Can someone please help me?

Can Someone Please Help Me?

Answers

Answer 1

Answer:i think it is c

Step-by-step explanation:


Related Questions

Help me please 14 points.

Answers

The best percentage bar graph that represents Camryn's data is:

C Winter | Spring | Summer | Fall

0% 20% 40% 60% 80% 100%

What is the use of a bar graph?

A bar graph's purpose is to visually convey relational information quickly. The bars show the value for a specific type of data.

This is because the graph correctly shows the percentage of students who prefer each season, with the bar for each season extending to the appropriate percentage mark on the graph. It also clearly labels each season under the corresponding bar.

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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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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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a system of equations is shown. y=3x+2 y=x-2 , Graph the system of equations to show its solution

Answers

To graph the two lines, we can plot two points on each line and connect them with a straight line. For y = 3x + 2, we can choose x = 0 and x = 1 to get the points (0, 2) and (1, 5), respectively. For y = x - 2, we can choose x = 0 and x = 1 to get the points (0, -2) and (1, -1), respectively.

In the graph: The red line represents y=3x+2 and the blue line represents y=x-2

Explain the term straight line

A straight line is a geometric figure that extends infinitely in both directions and has no curvature or bends. It is the shortest distance between two points and can be described using various mathematical equations, such as y = mx + b, where m is the slope and b is the y-intercept. Straight lines are used in various fields, including geometry, physics, and engineering, to represent and analyze the relationships between objects or points.

According to the given information

To graph the system of equations y = 3x + 2 and y = x - 2, we can plot the two lines on the same coordinate plane and find the point where they intersect.

First, we can find the point of intersection by setting the two equations equal to each other:

3x + 2 = x - 2

Simplifying, we get:

2x = -4

x = -2

Substituting this value of x back into one of the equations, we get:

y = (-2) - 2 = -4

So the solution to the system of equations is the point (-2, -4).

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If a 24-pound EP rib of beef costing $45.00 is purchased oven-ready, and 1/4 of it is lost during roasting, how much does a 6-ounce serving cost?

Answers

$15 is the cost of a 6-ounce serving cost.

What is the cost price?

The precise value that corresponds to the unit price paid is represented by the cost price. In some stock market theories, this value is utilized to establish the value of stock holdings and is used as a key determinant of profitability.

Here, we have

Given: If a 24-pound EP rib of beef costing $45.00 is purchased oven-ready, and 1/4 of it is lost during roasting.

EP = 24 lb costing $45

1/4th lost during roasting.

Remaining = 24 lb - (1/4) of 24 lb

= 24 lb - 6 lb

= 18 lb

Now, this roast should match the cost of the original EP.

Cost per lb = (cost of beef originally)/(quantity of roasted beef)

= 45/18 dollar per lb

Cost of 6-ounce serving cost = (45/18)×6 = $15.

Hence, $15 is the cost of a 6-ounce serving cost.

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10 workers can create 20 products in 40days. all workers are equally productive. A company has only 5 workers.

how many days will it take to create all 20 products?​

Answers

The number of days it will take 5 workers to create 20 products, found using the work rate for 1 worker is 80 days

What is the work rate of 1 worker?

Work rate is the rate at which a specified work is completed.

The number of days it will take 10 workers to create 20 products = 40 days

Therefore;

The number of days it will take 1 worker to create 20 products = 40 × 10 days = 400 days

Where 1 worker can create 20 products in 400 days, then;

The work rate for one worker indicates;

The number of days it will take 5 workers to create 20 products can be found by dividing the number of days it will take 1 worker to create the 20 products by 5

5 workers will take = 400 days ÷ 5 = 80 days

The number of days it will take 5 workers to create 20 products = 80 days

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There are 1176 students in a school. The number of girls is 28 less than the
number of boys. How many boys are there in the school?

Answers

Answer:

Let's assume the number of boys in the school as "B".

Then, the number of girls can be expressed as "B - 28".

According to the problem, the total number of students is 1176. Therefore, we can write an equation as follows:

B + (B - 28) = 1176

Simplifying the above equation, we get:

2B - 28 = 1176

Adding 28 to both sides, we get:

2B = 1176 + 28

2B = 1204

Dividing both sides by 2, we get:

B = 602

Therefore, there are 602 boys in the school.

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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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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Brenda earns $5 each week for chores. x represents the number of weeks brenda did her chores. t represents the total dollars she earned. create an equation representing this situation

Answers

The situation is modeled by the linear equation:

t = $5*x

How to write the equation?

We know that Brenda earns $5 each week for chores. The variable x represents the number of weeks brenda did her chores, and t represents the total dollars she earned.

Then if she works for x weeks, the amount that she earns is x times $5, then the equation will be a linear one:

t = $5*x

That is the equation.

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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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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

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

Answers

Answer:

I would say probability.

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).

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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Can anybody please help me with this. Quick
For each answer just type

1.
2.
3.

Answers

1. n - 4 = 12

2. n - 13 = 20

3. n + 9 = 25

4. n + 5 = 75

5. x + 6 = 13

6. n - 6 = 5

For 1 n = 16

For 2 n = 33

For 3 n = 16

For 4 n = 70

For 5 x = 7

For 6 n = 11

Hope that helps, :).

The value of y is directly proportional to the value
of x. If x = 8, then y = 12. What is the value of x when y = 30?

Answers

Answer:

If the value of y is directly proportional to the value of x, we can use the formula for direct variation to find the value of x when y = 30. The formula for direct variation is:

y = kx

where k is the constant of proportionality.

To find the value of k, we can use the values given in the problem:

y = kx

12 = k(8)

Solving for k, we get:

k = 12/8 = 3/2

Now that we know k, we can use the formula for direct variation to find the value of x when y = 30:

y = kx

30 = (3/2)x

Solving for x, we get:

x = (30)/(3/2) = 20

Therefore, when y = 30, x = 20

Suppose you wish to borrow $400 for five weeks and the amount of interest you must pay is $25 per $100 borrowed. What is the APR at which you are borrowing money?

Answers

If we borrowed amount of $400 for 5 weeks, then the APR at which the money is borrowed is 260.71%.

First, we calculate the total interest paid for borrowing $400 for five weeks.

The interest rate is $25 per $100 borrowed, so for $400 borrowed, the interest paid is : $25 × 4 = $100,

So, the total amount that needs to be paid-back is $400 (the original borrowed amount) plus $100 (the interest paid) = $500,

Next, we can use the APR formula to calculate, which is

⇒ APR = (Interest Paid/Amount Borrowed)/(Number of days) × 365 × 100,

In this case, the total interest paid is $100 and the total amount borrowed is $400, and

The number of days amount is borrowed is = 5×7 = 35 days,

Substituting the values,

We get,

⇒ APR = (100/400)/35 ×365 × 100 ≈ 260.71%

Therefore, the APR at which the money is being borrowed is 260.71%.

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What’s the volume of this? pls do step by step cus it’s for my homework and I have to show work

Answers

3.5 ft•2.5 ft is the base of the figure= 8.75 square ft

then multiply 8.75 times the height (3.75 ft) so the volume is 32.812 cubic ft

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.

100 Points! Algebra question, photo attached. Please show as much work as possible. Thank you!

Answers

Answer:

if f(x) = 3x, g(x) = x+4, and h(x) = x²-1, Find [h•(f•g)](3)

{h • (f • g)}(3) = 440

Step-by-step explanation:

To find {h • (f • g)}(3), we need to first evaluate the innermost function, f • g, then substitute the result into the outer function, h, and finally evaluate the resulting expression at x = 3.

Let's start by finding f • g:

f • g = f(g(x))

Substitute g(x) into f(x):

f • g = f(x + 4)

Now substitute f(x) into the above expression:

f • g = 3(x + 4)

Simplify:

f • g = 3x + 12

Now we can substitute this result into h(x):

h • (f • g) = h(3x + 12)

Substitute x = 3 into the above expression:

h • (f • g) = h(3(3) + 12)

Simplify inside the parentheses:

h • (f • g) = h(9 + 12)

Simplify further:

h • (f • g) = h(21)

Now let's evaluate h(21):

h(x) = x² - 1

h(21) = (21)² - 1

Simplify:

h(21) = 441 - 1

Final result:

{h • (f • g)}(3) = 440

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!

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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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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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 ;)

Consider the two-loop circuit shown below:

Ignore the red and pencil markings, just worry about the printed questions

Answers

The variables I₁ and I₂ using the matrix algebra and using the Cramer's rule are I₁ = 1 and I₂ = 1

Writing the system of equations in matrix form

From the question, we have the following parameters that can be used in our computation:

15I₁ + 5I₂ = 20

25I₁ + 5I₂ - 30 = 0

Rewrite as

15I₁ + 5I₂ = 20

25I₁ + 5I₂ = 30

Rewrite as

I₁     I₂

15    5    20

25   5    30

From the question, the matrix form is

AI = b

Ths matrix A from the above is

[tex]A = \left[\begin{array}{cc}15&5&25&5\end{array}\right][/tex]

Ths matrix B from the above is

[tex]B = \left[\begin{array}{c}20&30\end{array}\right][/tex]

And, we have the matrix I to be

[tex]I = \left[\begin{array}{c}I_1&I_2\end{array}\right][/tex]

Finding I₁ and I₂ using the matrix algebra

Start by calculating the inverse of A from

[tex]A = \left[\begin{array}{cc}15&5&25&5\end{array}\right][/tex]

So, we have:

|A| = 15 * 5 - 5 * 25

|A| = -50

The inverse is

[tex]A^{-1} = -\frac{1}{50}\left[\begin{array}{cc}5&-5&-25&15\end{array}\right][/tex]

Recall that

AI = b

So, we have

[tex]I = -\frac{1}{50}\left[\begin{array}{cc}5&-5&-25&15\end{array}\right] * \left[\begin{array}{c}20&30\end{array}\right][/tex]

Evaluate the products

[tex]I = -\frac{1}{50}\left[\begin{array}{c}5 * 20 + -5 * 30&-25 * 20 + 15 *30\end{array}\right][/tex]

[tex]I = -\frac{1}{50}\left[\begin{array}{c}-50&-50\end{array}\right][/tex]

Evaluate

[tex]I = \left[\begin{array}{c}1&1\end{array}\right][/tex]

Recall that

[tex]I = \left[\begin{array}{c}I_1&I_2\end{array}\right][/tex]

So, we have

I₁ = 1 and I₂ = 1

Finding I₁ and I₂ using the Cramer's rule,

Recall that the determinant of matrix A calculated in (a) is

|A| = -50

Replace the first column in A with b

So, we have

[tex]AI_1 = \left[\begin{array}{cc}20&5&30&5\end{array}\right][/tex]

Calculate the determinant

DI₁ = 20 * 5 - 30 * 5

DI₁ = -50

Replace the second column in A with b

So, we have

[tex]AI_2 = \left[\begin{array}{cc}15&20&25&30\end{array}\right][/tex]

Calculate the determinant

DI₂ = 15 * 30 - 20 * 25

DI₂ = -50

So, we have

I₁ = DI₁ / |A| = -50/-50 = 1

I₂ = DI₂ / |A| = -50/-50 = 1

So, we have

I₁ = 1 and I₂ = 1

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what is the next 3 numbers in this sequence 3, 2, 6, 5, 15, 14

Answers

Answer:

42, 41, 123

Step-by-step explanation:

3, 2, 6, 5, 15, 14

- 1 x3. - 1. x3. - 1

you just gotta look for the pattern thats the same in the sequence so the next three numbers would be x3, then - 1 then x3 again onto the numbers.

Answer:

The next three numbers are 42, 41, and 123

Step-by-step explanation:

3 - 1 = 2

2 * 3 = 6

6 - 1 = 5

5 * 3 = 15

15 - 1 = 14

The pattern is subtracting one and then multiplying by three.

14 * 3 = 42

42 - 1 = 41

41 * 3 = 123

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 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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Part 3: Hitting the baseball over the lights


Meanwhile at the ballpark Juan was practicing his hitting while talking to some friends. He started telling them how he hit the ball over the 50 foot light tower yesterday.



The formula for this hit is h(x) = -16xsquared + 60x + 4 , where h is the height of the ball and x is the number of seconds the ball is in the air.



How can Juan provide proof to the friends that he actually hit the ball over the tower?








How high did Juan actually hit the ball? Is Juan able to mathematically back up how high he says he hit the ball?

Answers

Juan's claim is plausible based on the given function because the maximum height of the ball is 62.875 feet, which is higher than the 50-foot light tower.

Maximum function

To prove that Juan hit the ball over the 50-foot light tower, we need to find the maximum height of the ball using the given function h(x) = -16x^2 + 60x + 4 and show that the maximum height is greater than 50 feet.

The maximum height of the ball occurs at the vertex of the parabolic function h(x), which is given by the formula x = -b/2a, where a = -16 and b = 60.

Substituting these values into the formula, we get:

x = -b/2a = -60/(2*(-16)) = 1.875

So the ball reaches its maximum height after 1.875 seconds. To find the maximum height, we can substitute this value of x into the original function h(x):

h(1.875) = -16(1.875)^2 + 60(1.875) + 4 = 62.875

Therefore, the maximum height of the ball is 62.875 feet, which is higher than the 50-foot light tower. So Juan's claim is plausible based on the given function.

Based on the given function h(x) = -16x^2 + 60x + 4, the maximum height that Juan hit the ball was 62.875 feet. Therefore, Juan's claim that he hit the ball over the 50-foot light tower is mathematically backed up by the function h(x). The maximum height of the ball is higher than the height of the tower, so it is possible that Juan hit the ball over the tower.

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