The solution is, b. x² = 12(y + 3) equation represents a parabola that has a focus of (0, 0) and a directrix of y = −6
What is parabola?The parabola is a plane curve which is mirror symmetrical and is approximately U-shaped. It fits several superficial different mathematical descriptions.
here, we have,
If the focus is (0,0) and the directrix is y=-6, the equation will be found as follows:
Let (x,y) be any point on the parabola. Find the distance between (x,y) and the directrix, then find the distance between (x,y) and the focus. Equate these two distance equations and the simplified equation in x and y is equation of the parabola.
The distance between (x,y) and (0,0) is √(x²+y²)
The distance between (x,y) and the directrix, y=-6 is ly+6l
Equate the two distance expressions and square on both sides
√(x²+y²)=ly+6l
x²+y²=(y+6)²
simplifying and bringing terms together we get:
x²-12y-36=0
make x² the subject:
x²=12y+36
x²=12(y+3)
Hence, Answer :b. x² = 12(y + 3)
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complete question:
Which equation represents a parabola that has a focus of (0, 0) and a directrix of y = −6 ?
a. x² = 12y
b. x² = 12(y + 3)
c. x² = −3y
d. x² = −3(y + 3)
Answer:
C
Step-by-step explanation:
Please help quick
10 points
Answer:
[tex]y = x - 1[/tex]
:))))))))))
Answer:
-1
Step-by-step explanation:
the line goes through the y axes and it goes over -1 as it passes
Increase £55 by 37%
Give your answer rounded to 2 DP.
Answer:
75.35
Step-by-step explanation:
I hope this helped
tan 235° = 2tan20°+ tan215°
Given : tan 235 = 2 tan 20 + tan 215
To Find : prove that
Solution:
tan 235 = 2 tan 20 + tan 215
Tan x = Tan (180 + x)
tan 235 = tan ( 180 + 55) = tan55
tan 215 = tan (180 + 35) = tan 35
=> tan 55 = 2tan 20 + tan 35
55 = 20 + 35
=> 20 = 55 - 35
taking Tan both sides
=> Tan 20 = Tan ( 55 - 35)
=> Tan 20 = (Tan55 - Tan35) /(1 + Tan55 . Tan35)
Tan35 = Cot55 = 1/tan55 => Tan55 . Tan35 =1
=> Tan 20 = (Tan 55 - Tan 35) /(1 + 1)
=> Tan 20 = (Tan 55 - Tan 35) /2
=> 2 Tan 20 = Tan 55 - Tan 35
=> 2 Tan 20 + Tan 35 = Tan 55
=> tan 55 = 2tan 20 + tan 35
=> tan 235 = 2tan 20 + tan 215
QED
Hence Proved
Solve the following equations:
A) 3x = 15
B) y + 7 = 13
Answer:
x=5
y=6
Step-by-step explanation:
a) 3x=15
/3
x=5
b) y+7=13
-7
y=6
8=y+3 solve for the variable
Answer:
5
Step-by-step explanation:
8 = y + 3
5 + 3 = 8
Therefore y = 5
Answer:
y = 5
8=y+3
8-3=y+3-3
5=y
hope it's helpful ❤❤❤❤
THANK YOU.
What is the value of X?
Answer:
x=12°
Step-by-step explanation:
180 - 90 = 4x - 2° + 3x + 8 °
90°= 7x + 6
90° - 6 = 7x
7x = 84
x= 84/7
x = 12
Sam invests $6,000 in a savings account at 6%
for 3 years. How much did he earn in interest?
answer: $1,080
explanation: interest = principal x rate x time
>> interest = 6,000 x 0.06 x 3
after multiplying, you get 1,080, which is the simple interest
**tip: turn the rate/percent into a decimal, then multiply
Ruth prepared 10 kilograms of dough after working 2 hours. How many hours
did Ruth work if she prepared 40 kilograms of dough? Assume the relationship
is directly proportional.
Answer:
8 hours
Step-by-step explanation:
A mechanic charges $20.00 an hour, h for labor plus parts. If the parts cost $217.00, write a linear equation that will find the total cost, c.
Answer:
y=20x+217
Step-by-step explanation:
Please help me graph
Y=1.5x
Will mark brainliest!!
