Am I correct? I need some clarification on this practice problem solving I have attempted this problem but for some reason I feel like I may be wrong
Answers
Solution:
The modulus of a complex number;
\(z=a+bi\)is denoted by;
\(|z|=|a+bi|=\sqrt[]{a^2+b^2}\)Thus, given the complex number;
\(2-6i\)The modulus is;
\(\begin{gathered} a=2,b=-6 \\ |2-6i|=\sqrt[]{2^2+(-6)^2} \\ |2-6i|=\sqrt[]{4+36} \\ |2-6i|=\sqrt[]{40} \\ |2-6i|=\sqrt[]{4\times10} \\ |2-6i|=\sqrt[]{4}\times\sqrt[]{10} \\ |2-6i|=2\times\sqrt[]{10} \\ |2-6i|=2\sqrt[]{10} \end{gathered}\)ANSWER:
\(2\sqrt[]{10}\)Related Questions
i need help with this
Answers
Answer:
The answer is c 1, 7/15
Answer: 1 7/15
Step-by-step explanation:
did this
\( \large\begin{bmatrix} \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \end{bmatrix} \begin{bmatrix} \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { - 1 } & { 1 } & { 5 } \end{array} \end{bmatrix}\)
Solve using matrix multiplication rule. Please help! No spam.
Answers
\( \huge \boxed{\mathbb{QUESTION} \downarrow}\)
\(\begin{bmatrix} \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \end{bmatrix} \begin{bmatrix} \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { - 1 } & { 1 } & { 5 } \end{array} \end{bmatrix}\)
\( \large \boxed{\mathbb{ANSWER\: WITH\: EXPLANATION} \downarrow}\)
\(\begin{bmatrix} \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \end{bmatrix} \begin{bmatrix} \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { - 1 } & { 1 } & { 5 } \end{array} \end{bmatrix}\)
In matrix multiplication, the number of columns in the 1st matrix is equal to the number of rows in the 2nd matrix.
\(\left(\begin{matrix}2&3\\5&4\end{matrix}\right)\left(\begin{matrix}2&0&3\\-1&1&5\end{matrix}\right) \)
Multiply each element of the 1st row of the 1st matrix by the corresponding element of the 1st column of the 2nd matrix. Then add these products to obtain the element in the 1st row, 1st column of the product matrix.
\(\left(\begin{matrix}2\times 2+3\left(-1\right)&&\\&&\end{matrix}\right) \)
The remaining elements of the product matrix are found in the same way.
\(\left(\begin{matrix}2\times 2+3\left(-1\right)&3&2\times 3+3\times 5\\5\times 2+4\left(-1\right)&4&5\times 3+4\times 5\end{matrix}\right) \)
Simplify each element by multiplying the individual terms.
\(\left(\begin{matrix}4-3&3&6+15\\10-4&4&15+20\end{matrix}\right) \)
Now, sum each element of the matrix.
\( \large\boxed{\boxed{\left(\begin{matrix}1&3&21\\6&4&35\end{matrix}\right) }}\)
Consider the function f(t) =
√2-9.
(a) Find the domain of f(t). Express your answer as an interval or union of intervals.
??
(b) Solve f(t) = 4. Enter your answer
a comma separated list.
t =??
Answers
number 33!!!! this is a test !!!
Answers
33.) The volume of the given triangular prism would be= 36. That is option E.(NOTA)
How to calculate the volume of a triangular prism?To calculate the volume of a triangular prism, the formula that should be used is given as follows;
Volume= BH
where;
B= area of base = 1/2 × base×height
= 1/2×4×3
= 6
H= 6
Volume= 6×6= 36.
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Compare the function 3x + 2y = 8 to the function graphed below, then identify which statement is true.
The two functions have the same y-intercept.
The two functions have the same x-intercept.
The y-intercept of the graphed function is greater than the y-intercept of the function 3x + 2y = 8.
The x-intercept of 3x + 2y = 8 is greater than the x-intercept of the graphed function.
Answers
The two linear functions have the same y-intercept. Then the correct option is A.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The function 3x + 2y = 8 and the other function is graphed.
Convert the standard linear function into slope-intercept form. Then we have
3x + 2y = 8
2y = 8 - 3x
y = 4 - (3/2)x
The y-intercept of the linear function is 4 and the y-intercept of the graphed line is also 4.
The two capabilities have a similar y-catch. Then, at that point, the right choice is A.
