Find the missing dimension of the prism. Round your answer to the nearest hundredth.

Volume = 72.66 in.?

Х

2 in.

Given:

The image of a lens crosses the x-axis at –2 and 3.

The point (–1, 2) is also on the parabola.

To find:

The equation that can be used to model the image of the lens.

Solution:

If the graph of polynomial intersect the x-axis at c, then (x-c) is a factor of the polynomial.

It is given that the image of a lens crosses the x-axis at –2 and 3. It means (x+2) and (x-3) are factors of the function.

So, the equation of the parabola is:

[tex]y=k(x+2)(x-3)[/tex]          ...(i)

Where, k is a constant.

It is given that the point (–1, 2) is also on the parabola. It means the equation of the parabola must be satisfy by the point (-1,2).

Putting [tex]x=-1, y=2[/tex] in (i), we get

[tex]2=k(-1+2)(-1-3)[/tex]

[tex]2=k(1)(-4)[/tex]

[tex]2=-4k[/tex]

Divide both sides by -4.

[tex]\dfrac{2}{-4}=k[/tex]

[tex]-\dfrac{1}{2}=k[/tex]

Putting [tex]k=-\dfrac{1}{2}[/tex] in (i), we get

[tex]y=-\dfrac{1}{2}(x+2)(x-3)[/tex]

Therefore, the required equation of the parabola is [tex]y=-\dfrac{1}{2}(x+2)(x-3)[/tex].

Note: All options are incorrect.

Answer:

7th graders in the school

Step-by-step explanation:

if she wants to know what 7th graders like, ask 7th graders since no one els would know as good as 7th graders themselves

Answer:

A.7th graders in the school

Step-by-step explanation:

Because she specifically wants to find the favorite activity of 7th grade students she should sample only 7th grade students to get the best and most accurate results.

(-5, -1)

Hope this helps! :)

Answer:

$1,976.25

Step-by-step explanation:

Since one square foot cost $ 7.50 we simply multiply that by 263.5.

263.5 × 7.50= $1,976.25

Answer:

x = 6

Step-by-step explanation:

[tex]\frac{-2}{3}x+9=\frac{4}{3} x-3[/tex]

-2x = -12

x = 6

Answer:

x = 6

Step-by-step explanation:

Answer:

16/13 is the answer.

26-10 is 16 and 2x5+3 is 13

Answer:

4

Step-by-step explanation:

26 - 25 + 3

Answer:

(c) 84

hope this helps!!!!

Answer:

Step-by-step explanation:

suface area of base=1/2×9×7.8=9×3.9=35.1 yd²

lateral surface area=3×1/2×9×10=135 yd²

total surface area=135+35.1=170.1 yd²

i assumed it is an equilateral triangular base.

as √(7.8²+4.5²)=9.0049≈9

y = -19

I started by adding 18 to both sides(inverse operation) then dividing by -2 to isolate the variable. What you do to one side must be done to the other

You can see that the MNO triangle is similar to MKL  then  [tex]\displsystyle\ \frac{NO}{KL} =\frac{x}{ML} => \frac{12}{22} =\frac{x}{27,5} => x=\frac{12\cdot 27,5}{22} =15[/tex]                                                                  [tex]\displaystyle\ Answer: \boxed{x=15}[/tex]

Answer:

B

Step-by-step explanation:

r^2 is 0.9997, and after 10 years it'll be 95660

Answer:

scale factor: 2

translation: (x+2, y+7)

Step-by-step explanation:

Answer:

Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, …

Answer:

Anthony

Step-by-step explanation:

Mehod I - Common denominator

Use common denominator of 5 * 8 = 40

Cody

3/5  = 24/40

Anthony

5/8 = 25/40

-----------------------------

Method II - convert to decimal

Cody

3/5 = 0.6

Anthony

5/8 = 0.625

------------------------

Either way

Anthony read a greater fraction

Answer:

Y=40 X=75

Step-by-step explanation:

i think im not 100% on that, been a long time since i did stuff with triangles

Answer:

gdjksbdifkfnfuwiaksujdbf

Answer:

A. 8

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

f(x) = 2ˣ

Step 2: Evaluate

Answer:

it's 8

Reason:

substitute x=3 into the function....it'd be 2³, which is 8

Answer:

390 points

Step-by-step explanation:

⇒ New score = (420 - 30) points

⇒ New score = 390 points

Joanne's score is now 390 points.

Answer:

C. Salaried pay. Salaried employees make more per week than hourly employees.

Step-by-step explanation:

edge 2021

Answer:

12:30

Step-by-step explanation:

Answer:

[tex]X=24[/tex]

Step-by-step explanation:

From the question we are told that:

Probability of  having a smoker [tex]P(s)=0.24[/tex]

Sample size [tex]n=130[/tex]

Generally the equation for Variance X is mathematically given by

 [tex]X= np(1-p) =[/tex]

 [tex]X= (130)(0.24)(1-0.24)[/tex]

 [tex]X = 23.712[/tex]

 [tex]X=24[/tex]

(2.75 x 10⁵ ) / (2.25 x 10² )

= (2.75 / 2.25) x 10⁵⁻²

= 1.2 x 10³ times .

(That's 1,200 times as many.)

I hope this helps!

Answer:

1221.2 times more

Step-by-step explanation:

number of bacteria last week = [tex]2.25*10^2[/tex]

= [tex]2.25*100[/tex]

= [tex]225[/tex]

number of bacteria this week = [tex]2.75*10^5[/tex]

= [tex]2.75*100000[/tex]

= [tex]275000[/tex]

[tex]275000 - 225 = 274775[/tex]

[tex]274775 / 225 = 1221.2[/tex]

Answer:

142

Step-by-step explanation:

angle <3 is supplementary to 5x + 3

5x + 3 + 21x - 5 = 180 (because two angles are supplementary as well)

26x  - 2 = 180 add 2 to both sides

26x = 182 divide both sides by 26

x = 7

<3 + 5x + 3 = 180 replace x with 7 and rewrite equation

<3 + 38 = 180 subtract 38 from both sides

<3 = 142

Answer:

The slope is -3, also written as -3/1.

Answer:

-3

Step-by-step explanation:

it is simply the (m) in y = mx + b

m is the slope

and b is the y intercept

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

It is y = -4/5x - 2 because you go left 4 and down 5 which makes both negative. And of course it is minus two.

Answer:

y=1/2x+5/2

Step-by-step explanation:

y=ax+b

vuông góc với y = –2x - 4 ⇒a.(-2) =-1⇒a=1/2

phương trình của đường thẳng đi qua điểm (3, 4) ⇒4=3.1/2+b⇒b=5/2

⇒y=1/2x+5/2

Answer:

3

Step-by-step explanation:

Answer:

The answer is number 2

Step-by-step explanation:

Since the price of a quarter is 25 cents we put the .25 it next to the Q and since dimes are worth 10 cents we put the .10 next to the D. D + Q should equal 30 since that is the total number of coins and the other should equal 4.80

Answer:

6.)

The answer is 63 inches because this value is closer to the mean and while the data is positively skewed (as in the mean is greater than the median) it's not by that much.

7.)

This would mean that the data is symmetric. By this, I mean that there would have to be an equal amount of data on either side of the mean. For example, for every entry 2 units below from the mean there must be one 2 units above the mean and so on. There would also have to be many entries on the mean/median (so that it would also be the mode)

8.)

We can observe that there are no real outliers that would heavily influence the data and so we can just take the mean

the mean of student A is: (68+72+73+67)/4= 70

The mean of student B is: (74+73+73+74)/4=73.5

We can see that student A, on average, is closer to 70 than student B and can therefore conclude that student A is more percise