We can see that sides HG and LK have a ratio of 8:31 between them. Since sides HE and LI are corresponding, then they must have the same ratio. So, we can formulate the following equation:
\(\begin{gathered} \frac{HG}{LK}=\frac{HE}{LI} \\ \frac{8}{31}=\frac{11}{LI}\text{ (Replacing)} \\ \frac{8}{31}\cdot LI=11\text{ (Multiplying by LI on both sides of the equation)} \\ 8\cdot LI=11\cdot31\text{ (Multiplying by 31 on both sides of the equation)} \\ LI=\frac{341}{8}\text{ (Dividing by 8 on both sides of the equation)} \\ LI=42.625\text{ (Dividing)} \\ \text{The answer is 42.6 (Rounding to the nearest tenth)} \end{gathered}\)Solve showing all the steps
Answer:
Step-by-step explanation:
Is the second exponent 6, or 6x ?
If it is 6x, then x = -½
I need help on this please? Thanks
Answer:
6x^2 -9
Step-by-step explanation:
1. From the table, you know that when x = 0, y = -9, this means that the initial value is -9. This means that the last option is not correct
*** y values -> output
2. Plug in a x - value from the table to figure out the right rule:
x = 2
First option: 6x - 9 -> 6*2 - 9 = 12-9 = 7
in the table, the output for x =2 is 15 so the first option is not correct
Second option: 6x^2 - 9 -> 6*(2^2) - 9 = 6*4 - 9 = 24 - 9 = 15
in the table, the output for x =2 is 15 so the second option is correct
For two n by n square matricies A and B,
suppose rankA = rankB = n-1.
Can rank(AB) become less than n-1 ?
(e.g. rank (AB) = n-2)
If so, I humbly ask you for an example.
Thank you very much.
No, the rank of the product of two n by n square matrices A and B, denoted as AB, cannot be less than n-1 if both A and B have ranks of n-1.
According to the Rank-Nullity theorem, for any matrix M, the sum of its rank and nullity is equal to the number of columns in M. In this case, the number of columns in AB is n, so the sum of the rank and nullity of AB must be n.
If rank(A) = rank(B) = n-1, it means that both A and B have nullity 1. The nullity of a matrix is the dimension of its null space, which consists of all vectors that get mapped to the zero vector when multiplied by the matrix. Since both A and B have rank n-1, their null spaces consist only of the zero vector.
Now, considering AB, if the rank of AB were less than n-1, it would mean that the nullity of AB is greater than 1.
However, this would violate the Rank-Nullity theorem since the sum of the rank and nullity of AB must be n, which is the number of columns.
Therefore, if rank(A) = rank(B) = n-1, the rank of AB cannot be less than n-1.
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Andrei, Amit and Andrew were each asked to factor the term 20x^620x
6
20, x, start superscript, 6, end superscript as the product of two monomials. Their responses are shown below.
Andrei Amit Andrew
20x^6=(2x)(10x^5)20x
6
=(2x)(10x
5
)20, x, start superscript, 6, end superscript, equals, left parenthesis, 2, x, right parenthesis, left parenthesis, 10, x, start superscript, 5, end superscript, right parenthesis 20x^6=(4x^3)(5x^3)20x
6
=(4x
3
)(5x
3
)20, x, start superscript, 6, end superscript, equals, left parenthesis, 4, x, cubed, right parenthesis, left parenthesis, 5, x, cubed, right parenthesis 20x^6=(20x^2)(x^3)20x
6
=(20x
2
)(x
3
)20, x, start superscript, 6, end superscript, equals, left parenthesis, 20, x, squared, right parenthesis, left parenthesis, x, cubed, right parenthesis
1) Which of the students factored 20x^620x
6
20, x, start superscript, 6, end superscript correctly?
Choose all answers that apply:
Choose all answers that apply:
(Choice A) Andrei
A
Andrei
(Choice B) Amit
B
Amit
(Choice C) Andrew
C
Andrew
(Choice D) None of the above
D
None of the above
Based on the given responses, the student who factored 20x^6 = (2x)(10x^5) correctly is Andrei. Therefore, the correct answer is (Choice A) Andrei.
Among the given responses, the student who factored 20x^6 = 20, x to the power of 6 correctly is Andrei. Andrei's factorization is (2x)(10x^5), which correctly represents the original term 20x^6. Therefore, the correct answer is (Choice A) Andrei.
Amit's factorization is (4x^3)(5x^3), which is incorrect because it breaks down the term into two factors with the same exponent, while the original term has an exponent of 6.
Andrew's factorization is (20x^2)(x^3), which is also incorrect as it does not accurately represent the original term 20x^6.
Hence, the only student who correctly factored 20x^6 = 20, x to the power of 6 is Andrei.
The right answer is A. Andrei who factored 20x^6 = (2x)(10x^5) correctly.
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The sum of eighteen and eight times a number is ninety.
what is the number?
Answer:
9
Step-by-step explanation:
9x8=72 72+18=90
10.50h + 15c + 50 Identify a coefficient, a variable, and a constant in this expression.
Answer:
50- Constant
c- Variable
10.50- Coefficient
Step-by-step explanation:
Write an equation of a line in slope-intercept form with the given slope and y-intercept.
A. Slope: -6, y-intercept: -2
B. slope: 1, y-intercept: - 12
Answer:
y = -6x - 2
y = x - 12
Step-by-step explanation:
Slope-intercept equation for line of slope m and y-intercept b:
y = mx + b
A. m = -6, b = -2
y = -6x - 2
B. m = 1, b = -12
y = x - 12
1. FUNDRAISING The Pep Club rented a shaved ice machine to sell shaved ice as a fundraiser. They paid an initial fee and then an hourly charge. The table shows the cost per hour. Find and interpret the rate of change and initial value. Assume the relationship between the two quantities is linear. Number of Hours, 3 2 1A Cost ($), y 30 40 45
First, find the slope (m)
\(m=\frac{y2-y1}{x2-x1}\)Use 2 points from the table:
(x1,y1) = (2,30)
(x2,y2) = (3,35)
Replace;
\(m=\frac{35-30}{3-2}=\frac{5}{1}=5\)slope = rate of change = cost per hour
to find the initial value, apply the slope intercept equation:
y= mx+b
where:
m= slope
b= inital value
replace (x,y) by a point from the table and solve for b
30 = 5(2) +b
30=10 +b
30-10= b
b=20
inital value = 20
To which subsets of numbers does 30/15 belong?
A whole, rational
B integer, rational
C whole, integer, rational
D natural, whole, integer, rational
Answer:
Step-by-step explanation:
For
The number 30 / 15 belongs to the whole, integer, and rational numbers. the correct option is C.
What is a number system?
A numeral system is a way of writing numbers; it's a way of mathematically notating a collection of numbers by utilizing a consistent set of digits or other symbols.
The number set from 0 to infinity are called whole numbers. The number set from negative infinity to positive infinity are called integers.
A rational number is one that can be stated mathematically as the ratio or fraction p/q of two numbers, where p and q are the numerator and denominator, respectively.
The given number 30 / 15 is in the form of a rational number that can also be written as 2. Then the number 30 / 15 can be the whole, integer, and rational number.
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The graph shows the distribution of the number of text messages young adults send per day.
A graph titled daily text messaging has number of text on the x-axis, going from 8 to 248 in increments of 30. Data is distributed normally. The highest point of the curve is at 128.
Which statement describes the distribution?
A) The distribution is approximately Normal, with a mean of 128 messages and a standard deviation of 98 messages.
B) The distribution is approximately Normal, with a mean of 128 messages and a standard deviation of 30 messages.
C) The distribution is approximately Normal, with a mean of 30 messages and a standard deviation of 128 messages.
D) The distribution is uniform, with a mean of 128 messages and a standard deviation of 30 messages.
The statement that describes the distribution based on the given information is:
A) The distribution is approximately Normal, with a mean of 128 messages and a standard deviation of 98 messages.
The statement that describes the distribution based on the given informationThe graph shows a normal distribution, as indicated by the shape of the curve. The highest point of the curve (the peak) is at 128, which represents the mean of the distribution.
The standard deviation measures the spread of the data, and based on the information given, it is 98. Therefore, option A accurately describes the distribution.
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Which figure is a triangular prism? Select all that apply.
A
B
c
D
Answer:
The answer choice is E.
Step-by-step explanation:
Answer:
A and C are triangular prisms
It takes andre 4 minutes to swim 5 laps. At this rate heswims how many laps per minute.
Answer: It takes him 1 minute and 25 seconds
Step-by-step explanation:
5 divided 4
4 times 1 = 4
5-4=1
put the decimal and make 1=10 Ans.: 1.25
4 times 2 = 8
10-8=2
put the 0 = 20
4 times 5 =20
20-20=100
Need help asap extra points
The most appropriate choice for equation of line in slope intercept form will be given by-
\(8x - 5y = 26\) is the required equation of line.
What is equation of line in slope intercept form?
General form of equation of line in slope intercept form is given by
y = mx + c where m is the slope of the line and c is the y intercept of the line.
The distance from the origin to the point where the line cuts the y axis is the y intercept
The distance from the origin to the point where the line cuts the x axis is the x intercept
Here,
\(8x - 5y = 4\\5y = 8x - 4\\y = \frac{8}{5}x - \frac{4}{5}\)
Slope of \(8x - 5y = 4\) is \(\frac{8}{5}\\\)
Slope of the line parallel to the given line = \(\frac{8}{5}\)
The line passes through (2, -2)
Equation of line =
\(y - (-2) = \frac{8}{5}(x - 2)\\5y + 10 = 8x -16\\8x - 5y = 16+10\\8x - 5y = 26\)
This is the required equation of line.
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Which of the following is equivalent to |x-1| <5?
X-1<5
5< x-1 <5
-5 < x-1 < 5
-5> x-1 < 5
Answer:
-5 < x-1 < 5
Step-by-step explanation:
Consider |a|. This has the value -a when a < 0. So, if we write the inequality ...
|a| < b
it is equivalent to two inequalities:
a < b . . . . for a ≥ 0
-a < b . . . for a < 0
Multiplying by -1. the latter inequality is ...
a > -b . . . for a < 0
Written using the < symbol, this is ...
-b < a
So, the original inequality can be written as the two inequalities ...
-b < a (for a < 0) or a < b (for a ≥ 0)
Since these are disjoint, we can form their union as ...
-b < a < b
__
Above, we have a = x-1, b = 5, so the inequality |x-1| < 5 can be written ...
-5 < x -1 < 5
Answer:
C) –5 < x – 1 < 5 on edge.
Step-by-step explanation: Edge 2021. I got it correct.
find the slope (5,4) (5,9)
Answer:
undefined
Step-by-step explanation:
To find the slope between two points, we can use the slope formula. The slope formula is:
\(m=\frac{y_2-y_1}{x_2-x_1}\)
where m is the slope and (x₁, y₁) and (x₂, y₂) are two points.
By plugging in (5, 4) and (5, 9) for (x₁, y₁) and (x₂, y₂) respectively, we get:
\(m=\frac{9-4}{5-5}=\frac{5}{0}\)
Note, we cannot divide by zero. By using the slope formula, we get that the slope is undefined.
I hope this helps. Happy studying.
Anu was checking her emails she casually told her friend siting next to her the ratio of unread emails in my inbox is 4:1 The total number of emails is 120 what is the number of unread emails in her inbox
In a case whereby Anu was checking her emails and she casually told her friend siting next to her the ratio of unread emails in my inbox is ratio 4:1 where the total number of emails is 120 then the number of unread emails in her inbox is 96mails.
How can the unread mails be calculated?The concept that will be used here is ratio. An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls)
The total mails in her box is 120
The we can represent the unread mails as 4x and read mails be 1x
This can be expressed as :
(4x+1x)=120mails
5x=120mails
x=120/5
x=24
This implies that the uread mails(4×24)
=96mails
Then the number of the read mail =(1×24)=24mails
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i asked a question a while ago and nobody has answered it pls help
Answer:
bet but need barinlyist
Step-by-step explanation:
Content
Calculator
|||
m³
A rectangular prism has a length of 2 meters, a width of 4 meters, and a height of 2 meters.
What is the volume of the prism?
Enter your answer in the box as a simplified mixed number or a decimal.
Basic
4.07 Quiz: Finding the Volume of a Prism
7.
If a rectangular prism has a length of 2 meters, a width of 4 meters, and a height of 2 meters. The volume of the prism is 16 cubic meters.
How to find the volume of the prism?The volume of a rectangular prism is given by the formula:
Volume = length x width x height
Substituting the given values, we get:
Volume = 2 meters x 4 meters x 2 meters
Simplifying this expression, we get:
Volume = 16 cubic meters
Therefore, the volume of the prism is 16 cubic meters.
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please Translate the triangle.
Then enter the new coordinates.
A (-2,4)
(-3,2)
< 9.3 >
A'([?], [])
B'([ ].[])
C'([] [])
Answer:
A' (7,7)
B' (10,4)
C' (6,5)
Step-by-step explanation:
Add 9 to every x value and 3 to every y value.
Answer:
A'(7,7)
B'(10,4)
C'(6,5)
Step-by-step explanation:
⭐What is a translation?
a translation is a type of transformation you can do to a figure to shift the figure up/down and left/right.⭐What is the translation notation?
\(T_ < x,y > (ABC) = (A'B'C')\)\(T_ < x,y >\) tells you how much to move the figure left/right and up/down. x = left/righty = up/downThe problem tells us to translate ΔABC 9 units to the right, and 3 units up because it is inside the <>, and the numbers are positive.
To translate the vertices of ΔABC, we have to add the respective x and y coordinates of the translation rule to each vertecie of ΔABC.
A(-2,4):
Add the respective x and y coordinates of the translation rule to the coordinates of the vertecieA'(-2+9, 4+3) = A'(7,7)B(1,1):
Add the respective x and y coordinates of the translation rule to the coordinates of the vertecieB'(1+9, 1+3) = A'(10,4)C(-3,2):
Add the respective x and y coordinates of the translation rule to the coordinates of the vertecieC'(-3+9, 2+3) = A'(6,5)⭐if this response helped you, please mark it the "brainliest"!⭐
The probability of the chance of a tornado would be considered:
A) Empirical Probability
B) Theoretical Probability
C) Subjective Probability
D) Conditional probability
Answer:
B)
Step-by-step explanation:
I’m pretty sure but sorry if I’m wrong
Find the area of the rectangle shown
7 1/2 ft
5 1/4ft
Answer:
39 3/8 ft ^2
Step-by-step explanation:
To find the area of a rectangle, multiply the length times the width.
A = l*w
= 7 1/2 * 5 1/4
Change the mixed numbers to improper fractions.
A = 15/2 * 21/4
=315/8
Change back to a mixed number.
8 goes into 315 39 times with 3 left over.
= 39 3/8
Answer:
Area = 39.375 ft²
(you can round to 39.4)
Step-by-step explanation:
Find the area of the rectangle shown
7 1/2 ft
5 1/4ft
7 1/2 = 7.5 ft
5 1/4 = 5.25 ft
Area = L x W
Area = 7.5 x 5.25
Area = 39.375
A residential community was polling households to find out whether they wanted to get their TV signal from a satellite or cable. The results are shown in the Venn diagram.
A circle labeled satellite 55 overlaps a circle labeled cable 75. Overlap is labeled 12. 4-column table with 3 rows. First column has no label with entries satellite, not satellite, total. Second column is cable with entries blank, 51%, blank. Third column is not cable with entries a, b, blank. Fourth column is labeled total with entries blank, blank, 100%.
What are the values of a and b in the relative frequency table for the survey results? Round answers to the nearest percent.
a = 82%, b = 3%
a = 38%, b = 50%
a = 38%, b = 3%
a = 93%, b = 19
The correct answer is:
a = 43%
b = 88%
To determine the values of a and b in the relative frequency table, we need to analyze the information provided in the Venn diagram and the given table.
From the Venn diagram, we can gather the following information:
The circle labeled "satellite" has a value of 55.
The circle labeled "cable" has a value of 75.
The overlap between the two circles is labeled as 12.
Using this information, we can complete the table:
First column - "Satellite":
Entries: Satellite, Not satellite, Total
Total: 55 (as given in the Venn diagram)
Second column - "Cable":
Entries: Blank, 51%, Blank
To find the value for the "Cable" entry, we need to subtract the overlap (12) from the total number of cable users (75).
Cable: 75 - 12 = 63
Therefore, the entry becomes: Blank, 51%, Blank
Third column - "Not Cable":
Entries: a, b, Blank
To find the value for "a," we subtract the overlap (12) from the total number of satellite users (55).
a: 55 - 12 = 43
To find the value for "b," we subtract the overlap (12) from the total number of households (100).
b: 100 - 12 = 88
Therefore, the entries become: 43, 88, Blank
Fourth column - "Total":
Entries: Blank, Blank, 100%
The total number of households is given as 100% (as stated in the question).
Therefore, the values of a and b in the relative frequency table are:
a = 43% (rounded to the nearest percent)
b = 88% (rounded to the nearest percent)
Hence, the correct answer is:
a = 43%
b = 88%
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Point A is located at (1, 2). Point B is located at (4, 6). Use this information to determine the length of the line, rounded to the nearest whole number.
If Point A is located at (1, 2) and Point B is located at (4, 6), the length of the line between points A and B is 5 units.
To determine the length of the line between points A and B, we can use the distance formula, which is a formula used to calculate the distance between two points in a coordinate plane. The distance formula is:
d = √((x₂ - x₁)² + (y₂ - y₁)²)
where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points and d is the distance between them.
Using the coordinates of points A and B, we can substitute their values into the distance formula to find the length of the line between them:
d = √((4 - 1)² + (6 - 2)²)
d = √(3² + 4²)
d = √(9 + 16)
d = √25
d = 5
Rounded to the nearest whole number, the length of the line is also 5 units.
In conclusion, we can use the distance formula to find the length of the line between two points in a coordinate plane. The distance formula uses the coordinates of the two points to calculate the distance between them. The resulting distance can be rounded to the nearest whole number, if needed.
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What is 19x( _________X26)=(19X39)X26
Answer:
(39 * 26)
Step-by-step explanation:
If (19 * 39) * 26
19 * (39 * 26)
Your answer is 39.
3 · {(300 - 70 ÷ 5) - [3 · 23 - (8 - 2 · 3)]}
Answer:
(657)
Step-by-step explanation:
Simplify the following:
3 (300 - 70/5 - (3×23 - (8 - 2×3)))
The gcd of -70 and 5 is 5, so (-70)/5 = (5 (-14))/(5×1) = 5/5×-14 = -14:
3 (300 + -14 - (3×23 - (8 - 2×3)))
-2×3 = -6:
3 (300 - 14 - (3×23 - (-6 + 8)))
8 - 6 = 2:
3 (300 - 14 - (3×23 - 2))
3×23 = 69:
3 (300 - 14 - (69 - 2))
| 6 | 9
- | | 2
| 6 | 7:
3 (300 - 14 - 67)
300 - 14 - 67 = 300 - (14 + 67):
3 ((300 - (14 + 67)))
| 1 |
| 6 | 7
+ | 1 | 4
| 8 | 1:
3 (300 - 81)
| | 9 |
| 2 | | 10
| | |
- | | 8 | 1
| 2 | 1 | 9:
3 (219)
3 (219) = (3×219):
(3×219)
3×219 = 657:
Answer: (657)
For an investment of 26,245, a quarterly statement reports that the account is 26,292. The statement reports that for the same quarter, the rate of return of the investment was - 0.02%. Given the information regarding the investment quarterly activity, does the reported rate of return seem reasonable?
No. The reported return rate appears lower than expected.
Rate of returnsTo determine whether the reported rate of return is reasonable or not, we can calculate the expected rate of return based on the investment amount and the ending value of the account.
First, we need to calculate the total number of quarters that have elapsed between the initial investment and the current quarter. Let's assume that the investment has been held for n quarters.
Then, we can use the following formula to calculate the expected rate of return:
Expected rate of return = (Ending value / Initial investment) ^ (1/n) - 1
Plugging in the given values, we get:
n = 1 (since we are only given information for a single quarter)
Initial investment = 26,245
Ending value = 26,292
Expected rate of return = (26,292 / 26,245) ^ (1/1) - 1 = 0.18%
Comparing the expected rate of return of 0.18% with the reported rate of return of -0.02%, we can see that they are quite different. However, it's important to note that a single quarter's rate of return may not be indicative of the overall performance of the investment.
Therefore, while the reported rate of return seems lower than expected, we would need to consider the performance over a longer period of time to make a more informed assessment of the investment's performance.
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Paul has $20,000 to invest. His intent is to earn 10.5% interest on his investment. He can invest part of his money at 7% interest and part at 12% interest. How much does Paul need to invest in each option to make 10.5% interest on his investment?
Paul should invest $
and $
to earn 10.5% on his investments.
how many times bigger is 6.4*10^9 than 1.3*10^9
Answer:
at least four times bigger
Suppose that the function g is defined, for all real numbers, as follows. Find g(-5) ,g (-2), and g(-1)
If the function g(x) is defined for all real-numbers, then the value of g(-5) is 7/2, g(-2) is -1 and g(-1) is 0.
A piecewise function is a function that is defined by different rules or formulas on different parts of its domain. The piecewise function "g(x)" is given as :
g(x) = {-(1/2)x + 1, for x<-2
= {-(x+1)², for -2≤x≤1
= {4 for x>1
We have to find the value of g(-5) ,g (-2), and g(-1),
For x = -5, the number -5 is less than -2, so the first function "-(1/2)x + 1" will be used,
⇒ g(-5) = -(1/2)(-5) + 1 = 5/2 + 1 = 7/2,
For x = -2, the number -2 lies in the interval "-2≤x≤1", so second function
"-(x+1)²" will be used,
⇒ g(-2) = -(x+1)² = -(-2+1)² = -(-1)² = -1,
For x = -1, the number -1 lies inn the interval "-2≤x≤1", so second function "-(x+1)²" will be used,
⇒ g(-1) = -(x+1)² = -(-1+1)² = -(0)² = 0,
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What is the common ratio of the geometric sequence 16, 24, 36, 54, ...?
2/3
1
8
3/2
Answer:
r = 3/2
Step-by-step explanation:
The common ratio (r) is the number that, when multiplied by the previous (n-1) term, gives the nth term of the geometric sequence (\(a_{n} =a_{n-1}*r\)). To find the common ratio, we can take any term and divide it by its preceding term (rearrange the formula to get \(r=\frac{a_{n}}{a_{n-1}}\)). If we take 24 and divide it by 16, we get the common ratio of 3/2 (\(r=\frac{24}{16}\), \(r=\frac{3}{2}\)). Hope this helps.