Please help 8 through 10

-42 is the constant for all values of x. If the given the functions f(x) = 3x - 21 and g(x) = 3x+21

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

Given an arbitrary number x, lets calculate,

⇒ f(x) - g(x)

                   =  3x - 21 - (3x+21)

                   = 3x - 3x -21 -21

                   = 0 - 42

                   = -42

and thus -42 is the constant for all values of x.

Learn more about  linear equations

brainly.com/question/14323743

#SPJ4

As time passes, the amount of money in the account increases.

The amount in the account increases by $45.

The amount of money in the account when he started depositing is  $197.

A linear function is a function that has one independent variable and one dependent variable. A linear function increases at a constant rate over a period of time. When drawn on a graph, a linear function is usually a straight line.

The form of linear functions is:

y = a + mx

Where:

Looking at the given table, it can be seen that as time passes, the amount of money increases.

Rate of increase = (change in the amount of money) / change in the months

(557 - 467) / (8 - 6)

= 90 / 2

= $45

Amount in the account at the beginning = account balance at 6 months - (rate of increase x 6)

467 - (6 x 45)

467 - 270 = $197

To learn more about linear functions, please check: https://brainly.com/question/26434260

#SPJ1

Answer: Cynthia will receive $5,400, Moses will receive $8,100, John will receive $13,500

Step-by-step explanation:

       First, we will see how many "portions" the money is broken up into.

2:3:5 can become 2 + 3 + 5 = 10

       Next, we will see how much money each "portion" is worth using division.

$27,000 / 10 = 2,700

       Finally, we will multiply to see how much each person will receive.

2:3:5

2 * $2,700 = $5,400 [Cynthia]

3 * $2,700 = $8,100 [Moses]

5 * $2,700 = $13,500 [John]

Answer:

Cynthia's money = $5,400

Moses' money = $8,100

John's money = $13,500

Step-by-step explanation:

The full ratii of the money will be 2+3+5 = 10

Cynthia's ratio = 2 × $27,000

10

= 2 × 2,700

= $5400

Moses' ratio = 3 × $27,000

10

= 3 × 2,700

= $8100

John's ratio = 5 × $27,000

10

= 5 × 2,700

= $13,500

Answer:

Step-by-step explanation:

1/2

area of ∆PQR/ area of ∆WUV = 1/9

The soultion of the given equation 1/4x - 3/4 = 7/x for x is 9.

According to the given question.

We have an equation 1/4x - 3/4 = 7/x.

As we know that, as we know that, an equation is a condition on a variable such that two expressions in the variable should have equal value.

Therefore, the solution of the equation 1/4x - 3/4 = 7/x is given by

1/4x - 3/4 = 7/x

⇒ 1/4x - 7/x -3/4 = 0

⇒  1- 28/4x = 3/4

⇒ 27/4x = 3/4

⇒ 27  = (3/4)(4x)

⇒ 27 = 3x

⇒ 27/3  = x

⇒ x = 9

Hence, the soultion of the given equation 1/4x - 3/4 = 7/x for x is 9.

Find out more inofrmation about equation here:

https://brainly.com/question/10413253

#SPJ4

Answer:

dnenejnejehdhsbshsbsjsnsksknsosbs

Answer:

something

Step-by-step explanation:

onther something

The F-value for the interaction is [tex]3.42[/tex]. It is determined by the interaction of gender and race.

What is F-value?

The calculation of the F-value is used on statistics in analysis of variance which is denoted as ANOVA. The calculated value is determined from the ratio of explained variance to unexplained variance. When the F-values in an ANOVA is higher that means the variance is higher in the sample.

The F-statistic value is also used in the regression analysis to calculate the mean between the population. It also depends on the null hypothesis and when the null hypothesis is true. That means the F-value is always close to one most of the time. It is named as F-value after Sir Ronald Fisher. The variance is the dispersion of the value.

To learn more about the F-value from the given link:

https://brainly.com/question/27809115

#SPJ4

Using substitution method, the solution of the given system of equations is (-9, -26)

A system of equation can be solved using:

The given system of equations:

y = 3x+1   ............   (1)

2x - y = 8  .............. (2)

Notice the y variable is already isolated on the left side. Therefore, we can immediately use the substitution method.

Substitute y = 3x+1 into equation (2):

2x - y = 8

2x - (3x + 1) = 8

-x -1 = 8

-x = 9

Multiply by (-1)

x = -9

Substitute back x = -9 into equation (1)

y = 3x + 1

   = 3.(-9) + 1

   = -27 + 1 = -26

Hence, the solution is (-9, -26)

Learn more on how to solve system of equations here:

https://brainly.com/question/28130925

#SPJ4

The area of the given polygon which is a rectangle is; 28 sq. units

We are given the coordinates of the polygon as;

A(3,7)

B(5,7)

C(3,-7)

D(5,-7)

Now, by close inspection of the coordinates, we can tell that this polygon is a rectangle. Thus, we can deduce that;

AB = 5 - 3 = 2

CD = 5 - 3 = 2

BC = 7 + 7 = 14

AD = 7 + 7 = 14

Formula for area of a rectangle is;

A = Length * Width

A = 14 * 2

A = 28 sq. units

Read more about Area of Polygon at; https://brainly.com/question/27410302

#SPJ1

Answer:

find the LCM of the dimensions of the slabs

=420

Step-by-step explanation:

that is the solution above

The property tax be on a house that has a market value of $420,000 is A. $9,828

An expression is a number, or a variable, or a combination of numbers and variables and operation symbols.

Now it is given that,

Assessed value of a house = 60% of current market value

Property tax = 3.9% of the assessment value

Now the given market value of a house is $420,000

Assessed value of a house = 60% of $420,000

⇒ Assessed value of a house = 0.60 * $420,000

⇒ Assessed value of a house = $252,000

Thus, Property tax = 3.9% of $252,000

⇒ Property tax = 0.039 *$252,000

⇒ Property tax = $9,828

Thus, the property tax be on a house that has a market value of $420,000 is A. $9,828

To learn more about expression :

https://brainly.com/question/14342707

#SPJ1

Answer:

Identify angle C. It is the angle whose measure you know.

Identify a and b as the sides that are not across from angle C.

Substitute the values into the Law of Cosines.

Solve the equation for the missing side.

Step-by-step explanation:

For a right triangle, use the Pythagorean Theorem. For an isosceles triangle, use the area formula for an isosceles. If you know some of the angles and other side lengths, use the law of cosines or the law of sines.

Answer:

What is the maximum rectangular area that can be enclosed by 460 ft of fencing?

Step-by-step explanation:

What is the maximum rectangular area that can be enclosed by 460 ft of fencing?What is the maximum rectangular area that can be enclosed by 460 ft of fencing?

Answer:

it might be 3.8169 to the 6th power or 9.6296 to the 2nd power.

Step-by-step explanation:

but I might be

Answer:

Simple Interest = Rs1560

Step-by-step explanation:

A = P (1 + rt)

A = final amount

P = initial principal balance =  Rs8000

r = annual interest rate   =  [tex]6\frac{1}{2}[/tex]% = 0.065

t = time (in years) = 3 years

A = 8000*(1 +(0.065*3)) = 8000*(1+0.195) = 8000*(1.195) = 1560

Simple Interest (A) = Rs1560

The range of the function g(x) = - 1 / 2 | x - 6 | + 1 is ( - ∞, 1].

We are given a function:

g(x) = - 1 / 2 | x - 6 | + 1

We need to find the range of the function.

Now, we can see that the tip of the function will be formed when | x - 6 | = 0

x - 6 = 0

x = 6

For x = 6, we have the value of g(x) as

g(x) = - 1 / 2 | 6 - 6 | + 1

g(x) = 0 + 1

g(x) = 1

Also, since - 1 / 2 is negative, the function will have range from negative infinity to 1.

So, the range of the function will become:

( - ∞, 1]

Therefore, the range of the function g(x) = - 1 / 2 | x - 6 | + 1 is ( - ∞, 1].

Learn more about range here:

https://brainly.com/question/2264373

#SPJ9

The cost of each video is found to be $0.99.

Two-variable linear equations If a, b, and r are all real numbers (and a and b are not both equal to 0), ax+by = r is known as a linear equation in two variables.

(The x and y are the "two variables.") The coefficients of a equation ax+by = r are the numbers a and b.

Now, as per the stated question;

Let the number of video be denoted by 'x'.

Let the number of songs be denoted by 'y'.

Then,

Tameron downloaded 2 videos and 7 songs $10.91 .

2x + 7y = 10.91   ......(equation 1)

Jake downloaded 3 videos and 4 songs for $ 9.93.

3x + 4y = 9.93   ......(equation 2)

Solving equation 1 and 2 by elimination method, we get

x = 1.956 and y = 0.99

Therefore, the cost of each video is $0.99.

To know more about linear equation in two variables, here

https://brainly.com/question/13951177

#SPJ4

The given statement exists true. If the measures of the base angles of an isosceles triangle are integers, then the sum of those angles is 2 times that integer, so the sum is an even number. The three angles added together must add to 180.

An isosceles triangle in geometry is one with at least two equal-length sides. It can be stated as having exactly two equal-length sides or at least two equal-length sides, with the latter definition containing the equilateral triangle as an exception.

The characteristics of an isosceles triangle are as follows: There is an agreement between two sides. The base of an isosceles triangle refers to the third side of the triangle, which is unequal to the other two sides. The two angles that are opposite the equal sides line up perfectly.

If the measures of the base angles of an isosceles triangle are integers, then the sum of those angles is 2 times that integer, so the sum is an even number. The three angles added together must add to 180.

An even number plus an odd number will be an odd number, and 180 exists always even.

To learn more about isosceles triangle refer to;

https://brainly.com/question/25812711

#SPJ4

The fractions in the simplest form is: = -73/24.

Given the expression involving fractions, -7/8 + (-2⅙), we would solve as shown below:

-7/8 + (-2⅙)

Convert the mixed fraction to improper fraction

= -7/8 + (-13/6)

Distribute to eliminate the parentheses

= -7/8 - 13/6

= (-21 - 52)/24

= -73/24

Learn more about fractions on:

https://brainly.com/question/17220365

#SPJ1

Answer:

Step-by-step explanation:

[tex]\displaystyle\\\frac{1}{1+\frac{1}{\sqrt{3} } }=\\\\\frac{1}{\frac{1*\sqrt{3} +1}{\sqrt{3} } } =\\\\\frac{1*\sqrt{3} }{\sqrt{3}+1 }=\\\\\frac{(\sqrt{3})(\sqrt{3}-1) }{(\sqrt{3}+1)(\sqrt{3}-1) }=\\\\\frac{(\sqrt{3})(\sqrt{3})-(1)(\sqrt{3}) }{(\sqrt{3})^2-1^2 } =\\\\\frac{3-\sqrt{3} }{3-1} =\\\\\frac{3-\sqrt{3} }{2}[/tex]

Answer:

x < -2

Step-by-step explanation:

-2x + 4 > 8

     -4      -4

-2x > 4

divide both sides by -2

x < -2

Because we divided by a negative number, the sign gets flipped. So, the answer is x < -2

Hope this helps!

Answer: base x height divided by 2

Step-by-step explanation:

multiple the base and height then divide by 2

   The vertex, focus and directrix of the parabola y = x²/4 are:

  The parabola is a geometric shape that is formed from the intersection of a vertical plane in a cone.

  The parabola is a quadratic function, it is composed of a vertex, or inflection point, a focus and a directrix.

  In this case we have an expression given by:

y = x²/4

   We must find the canonical equation:

(y - 0)² = 1/4 (x - 0)²

(x - 0)² = 4 (y - 0)²

has the form

(x - h)² = 4p(y - k)

  This means that the vertex of this parabola is

v = (h, k)

v = (0,0)

  To know the focus we must know the value of "p".

4p = 4

p = 1

f = (0, 1)

d = -1

Learn more about parabolas in:

https://brainly.com/question/11780596

#SPJ4

Step-by-step explanation:

Given that

To find

So, according to the question

we have,

We have to find the value in kilowatt / hours power for per year basis

So, We know

Days in one year = 365

power in 3 days = 12 kilowatt/hours

For calculate power in single day, we have to divide power in 3 days by 3.

So power in a single day  = 12/3 kilowatt/hours

                                          = 4 kilowatt/hours

Now we have to multiply days in one year with power in a single day

     power for per year basis

                              = days in one year x power in a single day

Now, putting the all values,

                            = 365 x 4 kilowatt/hours.

                            = 1460 kilowatt/hours.

Answer:

To learn more about multiply and division, please click on the link:

https://brainly.com/question/15270559

#SPJ9

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here's your solution :

[tex] \qquad \sf  \dashrightarrow \: \cfrac{r + 6}{3r - 6} + \dfrac{r + 1}{3r - 6} [/tex]

[ since the denominator is same, we can just add the numerators ]

[tex] \qquad \sf  \dashrightarrow \: \cfrac{r + 6 + r + 1}{3r - 6} [/tex]

[tex] \qquad \sf  \dashrightarrow \: \cfrac{2r + 7}{3r - 6} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{6}{x - 1} - \dfrac{5x}{4} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{6(4) - 5x(x - 1)}{4(x - 1)} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{24- 5x {}^{2} + 5x}{4x - 4} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{2x}{5x + 4} + \dfrac{6x}{2x + 3} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{2x(2x + 3) + 6x(5x + 4)}{(5x + 4)(2x + 3)} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{4 {x}^{2} + 6x+ 30 {x}^{2} + 24x}{10 {x}^{2} + 15x + 8x + 12} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{34 {x}^{2} + 30x}{10 {x}^{2} + 23 {x}^{} +12 }[/tex]

Answer:

The answer is it travels 180 meters.

Step-by-step explanation:

To get the answer of how many meters the frisbee traveled in 12 seconds, all you have to do is multiply the number of meters the frisbee can do in 1 second by the number of seconds it traveled. The equation would be 15 x 12 = ? which would equal 180. That is how I got the answer that the frisbee traveled 180 meters in 12 seconds.

I hope I helped!