The area of the lawn in the scale drawing is approximately 996 square feet.
1. Measure the length and width of the lawn in inches on the scale drawing.
Length = 16.5 inches
Width = 15.5 inches
2. Convert the measurements to feet by dividing the inches by 12.
Length = 16.5/12 = 1.375 feet
Width = 15.5/12 = 1.291 feet
3. Calculate the area of the lawn by multiplying the length and width.
Area = 1.375 x 1.291 = 1.75 square feet
4. Multiply the area by the scale factor (in this case, 560) to get the actual area.
Area = 1.75 x 560 = 996 square feet
learn more about area here
https://brainly.com/question/27683633
#SPJ4
3cos²∅ (1+tan²∅) = 3
Answer:
Reflection Paper on "Freedom Riders"
Ankit Mishra
title movie
freedom riders
instructions create a reflection paper that summarize the documentary and how brougth about social changes and lead to the Civil rigths act of 1964
please help me
2,3 pages
Please read the instructions please I need your help watch the movie and the instructions
Reflection Paper on "Freedom Riders" Documentary
The "Freedom Riders" is a powerful documentary that recounts the story of a group of civil rights activists who rode buses across the American South in 1961 to challenge the segregated public transportation system. The film provides a vivid and moving account of their journey and the challenges they faced along the way, from beatings and arrests to bombings and arson attacks. Through interviews with surviving freedom riders and archival footage, the film sheds light on the bravery and determination of these activists and the impact they had on the civil rights movement.
The freedom riders were inspired by the nonviolent protest movement led by Dr. Martin Luther King Jr. and other civil rights leaders. They believed that segregation was a moral wrong and that they had a duty to resist it through nonviolent means. Despite the danger they faced, the freedom riders refused to back down, putting their lives on the line for the cause of justice and equality.
The bravery of the freedom riders had a profound impact on the civil rights movement. Their actions galvanized support for the cause and drew national attention to the issue of segregation. The freedom rides sparked a wave of protests and civil disobedience across the South, and helped to build momentum for the passage of the Civil Rights Act of 1964. This landmark legislation banned segregation in public places and made it illegal to discriminate against someone on the basis of race, color, religion, sex, or national origin.
The "Freedom Riders" documentary serves as a powerful reminder of the sacrifices made by those who fought for civil rights in the United States. It highlights the courage and determination of the freedom riders and the impact they had on the country. It is an important film that teaches us about the past and the struggles of those who fought for justice and equality.
In conclusion, the "Freedom Riders" documentary is a powerful reminder of the sacrifices made by those who fought for civil rights in the United States. It highlights the bravery and determination of the freedom riders and the impact they had on the civil rights movement. The film serves as a testament to the power of nonviolent protest and the importance of standing up for what is right, even in the face of opposition. The lessons of the freedom riders should inspire us all to continue working towards a more just and equal society.
Ankit Mishra
3cos²∅ (1+tan²∅) = 3
This equation involves trigonometric functions and can be simplified using trigonometric identities.
Starting with the right-hand side of the equation, we have 3. On the left-hand side, we have the expression 3cos^2(θ)(1 + tan^2(θ)).
We can simplify the expression as follows:
cos^2(θ) = 1 - sin^2(θ)
and
tan^2(θ) = sin^2(θ) / cos^2(θ)
Substituting these identities into the expression on the left-hand side, we get:
3(1 - sin^2(θ))(1 + sin^2(θ) / (1 - sin^2(θ))
Expanding the product and simplifying, we get:
3
Thus, the equation is true and holds true for all values of θ.
Bob buys a big bag of beans for $2. 37. Find x, the number of dollars he gave the cashier if he received $17. 63 in change
Bob gave the cashier $15.26 for the bag of beans.
To find the value of x, we need to subtract the cost of the beans from the total amount given to the cashier. The cost of the beans is $2.37, and the change received is $17.63.
Therefore, the value of x can be calculated as:
x = Total amount given to the cashier - Cost of the beans
x = $17.63 - $2.37
x = $15.26
A cashier is an employee who works in a retail or service industry, responsible for handling cash, credit card payments, and providing customer service. They are often the first and last point of contact for customers in a business. Cashiers use a cash register or computer system to record transactions, and must be able to accurately count money, make change, and reconcile the cash drawer at the end of their shift.
They also need to be proficient in using technology, such as scanners and card readers, to process transactions. In addition, cashiers must have good communication skills to interact with customers, answer questions, and resolve any issues. Other responsibilities may include stocking shelves, maintaining a clean and organized workspace, and ensuring that customers receive accurate pricing and promotional discounts.
To learn more about Cashier visit here:
brainly.com/question/11110425
#SPJ4
classify each peptide chain as part of a parallel β sheet, part of an antiparallel β sheet, either type of β sheet, or not part of a β sheet.
The first figure represents Antiparallel β sheet. Second figure is parallel β sheet. Third figure represents neither of the two types. The fourth figure is also parallel β sheet and the fifth figure represents both types.
Antiparallel and parallel β-sheets are two different arrangements of the β-strands in a protein structure.
In an antiparallel β-sheet, the direction of the peptide bonds in the individual β-strands is opposed to each other, meaning that the N-terminal end of one strand points in the opposite direction from the N-terminal end of the neighboring strand. The hydrogen bonds between the strands run perpendicular to the direction of the peptide bonds and hold the strands together.
In a parallel β-sheet, the direction of the peptide bonds in the individual β-strands is the same, meaning that the N-terminal end of one strand points in the same direction as the N-terminal end of the neighboring strand. The hydrogen bonds between the strands run parallel to the direction of the peptide bonds and hold the strands together.
Both antiparallel and parallel β-sheets play important roles in the structure and function of proteins, and are found in many different types of proteins, including enzymes, transport proteins, and structural proteins.
Learn more about peptide bonds here brainly.com/question/15078143
#SPJ4
Complete question:
classify each peptide chain as part of a parallel β sheet, part of an antiparallel β sheet, either type of β sheet, or not part of a β sheet. options in document attached below.
Find the distance travelled by rahul, if he takes 6 rounds of a square field of side=120m
The distance travelled by Rahul, if he takes 6 rounds of a square field of side = 120m is 2880 meters.
We are given that Rahul takes 6 rounds of a square field of side length 120m. To find the total distance he travels, we need to calculate the perimeter of the square field and multiply it by the number of rounds.
The perimeter of a square is the sum of the lengths of its four sides. Since the side length of the square field is 120m, the perimeter is:
4 * 120m = 480m
This is the distance Rahul covers in one round around the square field.
To find the total distance he covers in 6 rounds, we multiply the distance covered in one round by the number of rounds:
480m * 6 = 2880m
So, Rahul covers a total distance of 2880 meters.
To learn more about distance click on,
https://brainly.com/question/19037886
#SPJ4
Find the total wingspan
Answer:
9.9 cm
Step-by-step explanation:
The right triangle has one-half the wing span as a leg.
The hypotenuse is 5.8cm and the other leg is 3cm
If we let the unknown leg of the triangle be x, by the Pythagorean theorem we know the sum of the squares of the two legs must be equal to the square of the hypotenuse .
So
x² + 3² = 5.8²
x² = 5.8² - 3²
= 33.64-9
= 24.64
x = √24.64
= 4.96
Total wingspan = 4.96 × 2 = 9.9 cm
Evaluate the expression.
[2³x (225+9)]-33
[2³ x (225 +9)] - 33 =
(Simplify your answer.)
a bucket that weights 70lb when filled with water is lifted at a constant rate, by a mechanical winch, from the bottom of a well that is 60 feet deep. a) compute the work required to lift the bucket from the bottom of the well to the top. (5pts) b) oops, we forgot to tell you! the chain that is being used to lift the bucket weighs 0.55 lbs per foot. now find the correct amount of work required to lift the bucket from the bottom of the well all the way to the top. (5pts) c) oh no! where is our head at today? we completely forgot to mention that the bucket has a hole in the bottom. it only weighs 35lb when it reaches the top, due to the water leaking out at a constant rate. now compute the real work required to lift the bucket from the bottom of the well to the top of the well. (recall that the bucket is being lifted at a constant rate, as well.) (5pts)
If the weight of the bucket is 70 lb , then the work required to lift the bucket from bottom is 135240 foot-pounds .
We use the formula : Work = Force × Distance to calculate the work done
where "Force" is weight of bucket filled with water and "Distance" is height it is lifted.
The weight of bucket filled with water is = 70 pounds.
We convert this to a force in pounds force, by using g = 32.2 feet per second squared ;
So , Force = Weight × Gravity
⇒ 70 lb × 32.2 ft/s² = 2254 lb-ft/s²
The distance that the bucket is lifted is = 60 feet ;
So , work required to lift bucket from bottom of well to top is :
⇒ Work = Force × Distance = 2254 lb-ft/s² × 60 ft
⇒ 135240 foot-pounds
Therefore , it will require 135240 foot-pounds of work to lift the bucket filled with water from the bottom of the well to the top.
Learn more about Work here
https://brainly.com/question/29032079
#SPJ4
The given question is incomplete , the complete question is
A bucket that weights 70lb when filled with water is lifted at a constant rate, by a mechanical winch, from the bottom of a well that is 60 feet deep.
Compute the work required to lift the bucket from the bottom of the well to the top .
Monique , vic, and Ramon played a card game . Monique had one- third the number of point that Ramon had. Vic had one- half the points that Ramon had. If Ramon had 240 points , how many points did Monique and Vic have.
A linear equation in one variable can have solution(s).
a. only 1
b. 2
c. 3
d. any number of
The cost of 4kg of radishes and 1. 5kg of carrots is £14. 80
The cost of 3kg of radishes and 2kg of carrots is £12. 50
Work out the cost of 1 carrots
Work out the cost of 1 radishes
The cost of one carrot is £1.6 and cost of one radish is £3.1 according to the quadratic equations we formed by the given data.
Here the cost of 4 kilo grams of radish and 1 and half kilo gram of carrot is £14.80.
Now, form a quadratic equation from the given data:
4[tex]\alpha[/tex]+1.5[tex]\beta[/tex]=14.80 --------(1)
Also given that the cost of 3kg of radishes and 2kg of carrots is £12. 50.
Similarly form a equation with that data:
3[tex]\alpha[/tex]+2[tex]\beta[/tex]=12.50 ----------(2)
Now simplify both equation 1 and 2
4[tex]\alpha[/tex]+1.5[tex]\beta[/tex]=14.80
3[tex]\alpha[/tex]+2[tex]\beta[/tex]=12.50
--------------------
4(3[tex]\alpha[/tex]+2[tex]\beta[/tex]=12.50)
3(4[tex]\alpha[/tex]+1.5[tex]\beta[/tex]=14.80)
-----------------------
12[tex]\alpha[/tex]+8[tex]\beta[/tex]=50
-(12[tex]\alpha[/tex]+4.5[tex]\beta[/tex]=44.4)
----------------------
3.5[tex]\beta[/tex]=5.6
[tex]\beta[/tex]=1.6
Therefore cost of one carrot is £1.6.
Now substitute the value is equation 1, we get:
4[tex]\alpha[/tex]=12.4
[tex]\alpha[/tex]=£3.1
Therefore cost of one radish is £3.1.
Learn more about quadratic equations:
https://brainly.com/question/19037377
#SPJ4
−4x+7=2y−3 how do i solve for x
get rid of y. that's all you have to do.
Ivy invested GH¢1000. 00 at 5% simple interest per annum for 5 years. How much was her investment worth after her investment ?
The total value of the investment of $1000.00 at 5% simple interest for 5 years equals $1,250.
Total principal 'P' amount invested by Ivy is equal to $1,000.
Time period of investment 't' = 5 years
Rate of simple interest 'r' = 5%
Simple interest = ( Principal × rate of interest × time ) / 100
⇒ Simple interest = ( 1000 × 5 × 5 ) / 100
⇒ Simple interest = $250
Total value of the invested principal amount is equal to
= Principal amount + simple interest
= $1,000 + $250
= $1,250
Therefore, the total investment value of the principal amount at simple interest rate for 5 years is equal to $1,250.
The above question is incomplete, the complete question is:
Ivy invested $1000. 00 at 5% simple interest per annum for 5 years. How much was her investment worth after her investment ?
Learn more about simple interest here
brainly.com/question/22621039
#SPJ4
Describe how the volume of three tennis balls, each with a diameter of 2.7 inches compares to the volume of their packaging, which is a cylinder that has the same diameter and a height of 8.1 inches. Explain or show your work.
Answer:
Step-by-step explanation:
The volume of the three tennis balls combined is approximately 4.88 cubic inches. The volume of the packaging cylinder is approximately 50.33 cubic inches. Thus, the volume of the three tennis balls is about 9.7% of the volume of their packaging cylinder.
To calculate this, we can use the formula for the volume of a sphere (V = 4/3 x π x r3) and the formula for the volume of a cylinder (V = π x r2 x h).
The radius of each tennis ball is half the diameter, or 1.35 inches. So, the volume of each tennis ball is 4/3 x π x (1.35)3 = 4.88 cubic inches.
The radius of the cylinder is the same as the diameter of each tennis ball, or 2.7 inches. The height of the cylinder is 8.1 inches. So, the volume of the cylinder is π x (2.7)2 x 8.1 = 50.33 cubic inches.
The volume of the three tennis balls is 4.88 x 3 = 14.64 cubic inches. The volume of the packaging cylinder is 50.33 cubic inches. Thus, the volume of the three tennis balls is 14.64 ÷ 50.33 = 0.097 = 9.7% of the volume of their packaging cylinder.
Use the following data sets to answer the question.
Set A: {20, 22, 24, 3, 28, 26, 30} Set B: (19, 47, 24, 17, 32, 51, 34}
Which statement about the data sets is true?
The data in Set A are skewed left. because the mean is less than the median. The data in Set B are symmetrical, because the mean is equal to the median.
The data in Set A are skewed right, because the mean is greater than the median. The data in set B are symmetrical, because the mean is equal to the median.
The data in Set A are symmetrical. because the mean is equal to the median. The data in Set B are skewed right, because the mean is greater than the median.
Answer:
The data in Set A are skewed left, because the mean is less than the median. The data in set B are symmetrical, because the mean is equal to the median.
Step-by-step explanation:
For prim people, this is the answer I got it right.
7 plums cost 63p
5 limes cost 60p
work out the cost of 1 plum
The cost of one plum in pence is 9p. The cost of 1 lime in pence is 12p.
Comparing the cost plum is cheaper.
The cost of 1 plum can be found by dividing the total cost of 7 plums by 7:
63 p / 7 = 9 p
Therefore, the cost of 1 plum is 9 p.
The cost of 1 lime can be found by dividing the total cost of 5 limes by 5:
60 p / 5 = 12 p
Therefore, the cost of 1 lime is 12 p.
Comparing the costs of 1 plum and 1 lime, we see that 1 plum costs 9 p and 1 lime costs 12 p. Therefore, the plum is cheaper per item.
To know more about Cost:
https://brainly.com/question/30147827
#SPJ4
____The given question is incomplete, the complete question is given below:
A grocery shop sells plums and limes. 7 plums cost 63 p. 5 limes cost 60p a) Work out the cost of 1 plum, in pence (p).
b) Work out the cost of 1 lime, in pence (p).
c) Which type of fruit is cheaper per item?
This equation shows how the accuracy of Johnny's watch is related to how long it's been since he last set it. s = d + 16 The variable d represents the number of days passed since Johnny last set his watch, and the variable s represents how many seconds behind the watch is. How far behind is Johnny's watch if he last set it 2 days ago?
If Johnny sets his watch 2 days ado then after two days watch will behind 18 seconds.
What is addition ?
Addition is a basic mathematical operation that combines two or more numbers to give a total or sum. It is one of the four elementary arithmetic operations, along with subtraction, multiplication, and division. The operation involves adding or combining the values of two or more numbers, which are called addends, to produce a new value, which is the sum or the total.
If Johnny last set his watch 2 days ago,
we can substitute d = 2 into the equation:
s = d + 16
To find out how many seconds behind his watch is.
s = d + 16
s = 2 + 16
s = 18
So, Johnny's watch is 18 seconds behind if he last set it 2 days ago.
To know more about addition check:
https://brainly.com/question/28222269
#SPJ9
Rectangle ABCD is graphed in the
coordinate plane. The following are the
vertices of the rectangle: A(5,5), B(7,5),
C(7, -1), and D(5, -1).
Given these coordinates, what is the length
of side BC of this rectangle?
Answer:
Rectangle ABCD is graphed in the
coordinate plane. The following are the
vertices of the rectangle: A(5,5), B(7,5),
C(7, -1), and D(5, -1).
Given these coordinates, what is the length
of side BC of this rectangle?
Step-by-step explanation:
The volume of a cube of side 2A is
Answer:
8a3
Step-by-step explanation:
volume of cube = Lcube
one side=length of cube
so
volume of cube= L3
=2a3
= 2A × 2A × 2A
= 8A3Calculate the length of the legs of the triangle.
Answer: 5
Step-by-step explanation:
magic the gathering is a popular card game. cards can be land cards, or other cards. we consider a game with two players. each player has a deck of 40 cards. each player shuffles their deck, then deals seven cards, called their hand. (a) assume that player one has 10 land cards in their deck and player two has 20. with what probability will each player have four lands in their hand? (b) assume that player one has 10 land cards in their deck and player two has 20.with what probability will player one have two lands and player two have three lands in hand? (c) assume that player one has 10 land cards in their deck and player two has 20. with what probability will player two have more lands in hand than player one?
Probability the player two have more lands in hand than player one is:
A) 0.0135
B) 0.102
What is probability?
The probability of an event is a number that indicates how likely the event is to occur. It is expressed as a number in the range from 0 and 1, or, using percentage notation, in the range from 0% to 100%. The more likely it is that the event will occur, the higher its probability.
Here, we have
Given: each player has a deck of 40 cards. each player shuffles their deck, then deals seven cards, called their hand.
A ) probability of each player having four lands in their hand
Given data:
player 1 has 10 land cards
player two(2) having 20 land cards
Hence, the probability can be calculated as
= 0.0135
B) probability of player one having two lands and player two having three lands in hand
Given data:
player one (1) has 10 land cards
player two has 20
Hence, the probability of player one having two lands and player two having three lands in hand can be calculated as attached below
= 0.102
To learn more about the probability from the given link
https://brainly.com/question/24756209
#SPJ1
Vocabulary Explain how to isolate the variable in the eqaution -2/3n = 7 + 15
The variable n in the original equation -2/3n = 7 + 15 is equal to -12.
What is equation?Equation is a physical and mathematical statement that describing physical phenomena and the relationship between different physical quantity typically consist of variable simple presenting physical quantity and then it personal variable maybe pointed search is the energy.
In order to isolate the variable in the equation -2/3n = 7 + 15, the first step is to subtract 7 from each side of the equation. This results in -2/3n = 8. Next, multiply each side of the equation by 3 to cancel out the 3 in the denominator. This leaves -2n = 24. Finally, divide each side of the equation by -2 to isolate the variable n. This results in the equation n = -12. Therefore, the variable n in the original equation -2/3n = 7 + 15 is equal to -12.
To know more about Equation click-
https://brainly.com/question/26408808
#SPJ1
The stem-and-leaf plot displays the distances that a heavy ball was thrown in feet.
2 0, 2, 5
3 1, 3, 4
4 1, 1, 5
5 0, 6
6 7
Key: 3|1 means 3.1
What is the mean, and what does it tell you in terms of the problem?
3.1 feet; The value means the furthest the ball went.
3.875 feet; The value means that a typical throw of the ball results in 3.875 feet.
4.1 feet; The value means this measurement had the most occurrences.
4.65 feet; The value means that a typical throw of the ball results in 4.65 feet.
The mean would be 35 feet.
The mean tells us that the typical throw of the ball results in a distance of approximately 3.5 feet.
what is Mean?
In arithmetic, mean is the sum of all the added values of all the data in a set divided by the number of data in the set.
To find the mean of the distances, we need to calculate the sum of all the distances and divide by the total number of distances:
(20+25+25+31+33+34+41+41+45+50+56+67) / 12 = 425 / 12 = 35.42
Rounding to one decimal place, we get the mean distance of approximately 3.5 feet.
However, it's worth noting that the stem-and-leaf plot shows some variability in the distances, with some throws going as far as 6.7 feet and some as short as 2 feet.
So while the mean can provide us with a measure of central tendency, it doesn't tell the whole story about the distribution of the distances.
Therefore, The mean would be 35 feet. The mean tells us that the typical throw of the ball results in a distance of approximately 3.5 feet.
To know more about mean visit,
https://brainly.com/question/1136789
#SPJ1
This question has two parts. First, answer Part A. Then, answer Part B.
The distance that Makayla travels on her skates varies directly with time as shown in the table.
Write a direct variation equation in the form y = kx to represent this relationship. Express the constant of variation as a decimal.
A linear clear variation is represented by the equation y = kx, in which k is the area under the curve y = mx + b and b is the zero-valued y-intercept.
Y KX Y is what kind of variation?The polynomial y = mx (commonly stylized y = kx), which seems referred to as a direct variation, can be obtained from the theory y = mx + b if m is a sufficiently small factor and b = 0. In other words, you may claim that y directly depends on x or that y is proportionate to x.
K in Y KX: What does it mean?The standard format for presenting a direct variation is y=kx. The letters "y" and "x" are variables, and the letter "k" is a constant. Making a table will allow you to identify those ordered pairs that statisfy the example of y=2x.
To know more about polynomial visits:
https://brainly.com/question/29135551
#SPJ1
9) An 8.2 km section of highway increases 870 m in elevation. The horizontal distance of the road is 8154m.
a) Calculate the slope to three decimal places
b) Calculate the angle of elevation to one decimal place. Tan x= opposite/adjacent
c) Calculate the percent grade to one decimal place. Percent Grade slope X 100
One number is 3 less than 4 times a second number. The difference of the
first number and twice the second number is 7. What are the two numbers?
Show your work.
Answer:
atq= let no.be x and y
x= 4y-3.......(1)
x-2y=7....(2)
subtracting both eqn
x-x+2y=4y-3-7
2y=4y-10
-2y= -10
y=5 ........second no.
first no...x=7+2y=7+10=17.......first no.
Step-by-step explanation:
scores on a certain test are normally distributed with a variance of . a researcher wishes to estimate the mean score achieved by all adults on the test. find the sample size needed to assure with 95 percent confidence that the sample mean will not differ from the population mean by more than units.
A sample size of 44 is needed to assure with 95% confidence that the sample mean will not differ from the population mean by more than 2.5 units.
To find the sample size needed to assure with 95% confidence that the sample mean will not differ from the population mean by more than 2.5 units, we can use the formula:
n = [ (z * σ) / E ]^2
where n is the required sample size, z is the critical value for the desired confidence level (95% confidence level corresponds to a z-value of 1.96), σ is the population standard deviation (given as the square root of the variance, which is √(70) ≈ 8.37), and E is the maximum error, or the maximum difference between the sample mean and population mean that we are willing to tolerate (which is given as 2.5 units).
Substituting the given values into the formula, we get:
n = [ (1.96 * 8.37) / 2.5 ]^2
n ≈ 43.48
Rounding up to the nearest whole number, we get a required sample size of n = 44.
Therefore, a sample size of 44 is needed to assure with 95% confidence that the sample mean will not differ from the population mean by more than 2.5 units, assuming a normal distribution with a population variance of 70.
Learn more about mean here brainly.com/question/29727198
#SPJ4
scores on a certain test are normally distributed with a variance of 70 . a researcher wishes to estimate the mean score achieved by all adults on the test. find the sample size needed to assure with 95 percent confidence that the sample mean will not differ from the population mean by more than 2.5 units.
Aquadratic equation is such that its roots are the HCF and LCM of the smallest
prime number and the smallest composite number, then quadratic equation 1s
With the root values 6 and 8 the quadratic equation is x² - 6x +8 = 0.
What is a quadratic function?
A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree.
The roots of the quadratic equation are -
HCF of smallest prime number, LCM of smallest composite number
The smallest prime number is 2.
So, the HCF of 2 is 2.
The smallest composite number is 4.
So, the LCM of 4 is 4.
If m and n are the roots of a quadratic equation ax² + bx + c = 0, then the sum of the roots is (m+n) and the product of the roots is (mn).
And then the quadratic equation becomes x² - (m+n)x +mn = 0.
So, here m = 2 and n = 4.
The sum of roots is -
(m + n) = (2 + 4) = 6
The product of roots is -
(mn) = (2 × 4) = 8
So, the quadratic equation is x² - 6x +8 = 0.
Therefore, the equation is x² - 6x +8 = 0.
To learn more about quadratic function from the given link
https://brainly.com/question/25841119
#SPJ1
Question 4 of 10
Given the inequalities y> 3x-1 and y<-2x+ 1 graphed on the same
coordinate grid, which of the following statements are true? Check all that
apply.
A. The line for y=-2x+1 will be solid.
B. Shading will be below the y=-2x+ 1 line and below the y= 3x - 1
line.
C. Shading will be above the y=-2x+1 line but below the y= 3x-1
line.
D. None of the above
SUBMIT
Answer:
Step-by-step explanation:
The correct answer is C. Shading will be above the y=-2x+1 line but below the y= 3x-1 line.
The line y=-2x+1 is a line with a slope of -2 and a y-intercept of 1. It represents the solutions that are greater than -2x+1.
The line y=3x-1 is a line with a slope of 3 and a y-intercept of -1. It represents the solutions that are less than 3x-1.
So, when you graph both of these lines on the same coordinate plane, the solutions that satisfy both inequalities will be the region that is above the line y=-2x+1 but below the line y=3x-1, and this is the region that will be shaded.
Angle QRS is an equilateral triangle. If QR is seven less than twice x, RS is 61 less than five times x, and QS is 11 more than x, find the value of x and the measure of each side
The value of x is 18 and the measure of each side is:
QR = RS = QS = 29
What is called equilateral?An equilateral triangle is a triangle that has all its sides equal in length. Since the three sides are equal therefore the three angles, opposite to the equal sides, are equal in measure. Therefore, it is also called an equiangular triangle, where each angle measure 60 degrees.
Now, According to the question:
Angle QRS is an equilateral triangle.
QRS is an equilateral triangle, thus all the three sides of the given triangle will be equal.
we have
QR = 2x - 7___(1)
RS = 5x - 61 ___(2)
QS = 11 + x_____(3)
Now, As all the sides of the triangle are equal, therefore
QR = RS = QS
⇒QR = RS
⇒2x - 7 = 5x - 61
⇒ -7 + 61 = 5x - 2x
⇒ 54 = 3x
⇒ x = 18
Put the value of x in above equations:
Thus, the measure of
QR = 2(18) - 7=29,
RS = 5(18) - 61 = 29 and
QS = 11 + 18 = 29.
Learn more about Equilateral Triangle at:
https://brainly.com/question/3461022
#SPJ4
suzy borrows $4500 and agrees to repay it all in equal monthly instalments over 3 years. Simple interest at 7.2% p.a is charged on a loan. find the amount of each instalment
The amount of Suzy's instalment every month if it is agreed to repay equal amount monthly is $152
What is the amount of each instalment?Simple interest = principal × rate × time
= 4500 × 0.072 × 3
= $972
Total amount to repay = $4500 + $972
= $5472
Repayment time = 3 years
Suzy will repay every month
3 years= 12 months × 3
= 36 months
Since,
the repayment is equal every month
Amount of instalment every month= $5472 / 36
= $152
Therefore, Suzy will repay $152 each month instalmentally.
Read more on simple interest:
https://brainly.com/question/20690803
#SPJ2