Answers
Related Questions
The perimeter of the rectangle is 80 cm. The area of the rectangle is acm2 . (i) show that x 2 40x + a = 0.
Answers
Answer:
Proved
Step-by-step explanation:
Given
[tex]p = 80[/tex] ---- perimeter
[tex]a \to area[/tex]
Required
[tex]x^2 + 40x + a = 0[/tex]
The perimeter is calculated as:
[tex]p = 2(x + y)[/tex]
Where
[tex]x,y \to[/tex] the rectangle dimension
So, we have:
[tex]2(x + y) = 80[/tex]
Divide by 2
[tex]x + y = 40[/tex]
Make y the subject
[tex]y = 40 - x[/tex]
The area of the rectangle is:
[tex]a = xy[/tex]
[tex]a = x * (40 -x)[/tex]
[tex]a = 40x -x^2[/tex]
Equate to 0:
[tex]x^2 - 40x + a = 0[/tex]
What is my answer if I Add
-9+84+(-2)
Answers
Answer:
73
Step-by-step explanation:
-9+84+(-2) =
-9+82 =
= 73
Hope this helps
2x+5y=20 y=-0.4x-1 i really need help over here
Answers
Answer:
x=6.25 and y=1.5
Step-by-step explanation:
Given equation
2x+5y=20
y=0.4x-1
Putting the value of y in above equation
2x+5(0.4x-1)=20
2x+2x-5=20
4x-5=20
4x=20+5
4x=25
x=6.25
Now,
y=0.4x-1( Given)
Putting the value of x=6.25 in above equation y
y=0.4(6.25)-1
y=2.5-1
y=1.5
Find value a when the angle between vectors U=(2,a) and V = (-6;8) is pie/4
Answers
Answer:
Step-by-step explanation:
The formula to find the angle between 2 vectors is
[tex]cos\theta=\frac{u*v}{|u||v|}[/tex] which is the dot product of u*v over the (magnitude of u times the magnitude of v). We also know that θ = [tex]\frac{\sqrt{2} }{2}[/tex]. Filling in that formula requires us to find the dot product of u and v, which is
u·v = (2×(-6)) + (a×8) so
u·v = -12 + 8a. Then we need the magnitudes of both u and v:
[tex]|u|=\sqrt{2^2+a^2}=\sqrt{4+a^2}[/tex] and
[tex]|v|=\sqrt{(-6)^2+8^2}=\sqrt{100}=10[/tex]
Putting all of together looks like this:
[tex]\frac{\sqrt{2} }{2}=\frac{-12+8a}{10\sqrt{4+a^2} }[/tex] . Cross multiply to get
[tex]10\sqrt{2}(\sqrt{4+a^2})=2(-12+8a)[/tex] which is tricky to simplify. You really need to know the rules for multiplying radicals to do this correctly. The simplification is
[tex]10\sqrt{8+2a^2}=-24+16a[/tex] and we need to solve for a. Begin by squaring both sides to get rid of the square root to get:
100(8 + 2a²) = 256a² - 768a +576 and simplify some more by distributing through the parenthesis to get
800 + 200a² = 256a² -768a + 576. Combine like terms to come up with
0 = 56a² - 768a - 224 and we need to factor that. Assuming since you're this far in math (pre-calc or maybe late algebra 2) you know how to factor, when you do, you get values for a of - .285714... and 14.
Therefore, the value for a is 14. I checked it...it works
Answer:
a = 14, U = (2, 14)
Step-by-step explanation:
the other answer is correct.
just to add the solution path for the quadratic equation
0 = 56a² - 768a - 224
in general, a quadratic equation usually expressed in x
0 = ax² + bx + c
has its solution as
x = (-b ± sqrt(b² - 4ac))/(2a)
for us here this looks like this then
a = (768 ± sqrt(768² - 4×56×-224))/(2×56) =
= (768 ± sqrt(589824 + 4×56×224))/112 =
= (768 ± sqrt(589824 + 50176))/112 =
= (768 ± sqrt(640000))/112 = (768 ± 800)/112
a1 = (768 + 800)/112 = 1568/112 = 14
a2 = (768 - 800)/112 = -32/112 = -0.29
and the negative solution would be for a vector solution in the wrong direction (down instead of up). as V is pointing up left, and the angle is only 45 degrees (pi/4), also U has to point up.
so, 14 is the solution for U.
its my final, please help!!!!!!!!!!
Answers
Answer:
both apply
Step-by-step explanation:
i guessed just do it
HELP TIMER Write the equation of a hyperbola centered at the origin with x-intercept +/- 4 and foci of +/-2(squareroot 5)
Answers
Given:
x-intercepts of the hyperbola are ±4.
The foci of hyperbola are [tex]\pm 2\sqrt{5}[/tex].
Center of the hyperbola is at origin.
To find:
The equation of the hyperbola.
Solution:
The general equation of a hyperbola:
[tex]\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1[/tex] ...(i)
Where, (h,k) is the center of the hyperbola, ±a are x-intercepts, [tex](\pm c,0)[/tex] are foci.
Center of the hyperbola is at origin. So, h=0 and k=0.
x-intercepts of the hyperbola are ±4. So,
[tex]\pm a=\pm 4[/tex]
[tex]a=4[/tex]
The foci of hyperbola are [tex]\pm 2\sqrt{5}[/tex].
[tex]\pm c=\pm 2\sqrt{5}[/tex]
[tex]c=2\sqrt{5}[/tex]
We know that,
[tex]a^2+b^2=c^2[/tex]
[tex](4)^2+b^2=(2\sqrt{5})^2[/tex]
[tex]16+b^2=20[/tex]
[tex]b^2=20-16[/tex]
[tex]b^2=4[/tex]
Taking square root on both sides, we get
[tex]b=\sqrt{4}[/tex] [b>0]
[tex]b=2[/tex]
Substituting [tex]h=0,k=0,a=4,b=2[/tex] in (i), we get
[tex]\dfrac{(x-0)^2}{4^2}-\dfrac{(y-0)^2}{2^2}=1[/tex]
[tex]\dfrac{x^2}{4^2}-\dfrac{y^2}{2^2}=1[/tex]
Therefore, the correct option is (d).
Find the volume in the shape
Answers
Answer:
1205.76 m^3
Step-by-step explanation:
given:
radius = 8m
height = 18 m
volume of a cone = πr2h/3
=3.14 * (8)^2 * 18/3
=3.14 *64 *18/3
=3617.28/3
=1205.76 m^3
the number 3.14063 written correct to 3 decimal places is
Answers
Answer:
3.141
Step-by-step explanation:
3 decimals is .xxx, and you round the last digit up, so it becomes 3.141
Answer:
3.141
Step-by-step explanation:
since the forth number behind the decimal place is bigger than 5 we round up the third number.
I hope this helps in anyway.
Leila buys candy that costs 8 dollars per pound. She will spend more than 40 dollars on candy. What are the possible numbers of pounds she will buy?
Answers
Answer:
She must buy more than 5 lbs
Step-by-step explanation:
First write the inequality
cost per pound * number of pounds > total cost
8 * lbs > 40
Divide each side by 8
8 lbs /8 > 40/8
lbs > 5
She must buy more than 5 lbs
a. We will attempt to answer the question "What is the average height of RCCC male students?" using data we collected the first week of this semester. Be sure to give explanations in context and include units when appropriate.
Describe the population of interest?
A sample of____(state the number) RCCC male students was taken. We found the sample mean____(symbol) to be Interpretation: In the sample of male RCCC students, the____"mean") height was approximately____inches.
The median is____Interpretation (use the one for mean as a guide):
The mode is____Interpretation (use the one for mean as a guide):
b. We know the measures of central tendency don't tell us the whole story, so we then investigated the measures of variation as well. We found that the heights had a range of_____with a standard deviation____(symbol) of_____(2 decimal places) and a variance_____(symbol) of (2 decimal places).
Height (inches) Note: There are 31 male heights.
1 70
2 70
3 70
4 70
5 71
6 64
7 64
8 65
9 65
10 66
11 66
12 67
13 67
14 68
15 68
16 68
17 69
18 72
19 72
20 72
21 72
22 73
23 73
24 73
25 73
26 73
27 73
28 74
29 75
30 75
31 75
32 75
70 70 70 70 71 64 64 65 65 66 66 67 67 68 68 68 69 72 72 72 72 73 73 73 73 73 73 74 75 75 75 22
Answers
The population of interest: Male RCCC students.
Sample size: 31.
The sample mean: 69.68 inches.
Median: 69 inches.
Mode: 70 inches.
Range: 11 inches.
Standard deviation: 3.32 (rounded to 2 decimal places).
Variance: 11.02 (rounded to 2 decimal places).
We have,
Mean:
To find the mean, we sum up all the heights and divide by the total number of data points (31 in this case):
Mean = (70 + 70 + 70 + ... + 75) / 31
Mean ≈ 69.68 inches
Median:
The median represents the middle value in the dataset when arranged in ascending order. Since the dataset has an odd number of values (31), the median will be the value in the middle position when ordered:
Median = 69 inches
Mode:
The mode represents the value(s) that occur most frequently in the dataset. In this case, the mode is the height that appears most often:
Mode = 70 inches
Range:
The range is calculated by subtracting the minimum value from the maximum value in the dataset:
Range = Maximum height - Minimum height
Range = 75 - 64 = 11 inches
Standard Deviation (σ):
To find the standard deviation, we can use the formula that involves finding the difference between each value and the mean, squaring those differences, averaging them, and taking the square root:
Standard Deviation (σ) ≈ 3.32 (rounded to 2 decimal places)
Variance (σ²):
The variance is the square of the standard deviation.
We can square the value of the standard deviation to find the variance:
Variance (σ²) ≈ 11.02 (rounded to 2 decimal places)
The height dataset (in inches) for the 31 male RCCC students is as follows:
1 70
2 70
3 70
4 70
5 71
6 64
7 64
8 65
9 65
10 66
11 66
12 67
13 67
14 68
15 68
16 68
17 69
18 72
19 72
20 72
21 72
22 73
23 73
24 73
25 73
26 73
27 73
28 74
29 75
30 75
31 75
32 75
Thus,
The population of interest: Male RCCC students.
Sample size: 31.
The sample mean: 69.68 inches.
Median: 69 inches.
Mode: 70 inches.
Range: 11 inches.
Standard deviation: 3.32 (rounded to 2 decimal places).
Variance: 11.02 (rounded to 2 decimal places).
Learn more about mean here:
https://brainly.com/question/23263573
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How do you solve a system of linear equations by graphing?
Answers
9514 1404 393
Explanation:
This is a self-answering question: you solve it by graphing the equations.
The solution is where the lines intersect. The point of intersection of the lines is the point that satisfies all the equations for the lines, hence is a solution to the system. If they do not intersect, there are no solutions. If the lines are coincident, there are an infinite number of solutions.
__
The equations can be graphed by any of a number of methods. (My favorite is to let a graphing calculator do it.) The method of choice depends on the coefficients and the form the equations are given in. Methods of graphing are a topic for a more lengthy discussion.
A square dancing contest has 245 teams of 4 pairs each. How many dancers are participating in the contest?
Answers
Answer:
1960 dancers
Step-by-step explanation:
your are on "ace" level and need help here ?
a pair is 2 people
4 pairs is therefore 4×2 people = 8
245 teams of 4 pairs or 8 people each means
245×8 = 1960 people
A high school has 32 players on the football team. The summary of the players' weights is given in the box plot. Approximately, what is the percentage of players weighing greater than or equal to 233 pounds
Answers
Answer:
[tex]\% = 11.96\%[/tex]
Step-by-step explanation:
Given
See attachment for box plot
Required
Percentage greater than or equal to 233
From the box plot, the maximum is:
[tex]Max = 244[/tex]
The minimum is:
[tex]Min = 152[/tex]
Percentage greater than 233 is calculated as:
[tex]\% = \frac{Max - 233}{Max - Min}[/tex]
[tex]\% = \frac{244 - 233}{244-152}[/tex]
[tex]\% = \frac{11}{92}[/tex]
Express as percentage
[tex]\% = \frac{11}{92}*100\%[/tex]
[tex]\% = \frac{1100}{92}\%[/tex]
[tex]\% = 11.96\%[/tex]
Use the grouping method to factor this polynomial.
x^3 + 2x^2 + 12x +24
A. (x^2+6)(x+2)
B. (x^2 +2)(x+6)
C. (x^2 +2)(x+12)
D. (x^2 +12)(x+2)
Answers
Answer:
[tex]( {x}^{2} + 12)(x + 2)[/tex]
Step-by-step explanation:
[tex] {x}^{3} +2 {x}^{2} +12x+24[/tex]
[tex]( {x}^{3}+2 {x}^{2} )+12x+24[/tex]
[tex] {x}^{2} (x+2)+12(x+2)[/tex]
[tex]( {x}^{2} + 12)(x + 2)[/tex]
Hope it is helpful...Rewrite each mixed number as a sum of two signed numbers,
3 1/5
-7 3/8
Answers
Answer:
31/5 as a mixed number: 6 and 1/5
-73/8 as a mixed number:-9 and 1/8
Step-by-step explanation:
Rewriting each mixed number as a sum of two signed numbers 3 1/5 and -7 3/8 are 3 and 1/5 and -8 and 5/8 respectively
The mixed number to rewrite as a sum of two signed numbers are as follows:
3 1 / 5-7 3 / 8Rewriting as a sum of the two signed numbers can be represented as follows;
3 1/5 = 16 / 5
-7 3/ 8 = - 59 / 8
Therefore,
3 1/5 will be 3 and 1/5
-7 3/ 8 will be -8 and 5/8
Note
3 + 1/5 = 3 1/5
-8 + 5/8 = -7 3/8
learn more on fraction here: https://brainly.com/question/24645582
El opuesto y el semejante de 8xy
Answers
Answer:
No entiendo
Step-by-step explanation:
Given m||n, find the value of x
Answers
Answer:
The answer is 104 degrees.
Step-by-step explanation:
M is equivalent to N, which means x is also 104 degrees.
Dan has an old lawn mower! It takes him 1 hour to mow the whole lawn. How many square yards does Dan cut in one minute? Hints: There are 60 minutes in 1 hour. To find the unit rate divide the area of the lawn by the amount of time it takes Dan to mow the whole lawn.
40 square yards per minute
400 square yards per minute
2400 square yards per minute
240 square yards per minute
Answers
Answer: You didnt mention how much Dan mows in 1 hour, but just do that divided by 60
Step-by-step explanation:
Find the median and mean of the data set below:
48,32,5, 13, 11, 22, 2
Answers
mean is 19
Answer:
the median is 13 and the mean is 13
what is equivalent to 7w +7w
Answers
Answer:
14w
Step-by-step explanation:
Hope this helps
PLS HELP TYSMMMM <33333333333333333333333333
Answers
Explanation:
Use order of operations PEMDAS to check:
54 ÷ (6 - 3) x 2
= 54 ÷ 3 x 2
= 18 x 2
= 36
Please say if im correct
If im correct, mark me brainliest tysm!
Have a nice day
-SpaceMarsh
Answer:
dvide 54 by 6 then the answer you get subrtact it by 3 then the answer you get multiply iy by 2 then thats will be your answer
Step-by-step explanation:
remember always use PEMDAS always add or subract wich ever comes first and if theres none of that then do Multiply or devide wich ever comes first ( btw your answer is ( 3 )
Element X is a radioactive isotope such that its mass decreases by 73% every
hour. If an experiment starts out with 680 grams of Element X, write a
function to represent the mass of the sample after t hours, where the rate of
change per minute can be found from a constant in the function. Round all
coefficients in the function to four decimal places. Also, determine the
percentage rate of change per minute, to the nearest hundredth of a percent.
Mi
Answers
Answer:
Step-by-step explanation:
The element decay percentage rate of change 2.22% per minute.
What is radioactive isotope?
Radioisotope, radionuclide, or radioactive nuclide, any of several species of the same chemical element with different masses whose nuclei are unstable and dissipate excess energy by spontaneously emitting radiation in the form of alpha, beta, and gamma rays.
Here, mass decreases by 73% every hour.
Weight of element X is 680 grams.
According to question,
f(t) = 680 (1 - 73%)ⁿ
f(t) = 680 (1 - 0.73)ⁿ
f(t) = 680 X 0.27ⁿ
f(t) = 680 X 0.9778ⁿ
f(t) = 680 X (1 - 0.02322)ⁿ
Thus, the element decay percentage rate of change 2.22% per minute.
Learn more about radioactive isotope from:
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Determine if each proportion on the left is True or False. Answer options on the right side may be used more than once.
True
False
28/16=14/8
3/5=9/15
4/32=10/78
3/4=12/16
Answers
Answer:
28/16=14/8 true
3/5=9/15 true
4/32=10/78 false
3/4=12/16 true
Step-by-step explanation:
DID IT ON BRIDGE
A local salesman has forty-five stacks of magazines. If the salesman plans to sell three-fifths of the stacks, how many stacks will he have left?
Answers
Answer:
2
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
An English teacher needs to pick 4 books to put on his reading list for the next school year. He has narrowed down his choices to 8 novels and 6 plays.
a. How many different ways can he choose the books to put on the list if he wants to include at least two plays?
b. Find the standard deviation.
Answers
Answer:
A) 3 ways
B) sorry don't know.
Step-by-step explanation:
2 P and 2 N
3P and 1 N
4P
So 3 ways.
Can anyone help me with this one plz
Answers
Answer:
its c my dude
Step-by-step explanation:
....................
answer is c because that is right plz brainliest and like plz
m) Factorise:
x2/9+1+9/x2
Answers
Answer:
Cannot be factored
Step-by-step explanation:
Given
[tex]\frac{x^2}{9} + 1 + \frac{9}{x^2}[/tex]
Required
Factorize
Take LCM
[tex]\frac{x^2}{9} + 1 + \frac{9}{x^2} = \frac{x^4+9x^2+81}{9x^2}[/tex]
The expression cannot be factored
The total cost of a truck rental, y, for x days, can be modeled by y=24x+39. What is the rate of change for this function?
Answers
Answer:
24 per day
Step-by-step explanation:
'x' = days, so since 24 is with x, the rate of change is 24
A 12 sided die is rolled. Find the probability of rolling and even number
Answers
Answer:
0.5
Step-by-step explanation:
Wanted outcome / possible outcomes = 0.5 in this case.
Find the solution(s) for x in the equation below.
x^2 - 25 = 0
A. x = -5
В. no solutions
C. x = 5
D. x = 5; x = -5
Answers
Answer:
D. x = 5; x = -5
Step-by-step explanation:
x^2 - 25 = 0
Add 25 to each side
x^2 - 25+25 = 0+25
x^2 = 25
Take the square root of each side
sqrt(x^2) = sqrt(25)
x = ±5
