The first three steps in determining the solution set of the system of equations, y = x2 - 2x + 8 and y = 2x + 11, algebraically
are shown in the table.
Step
Step 1
Step 2
Step 3
Equation
-X° -2x+8 - 2x+11
0 - x² + 4x+3
0-(x + 1)(x+3)
Which represents the solution(s) of this system of equations?
(-3,-1)
(-3,5)
(-3,5) and (-1,9)
(1, 13) and (3, 20)

Answer: 200.96 yd²

Step-by-step explanation: To find the area of a circle, start with the formula for the area of a circle.

[tex]Area = \pi r^{2}[/tex]

Notice that here, we're given the diameter instead of the radius. Remember that the radius is equal to half of the diameter so the radius of this circle will be equal to half of 16 yards or 8 yards.

So plugging into the formula, we have (π)(8 yd)².

A common mistake is to plug 16 yards into the formula but remember that we must plug in the radius and not the diameter.

Multiplying, (8 yd)² is equal to 8 yards × 8 yards or 64 yards².

So we have 64π yd².

So the area of the circle is 64π yd².

Now, remember that the irrational number π is approximately equal to 22/7 or 3.14 so we can estimate the area of the circle by plugging in 3.14 for π.

So we have (64)(3.14) which is equal to 200.96.

So the area of the circle is approximately equal to 200.96 yd².

Final answer:

The area of a circle with a diameter of 16 yards is 200.96 square yards, calculated using the formula A = πr², with π approximated as 3.14.

Explanation:

To calculate the area of a circle with a diameter of 16 yards, we first determine its radius, which is half the diameter. The radius (r) would therefore be 8 yards. We use the formula for the area of a circle, which is A = πr². Since we're using 3.14 for π, we plug in the radius to get the area:

A = 3.14 × (8 yd)²

A = 3.14 × 64 yd²

A = 200.96 yd²

Therefore, the area of the circle is 200.96 square yards.

Answer:

Infinitely many solution.

Step-by-step explanation:

The given system is

x = y + 4

y = x - 4

To graph the first equation, we write it in slope-intercept form to get: to

x=y+4

This implies y=x-4.

This has a slope of 1 and a y-intercept of -4.

The graph of this function is shown in the attachment.

The second equation is y=x-4.

This equation is identical to first equation, so its graph coincides with the first one.

The system has infinitely many solution.

The system of equations has infinitely many solutions.

The system of equations:

1. [tex]\( x = y + 4 \)[/tex]

2. [tex]\( y = x - 4 \)[/tex]

can be rearranged to show that they represent the same line:

1. [tex]\( y = x - 4 \)[/tex] (Rearranged from [tex]\( x = y + 4 \)[/tex])

2. [tex]\( y = x - 4 \)[/tex]

Graphing these equations shows that they are the same line, meaning every point on the line [tex]\( y = x - 4 \)[/tex] is a solution to the system.

Thus, the solution to the system of equations is all points [tex]\((x, y)\)[/tex] that satisfy [tex]\( y = x - 4 \)[/tex]. This means the lines intersect everywhere along [tex]\( y = x - 4 \)[/tex].

There is no single intersection point because they overlap completely.

Find the average rate of change of f(x) = 3(2)^x between x = 1 and x = 4

The average rate of change is 14

The rate of change is given by formula:

[tex]\text { Average Rate }=\frac{f(b)-f(a)}{b-a}[/tex]

Here the given interval is x = 1 and x = 4

Therefore, the formula becomes,

[tex]\text { Average Rate }=\frac{f(4)-f(1)}{4-1}\\\\\text { Average Rate }=\frac{f(4)-f(1)}{3}[/tex]

Let us find f(4) and f(1)

Given function is:

[tex]f(x)=3(2)^x[/tex]

Substitute x = 4 in function

[tex]f(4)=3(2)^4\\\\f(4) = 3 \times 16 = 48[/tex]

Thus f(4) = 48

Substitute x = 1 in function

[tex]f(1) = 3(2)^1\\\\f(1) = 6[/tex]

Now substitute the values back into formula

[tex]\text { Average Rate }=\frac{f(4)-f(1)}{3}\\\\\text { Average Rate }= \frac{48-6}{3}\\\\\text { Average Rate }= 14[/tex]

Thus average rate of change is 14

Answer: Yes

Step-by-step explanation:

id strongly prefer using the app? website desmos. it will help a lot.

To determine whether a triangle with given side lengths is a right triangle, we can use the Pythagorean theorem. If the sum of the squares of the two shorter sides equals the square of the longest side, then the triangle is a right triangle.

To determine whether a triangle with given side lengths is a right triangle, we can use the Pythagorean theorem. According to the theorem, if the sum of the squares of the two shorter sides equals the square of the longest side (hypotenuse), then the triangle is a right triangle.

Answer:

Width = 4 cm

Length = 16 cm

Step-by-step explanation:

We are given;

We are required to determine the dimensions of the rectangle;

In this case;

2 ( 2x + 8 + x) = 40

2 ( 3x + 8 ) = 40

6x + 16 = 40

6x = 24

 x  = 4

Thus; the dimensions of the rectangle are;

Width = 4 cm, and

Length = 16 cm

Answer:

$14

Step-by-step explanation:

given

Sharif : Jose ---> 2:7

this means that:

Fraction of total that Sharif gets = 2 / (2+7) = 2/9

Fraction of total that Jose gets = 7 / (2+7) = 7/9

we are given that Jose gets $49, hence

jose's fraction = 7/9 ,  represents $49

i.e

7/9 -----> $49

1/9 -----> $49 ÷ 7 = $7

Sharif's fraction = 2/9 -----> $7 x 2 = $14

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}y-6x=-3\\4y-24x=-16\end{array}\right\\\\\text{Divide both sides of the second equation by 4}\\\\\dfrac{4y}{4}-\dfrac{24x}{4}=\dfrac{-16}{4}\\\\y-6x=-4\\\\\text{We have received equations in which the left sides}\\\text{are the same and the right sides are different.}\\\\\bold{CONCLUSION}\\\\\text{The system of equations has no solution.}[/tex]

[tex]\left\{\begin{array}{ccc}a_1x+b_1y=c_1\\a_2x+b_2x=c_2\end{array}\right\\\\\text{If}\ a_1=a_2,\ b_2=b_2,\ c_1=c_2,\ \text{then the system of equations}\\\text{ has infinitely many solutions}\\\\\text{If}\ a_1=a_2,\ b_1=b_2,\ c_1\neq c_2,\ \text{then the system of equations}\\\text{has no solutions}\\\\\text{Other the system of equations has one solution.}[/tex]

Answer:

I guess the answer is 168yx.

Answer:

x^6 y^3 8x^6 y^5

Answer:

Step-by-step explanation:

50 + 12.50h = 143.75....where h = # of hrs

12.50h = 143.75 - 50

12.50h = 93.75

h = 93.75 / 12.50

h = 7.5 (or 7 1/2) hrs <====

Answer:

3 ounces of medication to be added to get 20%solution of medication

Step-by-step explanation:

To find:

The amount of medication to be added to 12 ounces of water to get a 20% solution

Let the amount of medication to be added =x

So total amount of mixture = amount of water + amount of medication

= 12+x

% medication =  (amount of medication÷total amount of the mixture)× 100

Therefore

% medication =(  x÷12+x)×100

20 =(  x÷12+x)×100

[tex]20 =\frac{x}{12+x}[/tex] X 100

20(12+x) =100x

240+20x =100x

100x-20x =240

80x =240

x =240÷80

x=3

so 3 ounces of medication to be added to get 20%solution of medication

Answer: d = v/26

Step-by-step explanation:

Answer: Its pretty basic

Step-by-step explanation:

Compare 4 centimeters to 300 centimeters.

Answer:

Hence the correct option is the fourth option.

Step-by-step explanation:

i) the data represented in the 10's is given by 16

ii) the data represented in the 20's is given by 22, 22, 25, 26

iii) the data represented in the 30's is given by 34, 35, 39

iv) the data represented in the 40's is given by 42, 42

v) the data represented in the 50's is given by 50

vi ) the data represented in the 60's is none

vii) the data represented in the 70's is given by 71

Therefore the data set is 16, 22, 22, 25, 26, 34, 35, 39, 42, 42, 50, 71 which is the answer in the fourth option.

Hence the correct option is the fourth option.

To find the total cost for Don's class trip, including the bus rental and theater tickets, the cost and number of tickets are required. Currently, with only the bus rental cost known at $168, we can't calculate the final total cost.

To solve the problem of determining the total cost of the bus rental and theater tickets for Don's class, we first identify the information given and what is required. We know the cost of the bus rental, which is $168. However, the question does not specify the cost of theater tickets. Therefore, to get the total cost, we would need the number of theater tickets needed and the price per ticket. Once these details are provided, the total cost can be calculated using the formula:

Total Cost = Cost of Bus Rental + (Number of Theater Tickets × Cost per Theater Ticket)

Without the cost and quantity of theater tickets, we can only provide the initial part of the answer, which is the cost of the bus rental.

Answer:

A) The teacher brought 384 fluid ounces of juice

B)NO, the teacher doesn't have enough juice to give each student a 12-fluid ounce glass of juice

Step-by-step explanation:

Given:

The total quantity of juice brought by the teacher for the field trip = 3 gallons of juice

The number of students in the field trip =  36

A)fluid ounces of juice

We know that

1 gallon  = 128 fluid ounce

So we have to convert the given 3 gallons of juice to fluid ounces

3 gallons of fruit juice [tex]= 3 \times 128[/tex] fluid ounces

3 gallons of fruit juice  =  384 fluid ounces

The teacher had 384 fluid ounces of fruit juice

B. enough juice to give each student a 12-fluid ounce glass of juice

The teacher wants to give 12 fluid ounce of juice to one student

So, to give 36 students

the teacher will need

=> [tex]36 \times 12[/tex]

=> 432 fluid ounces of juice

but the teacher has only 384 fluid ounces of juice .

Thus the teacher still  needs 48 fluid ounces of juice  

Answer:

RATIONAL

Step-by-step explanation:

Irrational Numbers. All numbers that are not rational are considered irrational. An irrational number can be written as a decimal, but not as a fraction. An irrational number has endless non-repeating digits to the right of the decimal point

Answer:

irrational

Step-by-step explanation:

Investments worth $4487.19 in total at the end of 3 years.

Solution:

Principal, P = 2000

Rate, R = 4% compounded quarterly

Rate, R = 3.75% compounded annually

Year, n = 3

Formula for compound interest when compounded quarterly:

[tex]Amount=P(1+\frac{\frac{R}{4} }{100})^{4n}[/tex]

Substitute P = 2000, R = 4% and n = 3

[tex]Amount=2000\times(1+\frac{\frac{4}{4}}{100})^{4\times3}[/tex]

              [tex]=2000\times(1+\frac{1}{100})^{12}[/tex]

              [tex]=2000\times(\frac{100+1}{100})^{12}[/tex]

              [tex]=2000\times(\frac{101}{100})^{12}[/tex]

              = 2253.65

Amount when compound interest calculated quarterly is 2253.65.

Formula for compound interest when compounded annually:

[tex]Amount=P(1+\frac{R}{100})^{n}[/tex]

Substitute P = 2000, R = 3.75% and n = 3

[tex]Amount=2000\times(1+\frac{3.75}{100})^{3}[/tex]

              [tex]=2000\times(\frac{100+3.75}{100})^{3}[/tex]

              [tex]=2000\times(\frac{103.75}{100})^{3}[/tex]

              = 2233.54

Amount when compound interest calculated annually is 2233.54.

Total amount = 2253.65 + 2233.54

                      = 4487.19

Hence, investments worth $4487.19 in total at the end of 3 years.

Answer:

Step-by-step explanation:

∠ABC = ∠BCD    { AB // CD; BC TRAVERSAL, alternate angles are equal}

∠ABC = 20

∠BCA = ∠BAC     {angles opposite to equal sides are equal}

∠BCA = ∠BAC = x

x + x + 20 = 180

2x = 180 - 20

2x = 160

x = 160/2

x = 80

The lines AB and CD are said to be parallel and thus, corresponding angles ∠CB and ∠BD, are equal in value. Hence the value of x is calculated by subtracting the value of known angle ∠BCD (20°) from the total sum of interior angles of a straight line (180°), obtaining a result of 160°.

In this given geometry problem, the lines AB and CD are parallel to each other and BC∠BCD = 20°. Since AB is parallel to CD, then the angles ∠CB and ∠BD, being corresponding angles, are equal. Hence, ∠CB also equals 20°.

Now, since ∠BCD and ∠CB make a straight line, the sum of their interior angles is equal to 180°. So, if we subtract the known 20° from 180°, we can find the value of unknown angle ∠BCD. Hence, x = 180° - 20° = 160°.

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Answer:

Ten amounts:

$ 13,979 $1,000 $100 $2 $10 $300 $4 $5 $200 $500

Step-by-step explanation:

Choose any numbers you want for the first 9 cash amounts. Then, find out the difference between the 9 cash amounts and 16,100. That will be the tenth amount.

Example:

I choose $1,000 $100 $2 $10 $300 $4 $5 $200 $500.

If I add them together, I get $2,121.

Remember that was 9 amounts, and we need 10.

To get the last amount, subtract what you have ($2,121) from what you need ($16,100).

16,100 - 2,121 = $13,979

The last amount will be $13,979.

Check your answer:

Add all of the ten amounts to get 16,100.

1,000 + 100 + 2 + 10 + 300 + 4 + 5 + 200 + 500 + 13,979

= 16,100

Therefore this answer is correct.

Answer:

no solution

Step-by-step explanation:

if you graph both equation the lines are parallel.

parallel = no solution

overlap = infinite solution

intersect = one solution

Answer:

13.3

Step-by-step explanation:

Because in order to get the a separated from the 0.9, you must divide the 0.9a by 0.9 to cancel the 0.9 out of the equation. That way, you are left with A. but in order to do that, you must divide both sides of the equation.

Ultimately, it ends up being 12 divided by 0.9, which is 13.3

Answer:

Number of favourable outcomes i.e. ‘a card of diamond’ is 13 out of 52 cards. Therefore, probability of getting ‘a card of diamond’ Number of favorable outcomes P(D) = Total number of possible outcome = 13/52 = 1/4 (v) a king or a queen. Total number of king is 4 out of 52 cards. Total number of queen is 4 out of 52 cards

Step-by-step explanation:

Answer:

4/13

Step-by-step explanation:

16/52 = 4/13

Answer:

The equation of line will be [tex]y=x+2.75[/tex]

Step-by-step explanation:

Given admission and [tex]6[/tex] sample costs $[tex]8.75[/tex]

And admission and [tex]9[/tex] samples costs $[tex]11.75[/tex]

Let cost of the sample is [tex]y[/tex] and number of sample is [tex]x[/tex]

Now, we will find the slope of line

[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{11.75-8.75}{9-6}\\\\m=\frac{3}{3}\\\\m=1[/tex]

Plug slope as [tex]1[/tex] and point [tex](6,8.75)[/tex] in the equation we get,

[tex](y-y_1)=m(x-x_1)\\y-8.75=1(x-6)\\y-8.75=x-6\\y=x-6+8.75\\y=x+2.75[/tex]

The equation of line will be [tex]y=x+2.75[/tex]

Answer:

The manual cost that will take to recreate by the firm is $ 90.51

Step-by-step explanation:

Given:

Number of words the manual contains= 16000

Number of words typed by a clerk in one hour and 20 minutes = 4160

To Find:

The total cost for recreating the manual = ?

Solution:

Step 1:  Finding the Number of hours is need to type 4160 words :

= [tex]1\frac{20}{60}[/tex] hours

[tex]\\\\=1\frac{1}{3}[/tex] hours

[tex]\\\\=\frac{4}{3}[/tex] hours

So it takes  [tex]\frac{4}{3}[/tex] hours to type 4160 word

Step 2 :  Finding the Number of hours is needed to type 1 word  

= [tex]\frac{4160}{\frac{4}{3}}[/tex]

=[tex]4160 \times \frac{3}{4}[/tex]

= 3120 words per hour

Step 3 :  Finding the Number of hours is needed to type 16000 words

=[tex]\frac{\text{ total number of words}} {\text{ number of words written per hour}}[/tex]

Substituting the values

= [tex]\frac{16000}{3120}[/tex]

=  5.1282 hours

Step 4 :  Finding the cost for recreating the manual.

= number of hours  x cost per hour

=   5.1282 x $17.65

=  90.51

Recreating the manual will cost the firm approximately $90.59.

To determine the cost of recreating the manual, we need to calculate both the time it will take for the clerk to type the entire manual and the total cost based on the clerk's wage.

First, we calculate the time required to type the manual. The clerk types 4,160 words in 1 hour and 20 minutes. To find out how many minutes that is, we convert 1 hour to minutes:

1 hour = 60 minutes

Therefore, 1 hour and 20 minutes is:

60 minutes + 20 minutes = 80 minutes

Now, we need to find out how many 80-minute blocks are required to type 16,000 words. We set up a proportion:

4,160 words / 80 minutes = 16,000 words / x minutes

Solving for x gives us:

x = (16,000 words x 80 minutes) / 4,160 words

x = (16 x 80) / 4.16

x = 1,280 / 4.16

x ≈ 308 minutes

Next, we convert the total time from minutes to hours since the clerk is paid by the hour:

308 minutes / 60 minutes per hour ≈ 5.13 hours

Now, we calculate the total cost by multiplying the total hours by the clerk's hourly wage, including benefits:

Total cost = 5.13 hours x $17.65/hour

Total cost ≈ $90.59

Therefore, recreating the manual will cost the firm approximately $90.59.

Answer:

15.1

Step-by-step explanation:

Answer:

15.1

Step-by-step explanation:

Since the digit in hundredths place is greater than 5, hence after removing the digit 6 we will add 1 in the tenth place. So the answer will become 15.1

Answer:

268.0 in²

Step-by-step explanation:

refer to attached graphic as reference

volume of cone, V = (1/3) πr²h

in our case, we are given r = 4" and h = 16"

substituting this into equation:

V = (1/3) πr²h

=  (1/3) ·(3.14) · (4)²· (16)

= 267.94667 in²

= 268.0 in² (nearest tenth)

The volume of the paper cone to the nearest tenth = 268.0 in².

Volume of cone, V = (1/3) πr²h

Where, h= height of the cone

r = radius of the cone

V= volume of the cone

In our case, we are given r = 4" and h = 16"

substituting this into the equation:

V = (1/3) πr²h

Substitute into the formula we have

The value of π = 3.14

V =  (1/3) ·(3.14) · (4)²· (16)

= 267.94667 in²

= 268.0 in² (nearest tenth)

Therefore, the volume of the cone = 268.0 in² (nearest tenth)

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Answer:

I will answer any question you ask me! You can call me by my nickname- Dark. If you have any questions, just ask me!

Step-by-step explanation:

Answer: At your service. I don't troll. I think it's pointless to troll because people on brainly are here for HELP not for Jokes.

Answer:

Step-by-step explanation:

y - y1 = m(x - x1)

slope(m) = -1

(-1,5)....x1 = -1 and y1 = 5

now we sub

y - 5 = -1(x - (-1)...not done yet...we can simplify this

y - 5 = -1(x + 1) <===

The solution is y = -x + 4

The equation of the line is y = -x + 4 and the slope of the line is m = -1

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

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

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the point be represented as P = P ( -1 , 5 )

Now , the slope of the line is

Slope m = -1

The equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 5 = -1 ( x - ( -1 ) )

On simplifying the equation , we get

y - 5 = -1 ( x + 1 )

y - 5 = -x - 1

Adding 5 on both sides of the equation , we get

y = -x + 4

Therefore , the value of A is y = -x + 4

Hence , the equation of line is y = -x + 4

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