Find the equation of the line through the points (-3,3) and (3,5) using point-slope form. Then rewrite the equation in slope-intercept form.
Given:
A line passes through the points (-3,3) and (3,5).
To find:
The equation of the line by using point slope form, then rewrite the equation in slope-intercept form.
Solution:
It is given that the line passes through the points (-3,3) and (3,5). So, the slope of the line is:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\dfrac{5-3}{3-(-3)}[/tex]
[tex]m=\dfrac{2}{6}[/tex]
[tex]m=\dfrac{1}{3}[/tex]
The point slope form of a line is:
[tex]y-y_1=m(x-x_1)[/tex]
Where, m is the slope.
The point slope form of the given line is:
[tex]y-3=\dfrac{1}{3}(x-(-3))[/tex]
[tex]y-3=\dfrac{1}{3}(x+3)[/tex]
The point slope form of the given line is [tex]y-3=\dfrac{1}{3}(x+3)[/tex].
We need to rewrite this equation in slope intercept form, i.e., [tex]y=mx+b[/tex], where m is slope and b is y-intercept.
The above equation can be rewritten as:
[tex]y-3=\dfrac{1}{3}(x)+\dfrac{1}{3}(3)[/tex]
[tex]y-3=\dfrac{1}{3}(x)+1[/tex]
[tex]y=\dfrac{1}{3}(x)+1+3[/tex]
[tex]y=\dfrac{1}{3}(x)+4[/tex]
Therefore, the slope intercept form of the given line is [tex]y=\dfrac{1}{3}(x)+4[/tex].
Solve for c.
-c/2+43 = 50
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{-\dfrac{c}{2}+43=50}[/tex]
[tex]\large\text{SUBTRACT 43 to BOTH SIDES}[/tex]
[tex]\mathsf{-\dfrac{c}{2}+43-43=50-43}[/tex]
[tex]\large\textsf{CANCEL out: 43 - 43 because that gives you 0}[/tex]
[tex]\large\textsf{KEEP: 50 - 43 because it helps solve for the c-value}[/tex]
[tex]\mathsf{50 - 43 = \bf 7}[/tex]
[tex]\large\text{NEW EQUATION: }\mathsf{-\dfrac{c}{2}=7}[/tex]
[tex]\large\textsf{MULTIPLY }\mathsf{\dfrac{2}{-1}}\large\textsf{ to BOTH SIDES}[/tex]
[tex]\mathsf{\dfrac{2}{-1}\times-\dfrac{c}{2}= \dfrac{2}{-1}\times7}[/tex]
[tex]\large\textsf{CANCEL out: your RIGHT SIDE of the equation because that gives}\\\large\textsf{you 1}[/tex]
[tex]\large\textsf{KEEP: }\mathsf{\dfrac{2}{-1}\times7}\large\textsf{ because that helps solve for the c-value}[/tex]
[tex]\uparrow\large\text{SIMPLIFY THE EQUATION ABOVE \& YOU HAVE YOUR}\\\large\text{C-VALUE}\uparrow[/tex]
[tex]\boxed{\boxed{\large\text{ANSWER: \huge\bf c = -14}}}\huge\checkmark[/tex]
[tex]\large\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Hello !
Answer:
[tex] \boxed{\sf c= -14} [/tex]
Step-by-step explanation:
We will try to find the value of c that satisfies the equality.
Given equation:
[tex] \sf -\dfrac{c}{2} + 43 = 50 [/tex]
Subtract 43 from both sides:
[tex] \sf -\dfrac{c}{2} + 43 - 43 = 50 - 43 \ \sf -\dfrac{c}{2} = 7 [/tex]
Multiply both sides by -2:
[tex] \sf -\dfrac{c}{2} \times (-2) = 7 \times (-2) \ \ \implies \boxed{\sf c = -14} [/tex]
Have a nice day ;)
which choices are equivalent to the exponential expression below?
Answer:
The answer is
B
D
F
Step-by-step explanation:
Squaring a fraction is like squaring a whole number really so you just square the fraction by multiplying it by itself.
