Answer:
The given equations are;
y = a·(x - h)² + k or y = a·x² + b·x + c
We have;
(x - h)² = 4·p·(y - k),
Where;
(h, k) are the x, and y coordinates of the vertex
p = The distance from the focus to vertex distance;
Comparing, we have;
y - k = a·(x - h)²
(y - k)/a = (x - h)²
(x - h)² = 4·p·(y - k)
4·p·(y - k) = (x - h)²
∴ 4·p = 1/a
p = 1/(4·a)
Therefore, the focus to vertex distance inversely proportional to the value of a
The distance of every point on the parabola is equidistant from the directrix and the focus
Therefore, the equation of the directrix is y = k - p
For example, we have;
y = 2·x² + 3·x + 1
h = -b/2a = -3/4
k = (4ac - b²)/4a = (4×2×1 - 3²)/(4×2) = -1/8
The coordinate of the focus is (h, k + p) = (-3/4, -1/8 + 1/8) = (-3/4, 0)
The directrix, y = k - p = -1/8 - 1/8 = -1/4
For a point x = 2, we have, y = 2·2² + 3·2 + 1 = 15
The coordinate of the point is (2, 15)
The distance of the point from the directrix = 15 - (-1/4) = 15 + 1/4 = 15.25
The distance of the point from the focus is √((2 - (-3/4))² + (15 - 0)²) = 15.25
Therefore, all points on the parabola have equal distances from the focus and the directrix
Step-by-step explanation:
need answers ASAP.
Answer: If you have solved to get x=6 just plug that back into the problem. You get 50
Step-by-step explanation:
Answer:
[tex]x = 6[/tex]
[tex]AB = 50[/tex]
Step-by-step explanation:
Since [tex]B[/tex] is the midpoint of [tex]\overline A \overline C[/tex], [tex]AB[/tex] and [tex]BC[/tex] are equal in length.
[tex]AB=BC[/tex]
[tex]4x+26 = 6x+14[/tex]
[tex]12=2x[/tex]
[tex]x=6[/tex]
To find the length of [tex]AB[/tex], we can use substitution:
[tex]AB=4x+26[/tex]
[tex]=4(6)+26[/tex]
[tex]=50[/tex]
∴[tex]AB = 50[/tex]
Hope this helps
can you please help me
Answer:
D
Step-by-step explanation:
the dilalation from triangle ART to triangle EFG is 2 1/5:
12/5
2 1/5
use the scale factor to find m
8 * 2 1/5
19 2/10
side GF is equal to side EG so m p 19 2/10
Answer:
finally :)
Step-by-step explanation:
have a great day
Vivienne has 5 pets, all of which are either birds or cats. Her pets have a total of 14 legs. Choose the system of equations that can be solved to find the number of birds that Vivienne owns, b, and the number of cats that Vivienne owns, e.
Answer:
the system of equations is
b + e = 5
2b + 4e = 14
and the solved system gets you to the conclusion that vivienne has 3 birds and 2 cats
Step-by-step explanation:
b is the amount of birds and e is the amount of cats so adding them together would give you 5, the total amount of pets. so this is the first equation:
b + e = 5
next, we know that birds have two legs and cats have 4, so those respective numbers times the amount of each animal will give you 14, the amount of legs. so the equation would be:
2b + 4e = 14
so the system of equations would be
b + e = 5
2b + 4e = 14
i wasnt sure if you also needed to solve it but here it is solved
b = 5 - e
2(5 - e) + 4e = 14
10 - 2e + 4e = 14
10 + 2e = 14
2e = 4
e = 2
so using subsitution you would get b by using the value of e in the first equation.
b = 5 - e
b = 5 - 2
b = 3
so vivienne has 3 birds and 2 cats.
The required number of birds and cats Vivienne have is 3 and 2 respectively.
What are simultaneous linear equations?Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.
Here,
Vivienne has 5 pets, all of which are either birds or cats.
Let the number of birds be x, and the number of cats be y,
x + y = 5, - - - - -(1)
Now, Her pets have a total of 14 legs. Since a bird has 2 legs and a cat has 4 lags
According to the question,
2x + 4y = 14 - - - - -(2)
Solving equations 1 and 2,
2x + 4 (5 -x) = 14
2x + 20 - 4x = 14
2x = 6
x = 3
Now,
3 + y = 5
y = 2
Thus, the required number of birds and cats Vivienne have is 3 and 2 respectively.
Learn more about simultaneous equations here:
https://brainly.com/question/16763389
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Evaluate the expression 5a + 12b for a = 5 and b = 12
PLEASE PLEASE help!
Answer:
I think the answer is 169
A truck driver earns $21.00 per hour for the first 40 hours worked in one week. The driver earns time-and-a-half, or $31.50, for each hour worked in excess of 40. The piece-wise function below represents the driver wage, w(h), as a function of the hours worked in one week, h. How much money does the truck driver earn in a week if he works 30 hours? *
Answer:
$21 x 30 = 630 (630 the answer)
Step-by-step explanation:
Please help..
Solve for x and y rounded to the nearest hundredth.
x = 5.33 and y = 4.67
x = 4.67 and y = 5.33
x = 10.5 and y = 12
x = 3.42 and y = 3
Step-by-step explanation:
A is answer
Ben needs to replace two sides of his fence. Once side is 367 9/100 meters long, and the other is 329 3/10 meters long. How much fence does Ben need to buy?
Answer:
696 39/100
Step-by-step explanation:
30 Points. i fr need to pass this test i dont feel like taking it again my senior year
Answer:
3x^3+2x^2+2x+5
Step-by-step explanation:
The answer is A
The area of a square depends on the length of its sides. Answer the questions below
regarding the relationship between the area of the square and the length of one side
of the square.
Answer:
The independent variable, x, represents the length of one side of the square, and the dependent variable is the the area of the square, because the the area of the square depends on the length of one side of the square.
A function relating these variables is D(x) = x^2.
So D(6) =36, meaning if 6 is the length of one side then 36 would be the area of the square.
Step-by-step explanation:
The question clearly stated that the area depends on the side length, making the side length the independent variable.
The formula for the area of a square is the side length squared.
Have a good day :)
The relationship between them is the formula for the area of a square is the side length squared.
What is the area of a square?The area of a square can be calculated as the square of the sides of a given figure.
The area of a square = side x side
The independent variable x is represents the length of one side of the square, and the dependent variable is the the area of the square, because the the area of the square depends on the length of one side of the square.
A function relating these variables is D(x) = x^2.
D(6) =36, meaning if 6 is the length of one side then 36 would be the area of the square.
It is stated that the area depends on the side length, making the side length the independent variable.
Therefore, The formula for the area of a square is the side length squared.
Learn more about the area;
https://brainly.com/question/1658516
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1. If m=1/2 and b=-4, what is the equation of the line?
Answer:
y=1/2x-4
Step-by-step explanation:
There are 25 trees on the Jackson’s property. Twenty percent of the trees are oak trees. Which equation can be used to find the number of oak trees on the property?
Answer:
See below
Step-by-step explanation:
Number of oak trees
[tex] = \frac{25}{100} \times 25 \\ [/tex]
will mark brainliest please help me with
Answer:
-1
Step-by-step explanation:
i added all of the and that got me the answer
BRAINLIEST PLEASE
Answer:
6x-7
Step-by-step explanation:
Is that the answer you are looking for?
If f(x) = 4x + 1 and g(x) = 2x – 3, then (g(f(x)) =
Answer g(x)=x2 + 2
Step-by-step explanation:
The graph of a proportional relationship is a straight line passing through the?
Answer:
Origin
Step-by-step explanation:
Here you go~
How do you get this annoying anime kid shut up?
Please help he annoying me, i think i do what you guys said on my last 2 questions.
Answer:
Insult his favorite anime lol. Works like a charm.
Step-by-step explanation:
Answer:
watch anime with them! and tell them they have taste cause same >_<
Which points on this vertical number line best represent the locations of 2.5 and minus 3 over 2 ?
