BRAINLIEST find the volume and surface area of a hypotenuse of a triangular right base that is 25 m . 7m height 24 m base? 22m length?

BRAINLIEST Find The Volume And Surface Area Of A Hypotenuse Of A Triangular Right Base That Is 25 M .

Answers

Answer 1

The volume and surface area of a triangular prism is 1,848 cubic meters and 1,694 square meters.

What is surface area?

The space occupied by a two-dimensional flat surface is called the area. It is measured in square units. The area occupied by a three-dimensional object by its outer surface is called the surface area.

the volume and surface area of a right triangular prism with base dimensions of 24 m and 7 m height and a length of 22 m.

The volume of a right triangular prism is given by the formula:

V = (1/2) * b * h * l

where b is the base width, h is the height, and l is the length. Plugging in the given values, we get:

V = (1/2) * 24 m * 7 m * 22 m = 1,848 m³

Therefore, the volume of the right triangular prism is 1,848 cubic meters.

The surface area of a right triangular prism is given by the formula:

SA = 2 * (b * h + l * h + b * l)

Plugging in the given values, we get:

SA = 2 * (24 m * 7 m + 22 m * 7 m + 24 m * 22 m) = 1,694 m²

Therefore, the surface area of the right triangular prism is 1,694 square meters.

Hence, the volume and surface area of a triangular prism are 1,848 cubic meters and 1,694 square meters.

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Related Questions

14. Use the tree diagram below to answer the question.
Small
Blue
White
Medium
Large
Small
Medium
Large
Small

Answers

The number of outcomes that contains blue shirts is 3

What is a Tree Diagram?

A tree diagram is a graphical representation of a hierarchy or branching structure, often used in fields such as mathematics, computer science, linguistics, and biology. It is called a tree diagram because it looks like a tree, with a single root node that branches out into multiple child nodes.

In mathematics, a tree diagram is used to represent the possible outcomes of a series of events or decisions, with each branch representing a different option or outcome.

The outcome for blue shirts is 3 because there is only small medium and large

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ABC is a right angled triangle. if B = 90°, AC = 96 cm, C = 30°. Find AB?

Answers

Answer:

We can use trigonometry to find AB.

First, we can use the fact that the sum of the angles in a triangle is 180° to find angle A:

A + B + C = 180°

A + 90° + 30° = 180°

A = 60°

Now, we can use the sine function to find AB:

sin A = opposite/hypotenuse

sin 60° = AB/96

AB = 96 * sin 60°

AB = 96 * √3/2

AB = 48√3

Therefore, AB is approximately 83.14 cm (rounded to two decimal places).

Find the area ___m^2

Answers

Answer: 28.27m^2

Step-by-step explanation:

Area of a circle: [tex]A = \pi r^{2} \\[/tex]

Given the diameter of 6m, we can divide that by 2 to get the radius and plug that into the formula.

6/2 = 3m

[tex]A = \pi (3)^2\\A= 28.27m^{2}[/tex]

My current grade is a 64.21%
7%-enrichment assignments
16%-homework assignments
19%-exam 1,2 and 3
20%-final exam
I have exam 3 next week, before final exam I want to up my grade to a 70% or above what grade would I need to get on my exam 3 to do so?

Answers

To calculate the grade you need on Exam 3 to reach a 70% or higher, you can use the following formula:

(0.07 x enrichment assignments grade) + (0.16 x homework assignments grade) + (0.19 x Exam 1 grade) + (0.19 x Exam 2 grade) + (0.19 x Exam 3 grade) + (0.20 x Final exam grade) = 0.70 x total grade

Since you want to know what grade you need on Exam 3 specifically, you can rearrange the formula to isolate for Exam 3:

Exam 3 grade = (0.70 x total grade - 0.07 x enrichment assignments grade - 0.16 x homework assignments grade - 0.19 x Exam 1 grade - 0.19 x Exam 2 grade - 0.20 x Final exam grade) / 0.19

Plugging in your current grades, we get:

Exam 3 grade = (0.70 x 100 - 0.07 x 64.21 - 0.16 x ? - 0.19 x ? - 0.19 x ? - 0.20 x ?) / 0.19

Since we don't have your grades for Homework assignments, Exam 1, Exam 2, and Final exam, we'll use variables instead. Let's call them:

H = homework assignments grade
E1 = Exam 1 grade
E2 = Exam 2 grade
F = Final exam grade

Substituting these variables, we get:

Exam 3 grade = (0.70 x 100 - 0.07 x 64.21 - 0.16 x H - 0.19 x E1 - 0.19 x E2 - 0.20 x F) / 0.19

Simplifying:

Exam 3 grade = (7 - 0.44947 - 0.16H - 0.19E1 - 0.19E2 - 0.20F) / 0.19

Exam 3 grade = (6.55053 - 0.16H - 0.19E1 - 0.19E2 - 0.20F) / 0.19

Now, let's say you want to achieve a minimum grade of 70%. In other words, you want your total grade to be at least 70%. Using the same formula, we get:

(0.07 x enrichment assignments grade) + (0.16 x homework assignments grade) + (0.19 x Exam 1 grade) + (0.19 x Exam 2 grade) + (0.19 x Exam 3 grade) + (0.20 x Final exam grade) = 0.70 x 100

Simplifying:

0.07 x enrichment assignments grade + 0.16H + 0.19E1 + 0.19E2 + 0.19 x Exam 3 grade + 0.20F = 70

Substituting the expression we derived earlier for Exam 3 grade:

0.07 x enrichment assignments grade + 0.16H + 0.19E1 + 0.19E2 + (6.55053 - 0.16H - 0.19E1 - 0.19E2 - 0.20F) / 0.19 + 0.20F = 70

Simplifying:

0.07 x enrichment assignments grade + 1.01005 - 1.05263H - 1.01053E1 - 1

Answer:

i would say at least a 70

and i hope you do well

hope this helps ;)

What is a rigid transformation and what are three types of rigid transformations?
*
10 points
Rigid Transformations are movement of figures where the size and shape change. Examples are translations, reflections and rotations.
Rigid Transformations have congruent preimages and images. Examples include translations, reflections, and rotations.
Rigid transformation have non-congruent preimages and images. Examples include reflections, rotations and translations.
Rigid Transformations use scale factors to create new images from preimages. Examples include maps, diagrams and drawings.

Answers

A rigid transformation and the three types of rigid transformations are: B. Rigid Transformations have congruent preimages and images. Examples include translations, reflections, and rotations.

What is a transformation?

In Mathematics and Geometry, a transformation can be defined as the movement of a point from its initial position to a new location. This ultimately implies that, when a geometric figure or object is transformed, all of its points would also be transformed.

Generally speaking, there are three (3) main types of rigid transformation and these include the following:

TranslationsReflectionsRotations.

In conclusion, rigid transformation are movement of geometric figures where the size and shape does not change because they have congruent preimages and images.

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C(n, k-1) + nC(n, k) = C(n + 1, k)​

Answers

The equation C(n, k-1) + nC(n, k) = C(n + 1, k) is known as the Pascal's rule or Pascal's identity, which relates the binomial coefficients C(n, k) and C(n + 1, k).

To understand how the equation works, we can break down each term:

- C(n, k-1) represents the number of ways to choose k-1 objects from a set of n objects.
- nC(n, k) represents the number of ways to choose k objects from a set of n objects, multiplied by the number of ways to choose one additional object from the remaining n-k objects.
- C(n + 1, k) represents the number of ways to choose k objects from a set of n+1 objects.

By combining these terms, we can see that the left-hand side of the equation represents the total number of ways to choose k objects from n+1 objects. This is equivalent to the right-hand side of the equation, which also represents the number of ways to choose k objects from n+1 objects.

Therefore, Pascal's identity can be used to simplify calculations involving binomial coefficients, making it a powerful tool in combinatorics and probability theory.

The model below represents the division problem 2\frac{1}{5}\div\frac{4}{5}2
5
1

÷
5
4

.

Answers

The equivalent value of the fraction is A = 11/4

Given data ,

Let the fraction be represented as A

Now , let the first fraction be p = 2 1/5

Let the second fraction be q = 4/5

Now , A = p/q

On simplifying the equation , we get

A = ( 2 1/5 ) / 4/5

A = ( 11/5 ) / ( 4/5 )

On further simplification , we get

A = ( 11/5 ) x ( 5 / 4 )

A = 11/4

Therefore , the value of A is 11/4

Hence , the fraction is A = 11/4

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Olivia mowed 4 lawns in 16 hours. What was her rate of mowing in hours per lawn?

Answers

on sait que :
4 pelouse = 16 heures
alors tu fais le nombre de pelouse divisé par le nombre d'heure soit :
4/16=0.25
donc le taux de tonte en heure est de 0.25


Answer:

Her rate of mowing lawns per hour is 4 lawns to one hour

Step-by-step explanation:so on a table you divide 4÷4=1 then you do the same thing for the 16÷4=4. So Oliva can mow 4 lawns per hour

Find the surface area of the triangular prism. The base of the prism is an isosceles triangle.

Answers

The answer of the given question based on the Rectangular prism is , the surface area of the given triangular prism is 3360 cm².

What is Rectangular prism?

A rectangular prism is a three-dimensional geometric shape with six rectangular faces. It is also known as rectangular parallelepiped or cuboid. A rectangular prism has a length (l), width (w), and height (h) and the formula for the volume of a rectangular prism is given as V = l * w * h.

To find the surface area of a triangular prism, we need to add up the areas of all of its faces. A triangular prism has two identical triangular bases and three rectangular faces.

First, let's find the area of the triangular base. We know that it is an isosceles triangle with a perpendicular height of 35 cm and base of 24 cm, and the length of the two equal sides is 37 cm. We can use the formula for the area of a triangle:

Area of base = (1/2) * base * height

Area of base = (1/2) * 24 cm * 35 cm

Area of base = 420 cm²

Since there are two identical bases, we can multiply this by 2 to get the total area of the triangular bases:

Total area of bases = 2 * 420 cm²

Total area of bases = 840 cm²

Now, let's find the area of the three rectangular faces. We know that the height of the prism is 35 cm, and the length of each rectangular face is equal to the base of the triangular base, which is 24 cm. To find the width of each rectangular face, we need to use the Pythagorean theorem to find the length of the altitude of the triangular base:

a² + b² = c²

where a and b are the two equal sides of the triangular base, and c is the base.

Substituting the given values, we get:

a² + b² = c²

37² + 12² = c²

1369 + 144 = c²

c² = 1513

c = √1513

c = 38.95 cm

Therefore, the altitude of the triangular base is approximately 35 cm, and we can use this value as the width of each rectangular face. So, area of each rectangular face is given:

Area of each rectangular face = length*width

Area of each rectangular face = 24 cm * 35 cm

Area of each rectangular face = 840 cm²

Since there are three identical rectangular faces, we can multiply this by 3 to get the total area of the rectangular faces:

Total area of rectangular faces = 3 * 840 cm²

Total area of rectangular faces = 2520 cm²

Finally, we can find the total surface area of the prism by adding the areas of the two triangular bases and the three rectangular faces:

Total surface area = Total area of bases + Total area of rectangular faces

Total surface area = 840 cm² + 2520 cm²

Total surface area = 3360 cm²

Therefore, the surface area of the given triangular prism is 3360 cm².

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The mean life of a new smart LED bulb is 20,000 running hours with a standard deviation is 2,250 hours. The data is normally distributed. If a home improvement store sold 18,000 of these light bulbs in the first year of production, how many light bulbs would you expect to last longer than 22,250 hours?

Answers

Answer: The expected number of bulbs that would last longer than 22,250 hours is approximately 2,857.

Step-by-step explanation:

To solve this problem, we can start by finding the z-score for 22,250 using the formula:z = (x - mean) / standard deviationz = (22,250 - 20,000) / 2,250 = 1Next, we need to find the proportion of bulbs lasting longer than 22,250. We can look up this proportion in a standard normal distribution table or use a calculator, which gives us a probability of 0.1587.Finally, we can use this probability to find the expected number of bulbs that will last longer than 22,250:Expected number of bulbs = probability * total number of bulbs sold Expected number of bulbs = 0.1587 * 18,000 = 2,857Therefore, we can expect that approximately 2,857 of the 18,000 bulbs sold will last longer than 22,250 running hours.

