Choose two values, a and b, each between 8 and 15. Show how to use the identity a^3+b^3=(a+b)(a^2-ab+b^2) to calculate the sum of the cubes of your numbers without using a calculator

Answer:

y = 250

Step 1:

To solve, we plug in 50x for y.

[tex]50x=200+10x[/tex]

Then, we subtract the 10x from the right side. Our goal is to get the x by itself first.

[tex]40x=200[/tex]

Then, we divide both sides by 40, since we have to get the x by itself.

[tex]\frac{40x}{40}=x\\\\\frac{200}{40} =5[/tex]

x = 5

Step 2:

Now that we found x, we plug in 5 to the original equation and solve from there.

[tex]y=200+10(5)\\y=200+50\\y=250[/tex]

y = 250

Answer:

Step-by-step explanation:

The expression used to model the volume, in gallons, is 12x^2-13x+3

When the through is empty it means that there is no water in it wich means that the expression used equals 0

● 12x^2-13x+3 = 0

The expression is quadratic equation so to solve it we will use the discriminant method

The discriminant is b^2-4ac

● b= -13

● a= 12

● c= 3

b^2-4ac = (-13)^2+4×12×3 = 25

25 > 0 so the discriminant is positive

We have two solutions

Let x and x' be the solutions

x = (-b-5)/2×a =(13-5)/24 = 8/24 = 1/3

5 is the root square of 25 (the discriminant)

x' = (-b+5)/2a = (13+5)/25 = 18/24 = 3/4

The solutions are 1/3 and 3/4

1/3 = 0.34

3÷4 = 0.75

The through can't be empty from water in two different times

So it will be empty when reaching one of the 2 solutions first

0.34 < 0.75

Then at 0.34 min the through is epty from water

Answer:

[tex]0 = 12x^2 - 13x + 3[/tex]

Step-by-step explanation:

The volume of the trough is modeled by the equation:

[tex]V = 12x^2 - 13x + 3[/tex]

The trough will be empty when the volume of water in it is 0. That is, the expression that would reveal when the trough is empty is:

[tex]0 = 12x^2 - 13x + 3[/tex]

We can further simplify it:

[tex]12x^2 - 9x - 4x + 3 = 0\\\\3x(4x - 3) - 1(4x - 3) = 0\\\\(3x - 1)(4x - 3) = 0[/tex]

Answer:

c y= 1/2x-8

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The slope is either 1/2 or 8. Because the line is not incredibly steep, it must be 1/2.

The y-intercept is where the line crosses the y axis. In this case, it's 8.

Therefore the equation must be y=1/2x+8.

The answer is B.

Answer:

B

Step-by-step explanation:

The line from the vertex to the base is a perpendicular bisector and divides the isosceles triangle into 2 right triangles with hypotenuse x

Using Pythagoras' identity in either of the 2 right triangles, then

x² = 12² + 5² = 144 + 25 = 169 ( take the square root of both sides )

x = [tex]\sqrt{169}[/tex] = 13 → B

Answer:

4/13 is the probability does a blue Jelly Bean is selected

Step-by-step explanation:

sample space = sum of all the jelly beans in the bag

sample space =5+6+7+8

sample space =26

probability = Jelly Bean selected / sample space

probability =8/26

probability =4/13

Answer:

y=2/3x-2

Step-by-step explanation:

All of the given options are in slope intercept form.

Slope intercept form is y=mx+b

This is where m is the slope fo the line and b is the y intercept

That said, we can simply plug the given values into the form.

y=(2/3)x+(-2)

Simplify

y=2/3x-2

Answer:

A. y= 2/3x-2

Step-by-step explanation:

The slope of a line is written in slope-intercept form, which is:

y= mx+b

where m is the slope and b is the y-intercept.

The line has a slope of 2/3 and a y-intercept of -2. Therefore,

m= 2/3

b= -2

Substitute these values into the slope intercept form.

y= mx+b

y=2/3x+(-2)

Adding a negative number (+-) can be simplified to just a negative(-)

y= 2/3x-2

Therefore, the equation of the line is A. y= 2/3x-2

Answer with  explanation:

Given: An airline company advertises that 100% of their flights are on time after checking 5 flights from yesterday and finding that these 5 were on time.

a) population: A large group of observations have characteristics related to the point of the study.

Here, population: "All flights operated by the company"

b) Sample: It is a subset of the population.

Here, Sample: "5 flights from yesterday"

(c)

Since the number of flights per day operated by an airline company is much larger than 5 ( generally in hundreds).

i.e. the sample is too small to be able to assure that the results are true.

Hence, this is not a representative sample.

(d) To determine the percentage of their flights that are on time we use the following formula:

(Number of flights are on time) ÷ (Total flights) x 100

Explanation:

We'll use the tangent ratio to connect the opposite and adjacent sides with the reference angle

tan(angle) = opposite/adjacent

tan(A) = 14/7

Then use the arctangent function (aka inverse tangent) to fully isolate A

A = arctan(14/7)

A = 63.4349 degrees approximately; make sure your calculator is in degree mode

Round this to the nearest whole number to get 63.

Answer:

A) it increases the mean value of the prizes.

Step-by-step explanation:

The median is resistant to large outliers, so it does not change if there is an especially large or small value. So, we can eliminate choices C and D.

I am actually not sure whether the data in the table count $100 as a large prize or a small one, but I am assuming it is a large prize. So, an extremely large prize would increase the mean value of the prizes.

Hope this helps!

The $100 gift card affect the measure of center of the data by increases the mean value of the prizes.

Option A is the correct answer.

It is the middles value of the given set of numbers after arranging the given set of numbers in an order.

We have,

The $100 gift card has a much larger value compared to the other prizes, and it is only given to one person.

Therefore, adding the $100 gift card to the prizes will significantly increase the total value of the prizes, which will affect the measures of center of the data.

The mean and median are two common measures of center in statistics. The mean is the sum of all the values divided by the number of values, while the median is the middle value when the data is arranged in order.

Adding the $100 gift card will increase the mean value of the prizes, but it will not affect the median value, since the median only depends on the order of the data, not the values themselves.

Therefore,

It increases the mean value of the prizes.

Learn more about median here:

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Answer:

It will be compressed vertically

Step-by-step explanation:

y = Cf(x) 0 < C < 1 compresses it in the y-direction

Since we are multiplying by 1/4 it will compress it by 1/4 in the y direction

Answer:

When you multiply the whole function by a constant, which can be identified as "C", you can have the following situations:

- If  the function is stretched.

- - If  the function is compressed.

You have that 0<1/4<1

Therefore, you can conclude that be compressed vertically.

Step-by-step explanation:

The given function is f (x) = x²

The new function is f 1 (x) = 1/4 x².

The general function of the form is f(x) = a · x²

i) If |a| < 1   the graph is compressed vertically by a factor of a.

ii)  If |a| > 1  the graph is stretched vertically by a factor of a.

Here:  a = 1/4 < 1

Answer:

Step-by-step explanation:

Equation of the line using point (0, 1) and slope 4/5 is

[tex]y - 1 = \frac{4}{5} (x - 0) \\ \\ 5y - 5 = 4x \\ \\ 5y - 4x = 5[/tex]

Hope this helps you

Answer:

D. [tex]\boxed{5y-4x=5}[/tex]

Step-by-step explanation:

Slope = m = 4/5

y - intercept = b = 1 (As from the point (0,1) , y-intercept is when x = 0)

So, the equation becomes

=> [tex]y = mx+b[/tex]

=> [tex]y = \frac{4}{5} x +1[/tex]

=> [tex]y - \frac{4}{5} x = 1[/tex]

Multiplying both sides by 5

=> [tex]5y-4x = 5[/tex]

Answer:

  6748'

Step-by-step explanation:

The long diagonal is the third leg of a triangle with the given side lengths and an angle between them that is the supplement of the given angle. Its length can be found from the Law of Cosines.

  a^2 = b^2 +c^2 -2bc·cos(A)

  a^2 = 3473^2 +4822^2 -2·3473·4822·cos(180° -72.23°)

  a^2 = 45,535,553.83

  a ≈ 6748.004

The longer diagonal is about 6758 feet long.

