Franklin is drawing a model of a rectangular swimming pool. He marks two points, A and B, on the coordinate plane and connects them to represent one side of the pool. Points C and D are reflections of B and A, respectively, across the x- axis. Each unit in the coordinate plane represents 1 meter. Draw a rectangle in the coordinate plane yo model the swimming pool. What is the area of the swimming pool?

There are several forms in which one can write the equation of a line. Have in mind that TWO variables should be included in the equation. These two variables are: x and y.

If you type the equation in a form that looks like:

A x + B y = C

where the A, B, and C are actual numbers (like for example: 3 x - 2 y = 5)

This is the standard form of a line. to recognize it notice that bith variables x an y appear in separate terms on the LEFT of the equal sign., and a pure number (no variables) appears on the right of the equal sign.

Another form of writing the equation of a line is in the so called "solpe-intercept" form. This form looks like:

y = m x + b

Notice that in this case the variable ÿ" appears isolated on the left , and on the right of the equal sign you get a term with the variable x, and another constant (pure number) term (b). Like for example in the case of:

y = 3 x

a)  2711/7576

b)  43

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Explanation:

a) 2711 are e-bikes and there are 3277+2711+1588 = 7576 total bikes. Divide the values to get 2711/7576 . This fraction cannot be reduced because the GCF of 2711 and 7576 is 1.

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b) There are 3277 bikes with fat tires out of 7576 total. Use a calculator to get 3277/7576 = 0.43255 approximately. This converts to 43.255% and then rounds to 43%

The percent sign is already typed in, so you just need to type in the whole number 43 for this box.

1) Firstly, let's find the composite function g(f(x)) plugging into the x variable in g(x) the function f(x):

2) To write that as the standard form, let's replace g(f(x)) with "y" and write the polynomial orderly to the greatest coefficient to the least one.

Answer:

The correct answer is C. Pi/2

Step-by-step explanation:

I got it wrong on edgen, and it told me the correct answer was C.

Answer:

Step-by-step explanation:

The number is 2.

222x4=888

Hence, the number am I is [tex]888[/tex].

What is the even number?

A number that is divisible by [tex]2[/tex] and generates a remainder of [tex]0[/tex] is called an even number.

Here given that,

I am an even number. I have three digits and they are all the same.

If you multiply me by [tex]4[/tex], all of the digits in the product are [tex]8[/tex].

The number is [tex]2[/tex] sp ot would be

[tex]222[/tex]x[tex]4=888[/tex]

Hence, the number am I is [tex]888[/tex].

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The Solution.

To find the slope of the line from the given graph:

First, we shall pick two coordinates in the graph, that is

This implies that

By formula, the slope is given as below:

substituting the values in the above formula, we get

So, the slope of the line is -3/2

b. From the graph, and from the slope being a negative value, it is clear that the line graph is Decreasing.

c. To estimate the vertical intercept is to find the y-intercept of the line.

Clearly from the graph, we can see that the vertical intercept is (0,2), that is, the point where the line cut the y-axis.

Therefore, the vertical intercept is (0,2).

We know the formula d=rt where d is distance, r is rate and t is time

Emmet:

d = 6 yd/s * t

Ayana:

d = 9 yd/s * t

We give Emmet 30 less yards to run

Emmet:

d - 30 = 6 yd/s * t

d = 6t + 30

Setting the equations equal to each other

9 * t = 6t + 30

Subtract 6t from each side

9t-6t = 30

3t = 30

Divide by 3

3t/3 = 30/3

t = 10 seconds

It will take 10 seconds for Ayana to catch up

Ayana:

d = 9 yd/s * t

d = 8 * 10 = 90 yds

Given:

An angle is x= 60 degrees.

Required:

Construct a pair of parallel lines with a set of alternate interior angles that measure X degrees.

Explanation:

First, draw a line then construct an angle of 60 degrees.

Now take a point B on the line that is making an angle of 60 degrees cut the arc from point B with the same measure of arc A.

Now cut the arcs from point A that join the line l and from C that joins m as with the same arc. Draw a line with the intersecting arc.

Thus the angle

will be an interior angle of measures 60 degrees.

Final Answer:

The figure is attached in the explanation part.

The solution of the linear equation y = 2 · x - 4 is x = 2.

Linear equations are first order polynomials. In this problem we need to solve for x in a linear equation, this can be done by means of algebra properties. The complete procedure is shown below.

Step 1 - We find the find the following expression:

y = 2 · x - 4                              

Step 2 - We make y equal to zero and we use the symmetric property for equalities:

2 · x - 4 = 0                              

Step 3 - By compatibility with addition, existence of additive inverse, modulative, associative and commutative properties

2 · x = 4                                    

Step 4 - By compatibility with multiplication, existence of multiplicative inverse and modulative, associative and commutative properties we get the following result:

x = 2            

The solution of the linear equation is x = 2.

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We have

first, we need to factorize the next term

so we have

Remember in order to sum a fraction the denominator must be the same

then we solve the multiplications (x-2)(x-3)

then we can factorize the numerator

so the simplification will be

the final result is

For the vertical asymptotes, we set the argument of the logarithm to be zero. Therefore,

The domain of the function can be found below

To solve this problem, we will first find the standard form of the circle equation. Given a circle of radius r and center (h,k), the standard form of the circle equation would be

In our case, we have h=8 , k=6 and r=10. So the equation for the given circle would be

The general form of the circle equation can be obtained from expanding the squares on the left side of the equality sign. Recall that

So, applying this to the standard equation we get

So our equation becomes

Operating on the left side, we have

By subtracting 100 on both sides, we get

which the general form of the equation of the given circle.

Using a graphing tool, we have that the circle's graph would be

step 1

we have that

44=(1/2)[180-arc} ------> by exterior angle

solve for arc

88=180-arc

arc=180-88

arc=92 degrees

give me a minute to draw a figure with letters to better understand the problem

we have that

x+?=180 degrees -------> by form a linear pair (supplemenatry angles)

x=arc=92 degrees ------> by central angle

so

?=180-92

?=88 degrees

therefore

Given:

The radius of the circular garden is 50 feet.

First, find the circumference of the circle.

As we know that 6 inches equal 1/2 feet.

Answer: There are 628 flowers will be needed for 314 feet circular garden.

Answer:

295.25mm

Explanation:

If the chemist mixes 2362mm of a solution and needs to divide it equally into 8 breakers, to determine how much solution should be poured into each breaker, we have to divide 2362mm divide 8;

We are asked to find the probability that a data value in a normal distribution is between a Z score of -1.52 and -0.34

From the Z-table, the probability corresponding to the Z-score -1.52 is 0.0643

From the Z-table, the probability corresponding to the Z-score -0.34 is 0.3669

So, the probability is

Option A is the correct answer.

The height of the pole according to the attached image and parameters given is; 220 cm.

It follows from the task content that the height of the pole is to be determined from the parameters given.

From observation, the triangle formed by the situation is a right triangle.

Hence, the height of the pole can be determined by Pythagoras theorem; where, c² = a² + b².

Therefore, we have;

221² = 21² + p²

p² = 48,841 - 21²

p² = 48,400

p = √48,400

p = 220.

On this note, the height of the pole is; 220 cm.

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Answer:

Explanations:

a) The scientific notation is generally expressed as;

A is any real numbers between 1 and 10

n is an integer

Given that the total surface area of North America is 9,540,000 square miles. This is expressed in scientific form as;

From the scientific notation, A = 9.54 and n = 6

b) Given the scientific notation as shown:

Writing in standard form means writing in the normal way we write numbers/decimals. Hence;

ANSWER

27 in³

EXPLANATION

The volume of a cube is the cube of its side length, L,

So, if a cube has a side length of 3 inches, then its volume is,

Hence, the volume of a cube with a side length of 3 inches is 27 cubic inches.

