Answer: Let's call the length of the rectangular court "L" and the width "W". Then, the perimeter of the court is 2 * (L + W) = 148 feet, so 2 * L + 2 * W = 148 feet.
And, according to the coach's estimate, the athlete ran a total of 4 * L + 7 * W = 353 feet.
We can use these two equations to find the dimensions of the court. Solving the first equation for W:
W = (148 - 2 * L) / 2.
Substituting this expression for W into the second equation:
4 * L + 7 * (148 - 2 * L) / 2 = 353
Expanding and simplifying the right side of the equation:
4 * L + 74 - 7 * L = 353
-3 * L = -279
L = 93 feet.
Finally, using the expression for W from the first equation:
W = (148 - 2 * L) / 2 = (148 - 2 * 93) / 2 = 32 feet.
So the dimensions of the sports court are 93 feet by 32 feet.
Step-by-step explanation:
Match the following terms with the correct definitions
Answer: The space inside a figure -- Area
The sum of all sides in a figure -- Perimeter
The distance vertically in a triangle -- Height
The distance horizontally in a triangle -- Base
Salma is going to an amusement park. The price of admission into the park is $10, and once she is inside the park, she will have to pay $5 for every ride she rides on. How much money would Salma have to pay in total if she goes on 6 rides? How much would she have to pay if she goes on r rides?
The money that Salma has to pay if she goes on 6 rides is $40 and if she goes on r rides then she has to pay 10+5r
What is a solution to a linear equation?A solution of an equation is any value of the variable that satisfies the equality, that is, it makes the Left Hand Side (LHS) and the Right Hand Side (RHS) of the equation the same value.
Given here: Admission price=$10 and ride fee= $5
Now if Salma goes for 6 rides than we have
Total fee= 10+5×6
=$40
And if Salma decides to go for r rides than we can express the total cost as some function of the number of rides r
T(r)=10+5r
Hence, The money that Salma has to pay if she goes on 6 rides is $40 and if she goes on r rides then she has to pay 10+5r
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number 8 only please help
Answer:
14/70
Step-by-step explanation:
581 divided by 8 with remainder
Answer:
581 divided by 8 should be 72 with a remainder of 5
Step-by-step explanation:
to check if i was correct i did 72 times 8 plus 5 and got 581
The accompanying data represent the miles per gallon of a random sample of cars with a three-cylinder, 1.0 liter engine.
(a)
Compute the z-score corresponding to the individual who obtained miles per gallon. Interpret this result.
(b)
Determine the quartiles.
(c)
Compute and interpret the interquartile range, IQR.
(d)
Determine the lower and upper fences. Are there any outliers?
LOADING... Click the icon to view the data.
The table is given as,
Z- Score -0.299
Q₁ 36.47
Q₂ 38.45
Q₃ 41.2
IQR 4.25
Lower fourth 30.375
Upper fourth 47.375
What is z- score?An illustration of a standardised score is the z-score. A z-score calculates how far a data point deviates from the distribution's mean by standard deviation.
Given:
Sample Data = 31.5, 36.0, 37.8, 38.5, 40.1, 42.2, 34.2, 36.2, 38.1, 38.7, 40.6, 42.5, 34.7, 37.3, 38.2, 39.5, 41.4, 43.4, 35.6, 37.6, 38.4, 39.6, 41.7, 49.3
(a) The value of z-score is calculated as follows,
μ =[tex]\sum_{i=1}^n X_i[/tex]/ n = 933.1 /24 = 38.88
σ = 3.61
z = X - μ / σ
= 37.8 - 38.88/3.61
= − 0.299
Therefore, the value of z-score is -0.299.
(b) Quartile:
Recalling the values: 31.5, 36, 37.8 ,38.5, 40.1 ,42.2, 34.2 ,36.2, 38.1, 38.7, 40.6 ,42.5, 34.7, 37.3 ,38.2, 39.5 ,41.4, 43.4, 35.6, 37.6 ,38.4 ,39.6 ,41.7, 49.3
Q₁ = ( n+1/4)th value
= (24+1/4)th value
= 6.25th value
= 36.2 + 0.25 x ( 37.3 − 36.2 )
= 36.47
and, M = ( n+1/2)th value
= (24+1/2)th value
= (24+1/4)th value
= 12.5 t h
= 38.4 + 38.5/2
= 38.45
Q₃ = 3( n+1/4)th value
= 3(24+1/4)th value
= 18.75 t h v a l u e
= 40.6 + 0.75 x ( 41.4 − 40.6 )
= 41.2
(c) Interquartile range = Q ₃ − Q ₁
= 41.2 − 36.47
= 4.25
Therefore, the IQR value is measure of spread of data, and here the value of IQR = 4.25.
(d) Lower fences = Q₁− 1.5 ( I Q R )
= 36.75 − 1.5 ( 4.25 )
= 30.375
Upper fences = Q ₃+1.5
= 41 + 1.5( 4.25 )
= 47.375
Hence, there is outliers since observations are not less than 30.375 and greater than 47.375.
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From the top of a 72 m high vertical cliff,
a boat has an angle of depression of 32
degrees. How far is the boat from the
base of the cliff? Round your answer to
the nearest whole number.
If from the top of a 72 m high vertical cliff, a boat has an angle of depression of 32° then the distance of boat from the base of the cliff is, 115 m.
What is an angle ?An angle is a mathematical term, which we can define, when two straight lines or rays meet at a common endpoint. The common point is called the vertex of an angle. The word angle comes from a Latin word named ‘angulus,’.
Interior angles:- The inner angle made by the intersection of two polygonal sides.
Exterior angles:- The outer angle made by the intersection of two polygonal sides.
We can use trigonometry to solve for the distance of the boat from the base of the cliff.
Let's call the distance from the base of the cliff to the boat "d".
Then we have:
tan(32°) = 72 / d
Solving for d, we get:
d = 72 / tan(32°)
d = 115.22
Rounding to the nearest whole number, d = 115.
So the boat is 115 meters away from the base of the cliff.
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Find the value of the variable m and YZ if Y is between X and Z, XY=9m−3 , YZ=6m+1 , and XZ=13m+6 .
The value of variable m is 4.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
We have to find value of m
As Y is between X and Z it is taken as the midpoint.
The values of XY, YZ and XZ are given as below.
XY=9m−3 , YZ=6m+1 , and XZ=13m+6 .
We need to find the value of the variable m.
If we add xy and yx we get xz.
So by the equation xy+yz=xz we get the value m.
9m-3+6m+1=13m+6
Add the like terms
15m-2=13m+6
15m-13m=2+6
2m=8
Divide both sides by 2
m=4
Hence, the value of variable m is 4.
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If the test scores of a class of 36 students have a mean of 73.1 and the test scores of another class of 28 students have a mean of 67.4, then the mean of the combined group is
The mean of the combined group can be calculated as follows:
Calculate the total sum of test scores of both classes:
Class 1: 36 students * 73.1 mean = 2631.6
Class 2: 28 students * 67.4 mean = 1888.32
Total: 2631.6 + 1888.32 = 4519.92
Calculate the total number of students:
Total students = 36 + 28 = 64
Divide the total sum of test scores by the number of students to find the mean:
Mean = 4519.92 / 64 = 70.9375.
Therefore, the mean of the combined group of 64 students is 70.9375.
discuss four contribution of the slave trade positive and negative effect
According to Eltis, the Atlantic economy became more beneficial to slavery as a result of the rising demand for commodities that could be produced at a low cost by slaves, such as sugar, coffee, tobacco, and cotton textiles.
What benefit did the slave trade provide? According to Eltis, the Atlantic economy became more beneficial to slavery as a result of the rising demand for commodities that could be produced at a low cost by slaves, such as sugar, coffee, tobacco, and cotton textiles.Afric a's impact of slavery.Competitors absorbed competitor states, destroying them utterly and decimating their populations.Towns and villages were depopulated, and millions of Africans were forcibly uprooted from their homes.During the slaving battles, many Africans died or remained in slavery in their native continent.The findings support the historical evidence by showing that the repercussions of the slave trades are seen in ethnic fragmentation, weakened governments, and a deterioration in the standard of domestic institutions.
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The expression (5y + 2)(y - 3) is equivalent to:
The first question is about algebra with two variables. To calculate the algebra, sum up all the same variable and count the value.
We have an mathematical expression: (5y + 2)(y - 3).
Find the equivalent value!
The equivalent value is
= (5y + 2)(y - 3)
= 5y² + (-15y) + 2y - 6
= 5y² - 13y - 6
The expression of (5y + 2)(y - 3) is equivalent to 5y² - 13y - 6.
The second question is about length in coordinate plane. The following is the formula for the length in coordinate plane.
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
A line segment with endpoints (-6, 2) and (3, 1).
Find the length!
From the endpoints, we have
x₁ = -6y₁ = 2x₂ = 3y₂ = 1The length is
d = √[(3 - (-6))² + (1 - 2)²]
d = √[9² + (-1)²]
d = √[81 + 1]
d = √82
Hence,
The equivalent value is 5y² - 13y - 6.The line segment has a length of √82.Learn more about algebra here:
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Which is the correct equation for finding the value of x?
A. 2x + 6 + 5x + 8x - 11 = 180
B. 5x + 2x + 6 = 180
C. 2x + 6 + 8x - 11 = 5x
D. 5x + 2x + 6 = 8x - 11
Answer:
C.
Step-by-step explanation:
1. 2x + 6 = 8x
2. 8x + 8x = 16x
3. 16x - 11 = 5x
In a random sample of 80 Americans, 36 wished that they were rich. In a random sample of 90 Europeans, 49 wished that they were rich. At α = 0.01, is there a difference in the proportions? Find the 99% confidence interval for the difference of the two proportions.
The difference between the percentage of Americans who want to be rich and the percentage of Europeans who want to be rich, according to our 95% confidence level, is between (-0.078, -0.101).
What is a confidence interval?The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within if you repeat the test.
In statistics, confidence is another word for probability.
Given In a random sample of 80 Americans, 36 wished that they were rich. In a random sample of 90 Europeans, 49 wished that they were rich.
Let p₁ = probability of Americans wanting to rich
p₂ = probability of Europeans wanting to rich
p₁ = 36/80 = 0.45
p₂ = 49/90 = 0.54
so CI = (p₁ - p₂) ± z₁(p₁p₂/n₁ + p₁p₂/n₂)
CI = (0.45 - 0.54) ± 1.96(0.0236)(0.243)
CI = -0.09 ± 0.0112
(-0.078, -0.101)
Hence the difference of the two proportions is between (-0.078, -0.101).
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Six players on the Sluggers baseball team are pitchers. The pitchers make up 25% of the
team. How many players are on the Sluggers baseball team
Answer:
24
Step-by-step explanation:
If there are 6 pitchers on the Sluggers and they make up 25% or 1/4th of the team, you can just add 6 (1/4th) to itself to 3 more times to gett 100% or 4/4ths.
6+6+6+6 (or 6×4) is 24.
2. Explain the relationship between the constant of proportionality and the unit rate. Be specific.
Answer: The constant of proportionality and the unit rate represent the same value. A constant of proportionality can be any value, including fractions and decimals. The main difference between the constant of proportionality and a unit rate is how they are written.
Which inequality represents the graph?
The inequality that represents the graph is option D: 13x - 3y - 14 < 0.
What is an inequality?
In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.
The x-intercept is a = 1.077
The y-intercept is b = -4.677
The equation of line having x-intercept a and y-intercept b is -
x/a + y/b = 1
The equation of line having x-intercept 1.077 and y-intercept -4.677 is -
x/1.077 + y/-4.677 = 1
y/-4.677 = 1 - x/1.077
y = (1 - x/1.077)-4.677
y = -4.677 + 4.677x/1.077
y = -4.677 + 4.342x
Multiply both sides by 3 -
3y = 3(-4.677 + 4.342x)
3y = -14.031 + 13.026x
Now, the line 3y = -14.031 + 13.026x divide the xy-plane in two regions and the region given in the graph is satisfied by the origin.
Also, the line 3y = 14.031 + 13.026x is dotted and not dark ,therefore, the points on the line are not included in the shaded region.
Therefore, the inequality that represents the shaded region is -
0 > - 3y - 14.031 + 13.026x ≈ 13x - 3y - 14 < 0
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I need help with this
How many digits do you need to number all 178 buildings on a street?
The number of digits which one would need to number all 178 buildings on a street is 426 numbers.
What is a Digit?This is referred to as a single symbol used alone or in combinations, to represent numbers in a positional numeral system.
1-9 = 1 × 9 = 9
10-99 = 90 × 2 = 180
100-178 = 79 × 3 = 237
The total = 9 + 180 + 237 = 426 numbers.
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HELPP!!!!!!!!!!
ASAPPP
Based on each given parallelogram, the correct answers are:
x = 9; y = 15m = 4; n = 10d = 126; z = 28unable to answer (not complete screenshot)∠B = 129°∠N = 85°LM = 13MN = 8.07LP = 7MQ = 16.4∠LMN = 80°∠NQL = 80°∠MNQ = 100°∠LMQ = 29°Let's try to solve each parallelogram problems
1. In paralellogram, each parallel sides have equal lengths; then:
x // 9; then x = 9
y // 15; then y = 15
2. In paralellogram, each parallel sides have equal lengths; then:
m + 1 // 5; then m + 1 = 5
m = 4
n // 10; then n = 10
3. In paralellogram, each parallel sides have equal lengths; then:
z - 8 // 20; then z - 8 = 20
z = 28
Opposite angles share the same size; then:
d - 21 = 105
d = 126
4. Uncomplete screenshot
5. In parallelogram, adjacent angles is supplementary to each other; then:
∠A + ∠B = 180°
51 + ∠B = 180°
∠B = 129°
6. In parallelogram, adjacent angles is supplementary to each other; then:
∠M + ∠N = 180°
95 + ∠N = 180°
∠N = 85°
In the given parallelogram LMNQ, the length of MP is 8.2 and PN is 7. Angle ∠MQN is 29° and ∠MLQ is 100°.
7. LM can be calculated by focusing on triangle MLQ. Under the Sinus Law, we can find that:
LM / sin LQM = MQ / sin MLQ
MQ is one of the parallelogram diagonal. MP is the mid point, then MQ is twice of MP.
MQ = 2(8.2) = 16.4
∠MLQ = 100°
∠LQN = 180° - 100°
∠LQN = 80°
∠LQN = ∠LQM + ∠MQN
80° = ∠LQM + 29°
∠LQM = 51°
LM / sin 51 = 16.4 / sin 100
LM / 0.78 = 16.4 / 0.98
LM = 12.9 = 13
8. LQ is parallel with MN; then they share the same length.
LQ = MN
MN can be calculated by focusing on triangle QMN. Under the Sinus Law:
MN / sin MQN = MQ / sin MNQ
∠MNQ is the opposite angle of ∠LMQ, then ∠MNQ = ∠LMQ = 100
MN / sin 29 = 16.4 / sin 100
MN = 8.07
9. LP = PN = 7
10. MQ = 2 x MP
MQ = 2(8.2)
MQ = 16.4
11. ∠LMN = ∠LQN = 80°
12. ∠NQL = 80°
13. ∠MNQ = ∠MLQ = 100°
14. ∠LMQ is the alternate interior angle of ∠MQN; then ∠LMQ = ∠MQN = 29°
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Please help ASAP
Find the area of the rectangle
What is the area of the rectangle?
The area of the rectangle is given by the equation A = ( 9x² - 64 ) yards²
What is the Area of a Rectangle?The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle
Area of Rectangle = Length x Width
Given data ,
Let the area of the rectangle be represented as A
Now , the equation will be
Let the width of the rectangle be W = ( 3x - 8 ) yards
Let the length of the rectangle be L = ( 3x + 8 ) yards
Now , Area of Rectangle = Length x Width
Substituting the values in the equation , we get
Area of Rectangle = ( 3x - 8 ) ( 3x + 8 )
On simplifying the equation , we get
Area of Rectangle = ( 3x )² - ( 8 )²
Area of rectangle A = ( 9x² - 64 ) yards²
Hence , the area of the rectangle is ( 9x² - 64 ) yards²
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Please help ASAP
Find the area of the rectangle
use a table to find the product of (3x+4)(x^2+3x-2) how are the terns in the table arranged m
Answer:
3x²+9x²-6x and add this
4x²+12x-8
Kindly, find the solution on the attachment.
Question
Each side of the base of a square pyramid measures 10 inches. The height of each lateral face of the pyramid is also 10 inches.
What is the surface area of the pyramid?
Enter your answer in the box.
in²
The surface area of the pyramid that has these measures is given as 300 inches square
How to solve for the surface area of the pyramidThe surface area of a square pyramid is the sum of the area of the base and the areas of the lateral faces.
The area of the base of the square pyramid is given by the formula for the area of a square:
A = s^2, where s is the length of one side of the square.
In this case, each side of the base measures 10 inches, so the area of the base is:
A = 10^2 = 100 square inches.
The lateral faces of the pyramid are triangles, and the surface area of each lateral face can be found using the formula:
A = (1/2)bh, where b is the length of the base and h is the height.
In this case, the height of each lateral face is 10 inches, and the base is a side of the square base, which measures 10 inches.
So the surface area of each lateral face is:
A = (1/2)(10)(10) = 50 square inches.
Since there are 4 lateral faces on a square pyramid, the total surface area of the lateral faces is 4 * 50 = 200 square inches.
Finally, the surface area of the pyramid is the sum of the surface area of the base and the lateral faces:
A = 100 + 200 = 300 square inches.
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Answer:
180 hope this helps!
Step-by-step explanation:
Graph the function. y=3/2x+1
if a/b - d = 2c/b, find the value of c when a = 3, b = 4 and d = 5
Answer: 23
Step-by-step explanation:
first we put the values a=3,b=4 and d=-5. in a/b-d=2c/b equation which is given in the question. so,it gives us 3/4+5=2c/4,3+20=2c/4×4,3+20=c.so,the value of c is 23
Answer:
[tex]\huge\boxed{\sf c = -17/2}[/tex]
Step-by-step explanation:
Given equation:[tex]\displaystyle \frac{a}{b} - d=\frac{2c}{b}[/tex]
Where, a = 3, b = 4, d = 5
[tex]\displaystyle \frac{3}{4} - 5 =\frac{2c}{4} \\\\Take \ LCM\\\\\frac{3-(5 \times 4)}{4} = \frac{c}{2} \\\\\frac{3-20}{4} = \frac{c}{2} \\\\\frac{-17}{4} = \frac{c}{2} \\\\Cross \ Multiply\\\\-17 \times 2 = 4 \times c\\\\-34 = 4c\\\\Divide \ both \ sides\ by \ 4\\\\-34/4 = c\\\\c = -17/2\\\\\rule[225]{225}{2}[/tex]
Degrees and Radians
any steps.
A coterminal angle is an angle that has the same initial point as another angle but has a different measure.
What is coterminal angle?A coterminal angle is an angle that has a different measure in degrees from another angle but the same initial point and direction. It is an angle that is similar to another angle in orientation but may be different in size. Coterminal angles are significant in trigonometry and have numerous uses in physics, engineering, and mathematics.
Angles are frequently measured in degrees in mathematics, and they can have a value between 0 and 360. It's crucial to remember that different measures might be assigned to the same angle based on the starting and finishing points. For instance, a 90-degree angle is one that begins at the positive x-axis and ends at the positive y-axis. Additionally, the same angle can be expressed as 450 degrees, -90 degrees, and so forth. These angles are all regarded as coterminal angles.
According to question:
1. Find a coterminal angle between 0 and 360:
a) -330 degrees: 330 + 360 = 690, or -330 + 360 * 2 = 360
b) -4350 degrees: 4350 + 360 * 12 = 180
c) 640 degrees: 640
d) -4420 degrees: 4420 + 360 * 12 = 280
2. Find a coterminal angle between 0 and 27:
a) 35TC: 35TC modulo 27 = 35 % 27 = 8
b) 12 MARX: not a valid angle
c) 18 degrees: 18
d) 14 34: not a valid angle
e) 13 x 1ST: not a valid angle
3. Find a positive and a negative coterminal angle for each given angle:
a) 257 degrees: 257, -103
b) 15 74: 74, 15 + 360 = 375, -285
c) 36 degrees: 36, -324
d) 12 degrees: 12, -348
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3 1/2 is = ?/2 ????????????????????????????
Answer:
7/2
Step-by-step explanation:
Please help
Given the function f(x) = -3x^3 +3x^2+ 3x + 3, which of the following is true?
-It is positive
-It is a cubic function
-The domain is all real numbers.
-It has at most 2 solutions
-it is a polynomial function
Answer: Given the function f(x) = -3x^3 +3x^2+ 3x + 3, the following is true:
-It is not necessarily positive or negative as the value of f(x) depends on the value of x.
-It is a cubic function as it contains an x^3 term.
-The domain is all real numbers as there are no restrictions on the input x.
-It has at most 3 solutions as it is a cubic function and cubic functions can have at most 3 real roots.
-It is a polynomial function as it is a finite sum of terms involving non-negative integer powers of x.
Step-by-step explanation:
) Write a system of equations to describe the situation below, solve using substitution, and
fill in the blanks.
D) Quinn has $625 in his retirement account, and Ryan has $627 in his. Quinn is adding $12
per day, whereas Ryan is contributing $10 per day. Eventually, the two accounts will contain
the same amount. What balance will each account have? How long will that take?
(0) Quinn and Ryan will each have a retirement account balance of $
days.
after
On solving the provided question, we can say that equation for Quinn = > 625 + 12x and equation for Ryan => 627 - 10x.
What is equation?A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.
Quinn has $625 in his retirement account, and Ryan has $627
Quinn is adding $12 per day
equation for Quinn = > 625 + 12x, x is no. of days
Ryan is contributing $10 per day
equation for Ryan => 627 - 10x, x is no. of days
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Use the graph or table to find the equation that represents the relationship.
The equations that represent each line are, respectively:
y = - 3 · x + 5 y = x - 4 y = 2 · x - 1 y = (4 / 5) · x - 4How to determine the equations of the line
According to Euclidean geometry, we can generate any line from two distinct points on a plane. Herein we find two tables and two Cartesian representations of the lines, of which we must construct the corresponding line equations, whose definition is shown below:
y = m · x + b
Where:
m - Slopeb - Interceptx - Independent variable.y - Dependent variable.The slope can be found by secant line formula:
m = Δy / Δx
Now we proceed to determine each equation of the line:
Case 1
Slope
m = [- 34 - (- 10)] / (13 - 5)
m = - 24 / 8
m = - 3
Intercept
b = y - m · x
b = - 10 - (- 3) · 5
b = - 10 + 15
b = 5
Equation of the line
y = - 3 · x + 5
Case 2
Slope
m = [- 3 - (- 11)] / [1 - (- 7)]
m = 8 / 8
m = 1
Intercept
b = y - m · x
b = 3 - 1 · 7
b = 3 - 7
b = - 4
Equation of the line
y = x - 4
Case 3
Slope
m = [0 - (- 1)] / (0.5 - 0)
m = 2
Intercept
b = y - m · x
b = - 1 - 2 · 0
b = - 1
Equation of the line
y = 2 · x - 1
Case 4
Slope
m = [0 - (- 4)] / (5 - 0)
m = 4 / 5
Intercept
b = y - m · x
b = - 4 - (4 / 5) · 0
b = - 4
Equation of the line
y = (4 / 5) · x - 4
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Find the distance between the following numbers on the real number line
a=-11, b=1
Answer:
Step-by-step explanation:
12.
1+|-11|=12
lol
Most jobs pay you per day.
A) True
B) False
Answer:
B) False
In most job, you will get paid on a weekly basis, usually on a Friday.
Step-by-step explanation:
Hope it helps! =D