Write the equation in standard form for the parabola with vertex (0,0) and directrix y=-6

Answers

Answer 1

Final answer:

To find the equation of a parabola with a vertex at (0,0) and a directrix of y=-6, we determine the focus is at (0,6), leading to the standard form equation of the parabola as y = 1/4x^2.

Explanation:

The question asks for the equation of a parabola in standard form given its vertex at (0,0) and directrix as y=-6. In parabolic equations, the standard form is usually y = ax^2 + bx + c for horizontal parabolas, or x = ay^2 + by + c for vertical parabolas. Given the vertex is at the origin (0,0) and the directrix is y = -6, this means the focus is at (0,6) because the distance from the vertex to the focus is equal to the distance from the vertex to the directrix but in the opposite direction.

For a parabola that opens upwards or downwards, the standard form is y = ax^2 (since the vertex is at the origin, b and c are 0). Given that the distance from the vertex to the focus (which is also the distance from the vertex to the directrix) is 6, the parabola opens upwards, and its focal distance (p) is 6. Hence, the value of 4p = 24, which leads us to conclude that a = 1/4. Therefore, the equation of the parabola is y = 1/4x^2.

Related Questions

Given: AC is the hypotenuse and BD is the altitude of △ABC. AD=27, CD=40, AB=e, BD=j, and BC=h
Find the value of e
How the literal devil am i supposed to do this, legit i've tried for hours first answer gets Brainliest

Answers

check the picture.

In triangle ABC:

m(B)=90°, let m(A)=α, and let m(C)=β

so m(B)+m(A)+m(C)=180°, so α+β=90°

In triangle ABD, m(A)=α, m(ADB)=90° so m(ABD) must be β, so that the sum completes to 180.

By the same logic, m(DBC)=α

so we have the following similarities of triangles: (let's go by the order α-β-90°):

ACB ≡ ABD ≡ BCD,

consider ABD ≡ BCD:

[tex] \frac{AB}{BC} = \frac{BD}{CD} = \frac{AD}{BD} [/tex]

substitute with the givens:

[tex] \frac{e}{h} = \frac{j}{40} = \frac{27}{j} [/tex]

from

[tex]\frac{j}{40} = \frac{27}{j}[/tex]

we have

[tex] j^{2}=40*27 =1080[/tex]

In triangle ABD, from the pythagorean theorem:

[tex] e^{2} = j^{2}+27^{2}=1080+729=1089[/tex]

so [tex]e= \sqrt{1089}= 42.53 (units)[/tex]

Remark: a direct solution can be given by Euclid's theorem, AB^2=AD*AC

[tex]AB^2=AD*AC[/tex] so

[tex] e^{2}=27*47[/tex], then take square root of e

Answer: 42.53 units

(4.4*10^6)*(3.9*10^4)
Scientific notation please help and explain

Answers

(4.4*10^6) = 4400000
and
(3.9*10^4) = 39000

The exponents on top of the 10 tells you how many decimals you're supposed to move it to. If it's a negative number, you'll need to move the same amount of decimals, but to the left side instead.
for example: 4.3*10^-3 =0.0043

in this case, however, you should refer to the Laws of Exponents.
(4.4*10^6)*(3.9*10^4)
= 4.4 * 3.9 * 10^6 * 10^4
= 17.16 * 10^(6+4) <-- Law of Exponents say that when you multiply exponents with the same base, you add the exponents together.
= 17.16 * 10^10

A 12 foot rope is cut into two pieces so that one piece is 3 feet less than twice the length of the other piece. how long is each piece?

Answers

12 feet long

1st piece = x

2nd piece = 2x-3

3x-3 =12

3x=15

x = 5

1st piece = 5 feet

2nd piece = 2*5=10-3=7 feet

Using technology, we found that Juan’s investment account can be modeled by the function, c(x)=3x2-2x+10, in thousands of dollars. What was Juan’s initial investment?

A)$5
B)$10
C)$5,000
D)$10,000

Answers

The function is [tex]c(x)=3 x^{2} -2x+10[/tex]

Initial investment is given when [tex]x=0[/tex], so substituting this into [tex]c(x)[/tex] we have

[tex]c(0)=3 (0)^{2}-2(0)+10 [/tex]
[tex]c(0)=10[/tex]

Hence, correct answer is B $10

Answer:

D) $10,000.

Step-by-step explanation:

We have been given a function [tex]c(x)=3x^2-2x+10[/tex], which represents Juan’s investment account in thousands of dollars. We are asked to find Juan's initial investment.

