1. Find the factored form of f(x) given it has x-intercepts (-3,0) and (4,0) and f(1)= -6. 2. Find the equation for f(x) given that it has roots of 2 and -3 and f(0)=12. Please someone help

Answers

Answer 1

Answer:

1) f(x) = 0.5*(x + 3)*(x - 4)

2) f(x) = -2*x^2 - 2*x + 12

Step-by-step explanation:

Wen we have a quadratic function like:

f(x) = a*x^2 + b*x + c*x

And it has roots at x1 and x2, we can write the function in the factored form as:

f(x) = a*(x - x1)*(x - x2)

then:

1) we have x-intercepts at: (-3, 0) and (4, 0) (then the roots of this function are x = -3 and x =4) and we know that f(1) = -6

we have:

x1 = -3

x2 = 4

then we can write f(x) as:

f(x) = a*(x - (-3))*(x - 4)

f(x) = a*(x + 3)*(x - 4)

Where a is a real number.

and now we can use the fact that f(1) = -6

then:

f(1) = a*(1 + 3)*(1 - 4) = -6

       a*4*(-3) = -6

       a*-12 =  -6

       a = -6/-12 = 1/2 = 0.5

Then the function is:

f(x) = 0.5*(x + 3)*(x - 4)

2) Now we have roots x = 2 and x = .3

Then:

x1 = 2

x2 = -3

Then this function is something like:

f(x) = a*(x - 2)*(x - (-3))

f(x) = a*(x - 2)*(x + 3)

Now we know that f(0) = 12.

then:

f(0) = a*(0 - 2)*(0 + 3) = 12

         a*(-2)*3 = 12

          a*(-6) = 12

          a = 12/-6 = -2

f(x) = -2*(x - 2)*(x + 3)

And we do not want this one written in factored form, so we can just distribute the multiplications to et:

f(x) =  -2*(x - 2)*(x + 3) = (-2*x + 4)*(x + 3) = -2*x^2 + 4*x - 6*x + 12

f(x) = -2*x^2 - 2*x + 12


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Answer:

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A storekeeper increased the price of hats by 5%.

Write an equation to calculate the increase of the total

cost, c, when the price of a hat is p dollars.

Select all that apply.

A c 1.50p

BC-,95p

cc 1.05p

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Ec-(1 + .05)p

Answers

Answer: c = 1.05p

Step-by-step explanation:

Price of the hat = p

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The measure of the second angle is 15 degrees more then the measure of the 1st angle. The measure of the 3rd angle is 45 degrees more than the measure of the 1st angle. Find the measures of the interior angles in the triangle.

Answers

Let the first angle be x

So, second angle = (x+15)°

and third angle= (x+ 45)°

Now,

x+ (x+15) + (x+45)= 180°. ( Triangle sum property)

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Hope it helps you. Please mark as brainliest if it does.

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Answer:

Please refer to the attached image.

LeBron bought a 8-pack of Powerade for $7.68. What is the unit rate for one bottle of Powerade?

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Answers

Answer:

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Step-by-step explanation:

All of them cannot be simplified.

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The masses of four vehicles and the net forces acting on them as they enter a highway are recorded in the table below. Vehicle Mass (kg) Force (N) Sedan 1400 5250 SUV 1900 5250 Truck 2100 5250 RV 2500 5250 Which vehicle has the greatest acceleration as it enters the highway?

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Answer:

if you use Newton's 2nd rule:

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Leslie purchased a new bar of soap. Three days after she originally used
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Assuming that Leslie uses the same amount of soap daily (and that she
used soap daily), write an equation that shows that amount of soap
remaining after d days of use. *Hint: slope intercept form and you will
need the slope formula

Answers

Answer:

The equation is:

y= 103 --23d

Step-by-step explanation:

The initial amount was 103 grams.

After one day of use the remaining amount of soap was 80 grams.

So the amount of time he spent in one day was:

Each day Leslie spends 23 grams of soap.

if d represents the number of days elapsed then, the amount of soap "y" that Leslie spends after days is:

y= 103 --23d

HELP!!!!

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Answers

Answer:

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Step-by-step explanation:

Answer:

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Step-by-step explanation:

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Answers

Answer:

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Answer:

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Answers

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Answer:

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Answer:

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i didn't understand what u wrote in choice

The coordinates of the point S of the line RS having midpoint T are found to be (10, -7).

What is mid point?

In geometry, the midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints. It bisects the segment.

here, we have,

The points that are given to us are R(-2,3) and T(4, -2).

The point T is the mid point of the line segment RS.

If A(a, b) and B(c, d) are the two points then the mid point M of the two points will be,

M = ((a+c)/2), ((b+d/2))

So, using the above modified form of section formula we can find the coordinates of the point S.

Assuming point S to be x and y.  

So, putting all the values,

(4, -2) = ((-2+x)/2), ((3+y/2))

Now, solving further, we get,

-1+x/2 = 4

-2+x = 8

x = 10

And,

3 + y = -4

y = -7

So, the coordinates are (10, -7).

To know more about mid point formula, visit,

brainly.com/question/30276996

#SPJ7

Which function matches the graph?
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Answers

Answer:

Its a or c sorry if im wrong

(hope this helps :D hehe)

Step-by-step explanation:

Answer:

Please insert a graph.

Step-by-step explanation:

If you submit a picture of the graph on here, I will see how how I can help.

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Answers

Answer:

no it is not correct

Step-by-step explanation:

it's kind of hard to explain in words so I'm sorry about that

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What is the smaller angle formed by the minute and hour hands at 3:30pm?


[asy]

unitsize(50);

draw(Circle((0,0),1),black+1);

dot((0,0));

for(real i=0;i<360;i+=6){

draw(0.96*(cos(i*pi/180),sin(i*pi/180))--(cos(i*pi/180),sin(i*pi/180)),black+0.5);

};

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draw(0.93*(cos(i*pi/180),sin(i*pi/180))--(cos(i*pi/180),sin(i*pi/180)),black+0.5);

label(string(i/30),0.83*(sin(i*pi/180),cos(i*pi/180)));

};


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draw(0.65*(sin(pi/6*(h)),cos(pi/6*(h)))--(0,0)--0.9*(sin(pi/30*m),cos(pi/30*m)),black+1,Arrows(TeXHead));

draw(anglemark(dir(-90),origin,dir(-15),5));

[/asy]

Answers

Answer:

75 degrees

Step-by-step explanation:

At 3:30, the hour hand is halfway between the 3 and the 4. The minute hand is exactly on the 6.

There are 360/12 = 30 degrees between each of the marked hours. The angle between the hands covers 2.5 of these gaps, so the angle between the hands is 2.5(30) = 75 degrees.

Hope this helps!

The angle between the hands at 3:30 pm is 90°.

What is the angle between the hands of a clock at 3:30 pm?

At that time, one hand points at the 3, and the other hand points at the 6.

Now, there is a rule to transform time into angles.

We know that a clock has 12 hours in a full revolution, and a circle has 360° in a complete revolution.

Then we know that:

12 hours = 360°

Then:

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So each between each number in the clock we have an angle of 30°.

Then, between 3 and 6 (3 hours) we have:

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The angle between the hands at 3:30 pm is 90°.

If you want to learn more about angles, you can read:

https://brainly.com/question/17972372

Solve the system below.
y = x2
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Answers

Answer:

since,

y = 2x and y = –2x + 15

then,

2x = –2x + 15

or, 4x = 15

or, x = 15/4

or, x = 3.75

Also,

y= 2x

= 2*3.75

= 7.5

Hope it helped

All the best!!

Answer:

Step-by-step explanation:

[tex]x^{2} = -2x^{2} +15[/tex]

add [tex]2x^{2}[/tex] to both sides

[tex]3x^{2} = 15[/tex]

divide each side by 3

[tex]x^{2} =5[/tex]

square root each side [tex]\sqrt{x^2} =\sqrt{5}[/tex]

[tex]x= 2.23606794[/tex] or rounded to the nearest hundredth [tex]x=2.24[/tex] or x = ±[tex]\sqrt{5}[/tex]

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