Please help. I don't understand this.​

Answer:

The answer is below

Step-by-step explanation:

A parabola is the locus of a point such that its distance from a given line (directrix) and a fixed point (focus) is always the same.

The equation of a parabola with a horizontal line as directrix is given by:

(x - h)² = 4p(y - k)

where y = k - p is the directrix and the focus = (h, k + p)

Given that parabola has a directrix at y = 2 and a focus at (5, 0)

Therefore:

y = k - p

k - p = 2          (1)

focus = (h, k + p) = (5, 0)

h = 5, k + p = 0

k + p = 0         (2)

Solve equation 1 and 2 simultaneously by adding both equations together:

2k = 2

k = 1

Substitute k = 1 in k + p = 0 to find p:

1 + p = 0

p = -1

Therefore h = 5, p = -1 and k = 1

Substitute the values of h, k and p into the equation of a parabola:

(x - h)² = 4p(y - k)

(x - 5)² = 4(-1)(y - 1)

(x - 5)² = -4(y - 1)

x² - 10x + 25 = -4y + 4

-4y = x² - 10x + 21

4y = 10x - x² - 21

Answer:

(7 x 100) + (4 x 100 ) + (8 x 1,000)

=700+400+8000

=1100+8000

Answer:

30

Step-by-step explanation:

That means that there are 6 pie pieces in each pie so just multiply by 5

another thing we can do is get rid of 1/6 by multiplying by 6 which means we also have to multiply 5 by 6

Answer:

$17.54

Step-by-step explanation:

15% percent of $15.25 is $2.29 so, add them together

$17.54 is the answer I think

Answer:

390 miles

Step-by-step explanation:

(45 x 4) + (35 x 6) = 390 miles

Answer: p(t) = (-16 ft/s^2)*t^2 + (57.4 ft/s)*t

Step-by-step explanation:

We can suppose that the only force acting on the object is the gravitational force, then the acceleration of the object will be equal to the gravitational acceleration.

Then we can write:

a(t) = -32 ft/s^2

Where the negative sign is because this acceleration is downwards.

Now, to get the vertical velocity of the object, we need to integrate over time to get:

v(t) = (-32 ft/s^2)*t + v0

where t represents time in seconds and v0 is the constant of integration, and in this case, is the initial vertical velocity.

In this case, the initial velocity is 57.4 ft/s upwards, then the velocity equation is:

v(t) = (-32 ft/s^2)*t + 57.4 ft/s

To get the position equation we need to integrate over time again, to get:

p(t) = (1/2)*(-32 ft/s^2)*t^2 + (57.4 ft/s)*t + p0

Where p0 is the initial height of the object, as it was launched from the ground, then the initial position is p0 = 0ft.

then the position equation (that is the function that represents the height of the object as a function over time) is:

p(t) = (1/2)*(-32 ft/s^2)*t^2 + (57.4 ft/s)*t

p(t) = (-16 ft/s^2)*t^2 + (57.4 ft/s)*t

Answer:

5 hours 8 mins?

Step-by-step explanation:

Answer:

b=35

Step-by-step explanation:

Diagonals of a parallelogram always bisect each other, splitting it into two equal sections.

This means, b-8 is equal to 2b-43

b-8 = 2b-43

b+35=2b

b=35

Let me know if this helps!

Answer:

Step-by-step explanation:

we will add like terms

-2x-2<8

we will add 2 on both sides

-2x<10

divide by 2

-x<5

multiply by -1

x>-5

Answer:

150°

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° ( n - 2) ← n is the number of sides

Here n = 12, then

sum = 180° × 10 = 1800°

Since there are 12 interior angles, then

size of each interior angle = 1800° ÷ 12 = 150°

Answer:

10

Step-by-step explanation:

2pi(5) is 31.42.

31.42/pi gets you exactly 10pi meters.

Answer:

I am not very sure, but I think the answer is

D.

Answer:

answer is d becuase i took the test and got it right

Step-by-step explanation:

the link is visable tho

Answer:

the answer is c

Step-by-step explanation:

Answer:

a)  f g(x) =  x³ - 5 x² + x -5

b) g(f(x) =  x³ - 5 x² + x -5

Step-by-step explanation:

Step(i):-

Given that f(x) = x² + 1 and g(x) = x-5

a)

      f(g(x)) = f(x-5) = (x-5)²+1 = x² - 10x +25 +1 = x² - 10 x +26

Step(ii):-

a) f g(x)  = f(x) g(x) = (x² + 1 )(x-5) = x³ - 5 x² + x -5

b)   g(f(x)  = g(x) f(x) = (x-5) (x²+1) =  x³ - 5 x² + x -5

Answer:

-55

Step-by-step explanation:

7x-6y=2

-2x-y=3

by substitution method

y=3+2x

7x-6(3+2x)=2

7x-18-12x=2

-5x=20

x=-4

-2(-4)-y=3

8-y=3

-y=3-8

y=5

therefore the value of x=4 and that of y=5

5x-7y=5(-4)-7(5)

=-20-35

=-55

Answer:

-4 is the slope

Step-by-step explanation:

Because the line is going downwards that makes it a negative and if you count the boxes rise over run. You look for the point where the line meets a box perfectly and then you count the boxes down which is 4 and across which is one which makes it -4/1. So the slope is -4.

Answer:

10

Step-by-step explanation:

When u cross multiply

[tex]5 \div x = 3 \div6[/tex]

= 3x=30(5*6)

= x=30/3

=x=10

Answer:

None of them. The proper expression(s) to split the debt are:

5400 / 8

or

8x=5400

Answer: Part A.  B origin    Part B. C(0,0)

Step-by-step explanation:

In a coordinate plane, there are two axes

1) x-axis which is the horizontal axis.

2) y-axis which is the vertical axis.

The intersection of both the axes is known as the origin whose coordiantes are (0,0), i.e. at this point value of x =0 and value of y =0.

Part A: The ordered pair that represents the intersection of the x-axis and y-axis is called the origin.

Part B: The coordinate. Part B the coordinates of the origin are (0,0).

Answer:

A 1,1

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

2

(a )square root of 2 (c)

Answer:

Step-by-step explanation:

Given:

Increase 386.3 by  4%.

To find:

The value for given statement.

Solution:

We have,

Initial value = 386.3

Increasing rate = 4%

The increased value is

[tex]\text{New value}=\text{Initial value + Increasing rate }\times \text{Initial value}[/tex]

[tex]\text{New value}=386.3+\dfrac{4}{100}\times 386.3[/tex]

[tex]\text{New value}=386.3+15.452 [/tex]

[tex]\text{New value}=401.752[/tex]

Therefore, the required value is 401.752.

Answer:

m = -1

Step-by-step explanation:

The slope of a line is calculated as ;

Given : (-2,3) and (2,-1)

m = Δy/Δx

m= -1-3 /2--2

m = -4 /4 = -1

The slope is -1

Answer:

Their race was 1/4 the length of Alex's 20km = 20 x 1/4 = 5 km

Alex than Deja and Jamie walked together : 20 - 5 = 15 km = 15000 m

Step-by-step explanation: