The image of a parabolic lens is projected onto a graph. The image crosses the x-axis at –2 and 3. The point (–1, 2) is also on the parabola. Which equation can be used to model the image of the lens?

y = (x – 2)(x + 3)
y = (x – 2)(x + 3)
y = (x + 2)(x – 3)
y = (x + 2)(x – 3)

Answers

Answer 1

Answer:

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

Step-by-step explanation:

Given

[tex]x_1 = -2[/tex]

[tex]x_2 = 3[/tex]

[tex](x,y) = (-1,2)[/tex] --- a point on the parabola

Required

The equation

First, calculate the equation from the zeros

[tex]y =k(x - x_1)(x - x_2)[/tex]

Substitute [tex]x_1 = -2[/tex] and [tex]x_2 = 3[/tex]

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

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

To solve for k, we substitute [tex](x,y) = (-1,2)[/tex]

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

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

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

Divide by -4

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

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

So, the equation is:

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

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

Answer 2

Answer: c

Step-by-step explanation:


Related Questions

(47.5+45.5+48.5+46.5+47+45+48+46+49)/9

:)

Answers

Answer:

47 and now I'm just typing so it lets me answer

Step-by-step explanation:

calculator

Giovanna has a score of

−5minus, 5 in Canasta. Vera's score is

Write an inequality that correctly compares the scores.

Answers

Answer:'

-9.7 minus, in 13

Step-by-step explanation:

Find (-3/7) / (-1 1/14).

45/98

2/5

2 1/2

-2/5

Answers

Answer:

option B .   [tex]\frac{2}{5}[/tex]

Step-by-step explanation:

[tex](-\frac{3}{7}) \div (-\frac{15}{14}) = (-\frac{3}{7}) \times (-\frac{14}{15}) = \frac{3 \times 14}{7 \times 15} = \frac{2}{5}[/tex]

Answer:

2/5

Step-by-step explanation:

(-3/7) / (-1 1/14) = 0.4

0.4 = 4/10

simplified = 2/5

I hope this helps uwu.

Every point on a circle is the same distance from a single location. What is
that location called?

Answers

Answer:

The center.

Step-by-step explanation:

That point is the center of the circle.

Hope that this helps!

which of the following systems of linear inequalities is represented by the solution graphed below?

Answers

Answer is A, y us smaller/equal to 2 and y is smaller/equal to X

Pythagoras


1.if the radius of the smaller circle is 3, find it’s area


2. Find the area of the yellow ring


3. Find the area of the white ring

Answers

Answer:

1. [tex]Area = 28.26[/tex]

2 and 3: See explanation

Step-by-step explanation:

Solving (1)

[tex]r = 3[/tex] --- radius

The area is:

[tex]Area = \pi r^2[/tex]

[tex]Area = 3.14* 3^2[/tex]

[tex]Area = 28.26[/tex]

There are no enough information to solve (2) and (3) as the radius and/or diameter are not provided.

However, the following formula will be used to calculate the required areas.

[tex]Area = \pi r^2[/tex] --- same process as (1)

(-32) +(-8) -(+40)+(40)+(78)-(46)​

Answers

Answer:

or -32-8-40+40+78-46=-8

Step-by-step explanation:

Answer:

-8 is the answer!!!!

Step-by-step explanation:

you can use calculaTor

Find the value of x. Give a reason to justify your solution.

Answers

Answer:

x =52

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the opposite interior angles.  (Exterior Angle Property)

x+72 = 90+34

x+72 = 124

x+72-72 = 124 - 72

x =52

9. Estimate the solution to the system
of equations by graphing. Write the
solution.
y=4-X
x + 3y = 5
( , )

Answers

5 is the answer
At least I think

a b and c of a right angled are in the ratio 7:18:11

the smallest angle is 35

work out angles a b and c

Answers

Answer:

a=35° b=90° c=55°

Step-by-step explanation:

7:18:11

total ratio=7+18+11

=36

The smallest angle(a)

7/36 x s=35

7s/36=35

7s=35x36

7s=1260

7s/7=1260/7

s=180°

second angle (b)

18/36x180

=90°

third angle (c)

11/36x180

=55°

A 5 kg stone falls from height of 100m and penetrate 2m in a layer of sand. The force applied by ground is

Answers

Answer:

49N

Step-by-step explanation:

Below is the calculation for the force applied:

It is given that the mass of stone is 5 kg and it falls from the height of 100 meters. Therefore, a force can be determined by multiplying the mass will a constant value of "a".

