The company should sell each widget for $28.25, to the nearest cent.
To maximize profit, we need to find the vertex of the parabola represented by the profit equation y = -2x^2 + 113x - 497. Since the coefficient of x^2 is negative, the parabola opens downwards, and the vertex represents the maximum point. The x-coordinate of the vertex of a parabola in the form of y = ax^2 + bx + c can be found using the formula -b/2a.
For the equation y = -2x^2 + 113x - 497, a = -2 and b = 113. Plugging these values into the formula gives us: x = -113 / (2 × -2) = -113 / -4 = 28.25. Therefore, to maximize profit, the company should sell each widget for $28.25, to the nearest cent.
Rearrange so x is independent variable. -4x-6=-5y+9
[tex]\text{Solve for x:}\\\\-4x-6=-5y+9\\\\\text{Add 6 to both sides}\\\\-4x=-5y+15\\\\\text{Divide both sides by -4}\\\\\boxed{x=\frac{5}{4}y-\frac{15}{4}}[/tex]
Y=3/4x
5/2x+2y=5
Show work
Answer:
x = 5/4
y = 15/16
Step-by-step explanation:
We are given y = 3/4x
and 5/2x +2y = 5
Substituting the value y=3/4 x in second equation we get
5/2x + 2(3/4)x = 5
8/2x = 5
4x = 5
and so , x = 5/4
substituting value of x in y = 3/4x we get,
y = 3/4 (5/4)
So, y = 15/16
which are the required values of x and y on solving the two given equations.
The solution to the equation is (5/4, 15/16)
Given the system of equations
Y=3/4x 5/2x+2y=5Substitute equation 1 into 2 to have:
5/2x + 2(3/4x) = 5
5/2x + 3/2x = 5
8/2x = 5
4xx = 5
x = 5/4
Snce y = 3/4x
y = 3/4(5/4)
y = 15/16
Hence the solution to the equation is (5/4, 15/16)
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Find the required measurements of the following trapezoids.
a=8 cm
b= 16 cm
h=12 cm
Compute the area.
cm2
Answer:
Area of trapezoid = 144 cm²
Step-by-step explanation:
The length of parallel sides are,
a = 8 cm
b = 16 cm
h = 12 cm
Formula area of trapezoid:-
[tex]A=\dfrac{1}{2}(a+b)\times h[/tex]
[tex]A=\dfrac{1}{2}(8+16)\times 12[/tex]
[tex]A=144[/tex]
Hence, the area of trapezoid is 144 cm²
Answer:
Hence, the area of trapezoid is 12 cm²
Step-by-step explanation:
Find the value of x. Round your answer to the nearest tenth.
A.) 52.6
B.) 52.9
C.) 6.2
D.) 6.5
Answer:
6.2
Step-by-step explanation:
sin 20 = x/18
solve for x
please help me. i don’t know how the answer is 1/12 so can you guys please explain step by step on why the answer is 1/12.
Answer:
see explanation
Step-by-step explanation:
P(head) = [tex]\frac{1}{2}[/tex]
P(4) = [tex]\frac{1}{6}[/tex]
P(head and 4 ) = P(head) × P(4) = [tex]\frac{1}{2}[/tex] × [tex]\frac{1}{6}[/tex] = [tex]\frac{1}{12}[/tex]
6 times the sum of a number and 5
Answer:
6(x+5)
Step-by-step explanation:
Answer: 6 x (x+5)
Step-by-step explanation: Since it is six times a number AND five, you want to do the addition equation first. To show this you place parentheses around a variable (x) plus 5. You add six in front of this because it comes first in the word problem.
(please help!) Two buses leave the bus station at 8 am. If Bus #1 makes its route in a total of 60 minutes and Bus #2 makes its route in a total of 80 minutes, at what time will the two buses meet again?
Answer:
12 pm noon
Step-by-step explanation:
The least common multiple of the two times is 240 minutes, or 4 hours. The buses will meet at the station again at noon.
__
60 = 20×3
80 = 20×4
The least common multiple is 20×3×4 = 240 minutes. There are 60 minutes in an hour, so this is 240/60 = 4 hours. 4 hours after 8 am is 12 pm, noon.
10x-7x=12 how to solve this
Answer:
x=4
Step-by-step explanation:
10x-7x=12
3x=12
divide both sides by 3
x=4
Answer: x = 4
Step-by-step explanation: To solve this equation, we can first combine our like terms on the left side of the equation which are the x's.
10x - 7x = 3x so we now have the equation 3x = 12.
