Answers
Answer:
C. 15.6
Step-by-step explanation:
Perimeter of WXYZ = WX + XY + YZ + ZW
Use the distance formula, [tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex] to calculate the length of each segment.
✔️Distance between W(-1, 1) and X(1, 2):
Let,
[tex] W(-1, 1) = (x_1, y_1) [/tex]
[tex] X(1, 2) = (x_2, y_2) [/tex]
Plug in the values
[tex] WX = \sqrt{(1 - (-1))^2 + (2 - 1)^2} [/tex]
[tex] WX = \sqrt{(2)^2 + (1)^2} [/tex]
[tex] WX = \sqrt{4 + 1} [/tex]
[tex] WX = \sqrt{5} [/tex]
[tex] WX = 2.24 [/tex]
✔️Distance between X(1, 2) and Y(2, -4)
Let,
[tex] X(1, 2) = (x_1, y_1) [/tex]
[tex] Y(2, -4) = (x_2, y_2) [/tex]
Plug in the values
[tex] XY = \sqrt{(2 - 1)^2 + (-4 - 2)^2} [/tex]
[tex] XY = \sqrt{(1)^2 + (-6)^2} [/tex]
[tex] XY = \sqrt{1 + 36} [/tex]
[tex] XY = \sqrt{37} [/tex]
[tex] XY = 6.08 [/tex]
✔️Distance between Y(2, -4) and Z(-2, -1)
Let,
[tex] Y(2, -4) = (x_1, y_1) [/tex]
[tex] Z(-2, -1) = (x_2, y_2) [/tex]
Plug in the values
[tex] YZ = \sqrt{(-2 - 2)^2 + (-1 -(-4))^2} [/tex]
[tex] YZ = \sqrt{(-4)^2 + (3)^2} [/tex]
[tex] YZ = \sqrt{16 + 9} [/tex]
[tex] YZ = \sqrt{25} [/tex]
[tex] YZ = 5 [/tex]
✔️Distance between Z(-2, -1) and W(-1, 1)
Let,
[tex] Z(-2, -1) = (x_1, y_1) [/tex]
[tex] W(-1, 1) = (x_2, y_2) [/tex]
Plug in the values
[tex] ZW = \sqrt{(-1 -(-2))^2 + (1 - (-1))^2} [/tex]
[tex] ZW = \sqrt{(1)^2 + (2)^2} [/tex]
[tex] ZW = \sqrt{1 + 4} [/tex]
[tex] ZW = \sqrt{5} [/tex]
[tex] ZW = 2.24 [/tex]
✅Perimeter = 2.24 + 6.08 + 5 + 2.24 = 15.56
≈ 15.6
Answer:CCCCCCCCCCCCCCCCC
Step-by-step explanation:
Related Questions
which expression is equivalent to c^2 - 4 / c + 3 /
Answers
Step-by-step explanation:
[tex] \frac{ {c}^{2} - 4 }{c + 3} [/tex]
[tex] \frac{(c - 2)(c + 2)}{(c + 3)} [/tex]
Each marble bag sold by Debra's Marble Company contains 8 yellow marbles for every 4 blue marbles. If a bag has 56 yellow marbles, how many blue marbles does it contain?
Answers
Answer:
28 blue marbles
Step-by-step explanation:
yellow: blue
8 4
To get to 56 yellow marbles multiply by 7
yellow: blue
8*7 4*7
56 28
There will be 28 blue marbles
Student is 19 years old in the world has a population of 6.7 billion assuming that the population continues to grow in annual rate of 1.1%, predict what the worlds population will be when the student is 52
Answers
9514 1404 393
Answer:
9.6 billion
Step-by-step explanation:
The population multiplier is 1+1.1% = 1.011 each year. After 52-19 = 33 years, the multiplier will be 1.011^33 ≈ 1.4348.
When the student is 52, the population of the world will be about ...
