What is the GCF of 42 and 70

ANSWER:

48 months

STEP-BY-STEP EXPLANATION:

According to the statement we can propose the following equation, where the price of the car is more than or equal to the amount of the lease. Just like this:

Let x be the number of months

We solve for x, just like this:

Therefore, for 48 months, the car rental will be lower

The first step to factor this expression is to find its roots (the values of 'n' that makes this expression equals zero)

To find the roots, we can use the quadratic formula:

(Using the coefficients a=2, b=7 and c=5)

So the roots of the expression are -5/2 and -1. Now, we can write the expression in this factored form:

So the factored form is (2n+5)(n+1)

The composition of the function (g o f)(5) is evaluated as: (g o f)(5) = g(f(5)) = 6.

To find the composition of a function, we have to first evaluate the inner function for the given value of x that is given as its input. After that, the output of the inner function would then be used as the input for the outer function, which would now be evaluated for the composition of the function.

Given the functions:

f(x) = x² - 6x + 2

g(x) = -2x

We need to find the composition of the function, (g o f)(5), where the inner function is f(x), and the outer function is g(x).

Therefore:

(g o f)(5) = g(f(5))

Find f(5):

f(5) = (5)² - 6(5) + 2

f(5) = -3

Substitute x = -3 into g(x) = -2x:

(g o f)(5) = -2(-3)

(g o f)(5) = 6

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Answer:

y = [tex]\frac{1}{3}[/tex] x + 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 3x + 6 ← is in slope- intercept form

with slope m = - 3

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-3}[/tex] = [tex]\frac{1}{3}[/tex] , then

y = [tex]\frac{1}{3}[/tex] x + c ← is the partial equation

to find c substitute (3, 2 ) into the partial equation

2 = 1 + c ⇒ c = 2 - 1 = 1

y = [tex]\frac{1}{3}[/tex] x + 1 ← equation of perpendicular line

We have to use the tangent of angle 40 to find the height of the tower.

The adjacent side is 20m, and the angle is 40 degrees, then

Therefore, the height of the tower is 16.8m

Hello!

Let's solve your expression:

Let's replace where's z by 6, look:

So the value of this expression when z=6 is 72.

The given statement is true.

This is a question of probability.

It is given in the question that:-

Chance of raining here = 50 %

Chance of raining on Mars = 10 %

The given statement is :-

There is a 45 % chance that it will rain in neither place.

Chance of not raining here = 100 - 50 % = 50 % = 1/2

Chance of not raining on Mars = 100 - 10% = 90 % = 9/10

Hence, chance of raining in neither place = (1/2)*(9/10) = 9/20

9/20 = (9/20)*100 = 45 %.

Hence, the given statement "There is a 45% chance that it will rain in neither place" is true.

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Using scales, the distance of the two cities on the map would be of:

distance on the map = actual distance/40

A scale on the map represents the ratio between the actual length of a segment and the length of drawn segment, hence:

Scale = actual length/drawn length

In this problem, the scale is of 1 inch to 40 miles, meaning that:

Each inch drawn on the map represents 40 miles.

Then the distance of the two cities on the map, in inches, would be given as follows:

distance on the map = actual distance/40.

If the distance was of 200 miles, for example, the distance on the map would be of 5 inches.

The problem is incomplete, hence the answer was given in terms of the actual distance of the two cities. You just have to replace the actual distance into the equation to find the distance on the map.

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Initial money = 70

then add

10 + 30 + 150 + 7 = 197

Now add both results

70 + 197 = 267

Answer is

You have $267

We will have the following:

In order to have PQ entirely in the quadrant II, the transformation must be:

*Translate PQ up 4 units and to the left 3 units. [Option K]

Explanation

For the first question

We are asked to write the equation of the circle given that

The equation of a circle is of the form

In our case

Substituting the values

For the second question

Given that

We will have to get the midpoints (center) first

Next, we will find the radius

Using the points (4,-3) and (11,-8)

Explanation

Calculating scientific notation for a positive integer is simple, as it always follows this notation:

Step 1

To find a, take the number and move a decimal place to the right one position.

so

Step 2

Now, to find b, count how many places to the right of the decimal.

Step 3

finally,

Building upon what we know above,

a= 1.9

b=3 (Since we moved the decimal to the left the exponent b is positive)

replace

therefore, the answer i

I hope this helps you

0.07x+0.11(3x+24000)=27040

we will solve for x

x=61,000 [ investment at 7%]

Investment at 11% = 3x + 24000

= 3(61000)+24000

= 207000 [ investment at 11%]

The Solution:

Given the graph below:

We are required to determine the function that best describes the above graph.

Step1:

Identify the roots of the function from the given graph.

This means that:

So, the required function becomes:

Therefore, the correct answer is [option A]

Answer:

There are 59251.5 decigrams in 209 ounces.

Step-by-step explanation:

We'll solve this using the rule of three.

We know that there are 28.35 grams in an ounce. This way,

This way,

And since we know there are 10 decigrams in a gram, we'll have that:

This way,

This way, we can conclude that there are 59251.5 decigrams in 209 ounces.

We know that a box of cereal states that there are 75 calories in a 3/4 cup.

To find the unit rate for calories cup we must represent the the situation with an equation

Then, to find the unit rate for calories we need to solve the equation for x

Now, to find how many calories there are in 2 cups we must multiply the unit rate for calories by 2

Finally, the answers are:

- The unit rate for calories is 100 calories/cup.

- In 2 cups there are 200 calories.

ANSWER

Degree: 4

Number of terms: 2

EXPLANATION

Answer:

Quotient:

Remainder:

P(-2):

Step-by-step explanation:

Remember that the remainder theorem states that the remainder when a polynomial p(x) is divided by (x - a) is p(a).

