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3 years ago

Sandra wrote p(x) = 30x + 5x2 in vertex form. Her work is below.

Mathematics

1 answer:

marta [7]3 years ago

8 0

Answer:

p(x) = 5(x + 3)² - 45

Step-by-step explanation:

Sandra wrote the function as p(x) = 30x + 5x².

So, this is a formula of a parabola, and this we have to convert into vertex form.

Now, rearranging the function we get

p(x) = 5(x² + 6x)

⇒ p(x) = 5(x² + 6x + 9) - 45

⇒ p(x) = 5(x + 3)² - 45

So, this is the vertex form and the vertex of the parabola is (-3,-45).

We know the formula of a parabola having vertex at (m,n) and axis parallel to positive y-axis is given by

(x - m)² = 4a(y - n)

⇒ $y = \frac{1}{4a} (x - m)^{2} + n$ (Answer)

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Sia ran 3/4 miles each day for 5 days did she run at least 6 miles

lana66690 [7]

No,
3/4 * 5=3.75
3.75 is less than 6.

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2 years ago

(3 pt) point v is graphed on a number line at –6. point u is 8 units away from point v on the number line. what could be the coo

lukranit [14]

Point v is graphed on a number line at -6...point u is 8 units away from v....notice that it doesn't say which way....so it can go either way....so we need to find 8 units away from -6 in both directions

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-6 - 8 = -14

so point u can be either at 2 or at -14...ur answers are A and D

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2 years ago

PLEASE HELP ME.Math work: The Head Chef has asked you to create a delicious baked dessert that will have the same volume if it i

nikklg [1K]

Answer:

Large baking dish of cylinder, cone and sphere.

Step-by-step explanation:

When we compute the volume of each of the small and large baking dish taking $\pi$ =3.14, we get

Volume of cylinder (small dish)= $\pi$ (r^2)(h)

=3.14( $\frac{3}{2}$ )^2*3

= $\frac{3.14*9*3}{4}$

= 21.195

Volume of cylinder (large dish)= $\pi$ (r)^2(h)= 3.14*(3)^2(3)

=84.78

Similarly, volume of cone (smaller dish)= $\frac{1}{3} \pi r^{2} h$

= 7.065

Volume of cone (larger dish)= 84.78

Volume of sphere(smaller dish)= $\frac{4}{3} \pi r^{3}$

= 14.13

Volume of sphere (larger dish) = 85.17 (approx)

Hence, we get that larger baking dish have approximately same volume.

Therefore, large baking dish of cylinder, cone, sphere will be chosen.

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2 years ago

Solve for x. 8/9x=32 Enter your answer in the box. x =

lorasvet [3.4K]

Answer:

x = 36

Step-by-step explanation:

Given;

(8/9)x = 32

Solving for x

Multiply through by 9

(8/9)×9 ×x = 32×9

8x = 32×9

Divide through by 8

8x/8 = 32×9/8

x = 36

6 0

3 years ago

47. A car travels at a constant speed of 50 miles per hour.

SIZIF [17.4K]

Answer:

The inverse of the given function is $t(d)=\frac{d}{50}$ . The time taken to travel 180 miles is 3.6 hours.

Step-by-step explanation:

It is given that a car travels at a constant speed of 50 miles per hour. A function for distance traveled is also given as d(t)=50t.

It is required to find the inverse of the function by expressing the time travel in terms of distance traveled and also find t(180).

To find the inverse, express time traveled in terms of distance traveled using normal algebraic methods and then substitute 180 for t and explain its results.

Step 1 of 2

The given function is d(t)=50t.

Consider d(t) as d and t as t(d) and rewrite the equation.

The rewritten function is d=50 t(d)

Divide by 50 on both sides of the equation.

$\begin{aligned}&d=50 t(d) \\&\frac{d}{50}=\frac{50 t(d)}{50} \\&t(d)=\frac{d}{50}\end{aligned}$

Step 2 of 2

Substitute 180 for $t$ in the simplified expression and interpret the results.

$\begin{aligned}&t(d)=\frac{d}{50} \\&t(d)=\frac{180}{50} \\&t(d)=3.6\end{aligned}$

The time taken to travel 180 miles is 3.6 hours.

3 0

1 year ago