The equation y = x + 1 defines the relationship between x and y, where x is the input and y is the output. Which statements about the graph of this relationship are true? Select two that apply.

A.The graph is a curved line.
B.The graph is a straight line.
C.the graph is a vertical line.
D.The graph represents a function.
E.The graph has no negative outputs.
F.The graph passes through the origin.

Answers

Answer 1

The graph is a straight line because y = x + 1 has a slope of 1 (and it's not changing so it can't be curved, neither is it ∞ so it can't be vertical). This graph does not pass through the origin because it has a + 1 at the end. It is a function because no input matches to 2 different outputs. It also has negative outputs because what if x was -50.

All in all, your answers are B and D.

Answer 2

Hey there!

Let's go through all of our options.

A) It's defintely not curved; it's written in slope intercept form and is indeed a straight line.

B) Yes, the graph is a straight line. Although it's at an angle, it has no curves or flaws, and is completely straight.

C) The graph is not vertical. It has a y intercept and slope and therefore isn't. That's because it has a rate of change, and it crosses the y axis at some point depending on the slope, or rise over run. Vertical lines really don't have that.

D) Yes, the graph is a function. This is because it does not have two x values for one y, and does not fail the straight line test, which states that you can place a straight line anywhere on the graph and it can only go through one point.

E) This is false. If we put in -5 as our input, we add 1 and get -4, which is a negative output. Your output here depends on the input you put in, and the sign usually remains considering it's +1.

F) This graph does not pass through the origin. This is because the origin has a point at 0,0 and since it's x+1, it would be 0,1 instead because your output is adding one to that 0.

Hope this helps!

Related Questions

William saw painting in a museum, and later found a picture of the same painting in a book. The actual painting measures 36“ x 54“. The picture of the paining measured 4“ x 6“. What is the scale factor for the dilation?

Answers

The scale factor is 1/9.

We compare the image to the actual painting:

4/36 = 1/9.

the ratio of 12:3 in simplest form

Answers

divide both sides by the common factor which is 3

12 /3 = 4 and 3/3 = 1

the final ratio is 4:1

The ratio 12:3 simplified is 4:1
Step 1: The LCM is 3
So divide 12 with 3 and you get 4
The divide 3 between 3 and you get 1
So your answer is 4:1
Hope this helps:D
Have a great rest of a brainy day!

Molly says that 4/8 is always the same as 1/2. Andrew says that 4/8 and 1/2 are equivalent fractions, but they could be different amounts. Use the models below to determine which student is correct. Explain.

Answers

They are equals, but, they can be used as a percentage for an amount. For example
1/2 kg = 500 g
1/2 ton = 500 kg

you are going to purchase a corvette for $60,00 the interest rate is 4% and you will be paying off the loan in 5 years. What will be your monthly payment?

Answers

Um I think you do 5 divide by 6000

what is the area in square centimeters of the trapezoid below the height is 6.4 and the base is 12.9 and 8.6

Answers

Hello!
----------
The area in square centimeters is 68.8.
----------
Have a great day!

Answer:

The area of given trapezoid is 68.8 cm²

Step-by-step explanation:

Given: A trapezoid with height 6.4 cm and parallel base is 12.9 cm and 8.6 cm.

We have to find the area of area of this trapezoid.

Area of trapezoid = [tex]\frac{1}{2}\times \text{sum of parallel sides}\times height[/tex]

Given : Height = 6.4 cm

and parallel base is 12.9 cm and 8.6 cm.

Substitute, we have,

Area of trapezoid = [tex]\frac{1}{2}\times (12.9+8.6)\times 6.4[/tex]

Simplify, we have,

Area of trapezoid = [tex]\frac{1}{2}\times 21.5\times 6.4[/tex]

Area of trapezoid = 68.8 cm²

Thus, The area of given trapezoid is 68.8 cm²

The number of students in the period 7 study hall at jins school is 4 times the number of students in Jin’s home room how many students are in the study hall if there are 16 students in Jin’s home room

Answers

I think it's 64. Not positive, but pretty sure it is.

She has 16 students in her home room
The study hall is 4 times as many

4*16 = 64
There must be 64 students in the study hall.

Yesterday, Jed's bank account balance was $26.34. Today, he made a withdrawal from his account. The current balance is $12.18. How much did he withdraw from his account?

$15.84

$26.34

$14.16

$16.84

Answers

he withdrew $14.16 for his account.

$26.34 - $12.18
=$14.16

Help please ....zzzghg

Answers

Answer: [tex]f=168[/tex]

Step-by-step explanation:

In the picture, there is a multiplication problem of [tex]f=56\times3[/tex]

We can use distributive property in it so that the multiplication problem become easier.

Distributive property:-[tex](b+c)a=ba+ca[/tex]

In the product, the larger number is 56

Write [tex]56=50+6[/tex]

Now, [tex]f=56\times3\\\Rightarrow\ f=(50+6)3\\\Rightarrow\ f=(50)3+(6)3\\\Rightarrow\ f=150+18\\\Rightarrow\ f=168[/tex]

What is the area of this figure? Enter your answer in the box. units² An irregular-shaped heptagon is graphed on a coordinate plane. The horizontal x-axis ranges from negative 6 to 6 in increments of 1. The vertical y-axis ranges from negative 6 to 6 in increments of 1. The vertices of the heptagon are located at begin ordered pair negative 3 comma 5 end ordered pair, begin ordered pair negative 1 comma 2 end ordered pair, begin ordered pair 1 comma 5 end ordered pair, begin ordered pair 3 comma 2 end ordered pair, begin ordered pair 3 comma negative 1 end ordered pair, begin ordered pair negative 5 comma negative 3 end ordered pair, and begin ordered pair negative 5 comma 2 end ordered pair.

Answers

I graphed the given points. A heptagon is a shape with seven sides. In the figure I graphed, I found familiar shapes like rectangle and triangles. I'll be using the formula of the triangle and rectangle when solving for its area.

Area of a triangle = (base * height) / 2
Area of a rectangle = length * width

I divided my graph into 3 parts. 1st part is the 2 triangles, 2nd part is the rectangle, 3rd part is the right triangle.

1st part
The 2 triangles each have a base of 4 units and a height of 3 units.
Area of a triangle = (base * height) / 2
A = (4 * 3)/2 = 12/2 = 6 square unit. per triangle.
Since there are 2 triangles, 6 sq.u * 2 = 12 sq.unit

2nd part
rectangle length = 8 units ; width = 3 units
Area of a rectangle = length * width = 8 * 3 = 24 sq. unit

3rd part
Right triangle: short leg = 2 units ; long leg = 8 units
Area of a right triangle = (long leg * short leg) / 2
Area of a right triangle = (8 * 2) / 2 = 16/2 = 8 sq. unit

Total area of the heptagon = 12 sq.u + 24 sq. u + 8 sq. u = 44 sq. unit.

A farmer has 300 ft of fencing with which to enclose a rectangular pen next to a barn. The barn itself will be used as one of the sides of the enclosed area.

What is the maximum area that can be enclosed by the fencing?

_______ft^2

Answers

This question can be answered in a number of ways depending on your level of mathematical sophistication (using calculus, graphing a parabola, and guess/check). I'll talk through all three in the order above.

They all start the same way: Let's call the length of the rectangle b and the width a. The perimeter of the rectangle (the distance all the way around -- that is, the length of the "fence") is 2a + 2b. Since the barn is used as one of the sides (let's say b) we can subtract b ... we don't need fencing for this side. That makes the perimeter 2a + b. Since we have 300 feet of fencing we set these equal: 2a + b = 300.

We can solve for b above by subtracting 2a from both sides of the equation so we get: b = 300 - 2a.

We are asked to maximize the area. The area of a rectangle is length times width. In this case, (a)(b) and since we just found an expression for b, we can substitute this to obtain: Area = [tex](a)(300-2a)=300a-2 a^{2} [/tex]. This is a parabola when graphed and we are asked to find where it's highest point occurs because this is where the area is greatest.

METHOD 1: Using Calculus
We are looking for the highest point of the equation [tex]Area = [tex](a)(300-2a)=300a-2 a^{2}[/tex]. Let's call the function R(a) since it is in terms of a. To find the maximum we take the first derivative, set it equal to zero and solve for a. As this is a parabola (with the leading coefficient being negative) it is concave down and the point we find will be the only maximum.

First we find the derivative of the function.
[tex]R(a)=(a)(300-2a)=300a-2 a^{2} [tex]

Next set it equal to 0 and solve for a.
R^{'}(a)=300-4a 0=300-4a -300=-4a 75 = a[/tex] [/tex]
This means that the maximum value (the largest area) occurs when a = 75.
At a = 75 the area is given by
What is the largest area? Let's us substitute 75 for a in the equation of the area. This gives: [tex]Area=a(300-2a)=(75)(300-(2)(75))=(75)(150)=11250[/tex] square feet.

METHOD 2: Graphing
We know that the area is given by. Area = [tex](a)(300-2a)=300a-2 a^{2} [/tex]. To make this more familiar let's use y for the area and x for the width (a). That means we have the equation: [tex](a)(300-2a)=300a-2 a^{2} [/tex].

This is a quadratic equation (the highest exponent of x is 2) and so the equation of a parabola (like the letter U or an upside down U). Since the leading coefficient is negative (-2) we know it opens downward (called concave down -- think of a frown). We are looking for the x-coordinate of the highest point called the vertex. We can find this by remembering that the x-coordinate of the vertex is given by [tex]x= \frac{-b}{2a} [/tex] where a is the leading coefficient the coefficient of the term with the x squared (here = -2) and a is the coefficient of the linear term (the one with x...here 300). That makes the x-coordinate of the vertex [tex]x= \frac{-300}{2(-2)}= \frac{-300}{-4}=75 [/tex].

The y-coordinate of the vertex is found by substituting 75 for x in the equation for the area. [tex]y=300x-2 x^{2} y=300(75)-2(75)^{2} [/tex]
[tex]y=22500- 2(5625) y=22500- 11250 y=11250[/tex]

Since we let x be the width of the rectangle. We know that the width is 75. The area of the rectangle we called y. So the maximum area is 11250 square feet which occurs when the width of the rectangle is 75.

You could have gotten to this point by generating a list of points for the parabola and graphing it carefully on graph paper (though it might not have been exact depending on how you scale your axis).

METHOD 3: Guess and Check
The area of the rectangle is given by Area = [tex](a)(300-2a)=300a-2 a^{2} [/tex]. Here you guess values for a, plug them into the formula to get the area and keep doing this until you are comfortable you have found the largest area. Not the best method but if it's a test and you forget everything else, it might get you close to an answer or even get you the exact answer (depending on how well you guess). It might take a while so I'd do this question last if this were a test.

What is the volume of a rectangular prism with side lengths14.7 m, 23.4 m, and 3.2 m?

Answers

think it may be 1100.736 because you would multiply the three numbers

A rectangular prism is a three-dimensional figure; therefore, the units of measure will be cubed when we find our answer. A rectangular prism also has three dimensions that are required to find the volume: Length, Width, and Height. These dimensions must all be multiplied by each other to find the volume. The values for these do not need to be specific; they can be interchanged at any moment. That being said, let's plug in these values for our variables.

Volume = Length x Width x Height; substitute values.
Volume = 14.7 x 23.4 x 3.2; multiply 14.7 by 23.4 first. This allows our units to be squared (units^2).
Volume = 343.98 x 3.2; multiply these two dimensions. This determines our units to be cubed- and furthermore- our volume.
Volume = 1100.736; remember to apply your proper units.

Your answer for this problem is 1100.736 m^3.

I hope this helps!

A soup recipe calls for 23/4 quarts of broth. An open can of broth contains 1/2 quart of broth. How much more broth do you need to make the soup?

Answers

Hey there!

For the beginning of the problem, I believe you meant to type "2 3/4" instead of "23/4". But to solve this, you can subtract the numbers 2 3/4 and 1/2 . . .

3/4 - 1/2 . . .

3/4 = 3/4

1/2 = 2/4

3 - 2 = 1

The denominator stays the same, so that leads you to the fraction 1/4 . . .

2 + 1/4 = 2 1/4.

2 3/4 - 1/2 = 2 1/4

You need 2 1/4 quarts of more broth to make the soup.

Hope this helps you.
Have a great day!

Find the correct selling price. Round to the nearest dollar.
What was the clerk's error?

Answers

a. $35.10. 1.3*30=35.1
b. I think the clerk thought 30% was 3 dollars, and he added 3 dollars to 27, which is 30.

HURRY PLEASE!!!!!

Mr. McElroy enjoys listening to his MP3 player, which has 2,000 songs in five different genres of music. He took a sample of the number of each type of song it played on two different one-hour sessions when it was set to play a random mix. The results are displayed in the table below. What is a good prediction for the number of rock songs Mr. McElroy has on his MP3 player?
A) 225
B) 550
C) 1100
D) 1667

Answers

550, that's the best answer

Answer:

Its B

Step-by-step explanation:

550 is the closest

the distance between two cities on a map is measured to be 4 inches. the actual distance between the cities is 448 miles. what is the scale of the map?

Answers

44.56 for the distance

ur answer would be 44.56

Light travels 3 x 10^5 kilometers in one second. How far does it travel in 6.7 seconds? Write your answer in scientific notation.

Answers

The distance covered by the traveling light in 6.7 seconds is 2.01 × 10⁶ kilometers.

What is the distance covered by the light in 6.7 seconds?

The speed formula is expressed as:

Speed = Distance / Time

Given the parameter:
Distance covered by the light = 3 × 10⁵ kilometers

Elapsed time = 1 second

Speed =?

The speed of the light is:

Speed = Distance / Time

Speed = 3 × 10⁵ kilometers / 1 second

Speed = 3 × 10⁵ kilometers per second

Now, we find the distance covered by the light in 6.7 seconds.

Speed = Distance / Time

Distance = Speed × Time

Distance = 3 × 10⁵ kilometers per second × 6.7 seconds

Distance = 2.01 × 10⁶ kilometers.

Therefore, the distance traveled is 2.01 × 10⁶ kilometers.

Learn more about speed here: https://brainly.com/question/27571996

#SPJ3

Four brothers each bought two hot dogs and a bag of chips at the football concession stand if the bag of chips was 1.25 and the total was 18.20 what was the price of one hot dog

Answers

1.25×4=5
18.20-5= 15.20
15.20÷4=3.8
The price of 1 hotdog is $3.80

Answer:

$3.8

Step-by-step explanation:

The price of a car has been reduced from $19,500 to $16,965. What is the percentage change of the price of the car?

Answers

Hello!

Because the price has been reduced, this is a percent decrease.

To calculate the percentage decrease, we must use a certain formula. The formula is:

[(Old Value - New Value) / Old Value * 100]

Substitute:

[( 19,500 - 16,965) 19,500 * 100] = 13

FINAL ANSWER:

The percent decrease is 13%.

Final answer:

The percentage change in the price of the car is a reduction of approximately 13%, calculated by taking the difference between the original and reduced prices, and then dividing by the original price and multiplying by 100.

Explanation:

To calculate the percentage change in the price of the car, you first find the difference in price and then divide it by the original price. Initially, the car was priced at $19,500 and then reduced to $16,965.

To find the difference, subtract the new price from the old price.

$19,500 - $16,965 = $2,535

Now, divide the difference by the original price and multiply by 100 to get the percentage.

($2,535 ÷ $19,500) × 100 = 13% (approximately)

The percentage change in the price of the car is a reduction of approximately 13%.

A rectangular prism has a length of 20 in., a width of 2 in., and a height of 3 1/4 in.

The prism is filled with cubes that have edge lengths of 1/4 in.

How many cubes are needed to fill the rectangular prism?

Enter your answer in the box.

To fill the rectangular prism,
cubes are needed.

Answers

1650 because a 1/4 inch cube is 1/4 x 1/4 x 1/4 for a volume of 1/64

Step-by-step explanation:

1650

car un cube de 1/4dcoespond à 1/4 x 1/4 x 1/4 pour un volume de 1/64

I= $30 p= $500 r= 3%

Answers

Equation is I=prt. So 30=500(.03)t. You solve for T. 30=15t the divide so t+2

Answer:2 years

Step-by-step explanation:

the bill for a stay in a hotel was $173 and the tax was an additional $15 what percent of the bill was the tax

Answers

the tax was about 8% of the bill

Please help!
4x(5y-x)-5y(4x-y)

Answers

4x(5y-x)-5y(4x-y)=20xy-4x^2-20yx+5y^2=-4x^2+5y^2=5y^2-4x^2

= 4x(5y-x) - 5y(4x-y)
= 20xy-4x²- 20xy+5y²
= -4x²+5y²

Find the length of x?

Answers

If we assume the triangles are similar, then
.. 15/10 = x/8
.. x = 8*(15/10) = 12

A bamboo shoot is 20 inches tall at the zero and gross 24 inches each day which functions show below can be used to determine height F(n) of the bamboo after n days

Answers

it is definitely D because on part 1 n=24n+20 and if n equals 0 than 24 (0) +20= 20 and that is true. on part 2 if n =0 than 24 (0)+ 20 (0-1)=20 than 20 (-1)=20 -20= 20. that statement is false because-20 does not equal 20. AND for part 3 n=1 and f (1-1) + 24= 44 so f (0) + 24 =44 and keep in mind f (0) equals 20 so 44=44 because 24+20 is 44. so that is a true statement too

It is given bamboo shoot is 20 inches tall when time is 0. It grows at the rate of 24 inches each day .

The y intercept b=20 and m= slope = 24.

Any equation can be written in the form y=mx+b where m is slope and b is y intercept.

The equation to determine height for n number of days can be written as

f(n)=24n+20

It can also be written as 24+the growth 1 day back or

F(n)=F(n-1)+24 where f(0)=20.

Among the given options equations 1 and 111 hold true

Option D is the right answer.

Heather was asked to graph 2x + 4y = 12 by using slope and y-intercept. Her graph is shown. Which choice supports the graph that she has drawn. A) The slope is positive 1 2 and the y-intercept is (0,3). B) The slope is negative 1 2 and the y-intercept is (0, 3). C) The slope is positive 1 2 and the y-intercept is (0, -3). D) The slope is negative 1 2 and the y-intercept is (0, -3).

Answers

Answer:

B) The slope is negative 1/2 and the y-intercept is (0, 3).

Step-by-step explanation:

First we rewrite the equation so we can easily find the slope and y-intercept. We do this by isolating the y-term:

2x+4y = 12

We want to subtract 2x from each side:

2x+4y-2x = 12-2x

4y = 12-2x

4y = -2x+12

Now we divide both sides by 4 (everything on both sides gets divided!):

4y/4 = -2x/4 + 12/4

y = -2/4x + 3

y = -1/2x + 3

The slope is -1/2 and the y-intercept is 3 (the point (0, 3)).

Her graph shows the y-intercept at (0, 3); this part is correct.

The graph also shows we go down one and over two between points; this is a slope of -1/2, which is correct.

A model car has a windshield with dimensions 1/18 the size of a real car windshield. The rectangular windshield of the real car has an area of about 2318 sq in, with a width of 61 in. What are the side lengths of the model car's windshield? Round to the nearest hundredth?

Answers

Width of the model car's windshield is around 3.39 inches and the length is approximately 17.45 inches.

The area of the real car windshield is 2318 sq in, with a width of 61 in. The scale of the model car's windshield is 1/18 of the real car windshield.

To find the dimensions of the model car's windshield, first, calculate the area of the model windshield by dividing the real area by the square of the scale factor. Then, find the width and length of the model windshield by using the square root of the calculated area.

In this case, the width of the model car's windshield is around 3.39 inches and the length is approximately 17.45 inches.

Answer:

2.11 inches

Step-by-step explanation:

You want the side length of the windshield of a 1/18 scale model of a car with a 2318 in² windshield that has a width of 61 inches.

Length

The side length of the actual windshield is found from ...

A = LW

L = A/W = (2318 in²)/(61 in) = 38 in

The length of the model windshield is 1/18 of this:

(38 in) × 1/18 = 2 1/9 in ≈ 2.11 in

The side lengths of the model car's windshield are 2.11 inches.

A campground consists of 9 square campsites arranged in a line along a beach. The distance from the edge of a campsite to the water at the end of the beach is 5 yd. The area of the campground, including the beach, is 1115 sq yd. What is the width of one campsite?

Answers

We know that each campsite is a square; we also know that all the sides of a square are equal; therefore the length and the width of each campsites are equal. Lets label [tex]x[/tex] to each side of our campsite. From the problem we know that the distance from the edge of a campsite to the water at the end of the beach is 5 yd, so the distance including our campsite will be [tex]5+x[/tex]. Also, since each campsite have length=x, the total length of the 9 campsites will be [tex]9x[/tex]. Now we have a big rectangle including the campground and the beach of length=[tex]9x[/tex] and width=[tex]5+x[/tex]. The area of a rectangle is [tex]A=(length)(width)[/tex], and from our problem we know that area is 1115 square yards, so we can set up an equation and solve for [tex]x[/tex] to find the width of each campsite:
[tex]1115=(9x)(5+x)[/tex]
[tex]1115=45x+9 x^{2} [/tex]
[tex]9 x^{2} +45x-1115=0[/tex]
Using the quadratic formula to solve the equation, we get that:
[tex]x=8.9[/tex] or [tex]x=-13.9[/tex]
Since distances cannot be negative, the solution is [tex]x=8.9[/tex]

We can conclude that the width of each campsite is 8.9 yards.

Answer:

i think it is 54

Step-by-step explanation:

The net of a square pyramid is shown below:

What is the surface area of the solid?

10 square inches
16 square inches
24 square inches
28 square inches

Answers

Answer: 28 square inches

Step-by-step explanation:

We know that the area of a triangle is given by :-

[tex]\text{A}=\dfrac{1}{2}*b*h[/tex], where b is base and h is the height of the triangle.

From the given picture, it cam be seen that alll the traingles area of same measure, the base of the triangle = 2 inches

The height of the triangle = 6 inches

Now, the area of a triangle is given by :-

[tex]\text{A}_1=\dfrac{1}{2}*6*2=6\ in^2[/tex]

Area of the square in the center =[tex](side)^2=(2)^2=4\ in^2[/tex]

Now, the total surface area of the pyramid is given by :-

[tex]\text{S.A.}=4+4(6)=28\ in^2[/tex]

leon used plant fertilizer on 4/7 of his potted flowers if he has 28 potted floewers on how many did he use plant fertilizer?

Answers

The answer is 16 flowers.

16 more flowers !!!! Thanks so muxh

Find f(-5) if f(n) = n3 + 3n2
A) -50
B) -7
C) 0
D) 22

Answers

[tex] f(-5) = (-5)^{3} + 3(-5)^{2}[/tex]
[tex]f(-5) = -125 + 3(25)[/tex]
[tex]f(-5) = -125 + 75[/tex]
[tex]= -50[/tex]

f(n) = n^3 + 3n^2
substitute the f(-5)
f(-5) = (-5)^3 + 3(-5)^2
solve
f(-5) = -125 + 75
f(-5) = -50

That is the solution
A.) -50

Hope this helps :)

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