A rectangular bedroom has an area of 117 ft. the length of the bedroom is 4ft more than the width. find the length and the width of the bedroom

The curved surface area of the cone is 144 cm².

A cone is a three-dimensional object that consists of a circular base and an vertex.

curved surface area = πrl

Where:

3.14 x 3 x 23 = 144 cm²

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Answer: the fourth one

Step-by-step explanation:

Answer:

D.) 8x¹²y³

Step-by-step explanation:

When an expression is raised to a power, you have to raise everything in the expression to the power when simplifying. This includes the coefficients and variables. When a variable already raised to a power is raised to another power, the powers are multiplied.

Therefore,

2³ = 8

(x⁴)³ = x⁴*³ = x¹²

(y)³ = y³

Combined, the final answer is 8x¹²y³.

Answer:

f(x)=4^x exponential growth,  -6^x exponential decay Step-by-step explanation:

Answer:

C

C

B

8 abd 9-11

236.4 million

66.9%

Answer: 3

Step-by-step explanation:

The sine of an angle is equal to the cosine of its complement, so

[tex]4x+10=2x+16\\\\2x+10=16\\\\2x=6\\ \\ x=3[/tex]

Answer:

Look at the pic for answer.

Step-by-step explanation:

All the equations have been solved

A quadratic equation is what can be represented by

ax² +bx+c = f(x)

It is given to solve the given quadratic equations

1.  x² = 25

x = ± 5

2. 16x² = 25

x² = 25/16

x = ± 5/4

3. (3x+2)²= 25

9x² +4+12x = 25

9x² +12x -21 = 0

3x(3x+7) -3(3x+7) = 0

x =1

x = -7/3

4. x² = 11x

x² -11x = 0

x (x-11) = 0

x = 0, 11

5. 3x²= 14x

3x² -14x = 0

x (3x - 14) = 0

x = 0 , 14/3

6. x²+2x = 3

x²+2x -3 = 0

x (x+3) -1(x+3) = 0

x = 1 ,-3

7.x²+2x -5 = 0

determined from the formula for the roots

x=−1±√6

x=1.44949

x=−3.44949

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Answer:

$12.

Step-by-step explanation:

1) if price of one doll is 'x', of one dress is 'y', then the condition 'buys one doll and one dress, it will cost her $21.00' can be written as x+y=21;

2) the condition 'buys two dolls and three dresses, it will cost her $51.00' can be written as 2x+3y=51;

3) it is possible to make up the system:

[tex]\left \{ {{x+y=21} \atop {2x+3y=51}} \right. \ = > \ \left \{ {{x=12} \atop {y=9}} \right.[/tex]

4) the price of one doll is 12$.

Answer:

52

Step-by-step explanation:

Using the cosine rule, BC = √(115² + 80² - 2(115)(80)(cos 72) ≈ 118.1 m (1 decimal place).

If we are given a triangle with two known sides and an included angle, the cosine rule that can be used to find the side opposite to the given angle is: a = √(b² + c² - 2bc(cos A)

We are given the following:

Plug in the values

BC = √(115² + 80² - 2(115)(80)(cos 72)

BC ≈ 118.1 m (1 decimal place)

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Answer:

d. 11:15

Step-by-step explanation:

1) officer1: distance 75 miles, velocity 60mil/h; officer2: distance 25 miles, velocity 55mil/h;

2) time, which is spent officer1 is: 75/60=1.25[h]=75 [min]. If the officer1 leaves his office at 10:00, the arrival time is 11:15;

3) time which is spent officer2 is: 25/55=5/11[h]≈27[min]. The arrival time is 10:27.

4) finally, the both officers are in the required location at 11:15.

Answer:

$14.4

Step-by-step explanation:

there are 2 adults so 2 children will get the discount

4.50 + 4.50 + 1.375 + 1.375 + 2.75 = $14.5

Answer:

Step-by-step explanation:

Answer:

I believe you forgot to add a picture

Answer:

B

Step-by-step explanation:

when x is 0 y=4(0)+12 y=12

y is 0 y=4(-3) +12 = 12=12

Answer:

f'(1)=-1

Step-by-step explanation:

You can just find the derivative using the power rule for d/dx (x^-1)=-1x^-2=-1/x^2 then find f'(1)=-1.

I used the limit definition of the derivative to find the slope in the picture attached

Answer:

5/17

Step-by-step explanation:

If we do the multiplication first, we get:

[tex]\frac{4-(12\div-12)}{13+(-8\div-2)}[/tex]

If we do the division next, we get:

[tex]\frac{4+1}{13+4} = 5/17[/tex]

The time taken by a group of 8 people working half the rate of the first group is 7.5 hours.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

We have:

A Group of 5 people can do a piece of work in 6hrs.

5 people, at a rate of 1, and the time taken is 6 hours

Work done is 30

8 people, at a rate of 1/2, and the time taken is x hours

8(1/2)x = 30

x = 60/8 = 7.5 hours

Thus, the time taken by a group of 8 people working half the rate of the first group is 7.5 hours.

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Using Chebyshev's Theorem, the minimum percentage of commuters in has a commute time within 2 standard deviations of the​ mean is of 75%.

When we have no information about the population distribution, Chebyshev's Theorem is used. It states that:

Hence, the minimum percentage of commuters in has a commute time within 2 standard deviations of the​ mean is of 75%.

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The solutions to the quadratic equation 50 - x² = 0 are x = ±5√2.

A quadratic equation is a second-order polynomial equation in a single variable x , ax2+bx+c=0. with a ≠ 0 .

The solution(s) to the quadratic equation 50 - x² = 0 can be found by setting the equation equal to zero and solving for x.

50 - x² = 0

To solve this equation, we can rearrange it as follows:

x² = 50

Taking the square root of both sides, we have:

x = ±√50

Simplifying the square root of 50, we get:

x = ±√(25 × 2)

x = ±√25 × √2

x = ±5√2

Therefore, the solutions to the quadratic equation 50 - x² = 0 are x = ±5√2.

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Answer:

Step-by-step explanation:

the numerator goes in side of the radical

Answer:

A

Step-by-step explanation:

By looking at the graph you can eliminate B as a choice since the denominator is 1+x which means it would have a vertical asymptote as x=-1 which doesn't correspond with the graph shown. You can also eliminate C since the function doesn't have a vertical asymptote as x=3 since the denominator of the function is 3-x meaning it would be undefined at x=3. It should be A since it appears to approaching 1 with a vertical asymptote at x=1 which corresponds with the denominator 1-x. If you plug in the value 0 as x you get 3 which is what is shown on the graph when x equals 0

Answer:

expression for (g + h)([tex]x\\[/tex]) = [tex]2x[/tex] + [tex]3x^2\\[/tex] and for (g - h)([tex]x[/tex]) = [tex]2x[/tex] - [tex]3x^2[/tex]

value of (g .h)(2) = 24

Step-by-step explanation:

function operations: Functions with overlapping domains can be added, subtracted, multiplied and divided. If f(x) and g(x) are two functions, then for all x in the domain of both functions we can find the sum, difference, product and quotient

given :

g([tex]x[/tex]) = [tex]2x[/tex]

h([tex]x[/tex]) = [tex]3x^2[/tex]

we know that ;

(g + h)([tex]x[/tex]) = g([tex]x[/tex]) + h([tex]x[/tex])

              =  [tex]2x[/tex]  + [tex]3x^2[/tex]

similarly;

(g - h)([tex]x[/tex]) = g([tex]x[/tex]) - h([tex]x[/tex])

             =  [tex]2x[/tex] - [tex]3x^2[/tex]

now,  

(g . h)([tex]x[/tex]) = 2([tex]3x^2\\[/tex])

             = 6[tex]x^2\\[/tex]

for (g .h)(2) = 6([tex]2^2[/tex])

                  = 6 × 4

                  = 24

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The cosine ratios which are correct for the ΔPQR are CosineP = r/q and CosineR = p/q.

We have,

Δ PQR,

Length of hypotenuse PR = q

The length of PQ = r,

And the length of QR = p

NOw,

We know that Trigonometric ratios of CosineΘ;

CosineΘ = Base/Hypotenuse

So,

CosineP = r/q

And,

CosineR = p/q

So, from the above find out values we can say that these values are given in option (a) and option (d).

Therefore, the cosine ratios which are correct for the ΔPQR are CosP = r/q and CosR = p/q.

