Your car's gas tank holds 13 gallons, and you expect to get about 25 miles per gallon on this winding road. to be sure you don't run out of gas, you never want to have less than 1 gallon in the tank. you start with a full tank of gas. will you need to stop for gas during the first day's drive? explain how you know, and show your work.

Answer:

9222.23333 is the value good sir :)

Step-by-step explanation:

Step-by-step explanation:

the slope is (y coordinate change / x coordinate change) when going from one point on the line to another.

the direction does not matter, but it is essential that once a direction is picked for one coordinate, we use the same one then also for the other.

I prefer to go from left to right, so (-5, 0) to (-4, 2) :

x changes by +1 (from -5 to -4).

y changes by +2 (from 0 to 2).

so, the slope is +2/+1 = 2/1 = 2.

The expressions that represents the vertical distance between the top of the mango tree and the tips of its roots is C. None of the above.

It should be noted that the mango tree stands 2.6 meters above the ground. Its roots extend 7/5 meters below the ground.

In this case, the vertical distance will simply be the difference between the values that are given.

This wasn't written on this case.

Therefore, the correct option is C.

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Answer:

True.

Step-by-step explanation:

(LHS) cos 6∘ cos 42∘ cos 66∘ cos 78∘

1/4 [cos(66∘+6∘) = cos(66∘-6∘)] • [cos(78∘+42∘)+cos(78∘-42∘)]

= 1/4(sin18∘+12)(-12+cos36∘)

[∵cos72∘ = cos(90∘−18∘) = sin18∘]

1/4[(5-√-1)/4+1/2][−1/2+(5-√+1)/4]

[∵sin(18∘ = (5-√-1)/4, and, cos 36∘ = (5-√+1)/4]

1/4(5-√+1)/4(5-√-1)/4 = (5-1)/64

= 4/64 = 1/16 (RHS)

Therefore, the cosine is equal to 1/16.

first off let's keep in mind that an absolute value is really a ± equation in disguise, so |5x -4| can pretty much be rewritten as ±(5x - 4), so is a dual equation, let's solve both for "x".

[tex]|5x-4|\leqslant 3x\implies \pm(5x-4)\leqslant 3x \\\\[-0.35em] ~\dotfill\\\\ +(5x-4)\leqslant 3x\implies 5x-4\leqslant 3x\implies 2x-4\leqslant 0\implies 2x\leqslant 4 \\\\\\ x\leqslant \cfrac{4}{2}\implies {\LARGE \begin{array}{llll} x\leqslant 2 \end{array}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]-(5x-4)\leqslant 3x\implies (5x-4)\stackrel{\stackrel{notice}{\downarrow }}{\geqslant} -3x\implies 8x-4\geqslant 0 \\\\\\ 8x\geqslant 4\implies x\geqslant \cfrac{4}{8}\implies {\LARGE \begin{array}{llll} x\geqslant \cfrac{1}{2} \end{array}}[/tex]

Check the picture below.

The histogram for these data is given at the end of the answer.

An histogram is a graph that shows the number of times each element of x was observed.

For this problem, there are 5 classes with a range of 30, as 59.5 - 29.5 = 30, hence the class width is of:

30/5 = 6.

From the data-set, we have that:

Considering this, the histogram is given at the end of the answer.

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Time taken by car to pass the truck in the same direction from the time the car enters the highway is approximately12.54 minutes with a truck speed 60mph and a car 67mph.

As given in the question,

Speed of a truck=60mph

⇒60 minutes = 60miles

⇒14 minutes = (60/60)×14

                     = 14 miles

Car speed =67mph

67 miles=60minutes

⇒1miles = (60/67) minutes

⇒14miles = (60/67)×14

                ≈12.54 minutes (approximately)

Therefore, time taken by car to pass the truck in the same direction from the time the car enters the highway is approximately12.54 minutes with a truck speed 60mph and a car 67mph.

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Answer: -26

Step-by-step explanation:

5 x -6 = -30

-30 + 4 = -26

5(-6) + 4 = -26

Answer:

10x + x^4/x-2

Step-by-step explanation:

Combine like terms

(10x + x^4)/(x-2)

Answer:1.c 2.b 3.a

Step-by-step explanation:

The angle with the name JWT is option (b)

The name of the angle is given as

JWT

The above means that

Two lines JW and WT intersects at point W

The point of intersection of these lines is the name of the angle

From the list of given option, we have option (b) that has the above property

Hence, the angle with the name JWT is option (b)

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Answer:

A = 1160

B = 1160 is already in standard form.

C = 1200

Answer:

$14 for 50 copies.

Step-by-step explanation:

Given that,

→ C(x) = 10.00 + 0.08x

Then the cost for 50 copies will be,

→ C(50) = 10.00 + (0.08 × 50)

→ C(50) = 10.00 + 4

→ [ C(50) = $14 ]

Hence, the total cost of $14.

The simple interest was $10.5 and the amount after 1 year would be $360.5 in her account.

Simple interest is defined as interest paid on the original principal and calculated with the following formula:

S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years. The rate of interest is in percentage r% and is to be written as r/100

We have been given data as

Principal amount (P) = $350

Time (T) = 1 year

The rate of interest (R) = 3%

Simple interest= P × R × T

Simple interest = 350 × 3/100 × 1

Simple interest = $10.5

So the amount after 1 year would be P + S.I. = 350 + 10.5 = $360.5

Therefore, the simple interest would be $10.5 and the amount after 1 year would be $360.5.

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Answer:

Step-by-step explanation:

2/5 or 4/10 or 8/20 or 16/40  

Yes Jake is correct we the scales are accurately represented.

From the information, the original scale factor for a scale drawing of a square swimming pool is 1/90, and the length of the original drawing is measured to be 8 inches.

Therefore, the original length will be:

= 8 ÷ 1/90

= 8 × 90

= 720 inches

Therefore, Jack is correct.

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Answer:

21g

Step-by-step explanation:

12 + 9 = 21 then add the variable.

After Simplify this expression 12 g + 9 g. We get, 21g.

To simplify this expression

12 g + 9 g,

Add ( 12 + 9) ,which is 21

So, 12 g + 9 g = 21 g.

Therefore, the final answer is 12 g + 9 g = 21 g.

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Python is a computer programming language often used to build websites and software, automate tasks, and conduct data analysis. Python is a general-purpose language, meaning it can be used to create a variety of different programs and isn't specialized for any specific problems.

Python 3 code:

function to print the numbers in list

def print_list(List):

 for entry in List:

   print(entry)

function to print the numbers and squares in list

def print_squares(List):

 for entry in List:

   print("Square of ", entry, " = ", entry*entry)

Call the functions now

input_list = [12,10,32,3,66,17,42,99,20]

print_list(input_list)

print_squares(input_list)

Sample Output:

12 10 32 3 66 17 42 99 20 Square of  12  =  144 Square of  10  =  100 Square of  32  =  1024 Square of  3  =  9 Square of  66  =  4356 Square of  17  =  289 Square of  42  =  1764 Square of  99  =  9801 Square of  20  =  400

Python 2.7 code:

function to print the numbers in list

def print_list(List):

 for entry in List:

   print entry

function to print the numbers and squares in list

def print_squares(List):

 for entry in List:

   print "Square of ", entry, " = ", entry*entry

Call the functions now

input_list = [12,10,32,3,66,17,42,99,20]

print_list(input_list)

print_squares(input_list)

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Answer: 18

Step-by-step explanation:

12 divided by 2 = 6

6 x 3 = 18

Answer:

the answer is 18

Step-by-step explanation:

this is because 12 divided by 2 = 6

6 x 3 = 18

Answer:

Step-by-step explanation:

subsitute x with value given in bracket

a) f(1) = (1)²  + 1 = 2

b) f(-3) = (-3)² + 1 = 10

c) f(b³) = (b³)² + 1 = b^6 + 1

d) f(x-1) = (x-1) +1 = x

Answer:

3(c+30)+4(c+30), 7c + 210, 3c+90+4c+120

Step-by-step explanation:

I this helps :D

Answer:

I think it's the first one

Step-by-step explanation:

because he went to class 3 times a week and u would need to multiply 3 by c minutes + 30 minutes ( u have to add them to find the total amount of minutes he exercised during one class and multiply that by 3 after adding them together bc he did that class 3 times which means he did the exercise 3 times so u multiply) then u add that with next week where he went 4 times and did c minutes+ 30 minutes. HOPE THIS HELPS!

Answer:  C, I think is correct

Answer:

[tex]y _{ \rm parallel} = - 5x +27[/tex]

Step-by-step explanation:

The equation of line p is in point-slope form , that's

[tex]y-y_1=m(x-x_1)[/tex]

Where:

Since line I is parallel to the line p , line I has the same slope as p. From the given equation of p , we can consider the slope of line p -5. Hence the slope of line I is also -5.

Now To determine the equation of I.

We have

So, the equation of line l is

[tex] y - 47 = - 5(x - ( - 4)) \\ \implies y - 47 = - 5 x- 20 \\ \implies \boxed{y _{ \rm parallel} = - 5x + 27}[/tex]

And we're done!

Answer:

x = [tex]\frac{4}{5}[/tex]

Step-by-step explanation:

4x - 10 = - 6x - 2 ( add 6x to both sides )

10x - 10 = - 2 ( add 10 to both sides )

10x = 8 ( divide both sides by 10 )

x = [tex]\frac{8}{10}[/tex] = [tex]\frac{4}{5}[/tex]

7) (x, TU, TB) = (4, 8, 13)

9) (x, RS, MN) = (8, 41, 41)

11) (AB, BC, AC) = (42, 42, 84)

In this question we have three cases of colinear line segments, each of them can be solved by using definitions from Euclidean geometry and algebraic handling:

Case 7 - TU = 2 · x, UB = 3 · x + 1, TB = 21

TB = TU + UB

21 = 2 · x + 3 · x + 1

21 = 5 · x + 1

5 · x = 20

x = 4

Then, the lengths of each line segment are:

TB = 21

TU = 2 · 4

TU = 8

UB = 3 · 4 + 1

UB = 13

The solutions are (x, TU, TB) = (4, 8, 13).

Case 9 - RS = 3 · x + 17, MN = 7 · x - 15

RS = MN

3 · x + 17 = 7 · x  - 15

4 · x = 32

x = 8

And the lengths of each line segment are:

RS = MN = 41

The solutions are (x, RS, MN) = (8, 41, 41).

Case 11 - AB = 2 · x - 8, BC = x + 17

AB + BC = AC

AB = BC

2 · x - 8 = x + 17

x = 25

And the lengths of each line segment are:

AB = 2 · 25 - 8

AB = 42

BC = AB

BC = 42

AC = 42 + 42

AC = 84

The solutions are (AB, BC, AC) = (42, 42, 84).

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Choosing different pairs of points we got different slopes, then we conclude that the 3 points don't lie on the same line.

Remember that if a line contains two points (x₁, y₁) and (x₂, y₂), then the slope of the line is:

a = (y₂ - y₁)/(x₂ - x₁)

Here the 3 points are on the same line if we get the same slope for any pair that we choose.

If we use the first two; (15, -12) and (28, 14), the slope is:

a = (14 - (-12))(28 - 15) = 8.67

If we use the second and third point (28, 14) and (32, 21), we get:

a = (21 - 14)/(32 - 28) = 6.125

We got different slopes, then we conclude that the 3 points don't lie on the same line.

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The table which represents the function g(x) is: answer option A.

x                g(x)

1                  -3

2                  3

3                  9

In Mathematics, a function can be defined as a mathematical expression which can be used to define and show the relationship that exist between two or more variables in a data set.

This ultimately implies that, a function typically shows the relationship between input values and output values of a data set, as well as showing how the elements in a table are paired (mapped).

When x = 1, the function f(x) is given by:

f(x) = 2x − 3

f(1) = 2(1) − 3

f(1) = 2 - 3

f(1) = -1.

Therefore, the function g(x) = f(3x) = 3 × -1 = -3.

When x = 2, the function f(x) is given by:

f(x) = 2x − 3

f(2) = 2(2) − 3

f(2) = 4 - 3

f(2) = 1.

Therefore, the function g(x) = f(3x) = 3 × 1 = 3.

When x = 3, the function f(x) is given by:

f(x) = 2x − 3

f(3) = 2(3) − 3

f(3) = 6 - 3

f(3) = 3.

Therefore, the function g(x) = f(3x) = 3 × 3 = 9.

In conclusion, the table which represents the function g(x) is as follows:

x                g(x)

1                  -3

2                  3

3                  9

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Answer: A

Step-by-step explanation:

rxl ontop

81 is equivalent to 3^4

What Is the Power of a Number?

The power of a number stands for how many multiples of the number there are. The power of a number is represented by something called an exponent

When a number is "raised to the second power," it means that the number is multiplied together twice, for example. When a number is "raised to the fifth power," it means that it is multiplied together five times.

we have to solve 3^4

here 3 raised to the fourth power

then 3 is multiplied together 4 times

3*3*3*3

81

Hence ,81 is equivalent tp 3^4

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