trapezoids JKLM is shown below. The coordinates of J,K,L,M, are (-5, -7), (5,-7), (3-4) and (-2,4), respectively. write an equation for KL in slope intercept form.
Answers
Question:
Solution:
To write an equation for a line, we need a point and direction of the line. The direction is represented by the slope. Now, the slope-intercept form of a line is given by the following equation:
\(y\text{ = mx+b}\)where m is the slope of a line and b is the y-intercept. Now, to find the slope m of this line we apply the following formula:
\(m\text{ = }\frac{Y2-Y1}{X2-X1}\)where (X1,Y1) and (X2,Y2) are points on the line. In this case, we can take the points:
(X1,Y1)= (3,4)
(X2,Y2)=(5,-7)
thus, the slope of the line KL is:
\(m\text{ = }\frac{Y2-Y1}{X2-X1}=\text{ }\frac{-7-4}{5-3}\text{ =}\frac{-11}{2}=\text{ -}\frac{11}{2}\)thus, the provisional equation of the line is:
\(y\text{ = -}\frac{11}{2}x+b\)now, to find b, we can take any point on the line and replace it in the above equation; then, solve for b. For example, we can take (x,y)=(3,4), thus:
\(4\text{ = -}\frac{11}{2}(3)+b\)this is equivalent to:
\(4\text{ = -}\frac{33}{2}+b\)solving for b, we get:
\(b=\text{ 4+}\frac{33}{2}=\frac{(2)(4)+33}{2}=\frac{8+33}{2}=\frac{41}{2}\)then
\(b=\text{ }\frac{41}{2}\)we can conclude that the slope-intercept form of the line KL is:
\(y\text{ = -}\frac{11}{2}x+\frac{41}{2}\)where x varies on the interval:
\(\lbrack3,5\rbrack\)
Related Questions
goes through the points (6,2) and (5, 4)
Answers
Use <, >, or = to compare the following decimals.
(a) 2.92 |?| 5.51
(b) 4.34 |?| 4.81
(c) 0.9 |?| 0.07
Answers
Answer:
A. < B. < C. >
Step-by-step explanation:
One aircraft has a capacity of 64 more seats than a second
aircraft. A third aircraft has 152 seats less than twice the seating
capacity of the second aircraft. If their total number of seats is
1900, find the number of seats for each aircraft.
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Therefore, the number of seats for each aircraft is 752, 688, and 1224.
Define Unitary method.The unitary method is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
What is multiplication?Multiplying in math is the same as adding equal groups. The number of items in the group grows as we multiply. Parts of a multiplication issue include the product, the two factors, and the product. The components in the multiplication problem 6 x 9 = 54 are the numbers 6 and 9, and the result is the number 54.
Let x be the number of seats for the second aircraft.
The first aircraft has x + 64 seats.
The third aircraft has 2x - 152 seats.
The total number of seats for all aircraft is x + (x + 64) + (2x - 152) = 1900.
Therefore, 3x = 2064, so x = 688.
The first aircraft has 688 + 64 = 752 seats.
The third aircraft has 2(688) - 152 = 1224 seats.
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Find the 70th term of the following arithmetic sequence 4,12,20,28
Answers
Answer:
556
Step-by-step explanation:
formula
L = a + (n - 1)*d
Givens
n = 70
a = 4
d = 8
Solution
t = 4 + (70 - 1)*8
t = 4 + 69*8
t = 4 + 552
t = 556
Use the Law of Sines to solve the triangle. Round your answers to two decimal places. (Let b = 5.1.)
Answers
Given:-
An image with triangle.
To find:-
The value of B,a,c.
So the laws of sines are,
\(\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}\)So now we substitute the known values. we get,
\(\frac{\sin16}{a}=\frac{\sin B}{5.1}=\frac{\sin125}{c}\)Now we find the value of B,
Since the sum of angles of the triangle is 180. we get,
\(\begin{gathered} A+B+C=180 \\ 16+B+125=180 \\ B+141=180 \\ B=180-141 \\ B=39 \end{gathered}\)So substituting the value we get,
\(\frac{\sin16}{a}=\frac{\sin 39}{5.1}=\frac{\sin125}{c}\)Now we find the value of a. we get,
\(\begin{gathered} \frac{\sin16}{a}=\frac{\sin 39}{5.1} \\ \frac{0.2756}{a}=\frac{0.6293}{5.1} \\ a=\frac{0.2756\times5.1}{0.6293} \\ a=2.2335 \end{gathered}\)Now we find c. we get,
\(\frac{0.2756}{2.2335}=\frac{\sin 125}{c}\)So
it is 4.5 miles from moulton to filby via Burnham and denton how far is it between denton and filby
Answers
Answer: I think that the answer is 3/4 miles
Step-by-step explanation:
Look at the graphs and their equations below. Then fill in the information about the coefficients A, B, C, and D.
Answers
A. The signal of each coefficient is given by:
A: positive.B: positive.C: negative.D: negative.B. The coefficient closest to zero is of B.
C. The coefficient with the least value is of C.
What is the transformations?The transformations are vertical stretch/compression of the absolute function.
Then the signal is defined as follows:
V format: positive, such as A and B.Inverted V format: negative, for C and D.The coefficient closest to zero is for the biggest vertical compression, which is of B, for which the graph stretches horizontally and compresses vertically.
The least value is for the biggest reflected stretching, which is in item c, in which the curve has a larger vertical stretch than in item d.
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Select the correct answer from each drop-down menu. Identify the investment type and complete the description. _____offer corporations a loan. Investors tend to choose this investment type because it offers______ and _____
1.a bonds 1.b real estate investment 1.c saving account 1.c stocks
2.a risk 2.b safety
3.a dividends base on company profits 3.b income based on an interest rate
Answers
Answer: bonds/safety/income based on an interest rate
Step-by-step explanation:
:)
ssume all information in example 1 above and the following additional information: Actual data for job 201 is give is given belowActual shirts completed for job 201………………2,000 shirtsActual direct material cost used………………...$30,000Actual direct cost incurred……………………...$20,000Actual direct labor hours used…………………. 400 hoursActual machine hours…………………………. 240 hoursInstruction: compute the applied factory overhead and determine the total cost of job 201 under each of the five bases. A) Physical output as allocation baseDirect materials cost as allocation base Direct labor cost as allocation base Direct labor hours as allocation baseMachine hours as allocation base
Answers
The applied overhead cost for job 201 is $36,000 and total cost for job 201 under direct materials cost as allocation base is $86,000.
Allocation base is a technique utilized in accounting to designate the cost of something to its use or product to recognize the price of the finished product.
Example provides the total overhead cost at $120,000 for the period, the base data of $100,000 direct material cost and 500 direct labor hours. The base data are used to calculate the predetermined factory overhead rate, which is used to apply overhead costs to work in progress.
The predetermined factory overhead rate is calculated by dividing the total overhead cost for the period by the base data. The predetermined factory overhead rate is multiplied by the actual activity in the allocation base to obtain the applied overhead cost.
Direct materials cost as allocation base $30,000 is the actual direct material cost used in job 201. The predetermined factory overhead rate is calculated by dividing the total overhead cost for the period by the direct material cost, which is $120,000/$100,000=120%.
The applied overhead cost for job 201 is $30,000*120% = $36,000.
Total cost for job 201 under direct materials cost as allocation base is $30,000+$20,000+$36,000 = $86,000.
-Direct labor cost as allocation base:
The actual direct labor cost used in job 201 is $20,000. The predetermined factory overhead rate is calculated by dividing the total overhead cost for the period by the direct labor cost, which is $120,000/$100,000=120%.
The applied overhead cost for job 201 is $20,000*120% = $24,000.
Total cost for job 201 under direct labor cost as allocation base is $30,000+$20,000+$24,000 = $74,000.
-Direct labor hours as allocation base:
The actual direct labor hours used in job 201 is 400 hours.
The predetermined factory overhead rate is calculated by dividing the total overhead cost for the period by the direct labor hours, which is $120,000/500 hours = $240 per hour.The applied overhead cost for job 201 is $240*400 hours = $96,000.
Total cost for job 201 under direct labor hours as allocation base is $30,000+$20,000+$96,000 = $146,000.
-Physical output as allocation base: The actual output in units completed for job 201 is 2,000 shirts.
The predetermined factory overhead rate is calculated by dividing the total overhead cost for the period by the output in units, which is $120,000/10,000 units = $12 per unit.
