Answer:
k=2
Problem:
if the equation x^2 +(k+2)x+2k=0 has equal roots,then the value of k is ..
Step-by-step explanation:
Since the coefficient of x^2 is 1, we can use this identity to aid us: x^2+bx+(b/2)^2=(x+b/2)^2.
So we want the following:
[(k+2)/2]^2=2k
Apply the power on the left:
(k+2)^2/4=2k
Multiply both sides by 4:
(k+2)^2=8k
Expand left side:
k^2+4k+4=8k *I used identity (x+c)^2=x^2+2xc+c^2
Subtract 8k on both sides:
k^2-4k+4=0
Factor using the identity mentioned a couple lines above:
(k-2)^2=0
Since zero squared is zero, we want k-2=0.
Adding both sides by 2 gives k=2.
A company that manufactures hair ribbons knows that the number of ribbons it can sell each week, x, is related to the price p per ribbon by the equation below.
x = 1,000 − 100p
At what price should the company sell the ribbons if it wants the weekly revenue to be $1,600? (Remember: The equation for revenue is R = xp.)
p = $ (smaller value)
p = $ (larger value)
Given:
The number of ribbons it can sell each week, x, is related to the price p per ribbon by the equation:
[tex]x=1000-100p[/tex]
To find:
The selling price if the company wants the weekly revenue to be $1,600.
Solution:
We know that the revenue is the product of quantity and price.
[tex]R=xp[/tex]
[tex]R=(1000-100p)p[/tex]
[tex]R=1000p-100p^2[/tex]
We need to find the value of p when the value of R is $1600.
[tex]1600=1000p-100p^2[/tex]
[tex]1600-1000p+100p^2=0[/tex]
[tex]100(16-10p+p^2)=0[/tex]
Divide both sides by 100.
[tex]p^2-10p+16=0[/tex]
Splitting the middle term, we get
[tex]p^2-8p-2p+16=0[/tex]
[tex]p(p-8)-2(p-8)=0[/tex]
[tex](p-8)(p-2)=0[/tex]
Using zero product property, we get
[tex]p-8=0[/tex] or [tex]p-2=0[/tex]
[tex]p=8[/tex] or [tex]p=2[/tex]
Therefore, the smaller value of p is $2 and the larger value of p is $8.
The function graphed to the left is
function.
and continues
The curve has
infinitely in one direction.
each
Each y-value is
corresponding x-value.
Answer: There is a circular
Step-by-step explanation:
Answer:
he function graphed to the left is
✔ a square root
function.
The curve has
✔ one distinct endpoint
and continues infinitely in one direction.
Each y-value is
✔ the square root of
each corresponding x-value.
Step-by-step explanation:
A square and an equilateral triangle have the same perimeter. The length of the side of the square os x+10. The length of the side of the triangle os 4x. What is the length of the triangle side
Answer:
20
Step-by-step explanation:
the perimeter of the square and the triangle are the same
4×(x + 10) = 3×4x
4x + 40 = 12x
40 = 8x
x = 5
=>
a triangle side is 4x = 4×5 = 20
find two rational number between 1/6 and 2/3
plz give me the ans
Step-by-step explanation:
the rational numbers between 1/6 and 2/3 are 2/6 ,3/6 .
Answer:
therefore the rational numbers between 1/6 and 2/3 are 2/6 ,3/6 .........
The path of a projectile launched from a 20-ft-tall tower is modeled by the equation y = -5x2 + 40x + 20. What is the maximum height, in meters
reached by the projectile?
Answer:
30.49 m
Step-by-step explanation:
To obtain the maximum height, we solve for the value x when dy/dx = 0.
Since, y = -5x² + 40x + 20
dy/dx = d[-5x² + 40x + 20]/dx
dy/dx = -10x + 40
Since dy/dx = 0,
-10x + 40 = 0
-10x = -40
x = -40/-10
x = 4
Substituting x = 4 into the equation for y, we have
y = -5x² + 40x + 20
y = -5(4)² + 40(4) + 20
y = -5(16) + 160 + 20
y = -80 + 160 + 20
y = 80 + 20
y = 100 ft
Since y is in feet, we convert to meters.
Since 1 m = 3.28 ft, 100 ft = 100 ft × 1 m/3.28 ft = 30.49 m
So, the maximum height, in meters reached by the projectile is 30.49 m
What is the measure of DE?
A) 51
B) 68
C) 85
D) 56
Answer:
Option (B) is correct
Step-by-step explanation:
The figure Jhows the graph of h(x) = px - 3+2 a translation of the parent function
g(x) = v. How is the graph of the parent function translated?
A) Right 3 units and up 2 units
OB) Right 2 units and up 3 units
C) Right 3 units and down 2 units
D) Left 3 units and up 2 units
pls help me in these questions
Answer:
1=85
2=10
3=108
Step-by-step explanation:
Number 1: Calculate each angle...and you know a straight line is 180°. N the interior sum of a quadrilateral is always 360°.
Number2: Use corresponding, alternate and interior angles method. It will help
Number 3: It's just about solving the interior sum of the pentagon
Answer:
2. 10 degrees
3. 108 degrees
Step-by-step explanation:
sorry I reposted it because the previous answer was deleted and plz mark me as a brainliest.
Marta’s math textbook weighs Four-fifths of a pound less than 4 times the weight of the book she is reading for her language arts class. If the weight of the math textbook is 2 and one-fifth pounds, which shows the correct equation and value of x, the weight of Marta’s book for language arts?
4 x minus four-fifths = 2 and one-fifth; x = three-fourths of a pound
Sam rolls a fair dice and flips a fair coin.
What is the probability of obtaining an odd number and a head?
Answer:
The probability that this occurs is 25%, as 3/6 (chance to roll an odd number) multiplied by 1/2 (chance to flip a head) is .25.
Step-by-step explanation:
Solve: [tex]x=4+\left(4x-4\right)\frac{1}{2}[/tex]
x = 2
x = 10
x = 2 or x = 10
no real solution
Answer: x = -2
Step-by-step explanation:
[tex]x=4+(4x-4)\frac{1}{2} \\x=4+\frac{4x}{2}-\frac{4}{2}\\x=4+2x-2\\x=2+2x\\x-2x=2\\-x=2\\x=-2[/tex]
Suppose that the scores on a statewide standardized test are normally distributed with a mean of 64 and a standard deviation of 2. Estimate the percentage of scores that were (a) between 60 and 68.
Answer:
95. 45%
Step-by-step explanation:
Given :
Mean score, = 64
Standard deviation = 2
Score between 60 and 68
P(Z < (x - mean) / standard deviation)
P(Z < (60 - 64) / 2) = P(Z < - 2) = 0.02275 (Z probability calculator)
P(Z < (68 - 64) / 2) = P(Z < 2) = 0.97725 (Z probability calculator)
P( score between 60 and 68)
P(Z < 2) - P(Z < - 2)
0.97725 - 0.02275 = 0.9545
Score between 60 and 68 = 0.9545 = 0.9545 * 100% = 95.45%
Find the length of CZ
A. 32
B. 45
C. 9
D. 1
Answer:
c
Step-by-step explanation:
just took it
Answer:
D. 1
Step-by-step explanation:
CA = 17
ZA = 16
CZ + ZA = CA
CZ + 16 = 17
CZ = 1
D. 1
Which of the following statements considered as always true?
A. All intersecting lines are perpendicular.
B. All parallel lines cut by a transversal line.
C. All perpendicular lines are intersecting line.
D. All transversal line is for parallel lines only
Can someone help with both questions 19 & 20
Answer:
19.
h=0, the result is 1000×2⁰ = 1000
this is the population of bacteria the excitement started with at the very beginning.
h=-3, the result is 1000×2-³ = 1000/(2³) = 1000/8 = 125
this is a calculation 3 hours backwards from the very start of the experiment, saying that if we started the experiment 3 hours earlier, this would have had to be the starting population of the bacteria so we would arrive at the same amount of population at any given time (value of h).
20.
D 25x⁶
Step-by-step explanation:
for 19 there is not more explanation. it is all ashtray in the answer.
for 20 we see that we are dealing with a square, so ask 4 sides have the same length.
one side is 5x³.
the area of a square is simply side².
so, here (5x³)² = 25x⁶
Grafico de deportes: fútbol 30%, atletismo 25%, tenis 5%, voleibol 10%, basquetbol 20%. Si 165 jóvenes prefieren el fútbol ¿cuantos prefieren el basquetbol?
Answer:
33 jóvenes prefieren el basquetbol.
Step-by-step explanation:
Hay 165 jóvenes.
De estos, 20% prefieren el basquetbol.
¿cuantos prefieren el basquetbol?
20% de 165, entonces:
[tex]20\% = \frac{20}{100} = 0.2[/tex]
[tex]0.2*165 = 33[/tex]
33 jóvenes prefieren el basquetbol.
Multiple choice question
Answer:
A. 35 square centimeters
Step-by-step explanation:
The area of a triangle is (b*h)/2.
7 * 10 = 70
70/2 = 35
Lani had 2,380 Pesos in a savings bank. She withdrew 500 Pesos. Then deposited 680. Write an adittion sentence to represent the situation. Find the sum of the money
Answer:
2560 Pesos
Step-by-step explanation:
How to find the amount of money in the savings account:
2380 - 500 = 1880
1880 + 680 = 2560
The addition equation: 1880 + 680 = 2560
The sum of the money: 2560 Pesos
The transformation which will map triangle PQR onto P'Q'R is
Given:
The graph of triangle PQR and triangle P'Q'R'.
To find:
The transformation that will map the triangle PQR onto P'Q'R'.
Solution:
From the given graph it is clear that the triangle PQR is formed in II quadrant and its base lies on the negative direction of x-axis.
The triangle P'Q'R' is formed in IV quadrant and its base lies on the positive direction of x-axis.
This is possible it the figure is rotated 180 degrees about the origin.
Therefore, the correct option is A.
Help quick pls
The product of three different positive integers is equal to 7^3. What is the sum of the three integers?'
Answer:
it must be 21
Step-by-step explanation:
I have very fast I think giving test just thank the answer after test mark me brainliest
help me with this problem please!!!!
Step-by-step explanation:
sorry I wanted to help you but my calculator is take out decimals sorry I don't know what to do
help asap plsss ----------------------
Answer:
g(x) = |x-7|+4
Step-by-step explanation:
If we imagine trying to find the vertex of f(x) or the lowest part, we can always input x and y into each equation and see if they equal on either side.
The vertex is at points (7,4)
4=|7-7|+4 : 4=4.
find the next four terms of the sequence 5, 4, 9, 13, 22
Answer:
38
Step-by-step explanation:
The first term of the given sequence is 9.
The second term is 13
= 9 + 4 . = 9 + 2 × 2.
The next number is 22.
= 13 + 9 . = 13 + 3 × 3 .
In the same way the next number of the given sequence will be
22 + 4 × 4 .
= 22 + 16 = 38.
I will mark brainliest!!
Solve for X. Thank you
Answer:
x = 4
Step-by-step explanation:
The segment inside the triangle is an angle bisector and divides the opposite side into segments that are proportional to the other two sides , that is
[tex]\frac{15}{20}[/tex] = [tex]\frac{x+2}{14-(x+2)}[/tex]
[tex]\frac{3}{4}[/tex] = [tex]\frac{x+2}{14-x-2}[/tex] = [tex]\frac{x+2}{12-x}[/tex] ( cross- multiply )
4(x + 2) = 3(12 - x) ← distribute parenthesis on both sides )
4x + 8 = 36 - 3x ( add 3x to both sides )
7x + 8 = 36 ( subtract 8 from both sides )
7x = 28 ( divide both sides by 7 )
x = 4
Find the midpoint of the line segment with end coordinates of:
(
−
2
,
−
4
)
and
(
−
1
,
−
5
)
Give coordinates as decimals where appropriate
Answer:
Step-by-step explanation:
The Midpoint formula is
[tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex] where the x's and y's come from the coordinates of the endpoints. Filling in:
[tex]M=(\frac{-2+(-1)}{2},\frac{-4+(-5)}{2})=(\frac{-3}{2},\frac{-9}{2})=(-1.5,-4.5)[/tex]
Which number completes the system of linear
inequalities represented by the graph?
y> 2x – 2 and x + 4y > _____
The system of linear inequalties that is represented by the graph is formed by the expressions y > 2 · x - 2 and x + 4 · y > - 12.
What system of inequalities generate the graph seen in the image?
Herein we have two inequalities generated by two linear functions whose form is described below:
f(x, y) > a (blue region) (1)
g(x, y) > b (red region) (2)
By direct comparison, we find that the limit of the red region is represented by the inequality y > 2 · x - 2. From the equation of the line we can derive an expression for the limit of the blue region:
Slope
m = [- 4 - (- 3)]/(4 - 0)
m = - 1/4
Intercept
b = y - m · x
b = - 3 - (- 1/4) · 0
b = - 3
Then, the inequation is represented by the linear equation:
y > - (1/4) · x - 3
4 · y > - x - 12
x + 4 · y > - 12
The system of linear inequalties that is represented by the graph is formed by the expressions y > 2 · x - 2 and x + 4 · y > - 12.
To learn more on inequalities: https://brainly.com/question/20383699
#SPJ1
Using the number line below, draw a box and whisker plot for the following data: 12,18,18,20,22,22,25,26,30,30,32,32,35,35,38,49,42
Answer:
Step-by-step explanation:
Population size: 17
Median: 30
Minimum: 12
Maximum: 49
First quartile: 21
Third quartile: 35
Interquartile Range: 14
Outliers: none
Ashvin want to replace the carpet in your living room and hallway with laminate flooring.
Find the total area of the hallway and living room.
Answer:
I’m sorry but you need to edit this question, it is incomplete.
Step-by-step explanation:
I see nothing, if there is supposed to be an image attached, please i attach it again, tnx!
I could help you though
Dorothy earned 840 last week for working 35 hours.is she works 40 hours,how much will she make
Answer:
960$
Step-by-step explanation:
First you want to find out how much money she makes per hour by doing 840/35. That equals 24, so now you multiply it by the amount of hours for this week. 24*40= 960$.
Hope this helps :D
