Step-by-step explanation:
Equation is y = -2*x + 1
Hope this helps..
I need help with this problem
20.25 square units are enclosed between the two curves.
How to find area?To find the area enclosed between the two curves, find their intersection points first.
Setting the equations equal to each other:
8x² - x³ + x = x² + 13x
Simplifying and rearranging:
x³ - 7x² - 12x = 0
Factoring out x:
x(x² - 7x - 12) = 0
Solving for x using the quadratic formula:
x = 0, x = 3, x = -4
The two curves intersect at x = 0, x = 3, and x = -4.
Next, determine which curve is on top of the other between these intersection points. We can do this by comparing their y-values for each x:
At x = -4, y = 128
At x = 0, y = 0
At x = 3, y = 27
So, the curve y = 8x² - x³ + x is on top of y = x² + 13x for x in the range -4 ≤ x ≤ 0, and y = x² + 13x is on top of y = 8x² - x³ + x for x in the range 0 ≤ x ≤ 3.
Now find the area between the curves using integration:
∫[from -4 to 0] [(8x² - x³ + x) - (x² + 13x)] dx + ∫[from 0 to 3] [(x² + 13x) - (8x² - x³ + x)] dx
Simplifying:
∫[from -4 to 0] (-x³ + 7x² - 12x) dx + ∫[from 0 to 3] (x³ - 7x² + 12x) dx
Integrating:
[-(1/4)x⁴ + (7/3)x³ - 6x²] from -4 to 0 + [(1/4)x⁴ - (7/3)x³ + 6x²] from 0 to 3
Simplifying:
(64/3) + (81/4) - (27/3) - (64/3) = 20.25
Therefore, the area enclosed between the two curves is 20.25 square units.
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Image transcribed:
(1 point) Find the area of the region that is enclosed between y = 8x² - x³ + x and y = x² + 13x.
The area is
Let f(x) = 2(x-3)^2
Write a function g whose graph is a reflection in the x-axis of the graph of f.
g(x) =
The reflected form of \(f(x) = 2\cdot (x-3)^{2}\) in the x-axis is \(g(x) = -2\cdot (x-3)^{2}\).
Mathematically speaking, a reflection of \(f(x)\) in the x-axis is represented by the following formula:
\(g(x) = -f(x)\) (1)
Where:
\(f(x)\) - Original function.\(g(x)\) - Reflected function.Let be \(f(x) = 2\cdot (x-3)^{2}\), then \(g(x)\) is:
\(g(x) = -2\cdot (x-3)^{2}\) (2)
Now we present a comparison between \(f(x)\) and \(g(x)\) in the image attached below.
The reflected form of \(f(x) = 2\cdot (x-3)^{2}\) in the x-axis is \(g(x) = -2\cdot (x-3)^{2}\).
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72 boxes out of 90 sold what percentage sold
Answer:
is what is the math thing at you need help with huh
Need to find the value of x. PLEASE help!!
Can someone please help me figure these out please
Step-by-step explanation:
20x+6=22x-6
6+6=22x-20x
12=2x
x=12/2
x=6°
13x+8=112
13x=112-8
13x=104
x=104/13
x=8°
Please help and I would really appreciate if the answer is correct
Answer:
The value for 6 is ones that's the answer
Answer:
14) 0.01 or 1/100
15) 0.06
16) 3.02
17) >
18)0.6
19) 100
20) 0.35
Help with the following equation 8x²-6x-5=x
Answer:
\(8 {x}^{2} - 6x - 5 = x\)
\(8 {x}^{2} - 7x - 5 = 0\)
x = (7 + √((-7)^2 - 4(8)(-5)))/(2×8)
= (7 + √(49 + 160))/16
= (7 + √209)/16
= -.4661, 1.3411 (to 4 decimal places)
Need help asap!! For this algebra
It is noticed that the factors then the x-intercepts are the same value as that of factors.
Given that, the quadratic equation represented on the graph in factored form is y=(x-3)(x+2).
From the graph, x-intercepts are x=-2 and x=3.
The vertex of the given quadratic graph is (0.5, -6)
Therefore, it is noticed that the factors then the x-intercepts are the same value as that of factors.
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two multiplicative sets s and t yield localizations with the same primes then actually they have the same saturation
Yes, this is true. If two multiplicative sets s and t yield localizations with the same primes, then the two localizations are the same, since the same prime ideals are being used to define the two localizations.
Yes, this is true. If two multiplicative sets s and t yield localizations with the same primes, then the two localizations are the same, since the same prime ideals are being used to define the two localizations.
Thus, the two sets s and t have the same saturation since they yield the same localization.
If two multiplicative sets s and t yield localizations with the same primes, then the two sets s and t have the same saturation since they yield the same localization.
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Using the following conversions between the metric and U.S. systems, convert the measurement. Round your answer to 6 decimal places as needed
1 meter ≈ 3.28 feet
1 Liter ≈ 0.26 gallons
1 kilogram ≈ 2.20 pounds
33.777 yd ≈ __________ km
Answer:
33.777 yd = 0.030886 km
Step-by-step explanation:
==>Given:
33.777 yd
==>Required:
Convert 33.777 yd to km to 6 decimal places, using the metric and U.S systems.
==>Solution:
To convert, note that 1 km = 1093.6133 yd.
Thus,
1 km = 1093.6133 yd
x km = 33.777 yd
Cross multiply
1 × 33.777 = 1093.6133 × x
33.777 = 1093.6133x
Divide both sides by 1093.6133, to solve for x
33.777/1093.6133 = x
0.03088569 = x
x ≈ 0.030886 (to 6 decimal places)
Therefore, 33.777 yd = 0.030886 km
Michael deposits $3000 into an account that pays simple interest at a rate of 2% per year. How much interest will he be paid in the first 6 years?
Answer:
$3360 in the first 6 years.
Step-by-step Explanation:
To get the answer, you need to do 3000 x 2%. That would get you 60. Then, you multiply 60 x 6 (6 for the 6 years) which would be 360. Finally, you add 360 to 3000 and your answer would be $3360.
I don't really understand this, how to set it up etc and i cant figure out how to get the actual answer. Im sorry i make no sense
Answer:
i also can't at all
Step-by-step explanation:
This is hard for me
The table represents a linear function.
What is the slope of the function?
-10
-5
5
10
Find the time which will yield Simple
interest of #1,800 on #2 400 at the rate of 5% per annum.
Answer:
2,014
Step-by-step explanation:
Mary was
counting steps while she walked around her
neighborhood. She realized that it took her 2,014 steps
to get from her apartment to the park. She also
realized that it took her 798 steps to get from her
apartment to the corner store. How many more steps
does it take Mary to get to the park from her apartment
than to the store?
what is 6/5 x 25/24 = ?
Elwin Osbourne, CIO at GFS, Inc., is studying employee use of GFS e-mail for non-business communications. A random sample of 200 e-mail messages was selected. Thirty of the messages were not business related. The 90% confidence interval for the population proportion is _________.
Answer:
The 90% confidence interval for the population proportion is
(0.10872, 0.19128)
Step-by-step explanation:
Explanation:-
Step(i):-
Given data A random sample of 200 e-mail messages was selected. Thirty of the messages were not business related
Given random sample size 'n' = 200
Given Thirty of the messages were not business related
let 'x' = 30
Probability of the messages were not business related or proportion
\(p = \frac{x}{n} = \frac{30}{200} = 0.15\)
Step(ii):-
The 90% confidence interval for the population proportion is
\((p - Z_{0.10} \sqrt{\frac{p(1-p)}{n} } , p + Z_{0.10} \sqrt{\frac{p(1-p)}{n} } )\)
Level of significance ∝ = 0.90 or 0.10
The critical value Z₀.₁₀ = 1.645
The 90% confidence interval for the population proportion is
\(( 0.15-1.645 \sqrt{\frac{0.15(1-0.15)}{200} } , 0.15 +1.645 \sqrt{\frac{0.15(1-0.15)}{200} } )\)
on calculation, we get
(0.15 - 0.04128 , (0.15 + 0.04128)
(0.10872, 0.19128)
Conclusion:-
The 90% confidence interval for the population proportion is
(0.10872, 0.19128)
help appreciated!! trying to catch up on homework, need just 20% more to pass the class!!!