The applied overhead cost for job 201 is $12*2,000 units = $24,000.Total cost for job 201 under physical output as allocation base is $30,000+$20,000+$24,000 = $74,000.
-Machine hours as allocation base: The actual machine hours used in job 201 is 240 hours.
The predetermined factory overhead rate is calculated by dividing the total overhead cost for the period by the machine hours, which is $120,000/5,000 hours = $24 per hour.
The applied overhead cost for job 201 is $24*240 hours = $5,760.
Total cost for job 201 under machine hours as allocation base is $30,000+$20,000+$5,760 = $55,760.
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How much is 15% on a bill of 57.45
Answers
Answer:
$8.62
Step-by-step explanation:
15% is practically 0.15, and when you say 15% OF 57.45, the "of" refers to multiplication. This means, 15% of 57.45 is basically 0.15*57.45, or 8.6175. Since we're talking about money, that would be rounded to $8.62
Answer:
$8.62
Step-by-step explanation:
"%" means "divide by 100"
"of" means "times"
15% of $57.45 = 0.15×$57.45 = $8.6175 ≅ $8.62
Which rational number is one tick mark to the right of Negative StartFraction 6 Over 4 EndFraction on the number line below?
Answers
Answer:
the answered is a
Step-by-step explanation:
hope this helps
Answer:
-1 3/4
Step-by-step explanation:
Solve the system of equations by adding or subtracting.S3x + y = 412x + y = 0The solution of the system is
Answers
Step 1:
Choose either Substitution or elimination method to solve system of equation.
Step 2:
If you choose substitution,
firstly, name the equation
3x + y = 4 .............................1
2x + y = 0 ..............................2
secondly, choose one of the equation and make one of the varable subject of the relation
2x + y = 0 .......................1
y = -2x
Step3
substitute y in equation 2
3x + (-2x) = 4
3x - 2x = 4
x = 4
Step 4:
find y from y = -2x
y = -2(4)
y = -8
( 4 ), ( -8 )
Answer:
x = 4
y = - 8
Step-by-step explanation:
3x + y = 4
2x + y = 0
(3x + y ) (-1 ) = 4 ( - 1 )
2x + y = 0
- ( 3x + y ) = - 4
2x + y = 0
Would 15 miles per gallon be a unit rate??
Answers
Yes, 15 miles per gallon would be a unit rate.
A unit rate is essentially a situation where the quantity is written with a 1 as the denominator (A unit rate is y over x, when x = 1).
What is the length of QR?
600
20
Q
R
Select the best answer from the choices provided.
Answers
Answer:
A. 10 HOPE IT WILL HELP YOU
Simplify i) ( x-y )( x−y )( x−y )
Answers
The simplified expression for ( x - y ) ( x - y ) ( x - y ) is x³ - x²y - xy² + y³.
To simplify ( x - y ) ( x - y ) ( x - y ), we can expand the expression using the distributive property of multiplication. We can also simplify the expression by combining like terms.
In using the distributive property of multiplication, we multiply each term in the first set of parentheses by each term in the second set of parentheses. This gives us:( x - y ) ( x - y ) ( x - y ) = ( x(x - y) - y(x - y) ) ( x - y )= ( x² - xy - xy + y² ) ( x - y )= ( x² - 2xy + y² ) ( x - y )
Now we can further simplify the expression by combining like terms. We can use the difference of squares formula to simplify the second set of parentheses.( x² - 2xy + y² ) ( x - y ) = ( x - y ) ( x - y )²= ( x - y ) ( x² - 2xy + y² )= x³ - x²y - 2xy² + xy² - xy² + y³= x³ - x²y - xy² + y³
Therefore, the simplified expression is x³ - x²y - xy² + y³.
Summary: To simplify ( x - y ) ( x - y ) ( x - y ), we expand the expression using the distributive property of multiplication. We simplify the expression by combining like terms. We use the difference of squares formula to simplify the second set of parentheses. Finally, we simplify the expression further by combining like terms. The simplified expression is x³ - x²y - xy² + y³.
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The ratio of the distances a driver and a 2-iron will drive a
golf ball is 5 to 4. If a golfer averages 240 yards with a 2-
iron, how far should she average with a driver?
Answers
The average distance is 300 yards
How to determine the average distance?The ratio is given as:
Driver : 2-iron = 5 : 4
When the iron driver is 240 yards, we have:
Driver : 240 = 5 : 4
Express as fraction
Driver/240 = 5/4
Multiply both sides by 240
Driver= 300
Hence, the average distance is 300 yards
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(-4, 7), (-6,-4) what is the slope for this
Answers
The slope of the line between two points A=(a,b) and B=(c,d) is given by the following formula:
\(m=\frac{b-d}{a-c}\)The two points given by the question are (-4,7) and (-6,-4). Then the slope of the line passing through these two points is:
\(m=\frac{7-(-4)}{-4-(-6)}=\frac{7+4}{-4+6}=\frac{11}{2}=5.5\)AnswerThen the answer is 5.5.
what is -(x - 8) simplified?
Answers
Instructions: Use the ratio of a 30-60-90 triangle to solve for the variables. Leave your answers as radicals in simplest form.
If you are using a screen-reader, please consult your instructor for assistance.
x=
y=
Answers
Using the ratio of the sides, we have:$x\sqrt{3} = 12\sqrt{3}$ (opposite the $60^{\circ}$ angle is 12$\sqrt{3}$)$x = 2\sqrt{3}\cdot6$ (the hypotenuse is $2x = 12\sqrt{3}$)Simplifying, we have:$x = 12\sqrt{3}$. Therefore $x=y=12\sqrt{3}$, which is our answer
In a 30-60-90 triangle, the sides have the ratio of $1: \sqrt{3}: 2$. Let's apply this to solve for the variables in the given problem.
Instructions: Use the ratio of a 30-60-90 triangle to solve for the variables. Leave your answers as radicals in simplest form. x=y=Let's first find the ratio of the sides in a 30-60-90 triangle.
Since the hypotenuse is always twice as long as the shorter leg, we can let $x$ be the shorter leg and $2x$ be the hypotenuse.
Thus, we have: Shorter leg: $x$Opposite the $60^{\circ}$ angle: $x\sqrt{3}$ Hypotenuse: $2x$
Now, let's apply this ratio to solve for the variables in the given problem. We know that $x = y$ since they are equal in the problem.
Using the ratio of the sides, we have:$x\sqrt{3} = 12\sqrt{3}$ (opposite the $60^{\circ}$ angle is 12$\sqrt{3}$)$x = 2\sqrt{3}\cdot6$ (the hypotenuse is $2x = 12\sqrt{3}$)Simplifying, we have:$x = 12\sqrt{3}$
Therefore, $x=y=12\sqrt{3}$, which is our answer.
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Pls ans I can’t get it
Answers
Answer:
1.u=1/2
2.b= -35
3.a= -8
A blue car travels 297.6 miles using 12 gallons of gasoline, and a red car travels 358.8 miles using 13 gallons of gasoline. Which car travels farther using 1 gallon of gasoline?
Answers
Answer: The red car travels farther using 1 gallon of gasoline.
Step-by-step explanation:
Blue Car:
297.6 ÷ 12 = 24.8
24.8 is the number of miles per gallon of gas for the blue car.
Red Car:
358.8 ÷ 13 = 27.6
27.6 is the number of miles per gallon of gas for the red car.
27.6 - 24.8 = 2.8
The red car travels farther using 1 gallon of gasoline.
Reuben made a shirt using 7/8yards of red fabric and 1/4yards of yellow fabric. How many more yards of red fabric did Reuben use?
Answers
Answer and Step-by-step explanation:
To find out how many more yards of red fabric Reuben used, we need to subtract the amount of yellow fabric from the amount of red fabric. Since the two fractions have different denominators, we need to find a common denominator before subtracting them. The least common multiple of 8 and 4 is 8, so we can rewrite both fractions with a denominator of 8:
7/8 - 1/4 = 7/8 - (1/4) * (2/2) = 7/8 - 2/8 = (7 - 2)/8 = 5/8
So, Reuben used 5/8 yards more red fabric than yellow fabric.
HELPPP ASAPPP !!!
2. Point A on the graph below represents Nate's house, and Point B represents Nate's favorite restaurant. B A If each unit on the graph represents 3/4 of a mile, how many miles does Nate live from his favorite restaurant?
Answers
Answer:
10miles I think
Step-by-step explanation:
The required distance between, Nate's house and the restaurant is 7.5 miles.
From the graph,
Consider point C on the graph, which is 6 and 8 units apart from A and B respectively.
The distance between, Nate's house and the restaurant is given as,
AB = √[AC² + BC²]
AB = √[6² + 8²]
AB = 10 units
Now 1 unit = 3/4 miles
AB = 10 * 3/4
AB = 7.5 miles
Thus, the required distance between, Nate's house and the restaurant is 7.5 miles.
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A spinner has six equal-sized sections numbered 1, 1, 2, 2, 3, and 4. What is the probability of spinning a 3?
Answers
Answer:
1/6 or 0.166666...
Step-by-step explanation:
1 out of 6, so 1/6
Identify the vertices of the feasible region and use them to find the maximum and/or minimum value for the given linear programming constraints.
System of Linear Programming:
z=−3x+5y
x+y≥−2
3x−y≤2
x−y≥−4
Maximum value of z:
Minimum value of z
Answers
The maximum value of the objective function is 26 and the minimum is -10
How to determine the maximum and the minimum values?The objective function is given as:
z=−3x+5y
The constraints are
x+y≥−2
3x−y≤2
x−y≥−4
Start by plotting the constraints on a graph (see attachment)
From the attached graph, the vertices of the feasible region are
(3, 7), (0, -2), (-3, 1)
Substitute these values in the objective function
So, we have
z= −3 * 3 + 5 * 7 = 26
z= −3 * 0 + 5 * -2 = -10
z= −3 * -3 + 5 * 1 =14
Using the above values, we have:
The maximum value of the objective function is 26 and the minimum is -10
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14x-(-5x+6-3x-4)=4(5x)+10
ayudaaa pora doy corona
Answers
Answer:
x = 10
General Formulas and Concepts:
Pre-Algebra
Distributive Property
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
Identify
14x - (-5x + 6 - 3x - 4) = 4(5x) + 10
Step 2: Solve for x
[Distributive Property] Distribute negative: 14x + 5x - 6 + 3x - 4 = 4(5x) + 10Combine like terms: 22x - 10 = 4(5x) + 10Multiply: 22x - 10 = 20x + 10[Subtraction Property of Equality] Subtract 20x on both sides: 2x - 10 = 10[Addition Property of Equality] Add 10 on both sides: 2x = 20[Division Property of Equality] Divide 2 on both sides: x = 10Find all missing angles in the diagram
Answers
I need help on this it is really hard to understand
Answers
What you have to do for the total is add up all the values in May, June, July and August for each row. And for average you need to find the average value for each row. If you don’t know how to do that you can use Microsoft Excel to help you, just put in all the numbers and then pick each number for each row and press “= average”
Answer:
Step-by-step explanation:
Row 1
Total = $3,440
Average = $688
Row 2
Total = $5,911.70
Average = $1,182.34
Row 3
Total = $8,802.34
Average = $1,760.47
Row 4
Sept. = $108.26
Total = $545.45
Row 5
Sept. = $19,892.25
Total = $108,017.60
If
R
=
{
x
|
x
>
0
}
and
S
=
{
x
|
x
<
3
}
, what is the number of integers in
R
∩
S
?
A. Zero
B. Two
C. Three
D. Four
Answers
As per the given data, the number of integers in R ∩ S is 2, and the correct answer is (B) Two.
In mathematics, the intersection of two sets is a set containing all elements that are members of both sets.
In symbols, the intersection of two sets A and B is denoted by A ∩ B, and it contains all elements that belong to both A and B.
The intersection of two sets contains only the elements that are present in both sets. In this case,
R ∩ S = {x | x > 0 and x < 3}
The integers that are present in this set are 1 and 2.
Therefore, the number of integers in R ∩ S is 2, and the correct answer is (B) Two.
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You are considering taking out a loan of $8,000.00 that will be paid back over 8 years with quarterly payments of $320.19. If the interest rate is 6.3% compounded quarterly, what would the remaining balance be immediately after the fourteenth payment?
The remaining balance would be $___________. (Round to 2 decimal places.)
Answers
Answer:
78.8
Step-by-step explanation: