ARCHAEOLOGY A farm lane in Ohio crosses two long, straight earthen mounds that may have been built about 2000 years ago. The mounds are about 200 feet apart, and both form a 63° angle with the lane, as shown. Are the mounds parallel? How do you know?

Answers

Answer 1

Yes. Because Mound 1 and Mound 2 form a pair of corresponding angles with that red transversal line (lane). Corresponding angles are congruent and parallel to each other.

1) Since both mounds share the same measure of the angle, then we can say that those mounds are yes, parallel to the lane since they both corresponding angles, and corresponding angles are parallel and congruent to each other.

2) So the answer is :

Yes. Because each mound 1 and Mound 2 form a pair of corresponding angles with that red transversal line. Corresponding angles are congruent and parallel to each other.

Related Questions

Last year, Kaitlyn had $30,000 to invest. She invested some of it in an account that paid 5% simple interest per year, and she invested the rest in an account that paid 9% simple interest per year. After one year, she received a total of $2580 in interest. How much did she invest in each account?First account:Second account:

Answers

Answer:

She invested an amount of $3,000 in the first accont and $27,000 in the second account

Explanation:

Here, we want to get the amount invested in each of the accounts

To get this,let us write the simple interest formula

Mathematically, we have this as:

[tex]I\text{ = }\frac{PRT}{100}[/tex]

Let the amount invested in the first account be $x, while that of the second account be $y

P represent the amounts invested

R is the rate of investment

T is the time (1 year)

The sum of these two is the $30000 she has to invest

Mathematically, we have this as:

[tex]x\text{ + y = 30000}[/tex]

Let us get the interests on each of the accounts

For the first account, we have the interest as:

[tex]I_1\text{ = }\frac{x\times5\times1}{100}\text{ = }\frac{5x}{100}[/tex]

For the second account, we have the interest as:

[tex]I_2\text{ = }\frac{y\times9\times1}{100}\text{ =}\frac{9y}{100}[/tex]

The sum of these two is the interest value, which is as follows:

[tex]\begin{gathered} I_1+I_2\text{ = }\frac{5x}{100}+\frac{9y}{100}\text{ = 2580} \\ \\ 5x\text{ + 9y = 258000} \end{gathered}[/tex]

So, we have two equations to solve simultaneously

The two equations are:

[tex]\begin{gathered} x\text{ + y = 30000} \\ 5x\text{ + 9y = 258000} \end{gathered}[/tex]

We can solve this by substitution

Let us substitute for y

[tex]y\text{ = 30000-x}[/tex]

Insert this into the second equation, we have this as:

[tex]\begin{gathered} 5x\text{ + 9(30000-x) = 258000} \\ 5x\text{ + 270000-9x = 258000} \\ 9x-5x\text{ = 270000-258000} \\ 4x\text{ = 12000} \\ x\text{ = }\frac{12000}{4} \\ x\text{ = 3,000} \end{gathered}[/tex]

Recall:

[tex]y\text{ = 30000-x = 30000-3000 = 27000}[/tex]

What this mean is that:

She invested an amount of $3,000 in the first accont and $27,000 in the second account

Find the distance between the two points.(-6, -3) and (194,42)The distance is(Type an exact answer, using radicals as needed.)

Answers

distance=205

Explanation

Step 1

the distance between is given by:

[tex]\begin{gathered} \text{distance=}\sqrt[]{(x_1-x_2)^2+(y_1-y_2)^2} \\ \text{where} \\ P1(x_1,y_1) \\ P2(x_2,y_2) \end{gathered}[/tex]

Let

P1(-6,-3)

P2(194,42)

Step 2

apply the formula.

[tex]\begin{gathered} \text{distance=}\sqrt[]{(x_1-x_2)^2+(y_1-y_2)^2} \\ \text{distance=}\sqrt[]{(-6-194)^2+(-3-42)^2} \\ \text{distance=}\sqrt[]{(-200)^2+-45^2} \\ \text{distance=}\sqrt[]{40000+2025} \\ \text{distance=}\sqrt[]{42025} \\ \text{distance}=205 \end{gathered}[/tex]

I hope this helps you

HELPP PLEASE

Answers

Choose A

( A is the answer <3)

Write the correct expression for the following statement.

The quotient of x and three

Answers

Answer:

[tex]\frac{x}{3}[/tex] or x/3 or x÷3

Find the difference between 3 /5 of 125 and 5/8 of 144

Answers

The answer to this question will be 15.