Now to solve for x, we want to get x by itself on the left side of the equation. Since x is being multiplied by 3, to get x by itself, we need to divide by 3 on the left side of the equation. Since we divided by 3 on the left side, we must also divide by 3 on the right side.
On the left side, notice that the 4's cancel out so we're simply left with x. On the right side we have 12 divided by 3 which is 4 so x = 4.
Finally, remember to check your answer by substituting a 4 back into the original equation.
So we have 10(4) - 7(4) = 12 or 40 - 28 = 12 or 12 = 12.
Since this a true statement, we know our answer is correct.
Remember to show all your work when solving equations.
A circle has a circumference of 20. It has an arc of length 4. What is the central angle of the arc,in degrees
Answer:
Step-by-step explanation: 72.1°
The circumference of the circle is given to be = 20
The first thing to do here is to calculate the radius of the circle from the circumference given,
Formula for circumference = 2πr or πd, where d is the diameter.
Make r the subject of the formula by equating it to 20
2πr = 20,
r = 20/2π, π = ²²/₇ or 3.142
r = 10/22/7
= ( 10 x 7 )/22
= 70/22
= 3.18.
Now since the radius is known, we could now calculate the central angle of the arc.
Arc length = 2πr∅°/360°, reducing this to lowest term now becomes
= πr∅°/180°
Therefore equate the formula to 4 and solve for ∅°, since the arc length is 4
πr∅°/180° = 4
Multiply through by 180°
πr∅° = 4 x 180°
πr∅°= 720
Divide through by πr to get ∅°
∅° = 720/πr
= 720/3.142 x 3.18
= 720/9.99
= 72.07
= 72.1°
The angle substended by the arc length 4 is 72.1°
The diagram shows triangle ABC.
ADB is a straight line.
The size of angle DCB: The size of angle ACD=2:1
Work out the size of angle BDC.
=======================================================
Explanation:
Check out figure 1 which is one of the attached images below.
In this diagram, I have angle A as 75 degrees and angle B as 51 degrees.
Angle C is therefore, C = 180-A-B = 180-75-51 = 54 degrees.
----------
Point D is somewhere between A and B such that it is on segment AB.
Figure 2 (also attached as an image) shows segment CD forming two angles DCB and ACD.
These are the blue and red angles respectively, such that the blue angle is twice as large as the red angle.
blue angle = 2*(red angle)
This is what it means when it says the ratio of the two angles is 2:1.
I have 2x as the blue angle and x as the red angle. We don't know what x is yet, but we do know that the x and 2x combine back to angle C = 54 degrees.
So,
(angle DCB) + (angle ACD) = angle C
(2x) + (x) = 54
3x = 54
x = 54/3
x = 18
Since x = 18, this means 2*x = 2*18 = 36
Therefore,
angle DCB = 2x = 36 degrees
angle ACD = x = 18 degrees
--------
Focus solely on triangle DCB. We found angle DCB = 36 degrees and we know that angle DBC = 51
The remaining angle y = angle BDC is...
(angle BDC)+(angle DCB)+(angle DBC) = 180
(y)+(36)+(51) = 180
y+87 = 180
y+87-87 = 180-87
y = 93
angle BDC = 93 degrees
Figure 3 shows the angles we found (basically I replaced x, 2x and y with their respective numbers).
The size of angle BDC is 0 degrees.
To find the size of angle BDC, you can use the fact that the sum of the angles in a triangle is always 180 degrees. Since angle ACD is 1 part and angle DCB is 2 parts, we can express their sizes as:
Angle ACD = x degrees
Angle DCB = 2x degrees
Now, you know that the sum of the angles in triangle ABC is 180 degrees. So, you can write the equation:
x (angle ACD) + 2x (angle DCB) + 180 degrees (angle BDA) = 180 degrees
Now, simplify and solve for x:
x + 2x + 180 = 180
Combine like terms:
3x + 180 = 180
Now, subtract 180 from both sides of the equation:
3x = 0
Finally, divide by 3:
x = 0
Now that you know the value of x, you can find the size of angle BDC (2x):
Angle BDC = 2x = 2(0) = 0 degrees
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PLEASE HELP!!! 45 PTS AND BRAINLIEST!!!
1) Complete the work for each method below:
Method A: Given f(x) = 3x - 4 and g(x) = x+4/3
Show that these are inverse functions by finding f^-1 (x) and showing that it is the same as g(x)
Method B: Given f(x) = 3x - 4 and g(x) = x+4/3
Show that these are inverse functions by showing that when the output of one function is used for the input of the other function, the final output is equal to the original input value. (you may choose any initial input)
Method C: Given f(x) = 3x - 4 and g(x) = x+4/3
Verify that these are the inverse function by showing that f(g(x)) = x AND g(f(x)) = x
Answer:
See explanation!
Step-by-step explanation:
Let us first give some principle theory to aid our solution.
Considering two functions [tex]A(x)[/tex] and [tex]B(x)[/tex], in order to show that function
which is the inverse of [tex]y=ax[/tex].
Now let as solve our problem. We are given the following:
[tex]f(x)=3x-4\\g(x)=\frac{x+4}{3}[/tex]
Method A: Show that these are inverse functions by finding f^-1 (x) and showing that it is the same as g(x).
Let us take [tex][f(x)=y]=3x-4[/tex] and "exchanging" our variables we have
[tex]x=3y-4\\x+4=3y\\\\y=\frac{x+4}{3}[/tex]
which is exactly the same with our given function of [tex]g(x)=\frac{x+4}{3}[/tex], so proved!
Method B: Show that these are inverse functions by showing that when the output of one function is used for the input of the other function, the final output is equal to the original input value. (you may choose any initial input)
For this case we will use a simple input let us say [tex]x=1[/tex]. Thus taking the [tex]f(x)[/tex] function and plugging in we have:
[tex]f(x=1) = 3(1)-4\\f(1)=3-4\\f(1)=-1[/tex]
Now let us take the output of [tex]f(1)[/tex] which is [tex]-1[/tex] and use it the input to our second function of [tex]g(x)[/tex], so we have:
[tex]g(x=-1) = \frac{(-1)+4}{3}\\ \\g(-1)=\frac{3}{3}\\ \\g(-1)=1[/tex]
so the output of the second function is equal to the original input value of the first function, hence proved!
Method C: Verify that these are the inverse function by showing that f(g(x)) = x AND g(f(x)) = x.
Basically we are asked to prove that both [tex]f(g(x))=g(f(x))=x[/tex]
To do so, we just replace one function into the [tex]x[/tex] value of the other function as follow:
[tex]f(g(x))=3(\frac{x+4}{3} )-4\\\\f(g(x))=x+4-4\\\\f(g(x))=x[/tex]
Lets repeat now for the opposite as follow:
[tex]g(f(x))=\frac{(3x-4)+4}{3}\\ \\g(f(x))=\frac{3x}{3}\\ \\g(f(x))=x[/tex]
Hence proved!
Which would be the best trend line for the given data set?
y=-3/2x+8
y=3/2x+5
y=2/3x+8
y=-2/3x+5
y=-2/3x+5
Step-by-step explanation:
From the scattered plot, it is evident that the line of best fit will have a negative slope from the way the plots are aligned.
Selecting the line of best fit that will cut the y axis at +5, the points can be estimated as;
(5,1.5) and (3.5,2.5)
The slope can be found as;
m=Δy/Δx
m=2.5-1.5/3.5-5 =1.0/ -1.5 = -0.67
Finding the equation as;
m=Δy/Δx
-0.66 = y-2.5/x-3.5
-0.66(x-3.5) = y-2.5
-0.66x+2.3=y-2.5
-0.66x+2.3+2.5=y
-0.66x+4.7=y
⇒⇒ y= -0.66 x + 4.7
⇒⇒y= -2/3 x + 5
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A taxi service charges a flat fee of $1.25 and $0.75 per mile. If Henri has $14.00, which of the following shows the number of miles he can afford to ride in the taxi?
m less-than-or-equal-to 17
m greater-than-or-equal-to 17
m less-than-or-equal-to 20.3
m greater-than-or-equal-to 20.3
Answer:
Option A M<17 m is less than or equal to 17
Step-by-step explanation:
Answer:
A.
