Hyperbolas are confusingggg

A skateboard halfpipe is being designed for a competition. The halfpipe will be in the shape of a parabola and will be positioned above the ground such that its focus is 30 ft above the ground. Using the ground as the x-axis, where should the base of the halfpipe be positioned? Which equation best describes the equation of the halfpipe?

(0, 60); y equals one over two hundred forty times x squared minus 60
(0, 60); y equals one over two hundred forty times x squared plus 60
(0, 15); y equals one over sixty times x square minus 15
(0, 15); y equals one over sixty times x squared plus 15

System of equations y = x² + 7x + 4 has one real root with the line y = x -5.

A quadratic equation is the polynomial equation of two degrees in one variable. The general form of a quadratic equation is  ax² + bx + c = 0.

The quadratic equation formula for the solution of roots.

[tex]\rm (\alpha ,\beta ) = [ -b[/tex]±[tex]\rm \sqrt{b^{2} - 4ac} /2ac[/tex]]

The discriminant is the [tex]\rm \sqrt{b^{2} - 4ac}[/tex] part of the quadratic equation

If D is greater than zero then the roots are real and distinct.

If D is equal to zero then the roots are real and equal.

If D is less than zero then the roots are imaginary and unequal.

y = x² + 7x + 4

From First option, System of equations

y = x² + x – 4

y = x – 5

So, x - 5 = x² + x – 4

x² + x – 4 - x + 5 = 0

x² + 1 = 0

discriminant = b²- 4×a×c

= 0²- 4×1×1

-4 < 0, therefore the equation has no real roots.

From Second option, System of equations

y = x² + 2x – 1

y = x – 5

So, x - 5 = x² + 2x – 1

x² + 2x - 1  - x + 5 = 0

x² + x + 4 = 0

discriminant = b²- 4×a×c

= 1²-4×1×4

-15 < 0   therefore, the equation has no real roots.

From Third option, System of equations

y = x² + 6x + 9

y = x – 5

So, x - 5 = x² + 6x + 9

x² + 6x + 9  - x + 5 = 0

x² + 5x + 4 = 0

discriminant = b²- 4×a×c

= 5²-4×1×4

9 > 0 therefore, the equation has two different real roots.

From Fourth option, System of equations

y = x² + 7x + 4

y = x – 5

So. x - 5 = x² + 7x + 4

x² + 7x + 4 - x + 5 = 0

x² + 6x + 9 = 0

discriminant = b²- 4×a×c

= 6²-4×1×9 = 0

0  therefore, the equation has one real root.

Since, System of equations y = x² + 7x + 4 has one real root with the line y = x -5.

Learn more about quadratic equations;

https://brainly.com/question/2263981

Answer:

D on edge

Step-by-step explanation:

The random selection of a blue marble is an illustration of probability

You should expected to pull a blue marble 10 times

The given parameters are:

Blue = 16

Red = 12

Green = 12

The total number of marbles is:

Total = 16 + 12 + 12

So we have:

Total = 40

The probability of selecting a blue marble is:

[tex]P(Blue) = \frac{16}{40}[/tex]

When 25 marbles are selected, the expected number of blue is:

[tex]Blue = n * P(Blue)[/tex]

So, we have:

[tex]Blue = 25 * 16/40[/tex]

[tex]Blue = 10[/tex]

Hence, the expected number of blue marbles is 10

Read more about expected values at:

https://brainly.com/question/15858152

[tex]sin(\theta )=\cfrac{\stackrel{opposite}{7}}{\underset{hypotenuse}{25}}\qquad \textit{let's find the \underline{adjacent side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \sqrt{25^2-7^2}=a\implies \sqrt{576}=a\implies 24=a~\hfill tan(\theta )=\cfrac{\stackrel{opposite}{7}}{\underset{adjacent}{24}}[/tex]

Answer:

  6 games

Step-by-step explanation:

The number of games can be found by determining the number of groups of 10 Maria can make.

 62/10 = 6.2

Maria can make 6 groups of 10 and will have a fraction of a group left over. Maria will be able to put together 6 of her board games.

Answer:

Its A

Step-by-step explanation

just trust me

The range of the provided inverse sine function in terms of x, and y y = sin-1x is [-π/2, π/2].

Range of a function is the set of all the possible output values which are valid for that function.

The trigonometry function given in the problem is,

[tex]y = \sin^{-1}x[/tex]

The above function can be written as,

[tex]\sin y = x[/tex]

The above function is the arc of sine function. The domain of arc of sine ranges from -1 to 1.

[tex]-1\leq x\leq1[/tex]

This is the domain of the inverse of sine function. In the attached image below, the graph of inverse sine function is plotted. The range of this function is,

[tex]-\dfrac{\pi}{2}\leq x\leq\dfrac{\pi}{2}[/tex]

Thus, the range of the provided inverse sine function in terms of x, and y y = sin-1x is [-π/2, π/2].

Learn more about the range of the function here;

https://brainly.com/question/2264373

Answer:

C {-pi/2,-pi/2}

Step-by-step explanation:

Answer:

x = 5

y = 2

Step-by-step explanation:

multiply by -2 the second equation and add the first equation to eliminate "x"

[tex]4x+5y=30\\-4x-10y=-40[/tex]

_______________

            [tex]-5y=-10\\y=\frac{-10}{-5} =2[/tex]

To find "x", substitute the value of "y" in any equation. I do it in the first

[tex]4x+5(2)=30[/tex]

[tex]4x+10=30[/tex]

[tex]4x=30-10\\x=20/4=5[/tex]

Hope this helps

Answer:

i got you

Step-by-step explanation:

first you will make the easiest equation into y=mx+b

2x=5y=20

subtract 2x from it self and 20, you will eliminate the 5 but keep the y then you will get y=2x+20

then you will substitute it into the y in the other equation 4x+5(2x+20)=30

after doin that you will multiply 5 by both the number in the parenthesis

4x+15x+100=30 add like terms 4x+15x =

19x+100=30 subtract 100 fromm itself and 30 you will get -70

-70 divided by 19x then you will get your answer

Answer:

3

Step-by-step explanation:

81^(¼) can also be witten as the fourth root of 81, which happens to be 3.

Answer:

3

Step-by-step explanation:

(3*(to the fourth power))1/4

Answer:

5 years

Step-by-step explanation:

by year five they both had the same amount

400-35=365

do that 5 times

225

100+25=125

do that 5 times

225

there you goo :)) on the chain up on the left from 3 to 48 they keep multiplying by 2, and the other one, they keep subtracting by 7

Answer:

Latisha rode 16 rides

Step-by-step explanation:

Look at picture attached. Have a blessed night!

Just slope intercept formula (y=mx+b). X represents the number of rides so you will need to myltiply that by $2.50. $9 is a one time fee so that would be of the b of the equation. That all equals the total Latisha piaid, $49. Then solve like so.

Answer:

i don't really know but I love pizza

The nth term Tn = n - 12 illustrates an arithmetic progression

The sum of the first 25 terms is 25

The nth term is given as:

Tn = n - 12

Calculate the first term

a = 1 - 12

a = -11

Calculate the second term

T2 = 2 - 12

T2 = -10

Calculate the common difference (d)

d = T2 - a

d = -10 + 11

d = 1

The sum of n terms is then calculated as:

Sn = n/2(2a + (n - 1) * d)

So, we have:

S25 = 25/2(-2 * 11 + (25 - 1) * 1)

Evaluate

S25 = 25

Hence, the sum of the first 25 terms is 25

Read more about arithmetic progression at:

https://brainly.com/question/6561461

Answer:

Step-by-step explanation:

2) definition of angle bisector

4) division property of equality

5) division property of equality

6) substitution property

7) SAS similarity

A statistically significant result will allow the medical center to conclude that the new procedure causes a reduction in recovery time.

A result is statistically significant if there's a very low probability that it could have occurred by chance.

What this means is that the reduction in the recovery time was truly as a result of the new procedure which is why it will be adopted by the medical center.

Read more about Statistically significant result here https://brainly.com/question/15848236

Answer:

39 sq inches

Area of sector = [tex]\frac{θ}{360}*\pi r^{2}[/tex]

Given: θ = 70°, radius (r) = 8 inches

Area of sector = [tex]\frac{70}{360} * \pi *8^{2}[/tex]

= 39.095

for further studies visit: https://brainly.com/question/22972014

hope it helps...

Step-by-step explanation:

class 6 to 8 students come here I will give you notes class is started come here fast I am waiting come with your name and class i am also girl come please please please please please please

Answer:

148°or 4x

Step-by-step explanation:

For a four sided Polygon (quatrilateral) the measure of four angles=360

Therefore,

2x+3x+4x +(x -10)=360

9x+x-10=360

10x-10=360

10x=360+10

10x=370

x=37

Therefore all angles are

74, 111, 148, 27

Therefore, largest angle = 148°

Answer:

3mm

Step-by-step explanation:

4 (3/4)

4x3/4

=3

brainiest please

Answer:

⠀

Step-by-step explanation:

⠀

We know,

[tex]{\longrightarrow \qquad \boldsymbol{\pmb{Perimeter_{(square)} \it=4a }}}[/tex]

⠀

Where,

⠀

Now, Substituting the values in the formula :

⠀

[tex]{\longrightarrow \qquad {\rm{Perimeter_{(square)} = \it4 \times \it \dfrac{3}{4} }}}[/tex]

⠀

[tex]{\longrightarrow \qquad {\rm{Perimeter_{(square)} = \it \cancel4 \times \it \dfrac{3}{ \cancel4} }}}[/tex]

⠀

[tex]{\longrightarrow \qquad {\boldsymbol {\pmb{Perimeter_{(square)} = 3 }}}}[/tex]

⠀

Therefore,

Answer: 12 units

Step-by-step explanation:

If you graph them on a graph you count the units between them and that is your anwser.

Answer:

12 units

Step-by-step explanation:

calculate DG using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2 -y_{1} } )^2[/tex]

with (x₁, y₁ ) = D (8, 3 ) and (x₂, y₂ ) = G (- 4, 3 )

DG = [tex]\sqrt{(-4-8)^2+(3-3))^2}[/tex]

     = [tex]\sqrt{(-12)^2+0^2}[/tex]

     = [tex]\sqrt{144+0}[/tex]

    = [tex]\sqrt{144}[/tex]

    = 12

Answer:

20+2C

Step-by-step explanation:

sum means addition

if Craig's age is c than twice his age is 2xC, also expressed as 2C

20+2C

hi there! so here's my answer

[tex] \rm \tiny\color{green}t = \frac{10}{9} \\ \\ \tt \: in \: alternative \: form \\ \\ \color{yellow} \rm \: t = 1 \frac{1}{9} \: \: \: or \: \: t = 1.1[/tex]

Step-by-step explanation:

[tex] \color{gray} \tt \: 16 = 2( - 8t - 1) \times (t - 2)[/tex]

[tex]\color{gray} \tt \: 16 = 2(- 9)(t - 2)[/tex]

[tex]\color{gray} \tt \: 16=^ \ 2*9(t-2)[/tex]

[tex]\color{gray} \tt \: 16=-18 (t-2)[/tex]

[tex]\color{gray} \tt \: 16 = - 18t + 36[/tex]

[tex]\color{gray} \tt \:16+18t=36[/tex]

[tex]\color{gray} \tt \:18t=36-16 [/tex]

[tex]\color{gray} \tt \:18t=20 [/tex]

[tex] \:\rm \tiny\color{green}t = \frac{10}{9} \\ \\ \tt \: in \: alternative \: form \\ \\ \color{yellow} \rm \: t = 1 \frac{1}{9} \: \: \: or \: \: t = 1.1[/tex]

hope it helps

Answer:

5x=15. I hope it can help you a lots. thanks.

Step-by-step explanation:

5x=14+1

5×=14.

Answer:

Step-by-step explanation:

We can use the interest equation (mind you it is the same thing as said in the problem) to solve this:

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

Where A is the resulting amount, r is the interest rate, n is the number of times compounded per year and t is the time.

[tex]A=1209(1+\frac{.082}{12} )^{12*26}[/tex]

A = $10,120.29

Step-by-step explanation:

x + y = 24

2x - y=21

I'm guessing the question was find both numbers.

3x = 35

x=15

3y = 27

y=9

Answer:

[tex]4x + 6y^{3} x^{2}[/tex]

Step-by-step explanation:

Simplify

Answer: 25%

Step-by-step explanation: the probability of drawing blue=5/20

divide 5 by 20= .25 then make .25 into a %:25% (you just move the decimal to the right twice)

He has 100 + 120 = 220 coins in his purse.

He has n + p coins if he has n nickels and p pennies.

6. D   ---> Length of all the sides

7. E    ---> a tool

8. A    ---> 3 sides

9. B    ---> 5 sides

10. C   ---> 4 sides

Answer:

Simplifying th exprsssion brings it down to zero

Hope this helps