Need help solving three questions on algebra homework

Answer:

2nd answer : it is equivalent but not completely factored

Step-by-step explanation:

the "pulling out" of 3 as factor was completely correct.

but

3(x² - 4) can be further factored.

remember :

(a + b)(a - b) = (a² - b²)

therefore,

(x² - 4) = (x + 2)(x - 2)

and then

3(x + 2)(x - 2)

would be a complete factorization.

Answer: B) The expression is equivalent, but is not completely factored

Step-by-step explanation:

The values of x and y for the parallelogram PQRS are respectively, 2 & 7

Opposite sides are parallel: The pairs of opposite sides of a parallelogram are always parallel to each other.

Opposite sides are equal in length: The pairs of opposite sides of a parallelogram are equal in length.

Given that,

The parallelogram PQRS has diagonals PR and SQ that intersects at T,

T is the midpoint of PR and T is the midpoint of SQ

If T is the midpoint of PR, then PT = TR

Given  PT = y and TR = 3x+1

y = 3x+ 1 _____(i)

Also, If T is the midpoint of SQ, then ST = TQ

Given QT=3y and TS=4x+13

3y = 4x+ 13 ____(ii)

Substitute equation 1 into 2;

3y = 4x+ 13

3(3x+1) = 4x+ 13

open the parenthesis

9x+3 = 4x+13

club like terms

9x-4x = 13-3

5x = 10

x = 10/5

x = 2

Substitute x = 2 into equation 1

From 1; y = 3x+1

y = 3(2)+1

y = 6+1

y = 7

Hence, the values are x = 2 and y = 7

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The complete questions :

Parallelogram PQRS has diagonals PR and SQ that intersect at T find the values of x and y PT=y TR=3x+1 QT=3y TS=4x+13

The required value of the expression at x = 4 and x = -4 is 81 and 1/81 while as x gets larger simultaneously 3ˣ approaching to infinity.

The function which is in format f(x) =aˣ where a is constant and x is variable,  the domain of this exponential function lies   (-∞, ∞).

Here,
Given expression,

= 3ˣ

put x = 4
= 3⁴ = 81

Now put x = -4
= 3⁻⁴
= 1/3⁴

= 1/81

Since x gets larger as x = 0, 1, 2, 3, and so on 3ˣ get 1, 9, 27, 81 and so on approaching to infinity.

Thus, the required value of the expression at x = 4 and x = -4 is 81 and 1/81 while as x gets larger simultaneously 3ˣ approaching infinity.

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Answer:

Common ratio, r = 3

Step-by-step explanation:

Common ratio is given by the ratio of one of the terms to the previous term and is a constant for the entire sequence

Here the first term is 17

Second term is 51

Second Term ÷  First Term
= 51 ÷ 17 =3

Third Term ÷ Second Term
= 153 ÷ 51 = 3

So common ratio is 3

In general, if aₙ is the nth term and aₙ₊₁ then the common ratio is given by:
aₙ₊₁ / aₙ

Answer: Decreased 40%

Step-by-step explanation:

Alright, we know they reduced $10.00 (25-15)

Now all we have to do is find the percentage, 10 is how much of 25?

10/25 =0.4

(to get 0.4 to a percentage multiply by 100)

The price was decreased by 40%

Answer:

Step-by-step explanation:

1.1. Advantages of Selling Prepaid Electricity

Two advantages of selling prepaid electricity are:

a) Reduced costs for the municipality: Prepaid meters eliminate the need for the municipality to send meter readers to each property and manually read the meter. This can save the municipality time and money.

b) Improved cash flow: By receiving payment before the electricity is used, the municipality can improve its cash flow as it will have funds available to purchase more electricity.

1.2. Number of Units Mr Nkomo Received When He Bought Prepaid Electricity for R68,02

The rate per kWh including VAT is R1,33. To determine the number of units Mr Nkomo received, we can use the formula:

Units = Amount / Rate

Units = R68,02 / R1,33

Units = 51.04 kWh

So, Mr Nkomo received 51.04 kWh of electricity when he bought prepaid electricity for R68,02.

1.3. Cost of 310 kWh of Electricity

The rate per kWh including VAT is R1,33. To determine the cost of 310 kWh of electricity, we can use the formula:

Cost = Units * Rate

Cost = 310 kWh * R1,33

Cost = R411,30

So, Mr Nkomo will have to pay R411,30 for 310 kWh of electricity.

1.4. Percentage Profit the Municipality Makes When a Customer Buys 290 kWh of Electricity

To determine the percentage profit the municipality makes when a customer buys 290 kWh of electricity, we need to calculate the cost price and the selling price of the electricity. The cost price of electricity is R1,33 per kWh. The selling price is given in the table as R144,72 for 2-50 kWh, R186,06 for 51-350 kWh, R261,87 for 351-600 kWh, and R308,37 for over 600 kWh.

Since the cost price is R1,33 per kWh and the selling price is different for different ranges of units, we need to calculate the cost and selling price for each range of units and find the average.

For 2-50 kWh:

Cost = 2-50 kWh * R1,33

Cost = 50 kWh * R1,33

Cost = R66,50

Selling price = R144,72

Profit = Selling price - Cost

Profit = R144,72 - R66,50

Profit = R78,22

Percentage profit = (Profit / Cost) * 100

Percentage profit = (R78,22 / R66,50) * 100

Percentage profit = 17.7%

For 51-350 kWh:

Cost = 51-350 kWh * R1,33

Cost = 350 kWh * R1,33

Cost = R466,50

Selling price = R186,06

Profit = Selling price - Cost

Profit = R186,06 - R466,50

Profit = R29,56

Percentage profit = (Profit / Cost) * 100

Percentage profit = (R29,56 / R466,50) * 100

Percentage profit = 6.3%

For 351-600 kWh:

Cost = 351-600 kWh * R1,33

Cost = 600 kWh * R1,33

Cost = R798,00

Selling price = R261,87

Profit = Selling price - Cost

Profit = R261,87 - R798,00

Profit = -536,13

Percentage profit = (Profit / Cost) * 100

Percentage profit = (-536,13 / R798,00) * 100

Percentage profit = -67.3%

For over 600 kWh:

Cost = over 600 kWh * R1,33

Cost = R1,33 * 1000

Cost = R1330,00

Selling price = R308,37

Profit = Selling price - Cost

Profit = R308,37 - R1330,00

Profit = -1021,63

Percentage profit = (Profit / Cost) * 100

Percentage profit = (-1021,63 / R1330,00) * 100

Percentage profit = -76.7%

The average percentage profit for the municipality is calculated by finding the total profit and total cost for each range of units and then dividing the total profit by the total cost.

For the range 2-50 kWh, the total profit is R78,22 and the total cost is R66,50, so the average percentage profit is (R78,22 / R66,50) * 100 = 17.7%.

For the range 51-350 kWh, the total profit is R29,56 and the total cost is R466,50, so the average percentage profit is (R29,56 / R466,50) * 100 = 6.3%.

For the range 351-600 kWh, the total profit is -536,13 and the total cost is R798,00, so the average percentage profit is (-536,13 / R798,00) * 100 = -67.3%.

For the range over 600 kWh, the total profit is -1021,63 and the total cost is R1330,00, so the average percentage profit is (-1021,63 / R1330,00) * 100 = -76.7%.

The average percentage profit for the municipality for the four ranges of units is calculated as follows:

Average percentage profit = (17.7% + 6.3% - 67.3% - 76.7%) / 4

Average percentage profit = -34.05%

Therefore, Mr Nkomo's claim that the percentage profit the municipality makes when a customer buys 290 kWh of electricity is more than 34% is NOT VALID.

Answer:

Right, Isosceles

Step-by-step explanation:

The little square in the corner means its right angled, so a right triangle. This also means that it cannot be acute or obtuse.

The two hash marks shows two sides are the same. So it is isosceles. This also means it cannot be scalene or equilateral.

The number that is closest to -1 is -0.82 while the number that is closest to -1/4 is -0.28.

In order to obtain the numbers that are close to a given number, we need to place the numbers side by side for a better understanding. For instance, the number 3 is closer to number 1 while the number 9 is closer to number 10.

Given the number line above, we can arrive at the conclusion that -0.82 is closer to -1 because by approximating the decimal, we will arrive at figure 1. Also, the number, -0.28 is closer to -1/4 or - 0.25 when converted to decimal.

Options;

A. -0.28

B. -0.82

C. -4/5

D. -1/5

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Answer:

  -5x⁵ +2x² -3/x³

Step-by-step explanation:

You want the quotient and remainder of (-15x⁸ +6x⁵ -9)/(3x³).

The quotient and remainder can be found by dividing term by term.

  [tex]\dfrac{-15x^8+6x^5-9}{3x^3}=\dfrac{-15x^8}{3x^3}+\dfrac{6x^5}{3x^3}-\dfrac{9}{3x^3}\\\\\\=\boxed{-5x^5+2x^2-\dfrac{3}{x^3}}[/tex]

__

Additional comment

The exponent rule is (a^b)/(a^c) = a^(b-c).

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The intervals of each behavior of the function are given as follows:

a) Increasing: (-∞, -1).

b) Decreasing: (-1, 1).

c) Constant: (1, 3).

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On solving the provided question, we can say that by fraction, 4/3 (orange Juice) + 3/4 apple juice + 2/3 cranberry juice + 3/4 lemon lime juice.

Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.

by fraction

4/3 (orange Juice) + 3/4 apple juice + 2/3 cranberry juice + 3/4 lemon lime juice.

16/12+9/12+8/12+9/12=42/12=3 and 1/2 cups.

20/3.5=5.7 or 6

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The US EIA should use a sample size of at least 25 for a margin of error of $0.10, at least 49 for a margin of error of $0.07, and at least 97 for a margin of error of $0.05 to report the average price of a gallon of regular gasoline with 95% confidence.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

We can use the formula for the margin of error for a 95% confidence interval:

margin of error = z× (standard deviation / √n)

where z is the z-score for a 95% confidence interval, which is 1.96.

a. The desired margin of error is $0.10:

0.10 = 1.96(0.25 /√n)

√n = 1.96×0.25 / 0.10

√n= 4.9

n = 4.9^2

n = 24.01

So the appropriate sample size for a margin of error of $0.10 is at least 25.

b. The desired margin of error is $0.07:

0.07 = 1.96 (0.25 / √n)

√n = 1.96 × 0.25 / 0.07

√n= 6.97

n = 6.97²

n = 48.53

So the appropriate sample size for a margin of error of $0.07 is at least 49.

c. The desired margin of error is $0.05:

0.05 = 1.96 (0.25 / √n)

√n= 1.96 × 0.25 / 0.05

√n= 9.8

n = 9.8²

n = 96.04

So the appropriate sample size for a margin of error of $0.05 is at least 97.

Therefore, the US EIA should use a sample size of at least 25 for a margin of error of $0.10, at least 49 for a margin of error of $0.07, and at least 97 for a margin of error of $0.05 to report the average price of a gallon of regular gasoline with 95% confidence.

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Answer:

50:7

Step-by-step explanation:

You just put ":" in between the numbers requested.

The value of x in the triangle is 5 units.

A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees. The perimeter of a triangle is the sum of the whole three sides of the triangle.

Hence,

x + 2x + 3 + x + 9 = 32

4x + 12 = 32

subtract 12 from both sides of the equation

4x + 12 = 32

4x + 12 - 12 = 32 - 12

4x = 20

divide both sides of the equation by 4

x = 20 / 4

x = 5

Therefore,

x = 5

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Answer:A decrease of 20%.

First we must subtract out new total from our old total.

9390 - 7512 is 1878. This means that there is a difference of 1878. Next we must divided both 7512 and 1878 into 9390.

7512/9390 is 0.8 & 1878/9390 is 0.2

As a percentage that is 80% and 20%.

This means that the new amount of sugar only makes up 80% of the old amount. That means that there was a decrease of 20% of kilograms of sugar.

I hope this helped & Good Luck <3 !!!

Translation the graph of the function  [tex]y=f(x)[/tex]a units to the right gives you the function [tex]y=f(x-a)[/tex]

If the graph of the function [tex]f(x)=3^{x}[/tex] is translated 6 units to the right, then the function becomes

[tex]g(x)=f(x-6)=3^{x-6}[/tex]

Answer: correct choice is A

The domain and the range of a function/graph/relation are defined as follows:

The problem is incomplete, hence the concepts of domain and range are presented, and then they are used to obtain the domain and the range.

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The solution to the question on the equilibrium of the cheese and bagels have been given below

a) If the equilibrium price of cream cheese and the equilibrium quantity of bagels have both risen, this could be caused by a fall in the price of flour, one of the inputs used to produce bagels.

This decrease in the cost of production would cause the supply of bagels to increase, leading to a rightward shift in the supply curve. At the same time, the demand for bagels would increase as consumers substitute away from other breakfast foods and toward bagels, leading to a rightward shift in the demand curve.

These two shifts would result in a higher equilibrium price for cream cheese, since bagels and cream cheese are complements. The increased demand for bagels would lead to an increase in the demand for cream cheese, causing the demand curve for cream cheese to shift rightward.

The diagram below illustrates this relationship. The initial equilibrium is at point A, with a price of P1 and a quantity of Q1. After the decrease in the price of flour, the supply curve for bagels shifts rightward to S', and the demand curve for bagels shifts rightward to D'. The new equilibrium is at point B, with a higher price of P2 and a higher quantity of Q2. The increase in the demand for bagels leads to an increase in the demand for cream cheese, causing the demand curve for cream cheese to shift rightward to D'''. The new equilibrium for cream cheese is at point C, with a higher price of P3 and a higher quantity of Q3.

b) If the equilibrium price of cream cheese has risen but the equilibrium quantity of bagels has fallen, this could be caused by a rise in the price of milk, one of the inputs used to produce cream cheese.

This increase in the cost of production would cause the supply of cream cheese to decrease, leading to a leftward shift in the supply curve. At the same time, the demand for cream cheese would decrease as consumers substitute away from cream cheese and toward other breakfast foods, leading to a leftward shift in the demand curve.

These two shifts would result in a higher price for cream cheese, but a lower quantity of bagels consumed. The decreased demand for cream cheese would lead to a decrease in the demand for bagels, causing the demand curve for bagels to shift leftward.

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Answer: 50 Cups

Step-by-step explanation:

16 cups in a gallon. so times that by 2, which equals 32. There are four cups in one quart so times 4 by 4 which is 16 and add to 32. 16 + 32 = 48

Two cups in a pint so add 2 to 48 which is 50

Answer:

You will get 25 cups if you mix 2 gallons, 4 quarts, and 1 pint.

Step-by-step explanation:

To convert between gallons, quarts, and pints, we need to use the following conversions:

1 gallon = 4 quarts

1 quart = 2 pints

Here's the step-by-step process to convert the given volume to cups:

Convert gallons to quarts: 2 gallons * 4 quarts/gallon = 8 quarts

Add the number of quarts from step 1 to the number of quarts given: 8 quarts + 4 quarts = 12 quarts

Convert pints to quarts: 1 pint * 1 quart/2 pints = 0.5 quarts

Add the number of quarts from step 3 to the number of quarts from step 2: 12 quarts + 0.5 quarts = 12.5 quarts

Convert quarts to cups: 12.5 quarts * 2 cups/quart = 25 cups

Therefore, you will get 25 cups if you mix 2 gallons, 4 quarts, and 1 pint.

Step-by-step explanation:

answer, verified answer

Answer:

Step-by-step explanation: The expression for f(x) is not a valid mathematical equation. It should specify the relationship between x and the output value of f(x). If the correct equation for f(x) is given, we can then find the expression for (f + g)(x) and g(x).

Assuming that the equation for f(x) is as follows:

f(x) = 12 + x

Then, the expression for (f + g)(x) can be found by adding f(x) and g(x):

(f + g)(x) = f(x) + g(x) = 12 + x + (5 - x) = 17

So, (f + g)(x) is a constant function with a value of 17 for all values of x.

And the expression for g(x) was already given:

g(x) = 5 - x

Answer:

x = 5, y = 1

Step-by-step explanation:

For x :

Substitute y into the equation : 5x + 3 ( -1/5x + 2 ) = 28

Simplify : 22/5x + 6 = 28

Isolate x : x = 5

For y :

Substitute x for 5 : y = -1/5 * 5 + 2

Solve: y = 1

The equation of line passing through the points (-2, 4) & (4, 2) is :

y = -1/3 x + 6

The value of b = 6

The equation of a straight line is a relationship between x and y coordinates, The general equation of a straight line is y = mx + c, where m is the slope of the line and c is the y-intercept.

To find the equation of the line passing through the two points (-2, 4) and (4, 2), we can use the point-slope form of a line. The point-slope form of a line is given by:

y - y₁ = m(x - x₁)

where m is the slope of the line and (x₁, y₁) is any point on the line.

To find the slope of the line, we can use the formula:

m = (y₂ - y₁) / (x₂ - x₁)

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

Plugging in the values for the given points, we get:

m = (2 - 4) / (4 - (-2))

m = -2 / 6

m = -1/3

Next, we can use one of the given points to write the equation in point-slope form:

y - 4 = -1/3 (x - (-2))

y - 4 = -1/3 x + 2

y = -1/3 x + 6

This is the equation of the line passing through the two given points (-2, 4) and (4, 2).

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In these triangles, the largest angle and the largest side have been measured. This means that the two smaller sides and the two smaller angles are proportional to each other. This is known as the triangle inequality, which states that the sum of any two sides of a triangle must be greater than the third side. This means that the two smaller angles and the two smaller sides of the triangle must add up to be larger than the largest angle or side.

The Triangle Inequality states that the sum of any two sides of a triangle must be greater than the third side. This means that two other inequalities can be written:

a > |c - b| and b > |c - a|,

where |x| is the absolute value of x. This means that the length of each side must be greater than the difference between the other two sides

Answer:yo no se como ablar ingles

Step-by-step explanation: perdoname

The total amount of interest that Alvin paid over the course, guven the value of the student loan and the interest rate is $ 6, 185

To find the interest paid, you need to find the total amount that Alvin paid in the 10 years that he was paying.

To do this, you first need to find the monthly payments. This will be an annuity as the amount will be the same throughout the student loan payment period.

The amount would be :

Student loan value = Amount x Present value interest factor of annuity, 120 periods, 4. 4 % / 12

The periods are :

= 10 years x 12 months

= 120 months

The amount is:

26, 000 = Amount x 96.939576551857

Amount = 26, 000 / 96.939576551857

Amount = $ 268. 21

The total paid over the 10 years is :

= 268. 21 x 120 months

= $ 32, 184. 9972

The interest is :

= 32, 184. 9972 - 26, 000 loan amount

= $ 6, 185

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Answer:

Step-by-step explanation:

To solve this problem, we must first use an equation that reflects the amount of acid in each solution and its relationship to the total volume of the resulting solution. We can use the following equation:

(C1 * V1) + (C2 * V2) = (C3 * V3)

Where:

C1 = concentration of the acid solution at 60% (in percent)

V1 = volume of the acid solution at 60% (in ml)

C2 = concentration of the acid solution at 30% (in percent)

V2 = volume of the 30% acid solution (in ml)

C3 = concentration of the resulting 50% acid solution (in percent)

V3 = volume of the resulting 50% acid solution (in ml)

In this case, we know the total volume of the resulting solution (V3 = 300 ml) and the desired concentration (C3 = 50%). We also know the concentration of one of the original solutions (C1 = 60%). So we can plug the known values ​​into the equation:

(60 * V1) + (30 * V2) = (50 * 300)

Clearing V1:

V1 = (300 * 50 - 30 * V2) / 60

Now that we have V1 as a function of V2, we can solve the problem to find the volume of the 60% acid solution to mix with the 30% solution. Substitute the known values ​​into the equation:

V1 = (300 * 50 - 30 * V2) / 60

V1 = (15000 - 30 * V2) / 60

V1 = 250 - (V2 / 2)

We can use this last equation to find the volume of the 30% solution that we must mix with the 60% solution:

V2 = 2 * (250 - V1)

Clearing V1:

V1 = 250 - (V2 / 2)

V1 = 250 - (2 * (250 - V1) / 2)

V1 = 250 - 250 + V1

V1 = 250

Therefore, we must mix 250 ml of 60% acid solution with 250 ml of 30% solution to produce 300 ml of 50% solution.

Answer:

Step-by-step explanation:

The square root of a number can be both positive and negative, so to find all possible values of d, we need to take both the positive and negative square root of 3520.

Starting with the positive square root:

d = √3520 = √(55^2 * 8) = 55 * √8 = 8 * √55

And for the negative square root:

d = - √3520 = - √(55^2 * 8) = - 55 * √8 = - 8 * √55

So the two possible values of d are 8√55 and -8√55.