A painter is hired to paint the interior walls of a large warehouse. The function f(x)=20,000−40x models the area in square feet that remain to be painted, where x represents the number of minutes the painter has worked from the 100-minute mark through the 200-minute mark of the project.

What is the practical range of the function?

A) all integers

B) all real numbers between 100 and 200 inclusive

C) all real numbers between 12,000 and 16,000 inclusive

D) integers from 100 to 200 inclusive

The cubic function with zeros -2, 5, and -6 is given by f(x) = (x + 2)(x - 5)(x + 6), derived from the zero-product property.

To find a cubic function with the given zeros of -2, 5, and -6, we can use a formula associated with the zero-product property. This property states that if a product of factors equals zero, then at least one of the factors has to be equal to zero. So if -2, 5, and -6 are the zeros of the function, the factors of the function would be (x + 2), (x - 5), and (x + 6).

The cubic function f(x) is then derived from the multiplication of these factors. Therefore the cubic function with the zeros -2, 5, and -6 will be f(x) = (x + 2)(x - 5)(x + 6).

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Answer:

9.8

Step-by-step explanation:

Answer:

Its A. 9.8 on APEX hope this helps!!

2.  KL = LM

3.  Definition of midpoint

4.  L is the midpoint of KM

5. Transitive Property of Congruence

m = [tex]\frac{1}{2}[/tex],   (x₁ , y₁) = (-2, -4)

y - y₁ = m(x - x₁)

y -(-4) = [tex]\frac{1}{2}[/tex](x - (-2))

y + 4 = [tex]\frac{1}{2}[/tex](x +2)

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

     y = [tex]\frac{1}{2}x[/tex] - 3

Answer: A

The correct answer would be diameter. A chord is a line segment connecting two points on a circle's circumference. When the chord passes through the center of a circle it is called a diameter.

Final answer:

The line segment that passes through the center of a circle and has both endpoints on the circle is called a diameter.

Explanation:

The line segment which passes through the center of a circle and has both endpoints on the circle is called a diameter.

A diameter is the longest chord in a circle and it divides the circle into two equal halves. It passes through the center, and any point on the circumference of the circle is equidistant from the center.

For example, in the circle below, AB is a diameter:

Proof:

Statement                                                   Reason

1. PV || QM                                                   Given

2. ∠1 is supplementary to ∠2                    Same-Side Interior Angles Theorem

3. m∠1 + m∠2 = 180°                                   Same-Side Interior Angle Theorem

4. ∠1 ≅ ∠3                                                   Given

5. m∠1 = m∠3                                              Definition of Congruent angles  => (If the angles are congruent, the measurements will be equal)

6. m∠3 + m∠2 = 180°                                Same side interior angle theorem (two angles on the same side make 180° if directly next to each other)

hope this helps

To prove that LT is parallel to MV, we can use the given information that angle 1 is congruent to angle 3. By showing congruence between triangles LTM and MVL, we can establish the proportionality of sides LT and MV, leading to the conclusion that LT is parallel to MV.

To prove that LT is parallel to MV, we need to use the given information that angle 1 is congruent to angle 3. Here's a step-by-step explanation:

Therefore, we have proved that LT is parallel to MV using the given information that angle 1 is congruent to angle 3.

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You have to observe that [tex] x^4 [/tex] and 625 are both squares (of [tex] x^2 [/tex] and 25, respectively). So, you can use the "difference of square" pattern for factorization:

[tex] a^2-b^2 = (a+b)(a-b) [/tex]

to write

[tex] x^4 - 625 = (x^2+25)(x^2-25) [/tex]

Note that, again, [tex]x^2-25[/tex] is a difference of square:

[tex] x^2-25 = (x+5)(x-5) [/tex]

On the other hands, [tex] x^2+25 [/tex] admits no factorization, because it's a second-degree polynomial (thus a parabola) with no solutions.

So, the whole expression becomes

[tex] x^4 - 625 = (x^2+25)(x+5)(x-5) [/tex]

Angle (3x+31)° and angle (2x-6)° are supplementary angles. Then the value of the variable x is 31°.

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

Angle (3x+31)° and angle (2x-6)° are supplementary angles. Then we have

(3x + 31)° + (2x - 6)° = 180°

5x + 25° = 180°

5x = 155°

x = 31°

Then the value of the variable x is 31°.

Your question was incomplete, probably the question was...

Find the value of x. Angles (3x+31)° and (2x-6)° are supplementary angles.

More about the angled link is given below.

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The value of  x equals 31°.

The value of (x) can be found by solving the equation formed by the two angles in the given question:

Given angles:

Linear pair property:  The sum of the measures of two angles forming a linear pair is (180°).

Now,

Set up the equation: (3x + 31) + (2x - 6) = 180

=>  (3x + 2x) + (31 - 6) = 180

=> 5x + 25 = 180

Solve for (x):  5x = 155 =>  x = 31

Therefore, the value of (x) is 31°.

