A map has a scale of 3.5 inches = 20 kilometers. If the distance between two cities on the map is 4.9 inches, what is the actual distance between the two cities?

Answer:

V = 67.0206 m3

Step-by-step explanation:

Answer: [tex]17ft^3[/tex]

Step-by-step explanation:

The volume of a cone can be calculated with the following formula:

[tex]V_{(cone)}=\frac{1}{3}\pi r^2h[/tex]

Where "r" is the radius and "h" is the height.

The radius is half the diameter, then "r" is:

[tex]r=\frac{4ft}{2}\\\\r=2ft[/tex]

Since we know that radius and the height, we can substitute them into the formula.

The volume of the cone  to the nearest cubic foot is:

 [tex]V_{(cone)}=\frac{1}{3}\pi (2ft)^2(4ft)[/tex]

 [tex]V_{(cone)}=17ft^3[/tex]

Answer:

Step-by-step explanation:

If the solution of the system of equations is {(x, y): x - y = 4} - infinitely many solutions, then this system is consistent and dependent.

x - 3y = 4            multiply both sides by 2

2x - 6y = 8

Therefore Q = -6

Answer:

○ b -5 ≤ x ≤ 3

Explanation:

The set of x-values is called the domain. Also, according to the graph, this range out to from negative five [left] to three [right].

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A proper fraction must have a denominator that is greater then the numerator.

If the numerator is the same as the denominator is the same then it can be simplified to 1.

If the numerator is greater than the denominator then the fraction is improper.

This means that the answer must be D) 3/4

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

d

Step-by-step explanation:

A proper fraction is when the numerator is less than the denominator

example is 2/3, 100/200 etc.

The area of the given parallelogram is 24 square units.

The area of a parallelogram is the product of the height and the base of the  parallelogram.

The height of the given parallelogram is

[tex]= (5-2)[/tex] units

[tex]= 3[/tex] units

The base of the given parallelogram is

[tex]= [7-(-1)][/tex] units

[tex]= 8[/tex] units

Therefore, the area of the given parallelogram is

[tex]= (8)(3)[/tex] square units

[tex]= 24[/tex] square units

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Answer: 0.35

Step-by-step explanation:

The linear graph y = 2x + 3 represents the relationship between the data provided.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have input and output in the table:

From the points:

(3, 9) and (6, 15)

[tex]\rm \left(y-9\right)=\dfrac{\left(15-9\right)}{6-3}\left(x-3\right)[/tex]

(y - 9) = 2(x - 3)

y = 2x + 3

Thus, the linear graph y = 2x + 3 represents the relationship between the data provided.

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Answer:

For 15 you put 3 dots. For 14 you put 2 dots. For 13 you put 2 dots again. And for 12 you put 1 dot.

Answer:

5i, -5i

Step-by-step explanation:

None 5i nor -5i could be a third root of the polynomial because if we had a complex root then by the complex conjugate root theorem, their conjugate would be a fourth root, while the polynomial which is a 3-degree polynomial can only have three roots according to the Fundamental Theorem of Algebra, which states that the number of roots of the polynomial is equal to the degree of the polynomial.

In other words, for example, if the third root was 5i then its conjugate -5i should be another root according to the complex conjugate root theorem; so we would end with four roots when we are only allowed -by the Fundamental Theorem of Algebra- to have three roots since it is a 3-degree polynomial.  The same reasoning applies for -5i whose conjugate is precisely 5i.

The other numbers are real numbers, so any of them can be a third root. Notice that it does not matter if the third root is again 5 or -5 since the real roots can be repeated (multiplicity greater than 1).

9514 1404 393

Answer:

  $5611

Step-by-step explanation:

We can't make use of your calculator, but we know the formula.

__

The future value of the investment is ...

  FV = P(1 +r)^t

  FV = $4300(1.03^9) ≈ $5611

The investment will be worth about $5611 after 9 years.

Answer:

-5/1

Step-by-step explanation:

Answer: Second option.

Step-by-step explanation:

You can calculate  the slope of the line with the following formula:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

You know the point G(1,-5) and  the point O(0,0), then, you can identify that:

[tex]y_2=-5\\y_1=0\\x_2=1\\x_1=0[/tex]

Now you need to substitute these values into the formula  [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex], then the slope of OG is:

 [tex]m=\frac{-5-0}{1-0}\\\\m=\frac{-5}{1}\\\\m=-5[/tex]

This matches with the second option.

Answer:

True

Step-by-step explanation:

Every rectangle is a parallelogram.

Answer: 11

Step-by-step explanation:

You can set up a ratio.

8/456 = x/627

Cross multiply and divide

8 • 627 = 5016

5016 / 456 = 11

Final answer:

It takes 11 hours to drive 627 miles when the rate is 57 miles per hour, which is derived from the given information that 456 miles are driven in 8 hours.

Explanation:

To determine the travel time for 627 miles when we know that 456 miles were driven in 8 hours, we can use the concept of direct variation. With direct variation, if two variables vary directly, as one increases, the other also increases by a constant multiplier known as the constant of variation (k). In this case, the distance traveled varies directly with the time spent driving.

First, we need to determine the rate of driving based on the information provided:

Now we can use the rate to calculate the time required to drive 627 miles:

It would take 11 hours to drive 627 miles at that rate.

Answer:

-12+8x^5

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ANSWER

[tex]\frac{ - 12}{1 + 8x} [/tex]

EXPLANATION

The given rational expression is

[tex] \frac{ - 12 {x}^{4} }{ {x}^{4} + 8 {x}^{5} } [/tex]

We factor to get;

[tex]\frac{ - 12 {x}^{4} }{ {x}^{4} (1+ 8 {x}) } [/tex]

We can see that:

[tex] {x}^{4} [/tex]

is common to both the numerator and the denominator.

We cancel out the common factors to obtain;

[tex]\frac{ - 12 }{ 1+ 8 {x}} [/tex]

Therefore the simplified form is

[tex] \frac{ - 12}{1 + 8x} [/tex]

Answer:

answer is a

Step-by-step explanation:

Answer:

Both A and B

Step-by-step explanation:

For functions you are just trying to make sure all the x's are different.  

So let's look at A:  The x's there are all different so it is a function

Now let's look at B: The x's there are all different so it is a function.

Both A and B

The expression to represent the number of items this online company sold n hours after 6am is 120 + 30n. Since the company had already sold 120 items at 6am, and then sells an average of 30 items every hour, the overall quantity of items sold is expressed by this linear formula.

This is a problem related to linear functions, as the company's rate of sales is constant throughout the day. We are given the company sold 120 items at 6 am, which is our starting condition or 'y-intercept'. Then, we know the company sells an average of 30 items per hour, our rate or 'slope', for the rest of the day.

Therefore, the expression to represent the number of items sold n hours after 6 am is 120 + 30n. Here, 120 represents the number of items sold by 6 am, 30 is the average rate at which items are sold per hour, and n is the number of hours after 6 am.

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The expression to represent the total number of items sold n hours after 6 am is 120 + 30n, where 120 is the initial amount at 6 am, and 30n is the number of items sold per hour after 6 am.

The question involves a linear equation to find the number of items sold by a company n hours after 6 am. Given that the company has sold 120 items by 6 am, and that it sells an average of 30 items per hour for the rest of the day, we represent this scenario with an expression. This can be expressed as 120 + 30n, where n represents the number of hours passed after 6 am.

This equation is made up of two parts: 120 represents the initial number of items sold by the company by 6 am, and 30n represents the number of items the company sells per hour (30) multiplied by the number of hours passed after 6 am (n). Hence, the total number of items sold after n hours will be the sum of these two values.

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For this case we must solve the following equation:

[tex]\frac {x + 4} {6x} = \frac {1} {x}[/tex]

We multiply by "6x" on both sides of the equation:

[tex]x + 4 = \frac {6x} {x}\\x + 4 = 6[/tex]

Subtracting 4 on both sides of the equation:

[tex]x = 6-4\\x = 2[/tex]

Thus, the result of the equation is 2.

