Can u guys simplify this?
(2x^-3y^5)^2*(x^7y^-11)

We will have the following:

So, the equation in vertex form is:

And in standard form:

***Explanation***

We know that the quadratic expression in vertex form follows:

Where (h, k) is the vertex of the expression. Now, we know that the vertex is (2, -8), so we replace those values and we obtain:

Now, in order to determine "a" we must replace one point (That is not the vertex) in the expression and solve for "a", and we are told that the point (4, 3) is in one of the solutions, so:

Thus, the expression in vertex form is then:

And to determine the standard form, we simply expand the equation in vertex form:

90 minutes for 3 typed pages; 60 minutes for a a typed pages write a proportion for each phrase and solve it​

we have that

90/3=60/a

solve for a

a=(60*3)/90

SOLUTION

Write out the given information

Construct the two- way frequency table

we must find b one of the parallel sides before proceeding to find h

from the diagram b = 7cm

The distance from 7 to 0 is 7 because the absolute value of 7 is 7.

Correct Answer: A

Answer:

(f o g)(x) = 8x³ + 2x - 6

(g o f)(x) = 2x³ + 2x - 12

Step-by-step explanation:

f(x) = x³ + x - 6; g(x) = 2x

(f o g)(x) = f(g(x))

f(g(x)) = (2x)³ + (2x) - 6

f(g(x)) = 8x³ + 2x - 6

(g o f) = g(f(x))

g(f(x)) = 2(x³ + x - 6)

g(f(x)) = 2x³ + 2x - 12

I hope this helps!

Answer:

A. angle B and angle C

Step-by-step explanation:

Line segments are named after the two points where they begin and end.

Answer:

Explanation:

Here, we want to get the measure of the angle marked AWL

The measure of this angle is simply half the measure of the big arc WHA

Mathematically, we have the measure of the angle as:

There are a total of 50 numbers that are between 1 and 50. Halft of these numbers are even (divisible by 2 ) and half of then odd.

There are 25 integers that are not even and in total there are 50 integers; thereofre, the probablity of finding an even integer is

25/50 = 1/2

To plot in the plane points with fraction number coordinates (x or y) you can rewrite the fractions as decimal numbers:

Then, you have the next coordinates;

(- 2.5, 2) and (1, -0.25)

And the next graph:

Use a line to link the points

LCM stands for Least Common Multiple.

And it is defined as the product of the two numbers divided by the GCD (greatest common divisor)

In our case, the product of 4 and 6 is 24, , and the greatest common divisor of 4 and 6 is "2". Therefore, the LCM of 4 and 6 is 24/2 = 12

Let me also use the Venn diagram that your teacher provided:

In the diagram we enter the factors that correspond to both numbers (4 and 6), and in the intersection of the two sets (intersection of the circle) we type a "2" which is the ONLY factor 4 and 6 have in common (the greatest common divisor of the two given numbers) So complete a diagram as follows:

We typed a 2in the area common to both numbers. Then your LCM is the product of 2 times 2 times 3 = 12

Notice the blue set (circle) contains the two factors for 4 (2 * 2) and the orange circle contains the two factor for 6 (2 * 3)

We set in the intersection of the two circles the factor that is common to both.

Do you want me to complete the second question with a Venn diagram as well? Perfect.

The second question is about the LCM of the numbers 12 and 8

Then we create a Venn diagram like the following, considering that the factor in common between 12 and 8 is 4, because 12 = 4 * 3 and 8 = 4 * 2

Again here, the factors 3 and 4 (that give 12) are typed in the blue circle. and the factors that form 8 (4 * 2) are typed inside the orange circle.

The factor that both share is in the middle "4". Therefore, now to find the LCM you simply multiply the three numbers shown in the Venn diagtam: 3 * 4 * 2 = 24

Then 24 is your LCM.

Considering the Set A and B given, Applying inclusion - exclusion principle the number of elements common to both Sets is 10

This is a counting techniques that ensures that elements are not counted twice

It is achieved by the formula:

(A ∪ B) = n(A) + n(B) - n(A ∩ B)  

The information from the question include the following

Set A contains 48 elements

Set B contains 16 elements

The total number elements in either Set A or Set B is 54

Applying inclusion - exclusion principle gives the formula

Set A + Set B - ( Set A ∩ Set B ) = Set A ∪ Set B

substituting the values gives

48 + 16 - ( Set A ∩ Set B ) = 54

48 + 16 - 54 = ( Set A ∩ Set B )

10 = ( Set A ∩ Set B )

( Set A ∩ Set B ) = elements Sets A and B have in common

Therefore the number of the elements common to Sets A and B  is 10

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Answer:

So first we can assume x= 1 bc there is no number for x

Step-by-step explanation:

So we Evaluate for x=1

1+|2−1|−5

1+|2−1|−5

=−3

Evaluate for x=1

So x+|x-5|+9

1+|1−5|+9

1+|1−5|+9

=14

Recall that the y-intercept of a graph is the point where the graph intersects the y-axis.

From the given graph we get that the line intersects the y-axis at (0,2).

Answer: Option C.

The time taken for Eric to finish the book is 3 1/2 hours.

A fraction simply means a part of a whole. It van also refer to any number of equal parts.

The information illustrated that Jessica finishes her book in 2 1 / 3 hours and that Eric takes 1 1 / 2

times longer than Jessica to finish his book.

In this case, the time that was used by Eric will be the multiplication of the fractions given. This will be illustrated as:

= 2 1/3 × 1 1/2

Change to improper fraction

= 7/3 × 3/2

= 7 / 2

= 3 1 / 2

Eric used 3 1/2 hours.

This illustrates the concept of multiplication of fractions.

The complete question is written below.

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Jessica finishes her book in 2 1/3.hours. Eric takes 1 1/2 times longer than Jessica to finish his book. How long did Eric take yo finish the book?

Solution:

Given:

The table of values is given:

From the table,

We see the data is a linear function. This is because a linear function has domain values at regular intervals.

Also, the linear equation can be formed as shown below, indicating it is a linear function.

Considering two points, (3,1) and (1,2)

where,

A linear equation is of the form;

From the above, has confirmed it is a linear function and not an exponential function, we can deduce that;

a) The function is not an exponential function.

b) The domain values (x-values) are at regular intervals

c) The range values (y-values) have a common difference of 1

Therefore, the correct answer is OPTION A

We have to analyze the given options to solve this problem.

Option 1.

The absolute value of -12 is larger than the absolute value of 12.

The absolute value is always a positive number:

To answer this question, we need to use the next formula for simple interest:

Where:

FV is the future value we need to find (in this case).

PV is the present value, that is, $400 (in this case).

i is the interest rate. In this case, we have 8% (0.08).

n is the number of periods (n = 3, in this case).

Then, we have:

That is, the FV is $496. Therefore, the simple interest is $(496-400 = 96).

Thus, the amount of simple interest that $400 would earn at 8% per year by the end of 3 years is $96 (option A).

In other words, the result can be obtained also if we have is $400 * (0.08)*3 = $96.

Solution:

Given the logarithmic expression:

According to the change of base formula,

Thus, expressing the logarithm expression in a natural logarithm,

Hence, we have

Find the proportion between liters of fuel

that is find 22/9 = 2.444

thats how much liters have more to consume

now multiply 2.444 by 81 , the kilometers she has drived

It gives as result 2.444 x 81 = 198 kilometers

Here, we want to get an equation

Firstly, since we do not have the number of weeks, we can represent it with a variable (a letter)

In this case, we shall be representing it with w

Since she saves $13 in a week, in w weeks, the amount saved will be;

13 * w = $13w

Now, recall that she has $75 before she started saving. What this mean is that at the end of the w weeks, the amount she will have will be ;

We now proceed to equate this to the total she wants to save and we finally have the complete equation below;

Tara needs to sell 20 scarves to break even.

The break-even point is the sales level that the seller must attain to make the total revenue equal to the total costs (fixed and variable).

There is no profit or loss at the break-even point (either in units or dollar values).

Selling price per unit = $18

Product cost per unit = $4

Contribution margin per unit = $14

Fixed cost per month = $280

Estimated production and sales units per month = 80 scarves

Break-even sales units = fixed costs/contribution margin per unit

= 20 ($280/$14)

Check:

Total revenue at 20 units = $360 (20 x $18)

Total costs at 20 units = $360 ($280 + $4 x 20)

Thus, for Tara to break even, she needs to sell 20 scarves per month.

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Answer with explanation:

We need to determine if what Tyler is saying is in fact equal to what his coach said, to get the final answer, we have to concert the resulting units in miles:

Taylor's answer:

Coach's answer:

In conclusion, The two answers are correct so the two models are indeed alike.

All in one, or one expression for each property?

a) Zero property

b) Multiplication property

c) Power property

d) All in one (this is the expression)

A bird sits on top of a Lamppost. The angle made by the lamp-post and a line from the feet of the bird to the feet of the Observer standing away from the Lamppost is 55°. the distance from the Lamppost and the Observer is 25 ft. estimate the height of the lamp post ​

we have that

see the attached figure to better understand the problem

so

tan(55)=h/25

solve for h

h=25(tan(55))

You divide 11 by 16, as follow:

0.6875

16 l 110

-96

140

-128

120

-112

80

-80

0

As you can notice, the result of the division is 0.6875 (here you have used the rules for the division of a number over a greater number, which results in a decimal)

Given :

The principal = 3,700

Assume a simple interest

The account growing at a rate allowing the money to double every 6 years.

So,

How much money would be in the account after 14 years, to the nearest dollar?​

So, we will substitute with r = 1/6, t = 14 years

So,

Rounding to the nearest dollar

So, the answer will be $12,333

INFORMATION:

We know that:

- John sells plain cakes for $8 and decorated cakes for $12.

- On a particular day, John started with a total of 100 cakes, and sold all but 4.

- His sales that day totaled $800.

And we must find the number of plain cakes and decorated cakes that he sold that day.

STEP BY STEP EXPLANATION:

To find them, we can represent the situation using a system of equations

Where, x represents the number of plain cakes that he sold and y represents the number of decorated cakes that he sold.

Now, we must solve the system:

1. We must multiply the equation (1) by -8

2. We must add equations (2) and (3)

3. We must solve equation (4) for y

4. We must replace the value of y in equation (1) and then solve it for x

So, we found that x = 88 and y = 8.

Finally, John sold 88 plain cakes and 8 decorated cakes.

ANSWER:

He sold 88 plain cakes and 8 decorated cakes that day.

Explanation:

f(x) is a logarithmic function. Logarithmic functions are zero when the argument is 1:

For greater values, the function is positive and for less values the function is negative.

Answers:

(1) x = -2

(2) x < -2. In interval notation x:(-∞, -2)

(3) x ≥ -2. In interval notation x:[-2, ∞)