The percentage of data items that lie below the z-score of 3 is 99.87%.
In a normal distribution, the z-score represents the number of standard deviations a particular data point is away from the mean. The table provided gives the percentiles corresponding to different z-scores.
To find the percentage of data items that lie below a z-score of 3, we can look up the corresponding percentile in the table. In this case, the percentile for a z-score of 3 is given as 99.87%.
This means that approximately 99.87% of the data items in a normal distribution are below a z-score of 3.
Similarly, to find the percentage of data items that lie above a z-score of 3, we can subtract the percentage below the z-score from 100%. In this case, it would be 100% - 99.87% = 0.13%.
This means that approximately 0.13% of the data items in a normal distribution are above a z-score of 3.
Thus, these percentages indicate the relative position of the data points within the distribution. It provides a measure of how extreme or rare a particular value is in comparison to the rest of the distribution.
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Help with this number line please. Thanks
Answer:
A. 4 3/4
B. 3 1/2
C. 3 1/4
D. 4 1/4
stuck on this question
1. Gavin buys 89 blue pansies and
86 yellow pansies. He will plant the flowers
in 5 rows with an equal number of plants
in each row. Draw a bar model to help you
find how many plants will be in each row,
O
17
Spiral Review
nose nilo que dise perdoooooooon xd
The diameter of the Sun is about 1.4 x 106 km. The diameter of the planet
Venus is about 12,000 km. What is the approximate ratio of the diameter of the Sun to the diameter of
Venus?
Answer:
1.17*10²
Step-by-step explanation:
Diameter of the sun is about 1.4 × 10⁶ km
1.4*10⁶ km = 1,400,000
Diameter of the planet venus is about 12000 km
12000 km = 1.2 × 10⁴
Ratio of the diameters
Sun : Venus
1.4 × 10⁶ km : 1.2 × 10⁴
1.4 × 10⁶ km / 1.2 × 10⁴
1.4 / 1.2 × 10^6-4
1.166 × 10²
Approximately
1.17 × 10²
A boy is playing a ball in a garden surrounded by a wall 2.5 m high and kicks the ball vertically up from a height of 0.4 m with a speed of 14 m/s . For how long is the ball above the height of the wall.
Answer:
2.5 sec
Step-by-step explanation:
Height of wall = 2.5 m
initial speed of ball = 14 m/s
height from which ball is kicked = 0.4 m
we calculate the speed of the ball at the height that matches the wall first
height that matches wall = 2.5 - 0.4 = 2.1 m
using = + 2as
where a = acceleration due to gravity = -9.81 m/s^2 (negative in upwards movement)
= + 2(-9.81 x 2.1)
= 196 - 41.202
= 154.8
v = = 12.44 m/s
this is the velocity of the ball at exactly the point where the wall ends.
At the maximum height, the speed of the ball becomes zero
therefore,
u = 12.44 m/s
v = 0 m/s
a = -9.81 m/s^2
t = ?
using V = U + at
0 = 12.44 - 9.81t
-12.44 = -9.81
t = -12.44/-9.81
t = 1.27 s
the maximum height the ball reaches will be gotten with
= + 2as
a = -9.81 m/s^2
0 = + 2(-9.81s)
0 = 196 - 19.62s
s = -196/-19.62 = 9.99 m. This the maximum height reached by the ball.
height from maximum height to height of ball = 9.99 - 2.5 = 7.49 m
we calculate for the time taken for the ball to travel down this height
a = 9.81 m/s^2 (positive in downwards movement)
u = 0
s = 7.49 m
using s = ut + a
7.49 = (0 x t) + (9.81 x )
7.49 = 0 + 4.9
= 7.49/4.9 = 1.53
t = = 1.23 sec
Total time spent above wall = 1.27 s + 1.23 s = 2.5 sec
please someone help me answer these correct
Answer:
The x-intercept of g(x) is (2, 0).
The y-intercept of g(x) is (0, -4).
Step-by-step explanation:
x-interceptThe x-intercept is the point at which the graph crosses the x-axis, so when y = 0.
To find the x-intercept of function g(x), find the coordinate pair in the table where g(x) = 0.
Therefore, the x-intercept is (2, 0).
\(\hrulefill\)
y-interceptThe y-intercept is the point at which the graph crosses the y-axis, so when x = 0.
To find the y-intercept of function g(x), find the coordinate pair in the table where x = 0.
Therefore, the y-intercept is (0, -4).
Which equation is equivalent to the given equation?
HELP
solving the system linear equation by substitution 2x-8y=10x=4y+7
No solution
Explanations:The given system of equations is:
2x - 8y = 10......................(1)
x = 4y + 7.............................(2)
Substitute equation (2) into equation (1)
2(4y + 7) - 8y = 10
8y + 14 - 8y = 10
8y - 8y = 10 - 14
0 = -4 ( This is false)
This means that the system of equations has no solutions
Also by oberving the two equations, we would see that they are parallel equations because they have equal slope (1/4). A system of parallel equations has no solution since there is no point of intersection.
12a + 5c = 2550 method of elimination
Answer:
i like you
Step-by-step explanation:
Write a linear function for the graph, and state and interpret the slope and y-intercept for the given scenario:
Bamboo grows very quickly. Use the information in the graph to write an equation that models the height (y) at time (x).
The linear function for the given graph is y = x + 20.
What is a linear function?
A straight line on the coordinate plane is represented by a linear function. It has one independent variable and one dependent variable. For slope (m) and y-intercept (b) form, the equation is given by:
y = mx + b
From the graph,
The coordinates of the given graph are (0,20) and (20,40)
Then, slope (m) = (40-20)/(20-0) = 20/20 = 1
and y-intercept (b) = 20
So, the equation will be y = 1x + 20
Hence, the linear function for the given graph is y = x + 20.
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Zoe is saving money to go on a trip to Mexico. She earns 16.75 for mowing the lawn . If Zoe mows the lawn 28 times how much money will she earn
469
do 16.75 x 28 which will equal to 469
Seven-ninths of the students surveyed like to participate in extra curricular activities after school. Which decimal is equivalent to the fraction of students who like to participate in activities after school
Answer
0.78
Explanation
The fraction of students who like to participate in extra curricular activities = (7/9)
In decimal form,
(7/9) = 0.78
Hope this Helps!!!
Answer:
0.78 because 7/9as a decimal is 0.78
After watching baking shows on T.V., Angie signs up for a cake-decorating class. To practice her new skills, she decorates a batch of cupcakes with sugar flowers. Angie puts 4 sugar flowers on each cupcake. In all, Angie puts 32 sugar flowers on the cupcakes.
Which equation can you use to find the number of cupcakes c Angie decorates?
Solve this equation for c to find the number of cupcakes Angie decorates.
Angie decorates 8 cupcakes after putting 4 sugar flowers on each cupcake.
To find the number of cupcakes c Angie decorates, we can use the equation:4c = 32where 'c' is the number of cupcakes Angie decorates.
4 represents the number of sugar flowers Angie puts on each cupcake, and 32 is the total number of sugar flowers Angie puts on the cupcakes.
To solve this equation for c, we need to isolate c on one side of the equation. We can do this by dividing both sides of the equation by 4. This gives us:c = 8
Therefore, Angie decorates 8 cupcakes.Here's how we get to this answer:4c = 32Divide both sides by 4 to isolate c:c/4 = 32/4c = 8
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URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100
POINTS!!!
Answer:
point
vertex
one
face
face
circular
length
area
volume