What are the slope of the two lines?

The base of the $4,560 which is 65% of the base is $7,015.38.

This  represented by the symbol %, is the division of any number by 100. The expression 25%, for example, means that 25 parts of a whole were divided into 100 parts.

The portion of 65% means that the amount given as $4,560 is only a part of the   whole amount known as base, which is unknown as the base, in other words, the base amount can be determined the portion divided by the percentage of the portion:

65%=$4560

1%=$4560/65

1%=$70.1538461538462

100%=$70.1538461538462*100

100%=$ 7,015.38

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Applying proportions, the decimal value is given by:

B. 32.064.

Santo got the wrong answer because he counted 6 and 4 as the tenths and hundredths digits, instead of hundredths and thousandths.

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using a rule of three, that can be either direct(cross multiplication) or inverse(line multiplication), deriving from proportional relationships. One example of application of proportions is for digit values in a number.

For this problem, we just have to apply the digit values of the number to find the decimal value, adding the factors, hence:

Hence:

30 + 2 + 0.06 + 0.004 = 32.064.

The decimal value is given by:

B. 32.064.

Santo got the wrong answer because he counted 6 and 4 as the tenths and hundredths digits, instead of hundredths and thousandths.

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The constant average rates of change of 1/6y + 3/8x = 24 is -9/4

Linear equations are equations that have constant average rates of change.

Note that the constant average rates of change can also be regarded as the slope or the gradient

The linear equation is given as

1/6y + 3/8x = 24

Multiply through the equation 1/6y+3/8x=24 by 24 to eliminate the fraction

So, we have

24 * 1/6y + 24 * 3/8x = 24 * 24

Evaluate the product

So, we have

4y + 9x = 576

Rewrite the equation as

So, we have

4y = - 9x + 576

Divide through the equation by 4

So, we have

y = - 9/4x + 144

A linear equation is represented as

y = mx + c

Where

m = rate of change

So, we have

m = -9/4

Hence, the constant average rates of change of 1/6y + 3/8x = 24 is -9/4

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Using the change of base formula the evaluated value of [tex]log_{3} 33[/tex]  is 3.184

Change of base formula is used to change the base of logarithm. It is used to write a logarithm of a number with a given base as the ratio of two logarithms each with the same base that is different from the base of the original logarithm.

According to the change of base formula :

[tex]log_{a} b = \frac{log_{x} b}{log_{x} a}[/tex]      

where base x is base 10

According to the question, we have to find the value of [tex]log_{3} 33[/tex]

Thus applying change of base formula we get

  [tex]log_{3} 33 = \frac{log_{10} 33}{log_{10} 3}[/tex]

calculating the value of log from the calculator we get,

    [tex]log_{3} 33 = \frac{1.519}{0.477}\\log_{3} 33 = 3.184[/tex]  

Thus using the change of base formula the evaluated value of [tex]log_{3} 33[/tex] is 3.184

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The logarithm function ( log 64 ) is not a common logarithm function as it does not have a base 10 but ahs a base e.

In mathematics, the common logarithm is the logarithm with base 10.

It is also known as the decadic logarithm and as the decimal logarithm function.

Here, we have the logarithm function as:

( log 64 )

Now, we can see that:

It does not have a base.

So, we will take the base as e.

So, it will not be a common logarithm function as having base 10 is an important characteristic of a common logarithm function.

Therefore, we get that, the logarithm function ( log 64 ) is not a common logarithm function as it does not have a base 10.

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25% in the decimal number system is 0.25.

So, we need to divide the number by 100 and we want to convert a number in percentage into decimals.

Then,

Therefore, 25% in decimals is 0.25.

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Answer:

12,300

Step-by-step explanation:

To round to the nearest hundred look at the tens place and if the number is a 5 or above add 1 to the hundreds place, in this case though the number is below 5 so you drop all the numbers behind it and nothing happens to the hundreds place

12,(3)46.6789

this is the hundreds place

12,3[4]6.6789

go to the tenths place and since the number is a 4 you drop it and the other numbers behind it.

