Answer:
-1/3x+3 = x-1
Step-by-step explanation:
The solution is (3,-2)
Check and see if the point solves the equation
-1/3x+3 = x-1
-1/3(3) +3 = 3-1
-1+3 = 3-1
2=2 yes
Answer:
C
Step-by-step explanation:
I need the answer explained
Answer:
1.33
Step-by-step explanation:
62 can only be subtracted from 82 once. So 82.46-62 would be 20.46. Since you can't subtract anymore you put a decimal point. 62x3=186 and 20.46-186=1.86 and you can subtract 186-186=0.
Will give brainliest answer
If a and b are positive numbers, find the maximum value of f(x) = x^a(2 − x)^b on the interval 0 ≤ x ≤ 2.
Answer:
The maximum value of f(x) occurs at:
[tex]\displaystyle x = \frac{2a}{a+b}[/tex]
And is given by:
[tex]\displaystyle f_{\text{max}}(x) = \left(\frac{2a}{a+b}\right)^a\left(\frac{2b}{a+b}\right)^b[/tex]
Step-by-step explanation:
Answer:
Step-by-step explanation:
We are given the function:
[tex]\displaystyle f(x) = x^a (2-x)^b \text{ where } a, b >0[/tex]
And we want to find the maximum value of f(x) on the interval [0, 2].
First, let's evaluate the endpoints of the interval:
[tex]\displaystyle f(0) = (0)^a(2-(0))^b = 0[/tex]
And:
[tex]\displaystyle f(2) = (2)^a(2-(2))^b = 0[/tex]
Recall that extrema occurs at a function's critical points. The critical points of a function at the points where its derivative is either zero or undefined. Thus, find the derivative of the function:
[tex]\displaystyle f'(x) = \frac{d}{dx} \left[ x^a\left(2-x\right)^b\right][/tex]
By the Product Rule:
[tex]\displaystyle \begin{aligned} f'(x) &= \frac{d}{dx}\left[x^a\right] (2-x)^b + x^a\frac{d}{dx}\left[(2-x)^b\right]\\ \\ &=\left(ax^{a-1}\right)\left(2-x\right)^b + x^a\left(b(2-x)^{b-1}\cdot -1\right) \\ \\ &= x^a\left(2-x\right)^b \left[\frac{a}{x} - \frac{b}{2-x}\right] \end{aligned}[/tex]
Set the derivative equal to zero and solve for x:
[tex]\displaystyle 0= x^a\left(2-x\right)^b \left[\frac{a}{x} - \frac{b}{2-x}\right][/tex]
By the Zero Product Property:
[tex]\displaystyle x^a (2-x)^b = 0\text{ or } \frac{a}{x} - \frac{b}{2-x} = 0[/tex]
The solutions to the first equation are x = 0 and x = 2.
First, for the second equation, note that it is undefined when x = 0 and x = 2.
To solve for x, we can multiply both sides by the denominators.
[tex]\displaystyle\left( \frac{a}{x} - \frac{b}{2-x} \right)\left((x(2-x)\right) = 0(x(2-x))[/tex]
Simplify:
[tex]\displaystyle a(2-x) - b(x) = 0[/tex]
And solve for x:
[tex]\displaystyle \begin{aligned} 2a-ax-bx &= 0 \\ 2a &= ax+bx \\ 2a&= x(a+b) \\ \frac{2a}{a+b} &= x \end{aligned}[/tex]
So, our critical points are:
[tex]\displaystyle x = 0 , 2 , \text{ and } \frac{2a}{a+b}[/tex]
We already know that f(0) = f(2) = 0.
For the third point, we can see that:
[tex]\displaystyle f\left(\frac{2a}{a+b}\right) = \left(\frac{2a}{a+b}\right)^a\left(2- \frac{2a}{a+b}\right)^b[/tex]
This can be simplified to:
[tex]\displaystyle f\left(\frac{2a}{a+b}\right) = \left(\frac{2a}{a+b}\right)^a\left(\frac{2b}{a+b}\right)^b[/tex]
Since a and b > 0, both factors must be positive. Thus, f(2a / (a + b)) > 0. So, this must be the maximum value.
To confirm that this is indeed a maximum, we can select values to test. Let a = 2 and b = 3. Then:
[tex]\displaystyle f'(x) = x^2(2-x)^3\left(\frac{2}{x} - \frac{3}{2-x}\right)[/tex]
The critical point will be at:
[tex]\displaystyle x= \frac{2(2)}{(2)+(3)} = \frac{4}{5}=0.8[/tex]
Testing x = 0.5 and x = 1 yields that:
[tex]\displaystyle f'(0.5) >0\text{ and } f'(1) <0[/tex]
Since the derivative is positive and then negative, we can conclude that the point is indeed a maximum.
Therefore, the maximum value of f(x) occurs at:
[tex]\displaystyle x = \frac{2a}{a+b}[/tex]
And is given by:
[tex]\displaystyle f_{\text{max}}(x) = \left(\frac{2a}{a+b}\right)^a\left(\frac{2b}{a+b}\right)^b[/tex]
simplify 27-{ 9+(12-5)÷4} with solution
Answer:
16.25
Step-by-step explanation:
first do 12 -5 = 7. then 7/4 = 1.75 then 9+1.75 = 10.75 and finally 27-10.75= 16.25
18. The maintenance department ordered $3,450 worth of supplies from a valve and fitting supplier. The
supplier will allow a 15% discount because of the large order. How much will the maintenance department
have to pay for the supplies?
A. $2,932.50
B. $3,398.25
C. $3,406.45
D. $2,954.50
Answer:
A) [tex]\$\ 2932.5[/tex]
Step-by-step explanation:
One is given that a certain amount of money was allotted to be spent on supplies. However, there was a discount applied to the purchase. One is asked to find the amount of money actually spent on the supplies.
$3450 was the initial price that was to be spent on supplies, however, a (15%) discount was applied to this price. Subtract (15) from (100) to find the percent value that was actually spent on supplies.
[tex]100-15=85[/tex]
(85%) of the allotted money was actually spent on supplies. Now one has to find out the numerical value of the amount spent. Divide (85) by (100) and then multiply it by the amount of money allotted to the purchase, to fin the amount actually spent on the purchase.
[tex]3450*(\frac{85}{100})\\\\=3450*0.85\\\\=2932.5[/tex]
I need help on this problem
9514 1404 393
Answer:
see attached
Step-by-step explanation:
(a) The graph is scaled by a factor of 2, and shifted up 1 unit. The scaling moves each point away from the x-axis by a factor of 2. The points on the x-axis stay there. The translation moves that scaled figure up 1 unit.
__
(b) The graph is reflected across the x-axis and shifted right 4 units. The point on the x-axis stays on the x-axis.
Write the equation of the line that passes through the points (0, 4) and (- 4, - 5) . Put your answer in fully reduced slope intercept form , unless it is a vertical or horizontal line
Answer:
y=9/4x+4
Step-by-step explanation:
Start by finding the slope
m=(-5-4)/(-4-0)
m=-9/-4 = 9/4
next plug the slope and the point (-4,-5) into point slope formula
y-y1=m(x-x1)
y1=-5
x1= -4
m=9/4
y- -5 = 9/4(x - -4)
y+5=9/4(x+4)
Distribute 9/4 first
y+5=9/4x + 9
subtract 5 on both sides
y=9/4x+4
Solve for y. 14y-6(y-3)=22
Answer:
y=0.5
Step-by-step explanation:
14y-6(y-3)=22
14y-6y+18=22
8y+18=22
8y=4
y=0.5
Then we check our work...
14(0.5)-6((0.5)-3)=22
7-6(-2.5)=22
7+15=22
7+15 does equal 22, so this solution is correct.
Find the value of x.
A. 57
B. 72
C. 90
D. 124
Answer:
90
Step-by-step explanation:
Angle Formed by Two Chords= 1/2(SUM of Intercepted Arcs)
105 = 1/2 (120+x)
210 = 120+x
Subtract 120 from each side
210-120 = x
90 =x
The value of Intercepted Arcs x will be 90. so option C is correct.
What is the relation between line perpendicular to chord from the center of circle?If the considered circle has center O and chord AB, then if there is perpendicular from O to AB at point C, then that point C is bisecting(dividing in two equal parts) the line segment AB.
Or
|AC| = |CB|
Angle Formed by Two Chords= 1/2 (Sum of Intercepted Arcs)
105 = 1/2 (120+x)
210 = 120+x
Subtract 120 from each side;
210-120 = x
90 =x
Hence, the value of Intercepted Arcs x will be 90. so option C is correct.
Learn more about chord of a circle here:
https://brainly.com/question/27455535
#SPJ5
The figure below is a rectangular prism.
Which edge is parallel to segment BD?
A. HK
B. BM
C. DK
D. AH
Mrs. Gomez has two kinds of flowers in her garden. The ratio of lilies to daisies in the garden is 5:2
If there are 20 lilies, what is the total number of flowers in her garden?
Answer:
28
Step-by-step explanation:
5 : 2
since this is a simplified ratio, they have a common factor. let's say it is 'x'
so now :
5x : 2x
we know that 5x is lilies, and we also know that she has 20 lilies, so:
5x = 20
x = 4
the daisies would be 2x so 2*4 = 8
total flowers is 20 + 8
28
1. In the past, Sam cashed his paycheck each month at Ready Cash, a check cashing service that
charges a 5% fee. He recently opened a checking account at Bank of America so he can now
deposit and/or cash his paycheck without a fee. If Sam is making $28,500 per year, how much will
he save by not going to Ready Cash anymore?
Step-by-step explanation:
28000 ÷ 100
=280
280 × 5
=1400
please explain it step by step
Surface Area of cones
Instructions: Find the surface area of each figure. Round your answers to the nearest tenth, if necessary.
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Answer:
64.1 ft²
Step-by-step explanation:
The area of the cone is given by ...
A = πr(r +h) . . . . for radius r and slant height h
A = π(2 ft)(2 ft +8.2 ft) ≈ 64.1 ft²
Define mean and median for a set of data
Answer:
The mean is the average number of a data set gotten by adding all the numbers then dividing by two.
the median is the middle number in a sorted set of data,either sorted in ascending order or descending order.
I hope this helps
To calculate mean:
• add up all the numbers,
• then divide by how many numbers there are.
Example:
Data: 5, 6, 10, 1
Add these all together, which is 22, then divide by 4 (because that is how many numbers there are), so:
the mean is 5.5
To calculate median:
Arrange your numbers in order.
Cross off numbers until you get to the middle.
If there is an even number of data, then find the two in the middle and find the middle of that.
Example:
Data: 5, 6, 10, 1
Arrange: 1, 5, 6, 10
So, the middle 2 are 5 and 6. In between these would be 5.5, so that is the median.
If the data was: 1, 5, 6, 8, 10,
then the median would be 6.
Prove that: sec⁴B - sec²B = tan⁴B + tan²B.
Step-by-step explanation:
sec⁴B - sec²B = sec²B(sec²B - 1)
= (1 + tan²B)(tan²B)
= tan⁴B + tan²B
= Right-hand side (Proven)
2. Write the equation of the line in point-slope form.
(-1,3) and (2,9)
Answer:
y - 9 = 2 (x - 2)
Step-by-step explanation:
y2 - y1 / x2 - x1 9 - 3 / 2 - (-1) 6/3 = 2
y - 9 = 2 (x - 2)
Please help me to find this answer
Step-by-step explanation:
angle of a triangle is 180, therefore to get the remaining one, subtract the sum of the two knows from 180, also for the second one; angle on a straight line is as well 180, since you have fine the interior one, subtract it from 180 to get the second answer
Answer:
so angles in a triangle add up to 180,
32+50+m<MQP=180
82+m<MQP=180
m<MQP=180-82
=98°
and angles on a straight line add up to 180 therefore
m<MQR=180-m<MQP
=180-98
=82
I hope this helps and if you don't understand feel free to ask
could anyone help me solve this? I’ve had several questions like this and I don’t understand how to solve it. I’ll give brainliest:)
Answer:
-2, - 1, - 2 and - 3
Step-by-step explanation:
As the graph depicts an odd function, it will follow the rule f(-x) = - f(x)
Find an equation of a plane containing the line r=⟨0,4,4⟩+t⟨−3,−2,1⟩ which is parallel to the plane 1x−1y+1z=−5 in which the coefficient of x is 1.
..?.. = 0.
The plane you want is parallel to another plane, x - y + z = -5, so they share a normal vector. In this case, it's ⟨1, -1, 1⟩.
The plane must also pass through the point (0, 4, 4) since it contains r(t). Then the equation of the plane is
⟨x, y - 4, z - 4⟩ • ⟨1, -1, 1⟩ = 0
x - (y - 4) + (z - 4) = 0
x - y + z = 0
Please Answer This!!! I NEEEDDD TOOO KNOWWWWW ANSWER!!!
Answer:
77.5
Step-by-step explanation:
Its rising at a constant rate between +10-15 each hour, so we if we were to add 25 or so to the 50, it would be close to 77.5, so I would assume the answer was B
Hi! I'd appreciate if you could help me on this question.
Liam is buying bottles of soda in packages that contain 8 bottles each. If the total number of sodas Liam bough t was between 45 and 50, how many did he buy? Explain your answer.
Answer:
48
Step-by-step explanation:
We need to find the multiples of 8
8,16,24,32,40,48
48 is between 45 and 50 so he must have bought 48
Answer:
6 bottles
Step-by-step explanation:
For this question we need to know the multiple of 8 which are:
8 x 1 = 8
8 x 2 = 16
8 x 3 = 24
8 x 4 = 32
8 x 5 = 40
8 x 6 = 48
8 x 7 = 56
There is only one multiple, which is greater than 45 but less than 50, which is 8x6 l.
This means he bought 6 bottles.
Answered by g a u t h m a t h
Simplify Square root (150n^2)
Answer:
12
Step-by-step explanation:
Help me please and thank you
Step-by-step explanation:
jlejej
are u using chrome os
Please help!
The quantities x and y are proportional.
x: 4 5 10
y: 10 12.5 25
Find the constant of proportionality (r) in the equation y=rx.
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Answer:
r = 2.5
Step-by-step explanation:
The constant of proportionality can be found by solving the equation for r:
r = y/x
Then any corresponding values of x and y can be used to find r:
r = 25/10 = 2.5
The constant of proportionality is 2.5.
help! due august 12th
PLS HELP
Find an equation of the line with a y-intercept of -3 and an x-intercept of -4.5
Answer:
y = - [tex]\frac{2}{3}[/tex] x - 3
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, - 3) and (x₂, y₂ ) = (- 4.5, 0 ) ← coordinates of intercepts
m = [tex]\frac{0-(-3)}{-4.5-0}[/tex] = [tex]\frac{0+3}{-4.5-0}[/tex] = [tex]\frac{3}{-4.5}[/tex] = - [tex]\frac{2}{3}[/tex]
The line crosses the y- axis at (0, - 3 ) ⇒ c = - 3
y = - [tex]\frac{2}{3}[/tex] x - 3 ← equation of line
Select the expression that has a value of 13.
9 + 3 x (2 ÷ 3) + 6
(9 + 3) x 2 ÷ 3 + 6
9 − (3 x 2) ÷ 3 + 6
(9 + 3 x 2) ÷ 3 + 6
Answer:
9 − (3 x 2) ÷ 3 + 6 is the answer
I need to know the answer please
Focusing on the center point of f(x) (0,0), we can see that it has moved to the left 4 units and up 3 units.
g(x) = [tex](\sqrt[3]{x + 4}) + 3[/tex]
Option C
Hope this helps!
Scientists have steadily increased the amount of grain that farms can produce each year. The yield for farms in France is given by y=−2.73x2+11000x−11000000 where x is the year and y is the grain yield in kilograms per hectare (kg/ha).
What does the y-intercept of this function represent?
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Answer:
the yield in year 0
Step-by-step explanation:
The y-value is the yield for farms in France in year x. The y-value when x=0 is the yield for farms in France in year 0.
_____
Additional comment
The reasonable domain for this function is approximately 1843 ≤ x ≤ 2186. The function is effectively undefined for values of x outside this domain, so the y-intercept is meaningless by itself.