Which value of y makes the inequality 3y^2+2(y-5)>8 true
A y=0
B y= -1
C y= -2
D y= -3
Answer:
Conclusion:
As y = -3 MAKES the inequality TRUE.
Therefore, option D i.e. y = -3 is true.
Step-by-step explanation:
Given the inequality
3y² + 2(y - 5) > 8
For y = 0
substitute y = 0 in the inequality
3y² + 2(y - 5) > 8
3(0)² + 2(0 - 5) > 8
3(0) + 2(-5) > 8
0 - 10 > 8
-10 > 8
FALSE!
-10 can not be greater than 8.
Hence, y = 0 does not make the inequality true.
For y = -1
substitute y = -1 in the inequality
3y² + 2(y - 5) > 8
3(-1)² + 2(-1 - 5) > 8
3(1) + 2(-6) > 8
3 - 12 > 8
-9 > 8
FALSE!
-9 can not be greater than 8.
Hence, y = 1 does not make the inequality true.
For y = -2
substitute y = -2 in the inequality
3y² + 2(y - 5) > 8
3(-2)² + 2(-2 - 5) > 8
3(4) + 2(-7) > 8
12 - 14 > 8
-2 > 8
FALSE!
-2 can not be greater than 8.
Hence, y = -2 does not make the inequality true.
For y = -3
substitute y = -3 in the inequality
3y² + 2(y - 5) > 8
3(-3)² + 2(-3 - 5) > 8
3(9) + 2(-8) > 8
27 - 16 > 8
11 > 8
TRUE!
11 is indeed greater than 8.
Hence, y = -3 MAKES the inequality TRUE.
Conclusion:
As y = -3 MAKES the inequality TRUE.
Therefore, option D i.e. y = -3 is true.
Answer:
D
Step-by-step explanation:
MMMM THE MODERATORS ARE MAKING ME FLIPPING ANGRY! I NEED SOMEONE TO ANSWER MY QUESTION PLEASE .
Answer:
780
Step-by-step explanation:
So 5% is 39 so 5% x 20 is 100% do the same with the 39 so do
39 x 20 = 780
Which multiple of 7 is greater than 45 and less than 50?
Answer:
49
Step-by-step explanation:
Answer
the answer is 49
Divide the polynomials.
Your answer should be a polynomial.
22 - 71 +12
I-3
Answer:
x - 4
Step-by-step explanation:
how do you graph y=-x-2?
Answer:
Ok i'm going to try to explain this
Step-by-step explanation:
So the X Intercept is -2, and the Y intercept is -2 aswell.
Every 1x, it does down by one. Here is a graph.
10e=1
What does E equal cause i need help
The value of e is 0.1 in the equation 10e=1.
In the equation 10e = 1, the letter "e" represents an unknown variable.
To find the value of "e," you need to isolate it on one side of the equation.
Divide both sides of the equation by 10:
(10e) / 10 = 1 / 10
This simplifies to:
e = 1/10
e=0.1
Hence, the value of e is 0.1.
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Is −5 a solution to the equation 6 + 5 = 5 + 8 +2? PLS HELP
Answer:
it is false
Step-by-step explanation:
Answer:
False
Step-by-step explanation
6+5 ?= 5+8+2
11≠15
False
With this equation it was asking you is 6+5 equal to 5+8+2
and the answer is no, false.
Billy is going on a road trip. The amount of gas g (in gallons) left in his tank varies inversely with the amount
of time he has been driving t in hours. He has 10 gallons left after 4 hours. Write the equation for this
situation.
40
Answer:
The equation to represent the situation is [tex]10 = \frac{k}{4}[/tex]
Step-by-step explanation:
It is given that:
Amount of gas left in tank varies inversely with the amount of the time.
Let,
g represents the gas
t represents the time
g ∝ 1/t
[tex]g = \frac{k}{t}[/tex]
Here, k represents the constant of proportionality.
Putting g = 10 and t = 4 in the equation
[tex]10 = \frac{k}{4}[/tex]
Therefore,
The equation to represent the situation is [tex]10 = \frac{k}{4}[/tex]
The distance traveled by a toy car can be modeled by D(t) = t3 − 3t2 + t − 3, where t > 3 represents time in seconds. If the car traveled for t − 3 seconds, identify the expression that represents the speed of the toy car.