Disclaimer : I attached the image of complete question

Answer:

Ratio of Cats to animals [tex]\frac{23}{50}[/tex]

Step-by-step explanation:

Total animals in the shelter = Total number of dogs + Total number of Cats

                                              =[tex]27+23[/tex]

                                              =[tex]50[/tex]

Ratio of Cats to animals        = Number of Cats / Total animals

                                               =[tex]\frac{23}{50}[/tex]

Based on the parallel lines, an angle that corresponds to ∠7 include the following: B. ∠3.

In Mathematics and Geometry, corresponding angles theorem is a theorem which states that corresponding angles are always congruent when the transversal intersects two parallel lines:

This ultimately implies that, the corresponding angles will be always equal (congruent) when a transversal intersects two parallel lines.

By applying corresponding angles theorem to the two parallel lines, we have the following congruent angles:

m∠3 ≅ m∠7

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Consider triangle MOP. This triangle is right triangle, because  m∠P=90°.

Since  m∠P=90°, m∠M=60°, then m∠O=180°-90°-60°=30°.

The leg opposite to the angle with measure 30° is half of the hypotenuse. Let the leg MP=x, then the hypotenuse MO=2x. By the Pythagorean theorem,

[tex]PO^2+MP^2=MO^2\Rightarrow PO^2=(2x)^2-x^2=4x^2-x^2=3x^2\Rightarrow PO=\sqrt{3}x.[/tex]

The perimeter of triangle MOP is

[tex]P_{MOP}=MO+PO+MP=x+2x+\sqrt{3}x=3x+\sqrt{3}x.[/tex]

Since [tex]P_{MOP}=12+4\sqrt{3},[/tex] then [tex]x=4.[/tex]

Answer: MP=4 units.

Answer:

mp=4 cuz in a 30-60-90 degree right triangle if the shorter leg is x, then the longer leg (po) is xsqrt3. Because the perimeter is 12+4sqrt3, that means the longer leg is probably 4sqrt3. because of this, then the shorter leg, mp is 4. Since the hypotenuse is equal to 2x, then it would be 2*4=8=PO.

[tex]f(x)=x^4-2x^3+2x-1=x^4-x^3-x^3+x+x-1\\\\=x^3(x-1)-x(x^2-1)+1(x-1)\\\\=x^3(x-1)-x(x^2-1^2)+1(x-1)\\\\=x^3(x-1)-x(x+1)(x-1)+1(x-1)\\\\=x^3(x-1)+(x-1)(-x(x+1)+1)\\\\=(x-1)(x^3-x(x+1)+1)\\\\=(x-1)(x^3-x^2-x+1)\\\\=(x-1)[x^2(x-1)-1(x-1)]\\\\=(x-1)(x-1)(x^2-1)\\\\=(x-1)(x-1)(x^2-1^2)\\\\=(x-1)(x-1)(x-1)(x+1)[/tex]

[tex]Used:\\\\a^2-b^2=(a-b)(a+b)[/tex]

Answer:

Answer:

78 dollars /6.5 hours = 12 dollars .

Your rate is 12 dollars per hour.

Step-by-step explanation:

Answer:

its c

Step-by-step explanation:

HE WOULD HAVE 64$ IN TOTAL

Answer:

-64

Step-by-step explanation:

its actually, -64 not 64.

Given

During a promotional event  

A sporting goods store gave a free t-shrit to every 8th customer and a free water bottle to every 10th customer.

Find out which customer has the first to get a free t-shirt and a free water bottle.

To proof

Definition of LCM ( Least common multiple )

The LCM of two numbers is the smallest number that they both divide evenly into.

As given in the equation

A sporting goods store gave a free t-shrit to every 8th customer and a free water bottle to every 10th customer.

Let take 8 be as one number and 10 be as another number.

LCM ( 8,10 ) = 2× 2 ×2 ×5

= 40

Also  

A sporting goods store gave a free t-shrit to every 8th customer and a free water bottle to every 10th customer.

This is shown in the table given below.  

As shown in the table the common value is 40.

Therefore  

The first to get a free t-shirt and a free water bottle is 40th customer.

Hence proved

Answer:

The 40th customer was the first to get a free t-shirt and free water bottle

Step-by-step explanation:

(A) Bella's TV ratio of sides: 36"/27" = 1.333...

Lenny's: 52"/29.25" = 1.777...

Bella's and Lenny's TVs are NOT similar - their side ratios are different. Bella's is 4:3 while Lenny's is close to 16:9.

(B) Bella's TV has an exact ratio of 4:3 (36/27=4/3) and so is the older type.

Lenny's TV has a ratio of 52"/29.25". Divide both 52 and 29.25 by 3.25 to get 16/9, or 16:9. So Lenny's is the newer type.

y = 1/3x

The slope is 1/3 ( the slope is the number with the variable x).

There is no other operation ( addition or subtraction) so the y- intercept is 0

The first point of the graph would be (0,0)

Calculate another point , lets use x = 3

y = 1/3(3) = 1

The second point is (3,1)

The line of the graph is an angled line which is located in quadrant 1 and 3.

See attached picture:

If 60 is 2 more than the product of 5 and N:

The product of 5 and N is when they are multiplied, so 5N is going to be part of the equation.

We know that 60 is 2 more than 5N, so 5N + 2 would be 60.

We can make an equation with this:

60 = 2 + 5N

Therefore, the equation would be 60 = 2 + 5N.

Hope this helps! :)

The equation that can be used to depict the information 60 is 2 more than the product of 5 and N will be 60 = 2 + 5N

From the information given, 60 is 2 more than the product of 5 and N and this will be written as 60 = 2 + 5N.

To further solve the equation, we can solve for N and this will be:

60 = 2 + 5N

Collect like terms

5N = 60 - 2

5N = 58

N = 58/5

N = 11.6

Therefore, the value of N will be 11.6.

In conclusion, 60 is 2 more than the product of 5 and N and this will be written as 60 = 2 + 5N.

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If we want to verify that g ( x ) is the inverse of f ( x ) we have to show that:

( f ° g ) = ( g ° f )

f ( g ( x ) )=  3 · ( 1/3 x ) = x

g ( f ( x ) ) = 1/3 · ( 3 x ) = x

Answer:

C ) 1/3 ( 3 x )

Answer:

Step-by-step explanation:

To verify if two functions are inverse, we have to find the composition of such functions, that is:

[tex]f(g(x))[/tex]; which results must be the variable [tex]x[/tex] to be inverse functions.

We know that: [tex]f(x)=3x;g(x)=\frac{1}{3}x[/tex].

Replacing on the composition:

[tex]f(g(x))=3(\frac{1}{3}x)=x[/tex]

Therefore, the expression that has to be used to verify that these functions are inverse is C.

I believe the answer is  -1/2.  

The formula for 'w' in terms of the perimeter 'P' and length 'l' of the rectangle is w = (P - 2l)/2.

To solve for 'w' in the formula for the perimeter of a rectangle, P = 2(l + w), we need to isolate 'w' on one side of the equation.

P = 2(l + w)

First, distribute the 2 to both terms inside the parentheses:

P = 2l + 2w

Now, subtract 2l from both sides to move it to the other side of the equation:

P - 2l = 2w

Finally, divide both sides by 2 to solve for 'w':

w = (P - 2l)/2

Therefore, the formula for 'w' in terms of the perimeter 'P' and length 'l' of the rectangle is:

w = (P - 2l)/2

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For this case we have:

We define the following variable

x : Speed of the car in South direction

By definition, we know that:

[tex]Distance = Speed * Time[/tex]

For the car in north direction:

[tex]D1 = V1 * T1\\D1 = 50mph * 3h\\D1 = 150 miles[/tex]

For the car in south direction:

[tex]D2 = V2 * T2\\D2 = x * 3\\D2 = 3x[/tex]

The distance between both cars, after 3 hours, is:

[tex]D = D1 + D2[/tex]

So, we have:

[tex]345 = 150 + 3x[/tex]

Clearing x;

[tex]3x = 345-150\\3x = 195\\x = 65[/tex]

Thus, the speed of the car in the south direction is [tex]x = 65mph[/tex]

Answer:

Option B

Answer: B. 65 MPH

Step-by-step explanation:

≈ 3927 litres

the volume (V) of a cylinder is calculated using the formula

V = πr²h ( r is the radius of base and h is the height )

V= π × 100² × 250 = 7853981.634 cm³

[tex]\frac{1}{2}[/tex] V = 3926990.817 = [tex]\frac{3926990.817}{1000}[/tex] ≈ 3927 litres

Hi, the answer is this...

Otylia's solution is: Incorrect

Because 4y+y is the same as 4y+1y

4y2 is the same as 4y x y

4y+y simplifies to 5y

Answer:

Otylia's solution is incorrect

Correct solution is 5y

Step-by-step explanation:

Otylia simplifies the expression 4y + y to 4y^2.

LEts simplify the expression 4y+y and check with Otylia's solution

4y and y are like terms

y or 1y are same

4y and 1y are like terms

To combine like terms, we add only the coefficient of y

So 4y + 1y = 5y

Otylia simplifies the expression 4y + y to 4y^2

4y^2 is not correct. So Otylia's solution is incorrect

If Monique used a total of 6 1/2 pounds of potatoes and each batch required 3/4 of a pound of potatoes, then you have to divide the total amount of pounds by an amount of pounds needed for one batch:

[tex]6\dfrac{1}{2}:\dfrac{3}{4}=\dfrac{13}{2}\cdot \dfrac{4}{3} =\dfrac{26}{3}=8\dfrac{2}{3}.[/tex]

Answer: [tex]8\dfrac{2}{3}.[/tex]

Answer:

Step-by-step explanation:It’s B and E