Answers
The equation of the line will be y = 4/3x + 3. The correct option is C.
What is an equation of the line?An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
The general form of the equation of the line:-
y = mx + c
m = slope
c = y-intercept
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
From the given graph the slope will be calculated as:-
Rise = 4
Run = 3
Slope = Rise / Run = 4 / 3
The y-intercept is 3.
The equation can be written as:-
y = mx + c
y = 4/3x + 3
Therefore, the equation of the line is y = 4/3x +3.
To know more about an equation of the line follow
https://brainly.com/question/18831322
#SPJ2
Related Questions
Solve the system 2x-2y=10 4x-5y=17
Answers
4x-4y=20,
given:4x-5y=17
y=3
pluck it in
2x-6=10
move the 6 to the right
2x=16
divide
x=8
y=3
Equation 2) 4x - 5y = 17
Multiply ALL of equation 1 by 2.
1) 2(2x - 2y = 10)
Simplify.
1) 4x - 4y = 20
2) 4x - 5y = 17
Subtract equations from one another.
y = 3
Plug in 3 for y in the first equation.
1) 2x - 2y = 10
2x - 2(3) = 10
Simplify.
2x - 6 = 10
Add 6 to both side.s
2x = 16
Divide both sides by 2.
x = 8
------------------------------------
Check your work by plugging in 8 for x, and 3 for y into the original equations.
2x - 2y = 10 & 4x - 5y = 17
1) 2x - 2y = 10
2(8) - 2(3) = 10
Simplify.
16 - 6 = 10
10 = 10
2) 4x - 5y = 17
4(8) - 5(3) = 17
Simplify.
32 - 15 = 17
17 = 17
Therefore, x = 8, y = 3
~Hope I helped!~
382 & 3/10 - 191 & 87/100= WHAT?
Answers
Carol ate 2/5 of the cake. Dima ate 3/5 of the REMAINING CAKE, mom ate the rest.
How many times more did Carol eat compared to Dima? PLEASE EXPLAIN, GIVING BRAINLIEST, PLEASE HELP.
Answers
Barb’s class has 18 bikes .tim’s class has some rows of bikes with 5 bikes in each row. Tim’s class has more bikes than barb’s class. How many rows of bikes could tim’s class have?
Answers
The perimeter of a square is 26.46 inches. What is the side length of the square?
Answers
Normally it would be:
P=s1+s2+s3+s4
for a square its simply
P=4s
26.46=4S
6.615=S
Each side is 6.615 inches
The side length of a square whose perimeter is 26.46 inches can be calculated by dividing the given perimeter by 4 (the number of sides in a square), resulting in a side length of approximately 6.615 inches.
Explanation:The subject of this question is Mathematics, with the specific topic being measurement and geometry. This question is applicable to Middle School grade levels. The student seeks to determine the side length of a square, knowing the perimeter is 26.46 inches.
To find the side length, we need to recall the formula for the perimeter of a square: P = 4s, where P represents the perimeter and s represents the length of a side. The student's square has a perimeter of 26.46 inches, so the equation would be 26.46 = 4s.
To isolate the value of s, we divide both sides of the equation by 4. This gives us: s = 26.46/4. Upon doing the division, we find that each side of the square is approximately 6.615 inches.
Learn more about Side Length of a Square here:https://brainly.com/question/24584437
#SPJ3
The table of values below represents a linear function and shows the height of a tree since it was transplanted. What was the height of the tree when it was transplanted?
Answers
The height of the tree when it was transplanted was:
4 feet
Step-by-step explanation:As we could observe that the given table represents a linear function.
The table is given as follows:
Year since it was 4 4.5 5
transplanted
Height (Feet) 12 13 14
We will find the linear function.
Let y denotes height and x denote year since it was transplanted.
We know that any linear function passing through two points (a,b) and (c,d) is given by:
[tex]y-b=\dfrac{d-b}{c-a}\times (x-a)[/tex]
Here let (a,b)=(4,12) and (c,d)=(5,14)
Hence, the linear function is calculated as follows:
[tex]y-12=\dfrac{14-12}{5-4}\times (x-4)\\\\\\y-12=2(x-4)\\\\\\y-12=2x-8\\\\\\y=2x-8+12\\\\\\y=2x+4[/tex]
Now the height of tree when it was transplanted is the value of y when x=0
Hence, when x=0 we have:
y=4
Hence, the height was:
4 feet
A rectangle has its base on the x axis and its upper two vertices on the parabola y = 9 − x2. (a) Draw a graph of this problem. (b) Label the upper right vertex of the rectangle (x,y) and indicate the lengths of the sides of the rectangle. (c) Express the area A as a function of x and state the domain of A. (d) Calculate the derviative of A and solve for the critical values. (e) What is the largest area the rectangle can have?
Answers
Answer:
(a) see attached(b) width: 2x; height: y = 9-x²(c) A=2x(9-x²) . . . 0 ≤ x ≤ 3(d) dA/dx = -6x² +18; x=±√3(e) 12√3 units²Step-by-step explanation:
(a) The attachment shows the graph of the parabola in blue. It also shows an inscribed rectangle in black.
(b) The upper right point of the rectangle is shown in the attachment as (x, y). The dimension y is the height of the rectangle. The x-dimension is half the width of the rectangle, which is symmetrical about the y-axis. Hence the width is 2x.
(c) As with any rectangle, the area is the product of length and width:
... A = (2x)(9 -x²) . . . . . the attachment shows a graph of this
... A = -2x³ +18x . . . . . expanded form suitable for differentiation
A suitable domain for A is where both x and A are non-negative: 0 ≤ x ≤ 3.
(d) The derivative of A with respect to x is ...
... A' = -6x² +18
This is defined everywhere, so the critical values will be where A' = 0.
... 0 = -6x² +18
... 3 = x² . . . . . . . divide by -6, add 3
... √3 = x . . . . . . . -√3 is also a solution, but is not in the domain of A
(e) The rectangle will have its largest area where x=√3. That area is ...
... A = 2x(9 -x²) = 2√3(9 -(√3)²) = 2√3(6)
... A = 12√3 . . . . square units . . . . ≈ 20.785 units²
The parabola y = 9 - x^2 is graphed, and a rectangle's vertices and area calculations are superimposed on it. The derivative of the area function gives critical values, determining the maximum area is 18 square units.
Explanation:To solve this problem, we must utilize quadratic equations, Two-Dimensional (x-y) Graphing, and calculus.
(a) To begin, we need to draw a graph of the parabolic equation y = 9 - x^2. The vertex of the parabola is at the point (0,9) since the x-coordinate of the vertex is -b/2a in a general quadratic equation of the form y = ax^2 + bx + c, and here a = -1 and b = 0.
(b) For the rectangle, the upper right vertex is at point (x, y=(9 - x^2)), with base length 2x and height (9 - x^2).
(c) The area (A=base * height) of the rectangle is then given by A = 2x * (9 - x^2). The domain of A is specified by the values of x for which A is defined. Here A is defined for all x ∈ (-∞, ∞).
(d) The derivative of A with respect to x is A’ = 2(9 - 3x^2), which can be set equal to zero, the solution of which gives critical values x = ±√3.
(e) By the second derivative test or comparing values at the endpoints and critical points, you can determine that the largest area is 18 square units when x = √3.
Therefore,
b) The upper right vertex is at point (x, y=(9 - x^2)), with base length 2x and height (9 - x^2).
c) Here, A is defined for all x ∈ (-∞, ∞).
d) The solution of which gives critical values x = ±√3.
e) The largest area is 18 square units.
