A triangle has vertices on a coordinate grid at R(-3,3)R(−3,3), S(-3,-9)S(−3,−9), and T(-9,-9).T(−9,−9). What is the length, in units, of \overline{RS}
RS
?

Step-by-step explanation:

When we plug in the values we get

[tex]f(g(x)) = ({x}^{2} - 3x + 1) - 4 \\ = {x}^{2} - 3x - 3 [/tex]

[tex]g(f(x)) = {(x - 4)}^{2} - 3(x - 4) + 1[/tex]

[tex] {x}^{2} - 3x - 3 = {(x - 4)(x - 4)} - 3x + 12 + 1 \\ {x }^{2} - 3x - 3 = {x}^{2} - 8x + 16 - 3x + 13 \\ \\ {x}^{2} - {x}^{2} - 3x + 8x + 3x - 3 - 16 - 13 = 0 \\ 8x - 32 = 0 \\ 8x = 32 \\ \frac{8x}{8} = \frac{32}{8} \\ x = 4[/tex]

Answer:

Cross two lines then put one line above the point of intersection and below the point of intersection. straightforward though

The maximum number of people who can go to the amusement park is 7 based on tickets cost of $20.50 per person

What is the total cost function for the amusement park?

The total cost is made up of cost of admission and parking and the tickets cost per person, which means that the total cost can be modeled as shown below based on the fact the number of persons that can attend is x

total cost=6.25+20.50x

total cost=155

155=6.25+20.50x

155-6.25=20.50x

148.75=20.50x

x=148.75/20.50

x=7(rounded to the nearest whole number)

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The logarithmic form of the equation is [tex]log_{\frac{1}{3} }(\frac{1}{27}) =3[/tex] .

We have given an equation [tex](\frac{1}{3})^3 =\frac{1}{27}[/tex] .

Taking log on both sides , we get

   [tex]log(\frac{1}{3})^3 =log(\frac{1}{27})[/tex]                    ..(1)

Applying the property of logarithm which is given by [tex]log_ab=bloga[/tex] in equation (1) ,we get

        [tex]3log(\frac{1}{3}) =log(\frac{1}{27})[/tex]

On rearranging the above equation , we get

         [tex]\frac{log(\frac{1}{27})}{log(\frac{1}{3})} =3[/tex]                          ..(2)

Applying the property of logarithm which is given by [tex]log_xy=\frac{log_ay}{log_ax}[/tex]\

  [tex]\frac{log(\frac{1}{27})}{log(\frac{1}{3})}[/tex]   can be written as  [tex]log_{\frac{1}{3} }\frac{1}{27}[/tex] using property

Putting in equation (2) , we get

     [tex]log_{\frac{1}{3} }(\frac{1}{27}) =3[/tex]

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The expression equivalent to [tex]\frac{12x^{4} }{4x^{16} }[/tex] is 3[tex]x^{-12}[/tex] or 3[tex]x^{4-16}[/tex].that is option C) is correct.

According to the question the expression that we have been given to us is :

               [tex]\frac{12x^{4} }{4x^{16} }[/tex]

Note that we know the property of exponent which states that if teh exponents with same base and different power are divided then the powers are subtracted. That is,  

                 [tex]\frac{x^{m} }{x^{n} } = x^{m-n}[/tex]          (1)

Now using this rule we will evaluate the equation given that is

             = [tex]\frac{12}{4} * \frac{x^{4} }{x^{16} } \\\\[/tex]

First we will divide 12/4 which gives 3 then we will apply the property of exponent to the exponent function which gives,

             = 3 [tex]x^{4-16}[/tex]

             = 3 [tex]x^{-12}[/tex]

Hence the expression equivalent to [tex]\frac{12x^{4} }{4x^{16} }[/tex]  is 3[tex]x^{-12}[/tex]or 3[tex]x^{4-16}[/tex] that is option C) is correct.

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The value for f(g(1))  = 1

Given:

           g(x) =3 x+2 and f(x)= x-2 / 3

           f(x)  = x-2 / 3

substitute x =1  into the function f(x). Then:

           f(1)  = 1-2 / 3

           f(1)  =  -1/3

Now, the next step is to substitute  f(1) into the function g(x)

           g(x) = 3 x+2

        g(f(1)) = 3 (-1/3)+2

         g(f(1)) = 1

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Answer:

Convert 93% to decimal and round. "Of" means to multiply.

93% = 0.93 ≈ 0.9

0.9 × 150(estimate) ≈ 135

Thus, the estimate is 135

Hope this helps!

Answer:

294 - 150 divided by 8 = A

Step-by-step explanation:

So, we already know, that we have $294 as our total. If we subtract $150, we get $144. The final step would be to divide it by $8 and that would be 18. There is 18 guests at the party.

Hope it helped!

Answer:

BC.

Step-by-step explanation:

Answer:

Line segment BC.

Step-by-step explanation:

Parallel lines are always the same distance apart at least. In this instance, FG and BC are parallel.

Answer:

You didn’t add the data chart. But I’ll try my best to help.

Step-by-step explanation:

If it landed on the same time multiple times than you will most likely land the same time again.

The complete statement is 30.9mm =  1. 21  in

Conversion of units is simply the conversion between different units of measurement for a particular quantity.

Given the statement;

30.9mm = in

It is important to note that;

25. 4 millimeters = 1 inch

Then;

30. 9 millimeters = x inches

Cross multiply

x ×  25. 4 = 30. 9 × 1

To make 'x' the subject

Divide both sides by 25. 4, we have;

x = 30. 9/ 25. 4

x = 1. 21 Inches

Thus, the complete statement is 30.9mm =  1. 21  in

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Answer:

The coordinates of G' after being translated is (-8,6)

Step-by-step explanation:

The original price of the helmet is 300.

In mathematics, a percent is a number or ratio expressed as a fraction of 100. It is often denoted using percentage sign "%".

Now it is given that,

Price of helmet = 195

Discount on helmet = 35% = 0.35

Let the original price be x.

Now since Price of helmet = 195

Thus, Original price = x - 0.35x = 0.65x

Hence we get

0.65x = 195

Dividing both the side by 0.65 we get

x = 195/0.65

Solving we get

x = 300

this is the required original price of the helmet.

Thus, the original price of the helmet is 300.

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The coupon gives Shanice 40% off the original price, based on the coupon of $20 on an original price of $50

What is the price after having considered the coupon?

The price of the pair of jeans after having considered the coupon is the original price of $50 minus the $20 coupon

price after the coupon=$50-$20

price after the coupon=$30

However, the task at hand is to determine the coupon as a percentage of the original price

coupon as % of original price=$20/$50

coupon as % of original price=40.00%

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Answer: (2,-2 )

Step-by-step explanation: That's where U is located on the Graph.

Answer: A=(pi)r^2

Step-by-step explanation:

multiply pi (3.14) times the radius to the power of 2.

The unit price that is going to be needed for the 31 minute ride would be 21.4 dollars.

We have the fare for 81 minutes to be $56. 70

Then we are to find the amount that would be needed for 31 minutes.

In order to get this value we would have to cross multiply

such that we would have

81 minutes = $56.70

31 minutes = ?

then 56 * 31 = 1736

1736 / 81

= 21.4 dollars.

Hence we would conclude that the unit price that is going to be needed for the 31 minute ride would be 21.4 dollars.

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The inequality expression is 8.8t < 55 + 6.6t and your friend will be ahead for at most 25 seconds

Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal

The given parameters are

Your rate, r1 = 6 miles per hour

Your friend's rate, r2 = 6.6 feet per second

Distance apart = 55 feet

Convert your rate to feet per second, we have

Your rate, r1 = 6 * 1.47 feet per second

Evaluate

Your rate, r1 = 8.8 feet per second

To calculate the time that your friend is ahead of you, we use the following expression

r1 * t < distance apart + r2 * t

So, we have

8.8t < 55 + 6.6t

Collect the like terms

So, we have

8.8t - 6.6t < 55

Evaluate the like terms

So, we have

2.2t < 55

Divide both sides by 2.2

So, we have

t < 25

Hence, the inequality expression is 8.8t < 55 + 6.6t and your friend will be ahead for at most 25 seconds

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Answer:

7.9

Step-by-step explanation:

yep

The value of QR is 5

A line segment can be defined as the part of a straight line bounded by two different end points, and also contains every point on the line between its endpoints.

From the information given, the line QS has segments, line QR , RS and QS with R and the midpoint between Q and S

Given the points;

We have that;

QR + RS = QS

substitute the values

5x + x + 3 = 9

collect like terms

6x = 9 - 3

6x = 6

Make 'x' the subject

x = 6/ 6

x = 1

But QR = 5x = 5(1) = 5

Thus, the value of QR is 5

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The complete question;

If R is the midpoint of QS and QR = 5x, RS = x + 3, and QS = 9, what is QR?

The number of times that the Great Wall of China is as long as the Panama Canal will be 2 × 10².

It should be noted that the Great Wall of China built in the 7th century BCE, is about 1 x 10⁴ miles long and the Panama Canal, built two thousand years later, is about 5 x 10^1 miles long.

Therefore, the number of times that the Great Wall of China is as long as the Panama Canal will be:

= 1 × 10⁴ / 5 × 10¹

= 2 × 10²

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Answer: The first one is 15 and the second one is 1.

Step-by-step explanation: I plugged in -4 where x is so the equation was (-4)^2-1 which equals 15.For other one i did the same thing except with the 2 so the equation was 3(2)-5 which equals 1.

Answer:

-2

Step-by-step explanation:

Integer math!

Answer:3) Find the domain of each, express answers in interval notation x+1 a) f(x) = 3x +2 b) f(x)=. 5 x² - 4x-12 x+1 for x < -2 ... 1 a) g(x) = f(x+10) b) g(x)

Step-by-step explanation:

The area of this rectangular object is equal to 12 × 10⁹ square microns.

Given the following data:

Mathematically, the area of a rectangle can be calculated by using this formula:

A = LW

Where:

Substituting the given parameters into the formula, we have;

Area of a rectangle = 6,000 microns × 2,000,000 microns

Area of a rectangle = 12 × 10⁹ square microns.

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answer is  y ≤ [tex]\frac{1}{3}x (-4)[/tex]

Given that,

Area of shaded inequality below solid line is positive

and  y-intercept of the solid line is equal to  - 4

therefore,

The inequality must be

y ≤ [tex]\frac{1}{3}x (-4)[/tex]

In Mathematics, inequality represents the mathematical expression in which both sides are not equal. If the relationship makes the non-equal comparison between two expressions or two numbers, then it is known as inequality in Maths. In this case, the equal sign “=” in the expression is replaced by any of the inequality symbols such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤) or not equal to symbol (≠). The different types of inequalities in Maths are polynomial inequality, rational inequality, absolute value inequality.

A system of linear inequalities in two variables includes at least two linear inequalities in the identical variables. When we solve linear inequality then we get an ordered pair. So basically, in a system, the solution to all inequalities and the graph of the linear inequality is the graph displaying all solutions of the system. Let us see an example to understand it.

the Linear inequality: 2x – y >1, x – 2y < – 1

The symbols ‘<‘ and ‘>’ express the strict inequalities and the symbols ‘≤’ and ‘≥’ denote slack inequalities. A linear inequality seems exactly like a linear equation but there is a change in the symbol that relates two expressions.

here is given step to easily find the value of inequality:

Step 1: The inequality is already in the form that we want. That is, the variable y y is isolated on the left side of the inequality.

Step 2: Change inequality to equality. Therefore, y > x + 1y>x+1 becomes y = x + 1y=x+1.

Step 3: Now graph the y = x + 1y=x+1. Use the method that you prefer when graphing a line. In addition, since the original inequality is strictly greater than symbol, \Large{>}>, we will graph the boundary line as a dotted line.

Step 4: The original inequality is y > x + 1y>x+1. The greater than symbol implies that we are going to shade the top area or region.

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[tex]125. 125^{\frac{1}{3} }[/tex] can be simplified into 625.

Prime factorization is the process of breaking down a number into its prime factors. Multiplying these prime numbers gives back the original number.

Prime factorization of 125 = 5 x 5 x 5 = [tex]5^{3}[/tex]

According to the law of indices, if a term with a power is raised to a power, then the powers are multiplied together.

i.e., [tex](x^{m})^{n} = x^{mn}[/tex]

Another law of indices says that if two terms having same base are multiplied together, then their indices are added.

i.e., [tex]a^{m} X a^{n} = a^{m+n}[/tex]

According to the given condition,

[tex]125. 125^{\frac{1}{3} }[/tex] = [tex]5^{3} .( 5^{3} )^{\frac{1}{3} }[/tex]

Applying the laws of indices mentioned above,

[tex]125. 125^{\frac{1}{3} }[/tex] = [tex]5^{3} .( 5^{3 X} ^{\frac{1}{3} })[/tex]

= [tex]5^{3} .( 5 )[/tex]  = [tex]5^{3 + 1}[/tex]

= [tex]5^{4} = 625.[/tex]

Thus,  [tex]125. 125^{\frac{1}{3} }[/tex] can be simplified into 625.

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Applying the linear pair postulate:

y = 30

m<ACB = 160°

According to the linear pair postulate, the sum of two adjacent angles that form a linear pair is equal to 180 degrees.

Given the following:

m<ACB = (4y + 40)°

m<DCE = (y - 10)°

Angles ACB and DCE are a linear pair. Therefore:

m<ACB + m<DCE = 180°

Substitute

(4y + 40) + (y - 10) = 180

Solve for y

4y + 40 + y - 10 = 180

Combine like terms

5y + 30 = 180

Subtract 30 from both sides

5y + 30 - 30 = 180 - 30

5y = 150

Divide both sides by 5

5y/5 = 150/5

y = 30

Find m<ACB:

m<ACB = (4y + 40)°

Plug in the value of y

m<ACB = 4(30) + 40

m<ACB = 120 + 40

m<ACB = 160°

Thus, applying the linear pair postulate:

y = 30

m<ACB = 160°

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Answer: 1b. 5x - 30, 1c. -8x - 32, -8x + 12, 1e. -6x + 21, 1f. 3( 3x - 9)

Step-by-step explanation:

You multiply the number outside of the parentheses by the numbers inside, if it's just an "x", you assume there's a 1 beside it, ex: 8(x + 2)... 8 multiplied by x will give you 8x, 8 multiplied by 2 will give you 16.

if the numbers are both negative when you multiply them it becomes a positive, ex: -8(x - 2)... -8 multiplied by x will be -8, and -8 multiplied by -2 will become positive 16.

But if one number is negative and the other is positive then the answer will be negative.