(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.
Answer:
Step-by-step explanation:
Given p>0, multiply the equation by 4p: (1/4p)*(x-h)^(2)+k=0
(x-h)^2+4kp = 0
k>0
4kp>0
(x-h)^2 = -4kp
So x has imaginary roots only. There is no real zeros of the polynomial.
k=0
4kp=0
(x-h)^2 = 0
x=h
So x has one real root and the polynomial has one zero
k<0
4kp<0
(x-h)^2 = -4kp
So x has two real roots and the polynomial has two real zeros.
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.
Subtract 2x2 + 6x – 5 from 7x2 + 3x + 4.
What is 2 to the power of 4 written in expanded form
Answer:
(4)2
4×4=16 or
(2)4
2×2×2×2=16
both are correct ☺️
Step-by-step explanation:
hope it helps you have a good day
4
A student created the function P(t) = 5(1 +4/100)^t to model the population of a town in thousands, t years after 1980. If the student misread the
population in the year 1980 and the correct population in that year was 6,000, what changes should he make in the function?
Change 5 to 6,000
Change 4 to 6,000
Change 5 to 6
O Change 4 to 6
Ο Ο
Answer:
change 5 to 6
Step-by-step explanation:
Three times a number, x, increased by four is equal to five times the number, x. Which equation can be used to solve
for x?
3x+5x4
3x+4-5x
3x +4+5x
3x-4-5x
Answer:
=5x⁴+3x
=-2x+4
=8x+4
=-2x-4
Step-by-step explanation:
hope it's help
A bookshelf has 36 fiction books and 44 non-fiction books. What percentage of the total books are non-fiction?
Answer:
55% of the total books are non-fiction.
Step-by-step explanation:
There are a total of 80 books, and there are 44 non-fiction books among them.
Divide 44 by 80, then multiply by 100 to get the percentage.
(44/80) × 100 = 55%
A cars gas mileage refers to its rate in miles traveled per gallon of gas. Kara's family is thinking about renting a camper that can travel 3 1/2 miles on 1/3 gallon of gas. Kara wants to know the gas mileage of the camper.
Answer: 10 ¹/₂ miles per gallon
Step-by-step explanation:
The gas mileage of the camper refers to the distance (in miles for this question) that the camper can travel on 1 gallon of gas.
The camper can travel 3¹/₂ miles on ¹/₃ gallons so the mileage is:
= Distance traveled/ Gallons used
= 3¹/₂ ÷ ¹/₃
= 7/2 * 3/1
= 21 / 2
= 10 ¹/₂ miles per gallon
What is the situation to 4x^2-25=07
Answer:
x = 2.83
Step-by-step explanation:
Answer:
x=2√2 or x=−2√2
^^Both are correct.^^
Step-by-step explanation:
Let's solve your equation step-by-step.
4x^2−25=7
Step 1: Add 25 to both sides.
4x^2−25+25=7+25
4x^2=32
Step 2: Divide both sides by 4.
4x2 /4 = 32 /4
x^2=8
Step 3: Take square root.
x=±√8
x=2√2 or x=−2√2
brainliest please?
a² . b² in expanded form
Answer:
(a x b)(a x b)
Find the volume of the irregular
figure.
1 cm
2 cm
3 cm
?
cm3
2 cm
1 cm
7 cm
Answer:
252 cm cubed
Step-by-step explanation:
29 cm 3
you multiply 1,2,3 and you get 6 !! and then you do 7,1,2, and you get 14 then you take 6 plus 14 = 20 !!
Can yall please put the formula as well x
Answer:
x = 10°
Step-by-step explanation:
(3x + 88) + (x + 36) + (2x -4) = 180°
6x + 120 = 180°
6x = 60°
x = 10°
The lengths of three ropes are 4 : 5 : 9. If the length of the shortest rope is 20 cm, find the length of the longest rope
What do I do.
500.34 + 4333
Answer:
add them
Step-by-step explanation:
500.34 + 4333 =4833.34
The diagonal of a rectangular tabletop measures 52 inches. If the width is 20 inches, what is the length of the tabletop rounded to the nearest hundredth inch?
See attachment for reply.
Two of the angles in a triangle measure 100° and 53°. What is the measure of the third angle?
Answer:
27*
Step-by-step explanation:
The angles in a triangle will ALWAYS add up to 180*
A gardener digs a flower bed that is 8 meters long and a meter wide. what is the area of the flower bed
8 meters
To calculate area you multiply length x width. So, 8 x 1 = 8
A store made 96 lb of peppermint bark for the holidays. The peppermint bark was split into 3/8 lb portions and boxes. 3/4 of the boxes were sold for $6 each before the holidays. The rest were sold at 2/3 of the pre-holiday price. How much money did the shop receive from the sales of the peppermint bark?
Answer: The shop has received $ 1724 from the sales of the peppermint bark.
Step-by-step explanation:
Given: Total quantity of peppermint bark = 96 lb
Number of [tex]\dfrac38[/tex] portions = [tex]96\div\dfrac38 =96\times\dfrac83=256[/tex]
[tex]\dfrac34[/tex] of boxes = [tex]\dfrac34\times256=[/tex] $192
These were sold for $6 each before the holidays.
i.e. Cost of [tex]\dfrac34[/tex] of boxes = [tex]192\times 6=\$1152[/tex]
2/3 of the pre-holiday price = [tex]\dfrac23\times6=\$9[/tex]
Rest of boxes = 256-192 = 64
Cost of rest of boxes = [tex]9\times64=\$ \ 576[/tex]
Total money received = $1152 + $572
= $ 1724
Hence, the shop has received $ 1724 from the sales of the peppermint bark.
A trapezoid has been rotated 90°
clockwise about the origin. Is it true that
the y-coordinates of the new trapezoid
are the same as the y-coordinates of the
original trapezoid? Explain.
Answer:
yes
Step-by-step explanation:
counterclockwise move it to the quadrant
directly to the left ,which is the second quaurter that means the x value only become negtive
Answer:
90 degree rule
(x,y)=(y.-x)
Step-by-step explanation:
A video game developer wants to know how long it takes people to finish playing their new game. They surveyed a random sample of 13 players and asked how long it took them (in minutes).
Complete question :
A video game developer wants to know how long it takes people to finish playing their new game. They surveyed a random sample of 13 players and asked how long it took them (in minutes).
1235
952
457
1486
1759
1148
548
1037
1864
1245
976
866
1431
Estimate the median time it will take all players to finish this game.
Find the interquartile range for this sample.
Answer:
1148 ; 549.5
Step-by-step explanation:
The ordered data:
457, 548, 866, 952, 976, 1037, 1148, 1235, 1245, 1431, 1486, 1759, 1864
The median value :
1/2 * (n +1)th term
n = 13
1/2 * 14 = 7th term
Median = 1148
The interquartile range :
Q3 - Q1
Q3 = 3/4(n+1)th term
Q3 = 3/4 * 14th term
Q3 = 10.5 th term
Q3 = (10 + 11)th term
Q3 = (1431 +1486) / 2= 1458.5
Q1 = 1/4(n+1)th term
Q1 = 1/4 * 14th term
Q1 = 3.5 th term
Q1 = (3 + 4)th term
Q1 = (866+ 952) / 2= 909
IQR = 1458.5 - 909 = 549.5
Answer:
Median:1054 mins
IQR:751.5
Step-by-step explanation:
Joey and his band have just recorded 14 new songs. The band decides that they want the new songs to form an album. How many ways can the 14 new songs be arranged on the album?
Answer:
87,178,291,200 ways
Step-by-step explanation:
Number of songs = 14
To Form an album with the 14 songs, the number of ways at which the 14 songs can be arranged is obtained by calculating the factorial of the number of songs ;
Number of ways in which the 14 songs can be arranged :
14! = (14 * 13 * 12 * 11* 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) = 87178291200 ways
A 5ft tall girl is standing 13ft from a 15ft tall lamppost. How long is her shadow?
Out of her 5 gigabyte data plan, Debbie has used 37%. How much data does she have left?
Answer:
3.15GB
Step-by-step explanation:
1000MB = 1GB
1000MB*5 = 5000MB
5000/100*37% = 1850MB USED
SO, 5000-1850 = 3150MB = 3.15GB
Heather buys 12 patio chairs for $366. Each chair costs the same amount.
Part A
Which equation represents the best estimate for the cost of each chair?
Part B
What is the exact cost of each chair
Heather also buys 12 patio lights for $63. She estimates the cost of each light to be about $5.
She then calculates the actual cost of each light to be $2.40. Use the drop-down
boxes to explain whether her calculation is reasonable
Factor the expression completely. 60x^4+54x^3 60x 4 +54x 3
Answer:
6x^3 (9x^361 + 10x+9)
Step-by-step explanation:
PLS HELP ME I WILL GIVE BRAIN THINGY
1/4e = 12
help plssss
Answer:
e=48
Step-by-step explanation:
1/4e=12
Multiply both sides by 4;
4*1/4e=12*4
Simplify ;
e=48
Hope this helped!!!
pls help due tonight
Arrange the expressions in increasing order of their values.
< <
Answer:
10⁰×10¹-1¹⁰ < 10⁰×10¹×1¹⁰ < 10⁰+10¹×1¹⁰ < 10⁰+10¹+1¹⁰
Step-by-step explanation:
10⁰×10¹-1¹⁰ = 9
10⁰×10¹×1¹⁰ = 10
10⁰+10¹×1¹⁰ = 11
10⁰+10¹+1¹⁰ = 12
Two angles are supplementary. The larger angle is 6 degrees less than twice the smaller angle. What is the degree measure of the larger angle?
can someone please help me
Answer:
y - 24 = - 7(x + 4)
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 4, 24) and (x₂, y₂ ) = (7, - 53)
m = [tex]\frac{-53-24}{7+4}[/tex] = [tex]\frac{-77}{11}[/tex] = - 7
Using m = - 7 and (a, b) = (- 4, 24 ) , then
y - 24 = - 7(x - (- 4)), that is
y - 24 = - 7(x + 4)