Answer:
The graph of the equation has a minimum.
When y = 0, the solutions are [tex]4 \pm 2\sqrt{3}[/tex]
The extreme value of the graph is (4,-12).
Step-by-step explanation:
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]
[tex]\Delta = b^{2} - 4ac[/tex]
Vertex of a quadratic function:
Suppose we have a quadratic function in the following format:
[tex]f(x) = ax^{2} + bx + c[/tex]
It's vertex is the point [tex](x_{v}, y_{v})[/tex]
In which
[tex]x_{v} = -\frac{b}{2a}[/tex]
[tex]y_{v} = -\frac{\Delta}{4a}[/tex]
Where
[tex]\Delta = b^2-4ac[/tex]
If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]y_{v}[/tex].
y = x2 – 8x + 4
Quadratic equation with [tex]a = 1, b = -8, c = 4[/tex]
a is positive, so it's graph has a minimum.
Solutions when y = 0
[tex]\Delta = b^2-4ac = 8^2 - 4(1)(4) = 64 - 16 = 48[/tex]
[tex]x_{1} = \frac{-(-8) + \sqrt{48}}{2} = \frac{8 + 4\sqrt{3}}{2} = 4 + 2\sqrt{3}[/tex]
[tex]x_{2} = \frac{-(8) - \sqrt{48}}{2} = \frac{8 - 4\sqrt{3}}{2} = 4 - 2\sqrt{3}[/tex]
When y = 0, the solutions are [tex]4 \pm 2\sqrt{3}[/tex]
Extreme value:
The vertex. So
[tex]x_{v} = -\frac{-8}{2} = 4[/tex]
[tex]y_{v} = -\frac{48}{4} = -12[/tex]
The extreme value of the graph is (4,-12).
Joan is a babysitter. She earns $8.50 per hour. Joan wants to buy a new phone that costs $161.50 with the tax included. Write an equation relating the number of hours she needs to babysit to the amount of money she earns. Find out how many hours Joan must babysit to buy the phone. Use h to represent the number of hours Joan babysits.
Answer:
8.5=161.50;h= 19 hours
Step-by-step explanation:
So its pretty easy all you have to do is multiply 8.5 x 19
A tosses one coin and B tosses two coins. The winner is the player who gets the most heads. In case of an equal number of heads A wins. (a) Compute the probability that B wins given that A gets 0 heads. (b) Compute the probability that B wins given that A gets 1 heads. (c) Compute the probability that B wins. (d) Change the game so that A tosses 2 coins and B tosses 3 coins. The winner is still the player who gets the most heads. In case of an equal number of heads A wins. Compute the probability that B wins in the new game.
Answer:
a) 3/4
b) 1/4
c) 1/2
d) 1/2
Step-by-step explanation:
A tosses one coin while B tosses two coins
a) P( B wins given A gets 0 heads )
In this scenerio for B to win, he needs to get at least 1 head i.e. P( B gets at least one heads)
= 1 - P(B get no head)
= 1 - (1/2)^2 = 3/4
b) P( B wins given A gets 1 head )
For B to win when A gets 1 head means that B will have to get 2 heads
i.e. P( B gets 2 heads ) = P( one head )^2 = ( 1/2 )^2 = 1/4
c) P( B wins )
P ( B wins ) = P(A get 0 head and B gets at least one head) + P(A get 1 head and B get 2 head)
= ( 1/2 * 3/4 ) + ( 1/2 * 1/4 ) = 1/2
d) P ( B wins the new game )
Given that: A tosses two(2) coin while B tosses three(3) coins
P( B ) = P(A gets 0 head and B gets one head) + P(A get 1 head and B get 2 or 3 heads ) + P(A get 2 head and B gets 3 heads )
=[ (1/4 *(1 -1/8) ] + (1/2 * 1/2) + ( 1/4 * 1/8 )= 1/2
In January 2013, a country's first-class mail rates increased to 52 cents for the first ounce, and 23 cents for each additional ounce. If Sabrina spent
$1742 for a total of 48 stamps of these two denominations, how many stamps of each denomination did she buy?
She bought
of the 52 cent stamps and
of the 23 cent stamps.
Answer:
She bought
22 of the 52 cent stamps and
26 of the 23 cent stamps.
Step-by-step explanation:
Given :
Total stamp increase = 48
Let number of 52 cent stamp = x
Number of 23 cent stamp = 48 - x
The cost equation :
0.52*x + 0.23*(48-x) = 17.42
0.52x + 11.04 - 0.23x = 17.42
0.52x - 0.23x = 17.42 - 11.04
0.29x = 6.38
x = 6.38 / 0.29
x = 22
Hence,
She bought 22 ; 52-cent stamps
And (48 - 22) = 26, 23-cent stamps
Last Monday local mall carriers delivered 1,344 pieces of mail. Of all the deliveries they made, 1/6 were magazines, 1/12 were packages, and the rest were letters. How many letters did the mail carriers deliver on Monday?
Answer:
1008 letters were delivered on Monday
Step-by-step explanation:
Total mail received = 1344
1/6 were magazines
1/12 were packages
the rest were letters
We have to find the exact number of magazines and packages received
Magazines = 1/6 of the total mail
Magazines = 1/6 × 1344
= 224 magazines
Packages = 1/12 of the total mail
Packages = 1/12 × 1344
= 112 packages
So now that we know the exact number of packages and magazines
We add those two numbers and subtract the result from the total mail
And the remainder is the letters delivered
Magazines = 224
Packages = 112
Magazines + Packages
224+112 = 336
Therefore, the letters received = 1344 - 336
= 1008
Which means that 1008 letters were delivered
What is the equation of a circle with center (4, 4) and radius 7?
Answer:
(x-4)^2 + (y-4)^2 = 49
Step-by-step explanation:
The equation of a circle is given by
(x-h)^2 + (y-k)^2 = r^2 where ( h,k) is the center and r is the radius
(x-4)^2 + (y-4)^2 = 7^2
(x-4)^2 + (y-4)^2 = 49
What is the exponent for x when the radical 18 is simplified completely?
Answer:
x⁶
Step-by-step explanation:
[tex]\sqrt[3]{x^{18}}=x^{18/3}= x^6[/tex]
Find the critical points of the given function and then determine whether they are local maxima, local minima, or saddle points.
f (x, y) = x^2 + y^2 + 2xyf(x,y)=x 2 +y 2 +2xy
Answer:
[tex]y =-x[/tex] ---- critical point
local minima
Step-by-step explanation:
Given
[tex]f(x,y) = x^2 + y^2 + 2xy[/tex]
Required
Determine the critical point
Differentiate w.r.t x
[tex]f_x =2x + 2y[/tex]
Differentiate w.r.t y
[tex]f_y =2y + 2x[/tex]
Equate both to 0
[tex]2x + 2y =0[/tex]
[tex]2y =0-2x[/tex]
[tex]2y =-2x[/tex]
Divide by 2
[tex]y =-x[/tex] ----- in both equations
Hence:
The critical point is: [tex]y =-x[/tex]
Solving (b):
We have:
[tex]f_x =2x + 2y[/tex]
[tex]f_y =2y + 2x[/tex]
This is represented as:
[tex]D = \left[\begin{array}{cc}2&2\\2&2\end{array}\right][/tex]
Calculate the determinant
[tex]|D| =2 * 2 -2 * 2[/tex]
[tex]|D| = 4-4[/tex]
[tex]|D| = 0[/tex]
The critical point is at local minima
what does X = to? will mark brainliest if it is an ACTUAL ANSWER
Answer:
x = 53
Step-by-step explanation:
The sum of the angles of a triangle are 180
x + ( x+2) + 72 = 180
Combine like terms
2x+74 =180
2x+74-74 = 180-74
2x =106
Divide by 2
2x/2 = 106/2
x =53
Phineas puts $600 into a certificate of deposit that earns 3.09%. If the money is
compounded monthly, how much will it be worth in 4 years?
Answer:
$678.83
Step-by-step explanation:
Given :
Principal, P = $600
Rate = 3.09% = 0.0309
Period, t = 4 years
Compounding times per period, n = 12 (monthly)
The compound interest formula :
A = P(1 + r/n)^nt
A = 600(1 + 0.0309/12)^(12*4)
A = 600(1 + 0.002575)^48
A = 600(1.002575)^48
A = 600 * 1.1313834
A = 678.83004
Worth in 4 years = $678.83
When too many variables are categorized in an analysis, several potential issues may occur. Which of the following is not one of the issues that may occur?
A. model performance suffers.
B. rarely occurring categories may not be captured accurately.
C.difficulty in differentiating among observations.
D. an increase in the number of categories as the data set becomes larger.
Answer: D. an increase in the number of categories as the data set becomes larger.
Step-by-step explanation:
When too many variables are categorized in an analysis, there are different potential issues may occur, some of these issues include:
• model performance suffers.
• rarely occurring categories may not be captured accurately.
• difficulty in differentiating among observations.
It should be noted that an increase in the number of categories as the data set becomes larger isn't one of the issues. Therefore, the correct option is D.
The shape of a carpet is a semicircle. Use 22 7 as an approximation for π. a) Find its area. b) Janice wants to put a fringed border on all sides of the carpet. How many feet of fringe are needed?
Answer:
Step-by-step explanation:
The solution is : a) area of the semicircle = 76.97 ft^2.
b) Janice wants to put a fringed border on all sides of the carpet : 36ft.
What is area ?Area is the measure of a region's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.
Here, we have,
given that,
The shape of a carpet is a semicircle.
from the given diagram, we get, the diameter = 14ft
now, we know that,
area of the semicircle = πr²/2
here, we have,
diameter = 14 ft
so, radius = 14/2 = 7 ft
so, area = π*7²
= 153.94
a.) so, area of the semicircle = 76.97 ft^2
again,
b) Janice wants to put a fringed border on all sides of the carpet,
so, the perimeter = π r + d
= 36ft
Hence, The solution is : a) area of the semicircle = 76.97 ft^2.
b) Janice wants to put a fringed border on all sides of the carpet : 36ft.
To learn more on Area click:
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Answer to the question?
Answer:
35
Step-by-step explanation:
AEC and AEB form a straight angle(180°)
180-40=140
AEV and AED are equal
140 divided by 4 = 35
1. Find the surface area of the shape
Answer:
hsjsm
Step-by-step explanation:
mmssdn jnhbxjs ẹnienbsd sywb
3 liters split into 10 people equally?
Answer:
3.3333333333333333333333333333333
Step-by-step explanation:
10 divide it by 3 and get your answer on what amount and fraction of liter each person will get.
Note:
Pls notify me if my answer is incorrect for the other users that will see this message. Thank you.
-kiniwih426
what is the solution to the equation 9x+27=9( x+2) +9
Let's solve the equation:
9x + 27 = 9 ( x + 2 ) + 9 ← Distribute 9 to the x and 2
9x + 27 = 9x + 18 + 9 ← Combine like terms
9x + 27 = 9x + 27 ← Subtract 27 from both sides
9x = 9x
0 = 0
{Infinitely many solutions would be correct because no matter what x is, it will always equal each other the both sides of the equation because it is 9 times x on both sides.}
hope this helps..........
Answer:
x=1
Step-by-step explanation:
9x+27=9(x+2)+9
9x+27=9x+18+9
9x+27=9x+27
9x=9x
x=1
State if the two triangles are congruent. If they are, prove by using a two column proof!!!
Answer:
you can prove that they are congruent if their angles are the same.
Which of the following is a point-slope equation of a line that passes through
the points (10,5) and (4, -7)?
A. y-5= 2(x-10)
B. Y-5 = -2(x-10)
C. y-10 = 2(x-5)
D. y-10 = -2(x-5)
Answer:
A
Step-by-step explanation:
m = Y2 - Y1/ X2 - X1
m= -7 - 5/ 4 - 10
m = -12/ -6
m = 2
y - y1 = m ( x - x1)
y - 5 = 2 (x - 10)
Two consecutive even numbers are such that five times the smaller number , subtracted from eight times the bigger gives 58. Find the two Numbers? show working
Answer:
[tex]14\text{ and }16[/tex]
Step-by-step explanation:
Let the smaller number be [tex]x[/tex]. Since they are consecutive even numbers, the larger number can be represented by [tex]x+2[/tex].
Therefore, we have the following equation:
[tex]8(x+2)-5x=58,\\8x+16-5x=58,\\3x=42,\\x=\boxed{14}[/tex]
Thus, the larger number is [tex]x+2=\boxed{16}[/tex]
A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find out the time at which the rocket will reach its max, to the nearest 100th of a second.
y=-16x^2+239x+127
Answer:
7.47 seconds
Step-by-step explanation:
From the quadratic equation the x coordinate of the vertex is
x = -b/(2a)
---------------------------
y = -16x² + 239x + 127
x = -239/ ( 2 * (-16) )
x = -239 / (-32)
x = 7.46875
Rounded
x = 7.47
Need some help on this one pls (marking brainlist) :D
Answer:
x = 24 i think
Step-by-step explanation:
Find the slope of the line
(4,4) (-5,-2)
Answer:
m = [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
m = slope
m = [tex]\frac{y^2-y^1}{x^2-x^1}[/tex]
m = [tex]\frac{-2-4}{-5-4}[/tex]
m = [tex]\frac{-6}{-9}[/tex]
m = [tex]\frac{6}{9}[/tex]
m = [tex]\frac{2}{3}[/tex]
Find the next two geometric terms 3/20, 1/5, 4/15,
Answer:
a_5 = 1,500
Step-by-step explanation:
1. Determine the given of the problem.
a_n – unknown sequence
a_1 – 3/20
r – ((3⁄2)/(3⁄20)) = 10
n – 5
2. Substitute the given to the formula of the geometric sequence.
a_n = a_1 r^(n-1)
a_5 = (3/20) (10)^(5-1)
3. Solve the given problem.
a_5 = (3/20) (10)^(5-1) - Subtract the exponent.
a_5 = (3/20) (10)^(4) - Multiply 1/10 to the exponent.
a_5 = (3/20)(10000) - Multiply it.
a_5 = (30000/20) - Divide it.
a_5 = 1,500 - Answer of the problem.
the answer is 1500
correct me if you want
solve for x 64 = 2^3x
Answer: X=0 , 1.03355778
Step-by-step explanation: Isolate the variable by dividing each side by factors that don't contain the variable.
PLEASE HELP ME !!!! WILL GIVE BRAINLIEST TO WHOEVER ANSWERS CORRECTLY
Answer:
Ok Its not that hard actually
Step-by-step explanation:
but still too much for me plz give brainliest to meee
Answer:
21
Step-by-step explanation:
4x-2=3x+19
4x-3x=19+2
x=21
PLEASE HELP! 10 POINTS! WILL GIVE BRAINLIEST!
The numbers of licensed drivers in four samples taken from a population of students are shown in the table below. Which of the following choices is most likely closest to the percentage of students in the population who are licensed drivers? Sample Size Number of Licensed Drivers 25 4 50 14 75 15 100 24 O A. 20% B. 24% C. 16% D. 28%
Using the percentage concept, the amount that is closest to the percentage of students in the population who are licensed drivers is given by:
B. 24%.
What is a percentage?The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:
[tex]P = \frac{a}{b} \times 100\%[/tex]
Higher sample sizes lead to more accurate estimates, hence the percentage is given by:
[tex]P = \frac{24}{100} \times 100\% = 24\%[/tex]
Which means that option B is correct.
More can be learned about percentages at https://brainly.com/question/10491646
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In a school 33% pupils study
biology and 16% study chemistry. if 9% study both science; what percent study
neither percent?
Step-by-step explanation:
DRAW VENN disgarm
say there are 100
33 - 9 = 24 study only Bio
16 - 9 = 7 study only chemistry
that is a total of 24 + 9 + 7= 40 that study at least one of them
so
100 - 40 = 60% play hockey instead
Please help, I’m so lost question in picture
How can the general term for the sequence shown below be defined for an, where n is a positive integer?
4, 11, 18, 25, ...
Answer:
25, 32
Step-by-step explanation:
4 - 11
7
11- 18
7
it is increasing by 7 so what is 25 plus 7?
32
A farmer wants to fence a rectangular area adjacent to a straight river with an extra partition running perpendicular to the river. If he has 3000 yards of fencing and no fencing is needed alone the river, then what is the maximum area he can enclose
Answer:
the maximum area enclosed = 1125000sq. ft.
Step-by-step explanation:
Let each side perpendicular to the river be "x".
Then the side parallel to the river is "3000-2x".
Now, area of the rectangle
A(x) = (3000-2x)x
A(x) = -2x^2+3000x
Which is a quadratic equation with a = -2 and b = 3000
Maximum area occurs where x = -b/2a
x = -3000/(-2×2) = 750 ft.
Therefore, width of rectangle x = 750 ft
Now, length = 3000-2(750) = 1500 ft.
Therefore, the maximum area enclosed = 1500×750 = 1125000 sq. ft.
What is the volume of three cubes, each with a side length of fraction 1 over 3 foot? V = s3, where s is the side length.
fraction 1 over 3 ft3
fraction 1 over 2 ft3
fraction 1 over 9 ft3
fraction 1 over 27 f
Answer: A
Step-by-step explanation its easy
Answer:
C. fraction 1 over 9 ft3
Step-by-step explanation:
Hope I helped!!