Тогатство

Give four rational numbers betwee1by2 and 6 by 7

MA_775_DIABLO [31]

Answer:

Therefore four rational numbers between 1 and 2 are 9/8, 5/4, 3/2, and 7/4 Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Parabola Equations - Algebra

mash [69]

Answer:

$h=-\frac{1}{6}x^2+2x$

Step-by-step explanation:

The height of the tunnel is modeled by:

$h=rx^2+tx$

Where r and t are constants.

We know that the maximum height of the tunnel h is 6 meters.

And at ground level, the width is 12 meters.

And we want to determine the equation of the parabola.

First, since this is a quadratic, our maximum height h will occur at the vertex of our equation.

The vertex is given by:

$(-\frac{b}{2a}, f(-\frac{b}{2a}))$

In our case, we have the function:

$h=(r)x^2+(t)x$

Hence, a=r; b=t; and c=0.

Therefore, our vertex is:

$\Rightarrow -\frac{t}{2r}$

Thus, if we substitute this back into our equation, we should get 6 since 6 is the maximum height which is determine by the vertex. In other words:

$(6)=r(-\frac{t}{2r})^2+t(-\frac{t}{2r})$

Simplify:

$6=r(\frac{t^2}{4r^2})-\frac{t^2}{2r}$

Simplify:

$6=\frac{t^2}{4r}-\frac{t^2}{2r}$

Combine fractions:

$6=\frac{t^2}{4r}-\frac{2t^2}{4r}=\frac{-t^2}{4r}$

Multiply both sides by the denominator:

$24r=-t^2$

Let's solve for the constant r. Divide both sides by 24. Hence:

$r=-\frac{t^2}{24}$

Now, we can use our knowledge of the width.

We know that the width is 12 meters at ground level.

Hence, when h=0, the <em>difference of our roots</em> is 12.

So:

$0=rx^2+tx$

We can factor:

$0=x(rx+t)$

By the Zero Product Property:

$x=0\text{ or } rx+t=0$

So, the first zero is 0.

Therefore, the second zero <em>must be 12</em> to ensure that our width is 12.

Let's isolate the second zero. Subtract t from both sides:

$rx=-t$

Divide both sides by r:

$x=-\frac{t}{r}$

We know that this zero must be 12. Thus:

$12=-\frac{t}{r}$

We have previously solved for r. Substitute:

$12=-\frac{t}{\frac{-t^2}{24}}$

Simplify:

$12=\frac{24}{t}$

Take the reciprocal of both sides:

$\frac{t}{24}=\frac{1}{12}$

Multiply both sides by 24. Hence, the value of t is:

$t=2$

Now, we can find r. r is given by:

$r=-\frac{t^2}{24}$

By substituting 2 for t, then, we acquire that:

$r=-\frac{(2)^2}{24}=-\frac{4}{24}=-\frac{1}{6}$

Therefore, for:

$h=rx^2+tx$

Our equation is:

$h=-\frac{1}{6}x^2+2x$

7 0

3 years ago

Please help! Im so stuck on this and cant figure it out

Reptile [31]

First, we split the figure into two shapes, a triangle and a trapezoid. First, we know that the length of the base of the right triangle is 2, because in a 30-60-90 triangle, the side next to the 60° is half of the hypotenuse. Then, the length of the height would be 2 times root 3, which is 3.46410161514. Height is 3.46410161514 meters and base is 2 meters. We multiply the base times the height, and we get 6.92820323028 meters squared. This is the area of the triangle. Since we know that the base of the triangle is 2, we can do 5-2 to find the first base of the trapezoid, which is 3. We know that the height is 3.46410161514, the first base is 3, and that the second base is 5, so we plug it into our equation which is base1 + base2 over 2 times the height. We plug it in and get approximately 13.85641. Then we round to the tenths place, and we get 13.86 meters squared of the figure. Brainliest?

5 0

3 years ago

Larry used a pattern of colors to make a cube train. He used a red cube, a blue cube, a red cube, and another red cube before he

OlgaM077 [116]

I think 18 red cubes.
Explanation: A cube has 6 sides, so you would use the pattern 6 times. There are 3 red cubes in each pattern, you use the pattern 6 times, meaning 3 × 6, so the cube train has 18 red cubes. I hope this helps!

8 0

3 years ago

5. Please convert the equation y-5=7(X-6) into slope

zysi [14]

Answer:

Solving the Equation would be: y= 7x-37, Finding the Function would be x= 37 over 7

Step-by-step explanation:

Function:

y-5=7(x-6)

0-5=7(x-6)

0-5=7x-42

-5=7x=42

-7x-5=-42

-7x=-42+5

-7x=-37

x=37 over 7

_________________________________

Solving the Equation:

y-5=7(x-6)

y-5=7x-42

y=7x-42+5

y=7x-37

y=7x-37, x ER

7 0

3 years ago