Learn more about Area of the Rectangle under the Parabola here:https://brainly.com/question/2253968
#SPJ3
(01.02) Choose the best definition for the following term: variable
Answers
A "Variable" is an inconsistent set of numbers. This set is subjected to change over time. The most common set or best demonstration would be an "input-output' Variable.
x = 0
y = 1 + 2x Substitute x = 0
y = 1 + 2(0) Any number times 0 is 0
y = 1 + 0 Simplify
y = 1
I hope this could help.
How do you write 7.25 in word form?
Answers
Hope this helps!
whenever there is a decimal point it goes first number behind it is tenths and the second is hundredths and so on, when say/writing the number behind the decimal point always add a TH at the end.
A salesperson's commission rate is 5 %. What is the commission from the sale of $ 44,000 worth of furnaces? Use pencil and paper. Suppose sales would double. What would be true about the commission? Explain without using any calculations.
Answers
5% = 0.05
0.05 * 44,000 = 2,200
So the salesperson makes 2,200 dollars from the sale of 44,000.
If sales doubled, then she would make the double amount.
a. The commission from the sale of $ 44,000 worth of furnaces is $1,800
b. Commission would double as well.
What is the percentage?A percentage is a minimum number or ratio that is measured by a fraction of 100.
We are given that salesperson's commission rate is 5 %
Then Commission paid on $36,000 worth of furnaces with a rate of 5% is:
= Amount of sales x commission rate
= 36,000 x 5%
= $1,800
If the sales were to double, the commission would be based on double the amount so it would double;
= 36,000 x 2
= $72,000
Commission = 72,000 x 5%
= $3,600
therefore Commission is doubled.
Learn more about percentages;
brainly.com/question/24159063
#SPJ3
is a=5x+5 is it proportional
Answers
Answer: No
Step-by-step explanation: It does not go through the origin (0,0) in a straight line. Also, it has a y-intercept, meaning it doesn't go through the origin (0,0) and goes through the line that is up and down; vertically.
Cody filled a container with 7 3/16 quarts of iced tea. how many 1/4 quart glasses can be served from the container
Answers
[tex]\bf \stackrel{mixed}{7\frac{3}{16}}\implies \cfrac{7\cdot 16+3}{16}\implies \stackrel{improper}{\cfrac{115}{16}} \\\\\\ \textit{how many times does }\frac{1}{4}\textit{ go into }\frac{115}{16}? \\\\\\ \cfrac{\quad \frac{115}{16}\quad }{\frac{1}{4}}\implies \cfrac{115}{16}\cdot \cfrac{4}{1}\implies \cfrac{115}{4}\implies 28\frac{3}{4}[/tex]
Given that P = (-4, 11) and Q = (-5, 8), find the component form and magnitude of vector QP
Answers
P = (-4,11)
Q = (-5,8)
The x-component of vector QP is
-4 - (-5) = 1
The y-component of vector QP is
11 - 8 = 3
The vector QP is
(1,3) or
[tex]\vec{QP} = \hat{i} + 3\hat{j}[/tex]
The magnitude of the vector is
√(1² + 3²) = √(10)
Answer:
[tex]\vec{QP} = \hat{i}+3\hat{j} \,\, or \,\, (1,3)[/tex]
The magnitude is √(10).
Answer:
<1, 3>, square root of ten
Step-by-step explanation:
Casey has a job doing valet parking. Casey makes an hourly rate of $4.55 per hour plus tips. Last week Casey worked 26 hours and made $898.55. How much in tips did Casey earn last week?
a. $34.56
b. $118.30
c. $157.25
d. $780.25
Please select the best answer from the choices provided
A
B
C
D
Answers
In this particular case, you just need to find the difference between what Casey earn hourly with his total earning..
The hourly wage that Casey earned in 26 hours:
$ 4.55 x 26 = 118.3
The total amount that casey earned in 26 hours:
$898.55
So, the amount that Casey earned through tips:
$898.55 - $118.3 = $780.25
Casey earned $780.25 in tips last week. This was calculated by first finding out her earnings from her hourly wage, and then subtracting this from her total earnings.
Explanation:First, we need to calculate how much Casey earns from the hourly rate alone. Given that Casey's hourly rate is $4.55 per hour and she worked for 26 hours last week, we multiply the two to get her earnings from the hourly wage, which is $4.55 * 26 = $118.30.
Then we need to find out how much Casey made in tips. Casey's total earnings last week were $898.55. We subtract the earnings from her hourly rate from her total earnings to find out how much she made in tips. So, $898.55 - $118.30 = $780.25.
Therefore, Casey earned $780.25 in tips last week, which corresponds to option D.
Learn more about Tips Calculation here:https://brainly.com/question/29775596
#SPJ12
caleb and emily are standing 100 yards from each other. caleb looks up at a 45 degree angle to see a hot air balloon. Emily looks yup at a 60 degree angle to see the same hot air ballon. approximate how far is the hot air ballon off the ground?
Answers
thus then
[tex]\bf \begin{cases} y=100-a\\ y=a\sqrt{3} \end{cases}\implies 100-a=a\sqrt{3}\implies 100=a+a\sqrt{3} \\\\\\ 100=a(1+\sqrt{3})\implies \boxed{\cfrac{100}{1+\sqrt{3}}=a} \\\\\\ \textit{what is the altitude \underline{y} then?}\qquad y=100-a \\\\\\ y=100-\cfrac{100}{1+\sqrt{3}}\implies y\approx 63.39745962156~yards[/tex]
The height of the air balloon is 63.4 yards.
What is a trignometry?Trigonometry is a branch of mathematics that uses variables to determine heights and distances. It is the study of the properties of right angled triangles and trigonometric functions and of their applications.
For the given situation,
The diagram below shows the situation described above.
The distance between Caleb and Emily = 100 yards
Let the distance from Caleb to the air balloon be 'x'
Let the distance from Emily to the air balloon be 'y'
Let height of the air balloon be 'h'
⇒ [tex]x+y=100[/tex]
⇒ [tex]x=100-y[/tex]
We know that, [tex]tan[/tex] θ = [tex]\frac{perpendicular }{base}[/tex]
Now consider the triangle with angle 45°,
[tex]tan 45[/tex]° = [tex]\frac{h}{x}[/tex]
We know that tan 45° = 1 and substitute x = 100-y,
⇒ [tex]1 = \frac{h}{100-y}[/tex]
⇒ [tex]h=100-y[/tex]
This is equation 1.
Now consider the triangle with angle 60°,
[tex]tan60[/tex]° = [tex]\frac{h}{y}[/tex]
We know that, tan 60° = √3
⇒ [tex]\sqrt{3} = \frac{h}{y}\\[/tex]
⇒ [tex]h=y\sqrt{3}[/tex]
This is the equation 2.
On equating equation 1 and 2,
⇒ [tex]100-y=y\sqrt{3}[/tex]
⇒ [tex]y+y\sqrt{3}=100[/tex]
⇒ [tex]y(\sqrt{3}+1 )=100[/tex]
⇒ [tex]y=\frac{100}{\sqrt{3}+1 }[/tex]
Thus height, [tex]h=y\sqrt{3}[/tex]
Substitute the value of y in h,
⇒ [tex]h=\sqrt{3}(\frac{100}{\sqrt{3} +1} )[/tex]
⇒ [tex]h=\frac{100\sqrt{3} }{\sqrt{3}+1 }[/tex]
⇒ [tex]h=\frac{173.205}{2.732}[/tex]
⇒ [tex]h=63.397[/tex]
⇒ [tex]h=63.4[/tex]
Hence we can conclude that the height of the air balloon is 63.4 yards.
Learn more about trigonometric ratios here
https://brainly.com/question/23932723
#SPJ2
The gas tank in the car holds 20 gallons of gasoline. You used up 4 gallons and 1 quart on your trip. How much gasoline is left in the tank?
Answers
20-4.25
=15.75
There is 15.75, or 15 3/4, gallons of gasoline left in the tank.
The correct answer is:
Total capacity of tank in quarts:
20 gallons = 20 × 4 = 80 quarts
Gasoline used in quarts:
4 gallons 1 quart = (4 × 4) + 1 = 17 quarts
Gasoline left in the tank in quarts:
80 − 17 = 63 quarts
Gasoline left in the tank in gallons and quarts:
63 quarts = 63 ÷ 4 = 15 remainder 3 = 15 gallons 3 quarts
help!! me asap!! please!!
Answers
Find the vertex of the parabola whose equation is y = x2 - 4x + 6.
Answers
Vertex Formula: [tex]x = \frac{-b}{2a}[/tex]
[tex]y = x^2 - 4x + 6 [/tex]
b = (-4)
a = 1
[tex]x=\frac{-b}{2a}[/tex]
[tex]x=\frac{-(-4)}{2(1)}[/tex]
[tex]x=\frac{4}{2}[/tex]
[tex]x=2[/tex]
So the vertex x point is at 2 so (x,y) = (2,y)
Now lets find the y by inserting 2 where the x is located in the equation:
[tex]y = x^2 - 4x + 6[/tex]
[tex]y = 2^2 - 4(2) + 6[/tex]
[tex]y = 4 - 8 + 6[/tex]
[tex]y = 2[/tex]
Now that we found the y for the vertex, we have (x,y) = (2,2) and (2,2) is our vertex. We can graph the equation to and see (2,2) is correct.
George bought 4 submarine sandwiches for a birthday party. if each person will eat 2/3 of a sandwich, how many people can George feed?
Answers
The number of people George can feed is 6.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given that, George bought 4 submarine sandwiches for a birthday party.
Each person will eat 2/3 of a sandwich
Number of people George can feed
= 4÷2/3
= 4×3/2
= 6
Therefore, the number of people George can feed is 6.
To learn more about the unitary method visit:
brainly.com/question/22056199.
#SPJ2
There are 24 student's in a science class. Mr. Sato will give each pair of student's 3 magnets. So far, Mr. Sato has given 9 pairs of students their 3 magnets. How many more magnets does Mr. Sato need zo.that each pair of student's habe exactly 3 magnets?
Answers
9 pairs already got their magnets. 12 - 9 = 3 pairs still need magnets.
each pair gets 3 magnets. So he needs 3*3 = 9 more magnets
9. Suppose a new groundskeeper decides that he has enough chalk to line 600 feet of the perimeter of the field. What is the maximum area of the field this chalk could outline, assuming the length remains 30 yards longer than the width?
Answers
Use the premises and conclusion to answer the questions. Premises: If an angle measure is less than 90°, then the angle is an acute angle. The measure of angle ∠B is 48°. Conclusion: ∠B is an acute angle. Is the argument valid? Why or why not? The argument is not valid because the conclusion does not follow from the premises. The argument is not valid because the premises are not true. The argument is valid by the law of syllogism. The argument is valid by the law of detachment.
Answers
If p and q are 2 propositions (or statements, or assertions) then,
Statement 1: If p, then q.
Statement 2: p
Conclusion: q
That is, if q follows from p, and if p is true, then q is true.
Statement 1: If angle ∠B measure is less than 90°, then ∠B is an acute angle.
Statement 2: The measure of angle ∠B is 48°
Conclusion: ∠B is an acute angle
Answer: The argument is valid by the law of detachment.
find the next three terms in the geometric sequence: 4, -12, 36, -108
Answers
mark has 160 yards of fencing to enclose a rectangular garden whose length is to be four times its width what will be the dimensions of the garden
Answers
perimeter = 2W+2L
Length = 4W
160 = 2W +2(4W)
160 = 10W
w = 160/10 = 16 yards
length = 16*4 = 64 yards
Check:
64*2 = 128, 16*2 = 32
128+32 = 160
Length = 64 yards, Width = 16 yards
WILL GIVE BRAINEST
use the elimination method to solve the system of equations.
2x+4y=10
3x-4y=5
a.(1,3)
b.(3,4)
c.(5,0)
d.(3,1)
Answers
3x - 4y = 5
5x = 15 add the 2 rows together
x = 3
substitute x = 3 into any of the two equations
2x + 4y = 10
2(3) + 4y = 10
6 + 4y = 10
4y = 4
y = 1
d. (3, 1)
hope this helped, God bless!
The formula s= sa/6 gives the length of the side, s, of a cube with the surface area, sa. How much longer is the side of the cube with a surface area of 180 square meters than a cube with the surface area of 120 square meters ?
Answers
they're on a ratio of 3:2, so if the small is 2, the large one is 3, and if the small one is 120, the large one is 180.
on a 3:2 ratio, 3 is larger than 2 by 1 unit, 1 is 50% of 2, or half, so the longer side is 50% larger.
Answer with explanation:
Side of cube = S
Surface Area of Cube = S.A
Relation between Side of a cube and surface area
[tex]S=\frac{S.A}{6}[/tex]
→If surface area of cube =180 Square meters
Side of cube (S)
[tex]S_{1}=\frac{180}{6}\\\\=30[/tex] meters
→ If surface area of cube =120 Square meters
Side of cube (S)
[tex]S_{2}=\frac{120}{6}\\\\=20[/tex] meters
[tex]S_{1}-S_{2}=30 -20=10\\\\S_{1}=S_{2}+10[/tex]
Side of cubic having surface area 180 square meters is greater by 10 meters, than a cube with the surface area of 120 square meters.
How many kilometers could the red car travel in 12 hours?
Answers
Express the Set -4x-6<2x+6 using interval notation
Answers
there's a parentheses at 2, (2, because "x" is greater than, not equal to, but greater than 2.
there's a parentheses at +∞), because ∞ is just a conceptual way to say it keeps on going, so is never reached.
The length of a rectangle is four times its width. If the area is 400 cm squared, find its perimeter
Answers
The perimeter of the rectangle with four times longer in length than its width and an area of 400 cm2 is 100 cm.
To solve this, let's assume the width of the rectangle is w centimeters. This would make the length 4w centimeters. Since the area of a rectangle is given by the product of its length and width, we have:
w x 4w = 400
Solving for w, we find that w2 = 100, so w = 10 cm.
Hence, the length is 4 x 10 = 40 cm.
The perimeter of a rectangle is given by the formula 2l + 2w, so substituting in our values:
Perimeter = 2(40) + 2(10) = 80 + 20 = 100 cm.
Therefore, the perimeter of the rectangle is 100 cm.
10 x 6 tens-unit form and standard form
Answers
Answer:
Standard form: 600
Unit form: 6 hundreds.
Step-by-step explanation:
We have been given a number [tex]10\times 6[/tex]-tens. We are asked to write our given number in unit form and standard form.
To write our given number in standard form, we will expand our given number as shown below:
6-tens [tex]6\times 10=60[/tex]
[tex]10\times 6[/tex]-tens would be [tex]10\times 60=600[/tex]
Therefore, our given number in standard form would be 600.
We know that unit form is writing a number using place value units.
We can see that our given number has 0 ones, 0 tens and 6 hundreds.
Therefore, our given number in unit form would be 6 hundreds.
We have that the Tens unit form of 10 x 6 and Standard form is mathematically
[tex]6*10^1[/tex]
6tens
From the question we are told that
10 x 6
10 x 6=60
Standard form is a number, between 1 and 10 multiplied by a power of 10
Generally the equation for the Standard form is mathematically given as
x*10^y
Therefore
the Standard form of 10 x 6 is mathematically given as
[tex]6*10^1[/tex]
And
Generally the equation for the Tens unit form of 10 x 6 is mathematically given as
x*tens(10)
Tens-unit form is mathematically given as
6tens
For more information on this visit
https://brainly.com/question/23366835?referrer=searchResults