(1)/(4p)(x-h)^(2)+k=0 Multiply the equation by 4p. Explain how different values of k affect the number of zeros of the polynomial. Consider k > 0, k = 0, and k < 0. Assume p > 0.​

Answers

Answer 1

Answer:

Step-by-step explanation:

Assume that  and multiply the equation  by 4p. Then you obtain the equation (x-h)^2+4pk=0.

1) If k>0, then 4pk>0 and the equation does not have real solutions and there is no zero.

2) If k=0, then 4pk=0 and . There is one solution x=h and there is one zero.

2) If k<0, then 4pk<0 and the equation  has two different solutions and there are two zeros.

Answer 2

Answer:

Given equation:

[tex]\frac{1}{4p} (x - h)^2 + k = 0[/tex]

Multiply this by 4p to get:

(x - h)² + 4pk = 0

Rewrite this as:

(x - h)² = 4pk

1) If p > 0 and k < 0

(x - h)² < 0, then no real solutions as left side is always positive

2) If p > 0 and k = 0

(x - h)² = 0, then x = h, one solution = 1 zero

3) If p > 0 and k > 0

(x - h)² > 0, then there 2 real solutions = 2 zeros:x = h ± 2[tex]\sqrt{pk}[/tex]

Related Questions

​Find the probability that first marble picked is green and second marble picked is red.
​Write your result as a percentage.


Answers

Since there’s 6 marbles and there’s 3 greens and 2 reds, we’re finding P(A and B). Where P(A) is first marble picked is green, and P(B) is second marble picked is red.

P(A) = 3/6

(Because the first marble as already been picked there’s 5 marbles left) so:

P(B) = 2/5

Now we have to find the probability of A and B

P(A and B) = 3/6 • 2/5 = 1/5 = 20%

Answer:

20%

Step-by-step explanation:

3 green, 1 brown, 2 red

3 + 1 + 2 = 6

Total: 6

The probability of picking a green one is 3/6 or 1/2.

———————————————————————

2 green, 1 brown, 2 red

2 + 1 + 2 = 5

New total: 5

The probability of picking a red one is now 2/5.

———————————————————————

First, we multiply them by each other.

2/5 x 1/2 = 1/5

Next, we convert 1/5 to a percentage to get our final answer.

1/5 x 20 = 20/100, which is 20%.

So our final answer is 20%.

Identify the equation of the circle B that passes through (5,1) and has center (3,0).

Answers

Answer:

Are you saying look for the slope? because if so can help

Step-by-step explanation:

Answer:   (x − 3)2 +  y2 = 5

a. (x + 3)2 +  y2 = 5

b. (x − 3)2 +  y2 = 25

c. (x − 3)2 +  y2 = 5

d. (x + 5)2 + ( y + 1)2 = 25

Step-by-step explanation:

Begin by determining the length of the radius for the circle. A radius is a line segment from the center of the circle to any point on the circle. Find the length of the radius using the Distance Formula.

r= √(x2 − x1)2 + (y2 − y1)2

Substitute the given values for the center of the circle and the point on the circle into the distance formula and solve for r.

r= √( 5− 3)2 + (1 − 0)2

= √22 + 12

= √4 + 1

= √5

So, the length of the radius is √5 units.

The equation of a circle with center (h, k) and radius r is (x − h)2 + (y − k)2 = r2. Substitute the value for the radius and the coordinates of the center of the circle into the equation.

(x − 3)2 +(y − 0)2 = (√5)2

Simplify.

(x − 3)2 + y2 = 5                                                                                            Therefore, the equation of the circle B that passes through (5, 1) and has center (3, 0) is (x − 3)2 +y2 = 5.

I need help, please!!!!!!!!!!!!

Answers

Answer:

Its d!!!!!! Welcome!

Step-by-step explanation:

How many different triangles can you make if you are given these two lengths for sides?

Answers

The number of triangles is an illustration of Triangle Inequalities theorem

There are infinitely many triangles that can be made given two side lengths

How to determine the number of triangles?

The side lengths of two sides are given as 18 inches and 25 inches.

Assume the third side of the triangle is x

Using the Triangle Inequalities theorem, we have:

a+b > cb+c > a,c+a > b

So, we have:

x +18 > 25

x > 7

x + 25 > 18

x > -7.

18 + 25 > x

x < 43.

Ignore the negative value.

So, we have the solution set to be 7 < x < 43.

This means that the third side can take any value between 7 < x < 43.

Hence, there are infinitely many triangles.

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[tex]f(x)=1/3(4-x)² what is the value of f(16)[/tex]

Answers

Answer:

wheneveryouseeanxonthe

rightputa16thatwhatf(16)

means.

f(16)=

3

1

(4−16)

2

f(16)=

3

1

(−12)

2

f(16)=

3

1

(144)

f(16)=48

[isyouranswer]

Step-by-step explanation:

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If i have 23 liters in a bucket and i pour it into 4 smaller buckets, how many liters will each bucket have?? PLS HELP

Answers

5.75 I THINK I’m not sure

Calculate the value of b.
(b-15)
3b°
(2b + 45°
Diagram not drawn accurately​

Answers

Answer:

b = 30

Step-by-step explanation:

The sum of the 2 angles above the line will equal the angle below the line

3b + b - 15 = 2b + 45

4b - 15 = 2b + 45 ( subtract 2b from both sides )

2b - 15 = 45 ( add 15 to both sides )

2b = 60 ( divide both sides by 2 )

b = 30

The ending time is 8:22 P.M. and the elapsed time is 2 1/4 hours what’s the starting time?

Answers

Answer:

6:07

Step-by-step explanation:

8:22 minus 2 hours is 6:22, 1/4 an hour is 15 minutes so 22 minus 15 is 7, leading to the answer of 6:07 being your start time.

construct the linear equation for the table

Answers

You can use demos graphing calculator it will help you a lot

Can you guys help me I’m a big stuck on this one ?!

Answers

Answer:

the first one

Step-by-step explanation:

AC and AE because it look like it’s going in a diff angle

Volume of Cylinders and Prisms

Answers

So what is the question?

Formula for finding cylinder:

π • r

This will find the area of the Base (B)

Then you multiply by the height given.

V= π• r • h

Just plug in the numbers

Formula for a rectangular prism:

Find the length • width

This is the area or base area (B)

Then multiply by the h

V= l•w•h

Hope this helps

8 On a map, a trapezoidal piece of farmland has base lengths of 1.25 inches and 1 inch, and a height of 1.1 inches. The scale on the map is 1 inch = 100 yards. What is the actual area of the farmland?

Answers

formula 3.35 times something

Find the surface area of the figure.
8 ft
19 ft
14 ft
12.1 ft
5 ft

Answers

Answer:

132.00

Step-by-step explanation:

The surface area of the composite figure is S = 706.4 feet²

What is a trapezoid?

The Trapezoid is a 4 sided polygon. Two sides of the shape are parallel to each other and they are termed as the bases of the trapezoid. The non-parallel sides are known as the legs or lateral sides of a trapezoid.

There are three types of trapezoids , and those are given below:

a) Isosceles Trapezoid

b) Scalene Trapezoid

c) Right Trapezoid

The area of the Trapezoid is given by

Area of Trapezoid = ( ( a + b ) h ) / 2

where , a = shorter base of trapezium

b = longer base of trapezium

h = height of trapezium

Given data ,

Let the area of the figure be S = 2 ( area of trapezium ) + 2 ( area of opposite rectangles ) + ( area of smaller rectangle ) + area of larger rectangle

On simplifying , we get

2 ( area of trapezium ) = ( a + b ) x h

2 ( area of trapezium ) = ( 19 + 5 ) x 12.1

2 ( area of trapezium ) = 290.4 feet²

Now , 2 ( area of opposite rectangles ) = 2 ( 14 x 8 )

2 ( area of opposite rectangles ) = 224 feet²

Area of smaller rectangle = 5 x 8 = 40 feet²

Area of larger rectangle = 8 x 19 = 152 feet²

Therefore , S = 290.4 feet² + 224 feet² + 40 feet² + 152 feet²

S = 706.4 feet²

Hence , the area of the figure is S = 706.4 feet²

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Is it
A.)A=35,B=34
B.)A=28,B=34
C.)A=35,B=28
D.)A=34,B=28


Answers

Answer:

D. A=34, B=28

Step-by-step explanation:

In the bulletin points, it says that seconds 3-5 are decreasing. That means that those heights can't be higher than second 2 (34). The only option that works is option D.

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

Option A is incorrect because it starts with 35ft which is higher than second 2(34) so that is automatically wrong.

Option B is incorrect because it is increasing instead of decreasing.

Option C is incorrect for the same reason as Option A: it starts with 35ft.

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

Therefore, the only correct option is Option D.

Have a nice day!!

If LADC measures 61°, what does ZABC measure?
А
С
B
D

Answers

Answer:

122

Step-by-step explanation:

61 x 2 = 122

CAN YHU MARK ME BRAINLIST

The measurement of angle ABC is 122°.

What are the properties of the circle?

The circumference, which is the distance around the object, the diameter, which is the length of a circle measured from one end to the other and passing through its center, and the radius, which is equal to half of the diameter, are the three key characteristics.

The general coordinate equation of a circle is:

(x-h)² + (y - k)² = r²

Where,(h, k) is the center of a circle, "r" is the radius of the circle.

Given, a figure of the circle that gives the center of the circle is B.

Since, the Centre angle is twice the size of the angle of the circumference, made by the same arc.

Since both angles, ∠ABC and ∠ADC are made by the same arc AC.

Thus,

The angle made on the center = 2 * the angle made on the circumference,

The angle made on centre = 2 * 61

The angle made on center = 122°

Therefore, The measurement of angle ABC is 122°.

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what is the highest fractions 2/4 5/6 3/2 1/9 4/5 8/2 ​

Answers

Answer:

8/2

eight halves

Step-by-step explanation:

please mark this answer as brainliest

Is -2 x 4 positive or negative? please help i have 19 missing assignments ​

Answers

Answer:

-8

Step-by-step explanation:

a negative number multiplied by a positive one gives as a result a negative number

-2 x 4 = -8

The two figures are similar. Complete sentences
a) Write the similarity statement.
b) Is the image of the dilation a reduction or an enlargement of the original figure? Explain.
c) What is the scale factor? Explain

Answers

Answer:

a)ABC ≅ A'B'C' (SSS) b) Enlargement c) Scale factor = 4

Step-by-step explanation:

a) ABC ≅ A'B'C' (SSS)

b) The figure is going through an enlargement, this is evident as the figures have a scale factor of 4. If we were to put them into a fraction like this -

6/24=12/48=15/60

The figures are getting bigger, so they are going through an enlargement.

c) To find the scale factor of like done above, we could put them into a ratio.

6/24=12/48=15/60

Which would result in the scale factor of 4.

A company sells $982 worth of
merchandise this month. This is $40
more than twice the amount
they sold last month. Write a equation
to determine how much they sold
last month.

Answers

Answer:

2x+40=982

Step-by-step explanation:

I will mark the brainiest!

Answers

Answer:

B: 375 ft^2

Step-by-step explanation:

20 x 15 + 10 x 15/2 = 375

Personal Finance
Which of these statements is false?
All states have state income taxes.
Different states have different tax rates.
Some states consider some income to be tax free.
Some states tax all taxable income at the same rate; they have a flat tax rate.

Answers

Answer:

Some states consider some income to be tax free. this statement is false

it would probably go with one of the first 2. they sound opposite of each other. probably go with the first 1?

sorry if I'm wrong

Marty has read 32% of his 400-page library book. How many pages has Marty read?

Answers

Answer:

128 pages

Step-by-step explanation:

[tex]0.32*400[/tex]

[tex]=128[/tex]

In total, Marty had read 128 pages of his book.

Find the surface area of the cube and show your work please : )

Answers

Answer:

150 cm.

Step-by-step explanation:

There 6 squares in a cube.

**SQUARES HAVE EQUAL SIDES.**

To find the area of an individual square, multiply the side length by itself twice. (x^2)

The side lengths of the squares are 5.

5 x 5 = 25.

25 is the area of each individual square.

Since there are 6 squares in total, multiply 25 by 6.

25 x 6 = 150.

Therefore, 150 cm is the surface area of the cube.

Write the quotient as a mixed number. 99 ÷ 5 = 19 R4
PLEASE HELP :(

Answers

Answer:

19 4/5

Step-by-step explanation:

99 = 5*19 + 499/5 = 19 + 4/599/5 = 19 4/5

Answer:

Solution given

99/5=19 4/5 is your quotient in mixed number.

Abigail's decorating business charges a initial fee of $100 plus an additional $13.50
for every hour worked. How much would Abigail earn for 3 hours worked?
O $113.50
O $127.50
O $154.00
O $140.50

Answers

Answer: $140.50

Step-by-step explanation: Just multiply $13.50 by 3 then add the $100 initial fee.

what expressions from the table are equivalent to that expression ?

Answers

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

The applicable rules of exponents are ...

  [tex]\displaystyle\sqrt[n]{x^m}=x^{\frac{m}{n}}\\\\(x^a)^b=x^{ab}\\\\(xy)^a=x^ay^a[/tex]

Yes
Yes
No
Yes
Yes
This is the order. I got it correct.

Someone answer this please

Answers

Answer:

x = -47/3

Step-by-step explanation:

R = 3x + 9y

7 = 3x + 9(6)

7 = 3x + 54

-47 = 3x

x = - 47/3

Can't be reduced because 47 is prime

Answer:

x=  -47/3

Step-by-step explanation:

So the information we already have is

7 = 3x + 9 * 6

9 * 6 = 54

now it is

7 = 3x + 54

The equation can also be

3x + 54=7

First subtract 54 from both sides

3x + 54 - 54= 7 - 54

3x= -47

Then divide both sides by 3

3x/3= -47/3

x= -47/3

Which equation represents a circle with a center point of (-2,3) that passes through the point (4, -3)?

PLEASE HELP ASAP IM GIVING BRAINLIEST

Answers

Answer:

[tex]A) (x+2)^{2} +(y-3)^{2} =72[/tex]

Step-by-step explanation:

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

[tex]=\sqrt{6^{2} +6^{2} } =6\sqrt{2 }[/tex]

[tex]equation:[/tex]

[tex](x+2)^{2}+(y-3)^{2} =(6\sqrt{2}^{2})\\[/tex]

[tex](x+2)^{2}+(y-3)^{2} =72[/tex]

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

hope it helps...

have a great day!!

The equation represents a circle is option (A) (x+2)^2 +(y-3)^2 = 72 is the correct answer.

What is a circle?

A circle is a collection of all points in a plane which are at a constant distance from a fixed point. A circle is a round-shaped figure that has no corners or edges.

For the given situation,

The center of the circle, (h,k) = (-2,3)

The point on the circle, (x,y) = (4,-3)

The radius of the circle is

[tex]r=\sqrt{(h-x)^{2} +(k-y)^{2} }[/tex]

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

⇒ [tex]r=\sqrt{6^{2}+6^{2} }[/tex]

⇒ [tex]r=\sqrt{72}[/tex]

The formula of equation of circle is

[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]

The circle has the center (h,k) = (-2,3) and radius is √72,

⇒ [tex](x-(-2))^{2}+(y-3)^{2}=(\sqrt{72} )^{2}[/tex]

⇒ [tex](x+2)^{2}+(y-3)^{2}=72[/tex]

Hence we can conclude that the equation represents a circle is option (A) [tex](x+2)^{2}+(y-3)^{2}=72[/tex] is the correct answer.

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What is the measure of the missing angle

Answers

Answer:

dont you just subtract 90-61 to get 29 since a triangle is 90 degrees

Liz flips a coin 30 times. Coin lands heads up 12 times and tails of 18 times. Each statement.

Answers

Answer:

Step-by-step explanation:

Its 50% for the first one

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