Peter gave away 5/12 of his marbles and had 70 left how many marbles he had at first

This is about interpretation of graphs.

Option C is correct.

From the graph, we can see the 2 lines representing function f(x) and function g(x).

Now for us to find the value of x in g(x) = k⋅f(x), we need get a mutual x-coordinate where we can easily read their respective y-coordinate values.

We see that the best point for that is where x = -3.

For f(x), when x = -3, y = 1

For g(x), when x = -3, y = -3

we can rewrite them as;

x = -3, f(-3) = 1 and x = -3, g(-3) = -3

Let us plug in the relevant values into g(x) = k⋅f(x) to get;

-3 = k(1)

Thus; k = -1/3

5.12 minutes ≈ 5 minutes 7.2 seconds

Distance. The length along a line or line segment between two points on the line or line segment.

Here, The flight path of the airplane is along the line ...

y = -125/135x = -25/27x

The perpendicular line through Mt. Rainier's location is ...

 y = 27/25(x -56) -40

In standard form, these two equations are ...

25x +27y = 0

27x -25y = 2512

The point of closest approach has the coordinates that are the solution to these two equations:

(x, y) = (33912/677, 31400/677)

The distance d from the origin to this point is given by the Pythagorean theorem (distance formula) as ...

d = 1256√(2/677) . . . . . km

This distance can be converted to time using the speed of the airplane:

1256√(2/677) X 60/800 =  94.2√(2/677) ≈ 5.120019 mins

Thus, 5.12 minutes after departing JBLM you will be closest to Mt. Rainier.

The attached graph shows the geometry of the problem.

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Answer:

D.All of the choice

Step-by-step explanation:

D.All of the choice

[tex](f+g)(x)=f(x)+g(x)\\\\f(x)=2x^2+3x\\g(x)=x-2\\\\(f+g)(2)=2\cdot2^2+3\cdot2+2-2=8+6=14[/tex]

The result follows from the fundamental theorem of calculus. Since [tex]f''(x)[/tex] is the derivative of [tex]f'(x)[/tex], we have

[tex]\displaystyle \int_0^c f''(x) \, dx = \boxed{f'(c) - f'(0)}[/tex]

(E)

The coordinates of the midpoint of the segment whose endpoints are W (-3,-7) and X (-8,4) will be (-11/2, -3/2). Then the correct option is D.

The complete options are given below.

1. (-11/2) -(11/2)

2.(-5/2)-(3/2)

3.(-5/2-(11/2)

4. (-11/2) -(-3/2)

Let C be the mid-point of the line segment AB.

A = (x₁, y₁)

B = (x₂, y₂)

C = (x, y)

Then the midpoint will be

x = (x₁ + x₂) / 2

y = (y₁ + y₂) / 2

The end points are given below.

(-3, -7) and (-8, 4)

We have

(x₁, y₁) = (-3, -7)

(x₂, y₂) = (-8, 4)

Then the mid-point will be

x = (- 3 - 8) / 2

x = -11 / 2

y = (-7 + 4) / 2

y = -3/2

Then the coordinates of the midpoint of the segment whose endpoints are W (-3,-7) and X (-8,4) will be (-11/2, -3/2).

Then the correct option is D.

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Answer:

(x-9)(x+8)

Step-by-step explanation:

Use the AC method

The net interest she would get on the amount deposited is $57,000.

The net interest is the total interest earned less tax.

Interest = amount deposited x simple interest x time

200,000 x 0.1 x 3 = $60,000

Net interest = $60,000 x (1 - 0.05)

$60,000 x 0.95

$57,000

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The complete question is

"Find the general solution of the given differential equation

y''-y=0, y1(t)=e^t , y2(t)=cosht

The function [tex]y(t)=e^t[/tex]  is the solution of the given differential equation.

The function y(t)=cosht is the solution of given differential equation.

The function is a type of relation, or rule, that maps one input to specific single output.

Given;

[tex]y_1(t) = e^t[/tex]

Given differential equations are,

y''-y = 0

 So that,  

[tex]y' (t) = e^t, y'' (t) = e^t[/tex]

Substitute values in the given differential equation.

[tex]e^t -e^t=0[/tex]

Therefore, the function [tex]y(t)=e^t[/tex]  is the solution of the given differential equation.

Another function;

[tex]y(t)=cosht[/tex]  

So that,  

[tex]y"(t)=sinht\\\\y"(t)=cosht[/tex]

Hence, function y(t)=cosht is solution of given differential equation.

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Answer:

a)

The GCF is 2k hence: 2k(2ck + 5k - 8c - 20)

b)

2k(2ck + 5k - 8c - 20)

After further factorization:

2k(k - 4)(2c + 5)

Answer:

19 months

Step-by-step explanation:

First off 682- 55 = 627. 627/33 = 19

Answer:

x = 12 half page advertisements

y = 8 full page advertisements

Step-by-step explanation:

42x + 86y = 1192

x + y = 20

y = 20 - x

Input (20-x) as y into the first equation

42x + 86(20-x)=1192

42x + 1720 - 86x = 1192

(42x - 86x) 1720 -1720= 1192-1720

-44x = -528

x = 12

12 + y = 20

y=8

a. 'x' represents half page advertisement and 'y' represents full page advertisement.

System of equation is given by 42x + 86y = 1192 , x + y =20.

b. Number of full page advertisement  Kathryn purchase is equals to 8.

c.  Number of half page advertisement  Kathryn purchase is equals to 12.

" System of equation is defined as the finite set of equations for which we find a common solution."

