percentage = y

stock sold per share × y= 125

125= 32.50y

y = 125/32.50

y= 3.85

y= 3.85*100%

Then the Dividend percentage = 3.85%

Growth rate=(required rate of return -Dividend percentage)

= 10.5 - 3.85 = 6.65

Therefore, the equilibrium expected growth rate is 6.65%

Answer:

It tells you that 1000g are in 1 kg. All you need to do is convert your 15 kg to 15000 g.

Answer:

Step-by-step explanation:

1 kg = 1000 g

15 Kg = 15 *1000 = 15000 g

7.75 g = 1 cm³

1 g = 1 ÷ 7.75 cm³

15000 g = [tex]\frac{1}{7.75}*15000 = 1935.48[/tex]

              = 1935 cm³

Inner diameter = 6 cm

Inner radius = r = 6/2 = 3 cm

Outer radius = R = inner radius  + thickness

  R = 3 + 2 = 5 cm

Volume of cylindrical pipe = 1935 cm³

[tex]\pi h*(R +r)(R - r) = 1935\\\\3.14 * h *( 5 + 3)(5 - 3) = 1935 \\\\3.14 * h * 8 *2=1935\\\\h = \frac{1935}{3.14*8*2}\\\\h = 38.52 = 39[/tex]

h = 39 cm

Answer:

Hypothesis

Step-by-step explanation:

The hypothesis is an educated guess that can be tested through experimentation.