Answer:
ok listen when looking at the graph the answer is easy its b
Step-by-step explanation:
Answer:
it is B
Step-by-step explanation:
because G and K , g is 2.5 and k -3/2
PLS HELPPP I'LL MARK BRAINLEST AND GICE 100 POINTS
Answer: b
Step-by-step explanation:
1. What is the measure of ∠ABC?
Answer:
I thought ik but i dont good luck!
Step-by-step explanation:
Answer:
∠ ABC = 55°
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
∠ ABD is an exterior angle of the triangle , then
6x + 5 = x + 45 + 3x
6x + 5 = 4x + 45 ( subtract 4x from both sides )
2x + 5 = 45 ( subtract 5 from both sides )
2x = 40 ( divide both sides by 2 )
x = 20
Then
∠ ABD = 6x + 5 = 6(20) + 5 = 120 + 5 = 125°
∠ ABD and ∠ ABC are adjacent angles and are supplementary, thus
∠ ABC = 180° - ∠ ABD = 180° - 125° = 55°
Find the equation of the line that passes through (5, -1) and
(-10, -10)
Answer:
y = 0.6x – 4
or
y = 3/5x -4
Step-by-step explanation:
Which equation is represented in the graph below?
please answer this question. The price of a computer was reduced from $400 to $300. By what percentage was the price of the computer reduced?
Answer:it was reduced by 25%
Source: trust me bro
Does anyone have any drink recommendations for Starbucks???
Answer this math problem tho
Me and a friend go to Starbucks I order a venti caramel frap and my friend orders the same. Both of our drinks plus 4 cake pops cost $17.75. I have $40 in cash how much do I have left after our order has been paid for???
Answer:
hmm try pumpkin spice fraptinao *sry ik i spelled it wrong
Step-by-step explanation:
If the graph of the linear equation ax-8y=15 has an x-intercept at (3,0), then what is the value of a?
====================================
Work Shown:
Plug in (x,y) = (3,0)
ax - 8y = 15
a(3) - 8y = 15 .... replace x with 3
3a - 8(0) = 15 ... replace y with 0
3a - 0 = 15
3a = 15
a = 15/3
a = 5
The equation updates to 3x - 8y = 15.
a) Estimate the value of 50.75 x 0.18
Answer:9.135
Step-by-step explanation: I had have this answer
Answer:
9.135
Step-by-step explanation:
PLS HELP I WILL MARK BRAINLEST!!!!!!!!!!
On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 1, negative 1) and (0, 1). Everything to the left of the line is shaded.
Which linear inequality is represented by the graph?
y > 2x + 2
y ≥ One-halfx + 1
y > 2x + 1
y ≥ One-halfx + 2
Answer:
the 3rd one
Step-by-step explanation:
i graphed it mentally and found out the slope was 2 and the y intercept is 1
Answer:
c
Step-by-step explanation:
Anyone know how to do this??
Answer:
no
Step-by-step explanation:
The blue dot is at what value on the number line? -10 -4
Answer:
The blue dot is at the value of -19
Step-by-step explanation:
There is a gap of 3 between each space
-19 -16 -13 -10 -7 -4
Answer:
-19
Step-by-step explanation:
i did it in khan and it was right
Find the x- and y-intercept of the line.
–3x + 5y = 75
a
x-intercept is 5; y-intercept is –3
b
x-intercept is –3; y-intercept is 5
c
x-intercept is –25; y-intercept is 15
d
x-intercept is 15; y-intercept is –25
Answer:
x intercept-25; y intercept is 15
Question: Find the missing side.
Answer:
17
Step-by-step explanation:
Use the Pythagorean Theorem, [tex]a^{2} +b^{2} =c^{2}[/tex]
In this situation, you would use the equation as [tex]8^{2} +15^{2} =x^{2}[/tex]
What is the first step in solving the equation 2/3x+1/3+2=5?
Subtract 3 from each side of the equation.
Add 2 to each side of the equation.
Combine like terms.
Multiply each side of the equation by 5.
Answer:
use photomath it'll you all