Answer:
There should be 8 of them
- 2 - 3i
- 2 + 3i
2 - 3i
2 + 3i
- 3 - 2i
- 3 + 2i
3 - 2i
3 + 2i
Thanks
absolute value is the real part squared + the complex part squared and the root of the things you get.
|a + ib|
= √(a²+b²)
so the sign doesn't matter
The expression 2x + 4x represents the cost of buying the same number of
cases of spring water, sold for $2 per case, and sparkling water, sold for $4
per case. What expression can be used to express the total cost?
Answer:
6x
Step-by-step explanation:
Combine like terms
Select the line that is equivalent to 5x + 2y = 6.
y equals short dash 2 over 5 x plus 6 over 5
y equals short dash 5 over 2 x plus 3
y equals 5 over 2 x minus 3
y equals 2 over 5 x minus 6 over 5
Answer:
B)
Step-by-step explanation:
To know which line is equivalent, we need to convert this equation from standard to slope-intercept form. We can take our original equation:
5x + 2y = 6
Minus 5x from both sides:
2y = -5x + 6
Then, divide by 2:
[tex]y = -\frac{5}{2}x + 3[/tex]
Looking at our options, we can see that
B) y equals short dash 5 over 2 x plus 3, is the same. So, B) is the answer.
Hope this helped!
Answer:
[tex]\textsf{B)} \quad y=-\dfrac{5}{2}x+3[/tex]
Step-by-step explanation:
Given equation:
[tex]5x+2y=6[/tex]
Subtract 5x from both sides of the equation:
[tex]\implies 5x+2y-5x=6-5x[/tex]
[tex]\implies 2y=-5x+6[/tex]
Divide both sides of the equation by 2:
[tex]\implies \dfrac{2y}{2}= \dfrac{-5x}{2}+ \dfrac{6}{2}[/tex]
[tex]\implies y=-\dfrac{5}{2}x+3[/tex]
{MARKING BRAINLIST} DUE IN 30 MINS (6th grade) PLEASE PLEASE HELP ME ASAAP
A coach listed the frequency of people who bought football tickets, and the data is displayed in the histogram.
A histogram titled Football Ticket Sales. The x-axis is labeled Number of Tickets and has intervals for 1 to 3, 4 to 6, 7 to 9, 10 to 12, and 13 to 15. The y-axis is labeled Frequency and begins at 0, with tick marks every 2 units up to 20. There is a shaded bar for 1 to 3 that stops at 12, for 4 to 6 that stops at 16, for 7 to 9 that stops at 10, and for 13 to 15 that stops at 1. There is no shaded bar for 10 to 12.
Which of the following best describes the spread and distribution of the data?
The data has an outlier in the 13 to 15 range and shows that a large group purchased tickets to the game.
The data is skewed with outliers and shows that not many tickets were sold.
The data is not skewed and does not have outliers, which shows that not many tickets were sold.
The data is bimodal with peaks in the data and shows that random amounts of tickets were sold for the game.
MAKE SURE YOU EXPLAIN!!! THANKS FOR HELPING <33
Have a great day :)
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Answer:
The data has an outlier in the 13 to 15 range and shows that a large group purchased tickets to the game.
Step-by-step explanation:
An outlier in a frequency distribution is a value or set of values that is significantly different from the rest of the data set points. There is not a strong mathematical definition for what an outlier is, one should examine the data and assess in a more or less subjective manner
Looking at the data we see that most of ticket sales fall in the range 1-10
There is nothing in the range 10-12 but then after that there is another interval 13-15 with a frequency count of 1. This interval represents an outlier - it is very much apart from the rest of the data
So statement 1 is the best choice
We can eliminate the second statement. Skewness means that the data is very asymmetrical and has a peak which is at extreme right or left. Looking at the graph we see that the data is pretty much symmetrical in the range 1 - 10
Third statement can be easily eliminated since we do have an outlier as explained
Fourth statement can also be easily eliminated. The mode of a distribution is the value that appears the most often. When plotting a histogram this value (interval will have the bar that is tallest). Here, the mode is in the interval 4-6 with a height of 16 which is the number of times any ticket sales in the range 4-6 occur.
A bimodal distribution will have two bars which are the highest and of equal value. We usually refer to these as peaks. Here there is only one peak and such a distribution is called a unimodal distribution.
Hope that helps you :)
Answer: the first option is correct
Step-by-step explanation:
I got it right on my quiz
Set up the equation to solve for the missing side length.
A
5
B
12
с
Answer:
The answer is, 5² + 12² = AC²
This is the Pythagorean theorem which states that sum of the squares of the two sides of a right angled triangle is equal to the square of the hypotenuse.
base² + height² = hypotenuse² or in this case, 5² + 12² = AC²
Pls mark as brainliest. I really need for no apparent reason. Cheers
Write a function that models the data.
The rule for the exponential function is y=42(1/2)^x
What is exponential decay function?A exponential decay is a function that, as the name implies, decays exponentially. So it decays fast at the beginning and slower as the value of the variable increases.
Here,
general form of exponential function is y=a(b)^x
a= y-intercept , b = multiplier
The initial y value 42 is multiplied by 1/2, we get next y value 21 as given in the graph, So, b = 1/2
y=a(1/2)^x
consider (x,y)=( 0,42)
=> x=0 and y=42
So 42=a(1/2)^0
=> 42=a
Thus, the rule for the function is y=42(1/2)^x
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The table is missing numbers and a rule, can someone please help! only the table at the bottom, ignore the top portion!
Check the picture below.
Arianys invests money in an account paying a simple interest of 3% per year. If m
represents the amount of money she invests, which expression represents her balance
after a year, assuming she makes no additional withdrawals or deposits?
Adrian must multiply his money by 1.03 to find his total balance in a year in one step.
What is simple interest?Borrowers must pay simple interest to lenders as a fee for a loan. Compound interest is not taken into account while calculating it; just the principal is used. Simple interest is applicable to all loans. It is also the form of interest that banks give their customers on their savings accounts. There are two techniques to compute interest: simple interest and compound interest. The principal, or initial amount of a loan, is used to compute simple interest. Compound interest, sometimes known as "interest on interest," is calculated using both the original amount and the total accumulated interest from prior periods.The following calculation must be done in order to determine what Adrian should multiply his current balance by in order to find his total balance in a year in one step, assuming that no money will be added to or subtracted from the investment. Adrian invests money in an account that offers simple interest of 3% per year.
Current balance = X
Interest = 3% = 3/100 = 0.03
Interest + principal = 1.03
1.03X = Total balance in a year
Therefore, Adrian must multiply his money by 1.03 to find his total balance in a year in one step.
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A trader buys some oranges at #50 each. He finds that six of them are rotten. He sells the rest at #80 each and makes a profit of #450. How many oranges did he buy?
The total number of oranges that the trader bought is 31
How to calculate the total number of oranges that the trader bought?A trader bought some oranges at the price of #50 each
He finds that Six of these oranges are rotten
He sells the remaining at #80
He makes a profit of #450
Therefore the number of oranges that the trader bought is
Let y represent the number of oranges that the trader bought
At a price of #50= 50x
6 oranges were rotten= x-6
Profit = 450
450= 80(x-6)-50x
450= 80x-480-50x
450= 80x-50x-480
450= 30x-480
450+480= 30x
930= 30x
x= 930/30
x= 31
Hence the trader bought 31 oranges
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398107.1706 to standard form
Answer:
3.981071706 × 105
Answer:
3.981071706 x 10^5
Step-by-step explanation:
In standard form, a number is written as a decimal multiplied by a power of 10. To convert 398107.1706 to standard form, we can move the decimal point until we have a number between 1 and 10 and a power of 10 that will make the original number.
398107.1706 = 3.981071706 x 10^5
Write the equation of the line that is parallel to the line 5x- 4y = 4 and passes through one point (-8, 2).
Answer:
y = 5/4x - 8
Step-by-step explanation:
first you convert the equation to y = mx + b
then you add the the -8 into the x and the 2 into the y and solve for b
b = -8 and since it is parallel same slope.
hope this helps :)
Consider the following triangle.
A
13
C
B
Based on the given information, what is the measure of the missing length, c?
Enter your answer as a number like this: 42.
12
Answer:
5
Step-by-step explanation:
We will use the Pythagorean theorem to solve this problem. We know [tex]a^{2} + b^{2} = c^{2}[/tex]. (a, in this case, will be c) Now, we can substitute in our numbers, giving us:
[tex]a^{2} + 12^{2} = 13^{2}[/tex]
Simplifying:
[tex]a^{2} + 144 = 169[/tex]
Subtract 144 from both sides gives us:
[tex]a^{2} = 25[/tex]
Square rooting both sides gives us:
[tex]a = 5[/tex]
So, the missing measurement (c) is 5.
Hope this helped!
If 40 shirts at the dry cleaners are hanging with 5 shirts in each row, how many rows are there?
Answer:
8
Step-by-step explanation:
8 x 5 = 40
4) If $8000 is deposited into an account earning compound interest at an annual interest rate of 4% for 10 years, and it is compounded quarterly (thus 4 times per year), how much money is in the account at the end of the 5 years? Round your answer to the nearest cent. Show you work.
5) For problem #4, how much interest was earned? Show you work.
Answer:
The amount of money in the account at the end of 5 years is $9,841.63.
Step-by-step explanation:
The compound interest formula is A = P(1 + r/n)^(nt) where A is the final amount, P is the principal (initial deposit), r is the annual interest rate (expressed as a decimal), n is the number of times interest is compounded per year, and t is the number of years.
In this case, P = 8000, r = 0.04, n = 4 (because interest is compounded quarterly), and t = 5 (because we are trying to find the balance after 5 years).
So the formula becomes:
A = 8000(1 + 0.04/4)^(4*5)
By plugging the number into the formula we can find the final amount after 5 years
A = $9,841.63
The amount of money in the account at the end of 5 years is $10,404.69, and the interest earned is $2404.69.
Explanation:To calculate the amount of money in the account at the end of 5 years, we need to use the compound interest formula: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
Substituting the given values into the formula, we have A = 8000(1 + 0.04/4)^(4*5).Simplifying this equation gives us A = 8000(1 + 0.01)^20.Calculating this equation results in A = 8000 * 1.01^20 = $10,404.69 (rounded to the nearest cent).To calculate the amount of interest earned, we subtract the initial deposit from the final amount: interest = A - P.
Substituting the given values into the equation, we have interest = $10,404.69 - $8000 = $2404.69 (rounded to the nearest cent).Learn more about interest here:https://brainly.com/question/14295570
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Please help with this problem
The sum of the two matrices will be [tex]A+B = \left[\begin{array}{ccc}-1&-13&7\\5&-14&0\\7&1&4\end{array}\right][/tex]. The correct option is A.
What is the matrix?A matrix, which is used to represent a mathematical object or an attribute of one, is a rectangular array or table containing numbers, symbols, or expressions that are organized in rows and columns.
The given matrices are:-
[tex]A = \left[\begin{array}{ccc}7&-6&2\\6&-5&-7\\2&-8&8\end{array}\right][/tex]
[tex]B = \left[\begin{array}{ccc}-8&-7&5\\-1&-9&7\\-5&9&-4\end{array}\right][/tex]
The sum of the matrix will be:-
[tex]A+B = \left[\begin{array}{ccc}(7-8)&(-6-7)&(2+5)\\(6-1)&(-5-9)&(-7+7)\\(2+5)&(-8+9)&(8-4)\end{array}\right][/tex]
[tex]A+B = \left[\begin{array}{ccc}-1&-13&7\\5&-14&0\\7&1&4\end{array}\right][/tex].
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If x-3 is directly proportional to the square of y and x = 5 when y= 2, find x when y = 6.
Answer: X=21
Step-by-step explanation:
Direction Evaluate the Expression
N·58 + (4x12-40) to the power of 2
After evaluating the expression 58 + (4x12-40) to the power of 2, we get 4356 or 4.356 ×10³ in scientific notation.
What is expression?An expression or mathematical expression is a finite combination of symbols that are well-formed in accordance with context-dependent rules. To help define the logical syntax and order of operations, mathematical symbols can be used to represent variables, operations, functions, brackets, punctuation, and grouping.
Authors frequently distinguish between a formula and an expression, with the former referring to a mathematical object and the latter to a statement about such an object.
We have been asked to evaluate the Expression
58 + (4x12-40) to the power of 2
⇒ (58 + (4x12-40))²
Use (a + b)² = a² + b² + 2ab
= 58² + (4x12-40)² + 2(58)(4x12-40)
= 3364 + (4x12-40)² + 116(4x12-40)
= 3364 + (48-40)² + 116(48-40)
= 3364 + (8)² + 116(8)
= 3364 + 64 + 928
= 4356
= 4.356 ×10³
Thus, After evaluating the expression 58 + (4x12-40) to the power of 2, we get 4356 or 4.356 ×10³ in scientific notation.
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bathroom which is also a square and has an area of 900cm². What is the measurement down one side of the mirror? cm
Answer:
30cm
Step-by-step explanation:
it will be the root of 900cm²
=30cm
Sandy's ice cream corner uses 9/10 of a bag of cups every day How many days would 10 bags of cups last?
Answer:
11 days
Step-by-step explanation:
It will last: 10/1 : 9/10 = 10/1 x 10/9 = 100/9 = 11,111... days
Answer: 11.1 days
Step-by-step explanation:
Everyday, Sandy uses 9/10 of a bag of cups.
Use unitary method.
9/10 bag - 1 day
10 bag - 10/(9/10) = 100/9 ≈ 11.1 days
Pls mark as brainliest. I really need for no apparent reason. Cheers
What is the value of 5 to the 4th power
5 raised to the fourth power (written as 5^4) is equal to 5 multiplied by itself 4 times. Mathematically, it can be written as:
5^4 = 5 * 5 * 5 * 5 = 625
So, the value of 5 to the fourth power is 625.
I hope this helps :)
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{5^4}[/tex]
[tex]\mathsf{= 5 \times 5 \times 5 \times 5}[/tex]
[tex]\mathsf{= 25 \times 25}[/tex]
[tex]\mathsf{= 625}[/tex]
[tex]\huge\text{Therefore, your answer should be: }[/tex]
[tex]\huge\boxed{\mathsf{625}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
5. Theresa's sugar cookie
recipe uses 1 1/3 cup
sugar. How much sugar
would Theresa need to
make 2 4/5 batches of
cookies? PLEASE HELP ITS DUE TOMORROW IM FREAKING OUT
Answer:
You will need 3 [tex]\frac{11}{15}[/tex] cups of sugar.
Step-by-step explanation:
1 1/3 x 2 4/5
another name for 1 is 3/3
3/3 + 1/3 = 4/3
Another name for 1 is 5/5
5/5 + 5/5 + 4/5 = 14/5
[tex]\frac{4}{3 }[/tex] x [tex]\frac{14}{5}[/tex] = [tex]\frac{56}{15}[/tex]
I can break 56 into 15 + 15 + 15 + 11
[tex]\frac{15}{15}[/tex] + [tex]\frac{15}{15}[/tex] + [tex]\frac{15}{15}[/tex] + [tex]\frac{11}{15}[/tex] another name for [tex]\frac{15}{15}[/tex] is 1
1 + 1 + 1 + [tex]\frac{11}{15}[/tex]
3 [tex]\frac{11}{15}[/tex]
A rectangle is [tex]\frac{1}{3}[/tex]yards long and [tex]\frac{2}{3}[/tex] yards wide. What is the area of the rectangle in yd2?.
Answer:
[tex]\frac{2}{9}[/tex]
Step-by-step explanation:
[tex]A=lw=\frac{1}{3} \cdot \frac{2}{3}=\frac{2}{9}[/tex]
Based on the triangles shown, Which congruence Statement is correct?
CAB ≈ RWT
ABV ≠ RWT
BCA ≈ RWT
CBA ≈ TWR
statement CBA ≅ TWR is true.
what is congruence theorem?
The theorem that states that two triangle is congruent when there three corresponding sides are equal and all three corresponding angles are also equal.
Which statement is true for congruent triangle?
given, triangle ABC and Triangle RWT both are right-angled.
we examined that three corresponding sides of ABC is equal to the corresponding sides of RWT and same for the three corresponding angles.
we measured, right angle A = right angle R
base length AB = base length RW
hypotenuse BC = hypotenuse WT
Side length AC = side length RT
angle C = angle T
angle B = angle W
as per the properties of congruence theorem ABC and RWT are congruent.
hence the statement CBA ≅ TWR is true.
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A survey was given to 280 people asking whether people like dogs and/or cats. 151 said they like dogs 138 said they like cats 47 said they don't like cats or dogs. How many said they liked cats but not dogs?
Answer: 80
Step-by-step explanation:
280-47=233 people who like cats or dogs
153+138=291 people who like cats, dogs, or both
291-233=58 people who like both
People who like cats = 138-58=80
A 400 g sample is composed of 100 g of cesium (Cs) and 300 g of iodine (1).
What is the percent by mass of Cs in the sample?
A. 50.0%
B. 70.0%
C. 25.0%
D. 75.0%
The percentage of mass of Cs in the sample is 25%
What is percentage?
In mathematics, a percentage is a number or ratio expressed as a fraction of 100. A percentage, indicates hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity.
To calculate the percentage of Cs in the sample
100/400 x 100
=25%
To calculate the percentage of cesium (Cs) in the sample
300/400 x 100
=75%
Hence, 25% is the percentage of Cs in the sample
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Hi can someone help me do this math problem? How would you do it in a ti-84 calculator or by hand?
The value of x, if x is a real number and the expression, [tex]\frac{x + 2\cdot \mathbf{i}}{1 + \mathbf{i}}[/tex] is a purely imaginary number is x = -2. The correct option is option b.
b. -2
What is an imaginary number?An imaginary number is a number which is obtained by finding the square root of a negative number.
