Use the number line below, where , RS=6y+2, ST=15y+9 and RT=5y-13. Find
the value of RS, ST, and RT *

Answer: (h-g)(-2)=18

Step-by-step explanation:

(h – g) (-2) means the same as subtracting h(-2) and g(-2). Since we are given h(x) and g(x), we can use them to solve. There are two ways to solve. One is to find h(-2) and g(-2), and then subtract them. Another way is to do (h-g)(x), then plug in x=-2. I will show both methods.

Method 1

h(-2)=2(-2)²-5(-2)+2                   [exponent]

h(-2)=2(4)-5(-2)+2                      [multiply]

h(-2)=8+10+2                               [add]

h(-2)=20

g(-2)=(-2)²-2(-2)-6                       [exponent]

g(-2)=4-2(-2)-6                            [multiply]

g(-2)=4+4-6                                 [add then subtract]

g(-2)=2

(h-g)(-2)=20-2                            [subtract h(-2) and g(-2)]

(h-g)(-2)=18

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Method 2

(h-g)(x)=2x²-5x+2-(x²-2x-6)      [distribute -1]

(h-g)(x)=2x²-5x+2-x²+2x+6        [combine like terms]

(h-g)(x)=x²-3x+8

(h-g)(-2)=(-2)²-3(-2)+8                [plug in x=-2, exponent]

(h-g)(-2)=4-3(-2)+8                    [multiply]

(h-g)(-2)=4+6+8                          [add]

(h-g)(-2)=18

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Now, we know that (h-g)(-2)=18. We confirmed this with both methods.

Step-by-step explanation:

F(x) = ∫ₓᵃ sin(2t) dt

Use the identity:

-F(x) = ∫ₐˣ sin(2t) dt

Take derivative using fundamental theorem of calculus.

-F'(x) = sin(2x)

F'(x) = -sin(2x)

Answer:

x = 17

Step-by-step explanation:

4x +22 = 90

4x = 68

x = 68/4

x = 17

h c=100-s thats the cooreect answer

Answer:

G

Step-by-step explanation:

ion kno how to explain‍♀️‍♀️

Answer:

Step-by-step explanation:

x+y=180

y=5*x+6

so

x+5x+6=180

6x=180-6

6x=174

x=174/6

x=29 degrees

y=29*5+6

y=145+6=151

y=151 degrees

Answer:

14x-4

Step-by-step explanation:

length:2x+3

width:5x-5

perimeter of rectangle:2(l+b)

:2(2x+3+5x-5)

:2(7x-2)

:14x-4

•••The perimeter of rectangle(p)=14x-4

Answer: Divide Kayak budget by rental rate

Step-by-step Explanation:

As Joshua is renting for himself alone, the two available options would be the Single Kayak and the Single Sea Kayak.

He can determine the number of hours to rent a Kayak for by dividing his Kayak Budget by the rental rate per hour of the 2 options available to him.

Budget available = $50

Rental rate = $15 per hour

Hours he can rent = 50/15

= 3.33 hours

Budget available = $50

Rental rate = $18 per hour

Hours he can rent = 50/18

= 2.78 hours

Answer:

V = 4316.75 π

Step-by-step explanation:

Given that:

[tex]y = 5 \sqrt{49 -x^2}[/tex] y = 0, x = 2, x = 4

[tex]V = \pi \int \limits ^{x=4}_{x=2} y^2 \ dx[/tex]

where;

y² = 25 (49 - x²)

[tex]V = 25 \pi \int \limits ^4_2 (49-x^2) dx[/tex]

[tex]V = 25 \pi [ (49x-\dfrac{x^3}{3}]^4_2[/tex]

[tex]V = 25 \pi [ 49\times 4 -\dfrac{4^3}{3} - 2][/tex]

[tex]V = 25 \pi [ 196-21.33 - 2][/tex]

[tex]V = 25 \pi [ 172.67][/tex]

V = 4316.75 π

Given :

Karen spent 3 2/5 hours on it and figures that she is about 4/8 done.

To Find :

How many more hours will she need to spend on this project .

Solution :

Simplifying time spend in normal fraction .

[tex]t=3\dfrac{2}{5}=\dfrac{(3\times 5)+2}{5}\\\\\\t=\dfrac{17}{5}\ hours[/tex]

Now , time taken to complete full project .

[tex]x=\dfrac{17}{5} \times \dfrac{8}{4}\\\\x=6.8\ hours[/tex]

Therefore , hours required to complete the project is 6.8 hours .

Hence , this is the required solution .

Answer:

La corredora correría 9 kilómetros y 24 pies.

Step-by-step explanation:

multiplique la longitud de una vuelta (1.54) por cuántos de ellos corrieron (6) para obtener cuántos kilómetros corrieron (9.24)

Answer:b

Step-by-step explanation:

Answer:d there is no relationship time and cost varies

Step-by-step explanation:

its conman sense

Answer:

X = 7n + 3

Step-by-step explanation:

x= dimes

n=nickels

X = 7n + 3

Answer:

55 and 56

Step-by-step explanation:

Let the first number = k

the second number = k + 1

k + k + 1 = 111

2k + 1 = 111

2k = 111 - 1

2k = 110

k = 110/2

k = 55

The two numbers are 55 and 56

Answer:

16.6666666667

Step-by-step explanation:

Answer:

16 2/3

Step-by-step explanation:

Step 1:

5/1 ÷ 3/10

Step 2:

5/1 × 10/3

Step 3:

50/3

Answer:

16 2/3

Hope This Helps :)

Answer:

11.4

Step-by-step explanation:

So we know that Triangle ACB is similar to Triangle EFD.

This means that their sides are proportional to each other.

We want to find x or side AB. To do so, we can set up a proportion.

The proportional side to AB is ED. Let's also use BC since we know its value. The proportional side to BC is DF. Thus:

[tex]\frac{AB}{ED}=\frac{BC}{DF}[/tex]

Substitute x for AB, 3.8 for Ed, 15 for BC, and 5 for DF. Thus:

[tex]\frac{x}{3.8}=\frac{15}{5}[/tex]

Reduce the right:

[tex]\frac{x}{3.8}=\frac{3}{1}[/tex]

Cross multiply:

[tex]x=11.4[/tex]

So, the value of x is 11.4

And we're done!

Answer:

[tex]Root = 0.44[/tex]

Step-by-step explanation:

Required

Determine the square root of [tex]\frac{50}{250}[/tex]

Start by simplifying the fraction

[tex]Digit = \frac{50}{250}[/tex]

Divide the numerator and denominator by 50

[tex]Digit = \frac{1}{5}[/tex]

Next, determine the square root;

[tex]Root = \sqrt{\frac{1}{5}}[/tex]

Split the squarer root

[tex]Root = \frac{\sqrt{1}}{\sqrt{5}}[/tex]

[tex]Root = \frac{1}{\sqrt{5}}[/tex]

Rationalize

[tex]Root = \frac{1}{\sqrt{5}} * \frac{\sqrt{5}}{\sqrt{5}}[/tex]

[tex]Root = \frac{\sqrt{5}}{5}[/tex]

[tex]Root = \frac{2.2360679775}{5}[/tex]

[tex]Root = 0.4472135955[/tex]

[tex]Root = 0.44[/tex] --- Approximated

Hi there!

~

Let's solve your equation step-by-step.

[tex]x^{2} =\ 255[/tex]

Step 1: Take square root.

[tex]x =[/tex] ± [tex]\sqrt{255}[/tex]

[tex]x = \sqrt{255}[/tex] or [tex]= - \sqrt{255}[/tex]

Hope this helped you!

Answer:

26.25 feet

Step-by-step explanation:

A percentage is simply a ratio of the whole.  If we assume 35 feet to be 100%, or the whole, then we can say the following:

0.75 * 35 == 26.25

Hence, 75% of 35 feet is 26.25 feet.

Cheers.

Answer:

A)  Sequence: -5, -10, -15, -20, -25, -30, -35, -40    cd = -5

B)  Sequence: -1, 2, 5, 8, 11, 14, 17, 20   cd = 3

C)  Sequence:  17, 19, 21, 23, 25, 27, 29, 31   cd = 2

D)  Sequence:  11, 16, 21, 26, 31 , 36, 41, 46   cd = 5

E)  Sequence:  -9, -6, -3, 0, 3, 6, 9, 12  cd = 3

Step-by-step explanation:

A)   Sequence: -5, -10, -15, -20, -25

The common difference (cd) - which is the number that we need to add to each term in order to get the next - is -5

and the next three terms are: -30, -35, -40.

B)  Sequence: -1, 2, 5, 8, 11,

The common difference is 3,   cd = 3

so the next three terms in the sequence are; 14, 17, 20  

C)  Sequence:  17, 19, 21, 23, 25,

the common difference is 2,  cd = 2

so the next three terms in the sequence are:  27, 29, 31  

D)  Sequence:  11, 16, 21, 26, 31

the common difference is 5,  cd = 5

so the next three terms of the sequence are: 36, 41, 46  

E)  Sequence:  -9, -6, -3, 0, 3,

the common difference is 3,   cd = 3

so the next three terms in the sequence are:  6, 9, 12

Answer:

515.25 is what she got left

Step-by-step explanation:

Answer:

Step-by-step explanation:

A rational number is a number that can be written as a ratio of two integers. The are expressed as fractions. Given the value 8/9, this value is a fraction and is written as a ratio of two integers 8 and 9.

The value is neither a real number, nor an integer because integers and whole numbers are not expressed as fractions.

Natural numbers are also whole numbers starting from 1 and above. Hence 8/9 is not a natural number as well.

Note that irrational numbers are also classified as real numbers and they can not be written as a ratio of two integers.

Conclusively, 8/9 is only classified as a rational number

Answer:

Hey there!

a.

2(x-1)-3=5

2x-2-3=5

b.

2x-5=5

c.

2x=10

d.

x=5

Let me know if this helps :)

Answer:

r = 1.4 %

Step-by-step explanation:

given p(principle) is 1,375$, r(interest rate) is unknown, t(time in years) is 2, and I(Interest / final balance) is 37.10$. The simple interest formula: I = prt can be rewritten as: r = I/pt to solve for r. 37.1 / ( 1325 × 2 ) = 37.1 / 2650 = 0.014 = ( 0.014 * 100 ) % = 1.4 %

Answer:

31.8

Step-by-step explanation:

24.67x129

=>31.82

=>31.8

Answer:

5

Step-by-step explanation:

on a graph all of the regular numbers are on the left

Answer:

m = 3/1

Step-by-step explanation:

m = (y2 - y1)/(x2 - x1) = (15 - 6)/(1 - (-2)) = 9/3 = 3/1

Answer:

20

Step-by-step explanation:

Answer:-20

Step-by-step explanation: 8/4+3=5 then -2*5 =-10*2 =-20