To calculate the quotient, we'll do the synthetic division as following:

Step one:

Write down the first coefficient without changes

Step two:

Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).

Add the obtained result to the next coefficient of the dividend, and write down the sum.

Step 3:

Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).

Add the obtained result to the next coefficient of the dividend, and write down the sum.

Step 4:

Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).

Add the obtained result to the next coefficient of the dividend, and write down the sum.

Now, we will have completed the division and have obtained the following resulting coefficients:

Thus, we can conlcude that the quotient is:

And the remainder is 13, which is indeed P(-2)

we get that measure of the supplemantary angle is:

1) Gathering the data

$3500 computer

17% down

3.7% interest rate.

2) Since we want to know how much is that down payment, we must turn that 17% into decimal form, then multiply it by the computer value:

17%=0.17

3500 x 0.17 = $595

3) So Christian must pay $595 as the down payment

The rate of interest that Ariana should get in order to end up with a final amount of $233,000 is 0.07%.

What is compound interest and how is it calculated?
The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest.
Mathematically, A = P (1 + (R/f))ⁿ ;
where A = amount that the depositor will receive
P = initial amount that the depositor has invested
R = rate of interest offered to the depositor
f = frequency of compounding offered per year
n = number of years.

Given, Amount that Ariana wants to end up receiving = A = $233,00
Principal amount that Ariana can invest = P = $62,000
Frequency of compounding offered per year = f = 1
Number of years = 20
Let the rate of interest offered to the depositor be = R
Following the formula established in the literature, we have:
233000 = 62000(1 + R)²⁰ ⇒ 3.76 = (1 + R)²⁰ ⇒ 1.07 = 1 + R ⇒ R = 0.07%
Thus, the rate of interest that Ariana should get in order to end up with a final amount of $233,000 is 0.07%.

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The information given in the table on the Value of a Car and the Age of the Car, gives;

First Part;

The dependent variable is; The Value of Car

The independent variable is; The Age of Car

Second part;

The situation is a function given that each Age of Car maps to only one Value of Car.

A dependent variable is an output variable which is being observed, while an independent variable is the input variable which is known or controlled by the researcher.

First part;

The given information in the table is with regards to how the car's value decreases with time, therefore;

Second part;

A function is a relationship in which each input value has exactly one output.

Given that the Values of the cars are all different, and no two car of a particular age has two values, therefore;

Given that the first difference varies depending on the age of the car, the function can be taken as a piecewise function

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You have to subtract the fractions:

You have to subtract a negative number, as you can see in the expression, both negatives values are together. This situation is called a "double negative" when you subtract a negative value, both minus signs cancel each other and turn into a plus sign:

Now to add both fractions you have to find a common denominator for both of them. The fractions have denominators 7 and 9, the least common dneominator between these two numbers is the product of their multiplication:

7*9=63

Using this value you have to convert both fractions so that they have the same denominator 63,

For the first fraction 12/7 multiply both values by 9:

For the second fraction 2/9 multiply both values by 7:

Now you can add both fractions:

Example: Triangles like ABC and EDC are similar by SAS similarity, because angle C is congruent in each triangle, and AC/EC = BC/DC = 2. By the definition of similarity, it follows that AB/DE = BC/EF = AC/DF = 2.

Answer:

Radius = 1.59 in

Diameter = 3.18 in

Area = 7.94 in²

Explanation:

The circumference of a circle can be calculated as:

Where r is the radius of the circle and π is approximately 3.14. So, replacing C by 10 in and solving for r, we get:

Then, the radius is 1.59 in.

Now, the diameter is twice the radius, so the diameter is equal to:

Diameter = 2 x r = 2 x 1.59 in = 3.18 in

On the other hand, the area can be calculated as:

So, replacing r = 1.59 in, we get:

Therefore, the answer are:

Radius = 1.59 in

Diameter = 3.18 in

Area = 7.94 in²

Answer:

See below

Step-by-step explanation:

If you are given slope (m) and intercept (b) , then write the line equation like this:

y = mx + b

Given:

The objective is to find the fraction of 3/17% of the quantity.

Consider the quantity as x. The fraction of 3/17% of the quantity can be calculated as,

Hence, the required fraction of quantity is 3/1700 of x.

Answer

Algebraic equation that shows the relationship is

P = 20S

Explanation

Number of college professors = P

Number of students = S

There are 20 times as many students as professors.

P = (S) (20)

P = 20S

Hope this Helps!!!

ANSWER

40807 cm³/min

EXPLANATION

The tank has the shape of a cone, with a total height of 9 meters and a diameter of 3.5 m - so the radius, which is half the diameter, is 1.75 m. As we can see, the relationship between the height of the cone and the radius is,

So the volume of water will be given by,

Where h is the height of the water (not the tank).

If we derive this equation, we will find the rate at which the volume of water is changing with time,

We want to know what is the change of volume with respect to time, and this is,

Because the height also changes with time. We know that this change is 24 cm per minute when the height of the water in the tank is 1 meter (or 100 cm), so we have,

This is the rate at which the water is increasing in the tank. However, we know that there is a leak at a rate of 12300 cm³/min, which means that in fact the water is being pumped into the tank at a rate of,

Hence, the water is being pumped into the tank at a rate of 40807 cm³/min, rounded to the nearest whole cm³/min.

In this problem, want to find the equation of a line that will be parallel to a given function through a point.

Recall that parallel lines have the same slope.

We are given the line

and the point

Notice that the equations is technically in slope-intercept form, by the value of the slope will be 0:

Therefore, the slope of the line through (-5,4) will also be zero. We can use that information to find the equation.

Using the form

we can substitute the point and the slope to solve for b:

So, the equation of our line is: