Communicating
about Mathematics-

How can defining your variables when writing a system of equations help you determine the
answer to the question being asked?

Answer:

324352

Step-by-step explanation:

Answer:

 $27,710.24

Step-by-step explanation:

You want to know the value of $6500 earning 7.25% interest compounded continuously for 20 years.

The formula for the amount in an account earning interest at rate r compounded continuously is ...

  A = P·e^(rt)

where P is the principal invested at rate r for t years.

Your amount is ...

  A = $6500·e^(0.0725·20) = $6500·e^1.45 ≈ $27,710.24

The account will be worth about $27,710.24 after 20 years.

Answer:

49.3

Step-by-step explanation:

3.40 x 2.90 x 5.00 = 49.3 :)))

Answer:

y = (4/3)x.

or in standard form it is

-4x + 3y = 0.

Step-by-step explanation:

The slope m = (8-4) / (6-3)

= 4/3

Using the point-slope form of a line:

y - y1 = m(x - x1)  

We use m = 4/3, x1 = 3 and y1 = 4:

y - 4 = 4/3(x - 3)

Multiply through by 3:

3y - 12 = 4(x - 3)

3y = 4x - 12 + 12

3y = 4x

y = (4/3) x

or in standard form it is

-4x + 3y = 0.

Answer:

add and subtract 1 and 1

Step-by-step explanation:

u have a 5. add one and subtract one is 6 and 4.

Hope this helps plz hit the crown :D

Answer:

5. ○ D. 600 in.­³

6. ○ C. 3900 in.³

Step-by-step explanation:

5.

Use the following formula to calculate the volume:

[tex]\boxed{\mathrm{Volume = length \times width \times height}}[/tex],

where:

• length = 24 in.

• width = [tex]12\frac{1}{2}[/tex] in.

• height = 2 in.

Substituting these values into the formula:

Volume = [tex]24 \times 12\frac{1}{2} \times 2[/tex]

             = 600 in³

∴ D. is the correct option.

6.

Here, we can see that the height of the water that Yolanda will put in the tank is 5 inches less than 18 in. because the sand takes up 2 in. and the gap at the top takes up 3 in.

• height of water = 18 - 3 - 2

                             = 18 - 5

                             = 13 in.

• length = 24 in.

• width = [tex]12\frac{1}{2}[/tex] in.

∴ Volume = [tex]24 \times 12\frac{1}{2} \times 13[/tex]

                = 3900 in³

∴ The correct option is C.

a. Mean of data set = 29

b. Median of data set = 29

c. Mode of data set= 25, 26, 30

d. Midrange of data set = 32.5

What is mode of data set?

Mode of a data set is the value that appears the most often in a data set.

Given that;

Super Bowl ages listed below,

41, 24, 30, 31, 32, 29, 25, 26, 26, 25, 30,

Now, Calculate mean of the data as,

Mean = 41 + 24 + 30 + 31 + 32 + 29 + 25 + 26 + 26 + 25 + 30 / 11

         = 319 / 11

         = 29

And, Calculate Median of data as;

Firstly arranged in ascending order,

24, 25, 25, 26, 26, 29, 30, 30, 31, 32, 41

Since, There are 11 numbers (odd).

Hence, Median = 29

And, Calculate Mode of data set as;

Since, Mode of a data set is the value that appears the most often in a data set.

So, Mode = 25, 26, 30

Since, Midrange of data set is exactly halfway between the minimum and maximum numbers in a set of data.

So, Midrange = 41 + 24 / 2

                    = 65/2

                    = 32.5

Thus, Mean of data set = 29

Median of data set = 29

Mode of data set= 25, 26, 30

Midrange of data set = 32.5

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The complete question is this;

Super Bowl Ages Listed below are the ages of the same 11 players used in the preceding exercise. How are the resulting statistics fundamentally different from those found in the preceding exercise?

41 24 30 31 32 29 25 26 26 25 30

Calculate the value of;

A. Mean

B. Median

C. Mode

D. Midrange

Answer:

A - 19

Step-by-step explanation:

correctly

Answer:

  326 ft²

Step-by-step explanation:

You want to know the area of the library, which is a composite shape.

The area of a composite shape is found by dividing it into shapes whose areas are easy to find. The area of the shape will be a combination of the areas of the simpler shapes.

The formula for the area of a rectangle is ...

  A = LW

Extending the middle horizontal line will divide the figure into two rectangles whose dimensions are given on the figure.

The upper rectangle is 30 ft wide and 5 ft high, so its area is ...

  A = (30 ft)(5 ft) = 150 ft²

The lower rectangle is 22 ft wide and 8 ft high, so its area is ...

  A = (22 ft)(8 ft) = 176 ft²

The area of the library will be the sum of these two rectangular areas:

  library area = 150 ft² +176 ft² = 326 ft²

The library area is 326 square feet.

__

Alternate solution

The area could be considered to be a rectangle that is 30 ft wide by 5+8=13 ft high, with a rectangle 30-22=8 ft wide and 8 ft high removed from the lower left corner. The difference in area between the overall rectangle and the removed rectangle is ...

  (30 ft)(13 ft) -(8 ft)(8 ft) = 390 ft² -64 ft² = 326 ft²

The method shown above does not require calculating missing dimensions, so is more straightforward.

Answer:

7. x = 105

8. x = 12

Step-by-step explanation:

7. subtract 52 and 53 from 180. equals 75. subtract 75 from 180. equals 105.

8. set the two equations equal to each other and solve. equals 12.

Answer:

D

Step-by-step explanation:

The coordinates of the point at a ratio of 4/5 for the line AB will be (4,4). The correct option is D.

A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.

Given that the line AB on the coordinate system is having a ratio of 4/5.

From the given data it is observed that the line AB is distributed in the fraction of 4:5. The point on this fraction has the coordinates ( 4,4).

Therefore, the coordinates of the point at a ratio of 4/5 for the line AB will be (4,4). The correct option is D.

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Answer:

[tex]\frac{x^5+y^5}{x+y}=x^4-x^3y+x^2y^2-xy^3+y^4[/tex]

Step-by-step explanation:

Given the expression

[tex]\left(x^5+y^5\right)\div \left(x+y\right)[/tex]

[tex]\mathrm{Apply\:factoring\:rule:\:}x^n+y^n=\left(x+y\right)\left(x^{n-1}-x^{n-2}y+\:\dots \:-\:xy^{n-2}\:+\:y^{n-1}\right)\:\quad \quad \mathrm{n\:is\:odd}[/tex]

[tex]x^5+y^5=\left(x+y\right)\left(x^4-x^3y+x^2y^2-xy^3+y^4\right)[/tex]

[tex]=\frac{\left(x+y\right)\left(x^4-x^3y+x^2y^2-xy^3+y^4\right)}{x+y}[/tex]

Cancel the common factor: x+y

[tex]=x^4-x^3y+x^2y^2-xy^3+y^4[/tex]

Thus,

[tex]\frac{x^5+y^5}{x+y}=x^4-x^3y+x^2y^2-xy^3+y^4[/tex]

Answer:

C. 3,632 boxes

Step-by-step explanation:

To solve this, we multiply 4/13 by 11,804 which gives 47,216/13, then when divided gives us 3,632.

Answer:

7/49 = 1/7

Step-by-step explanation:

sueuhsjadsi

Answer:

Points F, J, and H are collinear

Step-by-step explanation:

just took exam

The statement F, J, and H are collinear is not used to prove that ΔFGH is similar to ΔFIJ.

We have to find out which statement is wrong regarding ΔFGH is similar to ΔFIJ.

Here the statement points F, J, H are collinear are not used to prove the similarity of both triangle because if these three points are collinear than there is no triangle possible and when there is no triangle than how we prove similar to them.

So when F,J and H are collinear than we can't prove similar to both the triangles.

But in all the other points we can prove the similarity of both the triangles.

Hence the statement F, J, and H are collinear is not used to prove that ΔFGH is similar to ΔFIJ.

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Answer:

729

Step-by-step explanation:

If a number is both square and cube, it can be represented to an integer to the power of 6.

This means the next number is 3⁶ = 729.

The surface area of the ice cream waffle cone is found to be 263 square cm.

A cone is a shape formed by connecting a common point, known as the vertex, to all of the points of a circular base with a set of line segments (that does not contain the vertex).

Now, as per the given question;

The ice cream waffle is in the shape of the cone.

The diameter if the cone is given as 8.5 cm.

Then, the radius 'r'  of the cone will be 8.5/2 = 4.25 cm.

The slat height 'l' if the cone is 19.73 cm.

The formula for finding the surface area is;

SA = πrl

Substituting the values;

SA = π×4.25×19.73

SA = 263.43

SA = 236 cm.

Therefore, the surface area of the ice cream waffle cone is estimated as 236 cm².

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Answer:

7868

Step-by-step explanation:

⇒ This can be written algebraically (with a variable x) as:

562 ÷ x = 14

⇒ Convert the division as a fraction:

[tex]\frac{562}{x}[/tex] = 14

⇒ Multiply both sides by 562 to get rid of the fraction and to isolate the variable x:

562 · [tex]\frac{562}{x}[/tex] = 14 · 562

⇒ Simplify:

x = 7868

Answer: 7868

Hope this helps! :)

The average cost of tickets in Japan and Switzerland are  $17.49 and $13.42 respectively.

It would cost $79.31 to buy three tickets in Japan plus two tickets in Switzerland.

Three tickets in Switzerland plus two tickets in Japan would cost $75.24.

Therefore,

let

x = cost of Japan tickets

y = cost of Switzerland tickets

Hence,

3x + 2y = 79.31

2x + 3y = 75.24

3x + 2y = 79.31

3x + 4.5y = 112.86

2.5y = 33.55

y = 33.55 / 2.5

y = $13.42

3x + 2(13.42) = 79.31

3x = 79.31 - 26.84

3x = 52.47

x = 52.47 / 3

x = $17.49

Therefore, the average cost of tickets in Japan and Switzerland are  $17.49 and $13.42 respectively.

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Answer:

Step-by-step explanation:

Correct choice is B

Answer:

Solution given:

tan (2π-x)

=tan (360-x)

=-tanx

we have

tan x=²/5

so

-tan x=-2/5.

Answer:

2:1

Step-by-step explanation:

9 is double 4.5

The ratio in the form of n: 1 will be 2: 1.

A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.

Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.

The ratio is given below.

⇒ 9: 4.5

Simplify the ratio in the form of n: 1, then we have

⇒ 9: 4.5

⇒ 2: 1

The ratio in the form of n: 1 will be 2: 1.

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Answer:

-5 is a root

Step-by-step explanation:

It would help to see any possible answers for this if this is a multiple choice question, but if a factor of f(x) is (x+5), then -5 must be a root of a function.

To find roots, set factor equal to zero and solve:

x + 5 = 0

x = -5

Answer:

What are the choices?

Step-by-step explanation:

The answer is the last choice.

When x approaches positive infinity, the value of f(x) will also approach positive infinity too.

Notice how we substitute x in the equation with any positive numbers and we will get high f(x) value as the sign of positive infinity approach when x approaches positive infinity.

Answer:

1. 4:105

2. 12.5:1.7

3. 12:65

Answer:

1. 4:105

2. 12.5:1.7

3. 12:65

the person on top said the answer