Write the ratio as a fraction in simplest form.
6 out of 9

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]

Answer:

x-intercept = (-1,0)

y-intercept = (0,-3)

Explanation:

x-intercepts are points where the line crosses the x-axis.

y-intercepts are points where the line crosses the y-axis.

Answer:

D

Step-by-step explanation:

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.

The conversion factor used to convert kilometer per hour to meter per hour is [tex]1 \text{ meter } = \frac{1}{1000} kilometer[/tex]

Solution:

Given that average person's speed when riding a bike along a street is 18 kilometers per hour

To find: conversion factor used to convert the given speed to meters per hour

Given average speed = 18 km per hour

From the conversion parameters:

1 km = 1000 meters

or

[tex]1 \text{ meter } = \frac{1}{1000} kilometer[/tex]

So, we can use the above conversion factor to convert average speed into meters per hour

18 km per hour = 18000 meter per hour

So the conversion factor used to convert kilometer per hour to meter per hour is [tex]1 \text{ meter } = \frac{1}{1000} kilometer[/tex]

Thus option C is correct. 1000 meters for 1 kilometers

Answer:

its c

Step-by-step explanation:

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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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

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:

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

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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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:

B,C, and E

Step-by-step explanation:

A histogram is a graphical illustration of information in bars of diverse heights. A histogram displays the shape and spread of continuous sample data. The true statements about the data essay scores for high school sophomores and juniors in a contest are; the juniors tended to have higher essay scores than the sophomores, the medians of both data sets are equal and the histogram is the best way to show that both distributions are nearly symmetric.

Answer:

bce

Step-by-step explanation:

Answer:

x = 13.7

Step-by-step explanation:

This is a right triangle so we use the trig ratios. We need an angle of reference (not the right angle) and any side (which is given, hypotenuse = 47).

We can either find the angle at the top or the right to be the angle of reference, Θ (theta).

Angle at the top:

The two angles, 17° and the unknown interior angle add to 90° because they are complementary.

∠Θ = 90° - 17° = 73°

Now use the trig ratio cosine.

cosΘ = adjacent ÷ hypotenuse

cos(73°) = x / 47

x = 47cos(73°)

x = 13.74147.....    Round down the exact answer to nearest tenth

x ≈ 13.7                Answer

The value of x is the same as the side adjacent to the angle of reference I chose.

If I chose the other missing angle to be the angle of reference, I would use sine and x would be opposite.

Answer:

-4,5

Step-by-step explanation:

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)

Answer:

Monday: 70

Tuesday: 64

Wednesday: 50

Thursday: 55

Friday: 76

Step-by-step explanation:

Equations

Let's call x to the number of sandwiches ordered for Thursday's meeting. We know that for Wednesday’s, we'll need x-5 sandwiches, for Monday's, we'll need 20 more, i.e. (x-5+20)=x+15 sandwiches. For Tuesday's it will be 6 fewer than x+15, or x+9. Finally, for Friday's, it will be 12 more than x+9 or x+21. Summarizing:

Monday: x+15

Tuesday: x+9

Wednesday: x-5

Thursday: x

Friday: x+21

The fewest of them all is x-5 and is must be equal to 50

[tex]x-5=50[/tex]

[tex]x=55[/tex]

The number of sandwiches per day is

Monday: x+15=70

Tuesday: x+9=64

Wednesday: x-5=50

Thursday: x=55

Friday: x+21=76

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:

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:

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:

They are supplementary

Step-by-step explanation:

Two Angles are Supplementary when they add up to 180 degrees.

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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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: (x + 1 )(x+5)

Step-by-step explanation:

Given :

[tex]x^{2}[/tex] + 6x + 5

Compare with the general quadratic equation:

a[tex]x^{2}[/tex] + bx + c

To factorize , you are  to find two numbers that multiply to give ac , and add to give b.

After which you will re - write the middle number with those numbers.

From the given question , ac = 5[tex]x^{2}[/tex] , we are to find two numbers that will multiply to give 5[tex]x^{2}[/tex] and add to give 6x.

The numbers are 1x and 5x.

We will then replace the middle number by the two numbers , that is

[tex]x^{2}[/tex] + x + 5x + 5

x(x+1) +5( x +1)

(x+1)(x+5)

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.

The largest possible height of the plant is 1 inch, the smallest possible height is 0 inches, and the largest possible percent error in Jada's measurement is -25%.

To find the largest possible height of the plant, we need to round up the measurement of 3/4 inch to the nearest whole inch. In this case, that would be 1 inch. Therefore, the largest the actual height of the plant could be is 1 inch.

To find the smallest possible height of the plant, we need to round down the measurement of 3/4 inch to the nearest whole inch. In this case, that would be 0 inches. Therefore, the smallest the actual height of the plant could be is 0 inches.

The percent error in Jada's measurement can be found by calculating the difference between the approximate measurement and the actual measurement, dividing it by the actual measurement, and then multiplying by 100. In this case, the approximate measurement is 3/4 inch and the actual measurement could be between 0 and 1 inch. So, the largest possible percent error would be (3/4 - 1) / 1 * 100 = -25%, and the smallest possible percent error would be (3/4 - 0) / 1 * 100 = 75%.

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Answer:

27

Step-by-step explanation:

Answer:

72 cubes

Step-by-step explanation:

Attached is the picture drawn (though not great one), showing 6 cube on length of prism, 3 cubes on width and 4 cubes on height of prism.

Given: Length of prism= 6

           Width= 3

            Height= 4

To know the number of cubes, which can fill the entire prism, we need to find volume of prism.

∴ Volume of prism= [tex]length\times width\times height[/tex]

Volume of prism= [tex]6\times 3\times 4= 72[/tex]

∴ 72 units of cube can fill the entire prism.

Answer:

slope of parallel line and perpendicular line are 5 and -1/5 espectively

equation of parallel and perpendicular line are y = 5x + 22 [tex]y= \frac{-1}{5} x+\frac{6}{5}[/tex] respectively

Step-by-step explanation:

y = 5x - 4 is in the form

y = mx + c

where m is the slope of the line and c is the y intercept of thr line

therefore slope of the line = 5 and y intercept = -4

when an another line is parallel to the given line then the slope of both the lines are equal

therefore the slope the parallel line = 5

equation of a line passing through a given point [tex](x_{1} ,y_{1})[/tex] with slope m is given by [tex]y-y_{1} = m(x-x_{1} )[/tex]

given [tex](x_{1} ,y_{1})[/tex]= (-4,2)

therefore equation of line y-2 = 5(x+4)

therefore y = 2+ 5x+20

y = 5x + 22is the eqaution of required line.

when two lines are perpendiculer then

[tex]m_{1} m_{2}=-1[/tex]

where [tex]m_{1} and m_{2}[/tex] are slope of the lines therefore

m×5=-1

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

therefore eqaution of line passing through (-4,2) and with slope m= [tex]\frac{-1}{5}[/tex] is given by [tex]y - 2= \frac{-1}{5} (x+4)[/tex]

[tex]y= \frac{-1}{5} x+\frac{6}{5}[/tex]

We can see here that the line perpendicular to the given line, passing through (-4, 2), is (0, -6).

Let's first verify the given information and then find the point on the line perpendicular to the given line passing through (-4, 2).

Given line: y = 0.5x - 4

Slope of a line parallel to the given line:

The slope of the given line is 0.5. Parallel lines have the same slope. Therefore, the slope of a line parallel to the given line is also 0.5.

A point on the line parallel to the given line, passing through (-4, 2):

Since the slope of the parallel line is 0.5, and we know a point (-4, 2) that lies on it, we can find the equation of the parallel line using the point-slope form of a line.

Point-slope form: y - y1 = m(x - x1), where (x1, y1) is the given point, and m is the slope.

Substitute the values: y - 2 = 0.5(x + 4)

Now, let's find a point on the line perpendicular to the given line, passing through (-4, 2):

Slope of a line perpendicular to the given line:

Perpendicular lines have slopes that are negative reciprocals of each other. The slope of the given line is 0.5, so the slope of the line perpendicular to it is -1/0.5 = -2.

A point on the line perpendicular to the given line, passing through (-4, 2):

Using the point-slope form again, we can find the equation of the perpendicular line passing through (-4, 2).

Point-slope form: y - y1 = m(x - x1), where (x1, y1) is the given point, and m is the slope.

Substitute the values: y - 2 = -2(x + 4)

Now, we can find another point on the perpendicular line by setting x = 0:

y - 2 = -2(0 + 4)

y - 2 = -8

y = -6

So, another point on the line perpendicular to the given line, passing through (-4, 2), is (0, -6).

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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

Ok, so 27 is >, 30 is <, 13/5 is 2 3/5, 5 2/7 is 37/7, 9 3/4 is 39/4, and 23/3 is      7 2/3

I did not do #27 and #30, just did the table.