Answer:

A

Step-by-step explanation:

Answer:

a)2/5

Step-by-step explanation:

5:2 is correct

5/2 is nothing but 5:2

10:4 is also correct because when we simplify it we get5:2

Answer:

2x - 3x -6y - 5y +35x

Step-by-step explanation:

-3 multiplied by x is -3x

-3 multiplied by +2y is -6y

-5 multiplied by y is -5y

-5 multiplied by -7x is +35x

2x remains the same.

Answer:

c. 2x – 3x – 6y – 5y + 35x

Step-by-step explanation:

edge 2021

(:

Answer:

n = 2

Step-by-step explanation:

Here, we want to write the simplified form of the equation given in the question.

Firstly, we write the equation in an equation form:

4/5n -1/5 = 2/5n

5n(4/5n -1/5) = 2/5n(5n)

(4/5n * 5n) -(1/5)(5n) = 2

4- n = 2

n =4-2

n = 2

Answer:

The answer that I got was n=2

Step-by-step explanation:

Answer:

[tex]\sqrt{16}[/tex] = 4

[tex]\sqrt{25}[/tex] = 5

16x^2 - 40x + 25

= (4x - 5)^2

Hope this helps!

Answer:

4x-5, B

Step-by-step explanation:

EDGE 2020

Answer:

1.35 meters

Step-by-step explanation:

Let the original length of the string be x.

So, we started out with x centimeters. Rachel used 2/3 of it (the original amount) to tie some books together. Therefore, we now have:

[tex]x-\frac{2}{3}x[/tex]

centimeters of string left. This represents the original minus the amount she used.

Next, she used 1/3 of the remaining string. In other words:

[tex]x-\frac{2}{3}x-\frac{1}{3}(x-\frac{2}{3} x)[/tex]

The newly added terms is 1/3 of the remaining string length.

And she ends up with 30 centimeters. Therefore, we need to solve the equation for x:

[tex]x-\frac{2}{3}x-\frac{1}{3}(x-\frac{2}{3} x) =30\\\frac{1}{3}x-\frac{1}{3}x+\frac{2}{9}x=30\\\frac{2}{9}x=30\\ x=30\cdot \frac{9}{2}=135 \text{ centimeters}[/tex]

Therefore, the original length of the string was 135 centimeters or 1.35 meters (move the decimal two places to the left).

Answer:

135 cm or 1.35 m

Step-by-step explanation:

2/3(135) = 90

1/3(90) = 30

Answer:

18 types of apartments

Step-by-step explanation:

There are three options for bedrooms (2, 3, or 4), two options for bathrooms (1 or 2), and three options for location (lower, middle, or upper level).

The number of possible different apartments is:

[tex]n=3*2*3\\n=18\ types[/tex]

18 types of apartments are possible.

Answer:

B

Step-by-step explanation:

To calculate the square feet of fertilizer he would be needing to cover his garden, what we need to do is simply find the area of the garden

Mathematically that would be the length of the garden multiplied by its width since it is a rectangular sharped garden

The area is thus;

33 * 39 = 1287 ft^2

The answer is B.) (-1 1/5, 4 3/5)  /  [tex]\left(-1\:\frac{1}{5},\:4\frac{3}{5}\right)[/tex]

Answer:

x=1/4c+1/4k

Step-by-step explanation:

4x-c=k

move c over

4x=c+k

then divide by 4

x=1/4c+1/4k

hope this helps

Answer:

Hey there!

Circumference: [tex]2\pi r+95+95[/tex]

Area: [tex]\pi r^2+70(95)[/tex]

r=35

Circumference: 410

Area: 10498.

