To find an equation of a line, you have to know the value of slope first. We can find the value of slope by using the formula below:
[tex] \large \boxed{m = \frac{y_2 - y_1}{x_2 - x_1} }[/tex]
m-term represents the slope from y = mx+b.
We are given two coordinate points. Substitute the points in the formula.
[tex] \large{m = \frac{7 - 5}{3 - 0} } \\ \large{m = \frac{2}{3} }[/tex]
Therefore the slope is 2/3.
Next we find the y-intercept. In the form of y = mx+b where m = slope and b = y-intercept. We have got slope, except the y-intercept. We can find the y-intercept by substituting one of gjven points in the equation of y = mx+b.
Since we know the slope - we can rewrite the equation like below:
[tex] \large{y = \frac{2}{3} x + b}[/tex]
Then choose one of two points to substitute. I will choose (0,5). Therefore substitute x = 0 and y = 5.
[tex] \large{5 = \frac{2}{3} (0) + b} \\ \large{5 = 0 + b} \\ \large{b = 5}[/tex]
Thus the y-intercept is (0,5). Note that if the question gives you (0,a) point. That is the y-intercept of graph. So b = a if given (0,a).
Rewrite the equation by substituting the b-value.
[tex] \large{y = \frac{2}{3} x + 5}[/tex]
Hence, the equation of a line that contains those points is y = 2x/3 + 5
Answer
y = 2x/3 + 5Hope this helps! Let me know if you have any doubts.
find the number between 1 over 10 and 3 over 5
Answer:
7/20
Step-by-step explanation:
1 over 10 is .1
3 over 5 is .6
write them out
.1 .2 .3 .4 .5 .6
number between is .35
.35 = 35/100 = 7/20
7/20
A survey of a group of seventh graders and a group of teachers at a local middle school asked how many siblings
they each have. The dot plots below show the results.
Students Which compares the modes of the data?
Answer:
a
Step-by-step explanation:
what is. perfect square
Answer:
a four sided parallelogram where all angles are the same and all sides are the same length
Please only correct answers only I need to past this
Answer:
Multiplication properly of equality
A circle has a radius of 18 ft and an arc length of 11 π. What is the measure of the central angle of
the circle?
write an equation to represent the function.
input (x)
0
3
9
output
(y)
0
1
3
Answer:
Step-by-step explain
the answer is c
Answer pls
Maths questions
Attached paper question (Answer pls)
Answer:
25 wanted ice cream 10 wanted coffee 3/5 wanted ice teaWhy are (1, 2) and (2, 1) sot equal ordered pairs
Answer:
Step-by-step explanation:
(1,2) and (2,1) are not equal ordered pairs becasue their corresponding elements are not equal.
Two Ordered Pairs are said to be equal if the corresponding first components are equal alongside the corresponding second components are equal.
for example:
(3,1) and (3,1)
here corresponding element of 3 is 3 and of 1 is 1 .so they are called equal ordered pairs.
What is the volume of a sphere with a radius of 30.5 cm
The denominator of a fraction is greater than its numerator by 7. If
the numerator is increased by 1 and the denominator is increased by
4, the fraction becomes 1/3
. Find the original fraction.
Answer:
4/11
Step-by-step explanation:
Let :
x = numerator
x + 7 = denominator [tex]\frac{x}{x + 7}[/tex]
[tex]\frac{x}{x+7} + \frac{1}{4} = \frac{1}{3}[/tex]
[tex]\frac{x + 1}{x + 11} = \frac{1}{3}[/tex]
cross multiply
3(x + 1) = x + 11
3x + 3 = x + 11
combine like terms
3x - x = 11 - 3
2x = 8
x = 4
x + 7 = 4 + 7 = 11
original fraction = 4/11
the graph of the function f(x)=ax^2+bx+c is given below could the factor of f(x) be ( x + 2) (x - 3)?
Step-by-step explanation:
everything can be found in the picture
The graph of the function f(x)=ax²+bx+c could have the factor of f(x) be ( x + 2) (x - 3)
What is a function?A relation is a function if it has only One y-value for each x-value.
We can set two functions y₁=x+2 and y₂=x-3
Let us draw these two functions on the graph
We observe that the function f(x)=ax²+bx+c intersects y₁ and y₂.
y₁ intersects x axis at (-2, 0)
y₁ intersects y axis at (0, 2)
y₂ intersects x axis at (3, 0)
y₂ intersects y axis at (0, -3)
Hence, the graph of the function f(x)=ax²+bx+c could have the factor of f(x) be ( x + 2) (x - 3)
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Help plzzzz !!!!!!!!!
How do you know you're good at sleeping I need help
Answer:
You can do it with your eyes closed
Step-by-step explanation:
^^the question above in the photo
Answer:
11
Step-by-step explanation:
A rectangle has vertices E(4,8), F(2,8), G(2,-2) and H(-4,-2). The rectangle is dilated with the origin as the center of dilation so that G's is located at (5,5). Which algebraic reprensentation represents this dilation
Note: The image of G after the dilation must be G'(5,-5) instead of G'(5,5).
Given:
The vertices of a rectangle are E(4,8), F(2,8), G(2,-2) and H(-4,-2).
The rectangle is dilated with the origin as the center of dilation so that G's is located at (5,-5).
To find:
The algebraic representation that represents this dilation.
Solution:
If a figure is dilated by factor k with origin as the center of dilation, then the dilation is defined as:
[tex](x,y)\to (kx,ky)[/tex] ...(i)
Let the given rectangle is dilated by factor k with origin as the center of dilation. Then,
[tex]G(2,-2)\to G'(k(2),k(-2))[/tex]
[tex]G(2,-2)\to G'(2k,-2k)[/tex]
The image of G after dilation is G'(5,-5). So,
[tex](2k,-2k)=(5,-5)[/tex]
On comparing both sides, we get
[tex]2k=5[/tex]
[tex]k=\dfrac{5}{2}[/tex]
So, the scale factor is [tex]k=\dfrac{5}{2}[/tex].
Substituting [tex]k=\dfrac{5}{2}[/tex] in (i), we get
[tex](x,y)\to \left(\dfrac{5}{2}x,\dfrac{5}{2}y\right)[/tex]
Therefore, the required algebraic representation to represents this dilation is [tex](x,y)\to \left(\dfrac{5}{2}x,\dfrac{5}{2}y\right)[/tex].
9th one pls fast as soon as possible
Answer
Value of a3³+b³-3ab = -1
Explanation
Given a+b=-1----(1)
On cubeing both sides of equation (1), we get
(a+b)³ = (-1)³
Call 98%
we know the algebraic identity:
(x+y)³ = x³+y³ + 3xy(x+y)
=> a³ + b³ +3ab(a+b)= -1
=> a³ + b³ +3ab(-1)=-1
/* from (1)*/
=> a³ + b³-3ab = -1
Therefore,
Value of a³+b³-3ab = -1
Please give me brainliest (click on the crown) Thank you :)
Find the equation of the line that has a slope of — 2 and passes
through the point (-2,2). Write the equation in point-slope
form.
Answer:
y - 2 = -2(x +2)
Step-by-step explanation:
y - 2 = -2(x +2)
Brainliest for help please please
Answer:
5
Step-by-step explanation:
Multiply -1 on both sides to get rid of the negatives.
4x=20
Divide 4 on both sides
[tex]\frac{4x}{4}[/tex]=[tex]\frac{20}{4}[/tex]
Simplify
x=5
Answer:
5
Step-by-step explanation:
-4x= -20
or, x= -20/-4
or, x=5
the age of nicole is 3 times of christine now after five years nicole will be twice as old as krisin
Which of the following is equivalent to
2(x²-x) + (x²-x)?
Answer: The correct answer is 3x^2-3x
Step-by-step explanation:
I hope this help
If two lines in a linear system____, they have exactly one point in common.
Answer:
if two lines in a linear system INTERSECT, they have exactly one point in common.
Answer:
cross each other
Step-by-step explanation:
The point of intersection is the point where both lines will have the same coordinates.
Luca decides to play Wheel of Letters. To play the game, contestants spin a wheel with 26 equal sections, lettered A through Z. If the pointer landson any letter in the phrase "COUNTY FAIR," the contestant wins a prize.
part A
What is the probability that Luca will win wheel of letters?is your answer a theoretical probability or an experimental probability? explain.
Part B
Of the first 52 contestants, exactly 12 contestants win the game.how does the actual number of winners compared to the expected number of winners? what needs to happen for the experimental probability to approach the theoretical probability? explain
Answer:
Step-by-step explanation:
There are 6 qualifying letters, out of 26.
Thus, the probability that Luca will win through one wheel spin is
6/26, or 3/13, or 0.23.
This is a theoretical probability, since it could be calculated with the same result over and over. An experimental probability, on the other hand, would be the result if the probability stemmed from experimenting: making a list of all 26 letters and then spinning the wheel over and over again, perhaps 100 times, and recording how many times each of the 26 letters shows up.
Warm-Up
Construct a perpendicular bisector to PQ
by following these steps.
1. Move the compass center to P and
draw a long arc that intersects PQ.
Then move the compass to Q and
draw an arc that intersects the first
arc in two places.
Note that the perpendicular bisector to line PQ is constructed and attached accordingly. Here is how to do it.
Note that the first stage is to draw a line PQ. But this has already been done.
Next is to place the compass on P as shown in the image above. If you allow you compass (locked at the same degree) to rotate about point P, you will get a circle. However, that is not the objective.
If you also place your compass on point Q, locked to the same degree as when it was on P, and take a rotation around point Q, you will also get a circle.
At some point, you will notice that both circles intersect at two point, which we can call AB₁ and AB₂.
Now you are done with the compass. Take up your ruler, and place it such that it meet both AB₁ and AB₂ but allowing you space to mark a line connecting both points.
Next, using your live or online pencil tool, draw the line from AB₁ to AB₂. Now you have the Perpendicular bisector which you can call AB₁₂.
Note that a perpendicular bisector is a line or plane that intersects a line segment at its midpoint, forming a right angle and dividing the segment into two equal parts.
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Find the area of the figure.
What is the point used to write the equation y-2=4(x+5) in point slope form?
Answer: y−26=4(x−1)
Step-by-step explanation:
Can someone help me which expression is equal to 16
Answer:
D.(4^1/2)^4
hope this helps
have a good day :)
Step-by-step explanation:
Given the function f(x) = 2|x + 6| – 4, for what values of x is f(x) = 6?
x = –1, x = 11
x = –1, x = –11
x = 14, x = –26
x = 26, x = –14
Answer:
x = -1 , - 11,
Step-by-step explanation:
| x | = x
|- x | = x
f(x) = 2 | x + 6 | - 4
x = - 1 , f( - 1) = 2 | - 1 + 6 | - 4 = 2 | 5 | - 4 = 10 - 4 = 6 , True
x = 1 , f( 1 ) = 2 | 1 + 6 | - 4 = 2 | 7 | - 4 = 14 - 4 = 10 , False
x = 11, f( 11 ) = 2 | 11 + 6 | - 4 = 2 | 17 | - 4 = 34 - 4 = 30 , False
x = - 11, f( - 11) = 2 | -11 + 6 | - 4 = 2 | - 5 | - 4 = 10 - 4 = 6 , True
x = 14 , f( 14 ) = 2 | 14 + 6 | - 4 = 2 | 20 | - 4 = 40 - 4 = 36 , False
x = -14 , f( - 14 ) = 2 | - 14 + 6 | - 4 = 2 | - 8 | - 4 = 16 - 4 = 12 , False
x = - 26 , f( - 26) = 2 | -26 + 6 | - 4 = 2 | -20 | - 4 = 40 - 4 = 36 , False
x = 26, f( 26 ) = 2 | 26 + 6 | - 4 = 2 | 32 | - 4 = 64 - 4 = 60 , False
OR
Given f ( x ) = 6
f( x ) = 2 | x + 6 | - 4
6 = 2 | x + 6 | - 4
6 + 4 = 2 | x + 6| - 4 + 4 [ adding 4 to both sides ]
10 = 2 | x + 6 | + 0
5 = | x + 6 | [ dividing both sides by 2 ]
[tex]- 5 =\ ( x+ 6) \ = 5\\\\[/tex] [tex][ \ | x | = a\ => \ -a \ = x \ = a \ ][/tex]
[tex]- 5 - 6 = \ x + 6 - 6 \ = \ 5 - 6\\[/tex] [tex][ \ subtracting \ by \ 6 \ ][/tex]
[tex]-11 = \ x \ = - 1[/tex]
Slope of (4,9) (19, 13)
Hiroshi spends 30 minutes on history homework, 60 minutes on English homework, and x minutes on math homework. One fourth of his total homework time is spent on math. Which equation can be used to find the amount of time Hiroshi spends on his math homework?
StartFraction one-fourth EndFraction left-parenthesis x plus 30 plus 60 right-parenthesis equals x.(x + 30 + 60) = x
StartFraction one-fourth EndFraction left-parenthesis x right-parenthesis equals x left-parenthesis 30 plus 60 right-parenthesis.(x) = x(30 + 60)
StartFraction one-fourth EndFraction x left-parenthesis 30 plus 60 right-parenthesis equals x.x(30 + 60) = x
StartFraction one-fourth EndFraction left-parenthesis x right-parenthesis equals left-parenthesis 30 plus 60 right-parenthesis.(x) = (30 + 60)
Answer:
StartFraction one-fourth EndFraction left-parenthesis x right-parenthesis equals x left-parenthesis 30 plus 60 right-parenthesis.(x) = x(30 + 60)
Step-by-step explanation:
The equation that can be used is:
(1/4)*(30 min + 60 min + x) = x
So the correct option is the first one.
How to get the correct equation?
We know that Hiroshi spends:
30 minutes on history.60 minutes on English.x minutes on math.The total time is:
30 min + 60 min + x
And we know that one-fourth of the total time that he studies is spent on math, then we can write:
(1/4)*(30 min + 60 min + x) = x
This is the equation we need to solve.
Solving it gives:
30 min + 60 min + x = 4x
90 min = 3x
(90 min)/3 = x = 30 min.
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1. The function h defined by h(t)=(49 + 4.9t)(10 - t) models the height, in meters, of an object t seconds after it is dropped from a helicopter. Find or approximate the time when the object hits the ground. Explain your method.
2.The function h defined by h(t)=(49 + 4.9t)(10 - t) models the height, in meters, of an object t seconds after it is dropped from a helicopter.
From what height is the object dropped? Explain how you know.
Answer:
Step-by-step explanation:
Let's FOIL this out and get it into standard form. That gives us:
[tex]h(t)=-4.9t^2+490[/tex] For #1, then:
The height of something when it is on the ground is 0; that means that the h(t) is 0. This allows us to factor the quadratic and solve for t:
[tex]-4.9t^2=-490[/tex] and divide both sides by 4.9 to get
[tex]t^2=100[/tex] so
t = 10. Notice that one of the factors for that quadratic is 10 - t. That factor represents the time it takes to hit the ground. So you might ask why, then, we FOILed this out in the first place if the answer was ight in front of our noses. The reason is becase of #2 that is asking us what the initial height of the object was. That is found in the standard form...in the constant in particular. The initial height is 490 m. That's how you know (because the constant represents the height from which an object is dropped in either free fall, which this is, or in parabolic motion).
