Answer:
44 ten-dollar bills
Step-by-step explanation:
Assume that all 124 bills are ten-dollar bills,
124 x $10 = $1240
Total Value of Money : $840
$1240 - $840 = $400
There are $400 worth of five-dollar bills,
$400 / 5 = 80 (The number of five-dollar bills)
Therfore the number of ten-dollar bills,
124 - 80 = 44
Let's check:
44 x $10 = $440
80 x $5 = $400
Total = $440 + $400
= $840
A curve has equation y=4x^3 -3x+3. Find the coordinates of the two stationary points. Determine whether each of the stationary points is a maximum or a minimum.
Answer:
There are two stationary points
Local max = (-0.5, 4)Local min = (0.5, 2)Note that 1/2 = 0.5
==========================================================
How to get those answers:
Stationary points occur when the derivative is zero, when the graph is neither increasing nor decreasing (i.e. it's staying still at that snapshot in time).
Apply the derivative to get:
f(x) = 4x^3 - 3x + 3
f ' (x) = 12x^2 - 3
Then set it equal to zero and solve for x.
f ' (x) = 0
12x^2 - 3 = 0
12x^2 = 3
x^2 = 3/12
x^2 = 1/4
x = sqrt(1/4) or x = -sqrt(1/4)
x = 1/2 or x = -1/2
x = 0.5 or x = -0.5
----------------------
Let's do the first derivative test to help determine if we have local mins, local maxes, or neither.
Set up a sign chart as shown below. Note the three distinct regions A,B,C
A = numbers to the left of -0.5B = numbers between -0.5 and 0.5; excluding both endpointsC = numbers to the right of 0.5The values -0.5 and 0.5 are not in any of the three regions. They are the boundaries.
The reason why I split things into regions like this is to test each region individually. We'll plug in a representative x value into the f ' (x) function.
To start off, we'll check region A. Let's try something like x = -2
f ' (x) = 12x^2 - 3
f ' (-2) = 12(-2)^2 - 3
f ' (-2) = 45
The actual result doesn't matter. All we care about is whether if its positive or negative. In this case, f ' (x) > 0 when we're in region A. This tells us f(x) is increasing on the interval [tex]-\infty < x < -0.5[/tex]
Let's check region B. I'll try x = 0.
f ' (x) = 12x^2 - 3
f ' (0) = 12(0) - 3
f ' (0) = -3
The result is negative, so f ' (x) < 0 when [tex]-0.5 < x < 0.5[/tex]. The f(x) curve is decreasing on this interval.
The change from increasing to decreasing as we pass through x = -0.5 indicates that we have a local max here.
Plug x = -0.5 into the original function to find its paired y coordinate.
f(x) = 4x^3 - 3x + 3
f(-0.5) = 4(-0.5)^3 - 3(-0.5) + 3
f(-0.5) = 4
The point (-0.5, 4) is a stationary point. More specifically, it's a local max.
Side note: This is the same as the point (-1/2, 4) when written in fraction form.
----------------------
Let's check region C
I'll try x = 2
f ' (x) = 12x^2 - 3
f ' (2) = 12(2)^2 - 3
f ' (2) = 45
The positive outcome tells us that any number from region C does the same, and f ' (x) > 0 when [tex]0.5 < x < \infty[/tex]. The function f(x) is increasing on this interval.
Region B decreases while C increases. The change from decreasing to increasing indicates we have a local min when x = 0.5
Plug this x value into the original equation
f(x) = 4x^3 - 3x + 3
f(0.5) = 4(0.5)^3 - 3(0.5) + 3
f(0.5) = 2
The local min is located at (0.5, 2) which is the other stationary point.
The graph and sign chart are shown below.
The local min is located at (0.5, 2) which is the other stationary point.
How to Determine whether each of the stationary points is a maximum or a minimum?Stationary points occur when the derivative is zero, when the graph is neither increasing nor decreasing.
Apply the derivative to get:
f(x) = 4x^3 - 3x + 3
f ' (x) = 12x^2 - 3
Then set it equal to zero and solve for x.
f ' (x) = 0
12x^2 - 3 = 0
12x^2 = 3
x^2 = 3/12
x^2 = 1/4
x = 1/2 or x = -1/2
x = 0.5 or x = -0.5
The first derivative test to help determine if we have local mins, local maxes, or neither.
A = numbers to the left of -0.5
B = numbers between -0.5 and 0.5 excluding both endpoints
C = numbers to the right of 0.5
Thus, The values -0.5 and 0.5 are not in any of the three regions. They are the boundaries.
Let's try something like x = -2
f ' (x) = 12x^2 - 3
f ' (-2) = 12(-2)^2 - 3
f ' (-2) = 45
In this case, f ' (x) > 0 when we're in region A.
Let's check region B x = 0.
f ' (x) = 12x^2 - 3
f ' (0) = 12(0) - 3
f ' (0) = -3
The result is negative, so f ' (x) < 0 when f(x) curve is decreasing on this interval.
The change from increasing to decreasing as we pass through x = -0.5 indicates that we have a local max here.
Substitute x = -0.5 into the original function to find its paired y coordinate.
f(x) = 4x^3 - 3x + 3
f(-0.5) = 4(-0.5)^3 - 3(-0.5) + 3
f(-0.5) = 4
The point (-0.5, 4) is a stationary point, it's a local max.
Let's check region C x = 2
f ' (x) = 12x^2 - 3
f ' (2) = 12(2)^2 - 3
f ' (2) = 45
The positive outcome tells us that any number from region C does the same, and f ' (x) > 0 when The function f(x) is increasing on this interval.
Susbtitute this x value into the original equation
f(x) = 4x^3 - 3x + 3
f(0.5) = 4(0.5)^3 - 3(0.5) + 3
f(0.5) = 2
Hence, The local min is located at (0.5, 2) which is the other stationary point.
Learn more about equations here;
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.03 + six tenths equals
Help I will give brainlest
Which pair of triangles can be proven congruent by SAS?
Answer:
The first one
Step-by-step explanation:
SAS postulate says that if two sides and the included angle of a triangle are equal to two sides and the included angle of another triangle, then the one triangles are said to be congruent.
Mrs. Nisbet had 97 books in her classroom library. She received a grant to expand her classroom library. After spending the money, she had 213 books. What is the percent increase? *
Answer: 219
Step-by-step explanation:
Evaluate each expression
Answer:
4 * 4 ÷ 4 = 4
8 ÷ (2*2) = 2
Step-by-step explanation:
[tex]4 * 4 \div4\\\rule{150}{0.5}\\\text{Use PEMDAS}\\\\4 * 4 \div4\\\\4 * 1\\\\\boxed{4}[/tex]
==============================
[tex]8 \div (2*2)\\\rule{150}{0.5}\\\text{Use PEMDAS}\\\\8 \div (2*2)\\\\8 \div 4\\\\\boxed{2}[/tex]
I hope this helps.
what is the equation of the line that has a slope of three and goes through the point (-3,-5)?
A. y= 3x+4
B. y= 3x-14
C. y= 3x-4
D. y= 3x+12
Answer:
y=3x+4
Step-by-step explanation:
y-y1=m(x-x1)
y-(-5)=3(x-(-3))
y+5=3(x+3)
y=3x+9-5
y=3x+4
5. Which of the following linear expressions is a factor of the cubic polynomial x^3 + 9x² +16x-12?
(1) x+6
(3) r-3
(2) x-1
(4) x+2
Answer:
(1) x+6
Step-by-step explanation:
Possible rational zeroes include ±1, ±2, ±3, ±4, ±6, ±12
Check each answer choice with synthetic division:
1 | 1 9 16 -12
__1_10_26
1 10 26 | 14
-2 | 1 9 16 -12
__-2_-14_-4
1 7 2 | -16
-6 | 1 9 16 -12
__-6_-18_12
1 3 -2 | 0
Therefore, x+6 is a factor of the polynomial
Answer:
(1) x+6
Step-by-step explanation:
HW
Due Tuesday, December 7, 2021
1. Tracy's is having a 25% off sale. Dana wants to buy a coat that has
an original price of $83. What is the sale price?
Answer:20.75 after sale
Step-by-step explanation:
25/100 of 83 is 2075
2075/100 = 20.75
Someone help?
Find the problem:
-5x - 16 = 8x - 1
Fix the problem:
?
[tex]-5x -16 = 8x -1\\\\\implies 8x +5x = -16 +1 \\\\\implies 13x = -15\\\\\implies x = -\dfrac{15}{13}[/tex]
Plzzzz help I REALLY NEED HELP
Write a division problem with 1/3 as the dividend 3 as divisor. The find the quotient.
Answer:
1/9
Step-by-step explanation:
Find the monthly house payments necessary to amortize a 10.8% loan of $125,800 over 20 years.
.
The payment size is $
Answer:
13,586400000000001 per time
Step-by-step explanation:
ME: Honesty Armani wade
1. The owner of a flower shop sells 18 roses for $90. What is the cost in dollars per rose? Show
or explain how you know.
Answer:
The roses are sold individualy for $5.00.
Step-by-step explanation:
To find the answer, you divide 90 (the total amount) by 18 (the number of roses). Because we are doing division, you forget about the dollar sign (for now) and do the division. 90➗18=5. Since it is money, it would be $5.00
a
1. Baby Amelia's parents measure her height every
month. She was born 46 cm long and grows on
average 2.5 cm per month. Write a linear equation to
find Baby Amelia's height, y, after x number of
months. (3 pts)
Slope:
y-intercept:
(1 pt)
Equation:
(1 pt)
After how many months will Amelia be 66 cm? Show
your work:
After
months. (1 pt)
Answer: equation: y = 2.5x + 46
slope: 2.5
y intercept: 46
she will be 8 months old by the time she is 66 cm
Step-by-step explanation: the eqation is written in y= mx+b format, where m is the slope and b is the y intercept. You can solve the last part of the problem by using this equation and subbing 66 in for y.
y = 2.5x + 46
66 = 2.5x + 46
20 = 2.5x
8 = x
Line’s family has completed 70% of a trip. They have traveled 35 miles. How far is the trip?
Answer:
hi the answer to your question should be 50 miles
Step-by-step explanation:
hope this helps have a great day!
find the numbered angles 1 to10
Answer:
6
Step-by-step explanation:
im not sure but I think 6 is the answer
7 grade math hellp me
Answer:
32
Step-by-step explanation:
180 - 148 = 32
I hope this helps!
(07.03 LC)
Identify the factors of x2 - 8x - 20. (1 point)
O (x + 4Nx - 5)
O (x + 5)(x - 4)
O (x - 10)(x + 2)
O (x-2)(x + 10)
Answer:
(x - 10)(x + 2)
Step-by-step explanation:
We are looking for two things that multiply together to give us
x^2 - 10x - 20
These things are binomials, such as (x+2) or (x-7) or (x+8) or (x-5)
We know the first term in the binomial has to be x, because x times x is x^2.
And then we are looking for two numbers that multiply to -20 but also add up to -8.
-10 and 2 multiply to make -20 and add up to -8 so we pick the answer (x-10)(x+2)
Answer:
Option C
Step-by-step explanation:
x² - 8x - 20
x² - (10x - 2x) - 20
x² - 10x + 2x - 20
x(x - 10) + 2(x - 10)
(x - 10)(x + 2)
Hence
Option C is correct
if SOMEONE MAKE 4 SMOOTHIES WITH A RATION OF 2;3 WHAT IS AN EQUIVALENT RATIO
Answer:
8 smoothies: 4:6
2 smoothies: 1:1.5, etc.
Find all the perfect cubes between 1000 and 2000.
Phil must lay concrete down for his back patio and
purchased 23 cubic feet of concrete, what are possible
dimensions of the patio slab? Select all that apply.
Answer:
Concrete can be purchased by the cubic yard. How much will it cost to pour a slab 18 feet by 18 feet by 6 inches for a patio if the concrete costs $42.00 per cubic yard?
Step-by-step explanation:
I HOPE THIS HELPS
Pre college need help this
what is the equation of the line that passes through point [3,-1] and has a slope of 2
Answer:
y = 2x - 7
Step-by-step explanation:
lmk if you want an explanation
Part A. What is the unit rate in dollars per hour for each company?
The unit rate for the 1st company is 2,86.
The unit rate for the 2nd company is 2,50.
Part B. Analyze Relationships Which company offers the best deal? Explain your answer.
Part C. What if? Another company offers a rate of $0.05 per minute. How would you find the unit rate per hour?
Answer:
i thinks its
the unot rate for the 1st company is 2,86
Step-by-step explanation:
7. A boutique is offering a 25% discount on purchase made in cash. Calculate the cash price Janelle paid for articles totaled to $465.
Help please, I attached a screenshot
[tex] \frac{(7 {x}^{2} {y}^{4} ) ^{2} }{49 {x}^{6} {y}^{5} } \\ = \frac{ {7}^{2} {x}^{2 \times 2} {y}^{4 \times 2} }{49 {x}^{6} {y}^{5} } \\ = \frac{49{x}^{4} {y}^{8} } {49 {x}^{6} {y}^{5}} \\ = {x}^{4 - 6} {y}^{8 - 5} \\ = {x}^{ - 2} {y}^{3} \\ = \frac{y ^{3} }{ {x}^{2} } [/tex]
Answer:
[tex] \frac{y ^{3} }{ {x}^{2} } [/tex]
Hope you could get an idea from here.
Doubt clarification - use comment section.
please help! ASAP I need help fast!!
Answer: 4.8
Explanation: divide total needed of blue paint (3) by 1/2 to find the ratio, which is 6. then multiply that by 4/5 to get the total of yellow paint, which is 4.8
6
0 0 0
TIME RE
44
Jeremiah flies an airplane for 2.7 hours at an average speed of 304.6 miles per hour. How far did Jeremiah fly?
Answer:
112.81 miles
Step-by-step explanation:
304.6 divided by 2.7
Given the function defined in the table below, find the average rate of change, in
simplest form, of the function over the interval 4 < x < 7.
f(x)
3
5
4.
9
5
15
6
23
7
33
Answer:
Submit Answer
attempt 2 out of 2
Answer:
8
Step-by-step explanation:
It appears your table includes points (4, 9) and (7, 33). The average rate of change on the interval is the slope of the line between these two points:
m = (y2 -y1)/(x2 -x1)
m = (33 -9)/(7 -4) = 24/3 = 8
The average rate of change is 8.
Find the area of the region bounded by the graphs of the equations [tex]y=2x-x^2, y=0.[/tex] Provide a sketch. Show the work!
[tex]\\ \sf\longmapsto y=2x-x^2[/tex]
y=0[tex]\\ \sf\longmapsto 2x-x^2=0[/tex]
[tex]\\ \sf\longmapsto x^2-2x=0[/tex]
[tex]\\ \sf\longmapsto x(x-2)=0[/tex]
[tex]\\ \sf\longmapsto x=0,2[/tex]
⇒ y=2x−x2
y=0⇒ 2x - x² = 0
⇒ x² - 2x = 0
⇒ x ( x - 2 ) = 0
⇒ x = 0, 2