Round 2
5. A Cadillac Escalade gasoline tank has a capacity of 24
gallons. The car uses approximately 1 gallon for every 25
miles it drives. If the tank starts full, write an equation that
describes the amount of gas, g, left in the tank after it has
been driven for m miles.

The equation of volume will be V = [(1/2)t + 4]³. The surface area as a function of time will be A(s) = 3/2 t² + 24t + 96. The number of hours when the surface area equal 294 square inches will be 3 1/2 hours.

Functions are found all across mathematics and are required for the creation of complex relationships.

Part A: The equation that gives the volume at t hours after freezing begins will be

V = s³

V = [(1/2)t + 4]³

Part B: The surface area as a function of time, using composition, and determine its range will be

A(s) = 6(1/2 t + 4)²

A(s) = 6 (t²/4 + 4t + 16)

A(s) = 3/2 t² + 24t + 96

Part C: The number of hours when the surface area equal 294 square inches will be

294 = 6(1/2 t + 4)²

49 = (1/2 t + 4)²

7 = 1/2 t + 4

1/2 t = 3

t = 3 1/2 hours

More about the function link is given below.

https://brainly.com/question/5245372

#SPJ1

Answer:

+ 9 and - 4

Step-by-step explanation:

9 × - 4 = - 36

9 + (- 4) = 9 - 4 = 5

Answer:

The two numbers are :

9 and -4

9 x -4 = -36

9 + (-4) = 5

Step-by-step explanation:

Hope It Helps!!!

Answer:b

Step-by-step explanation:

Donte did a mistake that 'he did not apply the distributive property correctly for 4(1 3i)' option (A) is correct.

It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have an expression:

= 4(1 + 3i) – (8 – 5i)

= 4 + 12i - 8 + 5i  

He did not distribute the subtraction sign correctly for 8 – 5i.

= -4 + 17i

Thus, Donte did a mistake in that 'he did not apply the distributive property correctly for 4(1 3i)' option (A) is correct.

Learn more about the complex number here:

brainly.com/question/10251853

#SPJ1

Answer:

(A) is correct.

Step-by-step explanation:

Answer:

Step-by-step explanation:

3x + 2(x − 1) − 4 =

3x + 2x - 2 - 4 =

5x - 6

Answer:

Step-by-step explanation:

[tex]\bf 3x + 2(x - 1) - 4?[/tex]

Distribute.

Subtract the numbers.

Combine like terms.

The t-test for the two means is appropriate in this situation because women and men are independent samples.

Independent samples are chosen randomly, ensuring that their results are independent of other observations' values.

The premise that samples are independent underlies many statistical analyses. Others are made to evaluate non-independent sample sets.

The samples of men and women are independent since their results are independent of other observations' values.

The Independent Samples t-Test analyzes the means of two separate groups to see if there is statistical support that the population means values are statistically substantially different.

Learn more about Independent Samples here:

brainly.com/question/14099859

#SPJ4

The measure of angle ∠ACB is 70°. Then the correct option is C.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

∠ABC + ∠BCA + ∠CAB = 180°

        60° + ∠BCA + 50° = 180°

                           ∠BCA = 180° – 110°

                           ∠BCA = 70°

Then the correct option is C.

The complete question is given below.

Use the diagram showing m || n, as well as the relationships between interior and exterior angles of ΔABC, to answer the questions.

The measure of ABC is 60

The measure of BAC is 50

The measure of ACB will be

a. 50

b. 60

c. 70

d. 120

More about the triangle link is given below.

https://brainly.com/question/25813512

#SPJ1

Answer:

Use the diagram showing m || n, as well as the relationships between interior and exterior angles of ΔABC, to answer the questions.

The measure of angle ABC is

✔ 60

°.

The measure of angle BAC is

✔ 50

°.

The measure of angle ACB is

✔ 70

°.

Step-by-step explanation:

Answer:

[tex]2y - 8x = 3[/tex]

Step-by-step explanation:

[tex]y - 4x = 9[/tex]

[tex]2y - 8x = 18[/tex]

So 2y - 8x = 3 is parallel to y - 4x = 9.

Answer:

38 is the correct solution

Answer:

$123.21 (nearest cent)

Step-by-step explanation:

Annual Compound Interest Formula

[tex]\large \text{$ \sf A=P\left(1+r\right)^{t} $}[/tex]

where:

Given:

Substitute the given values into the formula and solve for A:

[tex]\implies \sf A=100\left(1+0.11\right)^{2}[/tex]

[tex]\implies \sf A=100\left(1.11\right)^{2}[/tex]

[tex]\implies \sf A=123.21[/tex]

Therefore, the value of the account in 2 years will be $123.21 (nearest cent).

Answer:

The angles are 72° and 108°

Step-by-step explanation:

Supplementary angles add up to 180°

Ratio of supplementary angles = 2 : 3

The angles are 2x , 3x

2x + 3x = 180

        5x = 180

          x = 180 ÷ 5

         x = 36°

2x = 2*36 = 72°

3x = 3*36 = 108°

Semiperimeter is used to find the area of various shapes including the equilateral triangle (False).

Semiperimeter is a term used in geometry to refer to half the perimeter of a polygon. It is generally used in formulas for triangles.

However, it is also part of calculations related to other geometric shapes. According to the above, it can be inferred that the semiperimeter can be used to find the area of various geometric figures.

Learn more about semiperimeter in: https://brainly.com/question/1594847

#SPJ1

2sin(x) - 1 =0

first, simplify and isolate sin(x)

2sin(x) - 1 = 0

2sin(x) = 1

sin(x) = 1/2

Then, do sin inverse of 1/2 which is 30 degrees

150 degrees also works because when you set 30 degrees as the reference angle in quadrant 2, you get 150 degrees. 180-30 = 150

C is the answer

Answer:

big bodie built

Step-by-step explanation:

i used to be dusty

Based on the calculations, the value of the given prefix expression is equal to 2205.

The preorder traversal of a tree (T) are typically used in discrete mathematics to determine the value of a prefix expression on a specific expression tree.

For the preorder traversal of this tree (T), we would start from the right most expression:

Prefix expression = * + 3 + 3 ↑ 3 + 3 3 3

Prefix expression = * + 3 + 3 ↑ 3 6 3

Prefix expression = * + 3 + 3  3⁶  3

Prefix expression = * + 3 3 729 3

Prefix expression = * + 3 732 3

Prefix expression = * 735 3   ⇒ 735 × 3

Value = 2205.

Read more on preorder traversal here: https://brainly.com/question/12947940

#SPJ11

Complete Question:

Given the following prefix expression:

* + 3 + 3 ↑ 3 + 3 3 3

What is the value of the prefix expression?

The correct answer is option A which is segment D which is closer to home.

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

From the given graph we can see that in segment D the distance between the home and the person is lesser than all the segments given in the graph.

Therefore the correct answer is option A which is segment D which is closer to home.

To know more about graphs follow

https://brainly.com/question/25020119

#SPJ1

Answer:

19.25(miles?)

Step-by-step explanation:

Assuming 3.5 is the x value or input of the function

3.5 x 5.5 = 19.25

Answer:

24

Step-by-step explanation:

The question is saying, how many three digit numbers can be made from the digits 3, 4, 6, and 7 but there can't be two of the same digit in them. For example 346 fits the requirements, but 776 doesn't, because it has two 7s.

Okay, on to the problem:

We can do one digit at a time.

First digit:

There are 4 digits that we can choose from. (3, 4, 6, and 7)

Second digit:

No matter which digit we chose for the first digit, there is only going to be 3 of them left, because we already chose one, and you can't repeat that same digit. So there are 3 options.

Third digit:

Using the same logic, there are only 2 options left.

We have 4 choices for the first digit, 3 choices for the second, and 2 for the third.

Hence, this is 4 * 3 * 2 = 24 three-digit numbers that can be made.

The number of passwords that would be allowed if users were allowed to reuse the letters and numbers is 30891577600

The given parameters are:

Password length = 8

Letters = 6

Numbers = 2

There are 26 letters and 10 digits.

Since the letters and the numbers can be repeated, then the number of passwords is:

Count = 26^6 * 10^2

Evaluate

Count = 30891577600

Hence, the number of passwords that would be allowed if users were allowed to reuse the letters and numbers is 30891577600

Read more about combination at:

https://brainly.com/question/11732255

#SPJ1

Answer:

24

Step-by-step explanation:

when you open up the parenthesis, you get -8x-3 which is 24.

negative x negative = positive

Answer:

3

Step-by-step explanation:

The equation of line is y = 92x – 182631. The slope is 92 and the y-intercept is the negative 182631. And the health expenditure in 2010 will be 2289.

Suppose the given points are (x₁, y₁) and (x₂, y₂), then the equation of the straight line joining both two points is given by

[tex]\rm (y - y_1) = \left [ \dfrac{y_2 - y_1}{x_2 - x_1} \right ] (x -x_1)[/tex]

In MODE, (second line), fix the number of decimal places to be 2.

Then the slope and the y-intercept values of the Lin Reg line will round to the nearest hundredth.

(x₁, y₁) → (1997, 1093)

(x₂, y₂) → (2002, 1553)

Then we have

y – 1093 = [(1553 – 1093) / (2002 – 1997)] (x – 1997)

y – 1093 = [460  / 5] (x – 1997)

y – 1093 = 92 (x – 1997)

           y = 92x – 182631

If x = 2010, then the value of y will be

y = 92 × 2010 – 182631

y = 184920 – 192631

y = 2289

Learn more about straight-line equations here:

https://brainly.com/question/380976

#SPJ1

Answer:

Should be C

Step-by-step explanation:

Only the same power number can be use to add or subtract :)

But why is A, B and C same kinda stuff?

The equation equivalent to the simple interest formula A = P(1 + rt), that Celo used is P = A/(1 + rt). Hence, the first option is the right choice.

Equivalent equations are the equations that are transformed from one equation to another equation, but the final values they give are equal. It's just the change of the variable on which the equation is derived.

The simple interest equation that Celo used is A = P(1 + rt).

This is currently used to find the final amount A.

On isolating P to one side of the equation in the following ways:

A = P(1 + rt),

or, A/(1 + rt) = {P(1 + rt)}/(1 + rt) {Dividing both sides by (1 + rt)}.

or, A/(1 + rt) = P {Simplifying}.

or, P = A/(1 + rt) {Changing sides}.

Thus, the equation equivalent to the simple interest formula A = P(1 + rt), that Celo used is P = A/(1 + rt). Hence, the first option is the right choice.

Learn more about equivalent equations at

https://brainly.com/question/22441071

#SPJ4

The expression that represents the product of negative three-fourths x and –8x is 6x^2

The statement is given as:

the product of negative three-fourths x and –8x

Rewrite properly as:

-3x/4 * -8x

Divide 4 and 8 by 4

-3x * -2x

Multiply -3 and -2

6x * x

Multiply x and x

6x^2

Hence, the expression that represents the product of negative three-fourths x and –8x is 6x^2

Read more about expressions at:

https://brainly.com/question/723406

#SPJ1

Answer:

answer is 6x2 or D

Step-by-step explanation:

Answer:

-6

30

22

8x² + 18x + 4

8x² - 2x - 6

Step-by-step explanation:

f(x) = 8x² + 2x - 6

f(0) = 8(0²) + 2(0) - 6 = -6

f(2) = 8(2²) + 2(2) - 6 = 32 + 4 - 6 = 30

f(-2) = 8 × (-2)² + 2(-2) - 6 = 32 - 4 - 6 = 22

f(x + 1) = 8(x + 1)² + 2(x + 1) - 6 = 8(x² + 2x + 1) + 2x + 2 - 6 = 8x² + 18x + 4

f(-x) = 8(-x)² + 2(-x) - 6 = 8x² - 2x - 6

So

[tex]\\ \rm\Rrightarrow r=\sqrt{a^2+b^2}[/tex]

[tex]\\ \rm\Rrightarrow r=\sqrt{(-3)^2+(\sqrt{3})^2}[/tex]

[tex]\\ \rm\Rrightarrow r=\sqrt{9+3}[/tex]

[tex]\\ \rm\Rrightarrow r=\sqrt{12}[/tex]

[tex]\\ \rm\Rrightarrow r=2\sqrt{3}[/tex]

Find theta

[tex]\\ \rm\Rrightarrow \theta=tan^{-1}(\dfrac{y}{x})[/tex]

[tex]\\ \rm\Rrightarrow \theta=tan^{-1}(\dfrac{\sqrt{3}}{3})[/tex]

[tex]\\ \rm\Rrightarrow \theta=tan^{-1}(\dfrac{-1}{\sqrt{3}})[/tex]

[tex]\\ \rm\Rrightarrow \theta=\dfrac{5\pi}{6}[/tex]

Polar form

[tex]\\ \rm\Rrightarrow r(cos\theta+isin\theta)[/tex]

[tex]\\ \rm\Rrightarrow 2\sqrt{3}(cos\dfrac{5\pi}{6}+isin\dfrac{5\pi}{6})[/tex]

Answer:

10hr/m because the average velocity is divided by number

Answer:

y = 1/2 x - 4

Step-by-step explanation:

point slope form would be

( y - - 3) = 1/2 (x-2)       you can re-arrange as

y = 1/2x -4