Each line represents a proportional relationship. Write an equation for each line. Show your work.
Answers
Answer:
The equation of line a is y = x
The equation of line b is y = [tex]\frac{2}{3}[/tex] x
Step-by-step explanation:
The equation of the proportional is y = m x, where
m is the slope of the line (constant of proportionality)The rule of the slope of a line is m = [tex]\frac{y2-y1}{x2-x1}[/tex] , where
(x1, y1) and (x2, y2) are two points on the line∵ Line a passes through points (0, 0) and (3, 3)
∴ x1 = 0 and y1 = 0
∴ x2 = 3 and y2 = 3
→ Substitute them in the rule of the slope above
∵ m = [tex]\frac{3-0}{3-0}=\frac{3}{3}[/tex]
∴ m = 1
→ Substitute in the form of the equation above
∴ y = (1)x
∴ y = x
∴ The equation of line a is y = x
∵ Line b passes through points (0, 0) and (3, 2)
∴ x1 = 0 and y1 = 0
∴ x2 = 3 and y2 = 2
→ Substitute them in the rule of the slope above
∵ m = [tex]\frac{2-0}{3-0}=\frac{2}{3}[/tex]
∴ m = [tex]\frac{2}{3}[/tex]
→ Substitute in the form of the equation above
∴ y = ([tex]\frac{2}{3}[/tex]) x
∴ y = [tex]\frac{2}{3}[/tex] x
∴ The equation of line b is y = [tex]\frac{2}{3}[/tex] x
Related Questions
The ratio of 6th-grade students to 7th-grade students in a soccer league is 15:10. If there are 100 students in all, how many 7th graders are there? *
Answers
Answer:
40 7th grade students.
Step-by-step explanation:
Ok so first we know the total equals 100. In order to divide the number of 6th graders and 7th graders equally, we add 15 and 10 which equals 25. Now, 100 divided 25 equals 4. Boom! We multiply 15 by 4 and that equals 60. This means there are 60 6th graders. We multiply 10 by 4 which means there are 40 7th graders. Now to check if we did it all right we add 60 and 40 which equals 100 STUDENTS IN ALL. This means we did it right. So it asked us for the amount of 7th graders which is 40! Hope this helps.
Zain has 12 shirts. Three shirts are red, 4 shirts are blue, and the rest are white. What is the ratio of white shirts to blue shirts?
Answers
Answer:
5:4
Step-by-step explanation:
Answer:
5:4
Step-by-step explanation:
3 shirts (red)
4 shirts (blue)
3+4=7-12=5
5 shirts (white)
1. Describe how the graph of y= x2 can be transformed to the graph of the given equation.
y = x2 + 8
Shift the graph of y = x2 up 8 units.
Shift the graph of y = x2 right 8 units.
Shift the graph of y = x2 left 8 units.
Shift the graph of y = x2 down 8 units.
Answers
Answer:
Step-by-step explanation:
Please write y = x^2. The " ^ " symbol indicates exponentiation.
Here's how we get from the graph of y = x^2 to the graph of y = x^2 + 8:
Graph y = x^2. Now translate the entire graph 8 units up.
WHAT IS THE ALGEBRAIC EXPRESSION FOR THE SUM OF N AND 9?
Answers
The algebric expression for the sum of N and 9 is [tex]\tt{ N + 8}[/tex]
The algebraic expression for the sum of N and 9 will be N + 9.
An algebraic expression simply means the idea of expressing numbers using alpahabets or letters without specifying their actual value.
Based on the information given, we have to add the variables. Therefore, the algebraic expression for the sum of N and 9 will be N + 9.
Read related link on:
https://brainly.com/question/19262784
I need help with 1(F)
Answers
Answer:
Step-by-step explanation:
1) e) -3 - (-1) = -3 + (+1) = -2
f) [tex]3\frac{7}{8}- (-1\frac{1}{4}) = \frac{31}{8}-(-\frac{5}{4})\\[/tex]
[tex]= \frac{31}{8} + (+\frac{5}{4})\\\\= \frac{31}{8} + \frac{5*2}{4*2}\\\\= \frac{31}{8} + \frac{10}{8}\\\\= \frac{31+10}{8}\\\\= \frac{41}{8}\\\\= 5\frac{1}{8}[/tex]
1E. The number 2A5A0A2 is divisible by 99. What is the digit A?
Answers
We know, a number is divisible by 9 if the sum of digits is also divisible by 9.
Also, since A is an digit, so A is in between 0 to 9.
2+A+5+A+0+A+2 = 3A + 9
3A + 9 should be divisible by 9.
3A + 9 = 9n
A = (9n -9)/3
For n= 1 :
A = 0
For n=2 :
A = 3
For n= 3 :
A = 9
After this A > 9 which is not accepted.
Therefore, the digit A can be 0, 3 and 9 .
Hence, this is the required solution.
The digit A that makes 2A5A0A2 to be divisible by 99 is;
A = 3
From study of divisibility of single digit numbers, it was discovered that a number can be divisible by 9 or a multiple of 9 provided the sum of digits is also divisible by 9.We are given the number 2A5A0A2
A is a single digit and as such will be between 0 and 9.
Thus, using the principle above;
2 + A + 5 + A + 0 + A + 2 = 3A + 9
Applying the principle;3A + 9 must be divisible by 9.
Thus;
3A + 9 = 9x
A = (9x - 9)/3
When x = 1;
A = 0
When x = 2;
A = 3
When x = 3;
A = 9
Since A is a single digit, then it means that x cannot be more than 4 as any value of x more than 4 will yield a value of A that is not a single digit.Now, when we place either the value of 0, 3 or 9 for A into the given number, the only one that yields a number that is divisible by 99 is A = 3
Read more at; https://brainly.com/question/19299358
You and your friend are baking some cookies for your classmates. The recipe you have called for ½ cup of sugar. If you don’t have a ½ measuring cup, what is another measurement you can use to equal ½?
Answers
Answer:
just need points
Step-by-step explanation:
find the exact values of the six trigonometric functions of 0
Answers
Complete question is;
Find the exact values of the six trigonometric functions 0 if the terminal side of 0 in standard position contains the points(-5,-4).
Answer:
Sin θ = -4/√41
Cos θ = -5/√41
tan θ = 4/5
Cosec θ = (√41)/-4
Sec θ = (√41)/-5
Cot θ = 5/4
Step-by-step explanation:
Now, we are given the point (-5, -4)
These are x and y points.
They will form a triangle and we know that from pythagoras theorem;
x² + y² = r²
Where r is the distance between the point and the origin
Thus;
r² = (-5)² + (-4)²
r² = 25 + 16
r = √41
So, y is the opposite side of the triangle while x is the adjacent side with r being the hypotenuse.
Thus, the trigonometric ratios are;
Sin θ = opp/hyp = -4/√41
Cos θ = adj/hyp = -5/√41
tan θ = opp/adj = -4/-5 = 4/5
Cosec θ = 1/Sin θ = 1/(-4/√41) = (√41)/-4
Sec θ = 1/cos θ = 1/(-5/√41) = (√41)/-5
Cot θ = 1/tan θ = 1/(4/5) = 5/4
- A teacher wanted to determine the effectiveness of two different learning tools—a computer program or a hands-on approach—for a particular concept she was preparing to teach. She will assign her students to one of the two methods to spend the whole class time to learn this concept. Which of the following variables would be moderated due to random assignment? a- the teacher b- time spent in class c- computer experience d- the different learning tools
Answers
Answer:
The answer is Computer Experience.
Step-by-step explanation:
what fraction of 9hours 30minutes
Answers
-8x-x=x-4x plz find for x
Answers
Answer: x=0
Step-by-step explanation:
Hi , the answer I choose was wrong , what is the correct answer ? Will choose brainlest so be quick
Answers
Answer:
SAS
Step-by-step explanation:
Answer:
it’s the first one
Step-by-step explanation:
Now think about how the rise of credit affected Americans and the economy.
Look at each of the following consequences of the rise of credit. Choose whether each consequence was a benefit or a problem. Select the answer that matches each consequence.
Making it more convenient to buy products:
X benefit
Helping demand for products stay high:
Pushing Americans to overspend:
Causing Americans to go into debt:
benefit
Answers
Benefit
Benefit
Problem
Problem
Credit has been defined as the borrowing of money by companies and consumers. The transactions of money result in a rise in the economy with the rise in money in the market. However, in some circumstances, there has been freezing of money results in the inter-lending to the firms. This results in an economic crisis.
(a) Making it more convenient to buy products:
It has been a benefit as there has been more money in the market resulting in the rise in the economy.
(b) Helping demand for products stay high:
It has been a benefit as there has been support to the economy with rise in credit.
(c) Pushing Americans to overspend:
This works as the problem, as the irregular spending with credit results in the freezing of the amount.
(d) Causing Americans to go into debt:
It has been a problem that here has been the credit crisis that will result of the credit rise.
For more information, refer to the link given below:
https://brainly.com/question/20650157
Which part of this graph shows a nonlinear relationship?
Answers
Answer:
4
Step-by-step explanation:
Answer:
#4 is the correct answer
Think of linear as a straight line, if you notice a curve like this one, it's going up exponentially, not in a steady rate.
Try me IF you can !!!!!!!!!!!
.
.
.
.
.
.
.
.
. 0+0=?
Answers
Answer: 0?
Step-by-step explanation:
Abcd is a Square, where AE=1.4. Use the properties of a square to determine the length of BD. Please help!
Answers
Answer:
2.8
Step-by-step explanation:
1.4 is AE correct?
Well then, BD is twice the length of that, so multiply by 2 to get 2.8.
Answer:
Step-by-step explanation:
2.9
Estimate 39 divided by 5
Answers
ummm.. i think its 7.8?
The value of the division of the number 39 by 5 is 7.8.
A mathematical procedure called division involves dividing a quantity or number into equal pieces or groups. It is used to calculate how many times one number (the divisor) may be subtracted from another (the dividend) in order to get an accurate answer or a quotient. It is the opposite operation of multiplication.
To estimate 39 divided by 5, we can use rounding to simplify the calculation.
Round 39 to the nearest multiple of 5. In this case, 39 is already a multiple of 5, so we don't need to round it.
Divide the rounded number by 5. Since 39 is already a multiple of 5, we can directly divide it by 5.
39 ÷ 5 = 7.8
So, an estimated value for 39 divided by 5 is 7.8.
To know more about division follow
https://brainly.com/question/30126004
#SPJ6
What’s the value of x?
Answers
Answer:
x=6
Step-by-step explanation:
We know that <AWV is 90, so we can set up an equation. This equation is 54+3x+18=90, we know this is true because the two smaller angles are complementary. Then to find x simply solve the equation.
First, add like terms
3x+72=90
Then, subtract 72 from both sides
3x=18
Finally, divide both sides by 3
x=6
1. A school gym has a width of 270 ft. Which of the following is equivalent to 270 ft?
90 yd
810 yd
9 yd
Not here
Answers
Answer:
It should be 90
Step-by-step explanation:
Because 270 divided by 3 is 90
The sum of the measures of two exterior angles of a triangle is 257. What is the measure of the third exterior angle?
Answers
At noon, a tank contained 10 cm of water. After several hours, it contained 7 cm of water. What is the percent decrease of water in the tank?
Please answer with explanation.
Answers
So 30%.was lost
Answer:
10cm - 7cm = 3cm
this 3cm is the decrease in the depth of water, let us find the percentage decrease.
%decrease=(decrease÷original depth) × 100%
%decreas=(3cm÷10cm)×100%
therefore we get 30%
A Subaru Outback and a Freightliner Cascadia truck leave an intersection at the same time. The Outback heads west at an average speed of 70 miles per hour while the Cascadia heads south at an average speed of 45 miles per hour. Find an expression for their distance apart d (in miles) at the end of t hours.
Answers
Answer:
d = 83.22tStep-by-step explanation:
The lines form legs of a right triangle, so the distance between the cars is the hypotenuse
The lines at t hours are:
70t and 45tSo the distance d is:
d = √(70t)²+(45t)² = √4900t²+2025t² = √6925t² = 83.22td = 83.22tLynn is making custom bricks. She combines 39 pounds of water and 48 pounds of brick dust in a mixing bucket. She spills 13 pounds of the mixture while stirring the contents. The mixture is then poured into small dirt holes to make bricks. Each brick requires 7 pounds of mixture, and the leftover mixture is washed out of the mixing bucket.
What is the greatest number of bricks Lynn can make?
(blank)( bricks
How many pounds of mixture will be washed out of the bucket if Lynn makes the greatest number of bricks?
(blank ) pounds
Answers
Answer:
Um, no lo sé, lo siento, solo necesito los puntos
Step-by-step explanation:
2. What is the thickness of the sediment along the east coast of North
America? I
Answers
Help me out! Brainliest if you give me a valid answer & explanation!
Q: Find the area of the shape below!
Answers
Answer:
Answer is 131 square ft
Step-by-step explanation:
You need to split the shape into two
12 times 8 equals 96
7 times 5 equals 35
Add together and get answer of 131
Hope I could help! Have a great day!
Solve the system of linear equations below.
x - 3y = -3
x + 3y = 9
A.
x = -12, y = 7
B.
x = 3, y = 2
C.
x = 6, y = 1
D.
x = 6, y = 2
Answers
Answer:
The answer is X=3, Y=2
hope this helps :)
The perimeter of a rectangular field is 364 yards. If the width of the field is 85 yards, what is its length?
Answers
Answer:
[tex]\huge\boxed{97 yards}[/tex]
Step-by-step explanation:
Important Information:
Perimeter of rectangle=[tex]Lenght+Length+width+width[/tex]
Method:
The first step to work this out is to multiply the width of 85 by 2, this gives you 170.This is because a rectangle has two sets of equal sides. This means that there two widths.
The next step is to subtract 170 from the perimeter of 364, this gives you 194. This is because the formula for the perimeter of a rectangle is[tex]Lenght+Length+width+width[/tex]. This means that in order to isolate the values of the lenght we must subtract the values of the width.
The final step is to divide the value of 194 by 2, this gives you 97. This is because that is the value for 2*the length. That means in order to work out the value of 1 you would need to divide by 2.
Step By Step:
1) Multiply 85 by 2.
[tex]85*2=170[/tex]
2) subtract 170 from 364.
[tex]364-170=194[/tex]
3) Divide 194 by 2.
[tex]194/2=97[/tex]
4x + 5 = 2x + 9, find the value of x
Answers
Answer:
x =2
Step-by-step explanation:
4x - 2x = 9-5
2x = 4
x = 4
How would I solve for this. Hurry and I will make u bra I lost
Answers
90+40+x+59=180
189 +x =180
we subtract 189
x= -9
Please help please please
Answers
Answer:
100
Step-by-step explanation:
5x2=10x10=100
Answer: It is 160cm.