Answer:
[tex]\displaystyle y=\frac{1}{4}x^2[/tex]
Step-by-step explanation:
Let (x, y) be a point on the parabola.
By definition, any point on the parabola is equidistant from the focus and the directrix
The distance from the focus is given by:
[tex]\begin{aligned} d&=\sqrt{(x-0)^2+(y-1)^2\\\\&=\sqrt{x^2+(y-1)^2}\end{aligned}[/tex]
The distance from the directrix is given by:
[tex]d=|y-(-1)|=|y+1|\text{ or } |-1-y|[/tex]
So:
[tex]\sqrt{x^2+(y-1)^2}=|y+1|^[/tex]
Square both sides. Since anything squared is positive, we can remove the absolute value:
[tex]x^2+(y-1)^2=(y+1)^2[/tex]
Square:
[tex]x^2+(y^2-2y+1)=y^2+2y+1[/tex]
Hence:
[tex]x^2=4y[/tex]
So, our equation is:
[tex]\displaystyle y=\frac{1}{4}x^2[/tex]
Jeremy has heard a lot of people in the club talking about tackling a 950-foot rock formation. Jeremy has set a limit that they won’t climb anything that takes longer than 7 hours, so they have enough time to travel to and from the place. Will it be possible to climb a 950-foot rock formation within Jeremy’s time constraint? Explain why or why not.
Answer: no Jeremys time is not constraint
Step-by-step explanation: The amount of minutes to climb up 1 foot of height would take around 2 to 3 minutes, however if you divide 950 with 2 you will get 475 minutes to climb, if we also convert to 475 into hours that will be 7.92 hours . so overall he will climb extra 92 minutes (i really hope this kinda helped)
If Devon took 20 min to drive 24 km, what was his R.O.C.? Answer in decimals.
Answer:
1.2 km/min
Step-by-step explanation:
ROC? rate of change? if not rate of change than my answer may not be correct
24km/20min = 1.2 km/min
24km/20min * 60min/1 hr= (24*60)/20=120 km/hr
Find the equation of the line that passes through the points (4,
11) and (-1,1). Write your answer in slope-intercept form. Bonus points for
writing it in the two other forms (make sure you label which form is which).
Step-by-step explanation:
the slope = (1-11)/(-1-4) = -10/(-5) = 2
the equation is : y -11 = 2(x-4)
=> y -11 = 2x -20
y = 2x -8 +11
y = 2x +3
other forms :
<=> 2x - y = -3
<=> 2x - y + 3 = 0
Which of the following are not polynomials? O A. x2 +x+1 O B. X-2 + x + 1 am. x + V3x+1 OD. 3+x+1 E. x + 0x2 + 2x + 2
Answer:
Option B
Step-by-step explanation:
Look.......Polynomial is something which has more than 3 term..So, as you can see option B has more than three.
CAN SOMEONE HELP THANKS 14 POINTS
Answer:
6,9,12
Step-by-step explanation:
A triangle cannot be considered a triangle unless the sum of the smaller two of the sides is greater than the larger side.
Answer:
(6, 9, 12)
Hope that this helps!
How to find the slope of a line passing through (-3,3) , (-5,9)
Answer:
slope = - 3
Step-by-step explanation:
[tex]slope, m = \frac{y_2 - y_1}{x_2 - x_ 1}[/tex] , [tex][ \ (x_ 1 , y_ 1 ) = ( -3 , 3 ) , \ (x_2 , y _ 2 ) = ( - 5 , 9 ) \ ][/tex]
[tex]slope = \frac{9 - 3}{-4 - ( -3 )} = \frac{6}{-5 + 3} = \frac{6}{-2} = -3[/tex]
find the volume of the rectangle
Answer:
3/16
Step-by-step explanation:
simply multiply all 3 numbers
If x^151+ 100 is divided by x+1 then the remainder is
Answer: 11 because it all works out.
Last week, a family ordered dinner through a local food delivery service. The food was $45. They had a coupon for 15% off the total bill.
The bill was $
when the coupon was applied.
decide which point lies on the line that is parallel to AB and passes through point P
Math help due soon thanks
Answers:
SkippingSee the diagram belowx = 7No they are not similar=======================================
Explanation:
SkippingWe peel the triangles apart as shown below. There's not much to say about it. The only thing I can think is that the larger horizontal side is 8+6 = 14 m.Due to the similar triangles, we can form the proportion x/4 = 14/8. The 14 is from 8+6. Cross multiplying leads to 8x = 56 which solves to x = 7.Focus on the triangle on the left. The missing angle is 180-95-35 = 50 degrees. The missing angle for the triangle on the right is 180-35-60 = 85 degrees. The angles don't all match up, so the triangles aren't similar.Select the graph that would represent the best presentation of the solution set.
|xl > 5
Please help I’ll give brainliest
Answer:
Answer is 670000 If you can please give me brainliest
You are baking a cake. The recipe asks for \frac{3}{5} 5 3 cup of butter and you want to make \frac{1}{5} 5 1 of the original recipe. How many cups of butter will you need?
Answer:
3/25 cup of butter
Step-by-step explanation:
You are baking a cake. The recipe asks for 3/5 cup of butter and you want to make 1/5 of the original recipe.
The calculation for the above question is given below:
1 recipe = 3/5 cup of butter
1/5 recipe = x
Cross Multiply
x × 1 recipe = 1/5 recipe × 3/5 cup of butter
x = 1/5 recipe × 3/5 cup of butter /1 recipe
x = 3/25 cup of butter
Therefore, you will need 3/25 cup of butter
Which expression is the same as 1 ten, 3 ones, and 9 thousandths?
Choose 1 answer:
Answer:
"B"
Step-by-step explanation:
WILL MARK BRAINLIST!!
Answer:
24 units
Step-by-step explanation:
Look at the coordinate plane. First start with the bottom side (LN). The line goes from -3 to 9. This means that the line is 12 units long. Now, look at the other sides. MN goes from 3 to 9, therefore, the line is 6 units long. Lastly, look at ML— -3 to 3, therefore, the line is 6 units long. Add them all up, (12+6+6) and it equals 24 units.
24 units
////////////
A hot air balloon is released and it rises at a speed of 15 mph. A
weather pattern introduces a wind headed west at 20 mph. The
hot air balloon is now redirected. What is the new direction of the
hot air balloon?
Answer:
The direction is 37 degree north of west.
Step-by-step explanation:
velocity of balloon, v = 15 mph upwards
velocity of wind, v' = 20 mph west wards
The direction is given by
[tex]tan\theta = \frac{15}{20}\\\\\theta = 37^o north of west[/tex]
Using √6241=79, Find the value of √62.41
Answer:
[tex] \blue{7.9} [/tex]
Step-by-step explanation:
[tex] \sqrt{6241} = 79 [/tex]
[tex] \sqrt{62.41} = [/tex]
[tex] = \sqrt{\dfrac{6241}{100} [/tex]
[tex] = \dfrac{79}{10}[/tex]
[tex] = \blue{7.9} [/tex]
Which expression is equivalent to 27 Σ 8n? N=0 hurry please my life depends on it
Given:
The expression is:
[tex]\sum\limits_{n=0}^{27}8n[/tex]
To find:
The expression that is equivalent to the given expression.
Solution:
According to the property of summation:
[tex]\sum\limits_{n=0}^{k}Cn=C\sum\limits_{n=0}^{k}n[/tex]
Where, C is a constant.
We have,
[tex]\sum\limits_{n=0}^{27}8n[/tex]
Using the above mentioned property of summation, we get
[tex]\sum\limits_{n=0}^{27}8n=8\sum\limits_{n=0}^{27}n[/tex]
The expression [tex]8\sum\limits_{n=0}^{27}n[/tex] is equivalent to the given expression.
Therefore, the correct option is C.
6ײ+3×y-2a×-ay (need answers)
Answer:
(If the x means the variable in your equation) 2a^2y+6x^2+3xy
Step-by-step explanation:
We have to simplify the equation to find the answer
6x^2+3xy−2a(−a)y
=6x^2+3xy+2a^2y
Through (1,0) slope = -1
Answer:
y = -1x+1
Step-by-step explanation:
The equation for a line in slope intercept form is
y = mx+b where m is the slope and b is the y intercept
y = -1x+b
Substitute in the point
0 = -1(1) +b
0 = -1+b
1 = b
The equation is
y = -1x+1
she does 3 sets of 8 pushups 7 days a week, how many pushups does she do in one week
Answer:
24 push ups3 x 8 = 24ksjsjsowjsnsoajjsodhew
if p(x) = x^3 + 1 is divided by (x + 2) , then the remainder is
PLS HELP!
Answer:
[tex]{ \bf{factor : x + 2}} \\ { \tt{divisor = - 2 }} \\ { \bf{f(x) = {x}^{3} + 1 }} \\ { \bf{f( - 2) = {( - 2)}^{3} + 1}} \\ { \bf{remainder = - 7}}[/tex]
Assignment
1
Which is rational?
a. 64
b. 17
C. 67.714819...
22. Which is irrational?
a. 75.106
c. 101
Identify each of the following as Rational or Irrational.
3 -42
4 65.4279
5
98
16
6
25
7 57.013013..
8
18.44333777...
9
-139.04
24
10
Which of the following is the equation of a line that passes though the points (2,5) and (4,3)
Answer:
y= -1x+7
or
y = -1x + b
Step-by-step explanation:
You want to find the equation for a line that passes through the two points:
(2,5) and (4,3).
First of all, remember what the equation of a line is:
y = mx+b
Where:
m is the slope, and
b is the y-intercept
First, let's find what m is, the slope of the line...
The slope of a line is a measure of how fast the line "goes up" or "goes down". A large slope means the line goes up or down really fast (a very steep line). Small slopes means the line isn't very steep. A slope of zero means the line has no steepness at all; it is perfectly horizontal.
For lines like these, the slope is always defined as "the change in y over the change in x" or, in equation form:
So what we need now are the two points you gave that the line passes through. Let's call the first point you gave, (2,5), point #1, so the x and y numbers given will be called x1 and y1. Or, x1=2 and y1=5.
Also, let's call the second point you gave, (4,3), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=4 and y2=3.
Now, just plug the numbers into the formula for m above, like this:
m=
3 - 5
4 - 2
or...
m=
-2
2
or...
m=-1
So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+b like this:
y=-1x+b
Now, what about b, the y-intercept?
To find b, think about what your (x,y) points mean:
(2,5). When x of the line is 2, y of the line must be 5.
(4,3). When x of the line is 4, y of the line must be 3.
Because you said the line passes through each one of these two points, right?
Now, look at our line's equation so far: y=-1x+b. b is what we want, the -1 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the two points (2,5) and (4,3).
So, why not plug in for x and y from one of our (x,y) points that we know the line passes through? This will allow us to solve for b for the particular line that passes through the two points you gave!.
You can use either (x,y) point you want..the answer will be the same:
(2,5). y=mx+b or 5=-1 × 2+b, or solving for b: b=5-(-1)(2). b=7.
(4,3). y=mx+b or 3=-1 × 4+b, or solving for b: b=3-(-1)(4). b=7.
See! In both cases we got the same value for b. And this completes our problem.
The equation of the line that passes through the points
(2,5) and (4,3)
is
y=-1x+7
Help are these correct ahahahahhh and explain pls
PLEASE HELP WILL MARK BRAINLIEST
4. If you color the perfect squares on a multiplication table, you will be coloring a_______ line.
A. Diagonal
B. Vertical
C. Horizontal
D. Zig-zag
Please helpppp
Answer:
A. Diagonal line
Answer:
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Step-by-step explanation:
Draw a graph of the linear equations x – 4y + 10 = 0 and x + 4y – 10 = 0. Find the coordinates of the vertices of the triangle formed by these lines along with the X-axis
Step-by-step explanation:
x-14y=0
x=0/14y
x=14y
14y
What is the value of x in the diagram?
Answer:
x = 30
Step-by-step explanation:
here 50 is hypotenuse as it is opposite of 90 degree.
x and x + 10 are the two other smaller sides of a right angled triangle respectively.
using pythagoras theorem,
a^2 + b^2 = c^2
x^2 + (x + 10)^2 = 50^2
x^2 + x^2 + 20x + 100 = 2500
2x^2 + 20x + 100 = 2500
2x^2 + 20x + 100 - 2500 = 0
2x^2 + 20x - 2400 = 0
2(x^2 + 10x - 1200) = 0
x^2 + 10x - 1200 = 0
x^2 + (40 - 30) - 1200 = 0
x^2 + 40x - 30x - 1200 = 0
x(x + 40) - 30(x + 40x) = 0
(x + 40)(x - 30) = 0
either x + 40 = 0 OR x - 30 = 0
x = 0 - 40
x = -40
x - 30 = 0
x = 30
x = -40,30
since the length and distance is not measured in negative ur answer will be 30
credit goes to sreedevi102
thank u very much . At first i was wrong and giannathecookie i m really sorry
Answer:
x = 30
Step-by-step explanation:
Using Pythagoras Theorem:
[tex]x^2 + ( x+ 10)^ 2 = 50^2\\\\x^2 + (x^2 + 100 + 20x ) = 2500\\\\x^2 + x^2 + 20x = 2500 - 100 \\\\2x^2 + 20x = 2400\\\\2x^2 + 20x - 2400 = 0\\\\2(x^2 + 10x - 1200) = 0\\\\x^2 + 10x - 1200 = 0\\\\x^2 + 40x - 30x - 1200 = 0\\\\x(x + 40 ) -30(x + 40) = 0\\\\(x+40)(x - 30) = 0\\\\x = -40, \ x = 30[/tex]
Since x is the measurement of a side, it can't be negative. Therefore x = 30