According to the question,

Cost of half page advertisement = $42

Cost of full page advertisement = $86

Number of advertisement Kathryn could purchase = 20

Total budget of Kathryn to purchase advertisement = $1192

'x' represents half page advertisement

'y' represents full page advertisement

As per the situation given system of equation we have,

42x + 86y = 1192                                 ______(1)

x + y = 20                        

x = 20 - y                                             _____(2)

Substitute the value of 'x' from  system of equation (2) in (1) we get,

[tex]42( 20 -y) +86y =1192\\\\\implies 840 - 42y +86y =1192\\\\\implies 44y = 1192-840\\\\\implies y = \frac{352}{44}\\ \\\implies y =8[/tex]

Substitute the value of y in (2) to get 'x' ,

[tex]x=20-8[/tex]

  = 12

Hence,

a. 'x' represents half page advertisement and 'y' represents full page advertisement.

System of equation is given by 42x + 86y = 1192 , x + y =20.

b. Number of full page advertisement  Kathryn purchase is equals to 8.

c.  Number of half page advertisement  Kathryn purchase is equals to 12.

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Based on the information given the length of one side of the hot tub is 4. 8 ft. So the correct option is B.

The complete question is given as:-

Ricardo has a square hot tub. He wants to build a square pool next to it that is a dilation of the hot tub using a scale factor of 5. Point Q is the centre of dilation. Square A B C D is dilated to create square A prime B prime C prime D prime. The length of B prime C prime is 24 feet. If the pool is to be 24 ft on each side, what is the length of one side of the hot tub? 4 ft 4.8 ft 6 ft 7.2 ft

The scale factor is defined as the proportion of the new image's size to that of the previous image. decision-making.

Length: Using this formula

Length=B prime C prime length/Scale factor

Where:

B prime C prime length=24 feet

Scale Factor=5

Let plug in the formula

Length=24ft/5

Length=4.8ft

In conclusion, the length of one side of the hot tub is 4. 8 ft.

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The square root property to the equation will be (x – 4)² = 25. And the solutions will be the negative 1 and 9.

The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2. Then we have

The equation is given below.

x² – 8x + 16 = 9 + 16

Then the equation can be written as

(x – 4)² = 25

x – 4 = ±5

x = 4 ± 5

x = -1, 9

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Answer: 3

Step-by-step explanation:

Answer:

Step-by-step explanation:

so...

on your new sheet of paper, draw a straight horizonal line label one end Y the other Z ( Y will be your vertex, point of angle )

then on original figure,  use a compass and put the in B and measure to A

on new sheet put the pin in Y and draw an arc ( lightly )

now back to orig and put pin in C and measure up to A

on new put pin onthe line so that when you draw an arc it will bisect the one you did previously. will will create a point . join the point to Y

hope that makes  some sort of sense.

Answer: y = 0.75x + 80

Step-by-step explanation:

let x = 1 mile

y = 0.75x + 80

Ria will not arrive before half past four because in total the activities that she did will take her at leat three hours and forty-five minutes.

The time can be determined by using the graph. In the graph, the time is represented by small squares. Each of this squares will be equivalent to 15 minutes.

You can infer this because Rita first drove for 30 minutes and in the graph the line goes from 0 in the x axis to two squares to the right (30/2 = 15 minutes.)

If she started this activities at 13:00 so she will go back home at 4:45.

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Answer:

1

Step-by-step explanation:

Although you did not give me the answer choices, I believe that the only possible answer is 1 because the only y value the graph is on is 1.

Answer:

the red parallelogram had x=6

for the blue one, other sides values must be known which is not in the picture

Step-by-step explanation:

The distributive property of multiplication over addition for rational numbers is (a) -3/4 × {2/3 + (-5/6)} = [-3/4 × 2/3] + [-3/4 × (-5/6)]

Which of the following is an example of distributive property of multiplication over addition for rational numbers

(a) -3/4 × {2/3 + (-5/6)} = [-3/4 × 2/3] + [-3/4 × (-5/6)]

(b) -3/4 × {2/3 + (-5/6)} = [3/4 × 2/3] - (-5/6)

(c) -3/4 × {2/3 + (-5/6)} = 2/3 + (-3/4) × -5/6

(d) -3/4 × {2/3 + (-5/6)} = {2/3 + (-5/6)} - 3/4

The distributive property of multiplication states that:

a * (b + c) = (a * b) + (a * c)

From the given question, we have:

-3/4 × {2/3 + (-5/6)}

This means that:

a = -3/4

b = 2/3

c = -5/6

Recall that a * (b + c) = (a * b) + (a * c)

So, we have:

-3/4 × {2/3 + (-5/6)} = [-3/4 × 2/3] + [-3/4 × (-5/6)]

Hence, the distributive property of multiplication over addition for rational numbers is (a) -3/4 × {2/3 + (-5/6)} = [-3/4 × 2/3] + [-3/4 × (-5/6)]

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Answer:

i think 345 if not sorry

Step-by-step explanation:

Answer:

[tex]3a^2+12a+12[/tex]

Step-by-step explanation:

first, you have to plug in x = a+2 into the function, which would look like:

[tex]f(a+2) =3(a+2)^2[/tex]

then, you can first simplify [tex](a+2)^2[/tex]. to do this, use the rule [tex](a+b)^2 = a^2 +2ab + b^2[/tex], so it would be [tex]a^2+(2*a*2)+2^2 = a^2 + 4a + 4[/tex]

this means your new equation is:

[tex]3(a^2+4a+4)[/tex]

you can then distribute the 3:

[tex]3*a^2+3*4a + 3*4 = 3a^2+12a+12[/tex]

let me know if there's anything you want me to clarify!

The function would become an exponential decay function.

Step-by-step explanation:

multiply 2×3 to get 6 and then multiply 6×4

or

multiply 3×4 to get 12 and then multiply 12×2