If S is the midpoint of RT, RS = 5x + 17, and ST = 8x - 31, find RS. Show work!

Answer:

60

Step-by-step explanation:

Answer:

Ishaan is currently 15 years old.

Step-by-step explanation:

Let B represent Ben's current age and I represent Ishann's current age.

Ben is four times as old as Ishaan. In other words:

[tex]B=4I[/tex]

Six years ago, Ben was six times as old as Ishaan. In other words:

[tex]B-6=6(I-6)[/tex]

Solve for I. Substitute:

[tex](4I)-6=6(I-6)[/tex]

Distribute:

[tex]4I-6=6I-36[/tex]

Subtract 4I from both sides and add 36 to both sides:

[tex]2I=30[/tex]

And divide both sides by two. Hence:

[tex]I=15[/tex]

Ishaan is currently 15 years old.

Answer:

Age of Ishaan = 15 years

Step-by-step explanation:

Let Ishaan's age = x years

Age of Ben = 4 * x = 4x years

6Years ago:

Age of Ishaan = x - 6

Age of Ben = 4x - 6

6 years ago, Ben was 6 times as old as Ishaan

So, Age of Ben = 6 * Ishaan's age

     4x - 6 = 6 *(x-6)

4x - 6 = 6x - 36

Add 36 to both sides

4x - 6 + 36  = 6x  

4x + 30 = 6x

Subtract '4x' from both sides

30 = 6x - 4x  

30 = 2x

2x = 30

Divide both by 2 sides

x = 30/2

x = 15

A graph of the image of ABC under a dilation whose center is P and scale factor is 1/3 is shown in the image below.

In Geometry, dilation can be defined as a type of transformation which typically changes the size of a geometric shape, but not its shape. This ultimately implies that, the size of the geometric shape would be increased (enlarged) or decreased (reduced) based on the scale factor applied.

In this exercise, we would use an online graphing calculator to plot the image of ABC after a dilation by a scale factor of 1/3 centered at P.

Based on the image (see attachment), we can logically deduce that each vertex is 1/3 times as far from center P as the original vertex and each segment is 1/3 times as long as the original:

AC = 6.7/3 = 2.2

AB = 12.4/3 = 4.1

CB = 12.7/3 = 4.2

Read more on dilation here: brainly.com/question/20482938

#SPJ1

Answer:

C

Step-by-step explanation:

distance between two points formula:

[tex]d = \sqrt{( x2 - x1) ^{2} + (y2 - y1) ^{2} } [/tex]

where the x and y values are derived from the known points

we are given the points (2, 4) and (8, -8)

given these two points let's define each variable

x1 = 2

x2 = 8

y1 = 4

y2 = -8

we now substitute in these values into the formula

[tex]d = \sqrt{(8 - 2) ^{2} + ( - 8 - 4)^{2} } [/tex]

now we evaluate the expression using PEMDAS

first we do the subtraction inside of the parenthesis

8 - 2 = 6

-8 - 4 = -12

d = sqrt(6)^2 + (-12)^2

next we do the exponents

6^2 = 36

-12^2 = 144

d = sqrt( 144 + 36 )

next do the addition inside of the parenthesis

144 + 36 = 180

d = sqrt ( 180 )

finally we do the square root of 180

sqrt ( 180 ) = 13 ( rounded to the nearest whole )

d = 13

The functions f and g have different axis of symmetry

The y-intercept of f is higher than the y-intercept of g

Over the interval [-6, -3], the average rate of change of f is more rapid than the average rate of change of g

The known value in the question includes the following

The given table of f(x) and x, from which we have;

The point of the minimum value, which is the vertex = (-3, -10)

The axis of symmetry, of a parabola is the vertical line passing through the vertex such that the y-values at equal distance from the line on either side are equal is the line x = -3

The y-intercept, which is the point the graph intercepts with the y-axis or where x = 0 is the point (0. 8)

Over the interval [-6, -3], the average rate of change of f = (-10 - 8)/(-3 -(-6)) = -6

From the graph of g(x), we have;

The axis of symmetry is the line x = -3

The y-intercept = (0, -2)

Over the interval [-6, -3], the average rate of change of g ≈ (6 - (-2))/(-3 -(-6)) = 8/3

Therefore, we have the correct options as follows;

The functions f and g have different axis of symmetry

The y-intercept of f is higher than the y-intercept of g

Over the interval [-6, -3], the average rate of change of f is more rapid than the average rate of change of g

Learn more about parabola here;

https://brainly.com/question/22213822

Answer:

[tex]4+2\sqrt{31}\text{ by } -4+2\sqrt{31}[/tex]

Or about 15.136 centimeters by 7.136 centimeters.

Step-by-step explanation:

Recall that the area of a rectangle is given by:

[tex]\displaystyle A = w\ell[/tex]

Where w is the width and l is the length.

We are given that the length is 8 centimeters longer than the width. In other words:

[tex]\ell = w+8[/tex]

And we are also given that the total area is 108 square centimeters.

Thus, substitute:

[tex](108)=w(w+8)[/tex]

Solve for w. Distribute:

[tex]w^2+8w=108[/tex]

Subtract 108 from both sides:

[tex]w^2+8w-108=0[/tex]

Since the equation is not factorable, we can use the quadratic formula:

[tex]\displaystyle x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

In this case, a = 1, b = 8, and c = -108. Substitute and evaluate:

[tex]\displaystyle \begin{aligned} w&= \frac{-(8)\pm\sqrt{(8)^2-4(1)(-108)}}{2(1)} \\ \\ &=\frac{-8\pm\sqrt{496}}{2}\\ \\ &=\frac{-8\pm4\sqrt{31}}{2} \\ \\ &=-4 \pm 2\sqrt{31} \end{aligned}[/tex]

So, our two solutions are:

[tex]w=-4+2\sqrt{31} \approx 7.136 \text{ or } w=-4-2\sqrt{31}\approx -15.136[/tex]

Since width cannot be negative, we can eliminate the second solution.

And since the length is eight centimeters longer than the width, the length is:

[tex]\ell =(-4+2\sqrt{31})+8=4+2\sqrt{31}\approx 15.136[/tex]

So, the dimensions of the rectangle are about 15.136 cm by 7.136 cm.

Answer:

56

Step-by-step explanation:

Zoe : hanna

3         7

Zoe got 24

3*8 = 24

so multiply each side by 8

Zoe : hanna

3*8         7*8

24           56

Hanna got 56

Answer: £21007.22

Step-by-step explanation:

First, find the interest amount using the formula SI = (P × R × T) / 100.

SI = (P × R × T) / 100 = (18790 × 5.9 × 2)/100 = 221722/100 = £2217.22

The total amount = principle amount + interest amount

= £18790 + £2217.22 = £21007.22

Answer:

Step-by-step explanation:

1

There are 71 people who are female OR study French OR both.

To find the number of people who are female OR study French OR both, we need to add the numbers in the Female row (excluding the "Total" column) and the numbers in the French column (excluding the "Total" row), and then subtract the number of people who study both French and are female, as they were counted twice.

Number of people who are female = 43

Number of people who study French = 28

Number of people who study both French and are female = 16

Total = Number of people who are female + Number of people who study French - Number of people who study both French and are female

Total = 43 + 28 - 16

Total = 71

So, there are 71 people who are female OR study French OR both.

To know more about people   here

https://brainly.com/question/13604758

#SPJ2

Answer:

length = 1696 m

breadth = 571 m

Step-by-step explanation:

perimeter = 4534 m

let breadth be b

so length = b + 1125 m

so

perimeter of rectangular garden = 2(l+b)

4534 m = 2(b+1125m+b) {substituting the value}

or, 4534 m = 2(2b+1125m)

or, 4534 m = 4b + 2250 m

or, 4534 m - 2250m = 4b

or, 2284m = 4b

or, b = 2284m/4

so, b  = 571m

so, l = b + 1125 m

= 571 m + 1125m

= 1696 m

Answer:

Take the gross amount of any sum (items you sell or buy) – that is, the total including any VAT – and divide it by 117.5, if the VAT rate is 17.5 per cent. (If the rate is different, add 100 to the VAT percentage rate and divide by that number.)

Answer:

divide by 117.5 if the rate different, add 100 to the percentage and divide by the number therefore multiply by 100 to get the total

Step-by-step explanation:

the formula to calculate vat percentage

Answer:

x =1 08

Step-by-step explanation:

Answer:

I Will explained you youuuuuu<uuuuuuuuuu

Answer:

10 the next day

Step-by-step explanation:

Using the least common multiple

3, 6, 8

The least common multiple is 24

24 hours from 10 the next day

Answer:

E500

Step-by-step explanation:

Given x the original price of the coat

437.5 + 0.125x = x

437.5 = 0.875x

x = E500

Answer:

Step-by-step explanation:

If AB and DE are equidistant from the center, that means that they are the same length. We set the equations equal to one another and solve for x:

3x - 7 = 5(x - 5) and

3x - 7 = 5x - 25 and

18 = 2x so

x = 9. Now we sub that into the expression for AB (or DE since they're the same length):

3(9) - 7 = 20

Both AB and DE measure 20 units.

Answer: $600

Step-by-step explanation:

Given

Anual makes [tex]\$12.50[/tex] an hour

For 48 hours, he makes

[tex]\Rightarrow 48\times 12.5\\\Rightarrow \$600[/tex]

Thus, he will make $600 for 48 hours

Answer:

angle bisector

Step-by-step explanation:

Since the line divided the top angle into two equal pieces we call this an angle bisector.

Answer:

x > -24

Step-by-step explanation:

-x/4 < 6

Multiply each side by -4, remembering to flip the inequality

-x/4  *-4> 6*-4

x > -24

[tex]\boxed{\large{\bold{\red{ANSWER~:) }}}}[/tex]

[tex]\bold{ Note - }[/tex]

Step-by-step explanation:

The real part (red) and imaginary part (blue) of the Riemann zeta function along the critical line Re(s) = 1/2. The first non-trivial zeros can be seen at Im(s) = ±14.135, ±21.022 and ±25.011. The Riemann hypothesis, a famous conjecture, says that all non-trivial zeros of the zeta function lie along the critical line.

Answer:

P + Q = 1

Step-by-step explanation:

Given: [tex]\frac{1+\sqrt{3} }{1-\sqrt{3} }[/tex]  = P - [tex]\sqrt{Q}[/tex]

This is a question on surd, so we need to rationalize the denominator to have;

[tex]\frac{1+\sqrt{3} }{1-\sqrt{3} }[/tex]  * [tex]\frac{1+\sqrt{3} }{1+\sqrt{3} }[/tex] = [tex]\frac{1+\sqrt{3}+\sqrt{3} + 3}{1+\sqrt{3}-\sqrt{3} -3 }[/tex]

   = [tex]\frac{4+ 2\sqrt{3} }{1-3}[/tex]

   = [tex]\frac{4+2\sqrt{3} }{-2}[/tex]

   = -2 - [tex]\sqrt{3}[/tex]

Thus,

-2 - [tex]\sqrt{3}[/tex] = P - [tex]\sqrt{Q}[/tex]

⇒ P = -2 and Q = 3

Therefore, the value of P + Q = -2 + 3

                                                 = 1

Thus,

P + Q = 1

Answer:

-3y/x^2

Step-by-step explanation:

-5/15 = -3

When dividing variables with powers, subtract the powers.

x^2 - x^4 = x^-2

y^3 - y^2 = y

z^4 - z^4 = 0

therefore we have -3 x^-2 y

Since we can't have negative powers, divide (move the x^-2 to the bottom and make positive)

-3y / x^2

Hope this helps! Let me know if I am wrong ^w^

Answer:

- y/3x^2

Step-by-step explanation:

The negative sign goes between y and 3x^2

Answer:

0

Step-by-step explanation:

LN is an horizontal segment. it means that the line is parallel to x axis so its slope is 0

Answer:

7/12

Step-by-step explanation:

10 white balls and 14 red balls = 24 balls

P( red) = number of red balls / total balls

           =14/24

           =7/12

Answer:

25.71

Step-by-step explanation:

πr + d

3.142(5) + 10

= 25.71

i think

Answer: u = [tex]\frac{7}{8}[/tex] or 0.875

Step-by-step explanation:

Let us convert this statement to a question

[tex]4^{2}[/tex]-8u-9 = 0

16-8u-9 = 0

-8u = 0+9-16

-8u = -7

u = -7 ÷ -8

u = [tex]\frac{7}{8}[/tex] or 0.875

Answer:

D is the answer

Step-by-step explanation:

39 is 3 times greater than 13 and 27 is 3 times greater than 9

Answer:

the perimeter is 30 units