Unit 4: Lesson 9: Parallel and Perpendicular Lines Unit Test Parallel and Perpendicular Lines does anyone have the answers for this 13 question test ??

Answer:

y = 3x - 11

Step-by-step explanation:

y=mx+b

1=3(4)+b

1=12+b

b=-11

Answer:

y = 3x –11

or 3x – y = 11 Standard form

Explanation:

using slope-intercept form, calculate b

1 = 3(4) + b

1= 12 + b

1 –12 = b

–11 = b rewrite the equation using this value.

y = 3x –11

The mean absolute deviation is 0.75

To calculate the mean absolute deviation (M.A.D.), you need to find the average of the absolute differences between each data point and the mean of the data set

From the information given, we have that the data set is;

8 9 9 7 8 6 9 8

Let's calculate the mean, we get;

Mean = (8 + 9 + 9 + 7 + 8 + 6 + 9 + 8) / 8

Mean = 64 / 8

Divide the values

Mean = 8

Let's determine the absolute difference, we get;

Absolute differences=

|8 - 8| = 0

|9 - 8| = 1

|9 - 8| = 1

|7 - 8| = 1

|8 - 8| = 0

|6 - 8| = 2

|9 - 8| = 1

|8 - 8| = 0

Find the mean of the absolute differences:

Average of absolute differences = (0 + 1 + 1 + 1 + 0 + 2 + 1 + 0) / 8

Absolute difference = 6 / 8 = 0.75

Learn more about mean absolute deviation at: https://brainly.com/question/447169

#SPJ1

Answer:84

Step-by-step explanation:

Answer:

84 hamburgers were sold

We can integrate this S = 2π ∫(1.1 to 4.4) (5√(4x + 25))/(2√x) dx over the given interval (1.1 to 4.4) to find the surface area.

We can evaluate the integral using numerical methods or a calculator to find the final answer.

We have,

To find the surface area of the revolution about the x-axis of the function f(x) = 5√x over the interval (1.1 to 4.4), we can use the formula for the surface area of revolution:

S = ∫(a to b) 2πy√(1 + (f'(x))²) dx

In this case,

f(x) = 5√x, so f'(x) = (d/dx)(5√x) = 5/(2√x).

Let's calculate the surface area:

S = ∫(1.1 to 4.4) 2π(5√x)√(1 + (5/(2√x)²) dx

Simplifying the expression inside the integral:

S = ∫(1.1 to 4.4) x 2π(5√x)√(1 + 25/(4x)) dx

Next, we can integrate this expression over the given interval (1.1 to 4.4) to find the surface area.

To find the surface area of revolution about the x-axis of the function

f(x) = 5√x over the interval (1.1 to 4.4), we need to evaluate the integral:

S = ∫(1.1 to 4.4) 2π(5√x)√(1 + 25/(4x)) dx

Let's calculate the integral:

S = 2π ∫(1.1 to 4.4) (5√x)√(1 + 25/(4x)) dx

To simplify the calculation, let's simplify the expression inside the integral first:

S = 2π ∫(1.1 to 4.4) (5√x)√((4x + 25)/(4x)) dx

Next, we can distribute the square root and simplify further:

S = 2π ∫(1.1 to 4.4) (5√(4x + 25))/(2√x) dx

Thus,

We can integrate this expression over the given interval (1.1 to 4.4) to find the surface area.

We can evaluate the integral using numerical methods or a calculator to find the final answer.

Learn more about the surface area of revolutions here:

https://brainly.com/question/32268747

#SPJ1

Answer:

Oliver needs to sell enough fruit to cover the production cost of 50 pineapples in order to turn a profit. If he sells each fruit at a rate of $x, how many fruits does he need to sell to break even on the production cost of all 50 pineapples?

Assuming that producing 50 pineapples cost $200, Oliver must sell fruits worth more than $200 to cover this cost. He must sell at least 50 pineapples at the rate of $x to break even on the production cost of all 50 pineapples.

Therefore, the minimum amount of fruit he needs to sell is calculated as:

$200/$x + 50.

Answer:

If Oliver sells each fruit at $5, then he must sell at least 40 fruits to cover the cost of producing all 50 pineapples ($200 / $5 per fruit = 40 fruits). To make a profit, he must sell more than 40 fruits.

If Oliver sells each fruit at $10, then he must sell at least 20 fruits to cover the cost of producing all 50 pineapples ($200 / $10 per fruit = 20 fruits). To make a profit, he must sell more than 20 fruits.

If Oliver sells each fruit at $15, then he must sell at least 14 fruits to cover the cost of producing all 50 pineapples ($200 / $15 per fruit = 13.33 fruits, rounded up to 14 fruits). To make a profit, he must sell more than 14 fruits.