Answer:

[tex]x = 2[/tex]

Option A

Answer:

A

Step-by-step explanation:

A line can be described as a one-dimensional element with length greater than its width. It is formed by connecting two or more points and can be used to create shapes, define forms, and indicate motion.

A line can be described as a point in motion. It is the simplest visual element and is characterized by its length being greater than its width. When two or more points are connected, a line is formed. For example, when you draw a line segment connecting two points on a paper, you create a line. Lines can be used to create shapes, define forms, and indicate motion. It is important to note that a line is one-dimensional and has no width or depth.

Answer:

118°

Step-by-step explanation:

Supplementary angles sum to 180°

let x be one of the supplementary angles, then

x + 62 = 180 ( subtract 62 from both sides )

x = 118°

The measure of the supplementary angles are 62° and 118°

Supplementary angles are two angles that have a sum of 180°.

Complementary angles are two angles that have a sum of 90°.

Given data ,

Let the sum of angles be represented as A

Now , let the first angle be represented as p

And , the value of p = 62°

Let the second angle be represented as q

Now , the value of q = q

For supplementary angles , the sum of the angles is 180°

So , on simplifying , we get

A = p + q = 180°

62° + q = 180°

Subtracting 62° on both sides of the equation , we get

q = 180° - 62°

q = 118°

Hence , the measure of the supplementary angles are 62° and 118° respectively

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Answer:

12.5%

Step-by-step explanation:

There are 4 walls to choose from, and 2 scenes to choose from. So the number of combinations is 2×4=8. One of those is the ocean scene on the gym wall. So the probability is:

P = 1/8

P = 12.5%

Answer:

3^x-8=8 then x=log_3(16)

3^(x-8)=8 then log_3(8)+8

Step-by-step explanation:

So if it is 3^x-8=8

then 3^x=16

and then convert to logarithmic form you write it as log_3(16)=x

_3 means the subscript (the base) is 3

So if it is 3^(x-8)=8

then the log form is log_3(8)=x-8

add 8 on both sides log_3(8)+8=x

The value of x that satisfies the given equation is 9.8929

From the question, we are to solve [tex]3^{x-8} =8[/tex] for x, using the change of base formula [tex]\log _{b} y = \frac{log _{} y}{log _{} b}[/tex]

From the given equation,

[tex]3^{x-8} =8[/tex]

Take [tex]log_3[/tex] of both sides,

That is,

[tex]\log _{3} 3^{x-8} = \log _{3} 8[/tex]

This becomes,

[tex](x-8)\log _{3} 3= \log _{3} 8[/tex]

Since [tex]\log _{x} x =1[/tex],

∴ [tex]\log _{3} 3 =1[/tex]

[tex](x-8)(1)= \log _{3} 8[/tex]

[tex]x-8= \log _{3} 8[/tex]

Using the change of base formula [tex]\log _{b} y = \frac{log _{} y}{log _{} b}[/tex]

[tex]\log _{3} 8=\frac{\log 8}{\log 3}[/tex]

Then,

[tex]x-8=\frac{\log 8}{\log 3}[/tex]

[tex]x-8=\frac{0.9031}{0.4771}[/tex]

x - 8 = 1.8929

x = 8 + 1.8929

x = 9.8929

Hence, the value of x that satisfies the given equation is 9.8929

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Answer:

The slope - intercept equation for this line is y = 17x - 55

Step-by-step explanation:

The general form of the slope-intercept form is

y = mx +b

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

We are given slope m = 17

we need to find b the y-intercept.

To find y-intercept we would use point(3,-4) and formula

y = -4

x = 3

m = 17

b=?

y = mx + b

-4 = (17)(3) + b

-4 = 51 + b

b = -4 -51

b = -55

So, y-intercept is -55

The slope - intercept equation for this line is y = 17x - 55

Answer:

(2,0)

Step-by-step explanation:

For given line AB:

y-intercept = b = -2

slope = m = y₂-y₁/x₂-x₁

= -3/2-(-4) = -3/6 = -1/2

Equation of line AB:

y = (-1/2)x - 2

Finding equation of line that is parallel to line AB and passes through the point C(2,2):

Substituting the slope from line AB into the equation of the line

y = (-1/2)x + b.

Substituting the given point (-2,2) into the x and y values 2 = (-1/2)-2 + b.

Solving for b (the y-intercept) , we get b = 1

Substitute this value for 'b' in the slope intercept form equation y = (-1/2)x + 1.

For x-intercept of the line, we let y = 0

0 = (-1/2)x + 1

x = -1(-2/1)

x = +2

So, the point on the x-axis that lies on the line that passes

through point C and is parallel to line AB is (2,0).

Distributive property means you multiply the number on the outside the parentheses (in this case it is 7) with every number/variable inside the parentheses ( in this case it would be 5 and -4) so...

7*(5 - 4) = (7 * 5) - (7 * 4)

Further evaluated you would get...

35 - 28

7

Hope this helped!

~Just a girl in love with Shawn Mendes

ANSWER

a relation only

EXPLANATION

The given graph shown in the attachment represents only a relation and not a function.

The reason is that, a vertical line drawn across this graph will intersect this graph at more than one point.

Since the graph fails to pass the vertical line test, the ordered pair represented by this graph represents a relation only.

Answer: First option.

Step-by-step explanation:

By definition, a relation is a function if each input value (value of "x") has only one output value (value of "y").

 In the figure you can observe that each x-coordinate has more than one y-coordinate. Then, since each input value (value of "x") does not have only one output value (value of "y"), you can say that it is not a function, but a relation only.

Therefore, the conclusion is:

The set of ordered pairs represented by the graph, can be described  as a relation only.

Answer:

29

Step-by-step explanation:

12/6 + 9(3) = 2 + 27 = 29

Answer:

29

Step-by-step explanation:

Answer:

B. 259

Step-by-step explanation:

32.9 × 7.5 = 246.75

Therefore, the number closest to 246.75 is 259

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The closest number is B. 259

To find the answer to this question, you need to multiply 32.9 by 7.5. The option that the product of those two numbers is closest to, is the answer.

= 32.9 x 7.5

= 246.75

= 247 rounded off

This number is closest to 259 as the difference between them is only:

= 259 - 247

= 12

The other options are wrong because:

= 247 - 232

= 15

= 247 - 220

= 27

= 265 - 247

= 18

The closest number is therefore 259.

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The answer would be...

1/2n - 1/6n = 10 + 1/8n

^^^That would be the last one

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

Step-by-step explanation:

Let the number = x

(1/2) x - (1/6) x = (1/8)x + 10

It's the third one down. The other two are wrong because the number is not represented in both terms on the left. The questions says 1/2 of the number

and 1/6 of the number.   Both require an x.

Answer:

Step-by-step explanation:

[tex]f(x)=x^2+4x+6\\\\a.\\f(-8)-\text{put x = -8 to the equation}\\\\f(-8)=(-8)^2+4(-8)+6=64-32+6=38\\\\b.\\f(x+4)-\text{exchange x to x + 4}\\\\f(x+4)=(x+4)^2+4(x+4)+6\\\\\text{use}\ (a+b)^2=a^2+2ab+b^2\ \text{and}\ \text{distributive property}\\\\f(x+4)=x^2+2(x)(4)+4^2+4x+(4)(4)+6\\\\f(x+4)=x^2+8x+16+4x+16+6\\\\\text{combine like terms}\\\\f(x+4)=x^2+(8x+4x)+(16+16+6)\\\\f(x+4)=x^2+12x+38[/tex]

[tex]c.\\f(-x)-\text{exchange x to -x}\\\\f(-x)=(-x)^2+4(-x)+6=x^2-4x+6[/tex]