Step-by-step explanation:
3/5p+1/5(40-p)=0 what value makes p true
The value of p that makes the equation true is -20
Step-by-step explanation:
To solve an equation of one variable
Simplify the equation if necessaryUse the mathematics operations to put the variable in one side and the numerical term in the other sideDivide both sides by the coefficient of the variable to find its value∵ The equation is [tex]\frac{3}{5}p+\frac{1}{5}(40 - p)=0[/tex]
- Simplify the left hand side
∵ [tex]\frac{1}{5}(40-p)=\frac{1}{5}(40)-\frac{1}{5}(p)[/tex]
∴ [tex]\frac{1}{5}(40-p)=8-\frac{1}{5}p[/tex]
- Substitute [tex]\frac{1}{5}(40-p)[/tex] in the equation by [tex]8-\frac{1}{5}p[/tex]
∴ [tex]\frac{3}{5}p+8-\frac{1}{5}p=0[/tex]
- Add the like terms
∴ [tex](\frac{3}{5}p-\frac{1}{5}p)+8=0[/tex]
∴ [tex]\frac{2}{5}p+8=0[/tex]
- Subtract 8 from both sides
∴ [tex]\frac{2}{5}p=-8[/tex]
- Divide both sides by [tex]\frac{2}{5}[/tex]
∴ p = -20
To check the answer substitute p by -20 in the equation, the left hand side is equal to the right hand side, then the answer is right
∵ left hand side = [tex]\frac{3}{5}(-20)+\frac{1}{5}(40-(-20))[/tex]
∴ left hand side = [tex]\frac{-60}{5}+\frac{1}{5}(40+20)[/tex]
∴ left hand side = [tex]\frac{-60}{5}+\frac{60}{5}[/tex]
∴ left hand side = 0
∵ Right hand side = 0
∴ Left hand side = Right hand side
∴ The value of p makes the equation true
The value of p that makes the equation true is -20
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Answer:
-20
Step-by-step explanation:
12) Cost of a hat: $39.95
Markup: 10%
Discount: 50%
Tax: 4%
Answer:
22.77
Step-by-step explanation:
39.95 * 1.14 (tax + markup) * 0.5 (discount) = 22.77 (rounded)
What is the vertex of g (x)=-3x^2+18x+2
Answer:
vertex=?
Step-by-step explanation:
given data:
g(x)=-3x^2+18x+2
find values of a,b,c:from the given equation
a=-3,b=18,c=2
x-value of the vertex:x=-b/2a
x=-(18)/2(-3)
x=3
y-value of the vertex:
put value of x in the given equation
y=-3(3)^2+18(3)+2
y=-27+54+2
y=29
Write down the x and y values as an ordered pair.
x=3 y=29
(3,29)
Which equation has a slope of -5/2 and a y-intercept of -2
[tex]\bf \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\qquad \implies y = \stackrel{\stackrel{m}{\downarrow }}{-\cfrac{5}{2}}x\stackrel{\stackrel{b}{\downarrow }}{-2}[/tex]
What expression is equivalent to 5(3-2n)+12n ?
Break it down please
Answer: Order if operations
Step-by-step explanation:
15-10n+12n
15+12n
Write a quadratic function whose zeros are -5 and -6
Final answer:
A quadratic function with zeros at -5 and -6 can be written as f(x) = (x + 5)(x + 6), which expands to f(x) = x² + 11x + 30.
Explanation:
To write a quadratic function whose zeros are -5 and -6, you start by remembering that if α and β are the zeros of a quadratic function, the function can be written as f(x) = a(x - α)(x - β) where a is a nonzero coefficient. In this case, -5 and -6 are the zeros, so our function is f(x) = a(x + 5)(x + 6).
For simplicity, if we choose a to be 1, the quadratic function simplifies to
f(x) = (x + 5)(x + 6)
f(x) = x² + 11x + 30.
Therefore, the quadratic function with zeros at -5 and -6 is f(x) = x² + 11x + 30.
Broccoli costs $1.50 per pound at the store. How much money does 32 ounces of the broccoli cost
Answer:No
Step-by-step explanation:
Simplify the following expression.
-7x² - 5x-6x² +4 + 15x
Answer: -13x^2 + 10x + 4
Step-by-step explanation:
group all of the same variables together to simplify the equation.
-7 - 6 = -13 // the x^2 value
-5 + 15 = 10 // the x value
4 is the only number without an exponent so leave it alone.
Answer:
-13x²+10x+4
Step-by-step explanation:
You need to group all of the same variables together:
-7x² - 5x - 6x² + 4 + 15x
-7x²-6x²-5x+15x+4
-13x²+10x+4
At what rate per annum will Rs.4500 amount to Rs.5715 in 3 years?
Answer:
5715x3=
Rs.17145
Step-by-step explanation:
The interest rate required for Rs.4500 to amount to Rs.5715 in 3 years is 9% per annum. This is obtained using the simple interest formula. Therefore, the annual rate is 9%.
To find the annual interest rate at which Rs.4500 amounts to Rs.5715 in 3 years, we use the formula for simple interest:
Final Amount (A) = Principal (P) + Interest (I)
Given:
Principal (P) = Rs.4500Final Amount (A) = Rs.5715Time (T) = 3 yearsFirst, we calculate the interest:
Interest (I) = A - P = Rs.5715 - Rs.4500 = Rs.1215Next, we use the simple interest formula:
I = P × R × TRearranging for the rate (R), we get:
R = I / (P ×T)Substitute the known values:
R = 1215 / (4500 × 3) = 1215 / 13500 ≈ 0.09Converting to a percentage:
R ≈ 9% per annumTherefore, the rate per annum required for Rs.4500 to grow to Rs.5715 in 3 years is 9%.
Ben wants to play a carnival game that costs $2. In his pocket he has 5
red tickets worth 35 cents each, and 15 blue tickets worth 10 cents each.
Which of the following systems of inequalities correctly represents the
constraints on the variables in this problem? Let rrepresent the red
tickets and b represent the blue tickets.
Answer:
R=$1.75 B=$1.50
Step-by-step explanation:
35r+10b=X
b is 10
r is 5
X=3.25$
Answer:
Step-by-step explanation:
R=$1.75 B=$1.50
35r+10b=X
b is 10
r is 5
X=3.25$
A bag contains 18
red gumballs and 6
yellow gumballs.
Without looking,
what is the
probability that you
will randomly
choose yellow
gumball?
Answer:
There are 24 gumballs, 6 of which are yellow.
P(yellow) = 6/24 = 1/4
Mrs. Smith has 50 students in her math class. If 40% of the students completed the homework, how many students did not complete the homework?
Answer:
30 students
Step-by-step explanation:
check the photo
a rectangular blue tile has a length of 4.25 inches and a width of 6.75 inches. a similar tile has a length of 12.75 inches.what is the width of the red tile.
Answer:
The width of the red tile would be [tex]2.25[/tex] inches.
Step-by-step explanation:
Given blue tile has a length of [tex]4.25[/tex] inches, and a width of [tex]6.75[/tex]inches.
Also, length of similar tile is [tex]12.75[/tex] inches.
Let us assume [tex]x[/tex] as the width of red tile.
It is given in the question that both tiles are similar.
So, their area will be the same.
Area of blue tile would be [tex]4.25\times 6.75=28.6875\ inch^2[/tex]
Area of red tile would be [tex]12.75\times x[/tex]
The area of blue tile would be equal to area of red tile.
[tex]28.6875=12.75\times x[/tex]
[tex]\frac{28.6875}{12.75}=x\\\\x=2.25[/tex]
So, the width of the red tile would be [tex]2.25[/tex] inches.
Four pounds of sugar costs $2.40 at the grocery store. What is the unit rate for the cost of sugar in relation to its weight?
A.$0.60 per pound
B. not enough information
C.$1.67 per pound
D.$2.40 per pound
Answer:
c
Step-by-step explanation:
solve this equation 4/2.40
Addie walked 2 1/2 miles in 45 minutes. Suzie covered 2 2/5 miles in 2/3 of an hour.
What was Addie's speed?
Addie's speed was [tex]3\frac{1}{3}\ mph[/tex]
Step-by-step explanation:
Given,
Distance walked by Addie = [tex]2\frac{1}{2}=\frac{5}{2}\ miles[/tex]
Time taken by Addie = 45 minutes
Converting the time into hours;
1 hour = 60 minutes
45 minutes = [tex]\frac{45}{60}=\frac{3}{4}\ hour[/tex]
Distance = Speed * Time
Speed = Distance/Time
Speed = [tex]\frac{5}{2} / \frac{3}{4}[/tex]
Speed = [tex]\frac{5}{2}*\frac{4}{3} = \frac{10}{3}\ mph[/tex]
Speed = [tex]3\frac{1}{3}\ mph[/tex]
Addie's speed was [tex]3\frac{1}{3}\ mph[/tex]
Keywords: speed, distance
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what is the solution of y= -5x + 1 and y= 3x - 2
Answer:
x=3/8, y=-7/8. (3/8, -7/8).
Step-by-step explanation:
y=-5x+1
y=3x-2
----------
-5x+1=3x-2
-5x-3x+1=-2
-8x+1=-2
-8x=-2-1
-8x=-3
8x=3
x=3/8
y=3(3/8)-2=9/8-2=9/8-16/8=-7/8
Which expression is equivalent to 8/15?
A. 8÷1/5
B. 8÷15
C. 15÷1/8
D. 15÷8
Answer:B
Step-by-step explanation: