Which is an equation of the parabola that intersects the x-axis at points (-1, 0) and (3, 0)? Show your work or explain how you determined your answer. A. y = x2 + 2x - 3 B. y = x2 + 3x + 2 C. y = x2 - 2x - 3 D. y = x2 - 3x + 2

Answers

Answer 1

Answer:

[tex]\displaystyle \large{y=x^2-2x-3}[/tex]

Step-by-step explanation:

The given points are (-1,0) and (3,0) to find an equation of parabola. Notice that they say or the given points are x-intercepts, which means they make it easier for us to find an equation of parabola using these x-intercepts.

Quick Note:

x-intercepts are simply the roots or solutions of quadratic equation, so if our root is x = -2 then we can write as (-2,0) and write back to x+2=0.

So what we are going to do is to write the roots’ equation back as [tex]\displaystyle \large{x+\alpha =0}[/tex]

Our points or roots are given, therefore:

If x = -1 then x+1=0

If x = 3 then x-3=0

Then multiply x+1 with x-3 because if (x-1)(x+3)=0 then x-1=0 or x+3=0:

[tex]\displaystyle \large{(x+1)(x-3)=0}[/tex]

Convert 0 to y since we want to find a function:

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

Expand the expressions in and simplify to standard form:

[tex]\displaystyle \large{y=x^2-3x+x-3}\\\displaystyle \large{y=x^2-2x-3}[/tex]

Therefore, the equation is [tex]\displaystyle \large{y=x^2-2x-3}[/tex]

__________________________________________________________

Summary

If we are given the points [tex]\displaystyle \large{(\alpha ,0)}[/tex] and [tex]\displaystyle \large{(\beta ,0)}[/tex] with wideness of the graph or a-value = 1 then the parabola equation is:

[tex]\displaystyle \large{y=(x-\alpha )(x-\beta )}\\\displaystyle \large{y=x^2-\beta x-\alpha x+\alpha \beta }\\\displaystyle \large{y=x^2-(\beta +\alpha )x+\alpha \beta }[/tex]

__________________________________________________________

Others

If you have any doubts about my answer, explanation or this question, do not hesitate to let me know in the comment!


Related Questions

help me please i so need help

Answers

Answer:

9

It is 9 because 9 is the only number that multiplied by itself is 81.

9, these are all referring to the square root of a number that is a perfect square. 2 x 2 = 4, 3 x 3 = 9, 4 x 4 = 16, 9 x 9 = 81.

A bakery made 100 donuts. In the display case, 40/100 were chocolate,

3/10 were glazed, and the rest were cinnamon. Which fraction of the donuts were cinnamon?



A.30/100

B.43/100

C.57/100

D.70/100

Answers

Answer:

Step-by-step explanation:

57 of them were cinnamon.

Explanation:

100-40 = 60 and 3 of those were glazed so that leaves us with 57

C because there’s 57 cinnamon and there’s 57 out of that 100 so 57/100

George and Sarah were building a cone-shaped sand castle. after some time, the diameter of the sand shaped cone was 12 in. and the height was 14 in. what is the approximate volume of the sand cone rounded to the nearest hundreth? (show your work. remember you can draw a picture to help you solve the problem). label your answers with the correct units. use 3.14 to approximate pi answer:

they kept adding sand, and ten minutes later the volume of the sand cone had increased by 30%. what is the approximate volume of the sand cone now? label your answers with the correct units. (show your work) use 3.14 to approximate pi answer:

Answers

Answer:

why you delete my answer before question

help me plssss ‼️‼️‼️

Answers

teddy bears = 80

hope it helps..!!!

Which values from the set {0, 12, 2.5, 4} make the inequality 8g < 4 true?

a.0
b.1/2
c.2.5
d.4

Answers

Answer:

a. 0

Step-by-step explanation:

Which values from the set {0, 12, 2.5, 4} make the inequality 8g < 4 true?

Our inequality:

8g < 4

Substitute each values from the set {0, 12, 2.5, 4} for g, to find which value makes the inequality true.

For 0:

8g < 4

8(0) < 4

0 < 4

This statemen is true, because 0 is less than 4

For 12:

8g < 4

8(12) < 4

96 < 4

This statemen is false, because 96 is NOT less than 4

For 2.5:

8g < 4

8(2.5) < 4

20 < 4

This statemen is false, because 20 is NOT less than 4

For 4:

8g < 4

8(4) < 4

32 < 4

This statemen is false, because 32 is NOT less than 4

Hope this helps!

If RV=w and SU=w–30, what is the value of w?

Answers

Answer:

w = 60

Step-by-step explanation:

the midsegment SU is half the measure of side RV , then

SU = [tex]\frac{1}{2}[/tex] RV , so

w - 30 = [tex]\frac{1}{2}[/tex] w ( multiply through by 2 to clear the fraction )

2w - 60 = w ( subtract w from both sides )

w - 60 = 0 ( add 60 to both sides )

w = 60

Can someone help me please

Answers

Both lines would be the same length.

4x-6 = 50

Add 6 to both sides:

4x = 56

Divide both sides by 4:

x = 14

Show that among all rectangles with area a the square has the minimum perimeter

Answers

Answer:

Step-by-step explanation:

c) d) When 3 is subtracted from the number, the remainder is 5.​

Answers

Answer:

so the equation would look like this, x - 3 = 5

the number or x = 8

Step-by-step explanation:

8 - 3 = 5

Hope this helps! :)

The area of a circle is 144 in 2. What is the circumference, in inches? Express you answer in terms of pi.

Answers

Answer:

24π inches

Step-by-step explanation:

The area of a circle is denoted by: , where r is the radius. Here, we know that the area is A = , so we can plug this in to find r:

A = [tex]\pi r^{2}[/tex]

[tex]144\pi = \pi r^{2}[/tex]

[tex]r^{2}[/tex] = 144

r = 12

The circumference is denoted by: , where r is the radius. We've found the radius so just plug 12 in for r:

Thus, the circumference is 24π inches.

Hope this helps!

Correct Question :

The area of a circle is 144π in². What is the circumference, in inches? Express your answer in terms of pi.

[tex] \: [/tex]

Step-by-step explanation:

Before finding the circumference of the circle, we have to find the radius of it.

We already know that,

[tex] \longrightarrow \qquad{ \underline {\boxed{ \pmb{ \mathfrak{ \pi r{}^{2} = \: \: Area_{(circle)}}}}}} \: \: \bigstar \\ \\ [/tex]

So, using this formula we'll find the radius and now we'll substitute the given values :

[tex] \longrightarrow \qquad{ \sf{ \pi \times r{}^{2} = \: 144 \pi }} \\ \\[/tex]

Cancelling π from both sides we get :

[tex]\longrightarrow \qquad{ \sf{ \cancel\pi \times r{}^{2} = \: 144 \cancel\pi }} \\ \\[/tex]

[tex]\longrightarrow \qquad{ \sf{ r{}^{2} = \: 144 }} \\ \\ [/tex]

[tex]\longrightarrow \qquad{ \sf{ r{}^{} = \: \sqrt{144} }} \\ \\ [/tex]

[tex]\longrightarrow \qquad{ \sf{ \pmb{ r{}^{} = \: 12 }}} \\ \\ [/tex]

So,

The radius of the circle is 12 inches.

[tex] \\ [/tex]

Now we'll find the circumference of the circle :

[tex] \\{ \longrightarrow \qquad{ \underline {\boxed{ \pmb{ \mathfrak{ \: \: Circumference_{(circle)} = 2 \pi r}}}}}} \: \: \bigstar \\ \\ [/tex]

Now, we'll substitute the required values in the formula :

[tex] \\ { \longrightarrow \qquad{ \sf{ \: \: Circumference_{(circle)} = 2 \times \pi \times 12}}} \: \: \\ \\ [/tex]

[tex]{ \longrightarrow \qquad{ \sf{ \: \: Circumference_{(circle)} = 2 \times 12 \pi }}} \: \: \\ \\ [/tex]

[tex]{ \longrightarrow \qquad{ \sf{ \pmb{ \: \: Circumference_{(circle)} = 24 \pi }}}} \: \: \\ \\ [/tex]

Therefore,

The circumference of the circle is 24π inches

For water to be a liquid, its temperature must be within 50 Kelvin of 323 Kelvin. Which equation can be used to determine the minimum and maximum temperatures between which water is a liquid?

|323

Answers

Answer:

its 323 so you were right :) if 323 is your answer lol

Step-by-step explanation:

abs(T-50)=323 Where T is in degrees Kelvin.

abs () means absolute value.

So T=323 plus or minus 50

Which of the following notes is G?

Answers

G in bass clef is the answer D!

Actually help PLSS
(will give brainliest)

Answers

Let's see point E in its original position: (3.-4)

Now lets transform the point (x,y) -->  (x + 8, y +5)

   

               (3, -4) --> (3 + 8, -4 + 5) --> (11, 1)

Therefore coordinate E's new position is (11, 1)

Hope that helps!

             

Which expression is equivalent to x + 11?
11 x
11 + x
11 - x
- x + 11

Answers

Answer:

11 + x

Step-by-step explanation:

x + 11 can be reversed as 11 + x and it would still mean the same thing.

11x means 11 * x so does not match

11 + x and x + 11 same this is correct answer tho

last two are also same  11 - x  and -x +11

Please help, I and I also need a thorough explanation, I don't understand this

Answers

Answer:

See below ↓

Step-by-step explanation:

Solve for x.

2.1.1

px + qx = ax (p + q) = ax = a / (p + q)

2.1.2

2x² - 5x + 2 = 02x² - 4x - x + 2 = 02x(x - 2) - 1(x - 2) = 0(2x - 1)(x - 2) = 0x = 1/2, 2

2.1.3

[tex](\frac{1}{2} )^{3x+1}[/tex] = 32[tex]2x^{-3x-1} = 2^{5}[/tex]-3x - 1 = 5-3x = 6x = -2

I can only answer 3 questions together at maximum so kindly post the rest of your questions 3 at a time separately.

Hope this helped~

Answer:

x = a/(p+q)

x = 2 or x = 1/2

x = -2

m≤ -1 or m<4

-1 , 0 , 1 , 2 and 3.....................since : -1 ≥ m < 4.

x = -3 and y = 9.

Step-by-step explanation:

The first one is just making x to be the subject of the formula by factorising p and q. Then dividing both sides by (p + q).

px + qx = a........................... x (p + q) = a............divide sides by ( p+q) to get the expression.

Solve quadratically for the second one.

For the third one, apply the laws of indices to work out.

32 = ( 1/2)^-5..............so, ( 1/2)^3x + 1   = ( 1/2)^-5.......Drop the base numbers since they are common.

3x + 1 = -5.........then solve to get x as -2.

For the fourth one, we solve for m by separating it into 2.

the first one is: -11 ≤ 3m - 8.

the second one: 3m - 8 < 4

then solve like a normal equation but maintain the inequality signs.

For the integral values, you'll get them from the answers because the answers are a range

The last one you solve simultaneously either by substitution or elimination method.

HOPE THIS HELPS

please solve this question faaaast​

Answers

Answer:

300-400

Step-by-step explanation:

The first step is finding the total of the data we have. So, we take 5 + 10 + 15 + 20 + 25 + 15 + 10 which equals 80.

The median is the middle point of all the data. If it's an odd number, you can calculate the median with the equation (n+1) / 2, plugging in the total amount of data for n.

When it's an even number though, there is no one middle point since the data splits evenly in 2, so we have to use 2 equations: n/2 & (n/2) + 1. Then, we find the average of those two data points. (Although, you don't have to do that for this particular question).

When we plug 80 in for n in both of these equations, we get 40 and 41.

To where this is in the question, we have to count up from the bottom of the chart. 1-5 is below 100, 6-15 is 100-200, 16-30 is 200-300, and 31-50 is 300-400.

Since 40 and 41 are between 31 and 50, the answer is 300-400.

Hope this helps! :)

please help i am confused.

Answers

Answer:

87.5 percent

Step-by-step explanation:

80 passed the first, 70 passed the second. 7/8 passed both. 7/8 as a percentage is 87.5.

Answer:

C. 87.5%

Step-by-step explanation:

[tex]P(A|B)[/tex]

this is what you are trying to find.

P(A | B) can be found by dividing the percentage who passed both, by the percentage who passed the first.

70/80 = 0.875

multiply by 100 to get percentage instead of decimal

87.5

Write the equation of a line in slope-intercept form that is parallel to y = 2x and goes through the point (1, 9).

this is geometry

Answers

Give me more details
So I can help you

Answer:

the answer is y = 2x + 7

Step-by-step explanation:

for it to be parallel has to have the slope

What is the length of the hypotenuse of the triangle?


Triangle A B C. Side A C is 7 feet and side C B is 4 feet. Hypotenuse A B is unknown.
StartRoot 22 EndRoot ft
StartRoot 33 EndRoot ft
StartRoot 57 EndRoot ft
StartRoot 65 EndRoot ft

Answers

Answer:

The last answer [tex]\sqrt{65}[/tex]

Step-by-step explanation:

[tex]7^2+4^2 = 65[/tex]

The formula to find it is [tex]a^2+b^2=c^2[/tex]

so [tex]\sqrt{65}[/tex] is correct

Answer:

√65 ft (Option D)

Step-by-step explanation:

This is Right Angled Triangle.

We'll solve this using the Pythagorean Theorem.

AC = 7ft which is the Base.

BC = 4 ft which is the Perpendicular.

AB is the Hypotenuse.

We know that,

[tex]{ \longrightarrow \pmb{\qquad \: (AB) {}^{2} = (AC) {}^{2} + ( BC) {}^{2}}}[/tex]

[tex]{ \longrightarrow \sf{\qquad \: (AB) {}^{2} = (7) {}^{2} + ( 4) {}^{2}}}[/tex]

[tex]{ \longrightarrow \sf{\qquad \: (AB) {}^{2} = 49 + 16}}[/tex]

[tex]{ \longrightarrow \sf{\qquad \: (AB) {}^{2} = 65}}[/tex]

[tex]{ \longrightarrow \sf {\pmb {\qquad \: AB}}} = \pmb{ \frak{\sqrt{65}}}[/tex]

Therefore,

The length of the Hypotenuse (AB) is √65 ft

Taylor's family took a road trip to Mount Rushmore. Taylor slept through the last 21% of the trip. If Taylor fell asleep after they had travelled 711 miles, what was the total length of the trip?

Answers

100-21= 79
711=79%
711/1=79/100
711/79=9
9x100=900

the trip was 900 miles all together. you can check if your answer is right by multiplying 900 by 0.79. If it comes out to 711, you are right.
Find attached the solution

how many solutions are there to the system of equations graphed below if the lines are parallel

Answers

Answer:

your answer would be zero

Step-by-step explanation:

Parllel lines never crosses or intercept, which means they have 0 solutions

Find the diameter when the circumference is 47.1 in

Answers

C = pi x d

3,14 x d = 47,1

d = 15

Last month, luke spent $1,300 on his mortgage (home loan payment), $320 for food, $280 on entertainment, $275 for his car payment, $60 on car insurance, and $75 on clothing. what was the difference for the month between his fixed expenses and variable expenses? brainly

Answers

Variable expenses: food, entertainment, and clothing

Fixed Expenses: mortgage, car payment, car insurance
1635 - 675 = 960.

Choose the student with the correct answer. Pls Help ;-;

Answers

Answer:

Frida

Step-by-step explanation:

y = 1000(2)^x

Mrs. Smith is saying that the number of termites will double each week, and Mr. Smith is saying that the number of termites will increase by 100% each week.

Let's just look at (2)^x. If we substitute numbers for x, we get:

x = 1 ⇒ 2x = 2 ⇒ 4 x = 3 ⇒ 8 x = 4 ⇒ 16x = 5 ⇒ 32x = 6 ⇒ 64x = 7 ⇒ 128

We can see that the output number doubles by 2, or in other words, increases by 100% of its value.

Therefore, Frida is correct in thinking that both Mr. and Mrs. Smith's interpretations are correct.

Using the BOX and WHISKER above, what is the LOWER QUARTILE of the information?

Answers

Answer:

Lower Quartile is 8 according to the diagram.

Find the circumference and the area of a circle with radius 4 ft

Answers

Answer:

C≈25.13ft

Step-by-step explanation:

C=2πr=2·π·4≈25.13274ft

HELP MEEEEEEEEEEEEEEEE

Answers

Surface area formula : B x H
So multiply 6 1/2 x 10 4/5

The answer is 351/5 or 70.5

marks obtained by the students are 12,16,14,13,19 and x . If their average marks is 15. find the value of x.
step by step
process by process
needed answer
making them as a brainlists ​

Answers

Answer:

x = 16

Step-by-step explanation:

Given:

Number of students = 6Average mark = 15

Therefore, total marks = 15 × 6 = 90

To find the value of x, add up the individual marks:

12 + 16 + 14 + 13 + 19 + x = 74 + x

Now equate this to the total number of marks found previously:

74 + x = 90

Solve for x:

⇒ 74 + x - 74 = 90 - 74

⇒ x = 16

Therefore, the value of x is 16.

There are 12 tomato plants for which 75 < h < 85
One of the tomato plants is selected at random.
Find an estimate for the probability that this tomato plant has a height greater than
82.5 cm

Answers

The histogram is an illustration of a discrete probability, and the probability that this tomato plant has a height greater than 82.5 cm is 0.40

How to estimate the probability?

The histogram is given such that the distribution of the plant heights is:

75 < h ≤ 85

To estimate the probability that this tomato plant has a height greater than 82.5 cm, we make use of the following formula

P(h >82.5) = P(85)

From the histogram, we have:

P(85) = 24/60

Evaluate

P(85) = 0.40

Substitute P(85) = 0.4 in P(h >82.5) = P(85)

P(h >82.5) = 0.40

Hence, the estimated probability is 0.40

Read more about probability at:

https://brainly.com/question/251701

Find the value of the unknown angle x.


The diagram is not drawn to scale.

Please answer. Thank you!

Answers

Answer:

x = 40°

Step-by-step explanation:

This is a quadrilateral. A quadrilateral is a plane figure that has four sides or edges, and also has four corners or vertices.

The interior angles of a simple quadrilateral ABCD add up to 360 degrees of arc.

Answer:

Angle x = 40°

Step-by-step explanation:

All angles of any quadrilateral sum up to 360°.

So here, already measure of 3 angles are given.

So if we add up all angles + Angle x then it sums up to 360°.

So, the following steps will lead you to the answer:

73° + 157° + 90° + Angle x = 360°

(Now add up the measure of the three given angles)

320° + Angle x = 360°

(Now, through transposition moves 320° to the RHS) (Remember when transposing the signs change)

Angle x = 360° - 320°

Finally,

Angle x = 40°

Hope it helps!!!

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