HW 3 Linear Function Models: Problem 9
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(3 points)
A new highway has just opened and tolls will be collected from vehicles using the highway. The toll will be 119 cents for cars which travel 20 miles of the
highway. The toll will be 184 cents for cars which travel 33 miles of the highway. Let T(d) be a function which gives the total toll (in cents) which will be
charged to a car which travels d miles along the highway. Assume T(d) is a linear function. Find T'(d).
T(d) =
What will be the toll to travel 96 miles?
cents

Answer:

x=

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

The angle in degrees between the two planes is approximately 159.460°.

The equation of the plane, whose form is a · x + b · y + c · z = d is equivalent to this vectorial form (a, b, c) • (x, y, z) = d, where (a, b, c) is the vector of coefficients. The angle between the two planes:

θ = cos⁻¹ [[(a₁, b₁, c₁) • (a₂, b₂, c₂)] / [||(a₁, b₁, c₁)|| · ||(a₁, b₁, c₁)||]]

If we know that (a₁, b₁, c₁) = (1, - 10, - 8) and (a₂, b₂, c₂) = (2, 5, 8), then the angle between the two planes is:

θ = cos⁻¹ [[(1, - 10, - 8) • (2, 5, 8)] / [√165 · √93]]

θ = cos⁻¹ [(-2 - 50 - 64) / √15345]

θ = cos⁻¹ (- 116 / √15345)

θ ≈ 159.460°

The angle in degrees between the two planes is approximately 159.460°.

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Answer:

B

Step-by-step explanation:

None of the provided options are irrational. Irrational numbers are those which cannot be expressed as the ratio of two integers. In other words, if represented in decimal form, they would continue indefinitely after the decimal point, such as the value of π. This also means, by definition, they cannot be both irrational and an integer.

They are all real numbers as they can represent a distance along a line (they could all be plotted on a number line or graph, for instance).

Only 0 and 4 out of the provided options are integers (whole numbers). As mentioned above, all integers are rational by definition.

The equation of a line that is parallel to y = 4x - 7 and goes through the point (4,1) is y = 4x - 15.

Given line: y = 4x - 7

Slope of line m₁ = 4

Two lines are parallel lines when the slopes of the lines are the same.

so, m₁ = m₂

m₂ = 4

Now, the equation of a line with slope 4 and passing through the point (4,1) is:

⇒ y - y₁ = m (x - x₁)

⇒ y - 1 = 4(x - 4)

⇒ y - 1 = 4x -16

⇒ y = 4x - 15

Hence the equation of a line that is parallel to y = 4x - 7 and goes through the point (4,1) is y = 4x - 15.

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The equation of the parabola that has vertex (0, -3) and also passes through the point (-8,5) is y = -1(x - 0)² - 3.

The vertex form of the equation of a parabola is:

y = a(x-h)² + k

where the vertex = (h, k)

The given vertex, (h, k) = (0, -3)

The line passes through the (-8, 5)

x =  -8,  y  =  5

Substitute x = -8, y = 5, h = 0, y = -3 into the equation to solve for a

y = a(x - h)² + k

 5 = a(-8-0)² + (-3)

 5 = a(-8)² - 3

-8a = 5+3

-8a = 8

  a = 8/-8

  a = -1

Substitute a = -1, h = 0, k = -3 into y = a(x - h)² + k

y = -1(x - 0)² - 3

The equation of the parabola that has vertex (0, -3) and also passes through the point (-8,5) is y = -1(x - 0)² - 3

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Answer:

A= (2xy^2)^3. (-1/2x^2yz) (gạch chéo là phần)

B=(-4x3y2z)(  x2y3)3xy

Step-by-step explanation:

ok :)

The total of three consecutive even numbers is 312.

The correct option is A.

Three numbers totaling 312 are consecutive, one of which being 104. Take one of the other numbers from 104=103 and add one to 104=105 for the third.

103 + 104 + 105 = 312.

Consecutive even numbers are consecutive even integers that differ by 2. If x is an even number, then x + 2, x + 4, and x + 6 are also even numbers. The difference between consecutive even numbers is two.

The formula for successive integers is quite simple. If x is the first consecutive integer, x+1 is the next, x+2 is the third, x+3 is the fourth, and so on. Consider the following example. 45 is 'x if it is the first consecutive integer in either a series of numbers.

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The value of the number is 15.

Let the first number be represented by x.

The second number will be:

(2 × x) - 2 = 2x - 2

Therefore, the addition of the numbers will be:

= x + 2x - 2 = 43

3x - 2 = 43

3x = 43 + 2

3x = 45

Divide

x = 45/3

x = 15.

Therefore, the number is 15

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Answer:

Option D: [tex]y=-2[/tex]

Step-by-step explanation:

The line is horizontal, which means the slope is 0. The line also crosses the y-axis at (0,-2). Thus y at 0 is equal to 2.

The equation representing the product of theirs fractions is -

(- 2/7) x (- 3/4)  and on solving this expression, we get 3/14.

In mathematics, fractions are represented as a numerical value, which defines a part of a whole.

Given that Cassie and Amy are playing a card flash game such that Cassie has a card with the fraction - 2/7 and Amy has a card with fraction - 3/7.

The equation that represent the product of their fractions is -

(- 2/7) x (- 3/4)

Now, solving the above expression, we get -

(- 2/7) x (- 3/4)

(1/7) x (3/2)

3/14

Therefore, the equation representing the product of theirs fractions is -

(- 2/7) x (- 3/4)  and on solving this expression, we get 3/14.

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Answer:

  5 + 10 + 15 = 30

Step-by-step explanation:

You want a sum of three multiples of 5 that does not end in 5.

Any odd multiple of 5 will end in 5. An even multiple will not.

In order for the sum to not end in 5, the total of the multipliers must be even:

  1×5 +2×5 +3×5 = 6×5 = 30

  5 +10 +15 = 30 . . . . . . three multiples of 5 whose sum does not end in 5

Answer:4

Step-by-step explanation:4(5x+6) = 4[tex]x[/tex]5x=20x   4[tex]x[/tex]6=24

Answer:

The answer is 4.

4 * 5x = 20x

4 * 6 = 24

So the result we get is 20x + 24

A random sample and a non-random sample for this situation are given below:

This refers to the statistical population where there is an equal chance of being selected by members of a population.

Hence, we can see that a random sample and a non-random sample for this situation are given above and this shows that each of them have equal chances of being selected (random sampling)

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The dimensions of a rectangle with an area of 12 ft.² and a diagonal of 5 feet are 4 feet and 3 feet.

From the information, we are given that the dimensions of a rectangle with an area of 12 ft.² and a diagonal of 5 feet.

It should be noted that the number will be:

= 4 × 3 = 12 ft²

It should be noted that 4² + 3² = 25 and the square root will give 5 which is also the diagonal.

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Answer: x=16

DF=105

Step-by-step explanation:

DF=DE+EF
9x-39=47+3x+10

9x-39=57+3x

9x=96+3x

6x=96

x=16

DF=9x-39

DF=9(16)-39

DF=144-39

DF=105

Answer:V≈113.1

Step-by-step explanation:

d Diameter 6

V=4

3πr3

d=2r

Solving forV

V=1

6πd3=1

6·π·63≈113.09734

Answer:If you use a graph and a table to solve an equation that shows two expressions equal to one another, how can you use algebra to check your answer? Choose the correct answer below. A. Rewrite the equation as two new equations, with the expression on each side of the original equation set equal to the answer you are checking, which is an estimate. Check to see if solving each of the new equations gives values of x  that are close to each other. If they are too far from each other, you may need to reexamine the table and graph. B. Input the answer into each expression and simplify. Check to see if the result gives exactly the same number on each side. If the numbers are not exactly equal, you may need to reexamine the table and graph. C. Input the answer into each expression and simplify. Check to see if the result, which is an estimate, gives numbers on each side which are close to each other. If they are too far from each other, you may need to reexamine the table and graph. D. Rewrite the equation as two new equations, with the expression on each side of the original equation set equal to the answer you are checking. Check to see if solving each of the new equations gives exactly the same values of x . If they are not equal, you may need to reexamine the table and graph.

Step-by-step explanation:

Using translation concepts, the vertices of the triangle after the rotation are given as follows:

G'(2,-2), E'(5,-4), F'(5,-1).

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

The rule for a 90º counterclockwise rotation around the origin is:

(x,y) -> (-y,x).

Hence the vertices should be given by:

The correct translation is graphed at the end of the question. You are doing a good job, just there was two small mistakes on the rule :).

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Rotation of a point through 189° about the origin When a point C(h, k) is rotated through 180° in either an anticlockwise or clockwise direction about the origin O, it takes the new position D(-h, -k).

The rotation formula will give us the precise location of a point after a finite degree of rotation. The rotation formula is determined by the type of rotation applied to the point in relation to the origin. A geometric two-dimensional shape can undergo four major types of transformation.

The rotation formula describes how a point rotates with respect to the origin. The rotation formula is used to determine the position of a point after it has been rotated. A rotation is a circular motion around a specific axis or point of rotation. In general, rotation can be done in two ways: clockwise and anti-clockwise or counter-clockwise.

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Answer:

A.

Step-by-step explanation:

[tex]0.75 > 7/12(0.58)[/tex]

Answer:

A

Step-by-step explanation:

0.58= 7/12 so 0.75 is more then -.8 so that is true.

The probability the at least of the people selected from 5 is vaccinated is 0.997.

The binomial distribution is a statistical probability distribution that summarizes the likelihood of a value taking one of two independent values under the specific set of assumptions or assumptions.

Because the five randomly chosen people are independent, the probability that they're all unvaccinated is (0.47)⁵,

The probability that at least one among them 5 has been vaccinated is;

= 1 - (0.47)⁵

= 0.997

Therefore, the probability that at least one of the five people chosen is vaccinated is 0.997.

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Answer:

use a calculator

Step-by-step explanation: the calculator doesn't lie I used a calculator

Answer:

1,000,000

Step-by-step explanation:

The value of (9)14+(−9)+(−9)14 is -9

The concept is used to Solve is BODMAS

(9)14+(−9)+(−9)14

126-9-126=-9

BODMAS, also known as the order of operations, is a series of operations in an arithmetic statement. Math is all about logic and certain common principles that help us with our calculations. So BODMAS is one of the basic principles for simplifying multi-operator formulations.

An expression or equation in arithmetic has two components:

Numbers \Operators

A character that combines two integers to form an expression or equation is known as an operator. The most popular operators in mathematics are Addition (+), Subtraction (-), Multiplication (), and Division (). Finding the solution to mathematical statements or equations with only one operator is rather straightforward.

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The true statement about the angles of the triangle OPQ  is the third statement that is  m∠P < m∠O < m∠Q.

It is given that:-

In triangle OPQ,

PQ = 19

QO = 11

OP = 20

We have to find which one of the six statements given in the question is correct.

We know that, in a triangle, if one side of the triangle is longer than the other side, then the angle opposite to the longer side will be larger than the angle opposite the shorter side.

Hence,

In triangle OPQ,

Angle opposite to side OP = ∠Q

Angle opposite to side PQ = ∠O

Angle opposite to side QO = ∠P

As,

QO < PQ < OP , Hence,

m∠P <  m∠ O < m∠Q

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In linear equation , 40   is the number of  minutes until they meet again at the  starting line.

What is  linear equation?

Juan walks  1/8  of a lap in one  minute

joe walks 1/10 of a  lap in one minute

The LCM of 8 and 10  = 40  = the number of  minutes until they meet again at the  starting line

In that time  Juan   walks  (1/8) * 40    = 5 laps

And Juan walks  (1/10)*40   = 4 laps

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Answer:

length = 105 yd

width = 35 yd

Step-by-step explanation:

Let L = length and W = width.

L = 3W

perimeter = 2(L + W)

280 =2(L + W)

L = 3W

We have a system of 2 equations. Let's use the substitution method to solve it. Substitute 3W for L in the first equation.

280 = 2(3W + W)

140 = 4W

W = 35

L = 3W = 3(35) = 105

length = 105 yd

width = 35 yd

The expression for the sum of 1 cubed, 2cubed and 3 cubed is 1² + 2³ + 3³ and the value is 36.

It should be noted that the information is to find the expression for the sum of 1 cubed, 2cubed and 3 cubed.

This will be:

= 1³ + 2³ + 3³

= 1 + 8 + 27

= 36

Therefore, the correct answer is 36.

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the tangent is only horizontal at the critical points of the equation, so

[tex]y=2x^3+3x^2-12x+3\implies \cfrac{dy}{dx}=6x^2+6x-12\implies \cfrac{dy}{dx}=6(x^2+x-2) \\\\\\ \stackrel{\textit{setting the derivative to 0}}{0=6(x^2+x-2)}\implies 0=x^2+x-2 \\\\\\ 0=(x+2)(x-1)\implies \boxed{x= \begin{cases} -2\\ 1 \end{cases}} \\\\[-0.35em] ~\dotfill\\\\ y=2(-2)^3+3(-2)^2-12(-2)+3\implies y=-16+12+24+3\implies \boxed{y=23} \\\\\\ y=2(1)^3+3(1)^2-12(1)+3\implies y=2+3-12+3\implies \boxed{y=-4} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \text{\LARGE (-2~~,~~23)\qquad (1~~,~~-4)}~\hfill[/tex]

Answer:

Step-by-step explanation:

The third term of the geometric progression will be 1 / 27 with common ratio 2 / 3.

We are given that:

2nd term of geometric progression = 1 / 18

5th term = 4 / 243

Now, we can also write it as:

2nd term = a r ( where r is the common ratio and a is the initial term.)

a r = 1 / 18

5th term = a r⁴

a r⁴ = 4 / 243

Now divide 5th term by 2nd term, we get that:

a r⁴ / a r = ( 4 / 243 ) / ( 1 / 18 )

r³ = 72 / 243

r³ = 8 / 27

r = ∛ (8 / 27)

r = 2 / 3

3rd term = a r²

a r² = a r × r

= 1 / 18 × 2 / 3

3rd term = 1 / 27

Therefore, the third term of the geometric progression will be 1 / 27 with common ratio 2 / 3.

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Your question was incomplete. Please refer the content below:

The 2nd and 5th term of a GP are 1/18 and 4/243 respectively find the 3rd term