can someone teach me how to isolate variables in algebra

Suppose \(f(x) =8^{3x\) and \(g(x) =8^{4x\), function operations that are correct include the following:

A. (f + g)(x) = \(8^{3x} + 8^{4x}\)

B. (f × g)(x) = \(8^{7x}\)

C. (f - g)(x) = \(8^{3x} - 8^{4x}\)

In Mathematics, an exponent is a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.

This ultimately implies that, an exponent is represented by the following mathematical expression;

bⁿ

Where:

By applying the division and multiplication law of exponents for powers of the same base to the functions, we have the following:

(f × g)(x) = \(8^{3x+ 4x}=8^{7x}\)

(f ÷ g)(x) = \(8^{3x- 4x}=8^{-x}\)

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Answer:

Your answer would be 9

Step-by-step explanation:

hope this helps

pls mak brainliest

Floyd needs 33 matches to make a rectangle with a length of 20 matches.

To find out how many matches Floyd needs to make a rectangle with a length of 20 matches, we can observe a pattern in the given information.

From the given data, we can see that as the length of the rectangle increases by 4 matches, the number of matches used increases by 8. This means that for every additional 4 matches in length, Floyd requires 8 more matches.

Using this pattern, we can calculate the number of matches needed for a rectangle with a length of 20 matches.

First, we need to determine the number of 4-match increments in the length of 20 matches. We can do this by subtracting the starting length of 3 matches from the target length of 20 matches, which gives us 20 - 3 = 17.

Next, we divide the number of 4-match increments by 4 to determine how many times Floyd needs to add 4 matches. In this case, 17 ÷ 4 = 4 with a remainder of 1.

Since Floyd requires 8 matches for each 4-match increment, we multiply the number of increments by 8, which gives us 4 × 8 = 32 matches.

Finally, we add the remaining matches (1 match in this case) to the total, resulting in 32 + 1 = 33 matches needed to reach a length of 20 matches.

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The statement "Every set can be considered a class" means that every object in set theory, including sets, can be considered a class. This is because classes are simply collections of objects, and sets are a type of collection.

The statement "If S is a set, consider the formula x S and the class {x: x = S}" means that if S is a set, then we can consider the formula x S, which states that x is an element of S, and the class {x: x = S}, which is the class of all objects that are equal to S.

In other words, the statement is saying that every set can be considered a class, and that we can define a class for any set by considering the formula that defines the set and the class of all objects that satisfy that formula.

For example, the set {1, 2, 3} can be considered a class by considering the formula x ∈ {1, 2, 3}, which states that x is an element of the set {1, 2, 3}, and the class {x: x ∈ {1, 2, 3}} is the class of all objects that are elements of the set {1, 2, 3}. This class is equal to the set {1, 2, 3}.

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Answer:

200

Step-by-step explanation:

The solution for a kite is multiply the two diagonals which in this case are both 20 and then divide the answer by 2

Answer:

Given that 1minute =3/7of the vessel

let the time taken in minutes to fill the whole of the vessel be' x' minute.

1min =3/7

xmin =whole vessel =1=7/7

=3x/7=1=x=7/3=2.3min=2min.3sec

Answer:

5400 needs to be paid after 2 years, and 400 will be paid in interest after 2 years

Step-by-step explanation:

.4 x 5000=200

5000+(2)200=x

5000+400=x

5400 needs to be paid after 2 years, and 400 will be paid in interest after 2 years

Answer:

Step-by-step explanation:

Dont really understand what your asking, is it fx=x+1? If so this should be it:

Answer:

4 + ( -7 X 2 ) = -10

Step-by-step explanation:

Check work:

-7 times 2 is -14.

4 + -14 = -10

Answer:

x=1/6 or x=0.1666666667

Step-by-step explanation:

The quadratic regressiοn equatiοn fοr the given data pοints is y = 5x² - 20x + 7

A secοnd-degree equatiοn οf the fοrm ax² + bx + c = 0 is knοwn as a quadratic equatiοn in mathematics. Here, x is the variable, c is the cοnstant term, and a and b are the cοefficients.

Tο find the quadratic regressiοn equatiοn fοr the given data pοints, we need tο fit a quadratic equatiοn οf the fοrm y = ax² + bx + c tο the data.

We can start by using the three given pοints tο set up a system οf three equatiοns:

\((1,-8): a(1)^2 + b(1) + c = -8\\\\(2,-4): a(2)^2 + b(2) + c = -4\\\\(3,6): a(3)^2 + b(3) + c = 6\)

SimpIifying each equatiοn, we get:

a + b + c = -8 (equatiοn 1)

4a + 2b + c = -4 (equatiοn 2)

9a + 3b + c = 6 (equatiοn 3)

AIternativeIy, we can use technοIοgy such as a caIcuIatοr οr spreadsheet tο sοIve the system.

SοIving the system using technοIοgy, we get:

a = 5

b = -20

c = 7

Therefοre, the quadratic regressiοn equatiοn fοr the given data pοints is:

y = 5x² - 20x + 7

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Answer:

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As per recipe, 700 g apples is enough to make apple crumble for 8 people.

For 6 people Shahina needs:

Since she has 550 grams of apple, which is more than 525 grams, she can make it for 6 people.

Answer:

With 550g of apples and enough other ingredients, Shahina can make apple crumble for 6 people according to the given recipe.

Step-by-step explanation:

Let's compare the recipe requirements with the available ingredients to determine whether Shahina can make apple crumble for 6 people with the given ingredients.

The recipe serves 8 people and requires the following quantities of ingredients:

Shahina has 550g of apples, which is sufficient to meet the apple requirement of the recipe.

Now, let's calculate the ratio of the other ingredients needed per person

For sugar:

240g / 8 people = 30g/person

For flour:

180g / 8 people = 22.5g/person

For butter:

40g / 8 people = 5g/person

Since the recipe is designed to serve 8 people, we can use these ratios to adjust the quantities for 6 people:

For sugar:

30g/person * 6 people = 180g

For flour:

22.5g/person * 6 people = 135g

For butter:

5g/person * 6 people = 30g

Comparing these adjusted quantities to the available ingredients, we see that Shahina has enough sugar, flour, and butter to make an apple crumble for 6 people.

Answer:

The answer would be $64.95

Step-by-step explanation:

Divide $25.98 by 2 and you'd get $12.99 as an answer.

Now multiply $25.98 by 2 and then add $12.99 to your answer.

Answer:

the supplement of 89° is the angle that when added to 89° forms a straight angle (180° )

Step-by-step explanation:

hope this helps have a good rest of your night/day :) ❤

Answer:

2/3x + 7 = 10

Step-by-step explanation:

Due to your wording, I believe this is what you might be looking for when you ask "2/3 a number x."

Answer:

43

Step-by-step explanation:

just trust me

Answer:

y=(-3/2)x+16

Step-by-step explanation:

Answer:

  4 and 6

Step-by-step explanation:

Look at the ways 24 can be written as a product.

  24 = 1×24 = 2×12 = 3×8 = 4×6

The sums of these factors are 25, 14, 11, 10. The factor pair you're looking for is the one that has a sum of 10:

  4 and 6

Answer:

d = sqrt(17)

Step-by-step explanation:

d = sqrt( x2 - x1)^2 + (y2 - y1)^2  )

d = sqrt( (4 - 5)^2 + (-3 - 1)^2 )

d = sqrt( (-1)^2 + (-4)^2  )

d = sqrt ( 1 + 16)

d = sqrt(17)

\(she \: paid = 2(1.69) + 1(1.49) + 1(1.09) + 0.68=6.64 \\ change = 10 - 6.64 = 3.36\)

Answer:

Y=1x-7

Step-by-step explanation:

First use two points to find the slope. I used the first 2. The formula is (y1-y2)/(x1-x2). So (6-8)/(1-3)= -2/-2 = 1. Then you plug in a point and the slope for the equation y1-y2=m(x1-x2). I am using the first point and m is the slope which is 1. Y-6 = 1(x-1)

y-6 = 1x -1 then get y by itself

y=1x-7

Answer:

uhm b but don't fully believe me if someone else answers i suggest using theirs

Step-by-step explanation:

Answer:

a ratio in which the second value is one

Step-by-step explanation:

Hope this helps!

Answer: How much of something per 1 unit of something else. Examples: • 100 cars pass by in 2 hours. The unit rate is 50 cars per hour. • You can paint 3 boards in half an hour. The unit rate is 6 boards per hour. • 200 sausages were eaten by 50 people. The unit rate is 4 sausages per person. • They need 5 m of thread to make 2 cm of cloth.

Step-by-step explanation: Just wanted to give a example if that doesn't help go to google and watch a video or do some reading about it!

The actual distance represented by 23.7 cm on the map is 355.5 km.

To find the ratio of the amount of money Mabaso has to the amount of money Thabo has and the amount of money Ally has, we can divide each amount by the smallest amount (which is R35) to simplify the ratio.

Mabaso has R140, Thabo has R70, and Ally has R35.

The ratio of Mabaso's money to Thabo's money is:

R140 ÷ R35 = 4

The ratio of Mabaso's money to Ally's money is:

R140 ÷ R35 = 4

Therefore, the ratio of the amount of money Mabaso has to the amount of money Thabo has and to the amount of money Ally has is 4:1:1.

To calculate the percentage discount of a steel table, we need to find the difference between the original price and the discounted price, and then divide it by the original price. Finally, we multiply the result by 100 to get the percentage.

Original price: R750

Discounted price: R600

Discount: R750 - R600 = R150

Percentage discount: (R150 ÷ R750) × 100 = 20%

So, the table has a 20% discount on Black Friday.

To convert 125 grams to kilograms, we divide the amount in grams by 1,000 (since there are 1,000 grams in a kilogram).

125 g ÷ 1,000 = 0.125 kg

Therefore, 125 grams is equal to 0.125 kilograms.

If a green grocer packs 12 apples in a plastic bag and has 285 apples, we divide the total number of apples by the number of apples per bag to determine the number of bags needed.

Number of bags needed: 285 apples ÷ 12 apples/bag = 23.75 bags

Since we can't have a fraction of a bag, we round up to the nearest whole number. Therefore, the green grocer would need 24 bags.

If the scale of a map is 1,500,000 and the measurement on the map is 23.7 cm, we can use the scale to determine the actual distance.

1 cm on the map represents 1,500,000 cm in reality.

23.7 cm on the map represents x cm in reality.

x = 23.7 cm × 1,500,000 cm = 35,550,000 cm

To convert cm to km, we divide by 100,000 (since there are 100,000 cm in a kilometer).

35,550,000 cm ÷ 100,000 = 355.5 km

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Answer:

C is the answer, please choose the letter C that's the answer

Answer:

\((3x+1)^2\)

Step-by-step explanation:

\(9x^2+6x+1=\\(3x+1)^2\)

You can confirm this by working and expanding backwards:

\((3x+1)^2=\\(3x+1)(3x+1)=\\9x^2+3x+3x+1=\\9x^2+6x+1\)

Hope this helps!

The factorized form of 9x² + 6x + 1 is indeed (3x + 1)².

To find the factorized form of the quadratic expression 9x² + 6x + 1 is (3x + 1)², we can expand the factorized form and compare it with the given expression to check if they are equal.

Expanding (3x + 1)² using the square of a binomial formula, we get:

9x² + 6x + 1

= 9x² + 3x + 3x + 1

= 3x (3x + 1) + 1 (3x + 1)

(3x + 1)² = (3x + 1)(3x + 1)

Comparing the expanded form of (3x + 1)² with the given expression 9x² + 6x + 1, we can see that they are equal.

Therefore, we have found that the factorized form of 9x² + 6x + 1 is indeed (3x + 1)².

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Answer:

12 feet

Step-by-step explanation:

The ladder is 12 feet up the wall.

The ladder forms a right triangle with the wall and the ground. You want to use Pythagorean theorem to solve the problem. a2+b2 = c2

Use the Pythagorean Theorem (a2+b2=c2) where b=9 and c=15. Solve for a.

(hope this helps can i plz have brainlist :D hehe)

Answer:

3. y = -4x + 2

4. y = 1/3x - 4

To find the slope count how many units it goes up nd down (rise) and left and right (run) ---> slope = rise/run

The b in y= mx + b is the y-intercept or the y variable.

Hope this helps, thank you :) !!

Answer:

Jane is 57  9/20 inches tall.

Step-by-step explanation: