Use the diagram below to answer the questions. Line q contains points J, K, and M. Point P is above line q between points K and M. A line connects points M and P. Another line connects points P and K. Point L is above point J. A line starts at point K and extends through point L. Which are shown on the diagram? Check all that apply. Line segment J L Ray K M Line J K Ray P K AngleLJK Ray M J

Answer:

a⁴b⁴ - c⁴

Step-by-step explanation:

The difference of squares formula states that (a - b)(a + b) = a² - b². In this case, a = a²b² and b = c² so a² - b² = (a²b²)² - (c²)² = a⁴b⁴ - c⁴.

Answer:

a^4b^4 - c^4.

Step-by-step explanation:

(a²b²-c²)(a²b²+c²)

Difference of 2 squares:

= (a²b²)^2 - (c²)^2

= a^4b^4 - c^4.

Answer:

C.) 4(750c-700t) ; D.) 2800t - 3000c

Step-by-step explanation:

Time taken :

Tatenda = t sec/m^2

Ciara = c sec/m^2

Tatenda = 700m^2 per week

Ciara = 750m^2 per week

Which expressions can we use to describe how many more seconds Tatenda spends than Ciara spends mowing lawns during 4

Total Time taken over four weeks :

Tatenda = 4(t * 700) = 4(700c)

Ciara = 4(c * 750) = 4(750c )

Number of seconds Tatenda spends more than Ciara : meaning Tatenda spends more seconds than

Tatenda - Ciara

4(700t) - 4(750c) = 4(700t - 750c)

4(700t - 750c)

Or

4(700t - 750c) = 2800t - 3000c

2800t - 3000c

Answer:

D. zero

Step-by-step explanation:

Since the graphs do not intersect, there are zero solutions.

The number of solutions on the graph is zero

The graph shows a linear equation (the straight line) and a non linear equation (the curve)

From the graph, we can see that the straight line and the curve do not intersect

This means that the graph do not have any solution

Hence, the number of solutions on the graph is zero

Read more about non-linear graphs at:

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Steps to find MAD:

Step 1. Calculate mean([tex]\overline{x}[/tex]) of the data using formula: [tex]\overline{x}=\dfrac{\sum x}{n}[/tex] ,  where x denotes data points and n is the number of data points.

Step 2. Calculate distance of each data point from mean :

Distance = [tex]|x-\overline{x}|[/tex]

Step 3. Divide  distance of each data point from mean by n:

MAD = [tex]\dfrac{\sum |x-\overline{x}|}{n}[/tex] , which is the final computation to find MAD.

Answer:

[tex]\Huge \boxed{3}[/tex]

Step-by-step explanation:

The function is given :

f(x) = 4x + 15

For f(-3), the input for the function f(x) is -3.

Replace the x variable with -3.

f(-3) = 4(-3) + 15

Evaluate.

f(-3) = -12 + 15

f(-3) = 3

The output for f(-3) is 3.

Answer: f(-3) = 3

Step-by-step explanation: Notice that f is a function of x.

So we want to find f(-3).

We find f(-3) by plugging -3 in for x,

everywhere that x appears in the function.

So we have 4(-3) + 15.

4(-3) is -12 so we have -12 + 15 which is 3.

So f(-3) is 3.

Answer:

A.) median; 1.5

Step-by-step explanation:

Hello!

The median is the number that is in the middle when the numbers are listed from least to greatest

0, 0, 1, 1, 2, 2, 2, 14

We can take one from both sides till there are one or two numbers left

0, 1, 1, 2, 2, 2

1, 1, 2, 2

1, 2

If there are two numbers left we add them then divide by 2 to get the median

1 + 2 = 3

3 / 2 = 1.5

The answer is A.) median; 1.5

Hope this helps!

Answer:

when you simplify you continue until you get to the simplest form but when you solve you continue until you get an answer. Solving gives you a value for a variable. You mean simplify and get 2x - 10 but when you solve you continue until you get x as 5

Step-by-step explanation:

Answer: ok, so simplifying is when you make something less complex or complicated. Solving means an expression can be used for representating  the solutions. for Example, say if you have the equation x+y=2x-1 is solved for the unknown x by the expression x=y+1. solving gives you the value for the variable. you know the difference by when you are simplifying you are trying to make the problem less complicated or less complex. and when you are solving you are trying to find the answer to the problem..

