Graph the function and state the domain and range.g(x)=x^2-2x-15Domain-Range-Graphed function-

Explanation:

Equate the given data to solve for x.

$200 + $12x = $644.

To determine the number of albums sold, Let x be the number of album sold by Floyd last month.

200 + 12x = 644

12x =644-200

12x = 444

x = 444/12

x= 37.

Floyd has sold 37 albums last month.

Answer:

The equation to determine the number of albums Floyd sold last month is 200+12x = 644.

and the number of album Floyd sold last month is 37.

Michael Mows = 1/3 of the yard

Mel mows the rest = 1-1/3 = 2/3 of the yard

Mel mows = 3/4 of the yard in an hour

After Michael mows 1/3 of the yard what fraction of the yard does Mel need to mow?​

1- 1/3 = 2/3 of the yard

How long will it take Mel to finish mowing the yard??

2/3 / (3/4) = 8/9 hours = 0.89 hours

Let's distribute those factors, and expand this:

There's no further way beyond that. Either we pick the factored form or the expanded version of that polynomial. As this is not an equation we stop it here.

We need to find the slope using the points (9, -24) and (13 , -21)

so, the slope = 3/4

Answer

2

Explanation:

f⁻¹(8) is equal to the value of x that makes f(x) = 8. So, taking into account the graph, we get:

Therefore, f⁻¹(8) = 2. So the answer is 2

qANSWER

Company B will pay more

Company A =

EXPLANATION

Both companies start by paying $42,000 per year.

Company A offers an increase of $1000 per year.

This means that after n years, he would have earned:

Earnings = 42000 + 1000n

where n = number of years after the first year

So, after 6 years, he would have worked 5 years after the first, so his earnings would be:

Earnings = 42000 + 1000(5) = 42000 + 5000

Earnings = $47000

Company B offers 7% more than the previous year. That means that his earnings are compounded.

His earnings can then be represented as:

where P = initial salary = $42000

r = interest rate = 7%

t = number of years spent = 6 years

Therefore, his earnings after the 6th year will be:

He would have earned $63042.

Therefore, Company B will pay more.

qANSWER

Company B will pay more

Company A =

EXPLANATION

Both companies start by paying $42,000 per year.

Company A offers an increase of $1000 per year.

This means that after n years, he would have earned:

Earnings = 42000 + 1000n

where n = number of years after the first year

So, after 6 years, he would have worked 5 years after the first, so his earnings would be:

Earnings = 42000 + 1000(5) = 42000 + 5000

Earnings = $47000

Company B offers 7% more than the previous year. That means that his earnings are compounded.

His earnings can then be represented as:

where P = initial salary = $42000

r = interest rate = 7%

t = number of years spent = 6 years

Therefore, his earnings after the 6th year will be:

He would have earned $63042.

Therefore, Company B will pay more.

ANSWER

2, 4 and 8

EXPLANATION

We have that in a triangle ABC, AB = 3 cm and BC = 5 cm.

To find the possible length of AC, we can apply the triangle inequality theorem.

It states that in any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side.

This means that:

So, we have that:

We have to disregard the third line, since the length of a triangle side can only be positive.

So, using the first 2 lines, we see that:

This means that from the options, the measure of AC can either be 2, 4 or 8.

Answer:

$11.48

Step-by-step explanation:

Change 15% to 0.15. then you multiply 13.50 by 0.15

13.50 x 0.15 = 2.025

Then you round 2.025

by rounding 2.025 you should get 2.03

with that you should subtract $13.50 by 2.03

13.50 - 2.03 = 11.48

I hope this helps :)

Answer:

2d⁻³/9d⁻⁹

Step-by-step explanation:

4 times d raised to the negative third power = (4 × d)⁻³ = 4d⁻³

18 times d raised to the ninth power = (18 × d)⁻⁹ = 18d⁻⁹

the equation as a quotient:

Expression = 4d⁻³/18d⁻⁹

Expression = 2d⁻³/9d⁻⁹

By definition, Addition is a mathematical operation.

In this case, you have the following Addition given in the exercise:

The percentage error is the ratio of the difference between the two readings and the actual

Error = 13.75 - 10

= 3.75

Percent error = 3.75/13.75

= 27.27%

Different estimates:

The length of the radius of a cylindrical pipe:

Plumber W:

Radius had a length: 3/5 inches.

Plumber X:

Radius had a length: sqrt(3/11) inches.

Plumber Y:

Radius had a length of 9/100 inches.

Plumber Z:

Radius had a length of 3/14/24 inches.

Turn them into decimals:

We can turn each length into decimal:

Plumber W: 3/5 = 0.6.

Plumber X: sqrt(3/11) = 0.522222..

Plumber Y: 9/100 = 0.09

Plumber Z: 3.14/24 = 0.13083

The list from the greatest to least:

We can order this list taking into account the following reasoning: when the number is near to zero, this number is less than the other in the list. Examples: 0.001, 0.0002, 0.00004 are very near to zero.

Additionally, when a number is near 1 (the unit), this number is greater than the other less near to 1.

Examples: 0.69, 0.73, 0.888, 0.99 are near to zero.

The numbers we got in the list are decimals numbers coming from fractions and the square root was taken to the estimation of plumber X. Therefore:

From list 0.6, 0.52222..., 0.09, 0.13083

The number nearest to zero is 0.09. Then, 0.13083 is greater than 0.09 but less than the others. The following number is 0.5222..., and the greatest is 0.6.

The list that shows these lengths in order from the greatest to least is:

{0.6, 0.5222..., 0.13083, 0.09}.

Which is equivalent to:

{3/5, sqrt(3/11), 3.14/24, 9/100}.

The correct answer is  A. 90 - d

Since the sum of all the angles in a triangle is 180° and one of the angle is 90° because the triangle is a right triangle. So the sum of the remaining angles is 90°.

And to find the other acute angle we use 90° - d.

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The rate at which the distance between the airplanes is changing is  668.2 mi/h.

In the given question,

Speed of Airplane A:

dA/dt = 451 mi/h

and the Speed of Airplane B:

dB/dt = 494 mi/h

Aircraft A and B will form a right triangle because Aircraft A is flying east and Aircraft B is flying north, and we can use Pythagoras' theorem to calculate their distance from one another.

Let P be the distance.

P² = A² + B²

Differentiating the above equation with respect to t,

2P(dP/dt) = 2A(dA/dt) + 2B(dB/dt)

Dividing each side of the equation by 2,

P( dP/dt ) = A( dA/dt ) + B( dB/dt )                  ..........(1)

Where dP/dt is the rate of change in distance between the two aircraft.

Now,

P² = A² + B²

P = √(A² + B²)

Substituting, A = 3 miles and B = 3miles;

P = √(3² + 3²)

P = √( 9+ 9)

P = √18

P = 3√2 miles

Substituting the value in the equation (i)

3√2 (dP/dt) = (3× 451) + (3× 494)

3√2 (dP/dt) = 2835

4.2426 × dP/dt = 2835

dP/dt = 2835/4.2426

dP/dt = 668.2 mi/h

Therefore, the rate at which the distance between the airplanes is changing is  668.2 mi/h

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Volume of the top of the prism: 460 cm^3

Volume of the bottom of the prism: 1 768 cm^3

Total volume of the figure: 2 228 cm^3

Explanation:

Volume of the top of the prism:

. Since it is a prism from trapezoid

. . Volume = Area of the trapezium base * heights between trapezium ends

Volume of the bottom prism:

. Since the price has a rectangular base:

Volume = Area of one base * height between reactangular bases

Area of one base :

Volume:

Total volume of the figure:

Volume of the top + Volume of the bottom = Total volume

NB:

To find any volume of a given prism, start with finding the area of one base, then multiply that area by the height (in other words the sides that link the two bases)

=(3x2 + 2x + 4) - (x2 + 2x + 1)

Combine like terms

=(3x2-x2)+(2x-2x)+(4-1)

=2x2+0+3

The 2x terms cancel each other to 0

=2x2+3

C) 2x2+3 is the answer.

Hope this helps!

Answer:

15x^2+17x+4

Step-by-step explanation:

(3x+2x+4)(x+2x+1)

Combine 3x and 2x to get 5x.

(5x+4)(x+2x+1)

Combine x and 2x to get 3x.

(5x+4)(3x+1)

Apply the distributive property by multiplying each term of 5x+4 by each term of 3x+1.

15x ^2+5x+12x+4

Combine 5x and 12x to get 17x.

15x^2+17x+4

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Using the matrix equation, the value of x and y are 5 and 2 respectively.

Consider the 2 by 2 matrix equations,

1/2 [ 4  8     ( x + 3 )   - 4 ] - 3[ 1  y+1    -1  - 2 ] = [ - 1  -5   7  4 ]

[ 2   4       (x+3)/2    -2] + [ - 3   -3y -3   +3  + 6] = [ - 1 - 5    7  4]

[ -1  -3y + 1    (x + 9)/2   + 4]  = [ - 1 - 5   7  4]

Therefore,

- 3y + 1 = - 5

Subtracting 1 from each side of the equation,

- 3y + 1 - 1 = - 5 - 1

- 3y = - 6

Dividing each side of the equation by - 3,

y = 2

And;

( x + 9 )/2 = 7

Multiplying each side by 2,

x + 9 = 14

Subtracting 9 from each side of the equation,

x + 9 - 9 = 14 - 9

x = 5

Therefore, the value of x and y is 5 and 2 respectively.

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In order to have grade A, the score needs to be in the top 9%.

Since the scores are normally distributed, the top 9% scores correspond to 91% of the area under the normal curve. That means we need to find a value of z in the z-table that corresponds to the value 0.91 (that is, 91%).

Looking at the z-table, the value of z for a probability of 0.91 is z = 1.34.

Now, to find the score that this value of z represents, we can use the formula below:

Rounding to the nearest whole number, the minimum score for grade A is 79.

