3. (05.06 MC)
Graph the system of Inequalities presented here on your own paper, then use your graph to answer the following questions:
y < 4x – 2
y>5/2x-2 (should be the greater than or equal to sign)
Part A: Describe the graph of the system, including shading and the types of lines graphed. Provide a description of the solution area. (6 points)
Part B: Is the point (-2,-2) Included in the solution area for the system? Justify your answer mathematically. (4 points)
(10 points)

Answer:

[tex](a)\ Area = 28.12cm^2[/tex]

[tex](b)\ Volume = 1437.33cm^3[/tex]

Step-by-step explanation:

Solving (a): The parallelogram

[tex]h = 7.6[/tex] --- height

[tex]b = 3.7[/tex] --- base

The area is calculated usng:

[tex]Area = base * Height[/tex]

[tex]Area = 3.7 * 7.6[/tex]

[tex]Area = 28.12cm^2[/tex]

Solving (b): The sphere

[tex]d = 14cm[/tex]

Required

The volume

First, calculate the radius

[tex]r = d/2[/tex]

[tex]r = 14cm/2 = 7c,[/tex]

The volume is calculated using:

[tex]Volume = \frac{4}{3} \pi r^3[/tex]

This gives:

[tex]Volume = \frac{4}{3} * \frac{22}{7} * 7^3[/tex]

[tex]Volume = \frac{4}{3} * 22 * 7^2[/tex]

[tex]Volume = \frac{4}{3} * 1078[/tex]

[tex]Volume = \frac{4*1078}{3}[/tex]

[tex]Volume = \frac{4312}{3}[/tex]

[tex]Volume = 1437.33[/tex]

Answer: -10, √_100, 11.5, √_220

Step-by-step explanation:

-10 is the least bc it just is and √_100 simplified is 10 and 11.5 is a little greater so duh and √_220 simplified is 14.83

17 percent of 24320 is 4134.4

basically minus that

so

24320 - 4134.4 = 20,185.60

Answer:

24320 - 4134.4 = 20,185.60

Step-by-step explanation:

:)

Answer:

20 students were absent

Step-by-step explanation:

Half means divide by 2:

40/2 = 20

Answer:

The profit is: [tex]Rs100000[/tex]

Step-by-step explanation:

Given

[tex]1 \to Rs20[/tex]

Required

Profit on 5000

Repesent this as: x

So, we have:

[tex]1 \to Rs20[/tex]

[tex]5000 \to x[/tex]

Cross Multiply

[tex]x * 1 = Rs20 * 5000[/tex]

[tex]x * 1 = Rs100000[/tex]

The profit is: [tex]Rs100000[/tex]

Answer:

i hope it helps mapriend

Answer:

A. 25 cm

Step-by-step explanation:

Perimeter of a polygon = the sum of all sides of the polygon

Therefore,

Perimeter of the given polygon = 5 + 6 + 8 + 6

Perimeter = 25 cm

Answer:

x–2, x ≠ -3

Step-by-step explanation:

Solution in the diagram

Answer:

100

Step-by-step explanation:

because if you add it all up you will find the sum

Answer:

n=15

Step-by-step explanation:

Answer:

n = 15

Step-by-step explanation:

1/5 * 15 = 3

This is 100% correct, if you don't believe me go to a new tab and type 1/5*15

It will say 3.

A remainder is the remaining amount of a number than comes out of a division. I'm not sure how to explain it better, so I'll give you an example:

Let's say you want to divide 5 by 2. We know that 5 can't be divided by 2 evenly, it won't give you a whole number. Instead it will give you a decimal 2.5.

In this case, 1 is the remainder and I will explain why! Do the long division for 5/2. 2 fits into 5 two times, so you multiply 2 * 2, which gives you 4. If you subtract that number from 5, you get 1. We know that 2 can't fit into one, therefore, 1 is the remainder. once you start getting into decimals, you can fit numbers into other numbers, which is why technically you can fit 2 into 5, but you can't fit it in evenly, if that makes sense!

I hope this example helps see what a remainder is. It's just the number in a long division that the divisor (in my example, 2 is the divisor) can't fit in!

Answer:

0.27 is the answer

I wish you luck in your assignments.

Answer:

Step-by-step explanation:

0.27

Answer:

50%

Step-by-step explanation:

16 litres = (16 x 1000) cm^3

             = 16000 cm^3

Hence,

Percentage = 8000/16000 x 100%

                    = 1/2 x 100%

                    = 50%

Answer:

A. x

Step-by-step explanation:

I calculated it logically

If earning 3250 per month over 10year period, At the end of 10th year, the amount on the account will be 390,000

To multiply means to add equal groups. When we multiply, the number of things in the group increases. The two factors and the product are parts of a multiplication problem. In the multiplication problem, 6 × 9 = 54, the numbers 6 and 9 are the factors, while the number 54 is the product.

The amount earned In a month is 3250.

There are 12 months In a year.

The total month in 10 years = 10× 12 = 120 months

The total amount in the account for 10years = 120×3250 = 390,000

Therefore there will be 390000 in the account at the end of 10th year.

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The equation 3y + 2 = 2x is not a direct variation

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

Variation = direct variation

3y + 2 = 2x

A direct variation is represented as

y = kx

Where k is the constant of proportion

When the equations y = kx and  3y + 2 = 2x are compared, we can see that

The equation 3y + 2 = 2x has a constant term

Hence, the equation is not a direct variation

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The weight of the circle is heavier than the weight of the square by the weight of the triangle

Examining the weights, can lead to a linear equation, the equation will have the follows parameters

let t represent triangle

let c represent circle

let s represent square

6s + 3t = 3s + 3c

6s - 3s + 3t = 3s + 3c

3s + 3t = 3c

divide through by 3

s + t = c

10 + t = c

From the equation 10 + t = c we can say that the weight of the circle is a triangle weight more than the square

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Answer:16(-1/2)^n-1

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The slop formula is [tex]\frac{rise}{run}[/tex] and in the first one the rise increase per y (x) is 2 units and the run (y) is 1 as we calculated the run as how many units x rises per y and A is the answer due to it being the one which follows the rule.

Answer:

b

Step-by-step explanation:

The sum of the solutions of the equation 4x(x - 3) = 23 is 3.

A quadratic equation is an algebraic expression in the form of variables and constants.

A quadratic equation has two roots as its degree is two.

Given, An equation 4x(x - 3) = 23.

Now, Distributing the terms in the LHS we have,

4x² - 12x = 23.

4x² - 12x - 23 = 0.

By applying Sridhar acharya's formula we have,

[tex]x_{1,\:2}=\frac{-\left(-12\right)\pm \sqrt{\left(-12\right)^2-4\cdot \:4\left(-23\right)}}{2\cdot \:4}[/tex].

[tex]x=\frac{3+4\sqrt{2}}{2},\:x=\frac{3-4\sqrt{2}}{2}[/tex].

Therefore, The sum of the solutions of the equation is,

x + x = (3 + 4√2)/2 + (3 - 4√2)/2.

= (3 + 4√2 + 3 - 4√2)/2.

= 6/2.

= 3.

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9514 1404 393

Answer:

  -2, 3

Step-by-step explanation:

For the product to be negative, exactly one of the two numbers must be negative. For the sum to be positive, the positive number must be larger than the absolute value of the negative number.

One such pair of numbers is -2 and 3.

__

Their product is -6; their sum is +1.

Answer:

[tex]14\pi[/tex] and [tex]16\pi[/tex]

Step-by-step explanation:

The equation for the circumference of circles is either [tex]d\pi[/tex] or [tex]2r\pi[/tex], with r being the radius and d being the diameter.

Question A

The diameter is stated as 14. Plug into the equation to get:

[tex]14\pi[/tex]

This is your answer in exact form.

Question B

The radius is stated as 8. Plug into the equation to get:

[tex]2(8)\pi[/tex]

[tex]16\pi[/tex]

This is your answer in exact form.

Answer:

1) 43.98

2) 50.27

Step-by-step explanation:

I hope this helps!

The value of x is equal to 3.

The length of diagonal LN is equal to 18 units.

The length of diagonal MP is equal to 15 units.

In Mathematics, the diagonal of a rectangle can be defined as a line segment that connects any two (2) of its non-adjacent vertices together while dividing the rectangle into two (2) equal parts.

This ultimately implies that, the length of each diagonal of a rectangle is always equal to each other. Therefore, the diagonals of any rectangle is always equal to one other.

We would determine the value of x by equating the length of each diagonal as follows;

LN = MP

7x - 3 = 4x + 3.

7x - 4x = 3 + 3

3x = 6

x = 6/2

x = 3.

Next, we would calculate length of each diagonal as follows;

LN = 7x - 3

LN = 7(3) - 3

LN = 21 - 3

LN = 18 units.

MP = 4x + 3.

MP = 4(3) + 3.

MP = 12 + 3

MP = 15 units.

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Complete Question:

LMNP is a rectangle. Find the value of x and the length of each diagonal.

LN = 7x - 3 and MP = 4x + 3.

Answer:

the axis of symmetry is: x=-5