Force = Mass x a

Force = 5 x 9.8

Force = 49 N

Since the action-reaction are equal and opposite so the each will apply the same force.

At a middle school, 30% of students buy lunch in the cafeteria and the remaining students bring lunch from home. A spinner with 10 equal-sized sections numbered 0-9 will be used to simulate the lunch trend. How can you design a simulation to guess whether the next 20 students buy lunch or bring lunch from home?
A:Assign the numbers 0–3 to represent students who buy lunch and the numbers 4–9 to represent students who bring lunch from home. Spin the spinner 20 times and count how many spins are between 0–3 and how many are between 4–9.
B:Assign the numbers 0–2 to represent students who buy lunch and the numbers 3–9 to represent students who bring lunch from home. Spin the spinner 10 times and count how many spins are between 0–1 and how many are between 4–6, then multiply the counts by 2.
C:Assign the numbers 0–2 to represent students who buy lunch and the numbers 3–9 to represent students who bring lunch from home. Spin the spinner 20 times and count how many spins are between 0–2 and how many are between 4–9.
D:Assign the numbers 0–3 to represent students who buy lunch and the numbers 4–9 to represent students who bring lunch from home. Spin the spinner 10 times and count how many spins are between 0–3 and how many are between 4–9.

Answers

Answer:

B

Step-by-step explanation:

I'm pretty confident that it is B

Find the equation of the line that passes through (2,7) and (7,12)

Answers

Answer:

equation of the line that passes through (2,7) and (7,12) is y=x+5

can someone PLEASE HELP me?? the answer has to be in simplest form and i keep getting it wrong. the ixl score needs to be at 68 and im only at 30. i really need this done please

explaining your answer to me will get you brainliest.

Answers

Answer: The formula for sector area is simple, multiply the central angle by the radius squared, and divide by 2: Sector Area = r² * α / 2. So you want to do that for every problem like this

Step-by-step explanation:s

Answer:  11pi/60

=========================================================

Explanation:

Let's ignore the area of the shaded slice for now. Instead, we'll find the area of the full circle

We plug in the radius r = 1 to find that

A = pi*r^2

A = pi*1^2

A = pi

The exact area of that full circle is pi square meters. You can think of an actual pie (the baked pastry, not the constant) with this area as a way to help conceptualize things.

If we wanted the whole circle, then we'd say pi is the answer. However, we only want a slice of that circle. The fractional amount 66/360 represents the slice we want. This fraction reduces to 11/60 after you divide both parts by 6. If you were to cut the pizza up into 60 slices, then you would shade 11 of them in to represent the green area.

Multiply 11/60 with the area pi to get the final answer 11pi/60

This answer is exact in terms of pi

To get an approximate value, you could replace pi with 3.14 to get 11pi/60 = 11*3.14/60 = 0.57567 meaning the green shaded area is roughly 0.57567 square meters. Use more decimal digits of pi to get a more accurate shaded area.

Bob works as a carpenter and needs to buy some tools for
work. A framing hammer costs $22. A 4-foot level costs
$18. A carpenter's square costs $7. What are Bob's total
expenses for these tools?

Answers

answer: 47. reason: 22 + 18 + 7 = 47

Can pls someone help I need help

Answers

a^2 + b^2 = c^2
9^2 + b^2 = 15^2
81 + b^2 = 225
225 - 81 = b^2
144 = b^2
square root of 144 = 12
b = 12

if 7=42,6=30,5=20 then 3=? find it's value​

Answers

Answer:

6

Step-by-step explanation:

7=42 is 7*6

6=30 is 6*5

5=20 is 5*4; it's multiplied by the number below it, so 3 will be 3*2

3 = 6

Step-by-step explanation:

Given: 7 = 42, 6 = 30, 5 = 20

7 (x 6) = 42

6 (x 5) = 30

5 (x 4) = 20

Follow the pattern

4 (x 3) = 12

3 (x 2) = 6

3 = 6

What solid 3D object is produced by rotating the triangle about line m? ANSWER ASAP. TROLL AND LINK ANSWERS REPORTED. WILL AWARD BRAINLIEST.

Answers

Answer:

A cone with diameter 6 units

Step-by-step explanation:

Rotating the triangle about line m will give us a cone with radius 3

If the radius is 3, the diameter is 2*r = 2*3 = 6

Answer:

Step-by-step explanation:

a cone with a radius of 5

Match them BRAINLIEST IF CORRECT ​

Answers

Answer:

1/2 for the red card

1/52 for queen of hearts

1/4 for clubs

3/13

Step-by-step explanation:

the red card is 1/2 because the only other color is black

there is only one queen of hearts

it is one of four possible symbols

because that is the only one left

I need some Help please!

Answers

Answer:

1) observational

2) sample

3) experiment

Answer:

1 no is observational

Step-by-step explanation:

2 no is sample

3 no is experiment

SJSKSJSKSJ d help :p

Answers

Answer:

Below

Step-by-step explanation:

Discount: 40% of $159 = $63.60

Price you pay: $159 - $63.60 = $95.40

In circle P, BC=24 ft.
What is the length of arc AC?

Answers

the length of arc AC = 30* BC/2= 30*12=360
AC = 360

write 36m÷9m in standard form

Answers

4x^2. This is the simplified answer

The expression (36m ÷ 9m) is equivalent to 4.

What is division in mathematics? What is a mathematical function, equation and expression?division : Division is the process of splitting a number or an amount into equal parts.function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.

Given is the following division as follows -

(36m ÷ 9m)

We have the following expression -

36m ÷ 9m

So, we can write -

(36m/9m)

36/9

4

Therefore, the expression (36m ÷ 9m) is equivalent to 4.

To solve more questions on functions, expressions and polynomials, visit the link below -

brainly.com/question/17421223

#SPJ2

what is the value of 64 2/3?

Answers

Answer:

[tex] \frac{194}{3} [/tex]

Step-by-step explanation:

[tex]64 \frac{2}{3} [/tex]

[tex]64 + \frac{2}{3} [/tex]

[tex]64 \times \frac{3}{3} + \frac{2}{3} [/tex]

[tex] \frac{64 \times 3}{3} + \frac{2}{3} [/tex]

[tex] \frac{64 \times 3 + 2}{3} [/tex]

[tex] \frac{192 + 2}{3} [/tex]

[tex] \frac{194}{3} [/tex]

Hope it is helpful...

URGENT: Graph y = cosx for -3\pi/2 <= x <= -pi/2

What is the largest value in the range?


A. -1

B. 0

C. 1/2

D. 1

Answers

I’m pretty sure it’s d

Subtract: (-137° + 6) - (-43°) Your answer should be in simplest terms. Enter the correct answer.​

Answers

Answer:

-9y⁹ + 6

Step-by-step explanation:

Subtracting a negative makes it positive

-13y⁹ + 6 + 4y⁹

combine like terms

-9y⁹ + 6

how much square units of 50 units

Answers

Answer:

7.07106781187

Step-by-step explanation:

if its just asking [tex]\sqrt50[/tex]

:D

I am stuck on this question.

Answers

Answer:

D. Yes; the graph passes the vertical line test.

Step-by-step explanation:

1. A and C are wrong since the number of x-values that a y-value have does not matter when it comes to functions.

2. When doing the vertical line test, it is done by drawing a vertical line (up to down) and then seeing if more than 1 point touches the line.

3. After drawing the vertical line you would see only 1 point touches the line which indicates that the graph passes the vertical line test.

4. Therefore, the answer is "D. Yes; the graph passes the vertical line test."

Helpppp i need this quick im taking a timed test!!!

Answers

Answer: c

Step-by-step explanation:

Answer:c

Step-by-step explanation: it makes the most sense

Find the distance from point P to RQ

Answers

Answer:

option A : about 2.8 units

Step-by-step explanation:

To find the distance from P to RQ , Find the distance from ( 1 , 1) to (3 , 3).

 [tex]Distance = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

                 [tex]= \sqrt{(3-1)^2 + (3-1)^2}\\\\= \sqrt{2^2 + 2^2 }\\\\= \sqrt{4 + 4 }\\\\= \sqrt{8}\\\\=2\sqrt{2}[/tex]

                 = 2.83 units

Answer:

A

Step-by-step explanation:

Remark

The distance you want is the point P to the (3,3). Then two lines meet as these two do, the shortest distance is the right angle distance. And that is how distance is defined.

Formula

d = sqrt( (x2 - x1)^2 + (y2 - y1)^2  )

Givens

x2 = 1

x1 = 3

y2 = 1

y1 = 3

Solution

d = sqrt( (1 - 3)^2 + (1  - 3)^2 )

d = sqrt( (-2)^2 + (-2)^2 )

d = sqrt ( 4 + 4)

d = sqrt(8)

d = 2√2

d = 2.8

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