1. An input-output table has constant differences. When the input is 3, the output is 10. When the input is 7, the output is 24. a. Find the constant difference. b. Find the output when the input is 0. C. Find the linear function that fits the table.

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

LM = 14

MN = 11

KM = ?

Step 02:

We must apply the triangle rules to find the solution.

Pythagoras Theorem

LM² = LN² + MN²

(14)² = LN² + (11)²

(14)² - (11)² = LN²

LN = 8.66

8.66 * 8.66 = 11 * KN

6.818 = KN

KM = KN + MN

KM = 6.818 + 11 = 17.818

The answer is:

The value of KM is 17.82

To solve this equation, we can follow the next steps:

First: we can sum similar terms like 3x + 3x.

6(x - 1) = 3x + 3x + 6

6(x - 1) = 6x + 6

Then, solve 6(x-1) using the distributive property:

6x - 6 = 6x + 6

Subtract 6x from both sides of the equation:

6x - 6x - 6 = 6x - 6x + 6

0 - 6 = 6

-6 = 6

Since the result is not congruent, we can say that this equation has no solution.

Volume of the rectangular-shaped gas tank = Length x Width x Height

Given

DEFG is a parallelogram and

Answer

Since adjacent angles of parallelogram are supplementary

D+E = 180

30 + E = 1`80

E = 180- 30 = 150

[tex]x^{\frac{3}{2}} y^{\frac{19}{2}}[/tex]is equivalent expression of [tex]\sqrt{xy^{3} }(x^{\frac{1}{2}}y^{4} )^{2}[/tex]

An expression is combination of variables, numbers and operators.

The given expression is

[tex]\sqrt{xy^{3} }(x^{\frac{1}{2}}y^{4} )^{2}[/tex]

The power of whole term is multiplied with power of each term

[tex]x^{\frac{1}{2}} y^{\frac{3}{2}} xy^{8}[/tex]

When variables are same the powers will be added

[tex]x^{\frac{3}{2}} y^{\frac{19}{2}}[/tex]

Hence, [tex]x^{\frac{3}{2}} y^{\frac{19}{2}}[/tex]is equivalent expression of [tex]\sqrt{xy^{3} }(x^{\frac{1}{2}}y^{4} )^{2}[/tex]

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In order to find the rate of change of the given line, use the following formula:

where (x1,y1) and (x2,y2) are two points of the line.

From the given graph you can select any pair of points, for example:

(x1,y1) = (2,400)

(x2,y2) = (4,1200)

replace the values of the previous coordinates in the formula for m:

Hence, the rate of change is 400

Iterative rule for the sequence 7,21 , 63,189

It is a geometry sequence, it solution is going to be:

In this case

Sustituing:

This is the answer, so when n=1

It is given that

Now to find the inverse of g

Let

So

Now we know that

So

And since

So

Given the expression:

if 'p' represents the profit in dollar and 's' represents the number fo sweaters that the store sells, then we have that the store makes 26 dollars per sweater.

We can see this since the equation is the same as a linear function with rate of change m:

Answer:

Explanation:

Given the expression:

First, the expression can be rewritten in the form below:

Next, we simplify:

The simplest form of the expression is:

30% off the prices means that the there is a discount of 30% on the original price.

If 30% discount is given, then it means that the new cost price will be = 100% -30% the original price

=> 70% the original price

Since the Electric Guitar was sold at $315

Then it means that 70% the original price = $315

Let the original price be P

then 70% of P = $315

70% of P = 0.7 x P = 0.7P

Question A.

We can then obtain P, the original price by equatin to $315

=> 0.7P = $315

To get P, divide both sides by the coefficient of P

P = $450

Orignal Price of Guitar = $450

Question B

Amount saved = Original Price - Selling Price

Amount saved = $450 -$315

=> Amount saved = $135

Vertical cross-section ⇒

Horizontal cross-section ⇒

Vertical cross-section  through base and two lateral faces ⇒

Answer:

In the image

Hope this helps!

Step-by-step explanation:

Answer:

a-17 is the answer for this question

EXPLANATION

The radius of a cone is given by the following relationship:

We have Volume=V= 2,110.08 cm^3 and the height is h=14cm

Replacing terms:

Multiplying both sides by 3:

Dividing both sides by 14*pi:

Applying the square root to both sides:

Switching sides:

Simplifying:

Simplifying:

The answer is r=12 centimeters

66

1) To round it off to the nearest whole number, let's consider that:

65.73 is > 65.5 then we can round it up

2) Hence, 65.73 after rounding it up is 66 and that's the answer.

Given the following functions:

f(x) = 3x

g(x) = x + 4

h(x) = x^2 - 1

Before simplifying g(f(-1)), let's first determine f(-1).

f(x) = 3x

f(-1) = 3(-1)

f(-1) = -3

g(x) = x + 4

g(f(-1)) = (-3) + 4

= -3 + 4

g(f(-1)) = 1

Therefore, the answer is 1.