6.7 billion × 1.4348 ≈ 9.6 billion
The five number summary of a dataset is given as
0, 4, 12, 14, 20
An observation is considered an outlier if it is below _______
An observation is considered an outlier if it is above _______
The five number summary of a dataset is given as
2, 8, 14, 18, 20
An observation is considered an outlier if it is below _______
An observation is considered an outlier if it is above _______
.
.
Answers
Given:
The five number summary of two data sets are given as:
a) 0, 4, 12, 14, 20
b) 2, 8, 14, 18, 20
To find:
The range for the outliers.
Solution:
We know that,
An observation is considered an outlier if it is below [tex]Q_1-1.5(IQR)[/tex]
An observation is considered an outlier if it is above [tex]Q_3+1.5(IQR)[/tex]
Where, IQR is the interquartile range and [tex]IQR=Q_3-Q_1[/tex].
The five number summary of two data sets are given as:
0, 4, 12, 14, 20
Here, [tex]Q_1=4[/tex] and [tex]Q_3=14[/tex].
Now,
[tex]IQR=14-4[/tex]
[tex]IQR=10[/tex]
The range for the outliers is:
[tex][Q_1-1.5(IQR),Q_3+1.5(IQR)]=[4-1.5(10),14+1.5(10)][/tex]
[tex][Q_1-1.5(IQR),Q_3+1.5(IQR)]=[4-15,14+15][/tex]
[tex][Q_1-1.5(IQR),Q_3+1.5(IQR)]=[-11,29][/tex]
An observation is considered an outlier if it is below -11.
An observation is considered an outlier if it is above 29.
The five number summary of two data sets are given as:
2, 8, 14, 18, 20
Here, [tex]Q_1=8[/tex] and [tex]Q_3=18[/tex].
Now,
[tex]IQR=18-8[/tex]
[tex]IQR=10[/tex]
The range for the outliers is:
[tex][Q_1-1.5(IQR),Q_3+1.5(IQR)]=[8-1.5(10),18+1.5(10)][/tex]
[tex][Q_1-1.5(IQR),Q_3+1.5(IQR)]=[8-15,18+15][/tex]
[tex][Q_1-1.5(IQR),Q_3+1.5(IQR)]=[-7,33][/tex]
An observation is considered an outlier if it is below -7.
An observation is considered an outlier if it is above 33.
A parallel plate capacitor has an area of 1.5 cm
2
and the plates are separated a distance of 2.0 mm with air between them. How much charge does this capacitor store when connected to a 12V battery?
Answers
Step-by-step explanation:
Given:
[tex]A=1.5\:\text{cm}^2×\left(\frac{1\:\text{m}^2}{10^4\:\text{cm}^2}\right)=1.5×10^{-4}\:\text{m}^2[/tex]
[tex]d = 2.0\:\text{mm} = 2.0×10^{-3}\:\text{mm}[/tex]
The charge stored in a capacitor is given by [tex]Q = CV.[/tex] In the case of a parallel-plate capacitor, its capacitance C is given by
[tex]C = \epsilon_0\dfrac{A}{d}[/tex]
where [tex]\epsilon_0[/tex] = permittivity of free space. The amount of charge stored in the capacitor is then
[tex]Q = \left(\epsilon_0\dfrac{A}{d}\right)V[/tex]
[tex]\:\:\:\:\:=\left[\dfrac{(8.85×10^{-12}\:\text{F/m})(1.5×10^{-4}\:\text{m}^2)}{(2.0×10^{-3}\:\text{m})}\right](12\:\text{V})[/tex]
[tex]\:\:\:\:\:=8.0×10^{-12}\:\text{C}[/tex]
Use the remainder term to find the minimum order of the Taylor polynomial, centered at 0, that is required to approximate the following quantity with an absolute error no greater than 10^-2.
√1.06.
n>= __________
Answers
Answer:
n ≥ 3
Step-by-step explanation:
Applying the remainder term in evaluating the minimum order of the Taylor polynomial
absolute error ≤ 10^-2
[tex]\sqrt{1.06}[/tex]
∴ n ≥ ?
The remainder term is the leftover term after computation ( dividing one polynomial with another )
attached below is the detailed solution
The minimum order of the Taylor polynomial, n≥3
What is Taylor polynomial?Taylor polynomial is a series of functions that has an infinite sum of terms that are expressed in terms of the function's derivatives.
[tex]\rm f(a)+\frac{f'(a)}{1!} (x-a)+\frac{f''(a)}{2!} (x-a)^{2} +....,[/tex]
Applying the Taylor series polynomial, the minimum order of the Taylor polynomial, centered at 0
[tex]\rm f(0)+\frac{f'(0)}{1!} (x-0)+\frac{f''(0)}{2!} (x-0)^{2} +....,[/tex]
f(x) = [tex]\sqrt{x+1}[/tex]
[tex]f'(x)=\frac{1}{2}[/tex]
[tex]f''(x)=3/8[/tex]
substituting in the Taylors series
T(x) = [tex]1+\frac{x}{2} -\frac{x^{2} }{8} +\frac{x^{3} }{16}[/tex]......
T(0.06) = [tex]1+\frac{0.06}{2} -\frac{0.06^{2} }{8} +\frac{0.06^{3} }{16}...[/tex]
T(0.06) =1.03
f(0.06) =
[tex]\sqrt{0.06+1}\\= 1.03[/tex]
Therefore, the minimum order of the Taylor polynomial, n≥3
Learn more about Taylor polynomial;
https://brainly.com/question/23842376
What is the slope of a relation with ordered pairs of (-5, 3) and (4.1).
9/2
2/9
-9/2
-2/9
2
-2
Answers
2/-9
-2/9 is the answer
PLEASE HELP ASAP, Thank you
Answers
9514 1404 393
Answer:
2.244
Step-by-step explanation:
Your answer looks like it may have a transcription error.
The period is reasonably computed as the difference of the x-values of the given points:
period = 4.114 -1.870 = 2.244 . . . seconds
7^300 chia 7 dư bao nhiêu
Answers
Answer:
dư 0... 7^300 chia 7 đc 7^299 mà
A car travels 12 km in 15 minutes.
Work out the average speed of the car in km/h.
Answers
Step-by-step explanation:
s=12km t=15m
15m--> km= 15/60= 0,25h
V=s/t
V=12km/0,25h
V= 48 km/h
Sally's paycheck this week was $100. She spent $220.45 for a shirt, $12.95 for a CD, $15 for gasoline, and put the balance in the bank.
a. What percent of her total pay was spent on the shirt?
b. What percent of her total pay did she put in the bank?
Answers
Answer:
A) 220.45%
B) 0%
Step-by-step explanation:
A) 220.45 / 100 = 2.2045 * 100 = 220.45%
B) Costs exceeded her paycheck, so 0% of her pay was leftover and put in the bank.
Answer: A) 22.045% , B) 75.16%
I guess its a typo and weekly salary was $1000
So weekly salary = 1000
Spent on shirt = $220.45
Spent on CD = $12.95
Spent on Gasoline = $15
A) 220.45/1000×100
= 22.045%
B) Total spent = 220.45 + 12.95 + 15
= $248.4
Total left with her = 1000 - 248.4
= $751.6
Total percent of pay she put in bank = 751.6/1000×100
= 75.16%
Must click thanks and mark brainliest
The area of a rectangle is 44 m^2, and the length of the rectangle is 3 m less than twice the width. Find the dimensions of the rectangle.
length :
width :
Answers
Answer:
Length:8
Width:5.5
Step-by-step explanation:
We're given area = 44m^2, and the formula for the area of a rectangle is the length multiplied by the width. So,
A = L * w = 44
We're given that the length is 3m shorter than 2 times the width, which is 2w - 3. "2w" is the same as "2 times the width", and the 3 is subtracted because it says 3m shorter than 2 times the width. So L = 2w - 3, and we can substitute that into our equation above.
(2w - 3)(w) = 44
2w^2 - 3w - 44 = 0
Use the quadratic formula here.
x = {3 ± √(-3)^2 - 4(-44)(2)}/2(2)
= {3 ± √9 + 352}/4
= (3 ± 19)/4
You'll get two answers, but remember, we're measuring the length of the sides of shapes, so it has to be positive. It's impossible to have negative lengths, so we're going to stick with the (3 + 19)/4 answer, which is 22/4, which is 5.5. However, we are not finished yet. This is just the width. Now we need to plug it into the equation for length, which was 2w - 3
2(5.5) - 3 = 11 - 3 = 8
The length is 8m and the width is 5.5m.
Find the equation of the line passing through the point (-7,2)(−7,2) that is perpendicular to the line 4x - 3y = 104x−3y=10.
Answers
Answer:
Step-by-step explanation:
Slope of the given line: m=4/3
Slope of the perpendiclar : m'=-3/4 (the inverse of the opposed of m)
Equation of the perpendiclar line: (passing through (-7,2))
[tex]y-2=(x+7)*\dfrac{-3}{4} \ or\\\\ y=-\dfrac{3x}{4} -\dfrac{13}{4}[/tex]
(A) A small business ships homemade candies to anywhere in the world. Suppose a random sample of 16 orders is selected and each is weighed. The sample mean was found to be 410 grams and the sample standard deviation was 40 grams. Find the 90% confidence interval for the mean weight of shipped homemade candies. (Round your final answers to the nearest hundredth)
(B) When 500 college students are randomly selected and surveyed; it is found that 155 own a car. Find a 90% confidence interval for the true proportion of all college students who own a car.
(Round your final answers to the nearest hundredth)
(C) Interpret the results (the interval) you got in (A) and (B)
Answers
The correct answer to the given question is "[tex]\bold{392.47\ < \mu <\ 427.53}[/tex],[tex]\bold{0.28 \ < P <\ 0.34}[/tex], and for Interpret results go to the C part.
Following are the solution to the given parts:
A)
[tex]\to \bold{(n) = 16}[/tex]
[tex]\to \bold{(\bar{X}) = 410}[/tex]
[tex]\to \bold{(\sigma) = 40}[/tex]
In the given question, we calculate [tex]90\%[/tex] of the confidence interval for the mean weight of shipped homemade candies that can be calculated as follows:
[tex]\to \bold{\bar{X} \pm t_{\frac{\alpha}{2}} \times \frac{S}{\sqrt{n}}}[/tex]
[tex]\to \bold{C.I= 0.90}\\\\\to \bold{(\alpha) = 1 - 0.90 = 0.10}\\\\ \to \bold{\frac{\alpha}{2} = \frac{0.10}{2} = 0.05}\\\\ \to \bold{(df) = n-1 = 16-1 = 15}\\\\[/tex]
Using the t table we calculate [tex]t_{ \frac{\alpha}{2}} = 1.753[/tex] When [tex]90\%[/tex] of the confidence interval:
[tex]\to \bold{410 \pm 1.753 \times \frac{40}{\sqrt{16}}}\\\\ \to \bold{410 \pm 17.53\\\\ \to392.47 < \mu < 427.53}[/tex]
So [tex]90\%[/tex] confidence interval for the mean weight of shipped homemade candies is between [tex]392.47\ \ and\ \ 427.53[/tex].
B)
[tex]\to \bold{(n) = 500}[/tex]
[tex]\to \bold{(X) = 155}[/tex]
[tex]\to \bold{(p') = \frac{X}{n} = \frac{155}{500} = 0.31}[/tex]
Here we need to calculate [tex]90\%[/tex] confidence interval for the true proportion of all college students who own a car which can be calculated as
[tex]\to \bold{p' \pm Z_{\frac{\alpha}{2}} \times \sqrt{\frac{p'(1-p')}{n}}}[/tex]
[tex]\to \bold{C.I= 0.90}[/tex]
[tex]\to\bold{ (\alpha) = 0.10}[/tex]
[tex]\to\bold{ \frac{\alpha}{2} = 0.05}[/tex]
Using the Z-table we found [tex]\bold{Z_{\frac{\alpha}{2}} = 1.645}[/tex]
therefore [tex]90\%[/tex] the confidence interval for the genuine proportion of college students who possess a car is
[tex]\to \bold{0.31 \pm 1.645\times \sqrt{\frac{0.31\times (1-0.31)}{500}}}\\\\ \to \bold{0.31 \pm 0.034}\\\\ \to \bold{0.276 < p < 0.344}[/tex]
So [tex]90\%[/tex] the confidence interval for the genuine proportion of college students who possess a car is between [tex]0.28 \ and\ 0.34.[/tex]
C)
In question A, We are [tex]90\%[/tex] certain that the weight of supplied homemade candies is between 392.47 grams and 427.53 grams.In question B, We are [tex]90\%[/tex] positive that the true percentage of college students who possess a car is between 0.28 and 0.34.Learn more about confidence intervals:
brainly.com/question/24131141
help fast I'm dum
and I'm sorry if I keep spamming this.
Curtis types 48 words in 1 minute how many words does Curtis type in 8 minutes? use the following equivalent rates to help solve the problem. how many words does Curtis type in 8 minutes?
Answers
Answer:
384
Step-by-step explanation:
Answer:
384 words
Step-by-step explanation:
Number of words typed in 1 minute = 48
So, number of words typed in 8 minutes
= Number of words typed in 1 minute × 8
= 48 × 8
= 384
So, Curtis types 384 words in 8 minutes.
Help please anyone???
Answers
9514 1404 393
Answer:
x^2/1 +y^2/81 = 1
Step-by-step explanation:
We know that the equation of a unit circle is ...
x^2 +y^2 = 1 . . . . . equation of a unit circle
We also know that replacing x with x/a in a function will expand the graph by a factor of 'a'. Similarly, replacing y with y/b will do the same in the vertical direction.
An ellipse is a circle that has had different expansion factors applied along its different axes. Here, the given points tell us the center of the ellipse is (0, 0), and that it has been expanded by a factor of 9 in the y-direction and a factor of 1 in the x-direction This means the equation for it would be ...
(x/1)^2 +(y/9)^2 = 1 . . . . . equation for desired ellipse
In the required form, this is ...
[tex]\dfrac{x^2}{1}+\dfrac{y^2}{81}=1[/tex]
(PLEASE HELP AGAIN SORRY)
Find x.
A) 11.53
B) 12.12
C) 16.45
D) 15.92
Answers
Answer:
x = 15.92
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp / adj
tan 53 = x / 12
12 tan 53 = x
x=15.92453
Rounding to the nearest hundredth
x = 15.92
Answer:
15.92
Step-by-step explanation:
A social media platform states that a social media post from a marketing agency has 7 hashtags, on average. A digital marketing specialist studying social media advertising believes the average number of hashtags used in a post from a marketing agency is different than the number stated by the social media platform. After completing a study, the digital marketing specialist found that the average number of hashtags used by a marketing agency in a social media post is 7.9 hashtags on average.
As the digital marketing specialist sets up a hypothesis test to determine if their belief is correct, what is their claim?
a. The average number of hashtags used in a social media post from a marketing agency is different than 7 hashtags.
b. The average number of hashtags used in a social media post from a marketing agency is different than 7.9 hashtags.
c. Marketing agencies use too many hashtags in a social media post.
d. The average number of hashtags used in a social media post from a marketing agency is 7 hashtags.
Answers
Answer:
a. The average number of hashtags used in a social media post from a marketing agency is different than 7 hashtags.
Step-by-step explanation:
A social media platform states that a social media post from a marketing agency has 7 hashtags, on average.
This means that at the null hypothesis, we test if the mean is 7, that is:
[tex]H_0: \mu = 7[/tex]
A digital marketing specialist studying social media advertising believes the average number of hashtags used in a post from a marketing agency is different than the number stated by the social media platform.
Keyword is different, so at the null hypothesis, we test if the mean is different of 7, that is:
[tex]H_1: \mu \neq 7[/tex]
Thus, the correct answer is given by option a.
3/4 pound of Colby cheese costs $1.69. Find the unit price per pound. (3/4 pound=12)
Answers
Answer:
2.25
Step-by-step explanation:
We can write a ratio to solve
1.69 x
------ = ---------------
3/4 lb 1 lb
Using cross products
1.69 * 1 = 3/4 *x
1.69 = 3/4 x
Multiply by 4/3
1.69 * 4/3 = x
x=2.25333
Rounding to the nearest cent
180 °
X °
26 °
X = ? °
Answers
Answer:
X = 64
Step-by-step explanation:
All of the angles are right angles (because of the square at one of the angles shown above). This means each angle equals 90 degrees. If X + 26 = 90, then X = 64 because 90 - 26 = 64. I hope this helps!
Answer: X = 64
Step-by-step explanation:
If f(x) = 3x-1 and g(x)= x+2 find (f-g) (x)
Answers
Answer:
2x-3
Step-by-step explanation:
f(x) = 3x-1
g(x)= x+2
(f-g) (x) = 3x-1 - (x+2)
Distribute the minus sign
= 3x-1 -x-2
Combine like terms
= 3x-x -1-2
=2x -3
Find hypotenuse,perpendicular and base
Answers
Answer:
Hypotenuse = XY = 17 cm
Base = YZ = 15 cm
Perpendicular = XZ = 8 cm
Which is the graph of the linear inequality 2x – 3y < 12? On a coordinate plane, a solid straight line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything to the right of the line is shaded. On a coordinate plane, a dashed straight line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything to the right of the line is shaded. On a coordinate plane, a dashed straight line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything to the left of the line is shaded.
Answers
9514 1404 393
Answer:
(c) On a coordinate plane, a dashed straight line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything to the left of the line is shaded.
Step-by-step explanation:
The x-coefficient is positive, so we can determine the shading from ...
2x ... < ... (pay attention to the x-term and the inequality symbol)
That is, the solution region will have x values that are less than those on the (dashed) boundary line. Lower x-values are to the left, hence shading is on the left side of the boundary. (That's all you need to know here to make the correct choice.)
_____
Additional comment
If the choices are "above" or "below", then you will want to look at the y-term and the inequality symbol. If the coefficient of the variable of interest is negated (as it is for y here), then you need to consider the inequality symbol reversed: -y < ... ⇔ y > .... Here, that means the shading is above the line. Since the slope of the line is positive, "left" and "above" are the same thing.
Answer:
c
Step-by-step explanation:
E2021
A group of high school students were surveyed about their handedness and their favorite sport. The results are displayed below.
Which of the following statements is not true, according to the graph?
The left-handed group has a higher percentage of people who prefer baseball.
The right-handed group has a lower percentage of people who prefer basketball.
The percentage of people who prefer soccer has a lower percentage in the left-handed group.
The percentage of people who prefer football is approximately the same for the right- and left-handed groups.
Answers
Answer:
The percentage of people who prefer football is approximately the same for the right- and left-handed groups.
Step-by-step explanation:
The bar for the right-handed group representing soccer is between 10% and 20% (below 20%) while the bar for the left-handed group representing soccer is at 20%.
Percentage of left-handed group of people who prefer soccer is higher than the right-handed group who prefer soccer. Therefore, they don't have the same percentage.
Answer:
D
Step-by-step explanation:
;)
What is the value of 3x^2 + 4y^2 if x = 2 y = 1
Answers
Answer:
16 is answer
Step-by-step explanation:
3(2)^2+4(1)^2= 3(4)+4(1)=12+4=16
what is 98×63-32×69=
Answers
Answer: plz marl brainilist
3966
Step-by-step explanation:
(98 × 63 - 32 × 69
98 * 63) - (32 * 69)
3966
Step-by-step explanation:
98 x 63 - 32 x 69 =
Multiply
6174 - 2208
Subtract
3966
If the cube root parent function is horizontally stretched by a factor of 4, then translated 5 units right and 3 units up, write an equation to represent the new function?
Answers
Answer:
The cube root parent function:
f(x) = [tex]\sqrt[3]{x}[/tex]Horizontally stretched by a factor of 4:
g(x) → f(1/4x) = [tex]\sqrt[3]{1/4x}[/tex]Translated 5 units right:
h(x) → g(x - 5) = [tex]\sqrt[3]{1/4x - 5}[/tex]Translated 3 units up:
k(x) → h(x) + 3 = [tex]\sqrt[3]{1/4x - 5} + 3[/tex]please solve thanks!
Answers
Answer:
x = 25
Step-by-step explanation:
The two angles form a straight line so they add to 180
5x-5 + 2x+10 = 180
Combine like terms
7x +5 = 180
Subtract 5 from each side
7x+5-5 = 180-5
7x = 175
Divide by 7
7x/7 = 175/7
x = 25
Answer:
the value of x = 25
Step-by-step explanation:
[tex]\sf{}[/tex]
♛┈⛧┈┈•༶♛┈⛧┈┈•༶
✌️
7. A 6 litre jug of lemonade contains 1.6 litres of lemon juice and the rest is water. How much lemon juice does a 1.5 litre bottle of lemonade contain?
Answers
Answer:
5.625 litres
Step-by-step explanation:
1. We have to find how many litres of of lemon juice does a 1 litre jug of lemonade contains :
6 litres ÷ 1.6 litres = 3.75 litres
2. How many litres of lemon juice does a 1.5 litre bottle of lemonade contain?
= 3.75 litres × 1.5 litres
= 5.625 litres #
Answer:
A 1.5 litre bottle of lemonade contains 0.4 litre of lemon juice
Step-by-step explanation
let x be the litre of lemon juice in 1.5 litre of lemonade
litre of lemon juice in 6 litre of lemonade = 1.6
so , [tex]\frac{6}{1.6} = \frac{1.5}{x}[/tex]
x = [tex]\frac{1.5 * 1.6}{6}[/tex]
x=[tex]\frac{2.4}{6}[/tex]
x = 0.4 litre
Find the eigenvalues of the matrix:
[-43 0 80]
[40 -3 80]
[24 0 45]
Answers
Answer:
-3
1 + 4 sqrt( 241 )
1 - 4 sqrt( 241 )
Step-by-step explanation:
We need minus lambda on the entries down the diagonal. I'm going to use m instead of the letter for lambda.
[-43-m 0 80]
[40 -3-m 80]
[24 0 45-m]
Now let's find the determinant
(-43-m)[(-3-m)(45-m)-0(80)]
-0[40(45-m)-80(24)]
+80[40(0)-(-3-m)(24)]
Let's simplify:
(-43-m)[(-3-m)(45-m)]
-0
+80[-(-3-m)(24)]
Continuing:
(-43-m)[(-3-m)(45-m)]
+80[-(-3-m)(24)]
I'm going to factor (-3-m) from both terms:
(-3-m)[(-43-m)(45-m)-80(24)]
Multiply the pair of binomials in the brackets and the other pair of numbers;
(-3-m)[-1935-2m+m^2-1920]
Simplify and reorder expression in brackets:
(-3-m)[m^2-2m-3855]
Set equal to 0 to find the eigenvalues
-3-m=0 gives us m=-3 as one eigenvalue
The other is a quadratic and looks scary because of the big numbers.
I guess I will use quadratic formula and a calculator.
(2 +/- sqrt( (-2)^2 - 4(1)(-3855) )/(2×1)
(2 +/- sqrt( 15424 )/(2)
(2 +/- sqrt( 64 )sqrt( 241 )/(2)
(2 +/- 8 sqrt( 241 )/(2)
1 +/- 4 sqrt( 241 )