Giving you the answer 12,300

Answer:

g(x) = | x + 2 | + 1

Step-by-step explanation:

the parent function f(x) = | x | has its vertex at the origin

the translated function has the form

g(x) = | x - h | + k

where (h, k ) are the coordinate of the vertex

the vertex of g(x) is at (- 2, 1 ) , then

g(x) = | x - (- 2) | + 1 , that is

g(x) = | x + 2 | + 1

The exponential function to model the height of the ball is

                  h = 72*[tex](1/2)^{n}[/tex]

According to the question we have been given that

         at first bounce the height of the ball is = 36 inches

and    at the second bounce the ball is at the height = 18 inches

The exponential model is given as

                             h = a.[tex]b^{n}[/tex]      (1)

 where h = height of the ball

            n = number of bounces

Putting the different values of h and n in equation (1) and getting the value of a and b, we get

 when h = 36 and n=1

                     36 = a.[tex]b^{1}[/tex]

                     36 = a.b   (2)

 when h = 18 and n =2

                     18 = a.[tex]b^{2}[/tex]

                     18 = a.b.b

                     18 = 36.b

                     b = 1/2

substituting the value of b in equation (2) we get

                    a = 72

Hence putting the value of a and b in equation (1),  the exponential function to model the height of the ball is

                   h = 72*[tex](1/2)^{n}[/tex]

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Answer:

5

Step-by-step explanation:

5+5=2(5)

10=10

The slope intercept form of the equation become y = (-1/3)x - 1/3.

According to the statement

We have to find that the slope intercept equation.

So, For this purpose, we know that the

Slope-intercept form is the equation of a straight line in the form y = mx + b where m is the slope of the line and b is its y-intercept.

From the given information:

y - 3x = 8

y = 3x + 8  

Slope = 3

And

Perpendicular lines have slopes that are negative reciprocals of each other. So, the new line will have a slope of = -1/3.

P(-4,1)

y - 1 = (-1/3)(x +4)

y - 1 = (-1/3)x - 4/3

y = (-1/3)x - 1/3.

So, The slope intercept form of the equation become y = (-1/3)x - 1/3.

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The distance between the points B and H on the coordinate plane is 4.48 units

See below for the complete question

The coordinates of the points B and H are given as:

(-2.63, 7) and (1.85,7)

Rewrite properly as

B = (-2.63, 7)

H = (1.85,7)

The distance between any two points on a coordinate plane is calculated using the following distance formula

d = √(x2 - x1)^2 + (y2 -y1)^2

Substitute the known values in the above distance equation

So, we have

d = √(-2.63 - 1.85)^2 + (7 - 7)^2

Evaluate the exponents

So, we have

d = √20.0704 + 0

Evaluate the sum

So, we have

d = √20.0704

Evaluate the exponent

So, we have

d = 4.48

Hence, the distance between the points B and H on the coordinate plane is 4.48 units

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Possible question

Find the distance between B (-2.63, 7) and H (1.85,7)

The solution to the inequality is x ≥ -10 2/3. On the graph, the solution to the inequality is to the right of the line

From the question, we are to solve the given inequality

The given inequality is

3x + 27 ≥ -5

Solving the inequality

3x + 27 ≥ -5

Subtract 27 from both sides of the inequality

3x + 27 -27 ≥ -5 - 27

3x  ≥ -32

Divide both sides of the inequality by 3

3x/3 ≥ -32/3

x ≥ -10 2/3

The graph of the inequality is shown below

Hence, the solution to the inequality is x ≥ -10 2/3. On the graph, the solution to the inequality is to the right of the line

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The equation is [tex]\frac{1}{2}x + \frac{1}{2}x[/tex]

Let the amounts of water that Sue's water bottle holds = x

According to the question,

given that,

Sue's water bottle holds the water = [tex]\frac{1}{2}x + \frac{1}{2}x[/tex] = [tex]\frac{2}{2}x[/tex] = x

Thus, assumption is true

Hence, the equation is [tex]\frac{1}{2}x + \frac{1}{2}x[/tex]

In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an ‘equal’ sign. The most basic and simple algebraic equations consist of one or more variables in math.

Different Types of Equations:

Some of the math equations used in algebra are:

Linear Equation

A linear equation may have more than one variable. A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation.

Quadratic Equation

This is a second-order equation. In quadratic equations, at least one of the variables should be raised to exponent 2.

Example:

[tex]a x^{2}[/tex] + b x + c = 0

Cubic Equation

This is a third-order equation. In cubic equations, at least one of the variables should be raised to exponent 3.

Example:

[tex]a x^{3}[/tex] + [tex]b x^{2}[/tex]+ cx + d = 0

[tex]a^{3}[/tex] – 27 = 0

Rational Equation

A rational equation is an equation that contains fractions with a variable in the numerator, denominator, or both.

Example:  

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

How to prove an equation

One way to prove that an equation is true is to start with one side (say, the left-hand side) and to convert it, by a sequence of equality-preserving transformations, into the other side. But remember that a proof must be easy to check, so each step deserves a justification. We keep the steps elementary, based on known facts of algebra. Also, a proof should always start with a statement of the claim that is being proved.

.

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Answer: The sum is always a rational number.

Step-by-step explanation:

Step-by-step explanation:

Given, sum of two rational numbers is always a rational number

We have to determine if the given statement is true or false

Consider two rational numbers 2/3 and 4/5

Sum of two numbers = 2/3 + 4/5

= [2(5) + 4(3)]/3(5)

= (10 + 12)/15

= 22/15

22/15 is a rational number.

Consider two rational numbers 2/3 and 1/3

Here, the denominators are same

Sum of two numbers = 2/3 + 1/3

= (2 + 1)/3

= 3/3

= 1/1

1/1 is also a rational number

Therefore, the given statement is true.

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{3}~,~\stackrel{y_1}{8})\qquad C(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x +3}{2}~~~ ,~~~ \cfrac{ y +8}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE B}}{(11~~,~~20)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x +3}{2}=11\implies x+3=22\implies \boxed{x=19} \\\\\\ \cfrac{ y +8}{2}=20\implies y+8=40\implies \boxed{y=32}[/tex]

The length of hJ is 17.

Given, the line HJ has a length

HJ = ?

HI = 14

IJ = 3

Since line HJ = HI + IJ

                       = 14+3

                        =17

Therefore the length of HJ will be 17.

A line section that can connect two places is referred to as a segment.

In other words, a line segment is just part of a big line that is straight and going unlimited in both directions.

The line is here! It extends endlessly in both directions and has no beginning or conclusion.

the measurement or extent of something from end to end; the greater of two or the greatest of three dimensions of a body is called length.

In geometry, a line segment is bounded by two distinct points on a line. Or we can say a line segment is part of the line that connects two points. A line has no endpoints and extends infinitely in both the direction but a line segment has two fixed or definite endpoints.

Types of Line Segment

Parallel Line. Two lines in the same plane either meeting each other or not.

Intersecting Lines.

Concurrent Lines.

Collinear Points.

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The total cost of business is 1,87,500

We are given the ratio of shares of two men. So, let the share of first person be 2x and share of second person be 3x.

It is also stated that smaller share is 75000. Out of the two shares, 2x is the smaller one. So, relating the two statements -

2x = 75000

x = 75000 ÷ 2

Performing division

x = 37500

So, finding the larger share now -

Larger share = 3x

Larger share = 3×37500

Performing multiplication

Larger share = 112500

Total cost of business = Smaller share + Larger share

Total cost of business = 75000 + 112500

Total cost of business = 1,87,500

Hence, the total cost of business is 1,87,500.

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Answer:

what is the question?

Step-by-step explanation:

There is no picture or question

Answer: Question

Step-by-step explanation:

we get the graph of the quadratic function by plotting the points on the graph paper.

We are given the quadratic function as:

f (x) = x²

We need to graph the function and find the values of the function for some given points of x.

For x = - 2, we get that:

f (x) = x²

f (- 2) = (- 2)²

f (- 2) = 4

For x = - 1, we get that:

f (x) = x²

f (- 1) = (- 1)²

f (- 1) = 1

For x = 0, we get that:

f (x) = x²

f (0) = (0)²

f (0) = 0

For x = 1, we get that:

f (x) = x²

f (1) = (1)²

f (1) = 1

For x = 2, we get that:

f (x) = x²

f (2) = (2)²

f (2) = 4

Plotting these points on the graph, we obtain the graph of the quadratic function.

Therefore, we get the graph of the quadratic function by plotting the points on the graph paper.

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Answer:

NM=FG

Step-by-step explanation:

Answer:

Segment EG and segment OM

Step-by-step explanation:

Comparing the lengths of segment EG and segment OM satisfies the side-side correspondence required for AAS congruence.

Answer:

78.75 or 78 3/4

Step-by-step explanation:

Answer:

7x+2

Step-by-step explanation:

-9x+8+2x-6

8-6

-9x+2+2x

combine like terms

-9x+2+2x

-9+2

7x+2

Answer:

1) [tex]m[/tex]∠JKL = 145°

2) [tex]m[/tex]∠IHG = 164°

3) [tex]m[/tex]∠NME = 50°

4) [tex]m[/tex]∠TUV = 178°

I hope this helps! (✿◠‿◠)

Answer:

64

Step-by-step explanation:

10^3 is 1000

64000/1000=64

Answer:-2/1

Step-by-step explanation:

rise is -2 and 1 is run

Answer:

36°C

Step-by-step explanation:

[tex]|-6(6)|=36[/tex]