Answer:

the afternoon is the right one

Recite the numbers in
each row.
29
42
77
30
43
78
31 32 33
44
45 46
79
80
81
го
Copyright © A Dab of Glue W

Answers

Note to recite the numbers, you have repeat alound the tiven numbers. Often, the purpose of recitation is to memorize and become aquatinted with.

Why do a recitation ?

Recitation is often a smaller subset of a larger lecture course, commonly conducted by teaching assistants, meant to offer time for conceptual knowledge application and extension of training that happens in lecture through problem-solving or discussion.

Consider this a learning process in which knowledge is recalled from memory.

You have been handed numbers to recite in this case. Reciting numbers can help you increase your numeric intelligence.

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An item is worth $240 now. This is 30% of what it was originally worth. What was it originally worth?

Answers

To find out how much the item was originally worth, we will use the formula:
OP= P/1 - %
OP is the original price and P is the price now and % is the, well, percent. So let’s put the numbers in. Remember that you must convert the percent to a decimal by dividing it by 100.
OP = 240/1 - 0.30
OP = 240/0.7
OP= 342.8571428571429
OP (rounded) = $342.86
So the original price of the item was $342.86 before the 30% cut.

Hope this helped!

Is (3, 5) a solution to this system of equations?
y = 5
Y= -5/3x+10

yes
E

Answers

Answer:

no

Step-by-step explanation:

-5/3x+10=5

-5/3x=5-10=-5

3x=-5/-5=1

=>x=1/3

Type the correct answer in each box.
The probabilities of a positive response for two government programs from the citizens in eight cities are given in the table.

City Positive Response
for Program 1 (%) Positive Response
for Program 2 (%)
Atlanta 77.80 82.10
Boston 86.40 86.60
Chicago 65.90 87.50
Dallas 73.80 80.90
Houston 69.70 79.40
Los Angeles 78.40 88.10
Miami 82.50 82.60
Newark 81.40 83.30
Total 68.80 81.70
The chance that a positive response is obtained from Chicago for program 1 is
%. The chance that a positive response is obtained from Chicago for program 2 is
%.

Answers

Programme 2 in Los Angeles will be well received by 22 out of 25 people.

what is Probability?

Given that the chances of a positive response from Los Angeles residents to two government programmes are 78.4% for Programme 1 and 88.1% for Programme 2, the likelihood of a positive response for Programme 2 given that the person is from Los Angeles must be calculated as follows:

88.1 / 100 = X 44.05 / 50 = X 22,025 / 25 = X

Therefore, Programme 2 will be well-received by 22 out of 25 people in Los Angeles.

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If a 95% confidence interval for is calculated to be (21.4 , 27.9) , what would be the result of a hypothesis test at a 5% significance level performed on the set of hypotheses?
H0: mean = 27
Ha: mean different 27

Answers

Based on the given 95% confidence interval of (21.4, 27.9), we can see that it does not include the hypothesized mean of 27 within its range. This means that the data used to calculate the confidence interval provides evidence against the null hypothesis (H0: mean = 27) and suggests that the true population mean is likely to be different from 27.

Since the confidence interval does not include the hypothesized mean of 27, we can reject the null hypothesis at the 5% significance level. In other words, we have enough evidence to conclude that the true population mean is different from 27 based on the given confidence interval.

This result is consistent with the alternative hypothesis (Ha: mean different from 27), which states that the true population mean is not equal to 27. Thus, we can reject the null hypothesis in favor of the alternative hypothesis at the 5% significance level based on the given confidence interval.

I really need help on question (if you solve your very smart ) . If answers correct I'll rate 5 stars , a thanks and maybe even brainy.

Billy has x pounds. Liam has twice as much money as billy. Nicola has 3 times as much money as liam. The total amount of money they have is £180 pounds.


A) form an expression in terms of x and find out how much money they have.

Answers

Answer:

Billy has £20, Liam has £40, and Nicola has £120. The total amount of money they have is £180, as given in the problem.

Step-by-step explanation:

Let's start by defining the variables:

Billy's money: x pounds

Liam's money: 2x pounds (twice as much as Billy)

Nicola's money: 3(2x) = 6x pounds (three times as much as Liam)

The total amount of money they have is £180, so we can write an equation:

x + 2x + 6x = 180

Simplifying the left side of the equation:

9x = 180

Solving for x:

x = 20

Now we can find out how much money each person has:

Billy: x = 20 pounds

Liam: 2x = 2(20) = 40 pounds

Nicola: 6x = 6(20) = 120 pounds

type 43 words per minute. If she maintains her typing speed without a break, how many words can she type in 2 hours and 15 minutes?

Answers

43 x 60 = 2,580 words per hour

2,580 x 2.25 = 5,805 words in 2 hrs and 15 mins

Hope this helps!

Answer: 6,450 words per minute

Step-by-step explanation:

Each hour is 60minutes long, making your total number of minutes 150.

The last step would be to multiply 150 by the wpm (43) and making the total number typed 6,450

1. What is Maxwell's filing status?
a. Single
b. Married filing jointly
c. Head of household
d. Dependent

Answers

Maxwell's filing status can be described as: b. Married filing jointly.

What is a filing status?

A filing status is a category that defines your tax-filing status based on your marital status and family situation. The filing status determines tax rate and standard deduction, as well as the eligibility for certain credits, deductions, and exemptions.

Maxwell can be described as married filing jointly because he and his spouse combined their income, deductions, and credits on one tax return. This status generally results in lower tax rates and a larger standard deduction compared to filing separately.

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3. Gabe has $100. He plans to buy a jersey for $55. He will spend the rest of his money on T-shirts, which cost $15 each. Which inequality could Gabe use to find s, the number of T-shirts he can buy?
A 55 + 15s ≤ 100
B 15 + 55s ≤ 100
C 55 + 15s ≤ 100
D 15 + 55s ≤ 100

Answers

A or C because each shirt is 15 so multiply however many shirts by 55 then add to the 55 and he can’t spend more than 100

PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!
Find the probability of drawing a green, then yellow, with replacement.
A bag has 4 green blocks, 6 red blocks, 7 blue and 3 yellow.

Answers

The probability of drawing a green block followed by a yellow block with replacement is 0.03, or 3%.

What is probability?

The probability of an event is calculated by dividing the total number of possible outcomes by the number of possible outcomes.

The likelihood of drawing a green block on the main draw is:

P(green) = (number of green blocks) / (total number of blocks)

P(green) = 4 / (4 + 6 + 7 + 3)

P(green) = 4 / 20

P(green) = 0.2

Since the blocks are replaced after each draw, the probability of drawing a yellow block on the second draw is still:

P(yellow) = (number of yellow blocks) / (total number of blocks)

P(yellow) = 3 / (4 + 6 + 7 + 3)

P(yellow) = 3 / 20

P(yellow) = 0.15

To find the probability of both events happening, we multiply the probabilities:

P(green, then yellow) = P(green) * P(yellow)

P(green, then yellow) = 0.2 * 0.15

P(green, then yellow) = 0.03

As a result, replacing a yellow block with a green one has a chance of 0.03, or 3%, being drawn.

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What strategy could you use to figure out when Beau is likely to win 500 trophies

Answers

Answer:

I would say probability.

Please what is the answer?

Answers

Answer:

When we have a set of points, we can find the distance between them using the formula:

[tex]d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex], where d is the distance, x1 and x2 are one point and y1 and y2 are another point.

OB:

Thus, for OB, we can allow O(6, 6) to be our x1 and x2 point and we can allow B(9, 6) to be our y1 and y2 point:

[tex]d=\sqrt{(6-9)^2+(6-6)^2} \\d=\sqrt{(-3)^2+(0)^2} \\d=\sqrt{(-9)} \\d=3[/tex]

Thus, the first part/step in the equation is your subtraction expression to find the length of OB.

AB:

For AB, we can allow A(9, 10) to be our x1 and x2 point and we can allow B (9, 6) to be our y1 and y2 point:

[tex]d=\sqrt{(9-9)^2+(10-6)^2}\\ d=\sqrt{(0)^2+(4)^2}\\ d=\sqrt{16}\\ d=4[/tex]

The first part/step is your subtraction expression for the length of AB.

find a. round to the nearest tenth. a=? cm

Answers

The value of (a) in given triangle is approximately 7.44 cm.

What do you mean by triangle?

A triangle is a three-sided polygon consisting of three sides and three vertices. The most important property of a triangle is that the sum of its interior angles  is  180 degrees.

Let ΔABC is a triangle

Given ∠ B = 75°

∠ C = 31.8°

AB = 12cm

AC = 22cm

find BC = ?

We can use the law of cosines to solve for BC:

BC² = AB² + AC² – 2(AB)(AC)cos(B)

We know that angle B = 75 degrees, so we can substitute:

BC² = 12² + 22² - 2(12)(22)cos(75)

Evaluating cos(75) with a calculator, we get:

BC² ≈ 144 + 484 - 572.59

BC² ≈ 55.41

Taking the square root of both sides gives us:

BC ≈ 7.44

Therefore, BC is approximately 7.44 cm.

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PLEASE I NEED HELP THIS DEPENDS ON WETHER I STAY IN MY SOFTBALL TEAM

Answers

Answer:

Circumference/Diameter = π

If the diameter is 2, then the circumference is 2π.

If the diameter is 6, then the circumference is 6π.

The top three prices for works of art sold at auction in 2013 totaled ​$308.0 million. These three works of art were a​ sculpture, a​ painting, and a photograph. The selling price of the painting was ​$49.4 million more than that of the photograph.​ Together, the painting and the photograph sold for ​$24.4 million more than the sculpture. What was the selling price of each​ work?

Answers

The selling prices of the sculpture, painting, and photograph were 166.5 million, 107.0 million, and 57.6 million respectively.

How to Determine the Selling Price?

Let's call the selling prices of the sculpture, painting, and photograph as S, P, and Ph respectively.

From the first sentence, we know that:

S + P + Ph = 308.0 million

From the second sentence, we know that:

P = Ph + 49.4 million

And from the third sentence, we know that:

P + Ph = S + 24.4 million

Now we can substitute the second equation into the third equation:

(Ph + 49.4 million) + Ph = S + 24.4 million

Simplifying:

2Ph + 49.4 million = S + 24.4 million

2Ph = S - 25 million

Substituting this into the first equation:

S + P + Ph = 308.0 million

S + (Ph + 49.4 million) + Ph = 308.0 million

2Ph + S = 258.6 million

Now we can substitute the equation we derived earlier:

S + 2Ph - 49.4 million = 258.6 million

S + 2Ph = 308.0 million

Substituting 2Ph = S - 25 million:

S + S - 25 million = 308.0 million

2S = 333.0 million

S = 166.5 million

Now we can use this value to find P and Ph:

P = Ph + 49.4 million

P + Ph = S + 24.4 million

Substituting S = 166.5 million in both equations:

P + Ph = 190.9 million

P = Ph + 49.4 million

Solving these two equations simultaneously:

Ph = 57.6 million

P = 107.0 million

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can someone please help me ASAP

please show your work on paper

Wrong Answers Will Be Reported !

Answers

The expressions are solved to give;

1.n = 1

2. h = 1

3. x = -5

4. n = 1/4

5. x = 7/2

6. p = 2/3

7. x = -12

8. n = 3

9. c = -1

10. x = 6

What are algebraic expressions?

These are expressions that are made up of term, variables, constants, factors and coefficients.

They are also made up of mathematical operations.

From the information given, we have;

1. 5n + n = 2n + 4

collect and add the like terms

4n = 4

Make n subject

n = 1

2. 5h + 2 = h - 2

collect and add the like terms

4h = 4

h = 1

3. 2x - 1 = 3x + 4

collect and add or subtract the like terms

-x = 5

x = -5

4. n = n + 1/5

cross multiply

4n = 1, n = 1/4

5. x + 5 = 3x - 2

collect like terms

-2x = -7

x = 7/2

6. p = p + 2/4

cross multiply

3p = 2

p = 2/3

7. 4(2 + x) = 3x - 4

expand the bracket

8 + 4x = 3x - 4

collect like term

x = -12

8. 5n + 2 = 3n + 4

collect like terms

n = 3

9. 3c - 2 = -3c - 8

collect like terms

6c = - 6

c = -1

10. 3x + 1 = 2x - 5

collect the like terms

x = 6

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Aaron writes an algebraic expression to represent the product of 14 and the difference of 18 and 3x. What are the factors in this expression

Answers

The factors in this algebraic expression are:

14 And (18 - 3x)

How to find he factors in the algebraic expression ?

An algebraic expression can also be written as a list of its constituent parts. Variables, constants, and operators are the components of an algebraic expression. Terms are separated from one another in an algebraic equation by the addition operation.

Algebraic Expressions can be factorized using many methods. The most common methods used for factorization of algebraic expressions are:

Factorization using common factors

Factorization by regrouping terms

Factorization using identities

The algebraic expression written by Aaron to represent the product of 14 and the difference of 18 and 3x is:

14 * (18 - 3x)

The factors in this expression are:

14

(18 - 3x)

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You are going to start a business making chicken sandwiches and hamburgers. You have a budget of $750. The chicken sandwich costs $2.75 to make and the hamburger costs $1.95 to make. Which inequality models the situation?
A. 2.75x+1.95y ≤ 750, where x is # of chicken sandwiches and y is # of hamburgers
B. 2.75x+1.95y = 750, where x is # of chicken sandwiches and y is # of hamburgers
C. 2.75x+1.95y ≥ 750, where x is # of chicken sandwiches and y is # of hamburgers

Answers

The correct option is A, the inequality is:

2.75x + 1.95y ≤ 750

Which inequality models the situation?

Let's define the variables we will be using:

x = number of chicken sandwiches

y = number of hamburgers.

We know that the budget is $750, and the chicken sandwich costs $2.75 to make and the hamburger costs $1.95 to make, then we can write the inequality:

"Total cost equal to or smaller than 750"

2.75x + 1.95y ≤ 750

That is what we can see in option A, so that is the correct one.

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The compliment of an angle is three times the measurement of the angle. Find the measurement of the larger angle

Answers

The greater angle has a 67.5° degree measurement. When two angles' measurements add up to 90°degrees, they are said to be complimentary.

How to calculate the larger angle?

Call that angle we're looking for "x" for convenience.

The degree that, if added to x, makes x equal 90° degrees is known as the compliment of x.

We now know that 3x, or 3 times x, is the compliment of x.

With this knowledge, we can construct the following equation:

x + 3x = 90°

combining comparable equations;

4x = 90°

x = 22.5°, when both sides are divided by 4.

As a result,

3x = 3(22.5°) = 67.5° degrees is the measurement of the greater angle, which is the complement of x.

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Given the functions, f(x) = −x+2, and g(x)=5x². Find:
i. f.g(x)
ii. g(f(x))
iii. ƒ.(g(x))²
iv. 8(x-1)

Answers

For the functions, f(x) = −x+2, and g(x)=5x²,

a) f∘g(x) =  5x² + 2

b) g(f(x)) = 5x² -20x + 20

c) f∘(g(x))² = 25x⁴

d) g(x - 1)    = 5x² - 10x + 5

Here, the functions are: f(x) = −x+2, and g(x)=5x²

a) f∘g(x)

We know that composite function f∘g(x) means f(g(x))

For function f(x) substitute x = g(x)

i.e., f(g(x)) = -(g(x)) + 2

                = -(5x²)  +2

                = 5x² + 2

b) g(f(x))

For function g(x) substitute x = f(x)

i.e., g(f(x)) = 5x²

                = 5(-x + 2)²

                = 5(x² -4x + 4)

                 = 5x² -20x + 20

c) f∘(g(x))²

First we find the (g(x))²= (5x²)²

                                     = 25x⁴

Now the composite function  f∘(g(x))² would be,

 f∘(g(x))² = f((g(x))²)

              = -(g(x))²+ 2

              = -(g(x))² + 2

d) g(x - 1)

Substitute x = x -1 in function g(x)

g(x - 1) = 5(x - 1)²

           = 5(x² - 2x + 1)

           = 5x² - 10x + 5

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