To find Juan's initial investment, we will substitute [tex]x=0[/tex] in our given function.

[tex]c(0)=3(0)^2-2(0)+10[/tex]

[tex]c(0)=3*0-0+10[/tex]

[tex]c(0)=10[/tex]

Since the function gives Juan's investment in thousands of dollars, so Juan's initial investment would be [tex]10\times \$1,000=\$10,000[/tex], therefore, option D is the correct choice.

Identify the domain of the exponential function shown in the following graph: y=10x

Answers

Answer: All real numbers (choice A)

We can replace x with any real number we want without worrying about restrictions. There won't be any issues such as dividing by zero or applying the square root to a negative number.

Find the range of the data. Scores: 81, 79, 80, 88, 72, 96, 86, 73, 79, 88 A) 22
B)24
C)28
D)23

Answers

Order: 96,88,88,86,81,80,79,79,73,72
96-72= 24
B.)24

Answer:

Option B - 24

Step-by-step explanation:

Given : Scores: 81, 79, 80, 88, 72, 96, 86, 73, 79, 88

To find : The range of the data?

Solution :

Range is defined as the difference between the smallest and the largest element of the data.

First we arrange the data into ascending order:

72,73,79,79,80,81,86,88,88,96

The smallest number is 72

The largest number is 96

The range of the data = largest number - smallest number

The range of the data = 96 - 72

The range of the data = 24

Therefore, Option B is correct.

Which number produces a rational number when added to 0.42?

Answers

Any whole or rational number. For example 1 if you want to keep it simple.

Is -1/2 rational or irrational

Answers

-1/2 is rational, have a good day

-1/2 is rational because it can be expressed as a ratio of 2 integers.

-1 and 2 are both integers because they are either whole numbers or of the opposite value (negative).

Help plz.. Evaluate this expression: -(-(-(-1)))?
Thanks.

Answers

negative times negative=positive
every pair of negative cancel out
-(-a)=a
so we can just keep flipping the signs
go inside to out

-(-(-(-1)))=
-(-(1))=
-(-1)=
1

The adams family is remodeling their family room. the room measures 14 feet by 20 feet, and the contractor wants $35 per square foot to remodel it. how much will it cost to remodel?

Answers

14 * 20 = 280 sq ft
$35 * 280 sq ft = $ 9,800

Answer:

It would cost $9800 to remodel the room.

Step-by-step explanation:

The Adams family is remodeling their family room.

Length of the room = 20 feet

Width of the room = 14 feet

To get area of the room we use the formula

Area = Length × Width

A = 20 × 14 = 280 feet²

The contractor wants $35 per square foot to remodel it.

So it would cost = 280 × 35 = $9800

It would cost $9800 to remodel the room.

What rank of the marine corps do you get the stripe on your pants?

Answers

A blood stripe is a scarlet stripe worn down the outside leg seams of trousers on the dress uniform of the United States Marine Corps.

This red stripe is :

2 inches (5.1 cm) for general officers,

1.5 inches (3.8 cm) for other officers, and

1.12 inches (2.8 cm) for enlisted Staff Noncommissioned Officers and Noncommissioned Officers.

Answer:

cpl and above. E-4 and above.

Step-by-step explanation:

Consider the function given by the graph. What are these values?
f(–2 ) =
f(0) =
f(4) =

Answers

Final answer:

The values of the function f(x) for the given graph are approximately -7, -18, and -29.

Explanation:

The values of the function f(x) for the given graph can be found by looking at the corresponding points on the graph.

For f(-2), we look at the point on the graph where x = -2. From the graph, we can see that f(-2) is approximately -7.

Similarly, for f(0), we look at the point on the graph where x = 0. From the graph, we can see that f(0) is approximately -18.

For f(4), we look at the point on the graph where x = 4. From the graph, we can see that f(4) is approximately -29.

f(-2) = -1
- f(0) = 3
- f(4) = 0

The values of the function at different points on the graph can be found by looking at the corresponding coordinates on the graph.

To find f(-2), we look for the point on the graph where x = -2. From the graph, it appears that the y-coordinate of this point is -1. Therefore, f(-2) = -1.

To find f(0), we look for the point on the graph where x = 0. From the graph, it appears that the y-coordinate of this point is 3. Therefore, f(0) = 3.

To find f(4), we look for the point on the graph where x = 4. From the graph, it appears that the y-coordinate of this point is 0. Therefore, f(4) = 0.

It is important to note that the given information about the arrows and points (0,3) to (-6,0) and (0,1) to (6,-2) is unrelated to finding the values of the function at the given points. These arrows and points might represent something else in the context of the graph, but they do not affect the calculations of f(-2), f(0), and f(4).

Find the least common multiple of 8c4 and 6c2 .

Answers

The least common multiple is the smallest term that can be divided to both terms without any remainder. For the two terms 8c^4 and 6c^2, you can determine it into two part. First, you find the LCM for 8 and 6. You find the prime number that is common between the two. That would be 2. For the variables c^4 and c^2, the 'prime variable' is c. Therefore, the least common multiple for 8c^4 and 6c^2 is 2c.

How much money will be in a bank account after 9 years if $7 is deposited at an interest rate of 5% compounded annually?

Answers

The formula is
A=p (1+r)^t
A future value?
P present value 7
R interest rate 0.05
T time 9 years
A=7×(1+0.05)^(9)
A=10.86

There exists a similarity transformation that maps ΔABC to ΔA′B′C′. The measure of angle A is 68°, and the measure of angle B is 46°. What is the measure of angle C in degrees?

Answers

There exists a similarity transformation that maps ΔABC to ΔA′B′C′. The measure of angle A is 68°, and the measure of angle B is 46°. What is the measure of angle C in degrees?

The answer is 66.

The measure of angle C in triangle ABC is 66 degrees, calculated by subtracting the sum of angles A and B from 180 degrees.

The measure of angle C can be determined by using the fact that the sum of angles in any triangle is always 180 degrees. Given that the measure of angle A is 68° and the measure of angle B is 46°, we can calculate the measure of angle C as follows:

C = 180° - A - B

C = 180° - 68° - 46°

C = 180° - 114°

C = 66°

Thus, the measure of angle C in ΔABC is 66 degrees.

which of the following represents the zeros of the function f(x) = 4x3 -13x2 -37x +10

Answers

(5,0) (1/4,0) (-2,0)

The depth of the water at the end of a pier changes periodically along with the movement of tides. On a particular day, low tides occur at 12:00 am and 12:30 pm, with a depth of 2.5 m, while high tides occur at 6:15 am and 6:45 pm, with a depth of 5.5 m. Let t = 0 be 12:00 am. Write a cosine model, d = acos(bt) + k, for the depth as a function of time. This amplitude is meters. a =

Answers

Answers:

1.5, -1.5, 12.5, 4pi/25, 4, D

Step-by-step explanation:

Answer:

1.5 meters

a = -1.5

12.5 hours

b = 4 pi/25

k = 4 meters

last option is D

Step-by-step explanation:

edg 23'

May I pretty please have some math help?

Answers

Answer: A.
The point on the graph of f⁻¹ (x) is (-5,4)

Explanation
Let f(x) = -(5/4)x.
This function passes through (4, -5) as specified, because
f(4) = -(4/5)*(4) = -5

Construct f⁻¹ (x) as follows:
Set y = f(x).
y = -(4/5)x
Switch x and y.
x = -(4/5)y
Solve for y
y = -(5/4)x
Set f⁻¹ (x) to y.
f⁻¹ (x) = - (4/5)x.

Test x=-5 to see if y=4.
f⁻¹ (-5) = -(4/5)*(-5) = 4 Correct!

Find the difference.

Correct and best explained answer gets brainliest.

Answers

9-5 =4

-4 +7=3

-1-6 =-7

so 4x^3+3x^2-7

A is the correct answer

What is the area of the trapezoid?

Answers

B because the triangle is 7 plus another 7 for the other triangle. The rectangle is 7 by 6 so that is 42. 42+7+7=56!

Solve the following system of equations algebraically. 2x = 5y + 8. 3x + 2y = 31

Answers

x=−12.301587 and y= 31/ 2

2x = 5y + 8. (1st)
3x + 2y = 31 so 3x = -2y + 31 (2nd)

multiply (1st equation) by 3 and (2nd equation) by 2

6x = 15y + 24
6x = -4y + 62
-----------------------subtract
0 = 19y - 38
19y = 38
y = 2

2x = 5y + 8
2x = 5(2) + 8
2x = 18
x = 9

answer
solution (9, 2)

Amy purchased 17 pencils and 18 pens for a fund-raiser at school and spent $61.50. Jocelyn purchased 10 pencils and 21 pens and spent $57. How much does each pencil cost?

Answers

x = pencils, y = pens

17x + 18y = 61.50....multiply by 21
10x + 21y = 57 ....multiply by -18
------------------------
357x + 378y = 1291.5 (result of multiplying by 21)
-180x - 378y = - 1026 (result of multiplying by -18)
-----------------------add
177x = 265.5
x = 265.5 / 177
x = 1.50 <== cost for a pencil
pens(y) cost 2.00

Using a calculator and the formula above, calculate the APR. Choose the correct answer.

Betty Buyer has a short term note at 16% interest per year.

To the nearest tenth, APR =
15.9
17.2
16.6

%.

Answers

APR=(1+r/12)^(12)-1
APR=(1+0.16÷12)^(12)−1
APR=0.172×100
APR=17.2%

A cricket ball is dropped into a cylindrical tank of water.
The ball sinks to the bottom of the tank.
The diameter of the cricket ball is 7.2 cm
The diameter of the cylindrical tank is 15 cm
Calculate the increase in height of the water in the tank.

Answers

* (in this question they didn't give me the volume of the cylinder or the height of the cylinder) -- the volume and height are NOT relevant.

the ball is 7.2 cm in diameter. Hence its volume is 4*(3.6)^3 * π/3
So, the volume the water occupies increases by this amount.
because the tank is cylindrical, this increase must also be cylindrical.
and the volume of the ïncreased cylinder is π*15^2 * h, where h is the increase in height of the water.
so h = (4*(3.6)^3 * π/3)/(π*15^2) = 4*(3.6)^3/(3*15^2)

* (in this question they didn't give me the volume of the cylinder or the height of the cylinder) -- the volume and height is NOT relevant.

the ball is 7.2 cm in diameter. Hence its volume is 4*(3.6)^3 * π/3
So, the volume the water occupies increases by this amount.
because the tank is cylindrical, this increase must also be cylindrical.
and the volume of the ïncreased cylinder is π*15^2 * h, where h is the increase in height of the water.
so h = (4*(3.6)^3 * π/3)/(π*15^2) = 4*(3.6)^3/(3*15^2)

Complete the statements about the key features of the graph of f(x) = x5 – 9x3. As x goes to negative infinity, f(x) goes to negative infinity, and as x goes to positive infinity, f(x) goes to positive infinity.
Choose all of the zeroes of f(x).
–3 with multiplicity 1
3 with multiplicity 1
0 with multiplicity 1
0 with multiplicity 3
3 with multiplicity 0

Answers

The function is [tex]f(x)= x^{5} -9x ^{3} [/tex]

1. let's factorize the expression [tex]x^{5} -9x ^{3} [/tex]:

[tex]f(x)= x^{5} -9x ^{3}= x^{3} ( x^{2} -9)=x^{3}(x-3)(x+3)[/tex]

the zeros of f(x) are the values of x which make f(x) = 0.

from the factorized form of the function, we see that the roots are:

-3, multiplicity 1
3, multiplicity 1
0, multiplicity 3

(the multiplicity of the roots is the power of each factor of f(x) )

2.
The end behavior of f(x), whose term of largest degree is [tex] x^{5} [/tex], is the same as the end behavior of [tex] x^{3} [/tex], which has a well known graph. Check the picture attached.

(similarly the end behavior of an even degree polynomial, could be compared to the end behavior of [tex] x^{2} [/tex])

so, like the graph of [tex] x^{3} [/tex], the graph of [tex]f(x)= x^{5} -9x ^{3} [/tex] :

"As x goes to negative infinity, f(x) goes to negative infinity, and as x goes to positive infinity, f(x) goes to positive infinity. "

The end behavior of f(x) has the same end behavior of [tex]x^3[/tex] and all the zeroes of f(x) wiil be: -3 with multiplicity 1, 3 with multiplicity 1, 0 with multiplicity 3.

Given :

[tex]f(x) = x^5-9x^3[/tex] --- (1)

The value of x at which f(x) becomes zero can be determine by eqaution the equation (1) to zero.

[tex]x^5-9x^3=0[/tex]

[tex]x^3(x^2-9)=0[/tex]

[tex]x^3(x-3)(x+3)=0[/tex]

Therefore, all the zeroes of f(x) will be:

-3 with multiplicity 1,

3 with multiplicity 1,

0 with multiplicity 3.

The end behavior of f(x) has the same end behavior of [tex]x^3[/tex]. As x goes to negative infinity, f(x) goes to negative infinity, and as x goes to positive infinity, f(x) goes to positive infinity.The graph of f(x) is attached below.

For more information, refer the link given below:

https://brainly.com/question/24153248

Which set of numbers can represent the side lengths, in centimeters, of a right triangle?

Answers

It might be (3,4,5) , (5,12,13) ....
The sides should satisfy the equation (a^2)+(b^2)=(c^2).
Hope it helps

Answer:

Any set of numbers that fit in Pythagoras theorem will represent that set.

Step-by-step explanation:

Though options are not given, but there is a standard way to get such combinations of number.

As it is a right triangle, we have to work on Pythagoras theorem.

The sum of squares of two other sides is equal to square of the hypotenuse.

Like : [tex]3^{2} +4^{2} =5^{2}[/tex]

Find the measure of each interior angle
Decagon in which the measures of each interior angles are x + 5, x + 10, x + 20, x + 30, x + 35, x + 40, x + 60, x + 70, x + 80, and x + 90

Answers

To find each interior angle of a decagon given as expressions with x, we sum the expressions and set equal to 1440 degrees, the total sum of interior angles. Solving for x, we find x=100 and then substitute to find each angle.

To find the measure of each interior angle of a decagon where the angles are given as expressions involving x, we must use the fact that the sum of interior angles in a polygon is (n-2)180 degrees, where n is the number of sides in the polygon. For a decagon, which has 10 sides, the sum would be (10-2)180 = 1440 degrees.

x + 5 + x + 10 + x + 20 + x + 30 + x + 35 + x + 40 + x + 60 + x + 70 + x + 80 + x + 90 = 1440

Combining like terms, we find that:

10x + 5 + 10 + 20 + 30 + 35 + 40 + 60 + 70 + 80 + 90 = 1440

10x + 440 = 1440

10x = 1440 - 440

10x = 1000

x = 100

Once x is found, we substitute back into each angle expression to find the measure of each interior angle:

x + 5 = 105 degrees

x + 10 = 110 degrees

x + 20 = 120 degrees

x + 30 = 130 degrees

x + 35 = 135 degrees

x + 40 = 140 degrees

x + 60 = 160 degrees

x + 70 = 170 degrees

x + 80 = 180 degrees

x + 90 = 190 degrees

The table shows the outputs, y, for different inputs, x: Input (x) 2 5 9 12 Output (y) 20 15 12 8 Part A: Do the data in this table represent a function? Justify your answer. (3 points) Part B: Compare the data in the table with the relation f(x) = 5x + 14. Which relation has a greater value when x = 9? (2 points) Part C: Using the relation in Part B, what is the value of x if f(x) = 64? (5 points)

Answers

yes, this data represents a function. A function will not have any repeating x values. It can have repeating y values, just not the x ones.
=====================
data in the table : when x = 9....this is already a point on the table (9,12)...so the value on the table, when x = 9, is 12

f(x) = 5x + 14....when x = 9
f(9) = 5(9) + 14
f(9) = 45 + 14
f(9) = 59

the relation with the greater value would be : f(x) = 5x + 14
=====================
f(x) = 5x + 14....when f(x) = 64
64 = 5x + 14
64 - 14 = 5x
50 = 5x
50/5 = x
10 = x <==

Answer:

D 17 2/9

Step-by-step explanation:

In the above figure, find the measure of angle AEB + the measure of angle CED.

A. 75
B. 93
C. 112
D. 140

Answers

Well, AEB is 28, and CED is 65,and you want to add them, so that would be 65+28, which equals 80+13=93, so the answer is b.

What is the area of a regular pentagon with an apothem of 14 inches long and a side 20 inches long?

Answers

Answer:

[tex]\text{Area of regular pentagon is }700 inches^2[/tex]

Step-by-step explanation:

Given that a regular pentagon with an apothem of 14 inches and a side of 20 inches.

we have to find the area of pentagon.

Apothem=a=14 inches

Side of pentagon= 20 inches

[tex]Perimeter=s=20\times 5=100 inches[/tex]

[tex]\text{Area of regular pentagon=}\frac{1}[2}\times perimeter \times apothem[/tex]

[tex]=\frac{1}{2}\times 100\times 14=700inches^2[/tex]

[tex]\text{Area of regular pentagon is }700 inches^2[/tex]

Answer:700in

Step-by-step explanation:

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