Solution

Let sin (47) = 0.7314. Enter an angle (B), in degrees,

where cos (B) = 0.7314 means

since the vaule of sin(A) = 0.7314

Hence the cos(B) = cos43 = 0.7314

The angle of B = 43°

The two endpoints of a line are given, and to find the equation we need to express it in the slope-intercept form written as follows;

y = mx + b, where m is the slope and b is the intercept of y.

To calculate the slope, we use the formular;

To solve this absolute value equation, we can use find the solutions as follows taking into account the definition of absolute value, then, we have:

Now, we can solve both equations to find the solution(s):

First case:

Second case:

Then, both solutions are the same, because of the absolute rule (this is the point when y = 0, that is the x-intercept for this function.)

Therefore, the solution set is {19/20}.

The combine things to make zero means we are combining same thing but off oppoite polarity or sign or direction.

The addition of zero to anything does not make anything to zero, it results in same quantity. So it is a false statement, as addition of zero does not chage anything, it results in original amount.

Answer:

(4) -2

Explanation:

Given the system of equations:

Set x as the subject in the second equation: x=6-y

Substitute x=6-y into the first equation:

The value of y that solves the system of equations is -2.

So we need to express 7 ft 6 in in inches and in feet. For this purpose is important to remember this relation:

So in a we need to express 7ft 6in in inches. This means we must convert the 7ft into inches and then add the result to 6in. If we use the rule of thre we get:

Then we get:

So the answer to part a is 90in.

For part b we can take the result of part a and convert it into feet. Using the rule of three again we get:

Then the answer to part b is 7.5ft.

Let

x ------> number of hours Job A

y -----> number of hours Job B

we have that

x+y=22 ------> x=22-y ------> equation 1

6.40x+6.60y=143.60 ------> equation 2

Solve the system of equations

substitute equation 1 in equation 2

6.40(22-y)+6.60y=143.60

solve for y

140.8-6.40y+6.60y=143.60

0.20y=143.60-140.8

0.20y=2.8

y=14 hours

so

x=22-14=8

therefore

This problem describes two points in a route of 4 hours. He went through 68 miles after the first two hours, and 132 miles after 4 hours of driving. We need to calculate the average rate of change.

The average rate of change is the division between the total distance and the time it took to travel that distance, so we have:

The average rate of change is equal to 33 miles per hour.

Given that the average payout for slots machines is 84 cents on each dollar.

We know that

The cost of return for every dollar spent is 100-84=16 cents.

The percent return on every dollar spent in playing slots is

The percent return on every dollar spent in playing slots is 16%.

Given that Mike borrowed an amount for 2 years at 2% simple interest, and paid back a total of $3952.

To Determine: The original money he borrowed

Solution:

The formula to find the amount for simple interest is

Where:

A is the Amount paid back

r is the rate

t is the time

Given that

Substitute the given into the formula

Hence, the Mike originally borrow $3,800

Given the function:

the domain of the function is all the possible values of x that can be substituted into the function f(x)

for the log functions:

x - 3 > 0

x > 3

So, the domain of the function is all real numbers greater than 3

so, the answer will be option C

Donavan has 6x + 1/2 x total number of fishes.

Let Donovan has x number of blue fishes.

Hence the number of red fishes = 5x

The number of gray fishes = 1/2  of x = 1/2 x

Total number of fishes = red + blue + gray = 5x + x + 1/2 x = 6 + 1/2 x

For something like an equation to have any importance, the coefficient involving at least any variable must not be 0. In actuality, the following equation would either be inconsistent (for b ≠ 0) and have no solution, or full n-tuples are solutions, as was mentioned for one variable, if any variable does actually have a zero coefficient.

A regular polynomial over such a field, from which the coefficients are drawn, can also be equalized to zero to produce a linear equation. Since linear equations typically do a good job of representing non-linear systems, they are used extensively in all branches of mathematics as well as in physics and engineering.

Therefore we can infer that Donavan has 6x + 1/2 x total number of fishes.

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My first step is always to draw a picture

We are told the length is 4 less than twice the width

l = 2w-4

We are told the perimeter is 34

P =2(l+w)

Substitute the first equation in for l

P = 2( 2w-4 + w)

Combine like terms

34 = 2( 3w-4)

Distribute the 2

34 = 6w -8

Add 8 to each side

34+8 = 6w-8+8

42 = 6w

Divide by 6

42/6 = 6w/6

7 =w

Now we can find l

l = 2w-4 = 2(7) -4 = 14-4 = 10

The question asks for the area

A = l*w = 10 *7 = 70

Given,

The data of the male and female for different age group is shown in question tab.

Required:

The percentage of the female population is made up by the age of group 5- 9.

From the given data,

It is clearly seen that the percentage of female for 5 - 9 age group is 11%.

Hence, the percentage is 11%.