14. A cleaning company charges by the square
foot. The company charged $600 to clean
4,800 square feet of space. How much
would the company charge to clean
12,000 square feet of space?

(A) $950
(B) $1,200
(C) $1,400
(D) $1,500​

Answer:

27.5 m/s

275 m

Step-by-step explanation:

99 km/hr × (1000 m / km) × (1 hr / 3600 s) = 27.5 m/s

Distance = rate × time

d = 27.5 m/s × 10 s

d = 275 m

Answer:

h(x) = 7 * (9/7) ^x

Step-by-step explanation:

h(x) = a b^x

When x=0 h(x) = 7

7 = a * b^0

7 = a *1

7 =a

Rewriting the equation

h(x) = 7 b^x

Let x=1

9 = 7 * b^1

9 = 7 * b

Divide each side by 7

9/7 =7b/7

9/7 =b

h(x) = 7 * (9/7) ^x

Answer:

Incorrectly distributing the 3 and (x-3).

Step-by-step explanation:

A common mistake when solving 3(x-3) <3 would be incorrectly distributing the 3 and (x-3).

Answer:

x = - [tex]\frac{1}{2}[/tex], x = 3

Step-by-step explanation:

Given

2x² - 5x - 3 = 0 ← in standard form

Consider the factors of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

product = 2 × - 3 = - 6 and sum = - 5

The factors are - 6 and + 1

Use these factors to split the x- term

2x² - 6x + x - 3 = 0 ( factor the first/second and third/fourth terms )

2x(x - 3) + 1 (x - 3) = 0 ← factor out (x - 3) from each term

(x - 3)(2x + 1) = 0

Equate each factor to zero and solve for x

2x + 1 = 0 ⇒ 2x = - 1 ⇒ x = - [tex]\frac{1}{2}[/tex]

x - 3 = 0 ⇒ x = 3

Answer:

80

Step-by-step explanation:

If there is any cyclic quadrilateral, which is a quadrilateral inscribed inside a circle, there is one simple property that is

the opposite angles add upto 180.

Thus we can say

96 + c = 180

and

d + 100 = 180

Since we need d, we use 2nd equation:

d + 100 = 180

d = 180 - 100

d = 80

the question is already in slope intercept form.

The y-intercept is 12.

y=mx+b whereas m=slope, and b=y-intercept.

hope this helped!

The function is linear function of a form,

[tex]f(x)=ax+b[/tex]

Which always intersects point,

[tex]P(x, n)[/tex]

Or in this case,

[tex]f(x)=2x+12[/tex]

The point is therefore,

[tex]P(x,y)\Longrightarrow\boxed{P(x, 12)}[/tex]

The y-intercept is 12.

Hope this helps.

r3t40

Answer:

Part A)

This quadratic expression can be factored by using the difference of squares pattern.

Part B) (5x+y) and (5x-y)

Step-by-step explanation:

Given:

25x^2-y^2

above polynomial can be factorize by using difference of squares formula

a2-b2=(a+b)(a-b)

25x^2-y^2= (5x-y)(5x+y)

so for part A)

correct option is  This quadratic expression can be factored by using the difference of squares pattern.

Part B)

As factored above in part A,

the factors of given polynomial 25x^2-y^2 are (5x+y)(5x-y)

so for part B) correct options are (5x+y) and (5x-y) !

Answer:

-6 - (-8) = 2.

Your number line might have a bubble at 2. Or it may show movement 8 units to the right of -6. Whatever it is, you should end up at the value of 2.

Step-by-step explanation:

We don't see a number line, but I can still show how to solve.

-6 - (-8) is the same as doing negative six plus negative one times negative 8. Or in number terms it would look like:

-6 + (- 1(- 8))

In the order of operations -- PEMDAS -- we do parenthesis first.

- 1( - 8) = 8, so we simplify by plugging this value back into the equation:

-6 + 8

-6 + 8 is the same as 8 - 6.

8 - 6 = 2

Your answer is 2.

Answer:

(1,-1)

That is the ordered pair where they cross.

Step-by-step explanation:

The solution of the system is where the pair of lines there cross at.

The intersection is in the fourth quadrant there so your guess should definitely be of the form (positive, negative).

Only one choice is that and it is B.

It really does look like they cross at (1,-1).

To describe how to get from the origin to the intersection, I would say you would need to travel right 1 unit and down 1 unit.

We can even plug in our pair into both equations and see if it works.

y=x-2

y=4x-5

So if we plug in (1,-1) and assuming it is a solution, then both equations will give us the same thing on both sides. Let's try it:

y=x-2

-1=1-2

-1=-1

That's the same thing on both sides.

y=4x-5

-1=4(1)-5

-1=4-5

-1=-1

Again that is the same thing on both sides.

(1,-1) is indeed our solution.

Both the graph and the verification told us that.

Answer:

1, -1

Step-by-step explanation:

A.P.E.X 2021

Answer:

C) m∠5 + m∠6 =180°

D) m∠2 + m∠3 = m∠6

E) m∠2 + m∠3 + m∠5 = 180°

Step-by-step explanation:

TRUST ME! JUST TOOK MY QUIZ ON E2020

The correct equations are:

m∠2 + m∠3 + m∠5 = 180°

m∠2 + m∠5 =  m∠4

m∠5 + m∠6 = 180°

m∠2 + m∠3 =  m∠6

Equation is an expression used to show the relationship between two or more numbers and variables.

From the diagram:

m∠2 + m∠3 + m∠5 = 180° (sum of angles in a triangle)

But:

m∠3 + m∠4 = 180° (angle in a straight line)  

m∠2 + m∠3 + m∠5 = m∠3 + m∠4

m∠2 + m∠5 =  m∠4

Also:

m∠5 + m∠6 = 180° (angle in a straight line)

But:

m∠2 + m∠3 + m∠5 = 180

m∠2 + m∠3 + m∠5 = m∠5 + m∠6

m∠2 + m∠3 =  m∠6

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Explanation:

Rewrite the left side in terms of sine and cosine, then rearrange.

[tex](1+\tan^2{A})+(1+\dfrac{1}{\tan^2{A}})=\dfrac{1}{\sin^2{A}-\sin^4{A}}\\\\(1+\dfrac{\sin^2{A}}{\cos^2{A}})+(1+\dfrac{\cos^2{A}}{\sin^2{A}})=\\\\\dfrac{\sin^2{A}+\cos^2{A}}{\cos^2{A}}+\dfrac{\sin^2{A}+\cos^2{A}}{\sin^2{A}}=\\\\\dfrac{1}{\cos^2{A}}+\dfrac{1}{\sin^2{A}}=\\\\\dfrac{\sin^2{A}+\cos^2{A}}{(\sin^2{A})(\cos^2{A})}=\\\\\dfrac{1}{(\sin^2{A})(1-\sin^2{A})}=\dfrac{1}{\sin^2{A}-\sin^4{A}} \qquad\text{Q.E.D.}[/tex]

See the attached picture for the solution.

Answer:

Option: C is the correct answer.

                   C. 80

Step-by-step explanation:

PG=9 in. The radius of the circle is 41 inches.

We know that the side CT is given by:

CT=CS+ST

The side CS is calculated by using the Pythagorean Theorem in ΔCSP

i.e.

[tex]CP^2=CS^2+SP^2\\\\i.e.\\\\[/tex]

as CP is the radius of the circle

and SP=PG=9 in.

i.e.

[tex]41^2=9^2+CS^2\\\\i.e.\\\\1681=81+CS^2\\\\i.e.\\\\CS^2=1681-81\\\\i.e.\\\\CS^2=1600\\\\i.e.\\\\CS=40\ units[/tex]

and

similarly in right angled triangle ΔPST

we have:

[tex]TP^2=ST^2+PS^2\\\\i.e.\\\\41^2=9^2+ST^2\\\\i.e.\\\\ST=40\ units[/tex]

Hence,

[tex]CT=CS+ST\\\\i.e.\\\\CT=40+40\\\\i.e.\\\\CT=80\ in.[/tex]

Answer:

C

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 4x + 9 ← is in slope- intercept form

with slope m = - 4

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-4}[/tex] = [tex]\frac{1}{4}[/tex], hence

y = [tex]\frac{1}{4}[/tex] x + c ← is the partial equation of the perpendicular line

To find c substitute (4, 5) into the partial equation

5 = 1 + c ⇒ c = 5 - 1 = 4

y = [tex]\frac{1}{4}[/tex] x + 4 ← equation of perpendicular line → C

Answer:

$60

The equation is x(5(2))=s or x(10)=s when x = number of weeks

Step-by-step explanation:

For 6 weeks, all you have to do is plug in the 6 where the x is.

6(5(2)) = s

6(10) = s

60 = s

or

6(10) = s

60 = s

Answer:

[tex]\large\boxed{f^{-1}(x)=9x-18}[/tex]

Step-by-step explanation:

[tex]f(x)=\dfrac{1}{9}x+2\to y=\dfrac{1}{9}x+2\\\\\text{exchange x to y and vice versa}\\\\x=\dfrac{1}{9}y+2\\\\\text{solve for y}\\\\\dfrac{1}{9}y+2=x\qquad\text{subtract 2 from both sides}\\\\\dfrac{1}{9}y=x-2\qquad\text{multiply both sides by 9}\\\\9\!\!\!\!\diagup^1\cdot\dfrac{1}{9\!\!\!\!\diagup_1}y=9x-(9)(2)\\\\y=9x-18[/tex]

Answer:

2^ (-1)

1/2

Step-by-step explanation:

Add the exponents which have common bases.

3 + (-4) = -1

2^ (-1)

1 / 2

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Answer:

The simplified form of the provided expression is [tex]2^{-1}\ or\ \frac{1}{2}[/tex]

Step-by-step explanation:

Consider the provided expression:

[tex](2^3)(2^{-4})[/tex]

Use the product rule of exponent:

[tex]a^m \cdot a^n=a^{m+n}[/tex]

Now use the above formula to simplify the provided expression.

[tex](2^3)(2^{-4})=2^{3+(-4)}[/tex]

[tex](2^3)(2^{-4})=2^{3-4}[/tex]

[tex](2^3)(2^{-4})=2^{-1}[/tex]

Hence, the simplified form of the provided expression is [tex]2^{-1}\ or\ \frac{1}{2}[/tex]

The domain of the function can be written as [-1,2]-{2}, therefore the function is defined from -1 to 2 except 2.

• Domain is the set of values for which the given function is defined.

• Range is the set of all values which the given function can output.

Since the dark point of the function show that is the beginning of the function therefore the function will be defined from that point to all values of x but will not be defined at the point where there is a blank dot, also, the function is defined till the line is drawn.

Thus, the domain of the function will be,

Domain: [-1,2]-{2}

Hence, the domain of the function can be written as [-1,2]-{2}, therefore the function is defined from -1 to 2 except 2.

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[tex]\huge{\boxed{\text{3) \bf{9, 40, 41}}}}[/tex]

A Pythagorean triple is a set of three numbers where [tex]a^2 + b^2 = c^2[/tex].

Trying 1:

[tex]1^2+3^2=10^2[/tex]

[tex]1+9=100[/tex]

[tex]10=100[/tex]

Incorrect.

Trying 2:

[tex]4^2+5^2=9^2[/tex]

[tex]16+25=81[/tex]

[tex]41=81[/tex]

Incorrect.

Trying 3:

[tex]9^2+40^2=41^2[/tex]

[tex]81+1600=1681[/tex]

[tex]1681=1681[/tex]

Correct!

Trying 4: (unnecessary, but practice is good)

[tex]16^2+30^2=44^2[/tex]

[tex]256+900=1936[/tex]

[tex]1156=1936[/tex]

Incorrect.

Answer:

-4 is the mimumum of y=-3+cos(x+4)

Step-by-step explanation:

The minimum value of y=cos(x) is -1.

The minimum value of y=cos(x+4) is still -1; the +4 inside the cosine function only affected the horizontal shift.

The minimum value of y=-3+cos(x+4) is -3-1 which is -4.  This brought the graph down 3 units so if the minimum was previously -1 and it got brought down 3 units then it's new minimum is -4.

Answer:

C

Step-by-step explanation:

[tex] \sec( \alpha ) = \frac{1}{ \cos( \alpha ) } \\ \\ \sec( \alpha ) = \frac{1}{ \frac{ad}{hip} } \\ \\ \sec( \alpha ) = \frac{hip}{ad} \\ \\ \sec( \alpha ) = \frac{41}{40} [/tex]

The value of the secθ is 41/40.

Trigonometry is mainly concerned with specific functions of angles and their application to calculations. Trigonometry deals with the study of the relationship between the sides of a triangle (right-angled triangle) and its angles.

For the given situation,

The diagram shows the right-angled triangle.

The sides of the right-angled triangle are

Hypotenuse side = 41 ft

Opposite side = 9 ft

Adjacent side = 40 ft

The value of secθ is

[tex]sec \theta =\frac{1}{cos \theta}[/tex]

where, [tex]cos \theta =\frac{adjacent}{hypotenuse}[/tex]

⇒ [tex]sec \theta =\frac{hypotenuse}{adjacent}[/tex]

⇒ [tex]sec \theta =\frac{41}{40}[/tex]

Hence we can conclude that the value of the secθ is 41/40.

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Answer:

The first graph represents how many of each order could be put in a bag hanging from the hook ⇒ 1st

Step-by-step explanation:

* Lets explain how to solve the problem

- The order of jumbo paperclips weighs 2 pounds

- x is the number of orders of paperclips

∴ The weight of the paperclips order is 2 × x = 2x

- The order of packing tape weighs 3 pounds

- y is the number of orders of packing  tape

∴ The weight of the tape order is 3 × y = 3y

- The weight of the total order is 2x + 3y

- The hook can hold no more than 6 pounds

∴ 2x + 3y ≤ 6

- Lets find the graph which represent this inequality

∵ The equation of any line is y = mx + c, where m is the slope of the

  line and c is the y-intercept

- The y-intercept means substitute x in the equation by 0

- The x- intercept means substitute y in the equation by 0

∵ The inequality is 2x - 3y ≤ 6

∵ The equation of the line is 2x + 3y = 6

- Subtract 2x from both sides

∴ 3y = 6 - 2x

- Divide both sides by 3

∴ y = 6/3 - 2/3 x

∴ y = 2 - 2/3 x

- Find the y-intercept

∵ x = 0

∴ y = 2

∴ The line intersect the y-axis at point (0 , 2)

- Find the x-intercept

∵ y = 0

∴ 0 = 2 - 2/3 x

- Add 2/3 x to both sides

∴ 2/3 x = 2

- Multiply both sides by 3

∴ 2 x = 6 ⇒ divide both sides by 2

∴ x = 3

∴ The line intersect the x-axis at point (3 , 0)

- From the figure the first and the second figures have the same

 x-intercept and y-intercept

∵ The inequality is 2x + 3y ≤ 6

- The sign ≤ means the line is sold and the shading is under the line

∴ The first figure is the answer

* The first graph represents how many of each order could be put in a

  bag hanging from the hook

Answer:

Option A.

Step-by-step explanation:

Let x is the number of orders of paperclips and y is the number of orders of packing tape.

An order of jumbo paperclips weighs 2 pounds and an order of packing tape weighs 3 pounds.

Total weight = [tex]2x+3y[/tex]

A hook in an office storage closet can hold no more than 6 pounds. It means total weight must be less than or equal to 6 pounds.

[tex]2x+3y\leq 6[/tex]

The related equation is

[tex]2x+3y=6[/tex]

Substitute x=0 in the above equation.

[tex]2(0)+3y=6[/tex]

[tex]3y=6[/tex]

[tex]y=2[/tex]

The y-intercept is 2.

Substitute y=0 in the above equation.

[tex]2x+3(0)=6[/tex]

[tex]2x=6[/tex]

[tex]x=3[/tex]

The x-intercept is 3.

Check the inequality by (0,0).

[tex]2(0)+3(0)\leq 6[/tex]

[tex]0\leq 6[/tex]

This statement is true, it means (0,0) is included in the shaded region.

The sign of inequity is "≤" it means the related line is a solid line and shaded region lie below the line.

Therefore, the correct option is A.

Answer:

D.

Step-by-step explanation:

The y-intercept is where the graph crosses the y-axis.

It crosses the y-axis at (0,5).

The graph is of f(t)=5*2^t where t is the number of years and the value of f(t) is the value of that coin after t years.

So we have (0,5) is on the graph of f which means f(0)=5.

f(0)=5 means at t=0 years the value of the coin is $5.

As per the y-intercept of a function, when the coin was purchased, the value of it was $5.

"The y-intercepts are points where the graph of a function crosses or touches the y-axis of the Cartesian Plane. "

The given function is

[tex]f(t)=5(2^{t})[/tex]

As per the graph of the given function, it starts from the point (0, 5).

Hence, it cuts the y-axis at point (0, 5).

Therefore, at the time of purchasing the coin, the value of the coin was at $5.

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Answer:  The required scale factor of the dilation is 4.  

Step-by-step explanation:  Given that the parallelogram FGHJ was dilated and translated to form similar parallelogram F'G'H'J'.

We are to find the scale factor of the dilation.

From the graph, we note that

JH = 2 units   and   J'H' = 8 units.

We know that

[tex]\textup{Scale factor of dilation}=\dfrac{\textup{length of a side of the dilated figure}}{\textup{length of the correponding side of the original figure}}.[/tex]

Therefore, the scale factor of the given dilation is

[tex]S=\dfrac{J'H'}{JH}\\\\\\\Rightarrow S=\dfrac{8}{2}\\\\\Rightarrow S=4.[/tex]

Thus, the required scale factor of the dilation is 4.  

Answer:

4 on edge

Step-by-step explanation:

The vertices of the triangle are the points where any pair of lines intersect.

We start by setting up the system

[tex]\begin{cases}y=-x+2\\y=2x-1 \end{cases} \iff -x+2=2x-1 \iff 3x=3 \iff x=1[/tex]

Using one of the two equations we can derive the correspondent y value:

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

So, one vertex is (1, 1)

We choose the other two pairs of lines to find the other vertices:

[tex]\begin{cases}y=-x+2\\y=x-2 \end{cases} \iff -x+2=x-2 \iff x=2 \implies y = 0[/tex]

[tex]\begin{cases}y=x-2\\y=2x-1 \end{cases} \iff x-2=2x-1 \iff x=-1 \implies y=-3[/tex]

So, the three vertices are (1, 1), (2, 0), (-1, -3).

Answer:

(1, 1), (2, 0), and (-1, -3)

Step-by-step explanation:

I got right on the test.

Answer:

A) 40

Step-by-step explanation:

The sum of the interior angles of a regular polygon is:

[tex](n - 2) \times 180[/tex]

For a hexagon, we put n=6

[tex](6 - 2) \times 180 = 4 \times 180 = 720[/tex]

Let x be the 6th interior angle, then

[tex]x + 110 + 120 + 90 + 140 + 125 = 720[/tex]

[tex]x + 585 = 720[/tex]

[tex]x = 720 - 585 = 135[/tex]

The largest interior angle is 140°

Therefore the least exterior angle will be:

[tex]180 - 140 = 40[/tex]

The correct choice is A

Answer:

640 miles per hour.

Step-by-step explanation:

I calculated this by 3200/5

Is this appropriate?

Answer: x^2-6x-8

Step-by-step explanation:

Step 1 : Factor - x^3-11x^2+22x+40: (x-5)(x^2-6x-8)/(x-5)

Step 2 : Divide, which should give you x^2-6x-8

Answer:

Step-by-step explanation:

Area of rectangle = x³-5x²+3x-15

Width of rectangle = x²+3

Length of rectangle= ?

We will apply the formula:

Area= length* width

Hence we know the area and width.

x³-5x²+3x-15/x²+3 = length

By dividing the terms we get (x-5).

Thus the correct option is x-5....

Answer:

12 cans with 3 left over

Step-by-step explanation:

It's pretty simple.

You already know you have 3 left over so all you have to do is 315 divided by 26.

315 ÷ 26 ≈ 12.12 but since you already know you have 3 left over, the answer would be 12.

Answer:

12 cans per carton

Step-by-step explanation:

Subtract the remainder of cans to the total amount.

315 - 3 = 312

Divide by the number of cartons.

312 / 36 = 12 cans per carton

Best of Luck!