Question:

Solve the following inequality:

Solution:

Consider the following inequality

solving for 12x, we get:

this is equivalent to:

solving for x, we get:

so that, the correct answer is:

One square has area 289 square meters, and the other has area

Then, since the sum of the two areas of the smaller squares is equal to the area of the big square, we have

The volume and surface area of a rectangular prism are given by the formulas below

In our case,

Thus, the answers are: Surface area=848ft^2, and Volume=1428ft^3

we have the expression

step 1

Factor 3

step 2

equate to zero

step 3

Solve

Rewrite as perfect squares

take the square root on both sides

the values of a are

a=4 and a=-3

therefore

Answer:

======================

We can represent the quadratic equation in vertex or standard forms.

Vertex form:

Standard form:

Use the vertex form with given coordinates of the vertex:

Use the other point to find the value of a:

The equation is:

Convert it to standard form:

Answer:

[tex]y=-6x^2-12x+2[/tex]

Step-by-step explanation:

Vertex form of a quadratic equation:  

[tex]y=a(x-h)^2+k[/tex]

where (h, k) is the vertex.

Given:

Substitute the given values into the vertex formula and solve for a:

[tex]\implies 2=a(0-(-1))^2+8[/tex]

[tex]\implies 2=a(1)^2+8[/tex]

[tex]\implies 2=a+8[/tex]

[tex]\implies a=-6[/tex]

Substitute the vertex and the found value of a into the vertex formula, then expand to standard form:

[tex]\implies y=-6(x-(-1))^2+8[/tex]

[tex]\implies y=-6(x+1)^2+8[/tex]

[tex]\implies y=-6(x^2+2x+1)+8[/tex]

[tex]\implies y=-6x^2-12x-6+8[/tex]

[tex]\implies y=-6x^2-12x+2[/tex]

Therefore, the quadratic function in standard form whose graph has the given characteristics is:

[tex]y=\boxed{-6x^2-12x+2}[/tex]

An exponential function which is represented by the table above is: f(x) = 4(1/2)^x

An exponential function simply refers to a mathematical function whose values are generated by a constant that is raised to the power of the argument. Mathematically, an exponential function can be modeled by using this equation:

f(x) = abˣ

Where:

From the table above, we would calculate the value of a and b:

At x = 0 and y = 4; the value of a (initial value) is 4.

Rate of change, b = Δy/Δx

Rate of change, b = 1/2

Substituting the parameters into the formula, we have;

f(x) = abˣ

f(x) = 4(1/2)^x

Check:

f(x) = 4 × (1/2)^x             f(x) =  4 * ( 1/2 )^x

f(x) = 4 × (1/2)²               f(x) = 4 × (1/2)⁻²

f(x) = 4 × 1/4                  f(x)  = 4 × 4

f(x) = 1                            f(x)  = 16

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For this type of problem we use the following formula:

where μ is the population mean, xi is each value from the population, and N is the size of the population.

First, we compute the population mean in order to do that we use the following formula:

Substituting each value of x_i in the above formula we get:

Now, we compute the difference of each x_i with the mean:

Squaring each result we get:

Now, we add the above results:

Dividing by N=5 we get:

Finally, taking the square root of 2.16 we obtain the standard deviation,

Answer:

Answer:

∠ FAE = 120°

Step-by-step explanation:

4x and 2x are a linear pair and sum to 180° , that is

4x + 2x = 180

6x = 180 ( divide both sides by 6 )

x = 30

then

∠ FAE = 4x = 4 × 30 = 120°

First let's calculate the slope of the straight line

For slopes that are perpendicular to each other we can use the following formula

Where

m1 = original slope

m2 = perpendicular slope

Now for the intersection

The equation of the line that passes through the point (-5,4) with a slope of -1/5 is

Given:

Solve the system of equations.

Equation (2) can be simplified as,

Moreover, the slope and y-intercept of both the equation of lines are the same.

It shows that the lines are coincident.

The system has an infinite number of solutions. Also, point (3,0) is one of the solutions.