3/5 of 125 = 3/5 x 125 = 75

5/8 of 144 = 5/8 x 144 = 90

So, 5/8 of 144 - 3/5 of 125 = 90 - 75 = 15

The difference between 3/5 of 125 and 5/8 of 144 is 15.

Answers

The end behaviours of the functions are

f(x) = 6x⁹ - 6x⁴ - 6: As x ⇒ +∝, f(x) ⇒ +∝ and as x ⇒ -∝, f(x) ⇒ -∝f(x) = -3x⁴ - 6x + 4x - 5: As x ⇒ +∝, f(x) ⇒ -∝ and as x ⇒ -∝, f(x) ⇒ -∝

How to determine the end behaviours of the functions?

Function 1

The equation of the function is given as

f(x) = 6x⁹ - 6x⁴ - 6

Calculate f(∝) and f(-∝)

So, we have

f(∝) = 6(∝)⁹ - 6(∝)⁴ - 6

Evaluate

f(∝) = ∝ - ∝ - 6

So, we have

f(∝) = ∝

Also, we have

f(-∝) = 6(-∝)⁹ - 6(-∝)⁴ - 6

Evaluate

f(-∝) = -∝ - ∝ - 6

So, we have

f(∝) = -∝

This means that

As x ⇒ +∝, f(x) ⇒ +∝ and as x ⇒ -∝, f(x) ⇒ -∝

Function 2

The equation of the function is given as

f(x) = -3x⁴ - 6x + 4x - 5

Evaluate the like terms

f(x) = -3x⁴ - 2x - 5

Calculate f(∝) and f(-∝)

So, we have

f(∝) = -3(∝)⁴ - 2(∝) - 5

Evaluate

f(∝) = -∝ - ∝ - 5

So, we have

f(∝) = -∝

Also, we have

f(-∝) = -3(-∝)⁴ - 2(-∝) - 5

Evaluate

f(∝) = -∝ + ∝ - 5

So, we have

f(∝) = -∝

This means that

As x ⇒ +∝, f(x) ⇒ -∝ and as x ⇒ -∝, f(x) ⇒ -∝

Answers

We are goinf to analise each case properly

1) As the radio show is asking it could be that their listners do not attend this demand. Then the error would be nonresponse.

2) As the students do the survey based of its readers it depends only of this part of the poblation. Then the error would be voluntary.

3) As the gym ask only to the first 20 members it makes the error would be convenience

So, the correct answer is B.

PLS HELP ASAP WILL GIVE BRAINLIST

Answers

I’m pretty sure it’s
X=2
Y=15

x is equal to two and y is equal to fifteen hope this helps you

Plant A is 2 inches tall and is growing
at 14 inches per week. Plant B is 12
inches tall but is only growing at
inch per week. How many weeks will it
take for Plant A to be the same height
as Plant B?

Answers

It will take Plant A 5 days to be the same height as Plant B and this can be calculated through unitary method of mathematical calculation.

Unitary Method: What is it?

The unitary technique used in here involves at first determining the value of a particular single unit, that is thus followed by the value of the necessary number of units.

What is an example of a unitary method?

A single or type of a distinct unit is referred to by the word of unitary.

Therefore, the goal of this strategy is to establish values in reference to a single unit.

The unitary technique, for instance, can be used to calculate how many kilometers a car will go on one liter of gas if it travels 44 km on two liters of fuel.

Plant A initial height = 2 inches

Growth rate = 14 inches/ week

= 2 inches/ day

Plant B initial height = 12 inches

Growth rate = 1 inch/ week

After 5 days we can see that plant A will be

2 + (5 x 2) = 12 inches

this is the same height as that of Plant B.

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Temperature is usually measured on the Fahrenheit scale (°F) or the Celsius scale (°C). Use the formula F = 1.8C+ 32 to convert from one scale to the other. The highest temperature ever recorded in Virginia Beach, Virginia, was 104°F. Find the temperature in degrees Celsius. 219°C 26°C b. 155°C d. 40°C

Answers

Answer:

The temperature in degrees Celsius is;

[tex]40^0C[/tex]

Explanation:

Given the formula for converting Temperature from Celsius to Fahrenheit as;

[tex]F=1.8C+32[/tex]

Where;

F = temperature in Fahrenheit

C = temperature in Celsius

To convert from Fahrenheit to Celsius, let us make C the subject of formula;

[tex]\begin{gathered} F-32=1.8C \\ C=\frac{F-32}{1.8} \end{gathered}[/tex]

To convert 104°F to Celsius, let us substitute the value into the derived formula;

[tex]\begin{gathered} C=\frac{F-32}{1.8} \\ C=\frac{104-32}{1.8} \\ C=40^0C \end{gathered}[/tex]

Therefore, the temperature in degrees Celsius is;

[tex]40^0C[/tex]

35.4 divided by 0.59

Answers

To do the operation, first the numerator and denominator by 100:

[tex]\frac{35.4\cdot100}{0.59\cdot100}=\frac{3540}{59}[/tex]

Now simplify

[tex]\frac{3540}{59}=\frac{59\cdot60}{59\cdot1}=\frac{60}{1}=60[/tex]

Therefore,

[tex]\frac{35.4}{0.59}=60[/tex]

Answer:

Step-by-step explanation: 35.4 / 0.59 = 60

savings 50,000 in 30 years with a saving compounded monthly at an interest rate of 6%. How much would I need to deposit a month?

Answers

If the saving compounded monthly at an interest rate of 6%. The amount you need to deposit a month is $8,302.

How to find the compound interest?

Using this formula to determine the principal amount

P = A / (1 + r/n) ^nt

Where:

P = principal = ?

A = amount = $50,000

r = interest rate = 6%

t = time = 30

Now let plug in the formula

P = $50,000 / (1 + 0.06/12) ^( 12 × 30 )

P = $50,000 / (1 + 0.005) ^ 360

P = $50,000 / (1.005)^360

P = $50,000 / 6.022575

P = $8,302

Therefore $8,302.10 is the amount deposited.

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Two forces 30-lb and 50-lb are pulling an object at an angle of 30°between them. Find the magnitude of the resultant force. Round answer to 2 decimal places.

Answers

Answer: The magnitude of the resultant force is 77.45-lb

Explanation:

Resultant is represented as R

During a physics lab, students added weights of different masses to aspring. After adding each weight to the spring, they measured how far theweight was from the lab tabletop, in centimeters. Then they graphed thedata and calculated the line of best fit to be y = -1 x + 10.25Weight Distance fromthe Tabletop (cm)108642Effect of Weightson a Spring0 50 100 150 200 250 300Mass (g)What does the x-intercept represent?-XAt 250 grams, the weight will touch thetabletop.With no weight, the spring is 10centimeters above the tabletop.The weight will be 250 centimetersabove the tabletop when the spring hasa mass of 10 grams on it.The spring stretches and the weight is 1centimeter closer to the tabletop forevery 25 grams added to it.

Answers

Solution:

Given the graph below:

where the equation of the line of best fit is expressed as

[tex]y=-\frac{1}{25}x+10[/tex]

The x-intercept represents:

The correct option is

continued - calculating gross payRemember, this is money round to the nearest Penny/hundredths place.

Answers

ANSWER:

Regular pay is $383.2

Overtime rate is $14.37

Overtime pay is $114.96

Gross pay is $498.16

STEP-BY-STEP EXPLANATION:

Assuming the overtime multiplier is 1.5 and the standard work week is 40 hours. Therefore, we calculate the regular payment like this:

[tex]RP=40\cdot9.58=383.2[/tex]

The overtime rate would be the value of the normal payment times the overtime multiplier, like this

[tex]OTR=9.58\cdot1.5=14.37[/tex]

Then we multiply the number of additional hours to the 40 hours allowed, that is, 8 (48 - 40), for which one gives overtime pay

[tex]OTP=8\cdot114.96=114.96[/tex]

Now the gross pay would be the sum of the regular payment with the overtime payment:

[tex]GP=114.96+383.2=498.16[/tex]

whats 2+2 i cant figure it out

Answers

Answer: 4

Step by step solution:

[tex]2+2=4[/tex]

Graph the line 3x + 6y =12.

Use the line tool and select two points on the line.

Answers

Answer: First divide everything by 3 to make it simpler. Then subtract 12 on both sides to get the equation "x+2y-12 = 0. You can then graph this.

Step-by-step explanation:

A farmer is going to divide her40 acre farm between two crops. Seed for crop A costs $30 per acre. Seedfor crop B costs $15 per acre. The farmer can spend at most $1050 on seed.If crop B brings in a profit of $70 per acre, and crop A brings in a profit of $180 per acre, how many acres ofeach crop should the farmer plant to maximize her profit?acres of crop Aacres of crop B

Answers

Given: A farmer is going to divide her40 acre farm between two crops

To Determine: How many acres of each crop should the farmer plant to maximize her profit

Solution

[tex]\begin{gathered} x=acres\text{ for crop A} \\ y=acres\text{ fro corp B} \end{gathered}[/tex][tex]\begin{gathered} Therefore: \\ x+y\leq40 \\ 30x+15y\leq1050 \\ Profit\text{ functon is} \\ P=70y+180x \end{gathered}[/tex]

The graph of the inequalitiesis as shown below

Neglecting the negative axis, the point that will maximize the profit are te points shown above with their coordinates

The coordinates will maximum profits are

[tex]\begin{gathered} Point1:(0,40) \\ Point2:(35,0) \\ Point3:(30,10) \end{gathered}[/tex]

Substitute the 3 points into the profit functions to determine thepoint that will given the maximum profit

[tex]\begin{gathered} P=180x+70y \\ Point1 \\ P1=180(0)+70(40) \\ P1=0+2800 \end{gathered}[/tex][tex]\begin{gathered} Point2 \\ P2=180(35)+70(0) \\ P2=6300+0 \\ P2=6300 \end{gathered}[/tex][tex]\begin{gathered} Point3 \\ P3=180(30)+70(10) \\ P3=5400+700 \\ P3=6100 \end{gathered}[/tex]

Hence, the point that will maximize profit is (35, 0), which is

35 acres of crop A, and

0 acre of crop B

Female
Male
Total
10
113
Snellville Stone
Mountain
12
14
26
316
10
20
30
Suwanee
8
16
24
Consider the following table with information about a sample of students from Phoenix High School and where they
live. If a person is randomly selected determine the following probability provided the condition: P(Female | Suwanee).
Total
30
50
80

Answers

If a person is randomly selected, the probability provided the condition is P(Female | Suwanee) is 1/3.

What is the probability?

Probability is used to determine the odds in favor or against a random event happening. The odds in favor or against an event happening has a probability value that lies between 0 and 1.

The higher the odds of an event happening, the closer the probability value would be to 1. If it is equally likely that the event might happen or not happen, the probability value will be 0.5.

P (Female | Suwanee) is the probability that a person is female given that the person is from Suwanee.

P (Female | Suwanee) = total number of females from Suwanee / total number of people from Suwanee

8 / 24 = 1/3

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Write Expression to represent the total area as the sum of the areas of each room

Answers

We are given the following areas:

The total area of the square is given by:

[tex]11(7+4)[/tex]

If we apply the distributive property we get:

[tex]11(7+4)=11\times7+11\times4[/tex]

Which is equivalent to determining the area of the interior rectangle and adding them together.

Answer:

11x7+11x4

Step-by-step explanation:

your welcome <3

Use the number line to find the coordinate of the midpoint of
¯¯¯¯¯
J
P
.

Answers

Answer: -1

Step-by-step explanation:

The midpoint of a segment is the same as the average of the coordinates of the endpoints. So, the midpoint is [tex]\frac{-7+5}{2}=-1[/tex].

What is 78,600 rounded to the nearest thousand

Answers

Answer:

79,000

Step-by-step explanation:

Answer:

79000.

Step-by-step explanation:

The equation of a line is: y = 4/7x - 12Which equation would have a line that is perpendicular to this line?1. y = - 4/7x - 12. y = - 7/4x - 53. y = 7/4x - 84. y = 4/7x - 2

Answers

Explanation

Let's recall the framework of the equation of a line:

We say that two lines are perpendicular if the slope of one line is minus the multiplicative inverse of the slope of the other one; mathematically, this amounts to the following equation:

[tex]m_1=-\frac{1}{m_2}.\leftarrow\begin{cases}m_1=\text{Slope of one line} \\ m_2=\text{ Slope of the other line}\end{cases}[/tex]

In this case, the slope of our line is 4/7. Then the slope (m) of any line perpendicular to it must satisfy

[tex]m=-\frac{1}{\frac{4}{7}}\text{.}[/tex]

Solving this equation for m, we get

[tex]\begin{gathered} m=-\frac{1}{\frac{4}{7}}, \\ m=-\frac{\frac{1}{1}}{\frac{4}{7}}, \\ m=-\frac{1}{1}\cdot\frac{7}{4},\leftarrow\text{ Flipping rule when dividing fractions} \\ m=-\frac{7}{4}. \end{gathered}[/tex]Answer

The answer is 2.

