A is the set of even numbers greater than or equal to 4 and less than or equal to 8B=1-29, -25,-24, -22, -21, 22, 27(a) Find the cardinalities of A and B.n(A)=3(b) Select true or false.12 € A22 € B67 A-24 € BTruen(B) = 1FalseX%S3

The given fractions are,

The LCD of fractions is the least common multiple of the denominators.

So, the LCD of the above fractions is,

Multiplying the numerator and the denominator of the fraction by a common term does not change the fraction.

So, the first fraction can be expressed in terms of the LCD as,

The second fraction can be expressed in terms of the LCD as,

We must simplify the following expression:

From the expression, we see that we have terms with variable a and terms with variable b. In order to simplify the expression, we add the terms with a together (which sums up 8a), and we do the same for the terms with b (which sums up 1b):

The solution is: 8a+b

Surface area of a rectangular prism:

Substitute 1.2 for all of the variables in the formula:

Using a calculator, you should get an answer of:

The answer is that the surface area of this shape is 8.64 yards.

we know that

f(4) is the value of the function f(x) when the value of x is equal to 4

so

For x=4

Look at the graph

The value of the function f(x) is equal to 3

therefore

ANSWER

P(x) = 2700(1.052)^t

P(4) = 3307. (Rounded to nearest student)

EXPLANATION

Given:

1. The current student population to be 2700

2. The growth rate = 5.2% = 0.052

Desired Outcome

1. The exponential growth model

2. Population of the students in 4 years

The Exponential Growth Model

Population in 4 years

Hence, the Exponential Growth Model P(x) = 2700(1.052)^t and the Population of the students in 4 years P(4) = 3307. (Rounded to nearest student)

The expression which is equivalent to the given expression (3y - 4) (2y + 7) + 11y - 9 is 6 y²+ 24y- 37

A finite collection of symbols that are properly created in line with context-dependent criteria is referred to as an expression, sometimes known as a mathematical expression.

A phrase is considered a mathematical expression if it contains at least two numbers or variables and one or more mathematical operations. This mathematical procedure makes it possible to multiply, divide, add, or subtract quantities.

Presented expression = (3y - 4) (2y + 7) + 11y - 9

Solving the expression we get= 6y²+21y-8y-28+11y-9

                                                   = 6y²+24y-37

There for the correct response is that the given expression is equivalent to = 6y²+24y-37

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Solution

Given

We want to determine if it's a Polynomial

A polynomial is an expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

Hence 4 - 8x + x^2 is a Polynomial

For a shape to be considered a parallelogram it has to meet the following conditions:

0. The opposite sides must be equal

1. The opposite sides are equal

2. Adjacent sides are supplementary

3. The diagonals bisect each other

4. The opposite sides are parallel

For the quadrilateral to be considered a parallelogram then, the conditions that should be met are:

MN=QP and MQ=NP

MN || QP and MQ || NP

The diagonals MP and NQ bisect each other.

∠M=∠P and ∠N=∠Q

From the given options, the second one and the third one are not enough to determine MNPQ as a parallelogram

Answer:

Step-by-step explanation:

Since y and x are inversely proportional, we'll have that:

For a given betha value. Since we have a pair of x and y values, we can plug them in the formula and find our particular value of betha, as following:

This way, our formula would be:

Plugging in x = 7,

we have two points (0, 6) and (4, 3)

this can be represented as (x, y)

the equation of a straight line is

y = mx + c

slope = m = y2 - y1/ x2 - x1

x1 = 0, y1 = 6, x2 = 4 and y2 = 3

slope = 3 - 6 / 4 - 0

slope = -3/4

slope = -3/4

from the equation of a straight line

(y - y1) = m(x - x1)

y1 = 6 and x1 = 0

y - 6= -3/4(x - 0)

y - 6 = -3/4x + 0

y = -3/4x + 6

the error he made was that he used - 6 instead of +6 in the final answer

In order to determine if the point (2, 7) is a solution to the given system of inequalities we just have to replace 7 for y and 2 for x and see if the two inequalities are met, like this:

7 ≥ -2 + 1

7 ≥ -1

As you can see, 7 is greater than -1 then the first inequality is met.

7 < 4(2) + 2

7 < 8 + 2

7 < 10

As you can see, the second inequality is also met, then (2, 7) is a solution for the system of inequalities.

In order to determine the surface area of the cube, use the following formula:

where a is the length of the side of a cube a = 11 m.

Replace the value of a into the formula for S:

Hence, the surface area of the given cube is 726m^2

The graph of the function is defined for x greater than or equal to -2 and less than 3. So domain of the function is,

The value of the function lies between -2 and 3. The function value is greater than or equal to -2 and less than 3. So range of function is,

Given:

To simplify the given rational expression, we first factor x^2-4x+4 by applying Perfect Square Formula as shown below:

Hence,

Now, we simplify the given expression:

Therefore, the answer is:

As given by the question

There are given that the series

Now,

For step 1:

Put n=1

Then LHS =1

And

So,

P(n) is true for n=1.

Now,

Step 2:

Assume that P(n) istrue for n=k

Then,

Adding 2k+1 on both sides

So, we get:

P(n) is true for n=k+1

By the principle of mathematical induction P(n) is true for all natural numbers n.

