Bob is driving home from his vacation to see the Grand Canyon. When he stops to check his map, he notices that he is 320 miles from home. He calculates that he should be able to cover 60 miles of road each hour on his journey home.

Dependent variable:
Independent variable:

Function notation:

Hello!

[tex]\large\boxed{V = 471cu ft}[/tex]

Find the volume of the cylinder using the formula:

[tex]V = h(\pi r^{2})[/tex]

We are given the diameter, so solve for the radius:

[tex]d = 2r\\\\10 = 2r\\\\r = 5 ft[/tex]

Use the given height and radius to solve for the volume:

[tex]V = 6(5^{2}\pi )\\V = 6 * 25\pi \\\\V = 471 cu ft[/tex]

Answer:

0

Step-by-step explanation:

-4 - -4 = 0

6-4 = 2

0/2 = 0

Answer:

change in y change in x

The change in x

is equal to the difference in x-coordinates (also called run), and the change in y

is equal to the difference in y-coordinates

m=y2−y1x2−x1

Substitute in the values of x

and y

into the equation to find the slope.

m=−4−(4)−3−(6)

m=8/9

Answer:

45

Step-by-step explanation:

by the definition of an isocoles triangle, defined by having two congruent sides,  (p-s, r-s), angles SPR and SRP are congruent. by the triangle sum theorem, (internal angles + to 180˚) 90˚ + 2a = 180˚. 2a =90, a = 45

Answer:

48.17

Step-by-step explanation:

Umm.. i don't really have time to explain but

A^2+B^2=C^2

36^2+32^2=48.17

Answer:

x=266/41

Step-by-step explanation:

1ft 7in/3ft 5 in=x/40

or,12in+7in/36+5=x/40

or,19in/41in=x/40

or,19*40/41=x

•°•x=266/41

Answer:

Step-by-step explanation:

To find the center and the radius, we need to put the equation in the (x-a)^2+(y-b)^2=r^2 [a is the x-coordinate, b is the y-coordinate, and r is the radius].

(x+6)^2+(y+7)^2 - 36 - 49 + 69 = 0

(x+6)^2+(y+7)^2 - 16 = 0

(x+6)^2+(y+7)^2 = 16

(x+6)^2+(y+7)^2 = 4^2

The center is (-6,-7) and the radius is 4.

Hope this helps!

Answer:

Results are below.

Step-by-step explanation:

Giving the following information:

Fixed costs= $5,000

Unitary variable cost= $25

First, we need to structure the total cost formula:

Total cost= fixed costs + unitary cost*number of units

Total cost= 5,000 + 25*x

x= number of units

For 100:

Total cost= 5,000 + 25*100= $7,500

For 150:

Total cost= 5,000 + 25*150= $8,750

For 200:

Total cost= 5,000 + 25*200= $10,00

For 250:

Total cost= 5,000 + 25*250= $11,250

For 300:

Total cost= 5,000 + 25*300= $12,500

Answer:

It does not represent a function.

It fails at (3,1), (3,-1), (3,-3.5). The points are variable, the x must stay the same to ensure you tested for VCL.

Step-by-step explanation:

The vertical line test is the easiest test to see if a line is a function. All you have to do is draw a vertical line across the "function". If AT ANY TIME, the vertical line intersects more than once with the "function", it has failed the vertical line test (VLT) and is not a function.

Please look at the image attached to see how to do the VLT. Please ignore my line drawing and mouse-writing :)

Answer:

This curved line is not a function. Two points where it fails the vertical line test are (3, 1) and (3, -1).

Step-by-step explanation:

edmentum answer

Equation : (7x + 9) + (5x + 3) = 180°

The two lines, say, line a and b are parallel and line y is a transversal. The two angles are called supplementary angles.

_________________________________

To find the value of x, we need to solve the equation.

(7x + 9) + (5x + 3) = 180

7x + 9 + 5x + 3 = 180

(7x + 5x) + (9 + 3) = 180

12x + 12 = 180

12x = 180 - 12

12x = 168

x = 168/12

x = 84/6

x = 42/3

x = 14

Value of x: 14

_________________________________

First angle = 7x + 9

= 7×14 + 9

= 98 + 9

= 107

Second angle = 5x + 3

= 5×14 + 3

= 70 + 3

= 73

Angle measures: 107° & 73°

Answer:

1 because it goes up 3 over 3      3/3=1

Step-by-step explanation:

Answer:

y=2/5x+28/5

Step-by-step explanation:

Answer: No Solution

Step-by-step explanation: In picture

If the function is translated using the rule (x + 1, y – 2), the resulting function will be g(x) = (x+1)² -2

Translation is a way of changing the position of a figure on an xy plane. Given the parent function

y = x²

If the function is translated using the rule (x + 1, y – 2), the resulting function will be g(x) = (x+1)² -2. The equivalent graph if the function is as shown  below.

Learn more on translation here: https://brainly.com/question/12861087

#SPJ1

Answer:

16.2

Step-by-step explanation:

The x is 6.6.

2x+3 = DE

2(6.6)+3

13.2+3

16.2

Hope this helps!

Answer:

15s-2s^2-4

Step-by-step explanation:

Step-by-step explanation:

15s-2s^2-4 and is the best

Answer:

A: answer is 0 because anything to the power of 0 is 1

B: 0 or 1 because 1 to the power of 1 is 1 and 1 to the power of 0 is also 1

Answer:

huhufht

Step-by-step explanation:

kdgkfndk

Answer: 12 miles

Step-by-step explanation:

From the question, we are informed that Marie walk 680 miles to the south pole and that the trip took 58 days and they travel the same distance each day.

The number of miles that they travel each day to the nearest whole number will be gotten by dividing 680 miles by 58. This will be:

= 680 miles / 58

= 11.72

= 12 miles to nearest whole number.

Answer:

he will pay 3.75 in tax

Step-by-step explanation:

first you do 50 times 0.075(which is 7.5%) to get your answer of 3.75

Answer:

dude it's easy

Step-by-step explanation:

Answer:

x<-15

Step-by-step explanation:

Answer:

Task

Kipton has a digital scale. He puts a marshmallow on the scale and it reads 7.2 grams. How much would you expect 10 marshmallows to weigh? Why?

Kipton takes the marshmallows off the scale. He then puts on 10 jellybeans and then scale reads 12.0 grams. How much would you expect 1 jellybean to weigh? Why?

Kipton then takes off the jellybeans and puts on 10 brand-new pink erasers. The scale reads 312.4 grams. How much would you expect 1,000 pink erasers to weigh? Why?

IM Commentary

The purpose of this task is to help students

Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left (5.NBT.1)

By setting the task in the context of weighing objects and bundles of 10, 100, and 1,000 objects, it helps students visualize that bundling 10 units of a given place value will create 1 unit of the next highest place value. For example, taking 10 of an item that weighs 4.2 grams will result in 42 grams because it is 10 groups of 4 grams that weights 40 grams all together, and 10 groups of 0.2 grams that weigh 2 grams all together. The task allows students to explore both the structure of our place value system and how we use that to efficiently multiply and divide powers of 10.

Though this task is written as questions to be discussed or answered by students, the parts of this task are most valuable as a set of scenarios to be infused throughout a unit on place value. The teacher can actually bring in a digital scale and go through a series of explorations with students. It might be natural to start with students weighing one object and making predictions about how much 10 or 100 of these objects would weigh. From there, the teacher may want to have students start weighing sets of 10 or 100 objects and work backwards to think about the weight of 1 object.

The digital scale has several advantages: the weight will always appear in decimal form, thereby making it perfect for students to start reasoning about shifts in decimal place value from a more intuitive place. Moreover, the digital scale will not always show the expected answer. For example, something that weighs 3.5 grams alone might weigh 35.4 grams (rather than 35 grams) when taken as a group of 10. This slight difference provides an excellent opportunity to talk about rounding error. It also requires students to think beyond the rules of sliding a decimal point to the right when multiplying by powers of 10.

If students were still developing the rules for multiplying and dividing by powers of 10, this task would also incorporate MP8, Look for and express regularity in repeated reasoning. It also incorporates parts of MP6, Attend to precision, in that a higher-level discussion will push students to reason why one marshmallow might weigh 7.2 grams, but 10 marshmallows might weigh 7.19 grams. See the solution for part (a) for further elaboration.

Solution

Solution:

10 marshmallows should weigh 72 grams. Students might use repeated addition, multiplication or reason that each digit’s place value will be multiplied by a factor of 10:

10×(7+0.2)(10×7)+(10×0.2)70+272===

If students have had practice using digital scales in class, some students might respond with guesses that are close such as 73 grams or 72.4 grams because the original 7.2 grams may have been rounded to the nearest tenth. If, for example, the original actual weight were 7.24 grams, then the weight of ten marshmallows on a scale that rounds to the nearest tenth of a gram would be 72.4 grams.

1 jellybean should weigh 1.2 grams. Students may come to the solution a number of ways.

Students might notice that dividing 12 by 10 could be expressed in fraction form 1210. Students might further reason that

1210=1010+210

or 1.2.

Students might alternately reason that 12÷10 is the same as

(10÷10)+(2÷10)=1+0.2=1.2

Students might also use the rule that they are beginning to develop about sliding the decimal point one place to the left to divide by 10.

1,000 pink erasers should weigh about 31,240 grams. Students may come to the solution a number of ways:

A student might reason that first, it would be necessary to find out what 100 erasers would weigh by multiplying by a factor of 10 and then further multiplying by another factor of 10 to find out what 1,000 erasers would weigh. This is represented by

312.4×10×10

In this solution method, the student reasoned that multiplying by a factor of 10 and then another factor of 10 would be the same as multiplying by a factor of 100:

312.4×10×10312.4×100100×(300+10+2+0.4)30,000+1,000+200+4031,240====

Another student might want to find the weight of a single eraser. If 10 erasers weigh 312.4 grams, then one eraser must weigh 31.24 grams. From there the student could multiply the weight of one eraser by a factor of 1,000:

1000×(30+1+0.22+0.04)30,000+1,000+200+4031,240==

Step-by-step explanation:

You would expect 1,000 pink erasers to weigh 31,240 grams.

If 10 erasers weigh 312.4 grams, and to get 1,000 you multiply by 100, if you multiply 312.4 by 100 you get 31240.

Or if you use rates

[tex]\frac{312.4}{10} =\frac{31240}{1000}[/tex]

(when you multiply by 100)

The question is incomplete:

Keith and Michelle went out to dinner. The total cost of the meal, including the tip, came to $53.70. If the combined tip came out to $9.60, and each friend spent an equal amount, how much did each friend pay not including the tip?

Answer:

Each friend paid $22.05 without including the tip.

Step-by-step explanation:

Since you know the total cost of the meal including the tip and the value of the combined tip, you can subtract the amount of the tip from the total cost and divide the result by 2 as they spent an equal amount:

$53.70-$9.60=$44.1

$44.1/2=$22.05

According to this, the answer is that each friend paid $22.05 without including the tip.

Answer: ∛2x / 2x+1

x cannot equal -1/2

Step-by-step explanation: f/g means we divide the f function by the g function

so that’s all we do!

then, remember, we can’t divide by 0. so 2x+1 can’t be 0. if we solve that out, we get that x can’t be -1/2, because that would make it 0. there’s our domain restriction!

Answer:

x < - 4

Step-by-step explanation:

Given

2x - 2 > 4x + 6 ( subtract 2x from both sides )

- 2 > 2x + 6 ( subtract 6 from both sides )

- 8 > 2x ( divide both sides by 2 )

- 4 > x , thus

x < - 4

Answer:

y=−34x+2.75

Step-by-step explanation:

Parallel lines have the same slope. Solve for the slope in the first line by converting the equation to slope-intercept form.

3x + 4y = 12

4y = –3x + 12

y = –(3/4)x + 3

slope = –3/4

We know that the second line will also have a slope of –3/4, and we are given the point (1,2). We can set up an equation in slope-intercept form and use these values to solve for the y-intercept.

y = mx + b

2 = –3/4(1) + b

2 = –3/4 + b

b = 2 + 3/4 = 2.75

Plug the y-intercept back into the equation to get our final answer.

y = –(3/4)x + 2.75