Hope this helps :)

Answer:

Area=  10498.5 cm²

Step-by-step explanation:

Area of rectangle= l x w

= 95 x 70 = 6650

Area of circle = πr²

= π x 35²

= 1225π

=3838.5 cm²

Area of shape: 6650 + 3848.5 = 10498.5 cm²

Answer:

6c1;   [tex]Area = 81.12m^2[/tex]

6cii:  See Explanation

Step-by-step explanation:

Given

[tex]A = 3p^2[/tex]

[tex]0 \leq p \leq 6[/tex]

Where A represents Area and P represents Width

Required

Solve 6c

Please note that because you only need 6c, I'll solve using calculations;

Solving 6ci:

Area of the cage, when width is 5.2m

Substitute 5.2m for p in[tex]A = 3p^2[/tex]

[tex]A = 3 * 5.2m^2[/tex]

[tex]A = 3 * 27.04m^2[/tex]

[tex]A = 81.12m^2[/tex]

Hence, the area of the cage is 81.12m²

Solving 6cii:

Area of the cage, when width is 40m

From the range of value of p:   [tex]0 \leq p \leq 6[/tex], 40m is out of range of the values of p

However, if the range is extended; the value of Area is as follows;

Substitute 40m for p

[tex]A = 3 * 40m^2[/tex]

[tex]A = 3 * 1600m^2[/tex]

[tex]A = 4,800m^2[/tex]

Hi there! Hopefully this helps!

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1 / 2 / 3 = 0.16666666666.  

0.16666666666 in fraction form:  1/6.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Firstly we need to divide 1 into halves (halves is "2", 1 / 2 = 0.5.)

Now that we have 0.5, we need to divide 0.5 by 3.

0.5 / 3 = 0.16666666666

Answer:

1/6

Step-by-step explanation:

Hey there!

Well let's start with,

1 ÷ 2 = .5

.5 ÷ 3 = .1666666 repeating

As a fraction it would be 1/6

Hope this helps :)

Answer:

Option B

Step-by-step explanation:

Hope it is right

The value of equation describes the line graphed is,

⇒ y = -1/5x - 4

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (0, -4) and (5, -5).

Now,

Since, The equation of line passes through the points (0, -4) and (5, -5).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (- 5 - (-4)) / (5 - 0)

m = - 1 / 5

Thus, The equation of line with slope - 1/5 is,

⇒ y - (-4) = -1/5 (x - 0)

⇒ y + 4 = -1/5x

⇒ y = -1/5x - 4

Therefore, The equation of line passes through the points (0, -4) and

(5, -5). will be;

⇒ y = -1/5x - 4

Learn more about the equation of line visit:

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Answer:

The car will travel approximately 13200  inches

Step-by-step explanation:

Notice that in one revolution, the car travels exactly the length of the tire's circumference, that is: [tex]2\,\pi\,R[/tex]

Then, in 200 revolutions the car will travel 200 times that amount:

[tex]200\,(2\,\pi\,R)=400\ \pi\,R[/tex]

So for the given dimension of the tire, and using the approximation [tex](\pi\approx22/7)[/tex], this distance would be:

[tex]400\ \pi\,R=400\,\,\frac{22}{7} \,\,10.5\,\,in=13200\,\,in[/tex]

Answer:

1)3/4 (other) 2)2/3   3)2/3   4)1/3(other) 5)1/4

Step-by-step explanation:

the reason all the ones that say other are other is because they dont fit into the 3/4 section or 1/4. we can figure out the answers by counting up the total amount of squares/triangles and then the shaded ones, and then putting them over each other, shaded amount on top, and then simplifying. or, if you can tell by seeing that there are only 3 boxes and one shaded for example, you can simply tell its 1/3 because its already laid out for you. hope this helped

Answer:

It would be the graph that has point (0,12) and is decreasing to the right.

Answer:

Step-by-step explanation:

($26.5 - $3 - $5.50) : $0.6/m =

= $18 : 0.6$/m

= 30 miles

Answer:

$60.00=Y× X

Step-by-step explanation:

You know she makes $60 but you need to figure out how many hours she works and how much an hour she makes working.