Fred's car van travel 368 miles on one tank of gas. His has tank holds 16 gallons what is the unit rate for mules per gallon

The sum of all the angles in a triangle is always 180°.

We can write the equation and solve for the missing angle:

Solving for x:

The measure of the unknown angle is 72 degrees.

SOLUTION

We want to solve for v in

This means we should make v the subject, that is make it stand alone. This becomes

Next, we divide both sides by m, we have

Lastly, we square root both sides we have

Hence the answer is

SOLUTION

We want to tell the graph that represents the function

The graph of this function is shown below

Comparing this to what we have in the options,

we can see that the correct answer is option D

We make expressions for each afirmation

Where X is the first day, Y second day and Z the third

1. the sum of the 3 days gives us 30

2. Second day is 4/5 of the first day

3.Third day is 3/2 of the second day

Whit the expressions I try to represent everything as a function of X

I must represent Z in function of X, for this I can replace Y of the second expression in the third expression

So I have:

And I can replace on the first expression

I must find X

So, if I have X I can replace on this expressions to find de value:

Where X is 10

To check:

The result is correct, therefore:

We have

We have with the third equation

We substitute in the first and second equation

Then we have

We substitute

if x=0

and if x=0

ANSWER

x=0

y=4

z=-2

It is required that we find an augmented matrix for the system.

Recall that a matrix that contains the coefficients and constant terms of a system of equations, each written in the standard form with the constant terms to the right of the equals is called an augmented matrix.

The given system of equations is:

The first, second, and third equations can be rewritten to get:

Hence, the augmented matrix using the system is:

A) To do that we will draw a line inside the triangle that is perpendicular to the base as I have don above.

B) We will also do the same for B

Given the polynomials, let's simplify the polynomials and label them.

Polynomial 1:

After simplifying, we have the simplified form:

Since the highest degree is 2, this is a quadratic polynomial.

It has 3 terms, therefore by number of terms it is a trinomial.

Polynomial 2:

Simplified form:

The highest degree is 1, therefore it is linear

It has 2 terms, therefore by number of terms it is a binomial

Polynomial 3:

Simplified form:

The highest degree is 0 since it has no variable, therefore it is a constant.

It has 1 term, by number of terms it is a monomial.

ANSWER:

Polynomial Simplified form Name by degree Name by nos. of ter

1 6x²-x-1 quadratic Trinomial

2 3x + 4 Linear Binomial

3 2 Constant Monomial

The polynomial that represents the rollercoaster, using the Factor Theorem, is given as follows:

y = 400(x - 1)²(x + 1)(x² + 0.1)(x + 5).

The Factor Theorem states that a polynomial function with zeros [tex]x_1, x_2, \codts, x_n[/tex], also represented by factors [tex]x - x_1, x - x_2, \cdots x - x_n[/tex] is given by the rule presented as follows:

[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]

In which a is the leading coefficient of the polynomial function with the given roots.

For this problem, the requirements are as follows:

The roots will be given as follows:

Hence the function is:

y = a(x - 1)²(x + 1)(x² + 0.1)(x + 5).

At x = 0, the function assumes a value of 250, hence the leading coefficient is obtained as follows:

0.5a = 200.

a = 400.

Thus the function is:

y = 400(x - 1)²(x + 1)(x² + 0.1)(x + 5).

Which has the desired features, as shown by the image at the end of the answer.

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ANSWER

3/4 : 3/3

EXPLANATION

We have the ratio of cups of banana to cups of apple juice to be 1/4 : 1/3

Equivalent ratios can be gotten by multiplying the ratio with a common integer.

This means we can multiply bot sides of the ratio with the same integer e.g. 2, 4, 7...

Since from the diagram, the next equivalent ratio is given (2/4 : 2/3), we can obtain the next equivalent ratio by multiplying the ratio by 3. That is:

3/4 : 3/3

Therefore, the correct option is 3/4 : 3/3

Common ratio = 1.75

17th term = 123,802.31

Given the following parameters:

Since the sequence is geometric, the nth term of the sequence is given as;

a is the first term

r is the common ratio

n is the number of terms

If the first term a1 = 16, then;

Similarly, if the fifth term a5 = 150.06, then;

Hence the common ratio to the nearest hundredth is 1.75

Next is to get the 17th term as shown;

Hence the 17th term of the sequence to the nearest hundredth is 123,802.31

For line 1 =

The coordinates given are (-8,-55) , (10,89)

The slope of the line is

For line 2 =

The coordinates given are (9,-44) , (4,-14)

The slope of the line is

The lines are not perpendicular or parallel because the slope of the lines does not satisfy the condition of perpendicular or parallel slopes.

Hence the answer is neither.

Given statement:

20 is the same as the sum of 4 and g

Let us break down the statement into parts and then write the equation

the sum of 4 and g:

This sum is equal to 20:

Hence, the equation is:

Solving for the variable:

Answer Summary

Problem

8 ( 11 - 2b ) = -4 ( 4b - 22 )

Solution

We can distribute the terms in the equation and we got:

88 -16b = -16b +88

If we add 16b in boh sides we got:

88 =88

Then for this case we can conclude that this equation has infinite solutions

To Show that if the diagonals of a quadrilateral bisect each other at right angles then it is a rhombus.

Proof:

Let ABCD be a quadrilateral such that the diagonals bisect each other,

Therefore,

the diagonal bisect at right angle.

Hence,

to prove: ABCD is rombus,

Rombus: its is a parallelogram, with all the sides equal.

so, to prove ABCD a parallelogram.

consider the triangle,

thus, traingle

consider the sides, AD and BC

with the transversal ac,

The angles,

are alterntaive angles. they are equal.

this implies, AD is parallel BC.

similarly, AB is parallel to DC.

Hence, AD II BC and AB II DC.

In ABCD the opposite sides are parallel,

This implies, ABCD is parallelogram.

Now, to prove that ABCD is a rombus.

for that all the sides of ABCD should be equal.

now, consider the triangle AOD and COD.

By SAS congruent rule,

Traingles,

Thus, by CPCT Corresponding parts of congruent triangles ,

AD= CD

we know that,

AD=CB and CD=AB

Thus, AD=CD=CB=AB.

hence, all the sides are eqaul and ABCD is parallelogram.

So, ABCD is a rhombus.

well, what's 40% of 20?

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{40\% of 20}}{\left( \cfrac{40}{100} \right)20}\implies 8[/tex]

This is a problem about combinations where the order doesn't matter. The solution is usually written as 7C2 (seven choose two) and has the value

Comment: 7C2 is the answer to the question "How many pairs (in our case, these pairs are seen as games played) can we form from a group of 7 things?".

1) As the Domain is the set of inputs (x) for that function, as we can see in the graph.

There's one point in the graph x =8, where should be an asymptote i.e. a vertical or horizontal line that prevents both graphs do not trespass.

So we can write the Domain as

D =(-∞, 8) U (8, ∞)

Because in this function, the point x=8 is not included, and from point 8 on the function continues.

The measure of the angle is 63 degrees

Let the angle in question be x degrees.

The supplement is (180 - x) degrees, and the complement is (90 - x) degrees.

Given that the supplement is 63 degrees more than twice the measure of its complement, we have the equation:

180 - x = 2(90 - x) + 63

Solving for x in the above:

180 - x = 180 - 2x + 63

2x - x = 180 - 180 + 63

x = 63

ANSWER:

- 10

STEP-BY-STEP EXPLANATION:

We have the following expression

We know that when dividing from, the nvert-and-multiply rule must be applied, as follows

Therefore the result of the operation is -10

Given:

The data set of the monthly rent paid by 7 tenants

990, 879, 940, 1010, 950, 920, 1430

We will find the mean of the data:

Mean = Sum/n

n = 7

Sum = 990+879+940+1010+950+920+1430 = 7119

Mean = 7119/7 = $1017

One of the tenants change from 1430 to 1115

The mean after the change will be as follows:

Sum = 990+879+940+1010+950+920+1115 = 6804

n = 7

Mean = 6804/7 = 972

So, the answer will be:

Mean before the change = 1017

Mean after the change = 972

The area enclosed by y² = 8 - x and (y + 1)² = −3 + x is 243.

We are given y² = 8 - x and (y + 1)² = −3 + x.

To sketch and calculate the area enclosed, find the intersection points:

y² = 8 - x ⇒ x = 8 - y²

Substitute x = 8 - y² in (y + 1)² = −3 + x:

(y + 1)² = −3 + 8 - y²

y² + 2y + 1 = −3 + 8 - y²

2y² + 2y - 4 = 0

y² + y - 2 = 0

(y - 1) (y + 2) = 0

y = 1, -2

Substitute y = 1, -2 in x = 8 - y²:

When y = 1, x = 8 - (1) ⇒ x = 7

When y = -2,  x = 8 - (-2)² ⇒ x = 4

Thus, the point of intersection is (4, -2) and (7, 1).

Graph of the region enclosed by y² = 8 - x and (y + 1)² = −3 + x:

The area of the enclosed region is given by:

A = [tex]\int \, \int \,dA[/tex]

[tex]=\int\limits^7_{-2} \, \int\limits^{3+ (y+1)^{2} } _{8 - y^{2} } \, dxdy[/tex]

[tex]=\int\limits^7_{-2} \, (x)^{3+ (y+1)^{2} } _{8 - y^{2} } \, dy[/tex]

[tex]=\int\limits^7_{-2} \, [{(3+ (y+1)^{2} )} -({8 - y^{2} })] \, dy[/tex]

[tex]=\int\limits^7_{-2} \, {(2 y^{2} + 2y -4) } \, dy[/tex]

[tex]=(\frac{2y^3}{3} + \frac{2y^2}{2} -4y)^7_{-2}[/tex]

[tex]=\frac{686}{3} + 49 - 28 + \frac{16}{3} - 4 - 8[/tex]

= 343

Hence, the area enclosed by y² = 8 - x and (y + 1)² = −3 + x is 243.

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Solution:

Concept:

The distributive property of multiplication states that when a number is multiplied by the sum of two numbers, the first number can be distributed to both of those numbers and multiplied by each of them separately, then adding the two products together for the same result as multiplying the first number by the sum.

The expression is given below as

Hence,

The final answer is

Given:

Edges of the polyhedron, E = 10

Vertices, V = 5

A polyhedron is a three-dimensional figure.

Let's find the number of faces using Euler's formula.

To find the number of faces of the polyhedron, we have the Euler's formula:

V + F - E = 2

Substitute values into the formula:

5 + F - 10 = 2

Combine like terms:

F + 5 - 10 = 2

F - 5 = 2

Add 5 to both sides:

F - 5 + 5 = 2 + 5

F = 7

Therefore, the number of faces of the polyhedron is 7

ANSWER:

7 faces

a) Since we are interested in the number of TVs that can be sold at $400, we need to use the Demand model equation and set p=400; thus,

The answer to part a) is 20 TVs per week.

b) Set N=N, then

Therefore, using p=300 and solving for N,

The answer to part b) is 720 TVs per week.

c) In part b), we found that when supply and demand are equal, p=300. Thus, the answer to part c) is $300

(a + 15) •2

Multiply each term in the parentheses by 2

a*2 + 15*2

2a + 30

With the points (8. 4) (-6, -6) (-10, 12) (2,-4). What are the new points if the

scale factor of dilation is X?

we know that

The rule of the dilation of a point is equal to

(x,y) -------> (ax, ay)

with a scale factor a

so

In this problem

the scale factor is x

therefore

(8. 4) --------> (8x. 4x)

The given equation corresponds to a parabola:

The y-intercept of the parabola is the point when it crosses the y-axis, at this point x=0, to determine this value you have to replace the formula with x=0 and calculate the value of y:

Solve the exponent first, then the multiplication

The y-intercept for the given function is (0,-18)

Given:

Principal (P)=$200

Rate of interest (r) =4%

time (t)=30 years

Number of times compounded per year(n) = 12

Required- the amount.

Explanation:

First, we change the rate of interest in decimal by removing the "%" sign and dividing by 100 as:

Now, the formula for finding the amount is:

Put the given values in the formula, we get:

Solving further, we get: