If f(x)=2x^2+3 and g(x)=x^2-7, find (f-g)(x).

The greatest common factor is 2z^2

How you find it is first you find the greatest common factor of the two numbers, which is 2 (2 is the greatest number that can be multiplied into 2 and 10; 2 times 1 = 2 and also 2 times 5 = 10)

Then you find the greatest common factor of the variables, which is z^2.

(z^2 is the largest that can go into z^3 and z^2 because z^2 times z = z^3 and z^2 = z^2)

After that, you just multiply them together to get 2z^2

Answer:

x = -1/12

Step-by-step explanation:

It is actually a rather simple proof. Before we get to that, it’s important to understand a couple of other things. Let’s consider the following infinite summation:

X = 1 - 1 + 1 - 1 + 1 - 1 ...

Rearranging the above equation a little bit, we get:

X = 1 - (1 - 1 + 1 - 1 + 1 - 1 ...)

If you look at the term inside the brackets, it in fact equals X. So let’s substitute that:

X = 1 - X

2X = 1

X = 1/2

Now let’s consider another sum.

Y = 1 - 2 + 3 - 4 + 5 - ...

Writing it in another way, we get:

Y = 0 + 1 - 2 + 3 - 4 + 5 + ...

Adding the above two equations:

Y + Y = (1 - 2 + 3 - 4 + 5 ...) + (0 + 1 - 2 + 3 - 4 + 5 ...)

Grouping the corresponding terms within the brackets, we get:

2Y = 1 + 0 - 2 + 1 + 3 - 2 - 4 + 3 + 5 - 4 ...

2Y = 1 - (2-1) + (3-2) - (4-3) + ...

2Y = 1 - 1 + 1 - 1 + 1 - 1 ...

But the summation on the right hand side is X. Let’s substitute it:

2Y = X

2Y = 1/2

Y = 1/4

Finally, let’s consider our original question at hand i.e. the sum of all natural numbers:

S = 1 + 2 + 3 + 4 + ...

We defined Y earlier as:

Y = 1 - 2 + 3 - 4 + ...

Subtracting Y from S:

S - Y = 1 - 1 + 2 + 2 + 3 - 3 + 4 + 4 + ...

S - Y = 4 + 8 + 12 + 16 + ...

We just calculated the value of Y to be 1/4. So let’s substitute it:

S - 1/4 = 4 x (1 + 2 + 3 + 4 + ...)

S - 1/4 = 4S

3S = -1/4

S = -1/12

Inflation refers to the general increase in prices of goods and services in an economy over a period of time.

A rise in meat prices may be an indication of inflation, but it is not necessarily an automatic or definitive sign of inflation.

Inflation can hurt savers and fixed-income earners, such as retirees on a fixed pension, as the purchasing power of their savings and income decreases.

The Consumer Price Index (CPI) is used to measure the rate of inflation by tracking the average price change of a basket of goods and services commonly purchased by households, including food, housing, transportation, and medical care.

The CPI measures the percentage change in prices from a base period and is calculated by dividing the cost of the basket of goods and services in the current period by the cost of the same basket in the base period and multiplying the result by 100.

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Answer:

The items arranged from least steep to steepest rate of change are:

Michele's spending: $125 to $75 over time, spending $10 per week.

Elisa's puppy's weight: Started at 4 pounds, gained 5 pounds per month until it was 9 months old.

f(t): -6.2x + 2.9, a linear function with a rate of change of -6.2.

g(x): 8.1x + 45.64, a linear function with a rate of change of 8.1.

So the correct order is:

Michele's spending

Elisa's puppy's weight

f(t)

g(x)

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

10x - 20 + 6x + 8 = 180

Supplementary angles

Answer:

x = 12

Step-by-step explanation:

The two given angles create a straight line (Definition of Straight Line). This means that:

[tex](10x - 20) + (6x + 8) = 180[/tex]

First, combine like terms. Like terms are terms that share the same amount of the same variables:

[tex](10x + 6x) + (8 - 20) = 180\\(16x) + (-12) = 180\\16x - 12 = 180\\[/tex]

Next, isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS is the order of operations and stands for:

Parenthesis

Exponents (& Roots)

Multiplications

Divisions

Additions

Subtractions

~

First, add 12 to both sides of the equation:

[tex]16x - 12 = 180\\16x - 12 (+12) = 180 (+12)\\16x = 180 + 12\\16x = 192[/tex]

Next, divide 16 from both sides of the equation:

[tex]\frac{16x}{16} = \frac{192}{16} \\x = \frac{192}{16}\\ x = 12[/tex]

12 is your answer.

~

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Answer:

Step-by-step explanation:

80.000

In this case, renting the huge van would be a more cost-effective option because it would run you $289 as opposed to $354.65 for the minivan.

To compare the costs of renting the minivan and the large van, we need to calculate the total cost for each option.

For the minivan, the cost per day is $24.95 and the cost per mile is $0.15. So, for 7 days and 1,200 miles, the total cost would be:

Total cost = 7($24.95) + 1,200($0.15)

= $354.65

For the large van, the cost is a flat rate of $289 per week with no additional charge for mileage. So, for 7 days and 1,200 miles, the total cost would be:

Total cost = $289

Therefore, renting the large van would be a better buy in this scenario, as it would cost $289 compared to $354.65 for the minivan.

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Answer:

The interest earned in $210.00

Step-by-step explanation:

i = prt

i = 3000(.07)(1)

i = 210.00

Helping in the name of Jesus.

Answer: x=5

Step-by-step explanation:

Not much calculations needed, but since we have two points where x=5, a vertical line that is equal to x=5 will hit both points. I attached it visually below!

The time it took Milan longer to clean the bathroom is 3 1/8 hours

Time taken for Milan to clean the bathroom = 3 1/4 hours

Time taken for Milan to clean the kitchen = 1/8 hours

Time taken longer for Milan to clean the bathroom = 3 1/4 hours - 1/8 hours

= 13/4 - 1/8

= (26-1) / 8

= 25/8

= 3 1/8 hours

In conclusion, it took Milan 3 1/8 hours longer to clean the bathroom.

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Answer:

70

Step-by-step explanation:

The non-labeled side (next to 130) has to be supplementary to the angle outside, hence it has to be 50. Since all the sides of an angle must add up to 180, we can subtract 60+50 to get 70. Hope this helps!

Answer:

70°

Step-by-step explanation:

Theorem:

The measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles.

130 = x + 60

x = 70

Answer: 70°

Correct answer is option A. If the height of the pyramid on the drawing was 3 1/2 inches, then the height of the actual pyramid is 98 feet

When a scale drawing or model is made, the actual object is typically much larger than the drawing or model. In order to represent the object in a smaller size, a ratio is used to scale down the dimensions. This ratio is can be in a fraction form or 'is to' form. We can use this ratio to easily calculate the dimensions of a replica from the actual object or vice versa.

To find the height of the actual pyramid, we need to use both scales given in the problem.

We can start by finding the height of the replica using the first scale:

1 inch on the drawing = 2 feet on the replica

So, 3.5 inches on the drawing = (3.5 * 2) feet on the replica = 7 feet on the replica

Now, using the second scale we can find the height of the actual pyramid:

1 foot on the replica = 14 feet on the actual pyramid

So, 7 feet on the replica = (7 * 14) feet on the actual pyramid = 98 feet

Therefore, the height of the actual pyramid is 98 feet.

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Answer:

radius = 72.00 units

Step-by-step explanation:

The general formula for circumference (C) of a circle is C = πd, where d is the diameter.  The formula using 3.14 for π is C = 3.14d   The diameter (d) is simply twice the radius (r) as d = 2r

Thus, we can rewrite the formula for circumference in terms of radius as C = 3.14(2r)

To solve for r, we can divide the circumference we're given by the product of 3.14 and 2 to find r:

[tex]C/(2*3.14)=r\\452.16(2*3.14)=r\\452.16/6.28=r\\72=r[/tex]

The measure of the arc angle is as follows:

m∠BAC = 228°

The central angle of an arc is the central angle subtended by the arc.  

The measure of an arc is the measure of its central angle.

The Central Angle theorem states that the central angle subtended by

two points on a circle is  twice the inscribed angle subtended by those

points.

Therefore, let's find m∠BAC

Hence,

m∠BC = Central angle

m∠BAC = 360 - 132

m∠BAC = 228 degrees

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The recursive equation for this table is given as follows:

f(n) = 3f(n - 1) + 1.

To obtain the recursive equation, we must obtain a pattern between a term and the previous term.

For this problem, we have that each term is the previous term multiplied by 3 and added by one.

Hence the recursive equation for this table is given as follows:

f(n) = 3f(n - 1) + 1.

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so, we know the diameter is 8, so that means its radius is half that, or 4.

[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=4\\ \theta =45 \end{cases}\implies A=\cfrac{(45)\pi (4)^2}{360}\implies A=2\pi ~ft^2[/tex]

Answer:

√(205)/13

Step-by-step explanation:

The table describes the relationship between membership status and attendance of classes under the principle of independence.

Option A is the correct answer.

We have,

This table describes the relationship between membership status and attendance of classes.

To determine if there is a relationship, we need to apply the principle of independence.

If the principle of independence holds, then the events "having a membership" and "attending one or more classes" are independent of each other, and similarly, the events "not having a membership" and "attending none of the classes" are independent of each other.

To check for independence, we can calculate the expected values for each cell assuming independence holds, and compare them to the observed values.

The expected value for "Have a membership" and "Attend one or more classes".

= (40/70) x (31/70) x 70

= 17.86

The expected value for "Have a membership" and "Attend none of the classes".

= (40/70) x (39/70) x 70

= 22.14

The expected value for "Do not have a membership" and "Attend one or more classes".

= (30/70) x (31/70) x 70

= 13.14

The expected value for "Do not have a membership" and "Attend none of the classes".

= (30/70) x (39/70) x 70

= 16.86

Comparing these expected values with the observed values, we see that they are reasonably close, indicating that the principle of independence holds.

Therefore,

We can conclude that this table describes the relationship between membership status and attendance of classes under the principle of independence.

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It is a right triangle so f² =  g² + h² not f² + g² = h²

What is the Pythagoras theorem?

A right triangle's three sides are related in Euclidean geometry by the Pythagorean theorem, also known as Pythagoras' theorem. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Here, we have

Given: Lindsay sketches a right triangle with lengths f, g, and h has shown. She uses the Pythagorean Theorem to write the equation f² + g² = h² to represent the triangle.

It is a right triangle.

∴ f² =  g² + h² not f² + g² = h²

Hence, It is a right triangle. f² =  g² + h² not f² + g² = h²

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Answer:

To find the probability that a randomly selected student who received a "C" was male, we need to calculate the total number of male students who received a "C" and divide it by the total number of students who received a "C".

Total number of male students who received a "C": 12

Total number of students who received a "C": 20

Probability that the student was male:

12/20 = 0.6

Therefore, the probability that a randomly selected student who received a "C" was male is 0.6, or 60%.

Answer:

y = -5/3 x - 13

Step-by-step explanation:

Parallel lines have the same slope.  The slope will be -5/3

y = mx + b

We will substitute -3 for y (-6,-3).

We will substitute -5/3 for m.

We will substitute -6 for x (-6,-3)

-3 = -5/3(-6) + b

-3 = [tex]\frac{30}{3}[/tex] + b

-3 = 10 + b  Subtract 10 from both sides

-3 - 10 = 10 - 10 + b

-13 = b

To write the equation, use -5/3 for m (the slope) and -13 for b (the y-intercept)

y = mx + b

y = -5/3 x - 13

Helping in the name of Jesus.

We can see here that the equation that best models the situation is: B.  13 - (60h/23) = 10.

Speed is a scalar quantity that describes how fast an object is moving, or the rate at which it covers distance. It is typically measured in units of distance per unit of time, such as miles per hour or meters per second.

Speed only tells us how fast an object is moving, without any information about the direction of motion or changes in direction.

We can see that if we find the time, h in hours, we will have:

h = (3 x 23)/60

Simplifying this expression gives us:

h = 69/60

Therefore, the equation is:

h = 1.15

(Note: 3 is gotten from 13 gallons - 10 gallons = 3 gallons that was used at that particular time and speed).

If we substitute h = 1.15 into our model equation, we will get the correct answer.

Thus, 13 - (60 × 1.15)/23 = 10.

∴ Option B is the correct answer.

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The total amount owed, to the nearest cent A = $ 3,283.44

Simple interest is interest that is only calculated on the initial sum (the "principal") borrowed or deposited. Generally, simple interest is set as a fixed percentage for the duration of a loan. No matter how often simple interest is calculated, it only applies to this original principal amount.

A = P + I where

P (principal) = $ 2,950.00

I (interest) = $ 333.44

A = P(1 + r/n)^nt

Where:

A = Accrued Amount (principal + interest)

P = Principal Amount

I = Interest Amount

R = Annual Nominal Interest Rate in percent

r = Annual Nominal Interest Rate as a decimal

r = R/100

t = Time Involved in years, 0.5 years is calculated as 6 months, etc.

n = number of compounding periods per unit t; at the END of each period

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Correct question:

Find the total amount owed, to the nearest cent, for a simple interest loan with a principal of $2950, an interest rate of 7.4% and a time period of 1.5 years. Show​

When Joann turns 18, she will have approximately $41,551.20 in her investment account.

FV = P * [(1 + r)^n - 1] / r

FV = future value

P = periodic payment ($300)

r = interest rate per period (0.04 / 2 = 0.02)

n = total number of periods (18 years * 2 = 36)

FV = 300 * [(1 + 0.02)^36 - 1] / 0.02

FV ≈ 300 * [2.3084] / 0.02

FV ≈ 34,626.00

Solve for inotial investment

FV_initial = PV * (1 + r)^n

FV_initial = 3000 * (1 + 0.02)^36

FV_initial ≈ 3000 * 2.3084

FV_initial ≈ 6,925.20

we have to add both future values

Total_FV = 6,925.20 + 34,626.00

Total_FV ≈ 41,551.20

When Joann turns 18, she will have approximately $41,551.20 in her investment account.

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Answer:

s = 10√3

Step-by-step explanation:

This is a 30°-60°-90° right triangle, so s, the length of the longer leg, is √3 times the length of the shorter leg. Since the length of the shorter leg is 10, s = 10√3.

At a certain restaurant, the hourly wage for a waiter is 20 percent greater than the hourly wage for a dishwasher, and the hourly wage for a dishwasher is half as much as the hourly wage for a cook's assistant. If a cook's assistant earns $13.00 an hour.

Let's break down the problem and use algebra to solve it step by step

1. Let x be the hourly wage for a dishwasher.

2. We know that the hourly wage for a waiter is 20% greater than the hourly wage for a dishwasher, so the hourly wage for a waiter is

x + 0.2x = 1.2x

3. We also know that the hourly wage for a dishwasher is half as much as the hourly wage for a cook's assistant, so

x = 1/2 * $13.00

x = $6.50

Therefore, the hourly wage for a dishwasher is $6.50.

4. We can substitute x = $6.50 into the expression we found for the hourly wage of a waiter

1.2x = 1.2 * $6.50

1.2x = $7.80

Therefore, the hourly wage for a waiter is $7.80.

5. Finally, we can calculate the difference in hourly wage between a cook's assistant and a waiter

Hourly wage difference = hourly wage for cook's assistant - hourly wage for waiter

Hourly wage difference = $13.00 - $7.80

Hourly wage difference = $5.20

Therefore, a waiter earns $5.20 less than a cook's assistant each hour.

In summary, we can use algebra to find that a dishwasher earns $6.50 an hour, a waiter earns $7.80 an hour, and a waiter earns $5.20 less than a cook's assistant each hour.

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x = how many acres

keeping in mind that  one yd² has 9 ft², and that an acre has 4840 yd²

[tex](300ft)(160ft)\implies 48000ft^2\implies \cfrac{48000}{9}\implies \cfrac{16000}{3}~yd^2 \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{ccll} acre&yd^2\\ \cline{1-2} 1 & 4840\\[1em] x&\frac{16000}{3} \end{array} \implies \cfrac{1}{x}~~=~~\cfrac{4840}{ ~~ \frac{16000}{3} ~~ }\implies \cfrac{1}{x}=\cfrac{14520}{16000} \\\\\\ 16000=14520x\implies \cfrac{16000}{14520}=x\implies 1.10\approx x[/tex]