I need help with putting 64/128 fully simplified and to a decimal

Answers

Given:

[tex]\frac{64}{128}[/tex]

To convert into decimal:

Explanation:

Let us write it as the factored form for each term.

[tex]undefined[/tex]

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{\dfrac{64}{128}}\\\\\mathsf{= \dfrac{64\div8}{128\div8}}\\\\\mathsf{= \dfrac{8}{16}}\\\\\mathsf{= \dfrac{8\div4}{16\div4}}\\\\\mathsf{= \dfrac{2}{4}}\\\\\mathsf{= \dfrac{2\div2}{4\div2}}\\\\\mathsf{= \dfrac{1}{2}}\\\\\\\huge\text{Therefore, the answer simplified is:}\\\huge\boxed{\mathsf{\dfrac{1}{2}}}\huge\checkmark[/tex]

[tex]\mathsf{\dfrac{1}{2}\rightarrow 1\div2 \rightarrow 0.5}\\\\\\\huge\text{Therefore your decimal form of }}\huge\boxed{\boxed{\rm{\dfrac{1}{2}}}}\huge\text{ is:}\\\\\huge\boxed{\mathsf{0.5}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

ANSWERS ASAP PLEASEEEEE

Answers

Answer:

y= -3x+3

Step-by-step explanation:

atleast I think so

f(x)=7x-3 for f(x)= -38

Answers

Answer:

f(x)= -269

Step-by-step explanation:

f(x)=7x-3

Since we know f(x)= -38, we can substitute x for -38.

So:

f(-38)=7(-38)-3

f(-38)= -266-3

f(x)= -269

Answer:

-7x=38+3

-7x=41/-7=5.8

Find odds in favor of winning ring and find against winning the ring

Answers

We have a randomly selected prize out of 9 objects (4 rings, 4 headsets and 1 camera).

a) We have to calculate the odds in favor of Mary winning a ring.

The odds can be expressed as the proportion (or quotient) between the probabilities of winning a ring and the probabilities of not winning a ring.

This will also be equal to the number of outcomes that will be a ring (4 elements are rings) divided by the number of outcomes that are not a ring (5 elements are not a ring):

[tex]o_{wr}=\frac{4\/9}{5\/9}=4:5[/tex]

b) Now, we have to calculate the odds against Mary winning a ring.

This will be the inverse of the previous result, as we have to divide the probability of not winning a ring by the probability of winning.

We can then write:

[tex]o_{nwr}=\frac{5\/9}{4\/9}=5:4[/tex]

Answer:

a) 4 : 5

b) 5 : 4

The model represents an equation. What value of x makes the equation true? Enter your answer in the box below

Answers

the value of x are that makes it true

A rectangular picture measures 32 by 28. when the picture is framed, a margin 2cm wide is left all the way round .1: what is the area of the picture without the frame?2:what is the area of the frame3:what is the area of the margin

Answers

1) The area of the picture without the frame will be A.

[tex]A=32\times28=896cm^2[/tex]

So the area without frame is 896 square centimeters.

2) If the frame is 2 cm all around then the length and width increase by 4.

So the length becomes 32+4=36cm and the width becomes 28+4=32.

The area of big rectangle which is the frame is A'.

[tex]A^{\prime}=36\times32=1152cm^2[/tex]

So the area of the frame is 1152 square centimeters.

3) The area of the margin will be the difference of the area of the frame and area of the picture, so it will be A'-A

[tex]A^{\prime}-A=1152-896=256cm^2[/tex]

So the area of the margin is 256 square centimeters.

The tree diagram represents an experiment consisting of two trials
P(A)=

Answers

Based on the parameters in the question, the value of probability P(A) is 0.60

How to determine the probability?

The given parameters from the tree diagram are:

Probability of event A: P(A only) = 0.6Probability of event A: P(A and C) = 0.3Probability of event A: P(A and D) = 0.7

The probability is calculated using the following probability formula

P(A) = P(A and D) + P(A and C)

Substitute the known values in the above equation

P(A) = 0.6 * 0.7 + 0.6 * 0.3

Evaluate the products

P(A) = 0.42 + 0.18

Evaluate the sum

P(A) = 0.60

Hence, the value of the probability of A is 0.60