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Answer:

[tex] {5}^{ \frac{1}{12} } = \sqrt[12]{5} [/tex]

Step-by-step explanation:

[tex] \frac{ \sqrt[3]{5} }{ \sqrt[4]{5} } = {5}^{ \frac{1}{3} } \div {5}^{ \frac{1}{4} } = {5}^{ \frac{4}{12} } \div {5}^{ \frac{3}{12} } = {5}^{ \frac{1}{12} } = \sqrt[12]{5} [/tex]

THIS IS THE ANSWER: 5 to the power of one-twelfth (Take a look at the image if this does not make sense) :))

:))

:)))   HAPPY SLAPPY!!!!

:))))

"UPDATE" : This was correct on my test. Also I realized to see the image in this answer keep your cursor on the side of your screen, not on the image :D

using elimination method

2x + 3y = 6 -----(1)

-

x + 3y = 12-------(2)

———————

x = 12

substitute x as 12 into equation (1) or (2), let's choose equation (1)

2(12) + 3y = 6

24 + 3y = 6

collect like terms

3y = 6 - 24

3y = 18

divide both sides by 3 ( to make y the subject of formula )

3y = 18

— —

3 3

y = 6

therefore X = 12 and y = 6

Hope this helps eh

Good luck ✅.

(i) The Maclaurin's series is:

1 ₊ x ₊ x²/2! . 1 ₋ 3x⁴/4! ₊ ...........

(ii) Integral of limit o to 1∫ e^sinx is 0

Maclaurin's expansion is as follows:

y(x) = y₀ ₊ x y₁(0) ₊ x²/2! y₂(0) ₊ x³/3! y₃(0) ₊ ........

y = e^sinx

y(0) = e^sin0

y(0) = 1

Differentiate y with respect to x

y₁(x) = e^sinx . cos x

y₁(0) = 1 [i.e y₁ = cosx.y]

y₁(0) = 1

Differentiate y₁ with respect to x

y₂(x) = cosc . y₁ ₋ sinx . y

∴ y₂(0) = 1 ₋ 0 = 1

Differentiate y₂ with respect to x

y₃ = cosx . y₂ ₋ (2 sinx ₊ cosx)y₁

y₃(0) = 1 ₋(0 ₊ 1)1

y₃(0) = 0

Differentiate y₃ with respect to x

y₄ = cosx . y₃ sinx . y₃ ₋ (2sinx ₊ cosx)y₂ ₋ (2cos x ₋ sinx) y₁

y₄(0) = 0 ₋ (3 . 0 ₊ 1)1 ₋ (2 ₋ o) 1

y₄(0) = -3

∴ From maclaurin's equation we get:

e^sinx = 1 ₊ x . 1 ₊ x²/2! . 1 ₊ x³/3! (0) ₊ x⁴/4! (₋3) ₊ ....

           =1 ₊ x ₊ x²/2! . 1 ₋ 3x⁴/4! ₊ ...........

Hence we get the the series expansion as 1 ₊ x ₊ x²/2! . 1 ₋ 3x⁴/4! ₊ ...........

(ii) limit 0 to 1∫e^sinx

integration formula ∫e^x dx = e^x + c

                    limit 0 to 1 ∫e^sinx = [e^sinx + c ]limit 0 to 1

                                                 = e^sin0 ₋ e^sin1

                                                 = 1 ₋ 1

                                                 = 0

Hence we get the answer as 0

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Answer: 54%

Step-by-step explanation:

You will need to divide these numbers.

[tex]6/11=0.54[/tex]

After you divide that, simplify that to a percentage by multiplying it by 100.

[tex]0.54 *100=54%[/tex]%

I hope this helps!!

Answer:

4(m+2)²

Step-by-step explanation:

Hope this help!!

The number best represents the slope of the graphed line is 1/2.

We have given the two points,

(-6,-7) and (4,-2) and slope-intercept is 8 units

[tex]y-y_{1}=m\left(x-x_{1}\right)[/tex]

y = y coordinate of the second point

[tex]y_1[/tex] = y coordinate of point one

m = slope

x = x coordinate of the second point

[tex]x_{1}[/tex]= x coordinate of point one

Therefore the

[tex]slope=\frac{y_2-y_1}{x_2-x_!}[/tex]

[tex]=\frac{-2-(-7)}{4-(-6)} \\=\frac{5}{10}\\ =\frac{1}{2}[/tex]

Therefore the correct option is 1/2.

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