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2 years ago

What is the x-coordinate of the vertex of the parabola whose equation is y = 3x² + 9x?

Mathematics

1 answer:

saveliy_v [14]2 years ago

3 0

Answer: -3/2

Step-by-step explanation:

The axis of symmetry, and thus the x-coordinate of the vertex, is given by $x=-\frac{b}{2a}$

So, the answer is $x=-\frac{9}{2(3)}=\boxed{-\frac{3}{2}}$

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12-22 plz help thanks

Kisachek [45]

12-22 = -10 because know I'm right and it says I have to put more words so just look at the first part

6 0

3 years ago

Given:

diamong [38]

Answer:

10-5 $\sqrt{2}$

Step-by-step explanation:

As per the attached figure, right angled $\triangle MDL$ has an inscribed circle whose center is $I$ .

We have joined the incenter $I$ to the vertices of the $\triangle MDL$ .

Sides MD and DL are equal because we are given that $\angle M = \angle L = 45 ^\circ.$

Formula for <em>area</em> of a $\triangle = \dfrac{1}{2} \times base \times height$

As per the figure attached, we are given that side <em>a = 10.</em>

Using pythagoras theorem, we can easily calculate that side ML = 10 $\sqrt{2}$

Points P,Q and R are at $90 ^\circ$ on the sides ML, MD and DL respectively so IQ, IR and IP are heights of $\triangle$ MIL, $\triangle$ MID and $\triangle$ DIL.

Also,

$\text {Area of } \triangle MDL = \text {Area of } \triangle MIL +\text {Area of } \triangle MID+ \text {Area of } \triangle DIL$

$\dfrac{1}{2} \times 10 \times 10 = \dfrac{1}{2} \times r \times 10 + \dfrac{1}{2} \times r \times 10 + \dfrac{1}{2} \times r \times 10\sqrt2\\\Rightarrow r = \dfrac {10}{2+\sqrt2} \\\Rightarrow r = \dfrac{5\sqrt2}{\sqrt2+1}\\\text{Multiplying and divinding by }(\sqrt2 +1)\\\Rightarrow r = 10-5\sqrt2$

So, radius of circle = $10-5\sqrt2$

8 0

3 years ago

John is 48 years old. He is planning on retireing when he is 65. He has opened an IRA with an APR of 3.5% compounded daily. If h

alex41 [277]

The amount of money that John would have in his account when he is ready to retire is $6,351,400.21.

<h3>How much would be in the retirement account?</h3>

The formula that can be used to determine the future value of the annuity is

Future value = Daily deposit x annuity factor

Annuity factor = {[(1+r)^n] - 1} / r

Where:

r = 3.5 / 365 = 0.0096%
n = (65 - 48) x 365 = 6205

Annuity factor = [(1.000096^6205) - 1] / 0.000096 = $8468.53

Future value = 750 x $8468.53 = $6,351,400.21

To learn more about annuities, please check: brainly.com/question/24108530

#SPJ1

3 0

2 years ago

(Problem of the Week)

ira [324]

Answer:

He won 13 times and lost 1 time

Step-by-step explanation:

divide 67 by 5 so 67÷5 you would get 13.4 you take the whole number 13 and multiply it by 5 and that will get you to 65 so then you only have 2 left over and if you lose you get 2 point so therefore you know that he lost only once

(13•5)+2=67

5 0

3 years ago

2 is less than or equal to x, and 8 is greater than x

Marysya12 [62]

Answer:

2 ≤ x 8>x

That is what the sighs look like

8 0

3 years ago