Step-by-step explanation:

Answer:

This is poorly written, so i will answer it as it was:

"Let f (x) = |2). Write a function g(x) whose graph is a vertical shrink by a factor of  A, followed by a translation 2 units up of the graph of f."

I don't really know what you do mean by I2), so i will answer it in a general way.

First, we do a vertical shrink of factor A.

A must be a number smaller than one and larger than zero., then if g(x) is a vertical shrink of factor A of the graph of f(x), we have that:

g(x) = A*f(x)

As 0 < A < 1

We will have that the graph of g(x) is a vertical compression of the graph of f(x)

Now we do a vertical shift of 2 units up.

A general vertical shift of N units up is written as:

g(x) = f(x) + N

Where N is a positive number.

So in our case, we have:

g(x) = A*f(x) + 2.

Where you will need to replace the values of A and f(x) depending on what the actual question says,

Answer:

[tex]\boxed{\sf Option \ 1}[/tex]

Step-by-step explanation:

The profit is revenue (R ) - costs (C ).

Subtract the expression of costs (C ) from revenue (R ).

[tex]10x-0.01x^2-(2x+100)[/tex]

Distribute negative sign.

[tex]10x-0.01x^2-2x-100[/tex]

Combine like terms.

[tex]8x-0.01x^2-100[/tex]

The first option has a positive 100, which is wrong.

The rest options are right, when we expand brackets the result is same.

Answer:

(x-12)² + (y-6)² = 36 (Option C)

Step-by-step explanation:

use circle formula

(x-h)² + (y-k)²= r²

h= 12 and k= 6 and r= 6

(x-12)² + (y-6)² = 6²

6 squared = 36 (6·6)

(x-12)² + (y-6)² = 36

Answer:

-49152

Step-by-step explanation:

The pattern is:

multiply for 4

then:

-3, -12, -48, -192, -768, -3072, -12288, -49152

Answer:

w = 100°

Step-by-step explanation:

Opposite angles in an inscribed quadrilateral in a circle are supplementary.

Therefore, [tex] w + 80 = 180 [/tex]

Subtract 80 from both sides

[tex] w + 80 - 80 = 180 - 80 [/tex]

[tex] w = 100 [/tex]

The value of w = 100°

Greetings from Brasil...

In a triangle the sum of the internal angles is 180 °.... Thus,

Ô = 180 - 30

Ô = 60

The desired area is the area of the rectangle triangle, minus the area of the circular sector whose angle 60

A1 = area of the rectangle triangle

TG B = OA/AB

AB = OA / TG B

AB = 6 / TG 30

AB = 6√3

A1 = (AB . OA)/2

A1 = (6√3 . 6)/2

A2 = area of the circular sector

(rule of 3)

 º                       area

360    ------------   πR²

60     ------------    X

X = 60πR²/360

X = 6π

So,

Then the area shaded is:

A = A1 - A2

Answer:

The number of measles vaccines that Dr. Potter give than polio vaccines is 30

Step-by-step explanation:

The parameters given are;

The number of doses given in a polio vaccine = 6 doses

The number of doses given in a measles vaccine = 3 doses

The number of vaccinations given by Dr. Potter last year = 60 vaccinations

The number of doses given in the 60 vaccinations = 225 doses

Let the number of polio vaccine given last year by Dr. Potter = x

Let the number of measles vaccine given last year by Dr. Potter = y

Therefore, we have;

6 × x + 3 × y = 225.......................(1)

x + y = 60.......................................(2)

From equation (2), we have;

x = 60 - y

Substituting the derived value for x in equation (1), we get;

6 × x + 3 × y = 225

6 × (60 - y) + 3 × y = 225

360 - 6·y + 3·y = 225

360 - 225 = 6·y - 3·y

135 = 3·y

y = 45

x = 60 - y = 60 - 45 = 15

Therefore;

The number of polio vaccine given last year by Dr. Potter = 15

The number of measles vaccine given last year by Dr. Potter = 45

The number of measles vaccines that Dr. Potter give than polio vaccines = 45 - 15 = 30 vaccines.

The number of measles vaccines that Dr. Potter give than polio vaccines =  30 vaccines.