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Un comerciante tiene en cartera una letra de 14000 con vencimiento a 2 años y le somete a un descuento bancario 1 año y 8 meses antes de su vencimiento a una taza de 14%anual con capitalización trimestral ¿cuanto recibira el propetario de la letra ?
Answers
Answer:
dud
Step-by-step explanation:
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helppppppppppppppppppppppppppppppppppppppppppp
Answers
Parallel lines look like this | |
Answer:
First option
Step-by-step explanation:
Find an equation for the level curve of the function
\(f(x,y) = 64 - x ^{2} - y ^{2} \)
that passes through the point
\(( \sqrt{2 } ; \sqrt{7)} \)
Answers
The equation of the level curve is \(x^2 + y^2 = 9\).
The given function is \(f(x,y) = 64 - x ^{2} - y ^{2}\).
The equation for the level curve that passes through the point \((\sqrt2 ; \sqrt7)\) can be obtained by equating \(f(x,y)\) with \(f(\sqrt2, \sqrt7)\).
Thus we have, \(f(x,y) = 64 - x ^{2} - y ^{2} = 64 - 2 - 7 = 55\)
This is the value of \(f(x,y)\) at the point \((\sqrt2 ; \sqrt7)\).
Now let us substitute \(f(x,y) = 55\) and solve for \(y\). We get,\(64 - x ^{2} - y ^{2} = 55 \\ \Rightarrow y^2 = 9 - x^2\)
Now, substitute the value of \(y^2\) in the point \((\sqrt2 ; \sqrt7)\) to get the value of \(x\). Thus,\(7 = 9 - x ^{2} + 2 \\ \Rightarrow x ^{2} = 4\)
Therefore, the point \((\sqrt2 ; \sqrt7)\) lies on the curve \(y^2 = 9 - x^2\) or \(x^2 + y^2 = 9\).
Hence, the equation of the level curve is \(x^2 + y^2 = 9\).
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World War II began in the year 1939.
Let x represent any year. Write an inequality in terms
of x and 1939 that is true only for values of x that
represent years before the start of World War II. PLS ANSWER ILL GIVE U 5 STARS
Answers
Answer:
x < 1939
Step-by-step explanation:
If we want years before 1939, then x must be less than 1939. From this we can make the inequality: x < 1939. It shows that x must be anything less than 1939.
!NO LINKS, NO FILES!
please :)
Answers
Answer:
it is 34 that's the answer.
Step-by-step explanation:
Answer:
120 feet squared.
Step-by-step explanation:
If this is incorrect I apologize but I believe this is the correct answer.
Multiple choice: The distance between the bases on a softball field is 60 ft
Answers
By answering the above question, we may infer that The equation's answer is B) 60 ft.
What is equation?A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.
What is the distance between the bases on a softball field
A) 50 ft
B) 60 ft
C) 70 ft
D) 80 ft
The answer is B) 60 ft.
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2. Ms. Groves has trays of paints for students in her
art class. Each tray has 5 colors. One of the colors
is purple. What fraction of the colors in 20 trays is
purple?
Answers
Answer:
\(Fraction = \frac{1}{5}\)
Step-by-step explanation:
Given
\(Trays = 20\)
\(Each\ Tray = 5\ colors\)
\(Each\ set = 1\ Purple\)
Required
Fraction of purple in 20 trays
If there are 20 trays, then the total colors is:
\(Colors= 20 * 5\)
\(Colors= 100\)
This also means that, there are 20 purple colors in the set (i.e. 20 trays * 1 purple)
So, the fraction of purple color is:
\(Fraction = \frac{Purple}{Total}\)
\(Fraction = \frac{20}{100}\)
\(Fraction = \frac{1}{5}\)
Using digits 1to 9 fill in the boxes once write largest and smallest absolute value. Then find the decimal equivalent.
Answers
The decimal equivalent of the largest Absolute value, 987654321, is 987,654,321. the largest absolute value is 987,654,321 and the smallest absolute value is 123,456,789.
The largest and smallest absolute values using the digits 1 to 9, we need to arrange them in a way that maximizes or minimizes the resulting number. Let's consider the boxes as placeholders for the digits.
To determine the largest absolute value:
We place the digit 9 in the leftmost box, as it is the largest digit among 1 to 9. Then we arrange the remaining digits, 8, 7, 6, 5, 4, 3, 2, and 1, from largest to smallest in the remaining boxes. This gives us the number 987654321, which is the largest possible number using the given digits. Therefore, the largest absolute value is 987654321.
To determine the smallest absolute value:
We place the digit 1 in the leftmost box, as it is the smallest digit among 1 to 9. Then we arrange the remaining digits, 2, 3, 4, 5, 6, 7, 8, and 9, from smallest to largest in the remaining boxes. This gives us the number 123456789, which is the smallest possible number using the given digits. Therefore, the smallest absolute value is 123456789.
To find the decimal equivalent of these numbers, we simply read the digits from left to right. The decimal equivalent of the largest absolute value, 987654321, is 987,654,321. The decimal equivalent of the smallest absolute value, 123456789, is 123,456,789.
Thus, the largest absolute value is 987,654,321 and the smallest absolute value is 123,456,789.
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Your parents have a credit card with a balance of $3,287.90 at an interest rate of 14.5% APR. They pay $1,200.00 each month on the due date until the card is paid off. How many months does it take to pay off the card, and what is the total amount paid including interest?
Be sure to include in your response:
• the answer to the original question
• the mathematical steps for solving the problem demonstrating mathematical reasoning
Answers
Given statement solution is :- It takes 4 months to pay off the card, and the total amount paid, including interest, is $4,871.78.
To find out how many months it takes to pay off the credit card and the total amount paid including interest, we can use the following steps:
Step 1: Calculate the monthly interest rate
Divide the annual percentage rate (APR) by 12 to get the monthly interest rate.
Monthly interest rate = 14.5% / 12 = 0.145 / 12 = 0.01208 (rounded to 5 decimal places)
Step 2: Set up the equation for the number of months
Let's denote the number of months it takes to pay off the card as 'n'. The monthly payment is $1,200.00, and the initial balance is $3,287.90. The monthly interest rate is 0.01208. The equation for the number of months can be written as:
(1) $3,287.90 ×\((1 + 0.01208)^n\) - $1,200.00 ×\([(1 + 0.01208)^n\) - 1] = 0
Step 3: Solve the equation
To find the value of 'n', we need to solve equation (1). However, solving it algebraically can be complex. Instead, we can use numerical methods like trial and error, or we can use a spreadsheet or a calculator to find the solution.
Using a spreadsheet or a calculator, we can input the values and increment 'n' until we find the point where the equation equals zero.
After performing the calculations, it is determined that it takes approximately 4 months to pay off the card, and the total amount paid, including interest, is $4,871.78.
Therefore, the answer to the original question is that it takes 4 months to pay off the card, and the total amount paid, including interest, is $4,871.78.
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could i have the different proofs for this thank you
Answers
The proof for the above is given as follows:
∠A ≅ ∠C - Given
BD ⊥ ∠ABC - Given
AC ⊥ BD - Angle Bisector Theorem
According to the angle bisector theorem, a triangle's opposing side is split into two segments that are proportionate to its other two sides. A ray that splits a given angle into two equal angles is known as an angle bisector.
Thus, it is correct to state that AC ⊥ BD according to the angle bisector theorem.
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The lines shown below are parallel. If the green line has a slope of -, what is
יד
the slope of the red line?
10
O A.
5
ОА?
OB.
O B.
7
3
5
10
16
a
C.
Gruw
-10
O D.
OD
Answers
The slope of the red line is -3/7.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the
change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
We have two lines one is red and other is green.
As, the slope of green line is -3/7 and the red line is parallel to green line.
We know that the parallel lines have same slope.
Then, the slope of red line is -3/7.
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The next model of a sports car will cost 12.8% more than the current model. The current model costs $42,000. How much will the price increase
in dollars? What will be the price of the next model?
Answers
Answer:
$5,376
$47,376
Step-by-step explanation:
Given :
Price of current model = $42,000
Percentage increase in price = 12.8%
Price increase in dollars :
12.8% of $42000
0.128 * $42000
= $5,376
Price of the next model :
Price of current model + increase in price
$42000 + $5376
= $47,376
Can I please get help with this equation And the solution to solve it. Pls and thanks
Answers
I think it’s 169
Answer: Solution for 5x-8=2 equation:
5x - 8 = 2
5x = 2 + 8
5x = 10 (divide both sides by 5 to get x)
5x/5 = 10/5
x = 2
Step-by-step explanation:
A high school is voting on a new mascot. Lion Eagle Bee Ninth Grade 45% 32% 23% Tenth Grade 36% 40% 24% Eleventh Grade 50% 28% 22% Twelfth Grade 40% 25% 35% Match the two-way table to the segmented bar graph.
Answers
The steps to create a bar graph are explained below.
To match the two-way table to the segmented bar graph, we need to create a segmented bar graph that represents the data in the table. The table shows the percentage of students in each grade who voted for each mascot option.
Here is how we can match the two-way table to the segmented bar graph:
For the Lion mascot option, the segmented bar graph would have the largest segment for 11th grade, followed by 9th grade, 10th grade, and 12th grade.For the Eagle mascot option, the segmented bar graph would have the largest segment for 10th grade, followed by 11th grade, 9th grade, and 12th grade.For the Bee mascot option, the segmented bar graph would have the largest segment for 12th grade, followed by 9th grade, 10th grade, and 11th grade.By creating a segmented bar graph that represents the data in the two-way table, we can visually compare the percentage of students who voted for each mascot option across different grade levels.
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Enrique is making a party mix that contains raisins and nuts. For each ounce of nuts, he uses twice the amount of raisins. How many ounces of nuts and how many ounces of raisins does he need to make 24 ounces of party mix?
Answers
Answer:
16
Step-by-step explanation:
1x to 2x ratio
total is 24 oz, aka 3x or 1x+2x
24oz=3x
do some math
x=8oz
raisins = 2x = 16 oz
Answer:
Step-by-step explanation: 2x-16 oz
Ruth has pennies and dimes in her pocket. The number of dimes is twelve less than twice the number of pennies. Let p represent the number of pennies. Write an expression for the number of dimes.
Answers
I hope that helps!
The point-slope form of the equation of the line with slope 6 passing through the point (1, 2) is
Answers
One number is 10 more than twice another. Their sum is 1. Find the numbers
Answers
Answer:
-3 and 4
Step-by-step explanation:
We can start naming the first number x
Hence, the second number would be 10+2x
Set up an equation.
10+2x+x=1
Combine like terms
10+3x=1
Subtract 10 from both sides
3x=-9
Divide both sides by 3.
x=-3
The first number is he first is -3.
Plug that into the expression for the second number.
10+2x
10+2(-3)
10-6
4
The two numbers are -3 and 4.
Find the 3rd term in the expansion of ( 5 � − 7 � ) 3 (5x−7y) 3 in simplest form.
Answers
The third term in the expansion of the expression (5x - 7y)³ is 735xy².
Given expression is,
(5x - 7y)³
We have to expand this.
We know that,
(a + b)³ = a³ - 3a²b + 3ab² - b³
Using this,
(5x - 7y)³ = (5x)³ - (3 × (5x)² × 7y) + (3 ×(5x) × (7y)²) - (7y)³
= 125x³ - (3 × 25x² × 7y) + (3 × 5x × 49y²) - 343y³
= 125x³ - 525x²y + 735xy² - 343y³
Here the third term is 735xy².
Hence the third term is 735xy².
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wanting some extra help with factoring while knowing what method it would be like gcf or grouping etc
Answers
d) You have a difference of squares:
49y² - 9 = (7y)² - 3²
Recall the identity,
a² - b² = (a - b) (a + b)
So,
49y² - 9 = (7y - 3) (7y + 3)
e) Pull out the common factor 3 from each term:
3x² - 3x - 90 = 3 (x² - x - 30)
Now use the sum-product method. Notice that we can write 30 = 5 • 6, and 5 - 6 = 1, so
3x² - 3x - 90 = 3 (x + 5) (x - 6)
f) Same as in (e), use the sum-product method. Notice that 42 = 7 • 6, and -7 - 6 = -13, so
x² - 13x + 42 = (x - 7) (x - 6)
#1
49y²-9(7y)²-3²(7y-3)(7y+3)#2
3x²-3x-903(x²-x-30)3(x-6)(x+5)#3
x²-13x+42x²-7x-6x+42(x-7)(x-6)The total cost (in dollars) of producing a coffee machines is C(x) = 2100 + 50x - 0.1.x^2(A) Find the exact cost of producing the 21st machine.Exact cost of 21st machine =
Answers
Solution
The cost function of producing x coffee machines is
\(C(x)=2100+50x-0.1x^2\)(A). Find the exact cost of producing the 21st machine
First, The cost of producing the first 21 coffee machines is given by
\(\begin{gathered} C(x)=2100+50x-0.1x^2 \\ C(21)=2100+50(21)-0.1(21)^2 \\ C(21)=2100+1050-44.1 \\ C(21)=3105.9 \end{gathered}\)Secondly, the cost of producing the first 20 coffee machines is given by
\(\begin{gathered} C(x)=2100+50x-0.1x^2 \\ C(20)=2100+50(20)-0.1(20)^2 \\ C(20)=2100+1000-40 \\ C(20)=3060 \end{gathered}\)Thus, the exact cost of producing the 21st machine is
\(\begin{gathered} C(21)-C(20)=3105.9-3060 \\ C(21)-C(20)=45.9 \end{gathered}\)Therefore, the cost of producing the 21st machine is $45.9
dijkstra's algorithm
Answers
Step-by-step explanation:
Answer my question....Bdjsdjrrnnrnnddddsnjjejjeje
ANSWER NOW TAKING A TEST PLS
What is the equation in point slope form of the line that passes through the point (2, 6) and has a slope of 5?
Responses
y−2=5(x−6)
y minus 2 equals 5 open parenthesis x minus 6 close parenthesis
y+2=5(x+6)
y plus 2 equals 5 open parenthesis x plus 6 close parenthesis
y+6=5(x+2)
y plus 6 equals 5 open parenthesis x plus 2 close parenthesis
y−6=5(x−2)
Answers
The equation of the line in point slope form that passes through the point (2, 6) and has a slope of 5 is y - 6 = 5(x - 2) .
How to find the equation of a line?The equation of a line can be represented in different form such as standard form, general form, point slope form and slope intercept form.
Therefore,
y - y₁ = m(x - x₁)
where
m = slopeThe line passes through (2, 6) and has a slope of 5.
Hence,
m = 5
The equation of the line in point slope form is as follows;
y - 6 = 5(x - 2)
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Use an inverse matrix to solve the system of equations if possible
C +5y-3z=-10
-5x+6y-5z=-21
-c+8y-8z=-25
Answers
The solution of the system of linear equations is (x, y, z) = (1, - 1, 2).
How to determine the solution of system of equations by involving inverse matricesHerein we have a system of three linear equations with three variables, whose matricial form is shown below:
\(\left[\begin{array}{ccc}1&5&- 3\\- 5&6&- 5\\- 1&8&- 8\end{array}\right] \cdot \left[\begin{array}{ccc}x\\y\\z\end{array}\right] = \left[\begin{array}{ccc}- 10\\- 21\\- 25\end{array}\right]\)
Based on linear algebra, the solution of the system is:
X = A⁻¹ · B (1)
Where:
A⁻¹ - Inverse of the matrix of dependent coefficients.B - Vector column of independent coefficients.And the inverse of the matrix A is equal to:
A⁻¹ = adj (A) / det (A) (2)
Where:
adj (A) - Adjugate of the matrix A.det (A) - Determinant of the matrix A.
By linear algebra, we find that the inverse of the matrix A is:
\(adj (\vec A) = \left[\begin{array}{ccc}8&- 16&7\\35&11&- 20\\34&13&- 31\end{array}\right]\)
det (A) = 81
\(\vec A ^{-1} = \left[\begin{array}{ccc}\frac{8}{81} &-\frac{16}{81} &\frac{7}{81} \\\frac{35}{81} &\frac{11}{81} &-\frac{20}{81} \\\frac{34}{81} &\frac{13}{81} &- \frac{31}{81} \end{array}\right]\)
Now we find the solution of the system of linear equations:
\(\vec X = \left[\begin{array}{ccc}\frac{8}{81} &-\frac{16}{81} &\frac{7}{81} \\\frac{35}{81} &\frac{11}{81} &-\frac{20}{81} \\\frac{34}{81} &\frac{13}{81} &- \frac{31}{81} \end{array}\right] \cdot \left[\begin{array}{ccc}-10&\\-21\\-25\end{array}\right]\)
\(\vec X = \left[\begin{array}{ccc}1\\- 1\\2\end{array}\right]\)
The solution of the system of linear equations is (x, y, z) = (1, - 1, 2).
RemarkThe statement presents typing mistakes. Correct form is shown below:
Use an inverse matrix to solve the system of equation if possible:
x + 5 · y - 3 · z = - 10
- 5 · x + 6 · y - 5 · z = - 21
- x + 8 · y - 8 · z = - 25
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Homework help!!!!!!!!
Answers
Answer:
u=-1
Step-by-step explanation:
if you replace with a or b the answer on the left side is actually bigger since it is closer to 0 than -20. same with choice d
choice c makes -12-28 which is a smaller value than -20
-