The specified expression is; [tex]\frac{x+2\cdot \mathbf{i}}{1 + \mathbf{i}}[/tex]
Multiplying the numerator and the denominator by the complex conjugate of the denominator, (1 - i), we get;
[tex]\frac{x+2\cdot \mathbf{i}}{1 + \mathbf{i}}\times \frac{1 - \mathbf{i}}{1 - \mathbf{i}} =\frac{x - x \cdot \mathbf{i}+2 \cdot \mathbf{i}-2\cdot \mathbf{i}^2}{1 - \mathbf{i}^2}[/tex]
[tex]\frac{x - x \cdot \mathbf{i}+2 \cdot \mathbf{i}-2\cdot \mathbf{i}^2}{1 - \mathbf{i}^2} = \frac{x + (2 - x)\cdot \mathbf{i} + 2}{1 - (-1)} =\frac{x + (2 - x)\cdot \mathbf{i} + 2}{2}[/tex]
Where x is real, for the number to be purely an imaginary number, we get;
[tex]\dfrac{x + (2 - x)\cdot \mathbf{i} + 2}{2} = \dfrac{x +2+ (2 - x)\cdot \mathbf{i} }{2} = \dfrac{0+ (2 - x)\cdot \mathbf{i} }{2}[/tex]
[tex]\frac{0+ (2 - x)\cdot \mathbf{i} }{2} = \frac{(2 - x)\cdot \mathbf{i} }{2} = \frac{(2-x)}{2} \cdot \mathbf{i}[/tex]
Therefore, for the number to be a purely imaginary number, then; x + 2 in the numerator following the multiplication of the numerator and the denominator by the complex conjugate of 1 + i, which is 1 - i, should be 0, and we get;
x + 2 = 0
x = 0 - 2 = -2
x = -2
The value of x such that the expression (x + 2·i)/(1 + i) is a purely imaginary number is; x = -2
The correct option is; b. -2
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9. Brenna decided to purchase 4 points in order to lower the interest rate on her
$175,000 mortgage. How much additional money does she need to bring to closing for
the points she wishes to purchase?
A linear function has the table of values shown. The information in the table shows the number of tickets sold on opening night of a movie as a function of the number of hours since the tickets have been on sale
The equation that represents the linear function is y =32x
What is a linear equation explain?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.
A linear function is represented as
y = mx + c
The slope is calculated as
m = y₂ - y₁/x₂ - x₁
m = 576 - 64/18 - 2
m = 512/16
m = 32
The linear equation is then calculated as
y = 32( x - 2 ) + 64
y = 32x - 64 + 64
y = 32x
Hence, the equation that represents the linear function is y =32x
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The complete question is -
A linear function has the table of values shown. The information in the table shows the number of tickets sold on opening night of a movie as a function of the number of hours since the tickets have been on sale. Number of Hours (x) 2 6 18
Number of Tickets Sold (y) 64 192 576
1.Write the equation that gives the number of tickets sold, y, as a linear function of the number of hours, x, since the tickets have been on sale.
Maths
Someone plsssss help
According to the problem the area of the rectangle is 28 cm^2.
What is area?Area is a measure of the size of a surface or region. It is usually expressed in square units, such as square meters (m2), square kilometers (km2), and square feet (ft2). Area can be found in two-dimensional shapes, such as circles, rectangles, and triangles, as well as in three-dimensional shapes, such as cubes and spheres. The area of a two-dimensional shape is the amount of space that it covers. The area of a three-dimensional shape is the total surface area of the object.
The area of a rectangle is calculated by multiplying the length by the width. In this case, the length of the rectangle is 7 cm and the width is 4 cm. Therefore, the area of the rectangle is 7 cm x 4 cm = the area of the rectangle is 28 cm^2.
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Please please look at the picture and answer the question thank uu
Answer:
3x
Step-by-step explanation:
To answer this question, we have to understand what a product is. A product is the result of multiplication. For example, the product of 5 and 5 is 25 because 5 × 5 = 25.
We can apply this concept to the given expression.
"the product of 3 and a number"
means:
3 × "a number"
And since the problem specifies that "a number" is represented by the variable x, we can replace it with that.
3 × x
This looks a bit confusing with the x-like multiplication sign, so we can remove that and make 3 a coefficient of x.
3x
Answer:
3*x
Step-by-step explanation:
We can break down the problem piece by piece. We have "the product". The product of what? The product of 3 and a number. The problem tells us to replace a number with x. So it is 3*x.
can someone please help me. i don’t get it
Step-by-step explanation:
(4-2)*180=360
80+7t+7t+14t=360
28t=280
t=10