Step-by-step explanation:

Sorry but I hope that helped you :)

Answer:

x=10,y=120

Step-by-step explanation:

3x-30=60 CDA

3x=30

x=10

again,

y+60=180 straight line

y = 120

The length of e is 29.53 inches.

In the following, the law of sine is presented in detail: In a triangle, the sine of angle A divided by side "a" equals the sine of angle B divided by side "b" equals the sine of angle C divided by side "c".

Given:

f= 33 inches

<F= 140, <D = 5

Now,

<E= 180 - (<F+ <D) = 180 - (140 + 5) = 35

Using Sine law

sin F / f = sin E/ e

sin 140 / 33 = sin 35 / e

0.642/ 33 = 0.573 / e

0.0194 e= 0.573

e= 29.53 inches

Hence, the length of e is 29.53 inches.

Learn more about sine law here:

https://brainly.com/question/17289163

#SPJ1

Answer:The reciprocal of 2/3 is 3/2. The product of 2/3 and its reciprocal 3/2 is 1.

Step-by-step explanation:

Answer:

The answer is below

Step-by-step explanation:

1

a) The symmetric equations for the line that passes through the point (a, b, c) and is parallel to the vector (e, f, g) is:

\(\frac{x-a}{e}=\frac{y-b}{f} =\frac{z-c}{g}\)

Therefore using the above equation to Find symmetric equations for the line that passes through the point  (4, −4, 8) and is parallel to the vector (−1, 4, −3) we get:

\(\frac{x-4}{-1}=\frac{y-(-4)}{4}=\frac{z-8}{-3} \\\\Therefore:\\\\\frac{x-4}{-1}=\frac{y+4}{4}=\frac{z-8}{-3}\)

b)i) The line would intersect the xy plane where z = 0. Hence:

\(\frac{x-4}{-1}=\frac{y+4}{4}=\frac{0-8}{-3}\\\\\frac{x-4}{-1}=\frac{y+4}{4}=\frac{8}{3} \\\\\frac{x-4}{-1}=\frac{8}{3}\ and\ \frac{y+4}{4}=\frac{8}{3}\\\\x=\frac{4}{3}\ and\ y=\frac{20}{3} \\\\Therefore\ the\ line\ intersect\ the\ xy\ plane\ at\ (\frac{4}{3},\frac{20}{3},0)\)

ii) The line would intersect the yz plane where x = 0. Hence:

\(\frac{0-4}{-1}=\frac{y+4}{4}=\frac{z-8}{-3}\\\\\frac{y+4}{4}=\frac{z-8}{-3}=4\\\\\frac{y+4}{4}=4\ and\ \frac{z-8}{-3}=4\\\\y=12\ and\ z=-4 \\\\Therefore\ the\ line\ intersect\ the\ yz\ plane\ at\ (0,12,-4)\)

iii) The line would intersect the xz plane where y = 0. Hence:

\(\frac{x-4}{-1}=\frac{0+4}{4}=\frac{z-8}{-3}\\\\\frac{x-4}{-1}=\frac{z-8}{-3}=1\\\\\frac{x-4}{-1}=1\ and\ \frac{z-8}{-3}=1\\\\x=3\ and\ z=5 \\\\Therefore\ the\ line\ intersect\ the\ xz\ plane\ at\ (3,0,5)\)

2)

Let the points be A(−6, 4, 1) and B(2, 6, 5). Let O be the midpoint of the two points A and B. Therefore O is the average of the x coordinates, y coordinates and z coordinate.

\(0=\frac{1}{2} (-6+2,4+6,1+5)=(- 2,5,3)\\\\\)

The normal vector (n) in the direction of line between A and B is:

n = AB = B - A = (2, 6, 5) - (−6, 4, 1) = (8, 2, 4)

n = 8x + 2y + 4z

The equation of the plane based on the normal vector and the midpoint 0 is:

Plane = 8x + 2y + 4z  = 8(-2) + 2(5) + 4(3) = 6

Therefore:

8x + 2y + 4z = 6

4x + y + 2z = 3

3) The normal vectors to the plane are:

\(n_1=(1,1,-1)\ and\ n_2=(4.-1,5)\)

The point of intersection O of the two planes is normal to the normal vectors, hence:

\(O=n_1*n_2=(1,1,-1)*(4,-1,5)\\\\O=(4, -9, -5)\)

A point that lies on both plane is gotten by substituting z = 0, hence:

x + y - (0) = 3,    and     4x - y + 5(0) = 5

x + y = 3    and    4x - y = 5

Solving simultaneously gives x = 8/5, y=7/5

From this two points we get:

AB = (-2-8/5, 1 - 7/5, 1-0) = (-18/5, -2/5, 1)

The vector normal to the plane (n) = (4, -9, -5) * (-18/5, -2/5, 1) = (-11, 14, -34)

\(B=A_o=-11(x-(-2))+14(y-1)-34(z-1)\\\\0=11x+22+14y-14-34z+34\\\\11x+14y-34z =42\\\)

Answer: 71.57

Step-by-step explanation:

You are going to use SOH CAH TOA to find the angle

because the opposite and adjacent are the sides from the reference angle use TOA (tanΘ=opp/adj)

TanΘ=\(\frac{9}{3}\)

now use that tan^-1 (9/3) on your calculator (make sure your calc is in degree mode)

71.57

Answer

30

Step-by-step explanation:

It would be 30 because you can mow 6 in 4 hours you would multiply 6x5 because 4x5 is 20 and that's the total hours.

Therefore, the correct response From these integral is option D   is.  

``` 10 + ∫₅¹  R(t) dt

An integral is a mathematical construct in mathematics that can be used to represent an area or a generalization of an area. It computes volumes, areas, and their generalizations. Computing an integral is the process of integration.

Integration can be used, for instance, to determine the area under a curve connecting two points on a graph. The integral of the rate function R(t) with respect to time t can be used to describe how much water is present in a tank.

The following equation can be used to determine how much water is in the tank at time t = 5 if there are 10 gallons of water in the tank at time t = 1.

``` 10 + ∫₅¹  R(t) dt

To know more about integral visit:

brainly.com/question/30900582

#SPJ1

A first course in differential equations with modeling applications ninth edition is a textbook that covers the basics of differential equations and their applications in mathematical modeling.

It begins with an introduction to the concepts of differential equations, including the definition, solution methods, and the concept of modeling. It then covers topics such as first-order linear equations, higher-order linear equations, systems of linear differential equations, and nonlinear equations. It also has a chapter on boundary-value problems, which is a type of differential equation that involves a set of boundary conditions that must be satisfied for the solution to be valid.

In order to solve differential equations with boundary-value problems, we must first define the boundary conditions that must be satisfied for the solution to be valid. This involves setting up the boundary conditions in terms of the dependent and independent variables of the equation. We then solve the equation using the boundary conditions and the equation itself. The solution is then used to calculate values for the independent and dependent variables at the boundary points. Finally, we can verify the solution by substituting the calculated values into the equation and seeing if the solution is valid.

Learn more about differential equations here:

https://brainly.com/question/14620493

#SPJ4

John has to deposit $1308.75 every year in order to have the same amount at retirement as Bob

Compound interest is the term used to describe interest that is earned on both the initial principal and the accumulated interest from earlier periods.

It is interest that is calculated on both the initial principal and any accumulated interest, in other words.

If we were to consider an investment of $100 with a 5% compound yearly interest rate as an example.

It would be seen that the total value of the investment would rise to $105 at the end of the first year thanks to interest earnings of $5 (5% of $100).

In the second year, interest would be calculated on both the original $100 and the $5 in accumulated interest if the interest accumulates annually, bringing the total to $110.25 ($105 + 5% of $105).

Read more about compound interest here:

https://brainly.com/question/24274034

#SPJ1

The required principal amount = $22.42

Amount to be earn (A)  = $80.08

Given rate of interest (r) = 4% = 0.04

And time (t) = 7 years

What is the principal amount for investment?

Principal is also the original amount of investment made in an asset, separate from any earnings or interest accrued.

Since we know the simple interest formula;

A = p(1 + rt)

Therefore, substituting the values;

80.08 =  p[1 + (0.04)(7)]

80.08 =  0.28p

P = 80.08/0.28

P = $22.42

Thus,  the required principal amount = $22.42

Learn more about principal amount visit:

https://brainly.com/question/2284670

#SPJ1

Answer:

Axis of Symmetry: x = -4

Vertex: ( -4, -6 )

Step-by-step explanation:

~ Part I ~

1. To find the axis of symmetry, rewrite y = x^2 + 8x + 10 in the parabola standard form ( 4p( y - k ) =  ( x - h) ^2 for an up-down facing parabola at  vertex ( h, k ) and a focal length |p|) ⇒ 4 * 1/4 ( y - ( - 6 ) ) = ( x - ( - 4 ) )^2

2. Therefore the parabola properties are ⇒ ( h, k ) =  ( - 4, -6 ), p = 1/4

3. Answer: x = -4

~ Part II ~

1. From the previous question, we got that the vertex should be ⇒ ( -4, -6 )

2. Answer: ( -4, -6 )

The correct names for the angle in the figure are:

∠ABC and ∠CBA

Answer:

x>8

Step-by-step explanation:

\(- 6x+ 30 < - 18 \\ - 6x < - 18 - 30 \\ - 6x < - 48 \\ \frac{ - 6x}{ - 6} < \frac{ - 48}{ - 6} \\ x > 8\)

Step-by-step explanation:

Continuation of the answer

4x=180 degrees

X=180/4=45 degrees.

Answer:

he will buy 4 tickets

Step-by-step explanation:

firts u have to mutilpy 7.50 by a number and start at 1 and go up till u get 30

hope this helps:)!!

Answer:

1. C

2. B

Step-by-step explanation:

Answer:

1) Add 16/25 to both sides.

2) Take the square root of both sides.

Answer:

2 2/5

Step-by-step explanation:

I hope this helps

Set up the division problem in long division format.

5/12

just divide this you should get your answer.

The correct result is 38

To solve this expression, let's calculate the terms that are in parentheses. That is, the operations are:

After, we'll remove the symbol - and finally - we'll

\(\large \sf (20-6+4) \times 2+2\)

\(\large \sf (14+4) \times 2+2\)

\(\large \sf 18 \times 2+2\)

\(\large \sf 36+2\)

\(\pink{\boxed{\large \sf 38}}\)

So, the answer will be 38

The solution to the given expression using PEMDAS Order of operations is: 38

The acronym for the order of operations we will use is called PEMDAS

PEMDAS is anacronym that means:

P is for parenthesis. E is for exponents. M is for multiplication. D is for division. A is for Addition. S is for subtraction

We are given the expression:

(20 - 6 + 4) × 2 + 2

Applying PEMDAS, we solve the parentheses first to get:

(18) × 2 + 2

Next is multiplication to get:

36 + 2 = 38

Read more about Order of Operations at:  https://brainly.com/question/345677

#SPJ2

The value of the Test statistic =z=-1.67

We have the value of sigma = 6, n = 260

In a hypothesis test, a test statistic—a random variable—is computed from sample data. To decide whether to reject the null hypothesis, you can utilize test statistics. Your results are compared to what would be anticipated under the null hypothesis by the test statistic. The p-value is computed using the test statistic.

Now using the formula of Test static

Test statistic will be:  \(\mathrm{z}=\frac{\overline{\mathrm{x}}-\mu}{\frac{\sigma}{\sqrt{\mathrm{n}}}}\\\)

Where, n = total number of sample = 100

\(\bar x\) = mean of the given data

\(\mu\) = total number of hours taken to receive a basic driving licence.

So, putting the value given in the question,

We will get the value of test static as:

\(=\frac{99-100}{\frac{6}{\sqrt{260}}}=-1.67\)

For more questions on Test static

https://brainly.com/question/15110538

#SPJ4

The parent function of the transformed function is y = f ( x ) = x

Given data ,

Let the parent function be represented as f ( x )

Now , the value of f ( x ) is

The transformed function is represented as y

where y = 2 ( x - 5 )

On simplifying , we get

y = 2( x - 10 )

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

The function is shifted horizontally left by 10 units and multiplied by a scale factor of 2 units.

Hence , the parent function is f ( x ) = x

To learn more about transformation of functions click :

https://brainly.com/question/26896273

#SPJ1

Answer:

We can simplify the given expression using the rules of exponents and radicals:

4xy³√ 27x^2y^5

= 4xy * ³√(27x^2y^5) (since y and ³√(27) cannot be simplified further)

= 4xy * ³√(3^3 * x^2 * y^3 * y^2)

= 4xy * 3xy * ³√y^2

= 12x^2y^2 * ³√y^2

Therefore, the expression 4xy³√ 27x^2y^5 simplifies to 12x^2y^2 * ³√y^2.

Step-by-step explanation:

Tamika Clark's total travel expense this month is $362.90.

Given that the supervisor for the county is Tamika Clark.

Every month, she makes the trip to the three schools in her district.

Her travel costs for this month include 246 miles at a cost of $0.55 per mile, $180.70 for meals, and $46.10 for other expenses.

We must determine the whole cost of her.

To calculate Tamika Clark's total travel expenses this month, we need to add up her expenses for miles traveled, meals, and miscellaneous items.

Miles traveled:

246 miles x $0.55 per mile = $135.30

Meals: $180.70

Miscellaneous: $46.90

Total travel expenses:

$135.30 (miles traveled) + $180.70 (meals) + $46.90 (miscellaneous) = $362.90

Therefore, Tamika Clark's total travel expense this month is $362.90.

Learn more about expense click;

https://brainly.com/question/29850561

#SPJ1

Answer:

i can help you

Step-by-step explanation:

mabey its hard for you