There are 3 blue marbles, 6 red marbles, 2 green marbles and 1 black marble in a bag. Suppose you select one marble at random. Find the probability for each of the following.
a) The probability of selecting a blue marble is P ( B ) = 1/4
b) The probability of selecting a green marble is P ( G ) = 1/6
c) The probability of selecting not a green marble is P' ( G ) = 5/6
What is Probability?The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible
Probability = number of desirable outcomes / total number of possible outcomes
The value of probability lies between 0 and 1
Given data ,
Let the number of blue marbles = 3
Let the number of red marbles = 6
Let the number of green marbles = 2
Let the number of black marbles = 1
So , the total number of marbles = 12
So , the probability is given as
The probability of selecting a blue marble is P ( B ) = 1/4
The probability of selecting a green marble is P ( G ) = 1/6
The probability of selecting not a green marble is P' ( G ) = 5/6
Hence , the probability is solved
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The complete question is attached below :
There are 3 blue marbles, 6 red marbles, 2 green marbles and 1 black marble in a bag. Suppose you select one marble at random. Find the probability for each of the following.
Which is the best estimate of 3.156 x 2.8 ?
Find segment ET. Please and thank you
Answer:
x=9
Step-by-step explanation:
Use the intersecting chord theorem:
RE*ET = UE*ES
Substitute values
21 (2x+2) = 30 (x+5)
Expand:
42x+42 = 30x + 150
transpose and simplify
42x-30x = 150 - 42
12x = 108
x = 9
A yogurt shop offers five different flavors of frozen yogurt and twenty different
toppings. How many choices are possible for a single serving of frozen yogurt with
one topping?
PLEASEEEEE HELPPPP IM BEGGING SOMEONE PLEASEEEEEEEE
Answer:
Step-by-step explanation:
answer is 98 degree because the relation between missing angle and 98 degree is alternate exterior angles and alternate exterior angles are always equal.
answer is 89 degree because the relation between missing angle and 89 degree is corresponding angles and corresponding angles are always equal.
in the 5th question
let's consider the angle there as A so angle A is 98 degree and by the relation of alternate angles the question mark (?) is 98 degree
in 6th question
by the relation of corresponding angles the question mark(?) is 89 degree
Ellie want to buy new shoes that is in sale for $80. She saved $60. How much more money does she need
Answer:
$20
Step-by-step explanation:
New shoes = $80
What Ellie Saved = $60
80 - 60 = 20
To make sure this is correct simply add 20 to 60.
60 + 20 = 80
Which is a measure of the missing angle in this triangle?
Let us assume the three angles to be angle 1, angle 2 and angle 3.
Angle 1 = 35°
Angle 2 = 120°
To find:-Angle 3.
Solution:-[tex]{\boxed{\mathcal{\red{The \:measure\:of\:the\:missing\:angle\:is\:25°. \:✅}}}}[/tex]
Step-by-step explanation:-We know that,
[tex]\sf\pink{Sum\:of\:angles\:of\:a\:triangle\:=\:180°}[/tex]
➪ ∠ 1 + ∠ 2 + ∠ 3 = 180°
➪ 35° + 120° + ∠ 3 = 180°
➪ 155° + ∠ 3 = 180°
➪ ∠ 3 = 180° - 155°
➪ ∠ 3 = 25°
[tex]\sf\red{Therefore, \:the\: measure \:of \:∠\: 3\: is \:25°.}[/tex]
To verify:-∠ 1 + ∠ 2 + ∠ 3 = 180°
✒ 35° + 120° + 25° = 180°
✒ 180° = 180°
✒ L. H. S. = R. H. S.
[tex]\boxed{Hence\:verified.}[/tex]
[tex]\bold{ \green{ \star{ \orange{Hope\:it\:helps.}}}}⋆[/tex]
Answer:
? = 25°
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
Subtract the sum of the given angles from 180° for missing angle, that is
? = 180° - (120 + 35)° = 180° - 155° = 25°
How can I calculate the maximum height of the ball? h=-16t^2+vt+h v is the initial velocity and I got 4.3cm h is the initial height and I got 14cm Range of the ball is 1.954m and the time in air is 2.1 When I solve the maximum height of the ball, it need to be ft/s.
Step-by-step explanation:
The path followed by the ball as a function of time is given by :
[tex]h=-16t^2+vt+h[/tex]
Where
v is initial velocity and h is initial height,
v = 4.3 cm/s = 0.043 m/s and h = 14 cm = 0.14 m
The equation becomes,
[tex]h=-16t^2+0.043t+0.14[/tex] ....(1)
It is a quadratic equation,
t = 0.095 s
Put the value of t in equation (1).
[tex]h=-16(0.095)^2+0.043(0.095)+0.14\\\\h=-0.000315\ m[/tex]
or
h = -0.00103 ft (negative sign shows height is in negative direction)
Can someone help me find the vertex?
Answer:
vertex = (2, 264)
Step-by-step explanation:
i just used desmos so um yeah im sorry
A paperweight in the shape of a hemisphere is shown. It has a volume of 231.6 cubic centimeters.
Enter the radius of the paperweight, in centimeters. Round your answer to the nearest thousandth.
Answer:
2/3*22/7*r^3=231.6
2/3*22/7=2.0952
2.0952*r^3=231.6
r^3=231.6/2.0952
r^3=
Step-by-step explanation:
2/3*22/7*r^3=231.6
2.0952r^3=231.6
r^3=110.5384
cuberoot 110.5384
=4.7992
Amy buys eight apples that each weigh 150 grams. She notices that they are on sale for $3.00 per kilogram, how much will the apples cost? Prove your thinking.
Answer:
$3.60
Step-by-step explanation:
8 apples × 150 grams
1200 grams
1 kilogram = 1000 grams
x. = 1200 grams
X = 1.2 kg
1kg = $3.00
1.2kg =$3.6
The cost of 8 apples that have weight 1.2 kilograms is,
⇒ $3.60
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
Amy buys eight apples that each weigh 150 grams.
And, She notices that they are on sale for $3.00 per kilogram.
Now,
Total weight of the apples is,
⇒ 8 × 150 grams
⇒ 1200 grams
⇒ 1.2 kilograms
Since, She notices that they are on sale for $3.00 per kilogram.
Hence, The cost of 8 apples that have weight 1.2 kilograms is,
⇒ $3.00 × 1.2
⇒ $3.60
Thus, The cost of 8 apples that have weight 1.2 kilograms is,
⇒ $3.60
Learn more about the multiplication visit:
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Please help me ASAP
Answer:
I think 12 is the answer
Step-by-step explanation:
In ∆ QOP
R and S is the midpoint of OQ and PQ
and RS is parallel to OP
Therefore , By BPT
∆QRS is similar to ∆ QOP
let QS length be 1 unit
therefore , QP is 2 unit ( because QS is half of QP )
RS / OP = QS / QP
18-4x / -9+7x = 1 / 2
after cross multiplying
36-8x = -9+7x
36+9 = 7x+8x
45 = 15x
x=3
we have OP length = -9+7x
put the value of x in above equation
-9+7×3
-9+21
12
Q = {1, 3, 5, 7, 9). Express it in description method and in rule method.
Answer:
{x:x is having odd number}
Max drives 85 km at an average speed of 110 km/h and then 7 km at 70 km/h without stopping.
What is the average speed for the whole journey to 1 dp?
Answer:
how much time did it take him???????
Step-by-step explanation:
HELP DUE IN 15 MINS!
Find the area of the bolded sector in the circle below.
Leave your answer in terms of pi. Just type what number should be multiplied to the
pi)
Area sector = ?? π
Answer:
Area of the sector = 47.52π
Step-by-step explanation:
Area of the sector of the circle;
A = ∅ / 360 * πr²
We know that;
∅ = 120
r = 12
So now we can substitute;
A = (120 / 360) * π(12)²
A = 0.33 * 144π
A = 47.52π
Hope this helps!
Use the Pythagorean theorem to find the unknown side of the right triangle.
Answer:
c=26
Step-by-step explanation:
10^2 + 24^2=c^2
100+576=c^2
676=c^2
c=26
Hope I helped, have a nice day :)
Answer:
The Answer is 26
Step-by-step explanation:
to find the hypothenuse you need to use this formula a²+b²=c² so 10x10 is 100 and 24x24 is 576. Add those up and find the square root. √676 is 26.
Hope this Helped
Please help and fast!!!!
( i accidently clicked an answer)
Answer:
16,734.06 ft2
Step-by-step explanation:
A = 2pir
A = 2 x pi x 73
A = 16741.5 ft2
Is (5, 8) a solution to this system of inequalities?
x + y ≤ 18
x ≥ 6
Answer:
No
Step-by-step explanation:
x + y ≤ 18
x ≥ 6
(5,8)
The second inequality states that x must be greater than or equal to 6, but x =5 so it is not a solution
Anyone can help ?
I'm from Indonesian :)
Answer:
624
Step-by-step explanation:
[tex] 2(\frac{1}{2} \times 6 \times 8 ) + (24 \times 8) + (24 \times 6) + (10 \times 24)\\ = 624[/tex]
Find the median of the values:
8, 13, 6,-1, 10, 0, -3, 5, 7,1
Answer:
To do this question, you need to put the numbers in least to greatest. Greatest to least will not work and will be incorrect.
It will be:
-3, -1, 0, 1, 5, 6, 7, 8, 10, 13
Now you have to cancel each number out from each end.
You will get the numbers:
5, and 6.
You have to find the average of this so:
5 + 6 = 11
11 ÷ 2 = 5.5
So the answer is 5.5.
Answer:
5.5
Step-by-step explanation:
First you would rearrange the numbers from smallest to biggest or vice versa then you cancel out equal number of numbers on both sides until you get to the middle. If it's an even amount of numbers, like 10, then there will be two in the middle instead of one so in that case you would add the two of them and then divide by two.
For example, -3, -1, 0, 1, 5, 6, 7, 8, 10, 13
you would cancel out until you get to the middle which would leave you with 5 and 6 so you add them and divide by two to get 5.5.
ummm I’m so bad at math lol
The correct option is B - Where the given data is plot correctly.
Find the height of triangle
Answer:
60
Step-by-step explanation:
First, divide 120 by two and get 60. Now do 120-60 to get 60. Set up proportion
60/x = x/60.
Cross multiply
x^2 = 3600
and now find the square root of 3600
60
The circumference of a circle is 7 π π ft. Find its diameter, in feet
Answer:
2.23
Step-by-step explanation:
100 points
If you tell me to use quizlet or give me a wrong answer or link you will be reported
[tex]\huge{ \mathbf{ \underline{ Answer }\: \: ✓ }}[/tex]
The sand we need to fill the cylinders is equal to the total volume of the six cylindrical posts .
Given terms ( common for each cylinder ) :
height (h) = 4 ftradius. (r) = 0.5 ft[tex] \large \boxed{ \mathrm{volume =\pi {r}^{2} h}}[/tex]
[tex]3.14 \times \dfrac{1}{2} \times \dfrac{1}{2} \times 4[/tex][tex] \mathrm{3.14 \: ft {}^{3} }[/tex]Since volume of each cylinder is equal, so total volume of six cylindrical post :
[tex]3.14 \times 6[/tex][tex] { \mathrm{18.84 \: ft {}^{3} }}[/tex]_____________________________
[tex]\mathrm{ ☠ \: TeeNForeveR \:☠ }[/tex]
Can someone help with this
Answer:
20
Step-by-step explanation:
Pretend you got 86% of the questions on a state test correct. The test had 120 problems. How many problems did you get correct?
Please show or explain your work
Answer:
1 17\43
Step-by-step explanation:
I did the math... i should be right...
Which of the following is the Perpendicular Bisector Theorem?
A. lf a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.
B. Ifa point is on the perpendicular bisector of a segment, then it is proportional from the endpoints of the segment.
C. lf a point is proportional from the endpoints ofthe segment then it lies on the perpendicular bisector of that segment
D. f a point is equidistant from the endpoints of the segment, then it lies on the perpendicular bisector of that segment.
Answer:
its Ifa point is on the perpendicular bisector of a segment, then it is proportional from the endpoints of the segment.