Given :

Two kinds of Beans :

1. Kidney Beans $1.18 per lb

The unit price = $1.18

2. O Lima Beans $213 for 2 lbs

The unit price = 2.13/2 = 1.065

Rounding to the nearest hundredth

So,

The unit

We will break the surface area of the tent up into its sides, the front and the back and the bottom.

Area of the sides: 2(5*7) = 70

Area of the front and the back: 2( 1/2 (6*4)) = 24

Area of the bottom: 7*6 = 42

Least amount of fabric required = 136ft

Solution:

According to the problem, a regular work week consists of 5 work days with 8 hours a day. This is equivalent to say:

5 x 8 hours every regular work week.

That is:

40 hours every regular work week

then, the money earned per hour is:

then we can conclude that the correct answer is:

$7.5

This problem invloves the topic of curved lines in a graph, curved lines or more speccifically curve line which looks like letter C (parabola) all follows a certain standard form of equation, which is;

For example you can see that the equation for the black curve line in our picture is y=x² and notice that this equation can also be written as y = (1)x² + 0. Which simillar to the standard form given above where a is just 1 (a=1) and b is just 0 (b=0).

Since our black curve line follows the same standard form of equation as stated above, we can conclude that the RED curve line follows the same form of equation.

To summarize the steps that we must do in order to find the equation of the RED line we will list them as,

1. Sample two(2) points in the graph to be used as reference points.

2. Use the sampled points in our standar eqation in order to find the variables "a" and "b".

3. When we have the variables "a" and "b", we can just directly substitute it into our standard equation to find the equation of our RED line.

Let's start.

1. Sample 2 points to be used as refernce points. (Note that we will find the easiest points

to determine)

Let us use the points (-3, -1) and (-2, 1) as shown in the picture.

2. Use the points (-3, -1) and (-2, 1) in our standard equation.

for our 1st point we have the equation 9a+b = -1, let us now proceed to our next point.

and for our 2nd point we have the equation 4a+b = 1, and by the process of subtitution and elimination we can now find "a" and "b", because we have two equations with two unknowns.

transforming eqatuin number 1 to

then substitue b = -1 -9a to the 2nd equation we have.

since a = -2/5, we can find b using,

therefore our a and b are;

3. We can now proceed in substituting it in our standard equation;

you can also simplify the final equation by multiplying all sides by 5,

therefore our final answer can be,

Answer:

Step-by-step explanation:

A quadratic function in vertex form is represented as:

Given the vertex (1,2) substitute it into the function:

As you can see, we still do not know the value for ''a'', use the point given (4,-7) substitute it (x,y) and solve for ''a'':

Hence, the equation of the function would be:

Using thales theorem:

SOLUTION

GIVEN

A polyhedron has 6 vertices and 12 edges.

TO DETERMINE

The number of faces

CONCEPT TO BE IMPLEMENTED

Euler’s formula for Polyhedron :

For polyhedron F + V = E + 2

Where F stands for number of faces , V stands for number of vertices , E stands for number of edges .

EVALUATION

Here it is given that a polyhedron has 6 vertices and 12 edges

V = Number of vertices = 6

E = Number of edges = 12

F = Number of faces = ?

By Euler’s formula

F + V = E + 2

⇒ F + 6 = 12 + 2

⇒ F + 6 = 14

⇒ F = 8

FINAL ANSWER

The number of faces = 8

We are given that each face of a pyramid is an isosceles triangle and that its vertex angle is 70 degrees. This problem can be exemplified in the following diagram:

Since the triangle is isosceles, its base angles are the same, and the sum of the interior angles must be equal to 180 degrees. Therefore, we have the following relationship:

Adding like terms, we get:

Now we solve for "x", first by subtracting 70 on both sides:

Now we divide both sides by 2

Therefore, the base angles of the pyramid are 55 degrees.

DEFINITIONS

The union of two sets contains all the elements contained in either set (or both sets). The union is notated A ⋃ B.

The intersection of two sets contains only the elements that are in both sets. The intersection is notated A ⋂ B.

Using a Venn Diagram, the union and intersection of two sets can be seen below:

GIVEN

The sets are given to be:

QUESTION

1) (A ∪ B): The terms of the two sets contained in either set or the two sets are

2) (A ∩ B): The elements that are in both sets are

Given that

We have a right-angled triangle and have to find angle A's tangent.

Explanation -

The triangle is shown as

Here we have,

X = 24 inches

Y = 45 inches

Z = 51 inches

Then, the tangent of angle A will be

So the correct option is B.

Final answer -

The length of the arc = 8π/3 mi

The length of an arc is given by the fomula:

The radius, r = 8 ml

The length of the arc = 8π/3 mi

Answer:

FALSE

Explanation:

Given the expression

50% of $277

This can also be written as;

= 50/100 * 277

= 1/2 * 277

= 277/2

= 138.5

Therefore 50% of $277 is $138.5 not $144 rendering the question FALSE