A stereo system is being installed in a room with a rectangular floor measuring 14 feet by 9 feet and a 7- foot ceiling. The stereo amplifier is on the floor in one corner of the room. A speaker is at the ceiling in the opposite corner of the room. What is the shortest connection

Answer:

-6

Step-by-step explanation:

m^2 - 36 = 0

Add 36 to each side

m^2 -36+36 = 0+36

m^2 = 36

Take the square root of each side

sqrt( m^2) = ± sqrt(36)

m = ±6

We know one root is 6

The other root is -6

Answer:

The two numbers are 28 and 7.

Step-by-step explanation:

Let the first number be x

Let the second number be y

The difference of x and y is x-y=21

The quotient of two numbers is x/y = 4

x-y =21    (This is equation 1)

x/y=4    (This is equation 2)  

By solving equation 2 we will get the value of x.

x/y=4

x=4y (Lets call it equation 3)

Now, put the value of x(equation 3) in (equation 1)

x-y=21

4y-y=21

3y=21

y=21/3

y=7

Now put the value of y in equation 3 to get the value of x

x=4y

x=4(7)

x=28

Solution Set {(x,y)(28,7)}

Answer:

28 and 7

Step-by-step explanation:

D. is the correct answer

Hopes this helps

Answer:

B

Step-by-step explanation:

We can solve this by finding the slope of the function that passes through the points (2,15) and (3,26). We can use the "formula" rise over run.

So we have:

(26-15)/(3-2) which gives us 11 as our slope. Now we must find the y intercept!

It is -7.

So the answer is B

Answer:

the equation is y = 11x - 7

B is correct option.

Step-by-step explanation:

The function passes through the points (2, 15) and (3, 26)

Slope can be calculated by the formula

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

using this formula, the slope is given by

[tex]m=\frac{26-15}{3-2}\\\\m=\frac{11}{1}\\\\m=11[/tex]

The slope intercept form of line is y = mx+b

here, m = 11

hence, the equation is  y = 11x +b

Now, using the point (2,15) to find b

15=11(2)+b

15 = 22 +b

b = -7

Hence, the equation is y = 11x - 7

B is correct option.

Answer:

-6

Step-by-step explanation:

A(n)=-6+(1-1)(1)

simplified, this equals:

A(n) = -6+(0)(1)

A(n)=-6+0

A(n) = -6, for any given n term.

Answer:

Midpoint

Step-by-step explanation:

Equidistant from the pre = image AA would be the middle

Answer:

Mid Point, thats all there is, its the answer, just that

Step-by-step explanation:

Answer:

[tex](f*g) (x) =2x^3-13x^2-7 [/tex]

Step-by-step explanation:

We have the following functions

[tex]f (x) = 2x+1[/tex]

[tex]g (x) = x^2-7[/tex]

To find [tex](f*g)(x)[/tex] we must multiply the function f (x) with the function g (x)

Then we perform the following operation

[tex](f*g) (x) =(2x+1)(x^2-7)[/tex]

Apply the distributive property

[tex](f*g) (x) =2x^3-14x^2+x^2-7 [/tex]

[tex](f*g) (x) =2x^3-13x^2-7 [/tex]

Finally we have that:

[tex](f*g) (x) =2x^3-13x^2-7 [/tex]

Answer:

A: Line Segment WX

Step-by-step explanation:

100% on edge 2020

Answer:

WX is correct

Step-by-step explanation:

Got a 100 in edge quiz.

[tex]\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ f(x)=\stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{+4}x\stackrel{\stackrel{c}{\downarrow }}{+12} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{4}{2(1)}~~,~~12-\cfrac{4^2}{4(1)} \right)\implies (-2~~,~~12-4)\implies (-2~,~8)[/tex]

well, the quadratic has a leading term with a positive coefficient, meaning is a parabola opening upwards, like a "bowl", comes from above down down down, reaches a U-turn, namely the vertex, and goes back up up up.

so the minimum value is at the vertex of course, and the minumum is well, just the y-coordinate of the vertex, 8.

Answer:

106.90 cm

Step-by-step explanation:

Given

Angle=30 degrees

Base=92.58 cm

So,

We will have to use the triangular ratios to find the hypotenuse.

The triangular ratio that will be used for this will be cosine because we know the value of angle and base since it involves both cosine will be used.

cos⁡θ=Base/Hypotense

cos⁡30=92.58/Hypotenuse

0.8660=92.58/Hypotenuse

Hypotenuse=92.58/0.8660

=106.90 cm ..

Answer:

Hypotenuse = 107.02

Step-by-step explanation:

Points to remember

If angles of a triangle are 30°, 60° and 90° then the sides are  in the ratio

1 : √3 : 2

It is given a right angled  triangle with angles 30°, 60°, 90°

and height = 95.58 cm

To find the hypotenuse

From the figure we can write,

Base : Height : Hypotenuse = 1 : √3 : 2 = Base : 92.58 : Hypotenuse

Therefore Hypotenuse = (92.58 * 2)/√3

  = 107.02 cm

Answer:

(4b + 5)

Step-by-step explanation:

To get 4b^2 you already have b^2 if you put b  inside the second set of brackets. But that would mean you don't have 4 anywhere to get 4b^2.

So the first step has to be

(b + 3)(4b

Now look at the 15 for a moment. It is plus 15. The only way you can get a plus 15 is if both signs are plus (after the b terms) or both terms are minus.

The middle term (17b) is plus so both terms after b are plus.

(b + 3)(4b +

Now we need something that multiplies to 15. 3*5 = 15. So the term you want is 5.

(b + 3)(4b + 5)

Does the middle term work?

5*b + 3*4b = 5b + 12b = 17b

Everything looks fine.

The second factor is 17b.

Answer:

2 11/12

Step-by-step explanation:

(50/3)/(40/7)

=50/3*7/40

=5/3*7/4

=35/12

=2 11/12

let's convert firstly, the mixed fractions to improper fractions and then divide.

[tex]\bf \stackrel{mixed}{16\frac{2}{3}}\implies \cfrac{16\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{50}{3}}~\hfill \stackrel{mixed}{5\frac{5}{7}}\implies \cfrac{5\cdot 7+5}{7}\implies \stackrel{improper}{\cfrac{40}{7}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{50}{3}\div\cfrac{40}{7}\implies \cfrac{\stackrel{5}{\begin{matrix} 50 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}}{3}\cdot \cfrac{7}{\underset{4}{\begin{matrix} 40 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}}\implies \cfrac{35}{12}\implies 2\frac{11}{12}[/tex]

Answer:

x = -8

Step-by-step explanation:

-2x-2=14

We want to solve for x

Add 2 to each side

-2x-2+2 = 14+2

-2x=16

Divide each side by -2

-2x/-2 =16/-2

x = -8

Answer:

The center of the circle is (-3,-2)

Step-by-step explanation:

we know that

The equation of a circle in standard form is equal to

[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]

where

(h,k) is the center

r is the radius

In this problem we have

[tex]x^{2} +y^{2}+6x+4y-3=0[/tex]

Completing the square

Group terms that contain the same variable, and move the constant to the opposite side of the equation

[tex](x^{2}+6x) +(y^{2}+4y)=3[/tex]

Complete the square twice. Remember to balance the equation by adding the same constants to each side.

[tex](x^{2}+6x+9) +(y^{2}+4y+4)=3+9+4[/tex]

[tex](x^{2}+6x+9) +(y^{2}+4y+4)=16[/tex]

Rewrite as perfect squares

[tex](x+3)^{2} +(y+2)^{2}=16[/tex]

therefore

The center of the circle is (-3,-2)

Answer: ITS D !! ON EDGE

Step-by-step explanation:

Answer:

31 seats

Step-by-step explanation:

Let x be the smaller van, and y be the larger one.

We know that y = x + 14

We also know that 2x + y = 65

If we replace y by its value in the second equation we have:

2x + (x + 14) = 65, then we solve

2x + x + 14 = 65

3x + 14 = 65

3x = 51

x = 17

We now know the smaller van has 17 seats.

To find how many seats are in the big one, we take the first equation:

y = x + 14

y = 17 + 14

y = 31

Answer:

A. [tex]h=\frac{SA-2B}{P}[/tex]

Step-by-step explanation:

We have been given a formula for the surface area of a container in shape of right prism. We are asked to solve for h for our given formula.

[tex]SA=Ph+2B[/tex]

First of all, we will switch sides for our given equation as:

[tex]Ph+2B=SA[/tex]

Now, we will subtract 2B from both sides of our equation.

[tex]Ph+2B-2B=SA-2B[/tex]

[tex]Ph=SA-2B[/tex]

Now, we will divide both sides of our equation by P.

[tex]\frac{Ph}{P}=\frac{SA-2B}{P}[/tex]

[tex]h=\frac{SA-2B}{P}[/tex]

Therefore, option A is the correct choice.

Answer:

A

Step-by-step explanation:We have been given a formula for the surface area of a container in shape of right prism. We are asked to solve for h for our given formula

First of all, we will switch sides for our given equation as:

Now, we will subtract 2B from both sides of our equation.

Now, we will divide both sides of our equation by P.

therefore its option A

Answer:

It's C on e2020

Step-by-step explanation:

Answer:

[tex]\large\boxed{y=-\dfrac{2}{3}x+\dfrac{13}{3}}[/tex]

Step-by-step explanation:

[tex]\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\\\m-slope\\b-y-intercept\\\\\text{The formula of a slope:}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\\\===============================[/tex]

[tex]\text{We have the point:}\\\\(5,\ 1)\ \text{and}\ (-4,\ 7).\ \text{Substitute:}\\\\m=\dfrac{7-1}{-4-5}=\dfrac{6}{-9}=-\dfrac{6:3}{9:3}=-\dfrac{2}{3}\\\\\text{We have the equation in form:}\\\\y=-\dfrac{2}{3}x+b\\\\\text{Put the coordinates of the point (5, 1) to the equation:}\\\\1=-\dfrac{2}{3}(5)+b\\\\1=-\dfrac{10}{3}+b\qquad\text{add}\ \dfrac{10}{3}\ \text{to the both sides}\\\\\dfrac{3}{3}+\dfrac{10}{3}=b\to b=\dfrac{13}{3}\\\\\text{Finally:}\\\\y=-\dfrac{2}{3}x+\dfrac{13}{3}[/tex]

Answer:

(4334/100)*93 = $ 4,030.62

Step-by-step explanation:

N/A

Answer:

7pi/2

Step-by-step explanation:

If was a full, the circumference or the arc length would be 2pi*r where r in this case is 7 so it would be 14pi.

Now this only a quarter of that, so this arc length is actually 14pi/4.

This can be reduced 14pi/4 =7pi/2

Answer:

3.5pi

Step-by-step explanation:

KA

The number of batches is 4.

When a problem arises if 4 is required for 2 of these things then how many things does 20 require?

We use the unitary method to solve the problem where we find how much is required for one thing and then multiply it by the required.

1/6 tub of peanut butter is used for one batch of cookies.

2/3 of it was used for the whole day.

So to find the total number of batches we divide the total tub used by the amount of tub used for one batch of cookies hence = 2/3/(1/6) = 4

Hence the answer to the given problem is 4.

Learn more about the Unitary method here

https://brainly.com/question/19423643

#SPJ2

This is a piecewise function because it is defined by more than two functions. Basically, we want to take the limit here. Recall that if a function [tex]f(x)[/tex]  approaches some value [tex]L[/tex]  as [tex]x[/tex]  approaches [tex]a[/tex]  from both the right and the left, then the limit of [tex]f(x)[/tex] exists and equals  [tex]L[/tex]. Here we won't calculate the limit, but apply some concepts of it. So:

a. [tex]as \ x \rightarrow +\infty, \ k(x) \rightarrow +\infty[/tex]

Move on the x-axis from the left to the right and you realize that as x increases y also increases without bound.

b. [tex]as \ x \rightarrow -\infty, \ k(x) \rightarrow 0[/tex]

Move on the x-axis from the right to the left and you realize that as x decreases to negative values y approaches zero.

c. [tex]as \ x \rightarrow 2, \ k(x) \rightarrow 0[/tex]

Since the function is continuous here, we can say that [tex]k(2)=0[/tex]

d. [tex]as \ x \rightarrow -2, \ k(x) \rightarrow 0[/tex]

The function is discontinuous here, but [tex]k(-2)[/tex] exists and equals 0 as the black hole indicates at [tex]x=-2[/tex].

e. [tex]as \ x \rightarrow -4, \ k(x) \rightarrow 2[/tex]

The function is also discontinuous here, but the black hole indicates that this exists at [tex]x=-4[/tex], so [tex]k(-4)=2[/tex]

f. [tex]as \ x \rightarrow 0, \ k(x) \rightarrow 4[/tex]

Since the function is continuous here, we can say that [tex]k(0)=4[/tex]

okay so we need to solve for x.

--

FIRST STEP:  12x^2+5x-4=12^2x+6 would turn into x2 + 5x - 4 = 2x + 6 so it'd have equal bases.

SECOND STEP: move any number with "x" in it to the left side. it ends up as  x2 + 3x - 4 = 6

THEN, we use the AC method to eliminate any unnecessary numbers.

you should end up with ( x - 2) (x + 5) = 0

SO, the answer is your third option. ( x = 2, x = -5)

Answer:

x=-5&x=2

Step-by-step explanation:

Since the bases on both sides of the equation are the same, they will cancel each other leaving the exponents

x²+5x-4 = 2x + 6

Collect like terms

x²+5x-2x-4-6=0

x²+3x-10=0

The highest power is 2 , so factorize

x²+5x-2x-10=0

x(x+5)-2(x+5)=0

(x+5)(x-2)=0

x = -5 or x = 2

Check

When x = -5

-5²+3*-5-10=0

25-15-10 =0

0=0

:.x=-5

When x=2

2²+3*2-10=0

4+6-10=0

0=0

Answer: -2,0 0,4

Step-by-step explanation:

let me know if you need help still UwU

Answer:

The function is positive from (-∞,-2) and (0,4).

Explanation:

To find the intervals where the function is positive, note where the line of the graph is above the x-axis.

As the functions goes toward negative infinity, the arrow of the graph is pointed up, so the function is positive starting from -∞ until x = -2, where it becomes negative.

The function once again goes above the x-axis at x = 0 and stays positive until x = 4. After this point, the function decreases forever, so (-∞,-2) and (0,4) are the only intervals where the function is positive.

Answer:

288 square units

Step-by-step explanation:

The formula for the area of a square when you know its diagonal is: [tex]\frac{1}{2} d^2[/tex]

So, since we know the half diagonal is 12, we need to multiply that by 2 to get the diagonal, which is 24.

Put 24 into the formula. [tex]\frac{1}{2} * 24^2[/tex]

Simplify the exponent. [tex]\frac{1}{2} * 576[/tex]

Finally, multiply. [tex]288[/tex]

Answer:

4,-2 and 1

Step-by-step explanation:

These are all quantities greater than -5

-5 < 4

-5 < -2

-5 < 1

So C, D and E

The given line that passes through the points (7,-4) and (-1,3).

The slope is

[tex]m = \frac{3 - - 4}{ - 1 - 7} = - \frac{7}{8} [/tex]

The point-slope form is obtained using:

[tex]y-y_1= m (x-x_1) [/tex]

When (7,-4) is used the point-slope form is

[tex]y + 4= - \frac{7}{8} (x - 7) [/tex]

We expand now to get;

[tex]y = - \frac{7}{8}x + \frac{49}{8} - 4[/tex]

This implies that,

[tex]y = - \frac{7}{8}x + \frac{17}{8}[/tex]

Answer:

1.Area of Porch =2.5m²

2.Number of people =3 people

Step-by-step explanation:

The porch area from the diagram has a dimension of 4 units by 10 units

One units =1cm

Thus the porch is drawn with dimensions of 4cm by 10 cm

Taking length is 10 cm and width as 4 cm, convert these dimensions according to the scale.

The scale is 1cm=0.25m

The width will be= 0.25×4=1 m

The length will be=0.25×10= 2.5m

Area of the porch is given by the formula;

length×width because its has a shape of a rectangle

Area of porch will be

=1m ×2.5m =2.5m²

2.

Find the dimensions of the tent

14 units by 10 units

Applying the scale on the dimensions by multiplying by 0.25

14×0.25=3.5m

10×0.25=2.5m

Width=2.5m

length=3.5m

Subtract the edge distance on both the length and width

Length will be=3.5-(0.25×2)=3.0m

Width will be=2.5-(0.25×2)=2.0m

Find the area remaining to be covered by the people while sleeping

=3.0×2.0=6m²

Area covered by sleeping bag and a ground mat

2m×1m=2m²

Number of people that can sleep in the tent

6m²÷2m²=3 people

Answer: Area of porch in metres [tex]= 2.5 m^{2}[/tex]

No. of people that can sleep in the tent = 0 (according to the given conditions)

Step-by-step explanation:

In the given figure we have the scale of 1 cm : 0.25 m which denotes that we have 0.25 m length in actual for every 1 cm on the figure. Also, each square in the figure measures 1 cm on each side.

From the fig. the dimensions of tent porch area are:

Length = 10 cm = [tex]10 \times 0.25[/tex]

[tex]= 2.5 m[/tex] on ground

Breadth= 4 cm = [tex]4 \times 0.25[/tex]

[tex]= 1 m[/tex] on ground

∴ Area of porch in metres = [tex]1\times 2.5[/tex]

Area of porch in metres [tex]= 2.5 m^{2}[/tex]