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Is the system of equations consistent and independent, consistent and dependent, or inconsistent?

y=−x−13y=−3x+2

Select the correct answer from the drop-down menu.

Answer:

27

Step-by-step explanation:

The question is incomplete, here is the complete question:

You and your friend are selling magazine subscriptions. You sell 8 fewer magazine subscriptions than your friend. Together you sell 42 magazine subscriptions. Write a system of linear equations that represents this situation.

The system of linear equations that represents this situation is:

x + y = 42

x - y = 8

Step-by-step explanation:

To solve the problem assume that

∵ Your friend sells x magazine subscriptions

∵ You sell y magazine subscriptions

∵ Together you sell 42 magazine subscriptions

∴ x + y = 42 ⇒ (1)

∵ You sell 8 fewer magazine subscriptions than your friend

∵ Your friend sells x magazine subscriptions

∵ You sell y magazine subscriptions

- That means y = x - 8

∴ y = x - 8

- Add 8 for both sides

∴ 8 + y = x

- Subtract y from both sides

∴ 8 = x - y

- Switch the two sides

∴ x - y = 8 ⇒ (2)

The system of linear equations that represents this situation is:

x + y = 42

x - y = 8

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To find the total number of cookies burnt in the day, which is the whole, we would use the formula 'whole = part / percentage', or 'whole = 439 / 0.25', which gives us 1756 cookies.

The subject of this question is Mathematics, specifically it's a problem on percent. The problem states that 439 cookies represented 25% of all the cookies the employee burnt that day. The question asks us to find the total number of cookies burnt by using this information.

When trying to find the whole from a percent, you can use the formula: whole = part / percentage. In this case, 'part' refers to the 439 cookies, and 'percentage' is 25% expressed as a decimal (0.25).

Using the formula, we find that the total (whole) number of cookies burnt is: whole = 439 / 0.25 = 1756 cookies. So, the new employee burnt 1756 cookies in the course of the day.

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Answer:

4 : 25

Step-by-step explanation:

Given the ratio of sides = a : b, then

ratio of areas = a² : b²

Thus

ratio of sides = 2 : 5, then

ratio of areas = 2² : 5² = 4 : 25

The missing figure is attached below.

Answer:

The first image from left.

Step-by-step explanation:

Given:

Rotation of the quadrilateral PQRS by 90 degree counterclockwise around the origin.

We know that, for a 90 degree counterclockwise rotation, the transformation rule for the coordinates is given as:

[tex](x,y)\to (-y,x)[/tex]

So, the 'x' and 'y' interchange their values after rotation and the 'y' value sign is reversed.

Now, let us check each option.

Option 1:

Coordinates of the original quadrilateral are:

P(5, 2.5), Q(1, 4), R(2, 2.5), and S(1, 1)

Now, after rotation by 90 degree counterclockwise, the coordinates of the transformed figure will be:

[tex](x,y)\to (-y,x)[/tex]. So,

P(5, 2.5) → P'(-2.5, 5)

Q(1, 4) → Q'(-4, 1)

R(2, 2.5) → R'(-2.5, 2)

S(1, 1) → S'(-1, 1)

Now, if we check the coordinates of P', Q', R' and S' on the first option, we see that they are same as calculated above. So, the correct option is option 1.

Option 2:

Coordinates of P are (5, 2.5) and coordinates of P' are (2.5, -5) which doesn't match with the transformation rule. So, this option is incorrect.

Option 3:

Coordinates of P are (5, 2.5) and coordinates of P' are (-5, 2.5) which doesn't match with the transformation rule. So, this option is incorrect.

Answer:

Part 1) The system of equations is

[tex]C=8n+12[/tex] ----> equation 1

[tex]C=10n[/tex] ----> equation 2

Part 2) The graph in the attached figure

Part 3) The number of gym visits must be greater than 6

Step-by-step explanation:

step 1

Find the system of equations that represent the situation

Let

C ----> the total cost in dollars

n ---> the number of gym visits

we know that

The linear equation in slope intercept form is equal to

[tex]C=m(n)+b[/tex]

where

m is the slope or unit rate of the linear equation

b is the C-intercept or initial value of the linear equation

First payment option ---> For Members

we have that

The slope or unit rate is equal to [tex]m=\$8\ per\ gym\ visit[/tex]

The C-intercept or initial value is [tex]b=\$12[/tex] --->one-time registration fee

substitute

[tex]C=8n+12[/tex]

Second payment option ---> For Non-Members

we have that

The slope or unit rate is equal to [tex]m=\$10\ per\ gym\ visit[/tex]

The C-intercept or initial value is [tex]b=\$0[/tex]

substitute

[tex]C=10n[/tex]

we have

[tex]C=8n+12[/tex] ----> equation 1

[tex]C=10n[/tex] ----> equation 2

Part 2) Upload a graph

using a graphing tool

The graph in the attached figure  

Part 3) After how many gym visits is the payment for the member option more beneficial than the payment for the nonmember option?

we know that

If the payment for the member option is more beneficial than the payment for the nonmember option, then the cost for the member option is less than the cost for the nonmember option

so

The inequality that represent this situation is

[tex]8n+12 < 10n[/tex]

solve for n

subtract 8n both sides

[tex]12 < 10n-8n[/tex]

[tex]12 < 2n[/tex]

Divide by 2 both sides

[tex]6 < n[/tex]

Rewrite

[tex]n > 6[/tex]

therefore

The number of gym visits must be greater than 6

Answer:

Step-by-step explanation:

m∠1 = 50°

m∠2 = 88°

Step-by-step explanation:

Each triangle's angles have to add up to 180°. Use supplementary angles theorem to help solve.

Answer:

m∠1 = 50°

m∠2 = 88°

Step-by-step explanation:

Each triangle's angles have to add up to 180°. Use supplementary angles theorem to help solve.

Answer:

4 pictures

Step-by-step explanation:

(6/7)/(3/14)=x/1

cross product

3/14*x=6/7*1

3/14x=6/7

x=(6/7)/(3/14)

x=(6/7)(14/3)

x=(6/1)(2/3)

x=12/3

x=4

The number of pictures which Karli and her friend can paint in a full hour is equal to 4 pictures.

What is algebra ?

Algebra is a branch of mathematics that deals with various symbols and the arithmetic operations such as division , multiplication , etc.

It is given that Karli and her friend can paint 6/7 of a picture in 3/14 of an hour.

Let's assume they can paint x number of pictures in a full hour.

So , the fraction by dividing 6/7 by 3/14 can be written equal to x .

i.e.,

[tex]\frac{6/7}{3/14}[/tex] = x

We need to do the cross product here :

[tex]\frac{3}{14}[/tex] × x = [tex]\frac{6}{7}[/tex]

or

x = ([tex]\frac{6}{7}[/tex]) ÷ ([tex]\frac{3}{14}[/tex])

We know that when dividing two fractions we need to change the division sign to multiplication sign by inverse the fraction value right to the division sign i.e.,

x = ([tex]\frac{6}{7}[/tex]) × ([tex]\frac{14}{3}[/tex])

x = 84 / 21

x = 4

Therefore , the number of pictures which Karli and her friend can paint in a full hour is equal to 4 pictures.

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Answer:

Step-by-step explanation:

Price of a hotdog = $0.86

An equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”.

For example, 2x – 5 = 13.

Here,

2x – 5 and 13 are expressions.

The sign that connects these two expressions is “=”.

Given,

2 burgers and 1 hotdog cost = $4.82

1 burger and 2 hotdogs cost = $ 3.70

The price is same

Let the price of burger be x and price of hotdog be y

then,

2x + y = 4.82   ---------(a)

x + 2y = 3.70  

Multiplying 2 in above equation

2x + 4y = 7. 40  -----------(b)

Subtracting equation (a) from equation (b)

2x + 4y - (2x+y) = 7.40 - 4.82

2x + 4y -2x -y = 2.58

3y = 2.58

y = 2.58/3

y = 0.86

Price of hotdog = $0.86

Hence, a hotdog costs $0.86.

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To round the fraction 14/27 to the nearest one-half, the answer would be 0 (choice A).

To round the fraction to the nearest one-half, we need to determine if the fraction is closer to zero, one-half, or one. Start by identifying which two one-half intervals the fraction falls between: 13/27 (closer to zero) and 15/27 (closer to one-half). As 14/27 is closer to 13/27, the answer is A. 0.

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Answer:

On this case if we analyze both slopes, we see that function 2 has a greater rate of change because have a slope greater on absolute value than the slope for Function 1 (|-5|>|4|). No matter if the sign is positive or no we are analyzing the rate of change and for this case we need to use the absolute value to find the solution.

Step-by-step explanation:

Assuming the following two functions:

Function 1: y = 4x + 8

Function 2:  

x y

2 20

4 10

6 0

We can find the slope for the second function like this:

[tex]m =\frac{10-20}{4-2}=-5[/tex]

And in order to find the intercept we can use any point for example (2,20) and we got:

[tex]20 =-5(2) +b[/tex]

And then [tex] b=30[/tex]

So our function 2 is given by: [tex] y =-5x +30[/tex]

On this case if we analyze both slopes, we see that function 2 has a greater rate of change because have a slope greater on absolute value than the slope for Function 1 (|-5|>|4|). No matter if the sign is positive or no we are analyzing the rate of change and for this case we need to use the absolute value to find the solution.

Answer:

The maximum number of packages that can be made  with each package have same number of each item is = 6

Step-by-step explanation:

Given:

Mr. Harris has 48 pencils and 30 notebooks.

To find the number of packages he can make with each package have same number of each item.

Solution:

Number of pencils = 48

Number of notebooks = 30

In order to find the number of packages he can make with each package have same number of each item, we will find the greatest common factor of the given numbers.

To find the G.C.F., we will list down the prime factors of each.

[tex]48=2\times 2\times 2\times 2\times 3[/tex]

[tex]30=2\times 3\times 5[/tex]

We find that the G.C.F. = [tex]2\times 3[/tex] = 6

Thus, the maximum number of packages that can be made  with each package have same number of each item is = 6

Answer:

Mixed number equation equals to 10=[tex]9\frac{9}{9}[/tex]

Step-by-step explanation:

Here we have to find mixed number equation that equal 10,

Let, x=10 ------------(equation 1)

Now multiplying both side of equation 1 by 10 we get,

[tex]x\times 10=10\times 10[/tex]

[tex]10x=100[/tex] ------------------(equation 2)

Now by subtracting equation 1 from equation 2 we get,

[tex]10x-x=100-10[/tex]

[tex]9x=90[/tex]

[tex]\therefore\ x=\frac{90}{9}[/tex] ------------------(equation 3)

Equation 3 can be written as,

[tex]x=9\frac{9}{9}[/tex]

Since, [tex]9\frac{9}{9} [/tex]

[tex]= \frac{(9\times 9)+9}{9}[/tex]

[tex]=\frac{81+9}{9}[/tex]

[tex]=\frac{90}{9}[/tex][/tex]

[tex]\therefore 9\frac{9}{9}=\frac{90}{9}[/tex]

Therefore mixed number equation that equals 10=[tex]9\frac{9}{9}[/tex]

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slopw and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (3, 2) and (x₂, y₂ ) = (5, - 1)

m = [tex]\frac{-1-2}{5-3}[/tex] = - [tex]\frac{3}{2}[/tex], thus

y = - [tex]\frac{3}{2}[/tex] x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (3, 2), then

2 = - [tex]\frac{9}{2}[/tex] + c ⇒ c = 2 + [tex]\frac{9}{2}[/tex] = [tex]\frac{13}{2}[/tex]

y = - [tex]\frac{3}{2}[/tex] x + [tex]\frac{13}{2}[/tex] ← equation of line

Answer:

The equation of the line passing through the given points is

[tex]y=-\frac{3}{2}x+\frac{13}{2}[/tex]

Step-by-step explanation:

GIven two points are (3,2) and (5,-1)

To find the equation of the line passing through these two points

Let [tex](x_{1},y_{1})[/tex] and  [tex](x_{2},y_{2})[/tex] be the two points (3,2) and (5,-1) respectively

Using the two points formula for finding slope:

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]m=\frac{-1-2}{5-3}[/tex]

[tex]m=\frac{-3}{2}[/tex]

Therefore [tex]m=-\frac{3}{2}[/tex]

By using  formula:

[tex]y=mx+c[/tex]

Here Let (x,y) be (3,2)

[tex]y=mx+c[/tex]

[tex]2=-{\frac{3}{2}}\times 3+c[/tex]

[tex]2=\frac{-9}{2}+c[/tex]

[tex]c=\frac{9}{2}+2[/tex]

[tex]c=\frac{9+4}{2}[/tex]

[tex]c=\frac{13}{2}[/tex]

Therefore substitute values of m and c in

[tex]y=mx+c[/tex]

[tex]y=-\frac{3}{2}x+\frac{13}{2}[/tex]

Therefore the equation of the line passing through the given points is

[tex]y=-\frac{3}{2}x+\frac{13}{2}[/tex]

Pat will bounce the ball 125 times in 150 seconds

Solution:

Given that,

Pat bounces a basketball 25 times in 30 seconds

To find: Number of times Pat will bounce the ball in 150 seconds

From given information,

30 seconds = 25 times

Therefore number of times ball bounces in 1 second is:

[tex]\text{1 second } = \frac{25}{30} \text{ times }[/tex]

So to find for 150 seconds, multiply both the sides by 150

[tex]150 \text{ seconds } = \frac{25}{30} \times 150 = 125 \text{ times }[/tex]

Therefore Pat will bounce the ball 125 times in 150 seconds

Answer:

125

Step-by-step explanation:

Answer:

-4,5

Step-by-step explanation:

Answer:

2 sheets of plywood will be needed.

Step-by-step explanation:

See the attached diagram.

Each three square plywood has area 1 units by 3 units = 4 feet by 12 feet = 48 feet square.  {Since each unit on the coordinate plane represents four feet}

Now, the two triangular plywood has area half of a unit square area.

So, two triangular plywood has total area = 1 unit by 1 unit = 4 feet by 4 feet = 16 feet square.

Therefore, the total area of plywood required to make the triangular prism is (48 + 16) = 64 feet square.

Now, if a sheet of plywood measures 4 ft by 8 ft i.e. 32 feet square, then the carpenter will need [tex]\frac{64}{32} = 2[/tex] such sheets of plywood. (Answer)  

Answer:A

Step-by-step explanation: HI

Answer:

4π

Step-by-step explanation:

Period is whenever a wave repeats itself. I highlighted the period.

The Period of the given function is 0 to 4π.

The time interval between two waves is known as a Period whereas a function that repeats its values at regular intervals or periods is known as a Periodic Function.

Here, graph starts from 0 and goes down. After π our graph starts increasing and acheive maximum at 3π and then start coming down to y = 0 at 4π.

It means that from 0 to 4π graph complete its one cycle and in the same trend it start repeating again.

Thus, the Period of the given function is 0 to 4π.

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Answer:

an-1-9

25n-1-9

25n-10=0

25n=0+10

25n=10

divide both sides by 25

25n/25 =10/25

n=2/5

Step-by-step explanation:

Answer:

n=1.4

Step-by-step explanation:

given  a=25

a=an-1-9..............(1)

put a=25 in equ (1)

25=25n-1-9

25=25n-10

25n=25+10=35

n=[tex]\frac{35}{25}[/tex]=1.4

n=1.4   answer

Answer:

(a) The equation is [tex]7h-2=56[/tex].

(b) Trey gets approximately $8.29 for each hour of work.

Step-by-step explanation:

Given:

Number of hours Trey works = 7

Amount of money he put aside for mom = $2

Total Amount he keeps each day = $56

We need to find the amount he gets for each hour.

Let 'h'  represent the amount (in dollars) Trey gets paid each hour.

Solving for part (a).

We need to write the equation to find the amount he gets paid for each hour.

Now we can say that;

Total Amount he keeps each day is equal to Number of hours Trey works multiplied by the amount he gets paid for each hour minus Amount of money he put aside for mom.

framing in equation form we get;

[tex]7h-2=56[/tex]

Hence the equation is [tex]7h-2=56[/tex].

Solving for part (b).

we need to solve the above equation to find the amount he gets paid for each hour.

On solving the equation we get;

Adding both side by 2 we get

[tex]7h-2+2=56+2\\\\7h=58[/tex]

Now Dividing both side by 7 using Division Property we get;

[tex]\frac{7h}{7} = \frac{58}{7}\\\\h \approx \$8.29[/tex]

Hence Trey gets approximately $8.29 for each hour of work.

Hudson: T = 200n + 2500

Kennedy: T = 250n + 2000

im no math teacher but i do a ton of questions like these, hope this helps

The equation for Mike job which represents the relationship between T and n for Hudson cars is $2500+$200n and for Kennedy used cars is $2000+$250n.

A linear equation is the equation in which the highest power of the unknown variable is one.

Mike wants a job as car salesmen. He receives two job offers.Let T represent the total monthly earning, in dollars, and let n represent the number of cars sold in a month.

Hudson's cars dealership offers Mike a salary of $2500 per month, plus a commission of $200 on every car he sells. Then the equation for this company is,

[tex]T=2500+200n[/tex]

Kennedy used cars dealership offers Mike a salary of $2000 per month, plus a commission of $250 on every car he sells. Thus, he equation for this company is,

[tex]T=2000+250n[/tex]

Hence, the equation for Mike job which represents the relationship between T and n for Hudson cars is $2500+$200n and for Kennedy used cars is $2000+$250n.

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14 bags of fertilizer are needed

Solution:

Given that You need to buy fertilizer for a circular flower bed with a diameter

of 13 feet

Diameter = 13 feet

[tex]radius = \frac{diameter}{2}[/tex]

[tex]radius = \frac{13}{2} = 6.5[/tex]

Therefore radius of circular flower bed is 6.5 feet

Area of circle is given as:

[tex]\text{ area of circle } = \pi r^2[/tex]

Substitute r = 6.5

[tex]\text{ area of circle } = 3.14 \times 6.5^2 = 132.665[/tex]

Given that one bag will fertilize 10 square feet

1 bag = 10 square feet

Then number of bags needed are:

[tex]\rightarrow \frac{132.665}{10} = 13.2665[/tex]

Thus approximately 14 bags of fertilizer are needed

Answer:

change to improper fractions first

6/8 + 6/24

make so there is a common denominator

6/8 × 3/3 = 18/24

now add

18/24 + 6/24 = 24/24 = 1

The inequality l + c ≥ 14 accurately represents the minimum total hours Jackson must work in both his jobs, landscaping and clearing tables, in a week.

The subject of this question is Mathematics, more specifically it involves the topic of inequalities. The grade level of this question would be high school as it deals with algebraic concepts.

The inequality that represents the number of hours that Jackson can work in a given week in landscaping (l) and clearing tables (c) would be l + c ≥ 14. This inequality allows for the total number of hours worked to be equal to or more than 14, as stipulated in the conditions.

This represents the total amount of hours Jackson can work in both jobs simultaneously. This inequality is valid as long as he works at least 14 hours, in total, from both jobs.

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Answer:

B On 2020 edge

Step-by-step explanation:

Answer:

1. New York City: The initial charge is $ 2.50 plus $ 0.50 per 1/5 mile when traveling above 12 mph or per 60 seconds in slow traffic or when the vehicle is stopped. There are other surcharges for overnight, rush hour or congestion.

2. Boston: First 1/7 Mile: $2.60  and each 1/7 Mile thereafter: $0.40.

3. Houston: First 1/11 mile  $2.80 , each additional 1/11 mile  $0.20 . Rate per mile after first mile  $2.20 and wait time per minute  $0.40.

Step-by-step explanation:

Normally, there's a standard fare for each city, so for answering the question we picked three well-known cities for comparing the fares.

1. New York City: The initial charge is $ 2.50 plus $ 0.50 per 1/5 mile when traveling above 12 mph or per 60 seconds in slow traffic or when the vehicle is stopped. There are other surcharges for overnight, rush hour or congestion.

2. Boston: First 1/7 Mile: $2.60  and each 1/7 Mile thereafter: $0.40.

3. Houston: First 1/11 mile  $2.80 , each additional 1/11 mile  $0.20 . Rate per mile after first mile  $2.20 and wait time per minute  $0.40.

Answer:

[tex]\displaystyle y = -4x[/tex]

Step-by-step explanation:

0 = 0 ± b

[tex]\displaystyle 0 = b \\ \\ y = -4x[/tex]

* Parallel Lines have SIMILAR RATE OF CHANGES [SLOPES], so −4 remains the way it is.

I am joyous to assist you anytime.

Heyo! ;D

The equation in slope-intercept form that represents a line that is parallel to y = -4x - 5 and passes through the point (0,0) would be Option C) y = -4x.

Hope this helps! If so, please lmk! Tysm!

Answer: 6xv( v - 3 )

Step-by-step explanation:

6xv² - 18xv

Looking into the equation critically, we could see that 6xv is common to the expression.

Therefore, the expression now becomes

6xv( v - 3 ).

Answer:

D) the system has no solution.

Step-by-step explanation:

A student is solving a system of equations by substitution and comes up with the solution -3=2.

So, the unknown variables are canceled out and there are only numbers in the equation but -3 ≠ 2.

If we assume that she solved the problem correctly, then there will be no solution for that system of equations because there is no variable remaining in the final equation to solve for. (Answer)