Answers
Answer:
40 and 50
Step-by-step explanation:
We know that River's mom drove for 45 minutes. Furthermore, at x miles per hour for a time amount y, she drove 10 miles, and at x+10 miles per hour for time amount z, she drove 25 miles. We can set up the equations like this:
x*y = 10
(x+10)*z = 25
y+z = 0.75
I knew to include time as the variable because time was given at the end, and is the only way possible to solve this. Furthermore, we can multiply x and y because we drive for x miles per hour for y hours, so
[tex]\frac{x miles}{hours} * \frac{yhours}{1} = xmiles*y[/tex]
I turned 45 into 0.75 as 45 is 3/4 of an hour, and y and z are in hours.
We're kind of stuck here, so it would be nice if we could limit the variables in an equation. One way to do this would be to solve for y in the first equation, so x=10/y. Then, we can plug that into the second equation to get
(10/y+10)*z=25
Combining that with the third equation, we can solve for z in the second equation to get that 25/(10/y+10)=z, and then plug that into the third to get that
y+25/(10/y+10) = 0.75
Multiplying both sides by 10/y+10 to get rid of the denominator, we get
10+10y+25=7.5/y+7.5
Then we multiply by y to get rid of the denominator
10y+10y²+25y=7.5+7.5y
Subtracting 7.5+7.5y to get everything on one side for a quadratic equation
10y²+27.5y-7.5=0
Plugging this into the quadratic equation, we get than y either equals -3 or 0.25. It's clear that you can't have negative time, so y = 0.25
Then, 0.75-0.25=0.5=z, and 10/0.25=40, so x=40, and x+10=50 for the 2 driving speeds
Related Questions
Use the substitution method to solve the system of equations. Choose the
correct ordered pair,
2y + 5x = 13
2y - 3x = 5
O
A (1,4)
B. (-3, 14)
O
O c. (3,7)
O D. (-1,9)
Answers
Answer:
A. (x , y) = ( 1, 4) is the SOLUTION of the given system of equations.
Step-by-step explanation:
Here, the given set of equations is:
2 y + 5x = 13 ....... (1)
2y - 3x = 5 ...... (2)
Now, to solve this question by SUBSTITUTION:
From (1), we get:
2 y + 5x = 13 ⇒ 2 y = 13 - 5 x
or, [tex]y = \frac{13 - 5x}{2}[/tex]
Put this value of y in (2) . We get
[tex]2y - 3x = 5 \implies 2\times\frac{(13-5x)}{2} - 3x = 5\\\implies 13 - 5 x - 3x = 5\\\implies- 8x = -8\\\implies x = 1[/tex]
Now, x = 1, put this value of x in (1),
2 y + 5x = 13 ⇒ 2y + 5(1) = 13
or, 2 y = 13- 5 = 8
or, y = 8 / 2 = 4, ⇒ y = 4
Hence, x = 1, y = 4 is the SOLUTION of the given system of equations.
In the image shown, line n is a transversal cutting lines l and m.
∠3 = 2x + 30
∠5 = 3x + 1
What is the measure of ∠5?
Answers
Answer:
88°
Step-by-step explanation:
Alternate interior angles are congruent. So, set the angles equal to each other and solve for x.
2x + 30 = 3x + 1
x = 29
So, ∠5 = 3x + 1 = 3(29) + 1 = 88°
Answer:
94
Step-by-step explanation:
had question on usa test prep
Select the correct answer.
Solve the following equation for
80x2 + 92x – 84 = 0
Answers
Answer:
x = 0.6 and x = -1.75
Step-by-step explanation:
80x2+92x−84=0
Use quadratic formula
x = (−b ±√(b2−4ac))/√2a
x = (-92 ± √(35344)) / 160
x = 95/160 and x = -280 / 160
x = 0.6 and x = -1.75
consider the equation y=16-x. which of the following statements is true
a. x is a function of y, but y is not a function of x.
b. y is a function of x, but x is not a function of y.
c. both x is a function of y and y is a function of x.
d. neither x is a function of y, nor is a function of x
Answers
Answer:
C. Both x is a function of y and y is a function of x
Step-by-step explanation:
A function is a relationship which assigns to each input (from the domain) value, a unique output (from the range).
y is a function of x means x is from domain, y is from range
x is a function of y means y is from domain, x is from range
1. Given [tex]y=16-x[/tex]
y is a function of x because for each x there is exactly one y corresponding to this x.