Answer:

(D) There are [tex]5 \frac{1}{2}[/tex]  three-fourths in [tex]4 \frac{1}{8}[/tex]

Step-by-step explanation:

We can see that in this model, the student tried to put [tex]\frac{3}{4}[/tex] into  [tex]4 \frac{1}{8}[/tex]. We know this because the top of Step 2 is  [tex]4 \frac{1}{8}[/tex] and he is counting how many fourths in the bottom.

So this becomes the division statement:

[tex]4 \frac{1}{8} \div \frac{3}{4}[/tex].

We can convert  [tex]4 \frac{1}{8}[/tex] into a mixed number by multiplying 8 and 4, then adding 1.

[tex]\frac{33}{8} \div \frac{3}{4}[/tex].

Multiply by the reciprocal:

[tex]\frac{33}{8} \cdot \frac{4}{3} = \frac{132}{24}[/tex]

Which simplifies down to

[tex]\frac{11}{2}[/tex], which is just [tex]5 \frac{1}{2}[/tex] in improper form.

Hope this helped!

Answer:

D

Step-by-step explanation:

Answer:

Step-by-step explanation:

This problem is on the mensuration of solids.

A sphere is a solid shape.

Given data

radius of sphere = 17 units

The volume of a sphere can be expressed as below

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

Substituting our data into the expression we have

[tex]volume = \frac{4}{3}*3.142*17^3[/tex]

[tex]volume = \frac{4}{3}*3.142*4913\\\\volume = \frac{61746.584}{3}= 20582.195[/tex]

The volume of the sphere is given as

20582.195 units

Answer:

By using The Pythagorean Theorem:

[tex]/Hypotenuse/^{2} = /Length of altitude/^{2} + /Length of leg/^{2} \[/tex]

/Hypotenuse/ = [tex]\sqrt\ /Length of altitude/^{2} + /Length of leg/^{2} \}[/tex]

Step-by-step explanation:

The Pythagorean theorem states that: Given a Right-angled triangle, the square of the hypotenuse equals the sum of squares of the other two sides ( Here, being the length of the altitude and length of leg). That is,

[tex]/Hypotenuse/^{2} = /Length of altitude/^{2} + /Length of leg/^{2} \[/tex] and hence,

/Hypotenuse/ = [tex]\sqrt\ /Length of altitude/^{2} + /Length of leg/^{2} \}[/tex]

For example, If the length of the altitude is 4m and the length of leg is 3m. Using The Pythagorean theorem, the length of the hypotenuse will be

[tex]/Hypotenuse/^{2} = /Length of altitude/^{2} + /Length of leg/^{2} \\\/Hypotenuse/ = \sqrt{/Length of altitude/^{2} + /Length of leg/^{2}} \\/Hypotenuse/ = \sqrt{4^{2} + 3^{2} }[/tex]

[tex]/Hypotenuse/ = \sqrt{16+9} \\/Hypotenuse/ = \sqrt{25} \\/Hypotenuse/ = 5m[/tex]

The length of the hypotenuse for the given example will be 5m.

This is how to find the length of an hypotenuse.

Answer:

60 ships.

Step-by-step explanation:

Let the total number of ships in the naval fleet be represented by x

One-third of the fleet was captured = 1/3x

One-sixth was sunk = 1/6x

Two ships were destroyed by fire = 2

Let surviving ships be represented by y

One-seventh of the surviving ships were lost in a storm after the battle = 1/7y

Finally, the twenty-four remaining ships sailed home

The 24 remaining ships that sailed home =

y - 1/7y = 6/7y of the surviving fleet sailed home.

Hence

24 = 6/7y

24 = 6y/7

24 × 7/ 6

y = 168/6

y = 28

Therefore, total number of ships that survived is 28.

Surviving ships lost in the storm = 1/7y = 1/7 × 28 = 4

Total number of ships in the fleet(x) =

x = 1/3x + 1/6x + 2 + 28

Collect like terms

x - (1/3x + 1/6x) = 30

x - (1/2x) = 30

1/2x = 30

x = 30 ÷ 1/2

x = 30 × 2

x = 60

Therefore, ships that were in the fleet before the engagement were 60 ships.

Answer:

156.6 square yards

Step-by-step explanation:

To find the surface area of the pyramid, find the area of each surface and add them together.

formula for area of a triangle = 1/2(b·h)

1. There are three triangles with a base of 9 and a height of 9

1/2(9·9) = 40.5

Multiply by the three triangles

40.5 · 3 = 121.5

2. There is one triangle with a base of 9 and a height of 7.8

1/2(9·7.8) = 35.1

3. Add the areas of all surfaces

121.5 + 35.1 = 156.6

Answer:

So the quotient of [tex]\frac{x^{2} + x - 6}{x^{2} -6x + 5} X \frac{x^{2} + 2x - 3}{x^{2} -7x + 10}[/tex] has (x + 3)² in the numerator and (x + 5)² in the denominator.

Step-by-step explanation:

[tex]\frac{x^{2} + x - 6}{x^{2} -6x + 5} X \frac{x^{2} + 2x - 3}{x^{2} -7x + 10}[/tex]

Factorizing the expressions we have

[tex]\frac{x^{2} + 3x -2x - 6}{x^{2} -x - 5x + 5} X \frac{x^{2} + 3x - x - 3}{x^{2} -2x -5x + 10}[/tex]

[tex]\frac{x(x + 3)- 2(x + 3)}{x(x -1) - 5(x - 1)} X \frac{x(x + 3) - 1(x + 3)}{x(x - 2) - 5(x - 2)}[/tex]

[tex]\frac{(x + 3)(x - 2)}{(x - 5)(x - 1)}X\frac{(x + 3)(x - 1)}{(x - 2)(x - 5)}[/tex]

Cancelling out the like factors, (x -1) and (x - 2), we have

[tex]\frac{(x + 3)(x + 3)}{(x - 5)(x - 5)}[/tex]

= [tex]\frac{(x + 3)^{2} }{(x + 5)^{2} }[/tex]

So the quotient of [tex]\frac{x^{2} + x - 6}{x^{2} -6x + 5} X \frac{x^{2} + 2x - 3}{x^{2} -7x + 10}[/tex] has (x + 3)² in the numerator and (x + 5)² in the denominator.

Answer:

Hey There!! The Correct answer is: The equation is w = 241(1.06)t

And here variable t represents the number of years since 2000.

In 2001 means t=2001 -2000 = 1

So we plug 1 for t in the given expression , that is w = 241(1.06)1 = 241 * 1.06 = 255.46

Therefore in 2001, it should be worth to 255.46.

And in the given expression 1.06=1 +0.06, where 0.06 is the annual percent of growth that is 6 % .

Hope It Helped!~ ♡

ItsNobody~ ☆

The projected annual percent of growth is 10% and the company worth in 2011 will be $587.74 millions. Then the correct option is C.

Consider the function:

y = a (1 ± r) ˣ

Where x is the number of times this growth/decay occurs, a = initial amount, and r = fraction by which this growth/decay occurs.

If there is a plus sign, then there is exponential growth happening by r fraction or 100r %.

If there is a minus sign, then there is exponential decay happening by r fraction or 100r %.

The projected worth (in millions of dollars) of a large company is modeled by the equation is given as,

[tex]\rm w = 206\times (1.10)^t\\\\w = 206\times (1+0.10)^t[/tex]

Then the projected annual percent of growth is 10%.

The variable t represents the number of years since 2000.

Then the company worth in 2011 will be

w = 206 × 1.1¹¹

w = $587.74 millions

The projected annual percent of growth is 10% and the company worth in 2011 will be $587.74 millions.

Then the correct option is C.

More about the exponent link is given below.

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Answer:

d. $50,499

Step-by-step explanation:

Given:

S = 40,000 (1.06)^t

Where,

t=4 years

S=40,000(1.06)^4

=40,000(1.26247696)

=50,499.0784

To the nearest dollar

S=$50,499

The answer is d. $50,499

Answer:

Zero

Step-by-step explanation:

2+6=8 which means it can't be. It has to be a length higher than 10

Answer:

SI=PRT/100

=10000*5*42/12*100

=1750

SI=1750

TOTAL AMOUNT=PRINCIPLE+SI

=10000+1750

=101750

Answer:

  2n+2 ways to win

Step-by-step explanation:

You generalize by observing patterns in the way you solve the smaller problems.

The number of winning moves is 2n+2: the total of the number of diagonals, columns, and rows.

For an n×n board, there are 2 full-length diagonals, n columns, and n rows, hence 2+n+n = 2n+2 ways to win.

Answer:

The third table is the correct answer

Step-by-step explanation:

Here in this question, we are concerned with determine which of the tables correctly represents what an exponential function is.

An exponential function is a function of the form;

y = x^n

where the independent variable x in this case is raised to a certain exponent so as to give the results on the dependent variable axis (y-axis)

In the table, we can see that we have 2 segments, one that contains digits 1,2 and so on while the other contains purely the powers of 10.

Now, let’s set up an exponential outlook;

y = 10^x

So we have;

1 = 10^0

10 = 10^1

1/10 = 10^-1

1000 = 10^3

1/100 = 10^-2

We can clearly see here that we have an increase in the value of y, depending on the value of the exponent.

However it is only this table that responds to this successive correctness as the other tables in the answer do have a point where they fail.

For example;

10^-2 is not 10 which makes the fourth table wrong

10^4 is not 100 which makes the first table wrong

we have same error on second table too

Answer:

Here's what I get  

Step-by-step explanation:

Part A

The graph shows a polynomial of odd degree. It is probably a third-degree polynomial — a cubic equation.

Part B

The standard form of a cubic equation is

y = ax³ + bx² + cx + d

The factored form of a cubic equation is

y = a(x - b₁)(x² + b₂x + b₃)

If you can factor the quadratic, the factored form becomes

y = a(x - c₁)(x - c₂)(x - c₃)

Part C

The zeros of the function are at x = -25, x = - 15, and x = 15.

Part D

The linear factors of the function are x + 25, x + 15, and x - 15.

Part E

y = a(x + 25)(x + 15)(x - 15) = a(x + 25)(x² - 225)  

y = a(x³ + 25x² - 225x - 5625)

Part F

When x = 0, y = 1.

1 = a[0³ +25(0)² - 225(0) - 5625] = a(0 + 0 - 0 -5625) = -5625a

a = -1/5625

Part G

[tex]y = -\dfrac{1}{5625}( x^{3} + 25x^{2} - 225x - 5625)\\\\y = \mathbf{ -\dfrac{1}{5625} x^{3} - \dfrac{1}{225}x^{2} + \dfrac{1}{25} x + 1}[/tex]

Answer

Actually, the answer should be -0.0007(x+20)(x+5)(x-15)

Step-by-step explanation:

This is continuing off of the previous answer

PART C

The zeros should be (15,0), (-5,0), and (-20,0)

PART D

x - 15, x + 5, and x + 20

PART E

a(x - 15)(x + 5)(x + 20)

Standard: [tex]a(x^{3} + 10x^{2} -275x-1500)[/tex]

PART F

The y-intercept is at (0,1), so we replace the x's with 0:

1 =[tex][(0)x^{3} +10(0)x^{2} -275(0)-1500][/tex] and this gives us (0+0-0-1500) which also equals -1500

Then we do [tex]\frac{1}{-1500}[/tex] which gives us -0.0006 repeating which rounds to -0.0007

a= -0.0007

PART G

Just place the numbers where they should go and your answer is

y =-0.0007(x + 20)(x + 5)(x - 15)  

the placement for (x + 20) (x + 5) and (x - 15) doesn't matter as long as they are behind -0.0007

Answer:

(3x-1) (x+1)

Step-by-step explanation:

3x^2 + 2x − 1

3x^2 factors into 3x and x

-1 factors into -1 and 1

We want a postive 2x

(3x-1) (x+1)

Answer:

(3x-1)(x+1)

Step-by-step explanation:

3x² + 2x − 1

when factorizing , first look at the constant number( in this case it is 1 prime number), then find the GCF if found.

(3x        )(x      )     first step : 3x*x=3x^2

(3x-      ) (x+   )      the sign for the constant is minus so the factoring has to be minus and plus on each side

(3x-1)(x+1)   look at the 2x it has positive sign, means the sign is plus:

3x-1

x+1

                        regular standard multiplication

3x(x)-1(x)+1(3x)-1

3x²+2x-1

Answer:

21

Step-by-step explanation:

4[tex]\frac{1}{5}[/tex] = [tex]\frac{21}{5}[/tex]

5 × [tex]\frac{21}{5}[/tex] = (5×21)/5

[tex]\frac{105}{5}[/tex] = 21