Answer:
[tex]t^2+1[/tex]
Step-by-step explanation:
We are given that
Distance traveled by a toy car
[tex]D(t)=t^3-3t^2+t-3[/tex]
Where t>3
Time taken by car =t-3 seconds
We have to find the expression which represents the speed of the toy car.
We know that
[tex]Speed=\frac{Distance}{time}[/tex]
Using the formula
[tex]Speed=\frac{(t^3-3t^2+t-3)}{t-3}[/tex]
[tex]Speed=\frac{t^2(t-3)+(t-3)}{t-3}[/tex]
[tex]Speed=\frac{(t-3)(t^2+1)}{t-3}[/tex]
[tex]Speed=t^2+1[/tex]
Hence, the expression which represents the speed of the toy car
[tex]t^2+1[/tex]
The expression that represents the speed of the toy car is [tex]t^2 + 1[/tex].
The calculation is as follows:Given that,
The distance traveled should be [tex]D(t) = t^3 - 3t^2 + t - 3[/tex]
Here t>3
Time taken by car = t -3 seconds
Now the expression should be
[tex]Speed = Distance \div time\\\\= ( t^3 - 3t^2 + t - 3) \div (t - 3)\\\\= t^2(t - 3) + (t - 3) \div (t - 3)\\\\= (t - 3) (t^2 + 1) \div (t - 3)\\\\= t^2 + 1[/tex]
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(06.01)
Solve the following system of equations and show all work.
y = x2 + 3
y = x + 5
can someone pls tell me if the equations are wrong or right and if wrong what is the proper equation
Answer:
the answer would be 12 apples pies andbakr
Brian can iron 3 shirts in 5 minutes. If Brian irons at a constant rate, how many shirts can he iron in 30 minutes? WILL GIVE BRANLIEST
Answer:
18
Step-by-step explanation:
Answer:
18
Step-by-step explanation:
30/5 = 6
6 * 3 = 18
Hi can someone help me plz??????
−6p=48
Help a kid out
Answer:
p = -8
Step-by-step explanation:
-6p = 48
divide both sides by -6
p = -8
evaluate 3z+6 when z=4
Answer:
18
Step-by-step explanation:
plug 4 for z
3(4)+6=18
Choose all of the points where the graph of the line 3x + 2y = 6 and the graph of the parabola y = x2 - 4x + 3 interact
Answer:
d yes that is the correct answer
can you help me plz
Tim and Kevin each sold candies and peanuts for a school fund-raiser. Tim sold 16 boxes of candies and 4 boxes of peanuts and earned $132. Kevin sold 6 boxes of peanuts and 20 boxes of candies and earned $190. Find the cost of each.
Answer:
Tim's Cost of the box of candy: 7$ for one box
Tim's Cost for the peanuts: $5 for one box
Kevin's Cost for the candy is: $8 for one box
Kevin's Cost for the peanuts are: $5 for one box
Step-by-step explanation:
Tim:
7x16=112
5x4=20
112+20=132
Kevin:
20x8= 160
5x 6=30
160+30 =190
is irrigation the artificial of application of water to the land or soil
I believe both is the answer to your question. In the definition of this word both land and soil are correct.
The definition of irrigation is:
"Irrigation is the artificial process of applying controlled amounts of water to land to assist in production of crops. Irrigation helps to grow agricultural crops, maintain landscapes, and revegetate disturbed soils in dry areas and during periods of less than average rainfall. "
Pls help semester ends to day pls help with both 16 and 17
Answer:
Step-by-step explanation:
16. -73.5 ft / 3 min = -24.5 ft/min
17. ($50.25 - $22.50 + $50.25 - $22.50 - $22.50) / 5 = $33 / 5 = $6.60
Answer:
16.-73.5÷3=-24.5 feet per minute
17.(50.25-22.5+50.25-22.5-22.5)÷5=6.6
which expression is equivalent to 3 x 3 x 3 x 3
Answer:
I can’t c anything where are the answers we’re choosing ?
Step-by-step explanation:
Answer:
raise 3^4 and ans is 81 or u can simply multiply.