2. Rewrite [tex]y=16-x[/tex] expressing x in terms of y:
[tex]y-16=-x\\ \\-x=y-16\\ \\x=16-y[/tex]
x is a function of y because for each y there is exactly one x corresponding to this x.
Final answer:
In the equation y = 16 - x, both x and y are functions of each other since each variable can be expressed as having a unique output for each input of the other. The correct answer is c. both x is a function of y and y is a function of x.
Explanation:
To determine which statement is true regarding the equation y = 16 - x, we need to understand the concept of a function. A function, in mathematical terms, is a relationship between two sets that assigns to each element of the first set exactly one element of the second set. In simpler terms, for a variable to be a function of another variable, each input should give us exactly one output. This leads us to the vertical line test, which is a visual way to determine if a curve is a graph of a function of x.
Looking at the given equation, y is expressed in terms of x, implying that for each value of x, there is exactly one value of y. This satisfies the definition of a function, so y is a function of x. Conversely, if we solve the equation for x, we get x = 16 - y, which similarly means that for each value of y, there is exactly one value of x, so x is also a function of y.
Given these points, the correct answer is c. both x is a function of y and y is a function of x. This is because each variable can be expressed as having a unique output for each input of the other variable, therefore both variables are functions of each other.
PLEASE HELP I PUT 70 POINTS!!!!!
Answers
1. 8/64=1/8
2. 5/16
3. 33/84
4. 15/45=3/9=1/3
Answer:
1. 8/64=1/8
2. 5/16
3. 33/84
4. 15/45=3/9=1/3
Step-by-step explanation:
Hassan keeps picking playing cards out of a standard deck of 52 cards, hoping that he will draw a queen. There are four queens in the deck. After looking at each card, he places it back in the deck. What is the probability that Hassan will draw a Queen in the first seven attempts?
A.) 43%
B.) 46%
C.) 57%
D.) 68%
Answers
Answer:43%
Step-by-step explanation:
just finished test
Answer:
C.) 57%Step-by-step explanation:
The events describe is about picking a card, and placing it back into the deck. This means that the total number of event won't change in each trial.
We know that there are 4 queens of 52 cards. So, the probability of picking a card and be a queen is
[tex]P=\frac{4}{52}=\frac{1}{13}[/tex]
However, in this case, we have to apply the experimental probability definition, because we have several attempts. This experimental probability is defined as the ratio between the time the event occurs (4) and the total number of trials (7). That is
[tex]P_{exp}=\frac{4}{7}=0.57 \ (or \ 57\%)[/tex]
Therefore, the right answer is C.
!!!!!!!!!!!!!!!!!!!!
Answers
Option 3
The solution for given expression is [tex]\frac{(x - 4)(x - 4)}{(x + 3)(x + 1)}[/tex]
Solution:Given that we have to divide,
[tex]\frac{x^2 -16}{x^2 + 5x + 6} \div \frac{x^2 + 5x + 4}{x^2 -2x - 8}[/tex] ---- (A)
Let us first factorize each term and then solve the sum
Using [tex]a^2 - b^2 = (a + b)(a - b)[/tex]
[tex]x^2 -16 = x^2 - 4^2 = (x + 4)(x -4)[/tex] ----- (1)
[tex]x^2 + 5x + 6 = (x + 2)(x + 3)[/tex] ----- (2)
[tex]x^2 + 5x + 4 = (x+1)(x + 4)[/tex] ---- (3)
[tex]x^2 -2x - 8 = (x-4)(x + 2)[/tex] ---- (4)
Now substituting (1), (2), (3), (4) in (A) we get,
[tex]\frac{(x + 4)(x -4)}{(x +2)(x +3)} \div \frac{(x+1)(x+4)}{(x-4)(x +2)}[/tex]
To do division with fractions, we turn the second fraction upside down and change the division symbol to a multiplication symbol at the same time. Then we treat this as a multiplication problem, by multiplying the numerators and the denominators separately.
[tex]\frac{(x + 4)(x -4)}{(x +2)(x +3)} \times \frac{(x - 4)(x + 2)}{(x + 1)(x + 4)}[/tex]
On cancelling terms we get,
[tex]= \frac{(x -4)(x-4)}{(x + 3)(x + 1)}[/tex]
Thus option 3 is correct
DOES ANYONE KNOW HOW TO DO THIS PROBLEM???? I AM NOT SURE HOW TO SOLVE THIS PROBLEM!!!!!!!!!!!!!!!!!
Answers
Answer:
Filled table below
Step-by-step explanation:
There are three columns to fill out according to the requirements of the question:
The observed time will be taken from the given table (or scattered points in the graph)
The predicted time will be computed from the equation of the best fit line
The residual will be the difference between both
For x=4.0, the time spent exercising is 4.5 hours
If we use the line, we have
[tex]y=-0.4x+7.02= -0.4(4.0)+7.02=5.42[/tex]
The residual is 5.42-4.5=0.92
For x=5.0, the time spent exercising is 6.5 hours
If we predict with the line, we have
[tex]y=-0.4x+7.02= -0.4(5.0)+7.02=5.02[/tex]
The residual is 5.02-6.5=-1.48
The values will be shown in the table below
The triangle shown below has an area of 50units squared. Find the missing side.
Answers
This solution uses the formula for the area of a triangle together with the Pythagorean theorem to determine the length of the missing side in a right triangle. Assuming one side and the area of the triangle are given, the step involves rearranging the area formula to solve for the missing side. The Pythagorean theorem guarantees the accuracy of this method.
Explanation:The subject of this question is Mathematics. The grade of this question is Middle School. Based on the information given, we are asked to find a missing side of a triangle with a given area.
Since this is a right triangle, we can use the Pythagorean theorem, which states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as x² + y² = h².
Assuming we know one side and the area of the triangle, we can use the formula for the area of a triangle, which is 1/2 * base * height = 50. If we know one of the other sides, let's say 'y', we can solve for the other side 'x' by rearranging this formula to solve for 'x', then substituting the known values.
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On a large map the distance from austin,texas,to milwaukee,wisconsin, is 13.7 inches. The actual distance is about 1000 miles.what is the distance on the same map from indianapolis,indiana,to louisville,kentucky, if the actual distance is about 100 miles?round your answer to the nearest tenth.
Answers
The distance from Indiana to Louisville is 1.37 inches on map.
Step-by-step explanation:
Distance from texas to milwaukee = 1000 miles
Distance on map = 13.7 inches
Distance from indiana to louisville = 100 miles
Distance on map = x
Using proportion;
Distance from texas to milwaukee: distance on map :: Distance from indiana to louisville : Distance on map
[tex]1000:13.7::100:x[/tex]
Product of mean = Product of extreme
[tex]100*13.7=1000*x\\1370=1000x\\1000x=1370[/tex]
Dividing both sides by 1000;
[tex]\frac{1000x}{1000}=\frac{1370}{1000}\\x=1.37\ inches[/tex]
The distance from Indiana to Louisville is 1.37 inches on map.
Keywords: Ratio, proportion, distance
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Can someone help real quick??
Answers
Answer:
AD=23
Step-by-step explanation:
18+5=23 combined factors
Answer:
AD=23
Step-by-step explanation:
Two fractions are given. For each one, write its decimal equivalent and determine if the decimal is terminating or non terminating 9/20 and 4/15
Answers
Answer:
9/20 yes, 4/15 not. See below
Step-by-step explanation:
Pick 9/20 and multiply numerator and denominator by 5:
9/20 = 45/100
We know that if we divide a number by 100 we need to move the coma as two places left, so:
9/20 = 45/100 = 0.45
And this is a terminal decimal as we know where it ends.
On the other hand if we pick 4/15 let try to divide it (here I will do it 'manually'):
4 |_ 15
we can divide 4 by 15, so we use 40 and begin with a comma
40 |_ 15
0.
15 enters 2 times in 40 with a rest of 10, so:
40 |_ 15
30 0.2
100
100 divided by 15 is 6 and we have 10 as rest again, and again and again...
40 |_ 15
30 0.266.....
100
100
....
So, we will have 0.266666666666666 infinitely. The decimal for 4/15 is non terminating and is 0.26666666666666666...
