Jamal is comparing his transportation options for an upcoming trip. He’s considering a rental car and a taxi service. Based on his planned routes during his trip, he expects a taxi service would cost about $128. Jamal could also get a rental car for a daily rate and unlimited miles. If Jamal’s trip will last 4 days and he expects to pay about $24 for gas, which graph shows the range of car rental rates that would be cheaper than the taxi service?

Answers

Answer 1

Answer:

Answer:

Graph A

Step-by-step explanation:

Say that the car rental rate stands for c dollars ( $ ). We know that Jamal's trip lasts for 4 days, paying $ 24 in expenses for gas, and $ 128 for taxi services. Based on these requirements for his trip the question asks for a graph that models this situation, but lets start with the inequality.

______

The big key here is the part " which graph shows the range of car rental rates that would be cheaper than the taxi service. " Our inequality must thus have the variable " c " on the same side as the payment for gas ($ 24 ), and must be less than the taxi service ( $ 128 ), or in other words a less than sign. Another point is the car rental rate. We know it stands for c, but it is dependent on the number of days. Hence we can conclude the following inequality,

24 + 4c < 128 - Subtract 24 from either side,

4c < 104 - Divide by 4 on either side, isolating c,

c < 26

The range of car rental rates that would be cheaper than the taxi service should be { c | 0 ≤ c < 26 }, knowing variable c stands for the car rental rates.

______

The graph that models this range should be the first one, option A. This graph is not accurate however, as it extends infinitely in the negative direction, and you can't have negative money, or rather be in debt - in this situation.

Answer 2

Answer:

Answer:

A is the answer

Step-by-step explanation:

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5. Identify the type and subtype of each of the fol-lowing problems.

a. Shawn has 15 marbles, which is 7 more mar-

bles than Kyle has. How many marbles does

Kyle have?

b. Tiffany has 12 blocks, 5 of which are cubes

and the rest cylinders. How many blocks are

cylinders?

c. Peter had some carrots. After he ate 3 of

them, he had 14 carrots left. How many car-

rots did Peter have before?

d. In a bag of 17 marbles, 9 marbles belong to

Kelly and the rest belong to Shauntay. How

many marbles belong to Shauntay?

Answers

Answer:

a) Kylie has 8 marbles

b) 7 Cylinders

c) 17 carrots

d) 8 marbles belong to Shauntay

Step-by-step explanation:

5. Identify the type and subtype of each of the fol-

lowing problems.

a. Shawn has 15 marbles, which is 7 more marbles than Kyle has. How many marbles does Kyle have?

Shawn = 15 marbles

S = K + 7

15 = K + 7

K = 15 - 7

K = 8 marbles

Kylie has 8 marbles

b. Tiffany has 12 blocks, 5 of which are cubes and the rest cylinders. How many blocks are cylinders?

T = 12 blocks

Cubes = 5

Cylinders = the rest

12 blocks = Cubes + Cylinders

Cylinders = 12 - Cubes

Cylinders = 12 - 5

Cylinder = 7

c. Peter had some carrots. After he ate 3 of them, he had 14 carrots left. How many carrots did Peter have before?

Number of carrots Peter has before

= Number of carrots he ate + Number of carrots he has now

= 14 + 3

= 17 carrots

d. In a bag of 17 marbles, 9 marbles belong to Kelly and the rest belong to Shauntay. How many marbles belong to Shauntay?

Total number of Marbles = 17

Kelly = 9 marbles

Shauntay = ?

Total = Kelly + Shauntay

Shauntay = Total - Kelly's marbles

= ( 17 - 9) marbles

= 8 marbles

8 marbles belong to Shauntay

Answer:

a) Kylie has 8 marbles

b) 7 Cylinders

c) 17 carrots

d) 8 marbles belong to Shauntay

Step-by-step explanation:

5. Identify the type and subtype of each of the fol-

lowing problems.

a. Shawn has 15 marbles, which is 7 more marbles than Kyle has. How many marbles does Kyle have?

Shawn = 15 marbles

S = K + 7

15 = K + 7

K = 15 - 7

K = 8 marbles

Kylie has 8 marbles

b. Tiffany has 12 blocks, 5 of which are cubes and the rest cylinders. How many blocks are cylinders?

T = 12 blocks

Cubes = 5

Cylinders = the rest

12 blocks = Cubes + Cylinders

Cylinders = 12 - Cubes

Cylinders = 12 - 5

Cylinder = 7

c. Peter had some carrots. After he ate 3 of them, he had 14 carrots left. How many carrots did Peter have before?

Number of carrots Peter has before

= Number of carrots he ate + Number of carrots he has now

= 14 + 3

= 17 carrots

d. In a bag of 17 marbles, 9 marbles belong to Kelly and the rest belong to Shauntay. How many marbles belong to Shauntay?

Total number of Marbles = 17

Kelly = 9 marbles

Shauntay = ?

Total = Kelly + Shauntay

Shauntay = Total - Kelly's marbles

= ( 17 - 9) marbles

= 8 marbles

8 marbles belong to Shauntaya) Kylie has 8 marbles

b) 7 Cylinders

c) 17 carrots

d) 8 marbles belong to Shauntay

Step-by-step explanation:

5. Identify the type and subtype of each of the fol-

lowing problems.

a. Shawn has 15 marbles, which is 7 more marbles than Kyle has. How many marbles does Kyle have?

Shawn = 15 marbles

S = K + 7

15 = K + 7

K = 15 - 7

K = 8 marbles

Kylie has 8 marbles

b. Tiffany has 12 blocks, 5 of which are cubes and the rest cylinders. How many blocks are cylinders?

T = 12 blocks

Cubes = 5

Cylinders = the rest

12 blocks = Cubes + Cylinders

Cylinders = 12 - Cubes

Cylinders = 12 - 5

Cylinder = 7

c. Peter had some carrots. After he ate 3 of them, he had 14 carrots left. How many carrots did Peter have before?

Number of carrots Peter has before

= Number of carrots he ate + Number of carrots he has now

= 14 + 3

= 17 carrots

d. In a bag of 17 marbles, 9 marbles belong to Kelly and the rest belong to Shauntay. How many marbles belong to Shauntay?

Total number of Marbles = 17

Kelly = 9 marbles

Shauntay = ?

Total = Kelly + Shauntay

Shauntay = Total - Kelly's marbles

= ( 17 - 9) marbles

= 8 marbles

8 marbles belong to Shauntay

Step-by-step explanation:

Which expressions are equivalent to 6 +(-x) + 2x + (-7)+ 2x? Check all that apply.
x + x + 6 - 7 + x
2x+2+x
3- X + 2x - 4 + 2x
X-1
X+1

Answers

Answer:

a and c

Step-by-step explanation:

Answer:

A- x + x + 6 – 7 + x

C- 3 – x + 2x – 4 + 2x

Step-by-step explanation:

EDG2021

How is the number 35.012 written in words?

Answers

thirty-five and twelve thousandths

thirty five point zero twelve

Solve the differential equation x^2 y"-xy' +y 0

Answers

Answer:

$y(x)\ =\ √(x)[C_1cos(√(3))/(2)logx+C_2sin(√(3))/(2)logx]$

Step-by-step explanation:

Given differential equation is

$x^2y$ (1)

Let's assume that

$x=e^t$

$=>\ t\ =\ logx$

then,

$(dx)/(dt)=e^t$

$and\ (d^2x)/(dt^2)=e^t$

We can write,

$(dy)/(dx)=(dy)/(dt).(dt)/(dx)$

$=e^(-t)(dy)/(dt)$

Similarly,

$(d^2y)/(dt^2)=(d^2y)/(dt^2).(dt^2)/(dx^2)$

$=e^(-2t).(d^2y)/(dt^2)$

Putting these values in equation (1), we will get

$e^(2t).e^(-2t).(d^y)/(dt^2)-e^t.e^(-t)(dy)/(dt)+y=0$

$=>(d^2y)/(dt^2)-(dy)/(dt)+y=0$

So, the characteristics equation can be given as

$D^2-D+1=0$

$=>D\ =\ (1+√(1-4))/(2)\ or\ (1-1√(1-4))/(2)$

$=>D=\ (1)/(2)+i(√(3))/(2)\ or\ (1)/(2)-i(√(3))/(2)$

Hence, the general solution of the equation can be give by

$y(t)\ =\ e^{(t)/(2)}[C_1cos(√(3))/(2)t+C_2sin(√(3))/(2)t]$

Now, by putting the value of t in above solution, we will have

$y(x)\ =\ e^{(1)/(2)logx}[C_1cos(√(3))/(2)logx+C_2sin(√(3))/(2)logx]$

$y(x)=\ √(x)[C_1cos(√(3))/(2)logx+C_2sin(√(3))/(2)logx]$

Hence, the solution of above given differential equation can be given by

$y(x)=\ √(x)[C_1cos(√(3))/(2)logx+C_2sin(√(3))/(2)logx]$

Find the angle between the diagonal of a cube of side length 9 and the diagonal of one of its faces, so that the two diagonals have a common vertex. The angle should be measured in radians. (hint: we may assume that the cube is in the first octant, the origin is one of its vertices, and both diagonals start at the origin.)

Answers

Firstly, we can sketch points as

O as (0,0,0)

B as (9,0,9)

E as (9,9,9)

now, we can find vectors

OB=(9,0,9)-(0,0,0)

OB=(9,0,9)

OE=(9,9,9,)-(0,0,0)

OE=(9,9,9)

we can use dot product formula to find angle

$OB\cdot OE=|OE|*|OB|cos(\theta)$

now, we can find values

$OB\cdot OE=(9,0,9)\cdot (9,9,9)$

$OB\cdot OE=9*9+0*9+9*9$

$OB\cdot OE=162$

$|OB|=√(9^2+0^2+9^2)$

$|OB|=9√(2)$

$|OE|=√(9^2+9^2+9^2)$

$|OB|=9√(3)$

now, we can plug these values

$162=9√(2)*9√(3)|cos(\theta)$

now, we can solve for theta

$\theta=cos^(-1)((162)/(81√(6) ) )$

$\theta=0.61548 radians$ ............Answer

The angle between the diagonal of the cube and the diagonal of one of its faces, with a common vertex, is approximately 1.23096 radians.

How did we get this value?

To find the angle between the diagonal of a cube of side length 9 and the diagonal of one of its faces, we can use trigonometry. Let's call the diagonal of the cube Dc and the diagonal of one of its faces Df.

The diagonal of a cube can be calculated using the Pythagorean theorem in 3D:

Dc = $√(9^2 + 9^2 + 9^2)$

= √(81 + 81 + 81)

= √(243) = 9√3

The diagonal of one of the cube's faces is simply the side length, which is 9.

Now, to find the angle between them, you can use the dot product formula and the formula for the angle between two vectors:

cos(θ) = (Dc ⋅ Df) / (|Dc| ⋅ |Df|)

Where:

- θ is the angle between the diagonals.

- Dc is the diagonal of the cube (9√3).

- Df is the diagonal of one of the faces (9).

- |Dc| and |Df| are the magnitudes of Dc and Df.

Now, plug in the values:

cos(θ) = (9√3 * 9) / (9√3 * 9)

cos(θ) = 27√3 / (81√3)

cos(θ) = 1/3

Now, you can find the angle θ in radians using the inverse cosine function (cos⁻¹):

θ = cos⁻¹(1/3)

θ ≈ 1.23096 radians

So, the angle between the diagonal of the cube and the diagonal of one of its faces, with a common vertex, is approximately 1.23096 radians.

learn more about vertex: brainly.com/question/21191648

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The base of a right rectangular prism has an area of 173.6 square centimeters and a height of 9 centimeters. What is the volume, in cubic centimeters, of the right rectangular prism?

Answers

Answer:

D) 1562.4 cubic centimeters

Step-by-step explanation:

volume = area of the base × height

volume = 173.6cm² × 9 cm

volume = 1562.4 cm³

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