Hence,

For all n.

Hence proved.

You have the following product:

27 x 8

To estimate the product by rounding 27 to 25, you consider that 25 x 8 is the same as adding 25 eight times.

Then, you have:

25 x 8 = 25 + 25 + 25 + 25 + 25 +25 + 25 +25

25 x 8 = 50 + 50 + 50 + 50 each pair of 25's add up 50

25 x 8 = 100 + 100 each pair of 50's add up 100

25 x 8 = 200

Hence, an estimation of the given product is 200, by considering 27 rounded to 25.

Explanation

we can fill up the dimensions as follow

The age of Mary is 15 years old.

To solve this, we have three expressions:

Where M is the age of Mary, J is the age of Jacob, T is the age of Uncle Tim and H is the age of Henry

Also teh problem give us an additional info, the age of Henry is 13. With this, we can replace the value of H in the thrid equation:

Now we can replace T in the second equation:

Finally, we can replace J in the first equation to get the age of Mary:

Thus, the age of Mary is 15 years old.

Given a line passes through the point (-4,6) and has a slope of 3

We will write the equation of the line in point-slope from

The formula of the point-slope form will be as follows:

Where (h, k) is the point that lies on the line and (m) is the slope

From the given:

m = 3

h = -4

k = 6

Substitute into the formula

so, the answer will be:

Volume of a rectangular prism = base length x width x heigth

Where;

Volume = 600 cm3

base length = 15

width = x

height = 8

Replacing:

600 = (15) (x) (8)

Isolate x

600/ (15)(8) = x

x = 600/ (8)(15)

option C

We will draw a sketch to see the position of the cable

From the figure, we can use the tangent ratio to find the height

By using the cross-multiplication

a) The height of the pole is 24.3 feet to the nearest tenth

To find the length of the cable we will use the cosine ratio

Switch L and cos(29.6)

b) The length of the cable is 49.1 feet to the nearest tenth

Let u make the first box x and the second box y.

If there is a proportional relationship between the number of bananas and their weights, it means that:

We can take the first pair and solve for x as follows:

We can solve for y in the same manner:

Therefore, the boxes are filled as shown below:

ANSWER:

C.

STEP-BY-STEP EXPLANATION:

We have the following function:

Using the substitution method, we can calculate the value of x, like this:

We must divide the 5 pound bag in 6 different containers, therefore:

Each container will hold 0.83 pet food

The slope intercept form equation is expressed as

y = mx + c

where

m represents slope

c represents y intercept

The formula for determining slope is expressed as

slope, m = (y2 - y1)/(x2 - x1)

From the information given,

y2 = 6, y1 = 2

x2 = 0, x1 = 4

Slope, m = (6 - 2)/(0 - 4) = 4/- 4

m = - 1

We would determine the y intercept, c by substituting m = - 1, y = 6 and x = 0 into the slope intercept equation. It becomes

6 = - 1 * 0 + c

6 = c

c = 6

The equation would be

y = - x + 6

To graph the solution set, first, we know that the border of the shaded area will be delimited by the dashed line:

Now, to know if the shaded area will be on top or below the line, we evaluate the point (0,0):

therefore, the origin is not a point of the solution set.

solution

For this case the tangent line to the circle and the point should be:

The reason is because the tangent line and the point needs to touch the circle just one time

We can rewrite the question as the probability of getting the event E is 23:77. Find the probability of getting the event not E.

The number 23:77 is a ratio and is it equivalent to:

To get the probability of the event not-E, we can proceed as follows:

So the probability for the event not-E is about 53/77 or 0.7013 (or a little more than 70%).

By elimination, it means that we should apply algebraic operations so we find the value of one variable. So first, lets multiply the first equation by 5. We get

Now, lets multiply by 2 the second equation

With this two equations, lets subtract the second equation from the first equation

We get

If we divide y by 19 we get

Now, using this value in the second equation we get

If we subtract 6 on both sides, we get

Finally, we divide by 5 on both sides and we get

Answer

Option B is correct.

64x³ + 27 = (4x + 3) (16x² - 12x + 9)

Explanation

We are told to factorize

64x³ + 27

To do this, we use the factorization of (x³ + y³) as a guide. First of,

(x + y)³ = (x + y) (x + y)² = (x + y) (x² + 2xy + y²)

(x + y)³ = x³ + y³ + 3x²y + 3xy²

So, we can write

x³ + y³ = (x + y)³ - 3x²y - 3xy² = (x + y)³ - 3xy(x + y)

= (x + y) [(x + y)² - 3xy]

= (x + y) (x² + y² + 2xy - 3xy)

= (x + y) (x² - xy + y²)

So, comparing (64x³ + 27) with (x³ + y³), we can see that

64x³ = (4x)³

27 = (3)³

(64x³ + 27) = (4x)³ + 3³

x³ + y³ = (x + y) (x² - xy + y²)

(4x)³ + 3³ = (4x + 3) [(4x)² - (4x × 3) + 3²]

= (4x + 3) (16x² - 12x + 9)

Hope this Helps!!!