A flock of 20 seagulls merges with a flock of cardinals. The new flock is bigger than either of the original ones, but still, it is no larger than 100 birds. How many birds were in the flock of cardinals?
Answers
Answer:
There are 80 birds in the flock of cardinals.
Step-by-step explanation:
Given,
Number of seagulls in a flock = 20
Total number of birds of new flock = 100
To find out the number of birds in cardinals we have to subtract number of seagull in flock from total number of birds of new flock.
Number of birds in cardinal = Total number of birds of new flock - Number of seagulls in a flock
Number of birds in cardinal = [tex]100-80=20[/tex]
Hence there are 80 birds in the flock of cardinals.
What is the answer for
-6n-2n=16
Answers
Answer:
n=-2
Step-by-step explanation:
-6n-2n=16
-8n=16
n=16/-8
n=-2
Explanation:
A sphere with a radius of 6 cm has the same volume as a cone with a height of 6 cm. What is the radius of the cone?
A) 2 cm
B) 4 cm
C) 8 cm
D) 12 cm
Answers
D) 12 cm is the right answer
Step-by-step explanation:
Given
[tex]Radius\ of\ sphere = r_s = 6\ cm\\Height\ of\ cone = h = 6 cm\\[/tex]
As the volumes of cone and sphere are same
[tex]V_s = V_c\\\frac{4\pi {r_s}^3}{3} = \frac{\pi {r_c}^2h}{3}[/tex]
Putting the known values
[tex]\frac{4\pi {6}^3}{3} = \frac{\pi {r_c}^2*(6)}{3}[/tex]
Dividing both sides by pi
[tex]\frac{4\pi {(6)}^3}{3\pi } = \frac{\pi {r_c}^2*(6)}{3\pi }\\\frac{4*{(6)}^3}{3} = \frac{{r_c}^2*(6)}{3}[/tex]
Multiplying both sides by 3
[tex]4*(6)^3 = 6{r_c}^2\\{r_c}^2 = \frac{4*(6)^3}{6}\\{r_c}^2 = 4 * 6^2\\{r_c}^2 = 144[/tex]
Taking Square root on both sides
[tex]\sqrt{{r_c}^2}=\sqrt{144}\\r_c = 12\ cm[/tex]
Hence,
D) 12 cm is the right answer
Keywords: Volumes, areas
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On a recent day, 8 euros were worth $9 and 24 euros were worth 27.
Answers
This question is incomplete, here is the complete question:
On a recent day, 8 euros were worth $9 and 24 euros were worth $27. Write an equation of the form y = kx to show the relationship between the number of euros and the value in dollars.
The equation that represents the relationship between the number of euros and the value in dollars is y = 1.125 x
Step-by-step explanation:
On a resent day;
8 euros were worth $924 euros were worth $27We need to write an equation of the form y = kx to show the relationship between the number of euros and the value in dollars
∵ The form of the equation is y = kx, where x is the number of
euros and y is the value in dollars
∵ 8 euros were worth $9
∴ (8 , 9) is an ordered pair belong to the equation
∵ 24 euros were worth $27
∴ (24 , 27) is another ordered pair belong to the equation
To find k substitute x and y in the equation by the coordinates of one of these two points
∵ x = 8 and y = 9
∵ y = kx
∴ 9 = 8k
- Divide both sides by 8
∴ 1.125 = k
- Substitute the value of k in the equation
∴ y = 1.125 x
To check the equation substitute x by the x coordinate of the 2nd point if it gives the same value of the y-coordinate of the point then the equation is true
∵ x = 24
∵ y = 1.125 x
∴ y = 1.125(24)
∴ y = 27 the same value of the y-coordinate of the point
∴ The equation is true
The equation that represents the relationship between the number of euros and the value in dollars is y = 1.125 x
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Which of the following shows a line with a slope of 2/3?
Answers
Answer:
B
Step-by-step explanation:
Remember that slope=rise/run. You can find the right graph with the slope of 2/3 very easily by counting, upward 2 and rightward 3.
Assume that a varies directly as b. What is the constant of proportionality if a = 8 when b = 2?
k = 16
k = 4
k=1/4
k=6
Answers
Answer:
k = 4
Step-by-step explanation:
Given that a varies directly as b then the equation relating them is
a = kb ← k is the constant of variation
To find k use the condition a = 8 when b = 2
k = [tex]\frac{a}{b}[/tex] = [tex]\frac{8}{2}[/tex] = 4
Answer:
K = 4
Step-by-step explanation:
Given that varies a directly as b then the equation relating them is
Simply implies that a is directly proportional to b, that is increase in a will cause increase in, and decrease in a will cause decrease in b, and vice versa, where k remains constant.
a α b
a = kb, where k is constant
To find k use the condition a = 8 when b = 2, we make k the subject of the formular
K = a/b
K = 8/2
K = 4
-5a + b = 8
7a + 9b = -32
Answers
Answer:
a=-2 and b=-2
Step-by-step explanation:
So I just used Elimination I made the top part the same as b then I just subtract and did some other stuff,hope the pic helps
Write a unit rate for the situation. Round to the nearest hundredth if necessary.
Traveling 212 km in 6h
Answers
Answer:
35.33 km/h.
Step-by-step explanation:
Given: Distance= 212 km.
Times= 6 hours
Now, finding unit rate (speed) for the situation.
Formula; Speed= [tex]\frac{Distance}{time}[/tex]
Speed (rate)= [tex]\frac{212}{6} = 35.3333\ km/h[/tex]
Speed (rate)= 35.3333≅ 35.33 km/h (nearest hundredth).
∴ Rate of the unit is 35.33 km/h
A geologist visits 40 volcanoes in Alaska and California.15% of volcanoes are in California.how many volcanoes does the geologist visit in California and how many in Alaska?
Answers
Answer:
The answer is 34
To solve this, percentage calculations were used. The geologist visited 6 volcanoes in California, which is 15% of 40, and the remaining 34 in Alaska.
The question requires us to calculate the number of volcanoes the geologist visited in California and Alaska. The total number of volcanoes visited is 40, and 15% are in California. To find the number of volcanoes in each state, we employ basic percentage calculations.
First, to find the number of volcanoes in California, we multiply the total number by 15% (or 0.15):
Number of volcanoes in California = 40 * 0.15 = 6.
To find the number of volcanoes in Alaska, we subtract the number of volcanoes in California from the total:
Number of volcanoes in Alaska = 40 - 6 = 34.
Therefore, the geologist visits 6 volcanoes in California and 34 volcanoes in Alaska.
jay spent 3/8ths of his life working for a company, if jay has been working for his current company for 15 years, how old is he ?
Answers
Answer:
40
Step-by-step explanation:
if 3/8 equals 15 that means 1/8 equals 5 because 15/3=5. now if we multiply 5 by 8 then we get 40 years
If jay has been working for his current company for 15 years, then his age is 40 years.
What is a fraction?A fraction is written in the form of p/q, where q ≠ 0.
Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.
Given, jay spent 3/8ths of his life working for a company and he has been working for his current company for 15 years.
Assuming Jay's age to be x years.
∴ (3/8) of x is 15 years.
(3/8)x = 15.
x = 15×(8/3).
x = 40.
So, Jay's age is 40 years.
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Are the ratios of the number of people to the number of rollercoaster cars in a proportional relationship? Explain your reasoning.
Answer in 2 complete sentences.
183=61
305=61
366=61
488=61
Answers
The ratios of the number of people to the number of rollercoaster cars are proportional because all the given ratios simplify to 6:1.
Explanation:To determine if the ratios of the number of people to the number of rollercoaster cars are in a proportional relationship, we must see if the ratios are equivalent. If we look at the provided ratios, 18:3, 30:5, 36:6, and 48:8, we see that when simplified all become 6:1. This indicates that the relationship is indeed proportional because the same ratio is maintained throughout all given pairs.
