unit linear relationships student handout 1 answer key

Answer:

y = -1/35x + 71/35

Step-by-step explanation:

slope of the perpendicular line = -1/35  (the negative reciprocal of 35)

use the point (1,2) and the point-slope form:

y - 2 = -1/35(x - 1)  now put it in slope-intercept form

y = -1/35x + 1/35 + 2

y = -1/35x + 71/35

0r,  y = -1/35(x - 71)

The equation of the line perpendicular to y = 35x − 4 and passing through the point (1, 2) is y = (-1/35)x + 71/35.

To find the equation of the line perpendicular to y = 35x − 4 and passing through the point (1, 2), we need to follow these steps:

y - 2 = (-1/35)(x - 1)

y - 2 = (-1/35)x + 1/35
y = (-1/35)x + 1/35 + 2
y = (-1/35)x + 71/35

So, the equation of the line perpendicular to y = 35x − 4 and passing through the point (1, 2) is y = (-1/35)x + 71/35.

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The solution for this system is (x,y,z) = (4,3,-2).

To solve this system of equations using Gaussian Elimination, start by adding 3 times the first equation to the second equation, then add 5 times the first equation to the third equation. This will give you a new set of equations in the following form:

x-3y+z=4

0+y-2z=5

0-8y+10z=24

Now, you can use Gaussian Elimination to solve for y and z. Subtract the second equation from the third equation to solve for z, then use that answer to solve for y in the second equation.

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Answer:

y=-x-2

Step-by-step explanation:

All of them are solved, but I will help to find the relationship.

I found the pattern in my head as I thought about absolute value and proportionality.

Feel free to ask more questions.

Zachary will need to earn a score of 23 on his sixth quiz to have a mean score of 22 for all six quizzes.

To find out what score Zachary needs to earn on his sixth quiz to have a mean score of 22,

We need to use the formula for the mean (or average) of a set of numbers:

Mean = (sum of all the scores) / (number of tests)

Zachary's mean score for the first five quizzes is 22.

Using the above as a guide, we have the following:

(20 + 25 + 22 + 18 + 24 + x) / 6 = 22

Evaluate the like terms

(109 + x) / 6 = 22

So, we have

109 + x = 132

Evaluate the like terms

x = 23

Hence, the score must be 23

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The remaining balance after the lease ends, given the information would be B. $ 12,160.26.

The remaining balance after the lease ends can be found by the formula :

= Value of lease - Amount paid towards principal over 3 years - down payment

Amount paid towards principal over 3 years :

= ( 429. 95 x 70 % ) x 12 months x 3 years

= $ 10, 834. 74

The remaining balance is therefore :

= 23, 495 - 10, 834. 74 - 500

= $ 12, 160. 26

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The first part of the question is:

You lease a car valued at $23,495.00 for 3 years at $429.95/month with a $500.00 down payment. If interest is 30% of the payments.

Answer:

Step-by-step explanation:

He received $16.20

because 30% of $54.00 is $16.20

Answer:

277

Step-by-step explanation:

Just add lol

Inequality g ≤ 26.4  means that the amount of fuel the truck can hold (represented by g) is at most 26.4 gallons.

What is Inequality ?

In mathematics, an inequality is a comparison between two values that shows whether they are larger than, less than, equal, or greater than or equal to each other.

Common symbols for inequalities include (less than), > (greater than), (less than or equal to), and (greater than or equal to).

The inequality that shows this would be:

g ≤ 26.4

This reads as "g is less than or equal to 26.4".

Therefore, g ≤ 26.4 means that the amount of fuel the truck can hold (represented by g) is at most 26.4 gallons.

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The explicit formula for an, the nth term of the sequence is a(n) = 7(2)^n-1

From the question, we have the following parameters that can be used in our computation:

7, -14,28,..

The above definitions imply that we simply multiply -2 to the previous term to get the current term

Using the above as a guide,

So, we have the following representation

First term, a = 7

Common ratio, r = -2

The sequence is represented as

a(n) = a(r)^n-1

So, we have

a(n) = 7(2)^n-1

Hence, the sequence is a(n) = 7(2)^n-1

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The value of (g - f) (x) is -3x² + 2x - 4

The value of (f + g) (x) is 3x² + 6x - 6.

The value of (g / f) (x) is (4x - 5) / (3x² + 2x - 1).

The value of (fg) (x) is 12x³ - 7x² -14x + 5.

The solution has been obtained by using operations on functions.

What are operations on functions?

Similar to how we operate on the terms of the functions, we can add, subtract, multiply, and divide functions with overlapping domains using the operations on functions.

We are given f(x) = 3x² + 2x - 1 and g(x) = 4x - 5

(g - f) (x)

⇒(g - f) (x) = g(x) - f(x)

⇒(g - f) (x) = (4x - 5) - (3x² + 2x - 1)

⇒(g - f) (x) = 4x - 5 - 3x² - 2x + 1

⇒(g - f) (x) = 2x - 4 - 3x²

⇒(g - f) (x) = -3x² + 2x - 4

(f + g) (x)

⇒(f + g) (x) = f(x) + g(x)

⇒(f + g) (x) = (3x² + 2x - 1) + (4x - 5)

⇒(f + g) (x) = 3x² + 2x - 1 + 4x - 5

⇒(f + g) (x) = 3x² + 6x - 6

(g / f) (x)

⇒(g / f) (x) = g(x) / f(x)

⇒(g / f) (x) = (4x - 5) / (3x² + 2x - 1)

(fg) (x)

⇒(fg) (x) = f(x) * g(x)

⇒(fg) (x) = (3x² + 2x - 1) * (4x - 5)

⇒(fg) (x) = 12x³ - 7x² -14x + 5

Hence, the required solutions have been obtained.

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Let's assume, if 10 out of 20 houses in the neighborhood are participating in the yard sale, the percentage of the neighborhood participating in the yard sale would be 50%.

A number or ratio that can be stated as a fraction of 100 is a percentage. If we need to compute a percentage of a number, we should divide it by its entirety and then multiply it by 100. The percentage therefore refers to a component per hundred. Per 100 is what the word percent implies. The letter "%" stands for it.

To calculate the percentage of the neighborhood participating in the yard sale, divide the number of houses participating by the total number of houses in the neighborhood and multiply by 100. For example, if 10 out of 20 houses in the neighborhood are participating in the yard sale, the percentage of the neighborhood participating in the yard sale would be 50%.

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675 cases divided by 135 cases per order equals five orders each year

a) If you order one case at a time, your yearly inventory cost is $6,750. This means that if you order one case of beans each year, it will cost you a total of $6,750.

b) To minimize your annual inventory cost, you should order 135 cases at a time. This is the number of cases that produces the minimum value for the cost equation, C = 200Q + 5,750.

c) By ordering 135 cases at a time instead of one, you will save $3,750 each year in inventory costs.

d) When you are minimizing your annual inventory cost, you should place your orders every five years. This is because 675 cases divided by 135 cases per order equals five orders each year.

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Answer:

10:21 AM

Step-by-step explanation:

To get the answer you subtract 4 hours and 47 mins from 3:08 pm

4 hours and 47 minutes before 3:08 pm is 10:21 am.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

To find the time 4 hours and 47 minutes before 3:08 pm, we can subtract 4 hours and 47 minutes from 3:08 pm.

First, let's convert 3:08 pm to 24-hour format:

3:08 pm = 15:08

Now we can subtract 4 hours and 47 minutes:

15:08 - 4:47 = 10:21

Therefore,

4 hours and 47 minutes before 3:08 pm is 10:21 am.

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The trigonometric equation [tex]\frac{2tanx}{1+tan^2x}[/tex] is equivalent to sin2x

An equation is an expression that shows how numbers and variables are related using mathematical operators like exponent, addition, multiplication, subtraction and division.

Trigonometric identity is used to show relationship between trigonometric functions. Some examples are:

1 + tan²x = 1/cos²x; tanx = cosx/sinx; sin2x = 2sinxcosx

Given:

[tex]\frac{2tanx}{1+tan^2x} \\\\but\ 1+tan^2x=\frac{1}{cos^2x};substituting:\\ \\= \frac{2tanx}{\frac{1}{cos^2x} } \\\\=2tanx*cos^2x\\\\=2*\frac{sinx}{cosx}*cos^2x\\ \\=2sinxcosx[/tex]

= sin2x

The trigonometric equation are equivalent.

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The new coordinates of the point (7, -4) after a 180-degree rotation are (-7, 4).

Transform the shapes on a coordinate plane by rotating, reflecting, or translating them. Felix Klein introduced transformational geometry, a fresh viewpoint on geometry, in the 19th century.

Here,
To find the new coordinates of the ordered pair (7, -4) after a 180-degree rotation,
Following the trasformation of 180-degree rotation,

(x, y) ⇒ (-x, -y)

So,
(7, -4) ⇒ (-7, 4)

Therefore, the new coordinates of the point (7, -4) after a 180-degree rotation are (-7, 4).

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The correct answer to the listed problems above in their correct scientific notation would be :

1.) 76,450,000 =7.645×10⁷

2.) 0.000327 = 3.27 × 10^-4

3.) 34,000 = 2.4 × 10⁴

4.) 116,000,000,000, = 1.16 × 10¹¹

5.) 0.024= 2.4× 10^-2

6.) 2,800= 2.8× 10³

7.) 100= 1 × 10²

8.) 0.00000qq= q.q × 10^-6

9.) q00,000= q × 10⁵

10.) 0.00633= 6.33 × 10^-3

Scientific notation is defined as a form that can be used to represent cumbersome numbers or very small numbers in a way that is most convenient.

The correct scientific notation of the given values are listed below with reasons:

1.) 76,450,000 =7.645×10⁷ and not =7.645×10⁸ when the decimal point is moved so that there is 1 non-zero value in front of the decimal point, the number of zero is 8 not 7.

2.) 0.000327 = 3.27 × 10^-4 and not 3.27 × 10⁴ as the value is less than 1.

3.) 34,000 = 3.4 × 10⁴. Correctly written.

4.) 116,000,000,000, = 1.16 × 10¹¹. Should be 11 not q.

5.) 0.024= 2.4× 10^-2 and not 24 × 10^-2

6.) 2,800= 2.8× 10³. Correctly written.

7.) 100= 1 × 10² and not 1 × 10³

8.) 0.00000qq= q.q × 10^-6. Correctly written.

9.) q00,000= q × 10⁵ and not q × 10^-5

10.) 0.00633= 6.33 × 10^-3 and not 63.3 × 10^-3. This is because the decimal point should be placed immediate after the first whole number.

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Answer: 6

Step-by-step explanation:

Let's start with what we know. We have the following equation:

x^2 + 7 = 43

Now, we subtract 7 from both sides.

x^2 = 36

Then we take the square root of both sides giving our final answer:

x = 6.

Answer:A

n open circle on the -1 and a closed circle on the 1.

Step-by-step explanation:

I belive it would be this.

Answer:

A closed circle on the -1 and a closed circle on the 1.

Step-by-step explanation:

|x| = 1

x = 1 or -x = 1

x = 1 or x = -1

Answer: A closed circle on the -1 and a closed circle on the 1.

The monthly payment on a 30-year, $100,000 mortgage with an interest rate of 6 percent is $599.55.

To find the monthly payment on a 30-year, $100,000 mortgage with an interest rate of 6 percent, we need to use the following formula:

Monthly Payment = (Loan Amount * Interest Rate) / (1 - (1 + Interest Rate)^(-Number of Payments))

First, we need to convert the interest rate from a percentage to a decimal by dividing it by 100:

Interest Rate = 6 / 100 = 0.06

Next, we need to calculate the number of payments over the life of the loan. Since there are 12 months in a year, and the loan is for 30 years, the number of payments is:

Number of Payments = 12 * 30 = 360

Now we can plug these values into the formula:

Monthly Payment = ($100,000 * 0.06) / (1 - (1 + 0.06)^(-360)) = $599.55

Therefore, A $100,000 mortgage with a 30 year term and a 6% interest rate has a $599.55 monthly payment.

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The value of a₄ is,

⇒ a₄ = 108

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

The value is,

⇒ a₁ = - 4

And, [tex]a_{n} = - 3a_{n - 1}[/tex]

Now, We can put n = 2;

⇒ a₂ = - 3 a₁

⇒ a₂ = - 3 x - 4

⇒ a₂ = 12

Put n = 3;

⇒ a₃ = - 3 a₂

⇒ a₃ = - 3 x 12

⇒ a₃ = - 36

Put n = 4;

⇒ a₄ = - 3 a₃

⇒ a₄ = - 3 x - 36

⇒ a₄ = 108

Thus, The value of a₄ is,

⇒ a₄ = 108

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Value of a₄ in sequence is -108.

In mathematics, geometric sequence, also known as a a geometric progression, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

Given,

a₁ = 4 and aₙ = -3aₙ₋₁

a₂ = -3a₂₋₁

a₂ = -3a₁

a₂ = -3(4)

a₂ = -12

a₃ =  -3(-12)

a₃ = 36

a₄ = -3a₄₋₁

a₄ = -3a₃

a₄ = -3(36)

a₄ = -108

Hence, -108 is value of a₄ of the sequence.

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The solution is w = 9/5.

Solve for w.



Start by multiplying both sides by (w-1)(w+2):



(w+7)(w+2) = (w+5)(w-1) + (w-1)(w+2)



Simplifying:



w² + 9w + 14 = w² + 4w + 5



Subtracting w² + 9w + 14 from both sides:



0 = -5w - 9



Dividing by -5:



w = 9/5



The solution is w = 9/5.

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The volume of cylinder is 3799.4 cubic feet when diameter is 22 ft and height is 10 feet.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

Let us find the volume of the cylinder which has diameter of 22 ft and height of 10 feet.

Diameter=2radius

Radius=22/2=11 feet.

V=πr²h

=3.14×11²×10

=3799.4 cubic feet.

Hence, the volume of cylinder is 3799.4 cubic feet when diameter is 22 ft and height is 10 feet.

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Answer:

Step-by-step explanation:

665,280 dived by 3 = 221760

221760 = distance

221760 = per 1 hour

I tried my best :}

Therefore, for the first  coordinate point (-x, y), the ultimate reflected points are (-x, -y) and (-x, -y), and for the second point, they are (x, -y) and (-x, -y) .

A coordinate system is a technique used to precisely find points or additional mathematical objects on a distance, such as Euclidean space, by using one or so more values or coordinates. To find a point or item on a double plane, one uses coordinates, which are pairs of numbers. Two numbers called the y and x matrices are used to describe a point's location on a two-dimensional plane. a set of numbers used to identify specific locations.

Here,

The x-coordinate remains constant and the y-coordinate is cancelled when a point on the coordinate plane is reflected over the x-axis (i.e. multiplied by -1). The y-coordinate remains constant and the x-coordinate is cancelled when a point is reflected over the y-axis.

Let's mirror the point (-2, 3) first over the x-axis and then over the y-axis as an illustration:

The x-coordinate remains constant while the y-coordinate is cancelled when reflecting over the x-axis. In light of this, the argument is (-2, -3).

The x-coordinate is cancelled while the y-coordinate remains constant when reflecting over the y-axis. In light of this, the argument is (2, -3).

We can reflect the coordinates (-x, y) and (x, -y) over the x-axis and then over the y-axis:

Therefore, for the first point (-x, y), the ultimate reflected points are

(-x, -y) and (-x, -y), and for the second point, they are (x, -y) and (-x, -y) .

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Therefore, Roberto needs 26 more inches of lumber. Answer: 26 inches.

an explanation of the relationship between the two phrases on either side of a sign. A single variable and an equal sign are typically present. It is equivalent to this 2. 2x - 4 Equals 2. The variable x is present in the earlier instance.

To solve this problem, we need to convert all the measurements to the same units. Let's convert 6 feet and 8 inches to inches:

6 feet = 6 x 12 inches = 72 inches

6 feet and 8 inches = 72 + 8 = 80 inches

So Roberto needs 80 inches of lumber to repair the deck.

He has 54 inches of lumber, so he needs:

80 - 54 = 26 inches

Therefore, Roberto needs 26 more inches of lumber. Answer: 26 inches.

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The height of the formation is [tex]31meter[/tex], to the nearest meter.

Height, altitude, and elevation all refer to the vertical distance between something's top and bottom or its base but something above it. Height is used to describe everything that may be measured vertically, high or low.

In essence, height relates to elevation, which is the height above a certain level. Furthermore, height refers to any quantifiable distance above a particular level as well as extend upwards (as it is from foot to head). For instance, the elevation of a tower, tree, person, mountain, etc.

We can use the tangent function to calculate the formation's height.

[tex]tan(36^{0} )=\frac{h}{3}[/tex]

Here, we have to multiply both sides by [tex]43[/tex] we get,

[tex]43tan(36^{0} )=h[/tex]

[tex]h=31meter[/tex]

Therefore, the height of the formation to the nearest meter is [tex]31meter[/tex].

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Answer: Read the step by step explanation for the answer

Step-by-step explanation:

We can use the Pythagorean theorem to find the hypotenuse of the right triangle formed by the given point (4, 3) and the origin (0, 0):

r = √(4² + 3²) = 5

Then we can use the coordinates of the point (4, 3) to determine the values of the trigonometric functions:

sin(θ) = opposite/hypotenuse = 3/5

cos(θ) = adjacent/hypotenuse = 4/5

tan(θ) = opposite/adjacent = 3/4

csc(θ) = hypotenuse/opposite = 5/3

sec(θ) = hypotenuse/adjacent = 5/4

cot(θ) = adjacent/opposite = 4/3

Therefore, the values of the six trigonometric functions of θ are:

sin(θ) = 3/5

cos(θ) = 4/5

tan(θ) = 3/4

csc(θ) = 5/3

sec(θ) = 5/4

cot(θ) = 4/3

The measure of the height of the tin in mm can be found using the steps below.

Measurement is the method of comparing the properties of a quantity or object using a standard quantity.

Measurement is essential to determine the quantity of any object.

Here, the activity is to measure the height of a tin.

Height of the tin is the vertical distance from the base of the tin to the top of the tin.

The height of the tin is the exact straight line measurement when the tin is placed upright on a flat surface.

The measurement has to be in millimeters.

So the best tool is the ruler.

Place the ruler vertically with the point 0 at the base line of the tin.

Mark the point in millimeters that the ruler coincides with the top of the tin.

Read the height to the nearest millimeter.

Hence the height of the tin can be measured as above.

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The values of x in the given equation, (x-7)^2=36, are x = 13 and x = 1. The correct options are the first and second options - x = 13 and x = 1

From the question, we are to determine the values of x in the given equation. The given equation is:

(x-7)^2=36

To solve the equation (x-7)^2=36, we can take the square root of both sides and solve for x:

(x-7)^2 = 36

Taking the square root of both sides:

x - 7 = ±6

Adding 7 to both sides:

x = 7 ± 6

So we get two possible values of x:

x = 7 + 6 or x = 7 - 6

x = 13 or x = 1

Hence, the correct values of x are:

x = 13

x = 1

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To find a plane containing a point P not on a given line l and parallel to l, we can follow these steps:

Choose any point Q on the line l.

Find the vector v that connects point Q to point P, i.e., v = P - Q.

Find the direction vector d of the line l.

Take the cross product of the direction vector d and the vector v, denoted by d x v.

The plane that contains point P and is parallel to line l can be represented by the equation ax + by + cz = d, where (a, b, c) is the vector d x v, and x, y, and z are the coordinates of any point on the plane.

Here's an example to illustrate the process:

Let's say we have a line l that passes through points A(1, 2, 3) and B(4, 5, 6), and a point P(7, 8, 9) not on the line. We want to find a plane containing point P and parallel to line l.

Choose any point Q on the line l. Let's choose Q(1, 2, 3) for convenience.

Find the vector v that connects point Q to point P: v = P - Q = (7-1, 8-2, 9-3) = (6, 6, 6).

Find the direction vector d of the line l: d = (4-1, 5-2, 6-3) = (3, 3, 3).

Take the cross product of the direction vector d and the vector v: d x v = <3, 3, 3> x <6, 6, 6> = <0, 18, -18>.

Write the equation of the plane: 0x + 18y - 18z = d. Since the plane is parallel to line l, we know that the coefficients of x, y, and z are all 0, except for the coefficients of y and z, which are the components of the vector d x v. Therefore, the equation simplifies to 18y - 18z = 0, or y - z = 0.

So the plane containing point P(7, 8, 9) and parallel to the line passing through points A(1, 2, 3) and B(4, 5, 6) can be represented by the equation y - z = 0.

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