Answers
Since the line enters the y-axis at (0,3) the y-intercept of the equation would be 3 (as according to the y=mx+b format where b is the y-intercept and m is the slope). The slope would be 3/2 since when you find two perfect points (I used (0,3) and (2,6)) and you use the rise over run method (move up 3 from (0,3) and 2 to the right to get to (2,6)), your slope is 3/2.
The equation of the line shown is y = (3/2)x + 3.
What is the equation of line?The general equation of a straight line is
y = mx + c,
where m is the gradient or slope, and
y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.
Now given points from the line passes are (0,3) and (-4,-3)
Therefore we have,
x₁ = 0
y₁ = 3
x₂ = -4
y₂ = -3
Now since the slope of the line is given as,
m = (y₂ - y₁)/(x₂ - x₁)
⇒ m = (-3 - 3)/ (-4-0)
⇒ m = -6/(-4)
⇒ m = 6/4
or, ⇒ m = 3/2
Now, for intercept c we can put any of points in the equation of line.
So, put (0,3)in the equation of line
3 = m(0) + c
3 = 0 + c
⇒ c = 3
Hence the required equation of line is given as,
y = mx + c
put the values of m and c,
y = (3/2)x + 3
which is the required equation of the line shown
Hence,the equation of the line shown is y = (3/2)x + 3.
To learn more about line:
brainly.com/question/14200719
#SPJ6
Related Questions
Find m∠abc
Geometry>Proving Angles Congruent
Answers
2x + 5x + 5 = 180
first, add 2x and 5x, then subtract 5 from each side
7x = 175
then divide both side by 7
x = 25
plug this value into the equation 5x + 5
5(25) + 5
and your answer will be 130
the measure of angle ABC (m∠ABC) is 130 degrees. it's essential to recognize that the sum of the angles along a straight line is always 180 degrees.
In this case, we have two angles, 2x and 5x+5, forming a straight line with an unknown angle (m∠ABC). So, we set up the equation:
2x + 5x + 5 = 180
Next, combine the like terms on the left side:
7x + 5 = 180
7x = 180 - 5
7x = 175
x = 175/7
x = 25
Therefore, the measure of angle ABC = 5x + 5
= 5(25) + 5
=130 degree
So, the measure of angle ABC (m∠ABC) is 130 degrees.
To know more about measure:
https://brainly.com/question/35479411
#SPJ3
You need five liters of yoda soda for every 12 guests if you have 36 guests how many liters do you need
Answers
A jar of coins contains dimes, pennies, and quarters. There are 220 pennies in the jar. There are 3 quarters for every 4 pennies, and there is 1 dime for every 3 quarters. How many dimes and quarters are in the jar?
A.55 dimes and 165 quarters
B.98 dimes and 293 quarters
C.73 dimes and 98 quarters
D.165 dimes and 55 quarters
Answers
Answer:
A. 55 dimes and 165 quarters
Step-by-step explanation:
Given,
The number of pennies in the Jar = 220,
∵ There are 3 quarters for every 4 pennies,
i.e. 4 pennies = 3 quarters,
⇒ 1 penny = [tex]\frac{3}{4}[/tex] quarter
⇒ 220 pennies = [tex]220\times \frac{3}{4}[/tex]
[tex]=\frac{660}{4}[/tex]
= 165 quarter.
Therefore, there are 165 quarters.
Now, there is 1 dime for every 3 quarters,
i.e. 3 quarters = 1 dime
⇒ 1 quarter = [tex]\frac{1}{3}[/tex] dime,
⇒ 165 quarters = [tex]\frac{165}{3}[/tex] = 55 dimes.
Therefore, there are 55 dimes.
Option 'A' is correct.
Translate the following statement to an inequality.
A number is at most seven.
x > 7
x < 7
x ≥ 7
x ≤ 7
Answers
Answer:
x ≤ 7
Yuuupeeee
The length and the width of a rectangle are both doubled. What is the ratio of the area of the larger rectangle to the area of the smaller rectangle?
I think it is 2:1. Am I right? If not, what is the ratio?
Answers
Small
A = lw
Large
A = (2l)(2w)
A = 4(lw)
Ratio is 4:1
A=(21)*(2w)=4*L*W
you are comparing 4lw to 1lw
the ratio is 4 to 1 or 4:1 or 4/1
a basketball court measures 94 feet in length and w feet in width. it's perimeter is 288 feet. which value of w makes the equation 2(94) + 2w = 288 true? A.50ft B. 55 feet C. 65 feet D. 60 feet
Answers
There are 365 days per year, 24 hours per day, 12 months per year, and 60 minutes per hour. how many minutes are in a month?
Answers
It is found that there are 43,800 minutes in a month.
What is the fundamental principle of multiplication?Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
We knowt that there are 365 days per year, 24 hours per day, 12 months per year, and 60 minutes per hour.
1 day = 24 hour
1 hour = 60 minutes.
1 minutes = 60 seconds
Therefore, 24 hours = 24 x 60 = 1440 minutes
There are 1440 minutes in one day.
Then 30 days = 30 x 1440 = 43,800
Hence, It is found that there are 43,800 minutes in a month.
Learn more about multiplications;
https://brainly.com/question/14059007
#SPJ5
The composition is applied to △RST to create the image of △R"S"T", which is not shown.
What are the coordinates of point S"?
Answers
Answer:
S''(-3/2, 9/2)
Step-by-step explanation:
In a dilation, the coordinates of every ordered pair in the pre-image are multiplied by the scale factor to create the ordered pairs of the image.
The first dilation has a scale factor of 1/2. This maps:
R(-6, 10)→R'(-6/2, 10/2) = R'(-3, 5)
S(-2, 6)→S'(-2/2, 6/2) = S'(-1, 3)
T(-10, 0)→T'(-10/2, 0/2) = T'(-5, 0)
The second dilation has a scale factor of 3/2:
R'(-3, 5)→R''(-9/2, 15/2)
S'(-1, 3)→S''(-3/2, 9/2)
T'(-5, 0)→T''(-15/2, 0)
This makes S'' have coordinates (-3/2, 9/2).
Answer: a :)
Step-by-step explanation:
What is the factored form of 5x2 + 28x + 15?
Answers
10+28x+15
25+28x
Which of the following illustrates the truth value of the given statements? A square root of 16 is 4, and the only square root of 9 is -3.
T F → F
T T → T
F T → F
F F → F
The intersection of two planes is a point, and two lines intersect in a point.
T T → T
F T → F
T F → F
F F → F
The alphabet has 28 letters, and a week has seven days.
T T → T
T F → F
F F → F
F T → F
Answers
FT ...F
FT ...F
PLEASE HELP!!!!Which equation shows y=3/4x−5/2 in standard form?
A) 3x−4y=10
B)4x−3y=10
C)4x−3y=−10
D)3x−4y=−10
2.What is the slope-intercept form of the linear equation x + 4y = 12? Enter your answer in the box.
3.Graph the equation on the coordinate plane. y=1/2x
Answers
Answer: 1. A) 3x−4y=10
2. [tex]y=-\frac{x}{4}+3[/tex]
3. In the attachment.
Explanation:
1. Given equation=[tex]y=\frac{3}{4}x-\frac{5}{2}[/tex]
To reduce it into standard form , multiply both sides by 4,we get
[tex]4y=4(\frac{3}{4}x-\frac{5}{2})\\\Rightarrow4y=3x-10......[distributive\ property]\\\Rightarrow3x-4y=10[/tex] which is option A.
2. Given linear equation : x+4y=12
The standard slope intercept form is given by y=mx+c where m is the slope and c is the constant.
To reduce given linear equation subtract x from both sides, we get
4y=12-x
Divide 4 on both sides.
[tex]\Rightarrow\ y=\frac{12-x}{4}=3-\frac{x}{4}\\\Rightarrow\ y=-\frac{x}{4}+3[/tex] is the slope-intercept form of the linear equation x + 4y = 12.
3. To graph equation [tex]y=\frac{1}{2}x[/tex] on the coordinate plane.
We need to find points to plot the line
Put x=0,we get y=0
Put x=2,we get y=1
Thus we have points (0,0) and (2,1) to plot the line on the graph.
Answer: 1. A) 3x−4y=10
Step-by-step explanation:
The product of three numbers is -216 but their sum is -18. What are these three numbers?
Answers
What is the equation, in point-slope form, for a line that goes through (2, −6) and has a slope of −3/4 ? y−6=3/4(x−2) y+6=−3/4(x−2) y+6=−3/4(x+2) y−6=−3/4(x+2)
Answers
The equation for point-slope is y-y1=m(x-x1). So just take the given info and plug it in. Since the y-point is negative, it becomes a positive in the equation.
Answer:
option 3 aka c
Step-by-step explanation:
A rectangle has a perimeter of 60 inches and length of 22 what is the width of the rectangle
Answers
perimeter = 2l +2w
length = 22
perimeter = 60
60 = 2(22) +2w
60 = 44 +2w
subtract 44 from both sides
16 = 2w
w = 16/2
w = 8
width is 8 inches
The function f(x) is graphed on the coordinate plane.
What is f(−2) ?
Enter your answer in the box.
f(−2)=
Answers
Answer:
The correct answer is f(-2)= -2
Step-by-step explanation:
One positive integer is 6 less than twice another. the sum of their squares is 569. find the integers.
Answers
Let y be the second integer
x=2y-6
x²+y²=596
(2y-6)²+y²=596
4y²-24y+36+y=569
4y²-23y+36-569=0
4y²-23y-533=0
y= -9.021 or 14.771
I have attached a graph below of the equation.
Since the integer has to be positive (mentioned in question), -9.021 cannot be a solution.
x=2y-6
x=2(14.771)-6
x=23.542
Hope I helped :)
How did the great pyramid of giza get 30 feet shorter?
Answers
It takes an older pump twice as long to drain a certain pool as it does a newer pump. working together, it takes the two pumps 3 hours to drain the pool. how long will it take the newer pump to drain the pool working alone
Answers
It would take the newer pump 4.5 hours to drain the pool working alone.
Given that,
It takes an older pump twice as long to drain a certain pool as it does a newer pump.
Let us assume that,
The time it takes for the newer pump to drain the pool alone is x hours.
Hence, According to the information given, the older pump takes twice as long, so it would take 2x hour to drain the pool alone.
Now, When both pumps work together, their combined rate of draining the pool is additive.
Therefore, the equation is,
[tex]\dfrac{1}{x} + \dfrac{1}{2x} = \dfrac{1}{3}[/tex]
Simplify the equation for x,
[tex]\dfrac{(2 + 1)}{2x} = \dfrac{1}{3}[/tex]
[tex]\dfrac{(3)}{2x} = \dfrac{1}{3}[/tex]
Cross multiplication,
[tex]3 \times 3 = 2x[/tex]
[tex]2x = 9[/tex]
Dividing both sides by 2:
[tex]x = 4.5[/tex]
Therefore, it would take the newer pump 4.5 hours to drain the pool working alone.
To learn more about the equation visit:
brainly.com/question/28871326
#SPJ4
A coin is tossed 10 times:
How many times do you expect to get heads?
How many times do you expect to get tails?
Answers
Final answer:
The expected number of heads and tails when tossing a coin 10 times is 5 each.
Explanation:
If you toss a coin ten times:
Expected number of heads: 5
Expected number of tails: 5
This is because for each toss, the probability of getting a head is 0.5 (50%) and the same for a tail. Over multiple tosses, the outcomes tend to approach these expected values.
Use the graph below to answer the following question:
What is the average rate of change from x = –4 to x = 1?
A. -3
B. -1
C. 0
D. 1
Answers
What is the slope of the line passing through the points (−3, 4) and (4, −1)?
35
−1
−57
3
Answers
The slope of a straight line passing through the points (x₁, y₁) and (x₂, y₂) is
[tex]m= \frac{y_{2}-y_{1}}{x_{2}-x_{1}} [/tex]
The two given points are (-3,4) and (4,-1). Therefore the slope is
[tex]m= \frac{-1-4}{4-(-3)} = \frac{-5}{7} [/tex]
Answer: [tex]- \frac{5}{7} [/tex]
Answer:
the answer is C. -5/7
What is the least angle measure by which this figure can be rotated so that it maps onto itself? 45° 90° 180° 360° Left right double headed arrow.
Answers
In mathematics, specifically geometry, the least angle measure by which a regular, symmetric figure can be rotated to map onto itself is usually 90°. This concept falls under the umbrella of rotational symmetry.
Explanation:The question is about rotation of objects in geometry. To identify the least angle measure for a figure to map onto itself, we need to know the shape of the figure. However, assuming the figure is regular and symmetric (a square or a rectangle for example), the least angle measure by which it can be rotated to map onto itself is 90°.
It's important to remember the concept of rotational symmetry. A figure has rotational symmetry if it can be rotated less than 360° around a central point and still appear the same. For instance, a regular rectangle or square has a rotational symmetry of 90°, since we can rotate it 90 degrees and it appears the same.
Learn more about Rotational Symmetry here:https://brainly.com/question/34193824
#SPJ2
ray bought 5 lemons and 3 limes for $7.20. Lia bought 4 lemons and 6 limes for the same price. How much would it cost to buy 1 lemon and 1 lime?
Answers
4x+6y=7.2--->4x+6y=7.2------------>4x+6y=7.2
-6x=-7.2---->x=7.2/6 or 1.27
4(1.27)+6y=7.2---->5.08+6y=7.2----> 6y=2.12
y=.35
x=lemons y=limes
Answer: The cost of 1 lemon is $1.2 and the cost of 1 lime is $0.4.
Step-by-step explanation:
Let x be the cost of 1 lemon and y be the cost of 1 lime.
Then for Ray, the equation representing total price will be :-
[tex]5x+3y=7.20[/tex]................................(1)
For Lia, the equation representing total price will be :-
[tex]4x+6y=7.20[/tex]..................................(2)
Dividing 2 on the both sides of equation (2), we get
[tex]2x+3y=3.60[/tex]...............................(3)
Subtracting (3) from (1), we get
[tex]3x=3.6\\\\\Rightarrow x=1.2[/tex]
Substitute value of x in (3), we get
[tex]2(1.2)+3y=3.6\\\\\Rightarrow2.4+3y=3.6\\\\\Rightarrow3y=1.2\\\\\Rightarrow y=0.4[/tex]
Thus, the cost of 1 lemon is $1.2 and the cost of 1 lime is $0.4.
−t/4=−3π
What is the answer to T
Answers
the value of (t) that satisfies the equation is approximately (37.6992).
Let's solve the equation [tex]\(-\frac{t}{4} = -3\pi\) for \(t\).[/tex]
Step 1: Multiply both sides by \(-4\) to isolate \(t\).
[tex]\[-\frac{t}{4} \times (-4) = -3\pi \times (-4)\][/tex]
This simplifies to:
[tex]\[ t = 12\pi \][/tex]
Step 2: Substitute the value of \(\pi\) to get the final answer.
[tex]\[ t = 12 \times 3.14159 \][/tex]
[tex]\[ t = 37.6992 \][/tex]
Therefore, the value of ( t ) is approximately ( 37.6992 ).
To solve the equation [tex]\(-\frac{t}{4} = -3\pi\) for \(t\)[/tex] , we first want to isolate (t) on one side of the equation. To do this, we can multiply both sides of the equation by (-4). This cancels out the fraction and leaves us with (t) on the left side:
[tex]\[-\frac{t}{4} \times (-4) = -3\pi \times (-4) \\t = 12\pi\][/tex]
Now, to get the numerical value of \(t\), we substitute the value of \(\pi\), which is approximately \(3.14159\), into the equation:
[tex]\[ t = 12 \times 3.14159 \][/tex]
[tex]\[ t \approx 37.6992 \][/tex]
Therefore, the value of (t) that satisfies the equation is approximately (37.6992).
complete question
−t/4=−3π
What is the answer to T
find sin x if cos x= 2/3 and x is in quadrant 4
Answers
This is actually pretty easy. All you have to do is know what quadrant your angle is in and that will determine the sign.
Quadrant1 = all trig functions are positive
Quadrant2 = sine is positive and cosine and tangent are negative
Quadrant3 = tangent is positive and sine and cosine are negative
Quadrant4 = cosine is positive and sine and tangent are negative
since your original angle is in quadrant 4 then the half angle will be in Quadrant 2
so the sine of the half angle is positive and the cosine of the half angle is negative
adjacent side = 2 and hypotenuse = 3 so opposite side will be -sqrt 5
so sin x = - sqrt5/ 3
Charlie drove 864 miles in 12 hours. at the same rate, how long would it take him to drive 504 miles?
Answers
It would take Charlie 7 hours to drive 504 miles.
The formula for this is Speed = Distance/Time. Time = Distance/Speed
864miles/12hrs = 72mph
With the same formula plug in 504 miles for Distance and leave time as X and speed will be 72mph.
72mph = 504miles/x
Cross multiply
72x = 504
Divide by 72
X = 7 hours
What is the 1st term when 3x3 − 7x + 6x4 − 2x2 is arranged in descending order?
3x3
−7x
6x4
−2x2
Answers
Because its power is the greatest.
To arrange in descending order means that you will write the largest value first followed by the other smaller ones. From the question given above, we have the following values:
3x3 = 9
6 x 4 = 24
-2 x 2 = -4 and we have -7x.
Thus, the largest value is 6 x 4.
Two step equations
6=a/4+2
Answers
4=a/4
4*4=a
16=a
a =16 is the solution of the given equation.
To solve the equation 6 = a/4 + 2, we'll perform two steps to isolate the variable 'a'.
Step 1: Subtract 2 from both sides of the equation:
6 - 2 = a/4 + 2 - 2
4 = a/4
Step 2: Multiply both sides of the equation by 4 to get rid of the fraction:
4 * 4 = (a/4) * 4
16 = a
Therefore, the solution to the equation is a = 16.
Learn more about algebraic Expression here:
https://brainly.com/question/953809
#SPJ6
Write the following inequality in slope-intercept form. −6x + 2y ≤ 42
Answers
y <= 6x + 42
Note: if it were a -2y, you’d have to flip the inequality sign when dividing by that negative 2.
:)
Answer: The required slope-intercept form is [tex]y\leq 3x+21.[/tex].
Step-by-step explanation: We are given to write the following inequality in slope-intercept form :
[tex]-6x+2y\leq 42~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We know that
the slope-intercept form of an inequality of the given form is as follows :
[tex]y\leq mx+c,[/tex] where m is the slope and c is the y-intercept.
From inequality (i), we have
[tex]-6x+2y\leq 42\\\\\Rightarrow 2y\leq6x+42\\\\\Rightarrow y\leq\dfrac{6}{2}x+\dfrac{42}{2}\\\\\Rightarrow y\leq 3x+21.[/tex]
Thus, the required slope-intercept form is [tex]y\leq 3x+21.[/tex].
Determine the intercepts of the line. y=-7x+3y=−7x+3
Answers
x intercept when y = 0
so
-7x + 3 = 0
-7x = -3
x = 3/7
y intercept when x = 0
so
y = 3
answer
x intercept (3/7 , 0)
y intercept (0, 3)
Answer:
Step-by-step explanation:
y=−7x+3x intercept when y = 0so-7x + 3 = 0-7x = -3 x = 3/7y intercept when x = 0 so y = 3
answer
x intercept (3/7 , 0)y intercept (0, 3)