Given the domain {-4, 0, 5}, what is the range for the relation 12x + 6y = 24? A. {2, 4, 9} B. {12, 4, -6} C. {-4, 4, 14} D. {-12, -4, 6}
Answers
The range is: B. {12, 4, -6}
Step-by-step explanation:
Given
12x + 6y = 24
Here x is the input and y is the output
So,
Replacing y with f(x)
[tex]12x +6f(x) = 24\\6f(x) = 24 - 12x\\\frac{6f(x)}{6} = \frac{24-12x}{6}\\f(x) = \frac{24-12x}{6}[/tex]
Domain = {-4, 0, 5},
We will put the elements of domain, one by one, to find range
[tex]f(-4) = \frac{24-12(-4)}{6}\\=\frac{24+48}{6}\\= \frac{72}{6}\\=12\\\\f(0) = \frac{24-12(0)}{6}\\=\frac{24}{6}\\= 4\\\\f(5) = \frac{24-12(5)}{6}\\=\frac{24-60}{6}\\=\frac{-36}{6}\\=-6[/tex]
Hence,
The range is: B. {12, 4, -6}
Keywords: Range, Domain, functions
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{12, 4, -6}
Step-by-step explanation:
The relation is given by the equation as 12x + 6y = 24 ........... (1)
Now, the domain of this function is {-4, 0, 5}
We have to find the range of this function corresponding to the given domain.
Now, for x = - 4,
12(-4) + 6y = 24 {From equation (1)}
⇒ 6y = 72
⇒ y = 12
Now, for x = 0,
12(0) + 6y = 24 {From equation (1)}
⇒ 6y = 24
⇒ y = 4
Now, for x = 5,
12(5) + 6y = 24 {From equation (1)}
⇒ 6y = -36
⇒ y = -6
Hence, the range for the relation is {12, 4, -6} (Answer)
The total cost of renting a vacation
home includes a deposit and a daily
rental fee of $125. A family rents a
vacation home for 5 days and pays $700.
Assume the relationship is linear. Find
and interpret the rate of change and the
initial value.
Answers
Answer:
y=125x+75
Step-by-step explanation:
Y= 125x+B
700=125(5)+B
700=625+B
700-625=625-625+B
75=B
The initial value, or deposit, for the vacation home is $75. The rate of change, or the cost per day, is $125. This constitutes a linear relationship where the total cost increases by a constant daily fee as the number of rental days increases.
Explanation:In this problem, the total cost of the vacation home equals the deposit plus (daily rental fee * number of days). The total cost came out to be $700 when the family rented the home for 5 days. Given that the daily rental rate is $125, that means that the cost of the rental alone was $125 * 5 = $625.
Subtract the cost of the rental from the total cost to find the deposit: $700 - $625 = $75. Therefore, the initial value is $75, which represents the deposit.
The rate of change, which is the cost per day, is $125. This means for every additional day the family rents the vacation home, they are charged an additional $125. So the relationship is linear because the total cost increases by a constant rate - the daily fee - as the number of days increases.
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I need help with question #24 please help me
Answers
Answer:
f=10
Step-by-step explanation:
$132 in the ratio 2 : 3 : 6
Answers
Answer:
24:36:72
Step-by-step explanation:
multiply 2,3,and 6 by 12 and you got the ratio 24:36:72, which adds to 132
Please answer this correctly
Answers
Answer:
60 minutes
Step-by-step explanation:
There are 3 feet in a yard, so a football field is 300 feet long.
Dive 300 by 5 to find the total minutes.
300 / 5 = 60
Answer:
1 hour
Step-by-step explanation:
100 yards = 300 feet
300 / 5 = 60
60 min = 1 hour
Answer: It would take 1 hour for sloths to walk across a 100-yard football field.
The values of x and y vary directly and one pair of values are given. Write an equation that relates x and y. x=1,y=0.5
Please help me!!
Answers
Answer:
y = 0.5x
Step-by-step explanation:
Given that x and y vary directly then the equation relating them is
y = kx ← k is the constant of variation
To find k use the condition x = 1, y = 0.5
k = [tex]\frac{y}{x}[/tex] = [tex]\frac{0.5}{1}[/tex] = 0.5
y = 0.5x ← equation of variation
Answer: 0.5
Step-by-step explanation:
M=4/5 y - intercept of -2
Answers
M=4/5 y - intercept of -2
y= mx+b - slope formula
slope is also m
b is the y-intercept
answer:
y= 4/5x-2
Answer:
y = [tex]\frac{4}{5}[/tex] x - 2
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = [tex]\frac{4}{5}[/tex] and c = - 2
y = [tex]\frac{4}{5}[/tex] x - 2 ← equation of line