Answer:
-615.12
Step-by-step explanation:
hope this helps
plz mark as brainliest!!
Wendy opened a savings account 15 years ago with a deposit of $2,340.73. The account has an interest rate of 4.7% compounded monthly. How much interest has
Wendy earned?
Answer:
$4661.77
Step-by-step explanation:
100 + 4.7 = 104.7%
104.7% = 1.047
$2340.73 x 1.047^15 = $4661.77
O E. $68.00
QUESTION 16
3.04 poi
You are a school photographer taking individual and class pictures for 2 classes of
21 students each. On average, each individual picture takes 3 minutes and a class
picture takes 10 minutes. About how long should it take you to get all of the
pictures?
O A. 1 hour 3 minutes
B. 1 hour 13 minutes
OC. 2 hours 6 minutes
OD. 2 hours 16 minutes
O E. 2 hours 26 minutes
Compute the odds in favor of obtaining a number divisible by 5 in a single roll of a die.
Answer:
1/6 or 16.7% chance
Step-by-step explanation:
A die has 6 sides, and there is only one side with a number divisible by 5, which is the number 5.
So, the probability of rolling a number divisible by 5 is 1/6.
= 1/6 or 0.167
The odds in favor of obtaining a number divisible by 5 will be 1/6 or 0.1667.
What is probability?Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.
The die is rolled for a single time. Then the total number of the events will be
Total event = 6 {1, 2, 3, 4, 5, 6}
The odds in favor of obtaining a number divisible by 5 will be
There is only one number that is divisible by 5 which is 5.
Then the number of favorable events will be
Favorable event = 1 {5}
Then the probability will be
P = 1 / 6
P = 0.1667
The odds in favor of obtaining a number divisible by 5 will be 1/6 or 0.1667.
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A lab technician is dividing a cell that has a diameter of 4.32×10−4 4 . 32 × 10 - 4 millimeters. Each of the new cells has a diameter measuring exactly one half of the diameter of the original cell. Which is the diameter of a new cel
Answer:
Bottom right option
Step-by-step explanation:
To find this, we can calculate:
1/2 * 4.32 * 10⁻⁴
= (1/2 * 4.32) * 10⁻⁴
= 2.16 * 10⁻⁴
The diameter of a new cell is 2.16×10−⁴millimeters
First step is to calculate 4.32×10−⁴ to the original numbers
4.32×10−⁴ =0.000432
Second step is to determine the diameter of a new cell
New cell diameter=0.000432×1/2
New cell diameter=0.000216
New cell diameter=2.16×10−⁴millimeters
Inconclusion The diameter of a new cell is 2.16×10−⁴millimeters
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Find the m∠DCA A. 10 B. 29 C. 116 D. 40
Hence, the m∠DCA is 59.2
What is an angle?An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs, and sometimes the arms of the angle.
How to solve?m∠DCB = (4x) + (6x-58) = 90
10x = 148
x = 14.8
m∠DCA = 4x
= 4(14.8)
= 59.2
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PLEASE NEED HELP ASAP!!!!!!! WILL GIVE BRAINLY!!!!!! what are the domain, range, and asymptote of h(x)=(0.5)^x-9
Answer:
[tex]\mathrm{Domain\:of\:}\:0.5^x-9\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:<x<\infty \\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}\\\\\mathrm{Range\:of\:}0.5^x-9:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)>-9\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-9,\:\infty \:\right)\end{bmatrix}\\\\\mathrm{Asymptotes\:of}\:0.5^x-9:\quad \mathrm{Horizontal}:\:y=-9[/tex]
Step-by-step explanation:
Domain:
The function has no undefined points nor domain constraints. Therefore, the domain is
[tex]...-\infty \:<x<\infty \:[/tex]
Definition: The domain of a function is the set of input or argument values for which the function is real and defined.
_________________________________________________
Range:
[tex]\mathrm{The\:range\:of\:an\:exponential\:function\:of\:the\:form}\:c\cdot \:n^{ax+b}+k\:\mathrm{is}\:\:f\left(x\right)>k\\k=-9[/tex]
[tex]f\left(x\right)>-9[/tex]
Definition: The set of values of the dependent variable for which a function is defined.
_________________________________________________
Asymptotes:
[tex]\mathrm{Vertical\:asymptotes\:of\:}0.5^x-9:\quad \mathrm{None}\\\mathrm{Horizontal\:Asymptotes\:of\:}0.5^x-9:\quad y=-9\\\mathrm{Horizontal}:\:y=-9x^{2}[/tex]
Write as an inequality "The difference of a number squared and three is at least twelve"
Answer:
using the equilateral formula of solution
Answer:
[tex]x^2-3\geq 12[/tex]
Step-by-step explanation:
[tex]x^{2} -3[/tex] is the difference of a number squared and three
is at least 12, means that is greater but not less
[tex]x^2-3\geq 12[/tex]
what is the domain of the function shown in the graph below?
answer type: interval, all real numbers, all values except one, all values except two
interval:
Answer: interval from -8 to 5
In interval notation, we would write [-8, 5]
The domain is the set of allowed x inputs to a function. The left-most point is (-8,0) so x = -8 is the smallest x value allowed. The largest x value allowed is x = 5 due to the point (5,0) being the right-most point.
The use of square brackets in interval notation says "include this endpoint as part of the interval".
Can someone tell me if I got the answer right? For the first one I got 2 and for the second one I got -1.
Answer:
see explanation
Step-by-step explanation:
f(g(2)) = f(0) = -2
g(f(1)) = g(0) = 0
Answer:
The correct answers for both of them is -2 and 0.
Step-by-step explanation:
I)
[tex](f\circ g)(2)=f(g(2))[/tex]
From the red graph, we can see that g(2) is 0.
Therefore, f(g(2)) is equal to f(0).
And from the blue graph, we can see that f(0) is -2.
Therefore:
[tex](f\circ g)(2)=-2[/tex]
II)
[tex](g\circ f)(1)=g(f(1))[/tex]
From the blue graph, we can see that f(1) is 0.
Therefore, g(f(1)) is equal to g(0).
And from the red graph, g(0) is 0.
Therefore:
[tex](g\circ f)(1)=0[/tex]
So, you got one correct. Nicely done!
Laura has a step of 50cm She walks along by taking two steps forward and one step back. What is the least number of steps counting forward and backwards step, she takes to reach a step 20m away? ~Thanks - don't know how to solve :(
Richard bought a car for $2,500. The value of the car depreciates by 5% each year,
What is the average rate of change in the value of the car during the first 3 years?
Round your answer to the nearest dollar.
-$232
- $116
-$119
- $357
Step-by-step explanation:
Hello, there!!!
The answer is option D.
I have given solution on the picture.
Hope it helps.....
If 120 is divided into 3 parts which are proportional to 1, [tex]\frac{1}{2} [/tex], and [tex]\frac{1}{6}[/tex], what is the middle part?
[tex]k+\frac{k}{2}+\frac{k}{6}=120\\\\6k+3k+k=720\\10k=720\\k=72[/tex]
72,36,12
answer: 36
help i want help i want help
Answer:
[tex] \boxed{127 \: {in}^{2} }[/tex]Option A is the correct option.
Step-by-step explanation:
Surface area of the rectangle base = 9 × 5 = 45 in²
Surface area of lateral square = ( 5 )² = 25 in²
Surface area of lateral rectangle = 6.4 × 5 = 32 in²
Surface area of top square = ( 5 )² = 25 in²
Surface area of two parallel trapezoids:
[tex] (\frac{1}{2} (9 + 5) \times 5) \times 2[/tex]
= 7 × 5 × 2
= 70 in²
Total surface area:
= 45 + 25 + 32 + 25 + 70
= 197 in²
Hope I helped!
Best regards!
Solve the equation 14=7(2x-4) using two different methods. Show your work. Which method do you prefer? Explain. need help thanks
Answer:
x=3
Step-by-step explanation:
14=7(2x-4)
14/7=2x-4
2=2x-4
2x=2+4
2x=6
x=6/2
x=3
------------
14=7(2x-4)
14=14x-28
14x=14+28
14x=42
x=42/14
x=3
The equation 14 = 7(2x - 4) can be solved using two different methods: the distributive property method and the inverse operations method. Both methods yield the same solution, which is x = 3. The preference between the two methods depends on personal preference and the specific equation being solved.
Distributive Property Method:
We'll distribute the 7 to the terms inside the parentheses:
14 = 7(2x - 4)
14 = 14x - 28
Next, we'll isolate the variable term:
14x = 14 + 28
14x = 42
Finally, we'll solve for x by dividing both sides of the equation by 14:
x = 42/14
x = 3
So the solution to the equation is x = 3.
Inverse Operations Method:
We'll use inverse operations to solve the equation step by step:
14 = 7(2x - 4)
Divide both sides of the equation by 7 to isolate the term in parentheses:
14/7 = 7(2x - 4)/7
2 = 2x - 4
Add 4 to both sides of the equation to isolate the variable term:
2 + 4 = 2x - 4 + 4
6 = 2x
Divide both sides of the equation by 2 to solve for x:
6/2 = 2x/2
3 = x
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Please answer and show steps. Will mark brainliest.
Answer:
13.4 meters
Step-by-step explanation:
About the diagram
Attached is a diagram of the problem. The directions North and East are shown so that the usual clockwise from +x measurement of angles will correspond to the bearing angles given in the problem. That is, the bearing of 120° is an angle of 120° measured from North toward East. (The mirroring across the line y=x can be a little mind-bending, but it is isomorphic, so all angles and lengths remain unchanged.)
The other feature of this diagram is the projection of the 3-D problem into two dimensions. Effectively, the center angle rabbit-O-coyote represents a plan view (in the plane of the ground), and the triangles coyote-O-C1 and rabbit-O-R1 represent side views (views in the vertical plane).
The side views let us work out the ground distances O-rabbit and O-coyote, so that we can find the ground distance rabbit-coyote as the problem requests.
__
Problem solution
The distance from the tree (O) to the rabbit is the "adjacent" leg of the 30° angle of elevation from the rabbit to the tree top. The 10 m tree height is the "opposite" leg of that rabbit-O-R1 right triangle. We know the ratio of opposite to adjacent sides gives the tangent of the angle, so we have ...
tan(30°) = 10/(rabbit distance from tree)
Solving for the rabbit distance, we get
rabbit distance = 10/tan(30°) ≈ 17.3205 m
Similarly, the coyote distance from the tree will be ...
coyote distance = 10/tan(20°) ≈ 27.4748 m
__
These are two legs of the rabbit-O-coyote triangle. The angle at O between the rabbit and coyote is 120° -97° = 23°. These values are sufficient to let us use the Law of Cosines to find the distance d from rabbit to coyote:
d² = r² +c² -2rc·cos(23°)
d² = 17.3205² +27.4748² -2·17.3205·27.4748·cos(23°) ≈ 178.769
d ≈ √178.769 ≈ 13.37 . . . . meters
The distance from the rabbit to the coyote is about 13.4 meters.
_____
Additional comment
Note that the angle of depression to the rabbit from the horizontal is the same as the angle of elevation from the rabbit. This lets us draw the diagram without a bunch of extra lines.
Select the correct answer from each drop-down menu.
35
30
25
Number of Roses
20
15
10
5
0
2
1
3
4
5
X
Number of Plants
According to the graph, the relationship between the number of rose plants and the number of roses is
Answer:
I think it is b
Step-by-step explanation:
How many numbers between 1 and 1000 do not contain the digits 8, and 9 ?
Answer:
998
Step-by-step explanation:
I haven't included the 1 or the 1000
Answer:
There are 200 numbers between 1 and 1000 that do not contain the digits 8, and 9.
Step-by-step explanation:
1-100
=(8,9,18,19,28,29,38,39,48,49,58,59,68,69,78,79,88,89,98,99)=20
101-200
=(108,109,118,119,128,129,138,139,148,149,158,159,168,169,178,179,188,189,198,199)=
201-300=20
.......
100*10=1000
20*10=200
Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the specified axis.
y = 6x − x2, y = 8; about x = 2
Answer:
[tex]\mathbf{V = [\dfrac{ 8 \pi }{3}] }[/tex]
Step-by-step explanation:
Given that:
y = 6x - x² , y = 8 about x = 2
To find the volume of the region bounded by the curves about x = 2; we have the radius of the cylindrical shell to be x - 1, the circumference to be 2 π (x -2 ) and the height to be 6x - x² - 8
6x - x² - 8
6x - x² - 8 = 0
-x² + 6x - 8 = 0
x² - 6x + 8 = 0
(x -4) (x - 2 ) = 0
So;
x = 2 , x = 4
Thus, the region bound of the integral are from a = 2 and b = 4
Therefore , the volume of the solid can be computed as :
[tex]V = \int \limits ^b _a \ 2x \times f(x) \ dx[/tex]
[tex]V = \int \limits ^4_2 2 \pi (x -2) (6x -x^2 -8) \ dx[/tex]
[tex]V = 2 \pi \int \limits ^4_2 (6x^2 - x^3 -8x -12 x - 2x^2 +16) \ dx[/tex]
[tex]V = 2 \pi \int \limits ^4_2 (8x^2 -x^3-20x +16) \ dx[/tex]
[tex]V = 2 \pi \int \limits ^4_2 ( -x^3+8x^2-20x +16) \ dx[/tex]
[tex]V = 2 \pi [\dfrac{ -x^7}{4}+\dfrac{8x^3}{3} -\dfrac{20x^2}{2} +16x]^4_2[/tex]
[tex]V = 2 \pi [\dfrac{ -(4^4-2^4)}{4}+\dfrac{8(4^3-2^3)}{3} -\dfrac{20(4^2-2^2)}{2} +16(4-2) ]^4_2[/tex]
[tex]V = 2 \pi [\dfrac{ -(256-16)}{4}+\dfrac{8(64-8)}{3} -10(16-4)} +16(2) ][/tex]
[tex]V = 2 \pi [\dfrac{ 4}{3}][/tex]
[tex]\mathbf{V = [\dfrac{ 8 \pi }{3}] }[/tex]
Find the first, fourth, and eighth terms of the sequence. A(n) = −5 ∙ 2x − 1
Answer:
The answer is option AStep-by-step explanation:
The rule for the sequence is
[tex]A(n) = 5. {2}^{x - 1} [/tex]
where x is the number of terms
For the first term
x = 1
That's
[tex]A(1) = 5. {2}^{1 - 1} [/tex]
[tex]A(1) = 5. {2}^{0} [/tex]
A(1) = 5(1)
A(1) = 5For the fourth term
x = 4
[tex]A(4) = 5. {2}^{4 - 1} [/tex]
[tex]A(4) = 5. {2}^{3} [/tex]
A(4) = 5(8)
A(4) = 40For the eighth term
x = 8
[tex]A(8) = 5. {2}^{8 - 1} [/tex]
[tex]A(8 ) = 5. {2}^{7} [/tex]
A(8) = 5(128)
A(8) = 640Hope this helps you
Answer:
The first option.
Step-by-step explanation:
The first term of the sequence would be...
A(1) = -5 * 2^(1 - 1)
= -5 * 2^0
= -5 * 1
= -5
The fourth would be...
A(4) = -5 * 2^(4 - 1)
= -5 * 2^3
= -5 * 8
= -40
The eighth would be...
A(8) = -5 * 2^(8 - 1)
= -5 * 2^7
= -5 * 128
= -640
So, the correct answer is the first option.
Hope this helps!
If we transform the parabola y=(x+1)^2+2 by shifting 7 units to the right and 5 units down, what is the vertex of the resulting parabola? Vertex of resulting parabola: (__ a0,__ a1)
Hey there! I'm happy to help!
The vertex form of a parabola is y=a(x-h)²+k. The h represents the horizontal transformation, while the k represents the vertical. The vertex of a parabola in this form is (h,k). The a represents a vertical stretch or shrink.
Our parabola is y=(x+1)²+2. This is already in vertex form, so we do not need to change the equation. There is no a (basically a=1), which means that the parabola has not been stretched or shrunk from its parent form.
We see that the h is -1. This is because in the original equation it is (x-h)², so it has to be -1 because the two negatives make a positive which is the +1. (x--1)=(x+1).
We see that the k value is 2.
Since the vertex is (h,k), this vertex is (-1,2).
However, we have to shift the parabola 7 units to the right and 5 units down. So, we add 7 to the x-value and subtract 5 from the y-value of the vertex.
(x,y)⇒(x+7,y-5)
(-1,2)⇒(6,-3)
Therefore, the vertex of the resulting parabola is (6,-3).
Have a wonderful day! :D
Three faucets fill a 100-gallon tub in 6 minutes. How long, in seconds, does it take six faucets to fill a 25-gallon tub? Assume that all faucets dispense water at the same rate.
Answer:
see below
Step-by-step explanation:
It would take 3 faucets 6/4 = 1.5 minutes to fill a 25-gallon tub since when the number of faucets stays the same, the volume of the tub and the time needed to fill the tub are directly proportional. However, when the volume of the tub stays the same, the number of faucets used and the time needed to fill the tub are inversely proportional, therefore, if I double the number of faucets used, it will half the time needed, so the answer is 1.5 / 2 = 0.75 minutes or 45 seconds.
Answer:
[tex]\large\boxed{45 seconds}[/tex]
Step-by-step explanation:
------------------------------------------------------------------------------------------------------------
Variable Key
Faucets = f
Minutes = m
Gallons = g
------------------------------------------------------------------------------------------------------------
Write an equation to display how long it takes for the 3 faucets to fill up a 100 gallon tub.
100g = 6m
Divide both sides of the equation by 6
m = 16.67g
This means that approximately 16.67 gallons are filled up per minute with 3 faucets. We found the measurement (gallons), which is based on the time (minutes). This is called the unit rate.
Now that we found the unit rate for 3 faucets, let's find the unit rate for 6 faucets by multiplying our unit rate by 2.
3f = 16.67g per minute
6f = (16.67g per minute)(2)
6f = 33.34 g per minute
We now know the unit rate for 6 faucets, so now all we have to do is divide that by 25 gallons, the second tub.
25g / 33.34 g = 0.75 minutes
Convert to seconds
0.75 minutes = 3/4 of a minute
1 minute = 60 seconds
Substitute
3/4(60)
[tex]\large\boxed{45 seconds}[/tex]
Hope this helps :)
PLEASE HELP I WILL GIVE BRAINLIEST!!!!! The box plots below show attendance at a local movie theater and high school basketball games: Two box plots are shown. The top one is labeled Movies. Minimum at 100, Q1 at 130, median at 165, Q3 at 185, maximum at 200. The bottom box plot is labeled Basketball games. Minimum at 135, Q1 at 225, median at 248, Q3 at 275, maximum at 300. Which of the following best describes how to measure the spread of the data? The IQR is a better measure of spread for movies than it is for basketball games. The standard deviation is a better measure of spread for movies than it is for basketball games. The IQR is the best measurement of spread for games and movies. The standard deviation is the best measurement of spread for games and movies.
Correct option is Option B: The standard deviation is a better measure of spread for movies than it is for basketball games.
Visual analysis for movies:
Movies data is more centric to mean and not skewed on a particular side.
Visual analysis for Basketball games:
Basketball games data is not centric to mean but is skewed or say more dense in right then left.
Property of standard deviation and its limitation:
Standard deviation just measures the deviation or spread with respect to mean of collected data. It is non- sensible for skewness of the data and thus more information is needed in such case.
Property of IQR and its limitation:
IQR is interquartile range. IQR generally is less powerful than standard deviation, but more powerful if the data is skewed and its variability has to be measured. It measures the range or say difference between [tex]Q_3 \: and \: Q_1[/tex]
In the movies data, the data is more collected and barely visible to be skewed. Thus standard deviation is best suited for this dataset.
In the basketball data, the standard deviation will fail to give good information about the data. The IQR, is better here since we've to measure variability or dispersion of data which is skewed.
Thus, option B: The standard deviation is a better measure of spread for movies than it is for basketball games; is correct option.
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pleeeaaaasseeeee help me!!!
determine the percent of change. round to the nearest whole percent if necessary. original: 250 new: 100
Answer:
going from new to original would be times 2.5
from original to new would be time 0.4
Step-by-step explanation:
new to original is the 250/100
original to new is 100/250
Answer:
-60%
Step-by-step explanation:
First, find the difference
250 - 100 = 150
Then divide the decrease by the original number
150/250 = 0.6
And to convert this to a percentage all you have to do is multiply it by 100
0.6(100) = 60
The percent of change is -60% which is a decrease since it's negative
Determine what type of model best fits the given situation: A model rocket fired straight up from the ground, where h is the height of the rocket and t is the time in seconds. A. none of these B. quadratic C. linear D. exponential
The type of model best fits the given situation is a quadratic equation
Quadratic equationQuadratic equations are equation that has a leading degree of 2.
From the given question, the motion of the rocket from the launch point to the landing point will be parabolic in nature and since the graph of a quadratic function is a parabola, hence the type of model best fits the given situation is a quadratic equation
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Match each number with its place in order from smallest (1st) to largest (6th). 1. 6th -56 2. 4th 90 3. 3rd -84 4. 1st 59 5. 2nd -80 6. 5th 48
Answer:
Numbers provided:
-56, 90, -84, 59, -80, 48
The smallest number is -84.
The highest number is 90.
1st: -84
2nd: -80
3rd: -56
4th: 48
5th: 59
6th: 90
Can you help me learn how to solve problems like these? I need to know the answer, but I also need to know how to do it because this isn't all of them.
[tex]\frac{1}{p-2} / \frac{4p^2}{p^2+p-6}[/tex]
[tex]\frac{6n}{3n+2} - \frac{2}{2n-2}[/tex]
[tex]\frac{2x}{3x^2+18x} + \frac{3}{2}[/tex]
[tex]\dfrac{\dfrac{1}{p-2}}{\dfrac{4p^2}{p^2+p-6}}=\\\\\\\dfrac{1}{p-2}\cdot\dfrac{p^2+p-6}{4p^2}=\\\\\dfrac{1}{p-2}\cdot\dfrac{p^2+3p-2p-6}{4p^2}=\\\\\dfrac{1}{p-2}\cdot\dfrac{p(p+3)-2(p+3)}{4p^2}=\\\\\dfrac{1}{p-2}\cdot\dfrac{(p-2)(p+3)}{4p^2}=\\\\\dfrac{p+3}{4p^2}[/tex]
--------------------------------------------------------------------
[tex]\dfrac{6n}{3n+2}-\dfrac{2}{2n-2}=\\\\\dfrac{6n(2n-2)}{(3n+2)(2n-2)}-\dfrac{2(3n+2)}{(3n+2)(2n-2)}=\\\\\dfrac{12n^2-12n-(6n+4)}{6n^2-6n+4n-4}=\\\\\dfrac{12n^2-12n-6n-4}{6n^2-2n-4}=\\\\\dfrac{12n^2-18n-4}{6n^2-2n-4}=\\\\\dfrac{2(6n^2-9n-2)}{2(3n^2-n-2)}=\\\\\dfrac{6n^2-9n-2}{3n^2-n-2}[/tex]
----------------------------------------------------------------------
[tex]\dfrac{2x}{3x^2+18x}+\dfrac{3}{2}=\\\\\dfrac{2}{3x+18}+\dfrac{3}{2}=\\\\\dfrac{2\cdot2}{2(3x+18)}+\dfrac{3(3x+18)}{2(3x+18)}=\\\\\dfrac{4+9x+54}{6x+36}=\\\\\dfrac{9x+58}{6x+36}[/tex]
Answer:
p^3−10p^2+1
—————— We find roots of zeros F(p) = p^3 - 10p^2 + 1 and see there
p^2 are no rational roots
Step-by-step explanation:
p^2
Simplify ——
p^2
1.1 Canceling out p^2 as it appears on both sides of the fraction line
Equation at the end of step 1
:1
((————-(4•1))+p)-6
(p^2)
STEP 2: working left to right
1
Simplify ——
p^2
Equation at the end of step 2:
1 /p^2 ((—— - 4) + p) - 6
STEP 3:
Rewriting the whole as an Equivalent Fraction
3.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using p^2 as the denominator :
4 4 • p^2
4 = — = ——————
1 p^2
Equivalent fraction
: The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
3.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
1 - (4 • p^2) 1 - 4p^2
———————————— = ———————
p^2 p^2
Equation at the end of step 3:
(1 - 4p^2)
(————————— + p) - 6
p^2
STEP 4:
Rewriting the whole as an Equivalent Fraction
4.1 Adding a whole to a fraction
Rewrite the whole as a fraction using p2 as the denominator :
p p • p^2
p = — = ——————
1 p^2
Trying to factor as a Difference of Squares:
4.2 Factoring: 1 - 4p^2
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 1 is the square of 1
Check : 4 is the square of 2
Check : p^2 is the square of p^1
Factorization is : (1 + 2p) • (1 - 2p)
Adding fractions that have a common denominator :
4.3 Adding up the two equivalent fractions
(2p+1) • (1-2p) + p • p^2 p^3 - 4p^2 + 1
———————————————————————— = ————————————
p^2 p^2
Equation at the end of step
4:
(p^3 - 4p^2 + 1)
—————————————— - 6
p^2
STEP 5:
Rewriting the whole as an Equivalent Fraction
5.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using p^2 as the denominator :
6 6 • p^2
6 = — = ——————
1 p^2
Polynomial Roots Calculator :
5.2 Find roots (zeroes) of : F(p) = p^3 - 4p^2 + 1
Polynomial Roots Calculator is a set of methods aimed at finding values of p for which F(p)=0
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers p which can be expressed as the quotient of two integers
The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient
In this case, the Leading Coefficient is 1 and the Trailing Constant is 1.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 -4.00
1 1 1.00 -2.00
Polynomial Roots Calculator found no rational roots
Adding fractions that have a common denominator :
5.3 Adding up the two equivalent fractions
(p3-4p2+1) - (6 • p2) p3 - 10p2 + 1
————————————————————— = —————————————
p2 p2
Polynomial Roots Calculator :
5.4 Find roots (zeroes) of : F(p) = p3 - 10p2 + 1
See theory in step 5.2
In this case, the Leading Coefficient is 1 and the Trailing Constant is 1.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 -10.00
1 1 1.00 -8.00
Polynomial Roots Calculator found no rational roots
Final result :
p3 - 10p2 + 1
—————————————
p2
Mariah bought a shirt for $28.50 and a belt. The total cost was $45.50. Which of the following equations can be used to find the cost of the belt? A. 28.50 + b= 45.50 B. 45.50 + b= 28.50 C. b= 28.50 - 45.50 D. b= 28.50 * 45.50 Please include work!!
Answer:
a is the answer 28.50 + b = 45.50
Step-by-step explanation:
so if i move 28.50 to the right side then it becomes b=45.50-28.50 and that equals to 17 . hope i helped have a great day
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Explanation:
28.50 = cost of shirt
b = cost of belt, some unknown value
45.50 = total cost (given)
28.50+b = total cost (add the first two items shown above)
equate the two total cost expressions to end up with 28.50+b = 45.50
Help
Find the lateral area of this cone.
Round to the nearest tenth.
Answer:
233.5 in²
Step-by-step explanation:
First we have to find the slant height.
5²+14²=c²
25+196=c²
221=c²
c=14.866
Now we can find the lateral area.
[tex]\pi[/tex]rl
[tex]\pi[/tex](5)(14.866)
=233.51566
To the nearest tenth=
233.5 in²
Is the function ƒ(θ) = 2cos( θ) an odd or even function?
Answer:
Even function.
Step-by-step explanation:
An odd function has symmetry with respect to the origin.
[tex]\text{A function is odd }\Leftrightarrow f(-x)=-f(x)[/tex]
The sine function is an odd function:
[tex]\sin(-\theta)=\sin(\theta)[/tex]
An even function has symmetry with respect to the y-axis.
[tex]\text{A function is even}\Leftrightarrow f(-x)=f(x)[/tex]
The cosine function is an even function:
[tex]\cos(-\theta)=\cos(\theta)[/tex]
Is the function [tex]f(\theta)=2\cos(\theta)[/tex] an odd or even function?
It is an even function.
What happens in the function is a vertical stretch by a factor of 2. The y-intercept is equal to 2.
PLEASE HELP ME WITH THIS QUESTION ANYTHING HELPS!
Answer:
x = 148
Step-by-step explanation:
CPD is a straight line so it equals 180
CPB + BCD = CPD
x + 32 = 180
Subtract 32 from each side
x+32-32 = 180-32
x =148