The cost of cupcakes is $1.25 and cookies costs $0.90.
Two equations that would be used to determine the required values can be derived from this question:
20x + 40y = 61 equation 1
30x + 30y = 64.50 equation 2
In order to determine the value of y, the following steps would be taken: Multiply equation 1 by 3 and equation 2 by 2.
60x + 120y = 183 equation 3
60x + 60y = 129 equation 4
Subtract equation 4 from 3
60y = 54
Divide both sides of the equation by 60
y = $0.90
Substitute for y in equation 1
20x + 40(0.9) = 61
20x + 36 = 61
20x = 61 - 36
20x = 25
x = 25 / 20
x = $1.25
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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.
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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.
9. What conversion factor can you use to convert miles to inches? Explain how you found it.
Answer:
You know that 1 mile = 5280 feet and 1 foot = 12 inches, so using these conversion factors you can go from one to the other.
I hope this answered you question!
Step-by-step explanation:
Find all the perfect cubes between 1000 and 2000.
.03 + six tenths equals
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:
Help I will give brainlest
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
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:
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.
(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
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.
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
Use the distributive property to multiply 4,345 x 2
Answer:
8690
Step-by-step explanation:
there is no distributive property just multiply using a regular calculator
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!
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]
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
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:
7. A boutique is offering a 25% discount on purchase made in cash. Calculate the cash price Janelle paid for articles totaled to $465.
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
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
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
A riverboat travels 54 km downstream in 2 hours. It travels 57 km upstream in 3 hours. Find the speed of the boat and the speed of the stream
Here we must write and solve a system of equations to find the speed of the boat and the speed of the stream. We will find that the boat's speed is 23km/h and the river's speed is 4km/h.
First, remember the relation:
Distance = Speed*Time.
Now let's define the variables we will be using:
B = boat's speedR = river's speed.When the boat travels downstream, the total speed of the boat is the speed of the boat plus the speed of the river, and we know that in that case it travels 54km in 2 hours, then:
54km = (B + R)*2h
When the boat travels upstream, we must subtract the speed of the river. In that case, we know that the boat travels 57km in 3 hours, then we have:
57km = (B - R)*3h
Then our system of equations is:
54km = (B + R)*2h
57km = (B - R)*3h
To solve this, first, we need to isolate one of the variables in one of the equations, let's isolate B in the second one:
57km = (B - R)*3h
57km/3h + R = B
19 km/h + R = B
Now we can replace that in the other equation:
54km = (B + R)*2h
54km/2h = B + R
27 km/h = B + R = (19 km/h + R) + R
Now we can solve this for R:
27 km/h = 19km/h + 2*R
27 km/h - 19km/h = 2*R
8 km/h = 2*R
(8km/h)/2 = 4km/h = R
Now that we know the value of R, we can use:
B = 19 km/h + R = 19 km/h + 4km/h = 23 km/h
So the boat's speed is 23km/h and the river's speed is 4km/h.
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7 grade math hellp me
Answer:
32
Step-by-step explanation:
180 - 148 = 32
I hope this helps!
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
find the numbered angles 1 to10
Answer:
6
Step-by-step explanation:
im not sure but I think 6 is the answer
Please help, I will give good rating and brainliest of possible!!
Thank you!!!!!!!!
Answer:
[tex]g(x)=x+8[/tex]
Step-by-step explanation:
Translating a function up is very simple, all you need to do here is add 8.
If you want to think of it logically,
[tex]f(x)=x[/tex]
the whole right side of the function here can be our output. If x is 8, then the output, or height, is also 8. if you wanted to translate that up to 10, you'd simply need to add 2 to it, meaning [tex]x+2[/tex]. Then, at any given point on the function, it'd be 2 higher than it would be otherwise.
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.