Find the equation for the line that passes through the points and . State your
equation with whole numbers and/or fractions, not decimals.

Answer:

The parabola x²=8y has,

vertex: (0,0)

focus: (0,2)

directrix: y=-2

so that option is the answer,

btw, the parabola opens up to the top and axis of symmetry is x=0

Answer:

It's A!

Step-by-step explanation:

Got it correct on my test! :)

Answer:

ΔT = -75°F

Step-by-step explanation:

ΔT = T₁ - T₀ = 350 - 425 = -75°F

Answer:

y = 3(x-1)^2 -3

Step-by-step explanation:

y = 3(x+5)^2 - 2

vertex: (-5, -2)

1 unit down :

-2 - 1 = -3

6 units to the right:

3(x+5-6)^2 -2

3(x-1)^2 - 2

make what's in the parenthesis equal to 0:

(x-1)^2 = 0

x = 1

or

-5 + 6 = 1

new vertex : (1, -3)

equation : y = 3(x-1)^2 -3

Translation involves shifting of points from one position to another. The equation of the new parabola is: [tex]y = 3(x - 1)^2 - 3[/tex]

Given that:

[tex]y = 3(x + 5)^2 - 2[/tex]

[tex](h,k) = (-5,-2)[/tex] --- vertex

The general equation of a parabola is:

[tex]y = a(x - h)^2 + k[/tex]

By comparison:

[tex]a = 3\\ h = -5 \\ k= -2[/tex]

When the vertex is shifted 1 unit down, the rule is:

[tex](x,y) \to (x,y-1)[/tex]

So, we have:

[tex](x,y) \to (-5,-2-1)[/tex]

[tex](x,y) \to (-5,-3)[/tex]

When the vertex is shifted 6 unit right, the rule is:

[tex](x,y) \to (x + 6,y)[/tex]

So, we have:

[tex](h,k) \to (-5 + 6,-3)[/tex]

[tex](h,k) \to (1,-3)[/tex]

This means that:

[tex]h = 1\\ k =-3[/tex]

Recall that:

[tex]a =3[/tex]

Substitute these values in:

[tex]y = a(x - h)^2 + k[/tex]

[tex]y = 3(x - 1)^2 - 3[/tex]

Hence, the equation of the new parabola is: [tex]y = 3(x - 1)^2 - 3[/tex]

Read more about translations at:

https://brainly.com/question/12463306

Answer:

the slope -3, slope meaning rate of change and y intercept is 1.

hope that answers your question

(used desmos to graph, good stuff!!!)

Answer:

y = 6

I hope this helps you out!

Answer:

h.

[tex] \frac{9 {x}^{10}(y. {x}^{3}) {}^{2} }{y.x(3 {x}^{3}) {}^{3} } \\ \\ = \frac{9 {x}^{10}(y {}^{2} )( {x}^{6} ) }{3y. {x}^{10} } \\ \\ = \frac{ {3}^{2} {x}^{16} {y}^{2} }{3y {x}^{10} } \\ \\ = 3y {x}^{6} [/tex]

j.

[tex] \frac{(3x. {y}^{7} ) {}^{2}. {x}^{5} }{3 {x}^{7} {y}^{4} } \\ \\ = \frac{3 {x}^{2} . {y}^{14} . {x}^{5} }{3 {x}^{7} {y}^{4} } \\ \\ = \frac{ {3x}^{7} {y}^{14} }{3 {x}^{7} {y}^{4} } \\ \\ = {y}^{10} [/tex]

Answer:

(x,y) -> (-y,x), second option.

Step-by-step explanation:

Rotation of 90 degrees about the origin:

The rule for a rotation of a point (x,y) 90 degrees about the origin is given by:

(x,y) -> (-y,x)

This is that the question asks, and so, this is the answer, which is the second option.

Answer:

150

Step-by-step explanation:

Increase = New Number - Original Number.

divide the increase by the original number and multiply the answer by 100.

Answer:

✔ positive

✔ 1

✔ closely

✔ increases

ED2021

Answer:

f(3) = 6

Step-by-step explanation:

If f(1)=10, then f(1+1)=f(1)-2

f (2) = 10 - 2 = 8

Therefore f(3) = f(2) - 2 = 8 - 2 = 6

Answer:

21

Step-by-step explanation:

you divide 10.50 by 50

Answer:

Slope: 1

Y-intercept: (0,3)

Step-by-step explanation:

The y intercept is when the slope reaches the y-axis line. In this case, it is given to us. Anything that is formed like this: (0, y) is the y-intercept.

Y intercept: (0, 3)

For slope, you can use the formula rise over run. [tex]\frac{Rise}{Run}[/tex]

From the picture, I have drawn the rise over run, which is [tex]\frac{3}{3}[/tex], which is also 1.

Slope: 1

Hope this helped.

Answer: 1

Step-by-step explanation: got it right on edge

Answer:

N(t) = 0.188t + 22.76

Step-by-step explanation:

Number of licensed drivers in 2004 = 22.76 million

Number of licensed drivers in 2009 = 23.7 million

Number of licensed drivers, N as a function of t since year 2004 ;

General form of a linear function :

y = mx + c

c = intercept ; m = slope

Intercept c = value of y ; when x = 0

Here, population after uerssmmx,

Hence,

In 2004 ;

22.76 = mx + c

x = 0

22.76 = c

Number in 2009

x = number of yesrs after 2004 ; x = 2000 - 2004 = 5years

We can find the slope :

y = m*5 + 22.76

y = 23.7 in 2009

23.7 = 5m + 22.76

23.7 - 22.76 = 5m

m = 0.94 / 5

m = 0.188

Hence, the linear function can be written as :

N(t) = 0.188t + 22.76

Answer:

0.0005m^3

Step-by-step explanation:

V=1/3hπr²

h=6m

d=12m

r=12÷2=6m

V=1/3×6×(3.14)×36

V=1/2034.72

V=0.0005m^3

Answer:

(2,-1)

Step-by-step explanation:

Solved using math.

Answer:

The solution is (2, -1) to show this by graphing do y = -1 by making a straight horizontal line at (0,-1) . And then for the other equation make a line where it starts at (0,4) and passes point (2,-1). Just plot those two points and connect them and you'll have made the line.

Step-by-step explanation:

Answer:

y-3 = -4(x+2)

Step-by-step explanation:

Point slope form is

y-y1 = m(x-x1)  where m is the slope and (x1,y1) is a point on the line

y-3 = -4(x --2)

y-3 = -4(x+2)

Answer:

4

Step-by-step explanation:

twice her age:

10*2 = 20

24-20 = 4

Answer:

4 i believe that's the answer

Answer:

Hello,

This sequence is geometric with a ratio of -3

the first term is 6

Step-by-step explanation:

[tex]u_1=6\\u_2=-18=6*(-3)=u_1*(-3)\\u_3=54=-18*(-3)=u_2*(-3)=u_1*(-3)^2\\u_4=-162=u_3*(-3)=u_1*(-3)^3\\\\...\\u_{n+1}=u_1*(-3)^n\\\\\displaystyle \sum\limits^\infty _{i=1}u_i = \lim_{n \to \infty} \sum\limits^n _{i=1}u_1*(-3)^{i-1}\\=6*\lim_{n \to \infty} \sum\limits^\infty _{i=1}(-3)^{i-1}\\=6*\frac{1-(-3)^n}{1-(-3)} \\=\dfrac{3}{2} *({1-(-3)^n)\\[/tex]

serie does not converge.

Answer:

loses  14 cents

- $0.14

Step-by-step explanation:

90%  $0.30   $(0.30)  $(0.27)

9%  $1.00   $0.40   $0.04  

1%  $10.00   $9.40   $0.09  

   $(0.14)

The exponential function that models the number of trees after t years is given by:

[tex]A(t) = 800\left(\frac{3}{4}\right)^t[/tex]

Hence, after 2 years, 450 trees will be remaining, as the graph at the end of this answer shows.

A decaying exponential function is modeled by:

[tex]A(t) = A(0)(1 - r)^t[/tex]

In which:

In this problem:

Then, the equation is:

[tex]A(t) = A(0)(1 - r)^t[/tex]

[tex]A(t) = 800(1 - \frac{1}{4})^t[/tex]

[tex]A(t) = 800\left(\frac{3}{4}\right)^t[/tex]

After 2 years:

[tex]A(2) = 800\left(\frac{3}{4}\right)^2 = 450[/tex]

450 trees will be remaining.

You can learn more about exponential functions at https://brainly.com/question/25537936

Answer:

y-3 = 2(x-1)

Step-by-step explanation:

Point slope form is

y-y1 = m(x-x1)

where m is the slope and (x1,y1) is a point on the line

y-3 = 2(x-1)

Answer:

3=2x+1

Step-by-step explanation:

Use the equation y=mx+b

where y is the y component, x is the variable and b is the x intercept

please mark this answer as brainlist

Answer:

Is answer 22 units sqaure ?

The equation of the circle is  [tex](x - 2)^2 + (y - 3)^2 = 16[/tex] . The option C is the correct option.

Given that the centre of the circle is (2,3) and circle has radius 4.

To find the equation of the circle, use the general equation of the circle as:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Where (h, k) is the centre of the circle and r is the radius of the circle.

Since, h = 2, k = 3 and radius r = 4.

Therefore, the equation of the circle:

[tex](x-h)^2+(y-k)^2=r^2\\(x-2)^2+(y-3)^2=4^2\\(x-2)^2+(y-3)^2=16[/tex]

The equation of the circle cantered at (2,3) and has a radius of 4 is  [tex](x - 2)^2 + (y - 3)^2 = 16[/tex] .

Therefore, The equation of the circle cantered at (2,3) and has a radius of 4 is  [tex](x - 2)^2 + (y - 3)^2 = 16[/tex] .

Learn more about Diameter here:

https://brainly.com/question/32968193

#SPJ2

Answer:

D.

Step-by-step explanation:

D. This contains an x^2 and is called a parabola ( curved line like a U).

Answer:D

Step-by-step explanation: d is the correct answer

Answer:

Devaughn = 31, Sydney = 25

Step-by-step explanation:

(56-6)÷2= 25

So they would both be 25 if they were the same age but Devaughn is 6 years older so 25+6=31

ATQ

[tex]\\ \sf\longmapsto x+x+6=56[/tex]

[tex]\\ \sf\longmapsto 2x+6=56[/tex]

[tex]\\ \sf\longmapsto 2x=56-6[/tex]

[tex]\\ \sf\longmapsto 2x=50[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{50}{2}[/tex]

[tex]\\ \sf\longmapsto x=25[/tex]

Answer:

csc = 6/5= 1.2

cot = √(11)/5= 0.6633

sin = 5÷6= 0.83333