Answer:
|z| = |a + ib| = [tex]\sqrt{a^{2} + b^{2}}[/tex].
Step-by-step explanation:
By the definition of complex numbers the modulus of any complex number z = x + iy is given by |z| = |x + iy| = [tex]\sqrt{x^{2} + y^{2}}[/tex].
Say for example, z = 3 + 4i is a complex number then
|z| = |3 - 4i| = [tex]\sqrt{3^{2} + 4^{2}} = 5[/tex]
In a complex plane modulus of a complex number z = x + iy means the distance of the point (x, iy) from the origin. (Answer)
candace is at a coffee shop and knows she can spend more than $52 before tax she sees this price list in the coffee shop
[tex]21+7.50p\leq 52[/tex]
Explanation:For inequalities, "a is no more than b" can be written as:
[tex]a\leq b[/tex]
Here we know Candace that can spend no more than $52 before tax. She can spend a certain amount of money in both Dark Roast coffee and Morning Blend coffee. So she spends:
2 pounds of Morning Blend coffee.p pounds of Dark Roast coffeeTherefore:
Amount of money for Morning Blend coffee:
[tex]2\times 10.50=\$21[/tex]
Amount of money for Dark Roast coffee:
[tex]p\times 7.50=\$7.50p[/tex]
So the total amount of money:
[tex]21+7.50p[/tex]
Finally, the inequality becomes:
[tex]21+7.50p\leq 52[/tex]
Besides, in order to know how many pounds she can spend let's solve for p:
[tex]7.50p\leq 52-21 \\ \\ 7.50p\leq 31 \\ \\ p\leq 4.13[/tex]
So she can spend less that 4.13 pounds.
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Final answer:
The correct inequality to determine the possible values for the number of pounds of Dark Roast coffee, p, along with 2 pounds of Morning Blend coffee for $52 or less is 9p + 15.10 ≤ 52. This inequality can be used to solve for p, the number of pounds of Dark Roast coffee Candace can buy which is p ≤ 4.1.
Explanation:
Calculator Candace wants to determine the number of pounds of Dark Roast coffee, represented as p, she can buy if she purchases 2 pounds of Morning Blend coffee for a total of $52 or less. The price of the Morning Blend coffee is $7.55 per pound. To calculate this, we need to create an inequality that represents the scenario:
The cost for 2 pounds of Morning Blend coffee: 2 x $7.55 = $15.10The maximum amount Candace can spend: $52Now, the inequality will consider the total price of the Morning Blend coffee and add the price of the Dark Roast coffee (which is $9.00 per pound). So the inequality should look like this:
9p + 15.10 ≤ 52
This inequality can be used to solve for p, the number of pounds of Dark Roast coffee Candace can buy which is p≤4.1.
Which number has exactly 3 factors?
2
4
6
8
Answer:
Given a number N, print all numbers in range from 1 to N having exactly 3 divisors. Examples: Input : N = 16 Output : 4 9 4 and 9 have exactly three divisors. Divisor Input : N = 49 Output : 4 9 25 49 4, 9, 25 and 49 have exactly three divisors.
Step-by-step explanation:
Kira ran three times last week. Here are the distances she ran (in kilometers).
19.16, 13, 8.27
What is the total distance Kira ran on these three days?
Answer:
40.43 Kilometers
Explanation:
19.16, 13, 8.27
19.16 + 13 + 8.27
= 40.43
Final answer:
The total distance Kira ran during the three days is the sum of the individual distances she ran on each day, which is 40.43 kilometers.
Explanation:
The total distance Kira ran on the three days is the sum of the distances she ran on each day. To find the total distance, you simply need to add up the three individual distances.
Add the first distance: 19.16 km
Add the second distance: 13 km
Add the third distance: 8.27 km
Calculate the sum: 19.16 km + 13 km + 8.27 km = 40.43 km
Therefore, the total distance Kira ran during the three days is 40.43 kilometers.
Shirts are nine dollars each you have a coupon that saves you five dollars off your purchase how much would it cost you to buy 6 shirts
Answer:$49.00
Step-by-step explanation:
9x5-5=$49
Which algebraic expression is equivalent to the expression below? 9(2x - 6) A. 9x - 3 B. 18x - 54 C. 9x - 8
Answer:
B
Step-by-step explanation
multiply 2 and 6 by 9
Answer:
its b
Step-by-step explanation:
What 3 ratios that are equivalent
Answer:
1:2, 2:4, 3:6
Step-by-step explanation:
If you times 1:2 by 2, you get 2:4. If you times 1:2 by 3, you get 3:6.
You have to multiply each individual number in the ratio.
Answer:1:3
2:6
4:12
Step-by-step explanation:
Multiply the binomials (4x + 7) and (2x - 8).
Answer:
8x^2-18x-56
Step-by-step explanation:
(4x+7)*(2x-8)=
4x*2x+4x*(-8)+7*2x+7*(-8)=
8x^2-32x+14x-56=
8x^2-18x-56
Solve for x and y
5x + 3y = 7
y = 4
Answer: x= -1 y= 4
Step-by-step explanation:
We are going to solve this using substitution.
Here is the work...
5x+3(4)=7
That is what it woud look like because y is equal to 4.
3 times 4 is 12.
So now we have...
5x+12=7
Now we want to get All the common factors together...
To do this we will subtract 12 from 7 and we get -5.
Here is our equation now...
5x=-5
Now we divide x by 5 to get x alone, but we also divide -5 by 5.
x=-1
Now all we have to do to solve for y is put x in an equation.
In this case here is what we will do...
5(-1)+3y=7
Multiply...
-5+3y=7
Now we need to get the common factors together so lets add 5 to 7.
3y=12
3y/3=y
12/3=y
y=4
But that is already in your problem...OOF.Dont worry its still correct.
To solve the system, substitute y=4 into the first equation, leading to x=-1. Thus, the solution is x=-1 and y=4.
Explanation:To solve the system of equations 5x + 3y = 7 and y = 4, we can start by substituting the value of y from the second equation into the first equation. We are given y directly, so the substitution is straightforward.
Substituting y = 4 into the first equation:
5x + 3(4) = 75x + 12 = 75x = 7 - 125x = -5x = -1So, the solution to the system of equations is x = -1 and y = 4. We can say that x and y are variables, and in this case, y is dependent on x in other linear equations but is given directly here.
Please help me on this math problem!
Answer:
427 feet.
Step-by-step explanation:
Rationalise: [tex]\frac{\sqrt{48} }{\sqrt{3} }[/tex]
Answer:
4
Step-by-step explanation:
Root(48)/Root(3)
= root(48/3)
= root(16)
=4
What is the median value of the data set shown on the line plot?
LMK answer fast!!
Answer:
i cant solve it for you but i will tell you how to do it
Step-by-step explanation:
You add them all up from least to greatest on a piece of paper then use your two fingers starting from the least and the greatest and go down the line if you get more than 1 number you must add them both up and divide by 2.
A and B are independent events.
P(A) = 0.40
P(B) = 0.30
what is P(A|B)?
Answer: P(A|B) = 0.40.
Step-by-step explanation: Since A and B are independent events, P(A|B) = P(A).
Therefore, P(A|B) = 0.40.
The probability of A given B is 0.40.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
Example:
The probability of getting a head in tossing a coin.
P(H) = 1/2
We have,
Since A and B are independent events, we know that:
P(A and B) = P(A) x P(B)
But since they are independent, we also know that:
P(A and B)
= P(A) x P(B|A)
= P(B) x P(A|B)
Thus:
P(A|B) = (P(A) x P(B|A)) / P(B)
We are given that P(A) = 0.40 and P(B) = 0.30.
We don't know P(B|A), but since A and B are independent, we know that:
P(B|A) = P(B)
So,
P(A|B) = (0.40 x 0.30) / 0.30 = 0.40
Thus,
The probability of A given B is 0.40.
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What the answer is to question number 4
6a + 3 in Number of Terms
The expression '6a + 3' consists of two terms: '6a' and '3'. In mathematical expressions, terms are separated by addition or subtraction operations.
Explanation:The expression given, 6a + 3, is a mathematical expression that involves operations of addition and multiplication. In this expression, there are two terms separated by a plus sign. To clarify, a term refers to the separated parts of an expression when it is written as a sum or difference. This expression contains one numerical value (3) and one algebraic term (6a).
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I need help everyone so what is 9x9
The value of 9 × 9 is 81.
What is Multiplication?Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.
a × b means that a is added to itself b times or b is added to itself a times.
The question is to find the product of 9 × 9.
By the definition of multiplication, 9 × 9 is the addition of the number up to 9 times.
That is, 9 × 9 can also be written as,
9 × 9 = 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9
Adding number 9 to itself 9 times we get 81.
So 9 × 9 = 81
Hence the product after multiplying 9 with 9 is 81.
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p² +6r - 27
factoring quadratics
Step-by-step explanation:
look at the picture shown
a fruit punch recipe requires 12 teaspoons of sugar for every 3 quarts of water. at this rate how much sugar is needed for 9 quarts of water
36 teaspoons. since the number of quarts is multiplied by 3, multiply the number of teaspoons as well. 12 × 3 = 36
The ratio of girls to boys in the 6th grade is to 6to7 how many girls are there if there are 364total students
Answer:
168 girls.
Step-by-step explanation:
There are a total of 6 + 7 = 13 'parts'.
So one part = 364 / 13 = 28.
So the number of girls = 6 * 28
= 168.
HELP!! PLEASE... ANSWER
5. Determine whether each pair of triangles is similar. Justify your answer.
Answer:
A
Step-by-step explanation:
Consider Δ JKL and Δ GDF
If the ratios of corresponding sides are equal then the triangles are similar.
[tex]\frac{JK}{GD}[/tex] = [tex]\frac{24}{20}[/tex] = [tex]\frac{6}{5}[/tex]
[tex]\frac{xJL}{GF}[/tex] = [tex]\frac{18}{15}[/tex] = [tex]\frac{6}{5}[/tex]
[tex]\frac{KL}{DF}[/tex] = [tex]\frac{12}{10}[/tex] = [tex]\frac{6}{5}[/tex]
Since the ratios are equal then Δ JKL and Δ GDF are similar by SSS postulate.
3x-15=2x+3 Find QR
It says the answer is 39 but I can’t figure out how they got 39. Please help
Answer:
look at the picture shown
on a 45-45-90 angle and the hypotenuse is 2 square root of 14 what is x and y?
Final answer:
In a 45-45-90 triangle, with a hypotenuse of 2√14, both legs x and y are equal and their lengths can be found by dividing the hypotenuse by √2, which results in lengths of √14 for each leg.
Explanation:
In a 45-45-90 triangle, also known as an isosceles right triangle, the legs are of equal length and the hypotenuse is √2 times the length of one leg. If the hypotenuse is given as 2√14, we can use the fact that the hypotenuse is √2 times the length of a leg to find the length of the legs x and y.
Let x represent the length of one leg and y represent the length of the other leg. Since the triangle's legs are equal in this special triangle, x = y. The relationship between the legs and the hypotenuse in a 45-45-90 triangle can be expressed using the Pythagorean Theorem:
x² + y² = hypotenuse²
Solving for x and y, we get:
x = y = hypotenuse/√2 = (2√14)/√2 = √14
Therefore, in a 45-45-90 triangle with a hypotenuse of 2√14, both x and y, which are the lengths of the legs, are √14.
Round the following
numbers to the nearest 100.
817 →
368 →
1,4 51 →
Answer:
817 ---- 800
368 ---- 400
1,451 ---- 1500
Solve the system of linear equations by substitution.
3x−2y=15
y=2x−11
The solution set is (7,3).
Step-by-step explanation:
Given system of equations is;
3x−2y=15 Eqn 1
y=2x−11 Eqn 2
Substituting value of y from Eqn 2 in Eqn 1
[tex]3x-2(2x-11)=15\\3x-4x+22=15\\-x+22-15=0\\7=x\\x=7[/tex]
Putting x=7 in Eqn 2
[tex]y=2(7)-11\\y=14-11\\y=3[/tex]
The solution set is (7,3).
Keywords: linear equation, substitution method
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what would a line look like if the equation is y=2
Which equation can be solved by using this system of equations?
[y= 3x2 - 7x2 + 5
Ly = 7x4 + 2x
Question:
Which equation can be solved by using this system of equations?
y = 3x^3 - 7x^2 + 5
y = 7x^4 + 2x
A.) 3x^3 - 7x^2 +5 = 0
B.) 3x^3 - 7x^2 + 5 = 7x^4 +2x
C.) 7x^4 +2x = 0
D.) 7x^4 +3x^3 -7x^2 +2x + 5 = 0
Answer:
Option B: [tex]3x^{3} -7x^{2} +5=7x^{4} +2x[/tex] is used to solve this system of equations.
Explanation:
The two equations are [tex]y=$3 x^{3}-7 x^{2}+5$[/tex] and [tex]y=$7 x^{4}+2 x$[/tex]
Using substitution method, let us substitute [tex]y=$7 x^{4}+2 x$[/tex] in the equation [tex]y=$3 x^{3}-7 x^{2}+5$[/tex], we get,
[tex]3x^{3} -7x^{2} +5=7x^{4} +2x[/tex]
Thus, [tex]3x^{3} -7x^{2} +5=7x^{4} +2x[/tex] is used to solve this system of equations.
Hence, Option B is the correct answer.
Answer:
Answer is B. 3x^3-7x^2+5 = 7x^4+2x
Step-by-step explanation:
got it right!
hope this helps
The sum of two numbers is 39. The smaller number is 11 less than the larger number. What are the numbers
Answer:
14 and 25
Step-by-step explanation:
x = smaller number
y = larger number
x + y = 39
x = y - 11
now we sub
y - 11 + y = 39
2y - 11 = 39
2y = 39 + 11
2y = 50
y = 50/2
y = 25 <=== larger number
x = y - 11
x = 25 - 11
x = 14 <==== smaller number
The problem can be solved by setting up and solving two algebraic equations. The two numbers in question are 25 and 14.
Explanation:The subject of this problem is algebra. To solve it, we can set up two equations based on the problem's statements, and then solve those equations.
First, we know that the sum of two numbers is 39, so we can write that as: x + y = 39 (Equation 1).
Second, we know that the smaller number is 11 less than the larger number. Assuming x is the larger number and y is the smaller one, we can write this as: y = x - 11 (Equation 2).
To solve these equations in parallel, insert Equation 2 into Equation 1, that results in: x + (x - 11) = 39. Solving this equation simplifies to 2x = 50, so x = 25. Substitute x = 25 in Equation 2, we get: y = 25 - 11 = 14. So, the two numbers are 25 and 14.
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Combine 2d + 5d
Answer please ?
Answer:
7D
Step-by-step explanation:
2D + 5D
Add the figures
What is the area of this figure?
Enter your answer in the box.
m²
Area of the figure is 532 m².
Solution:
In the given image the shape is splitted into 2 shapes.
First shape is the square.
In square 4 sides are equal.
Area of the square = side × side
= 18 m × 18 m
Area of the square = 324 m²
Second shape is the triangle in the bottom.
Base of the triangle = 18 m + 8 m = 26 m
Height of the triangle = 16 m
Area of the triangle = [tex]\frac{1}{2}\times{\text{base}}\times{\text{height}}[/tex]
[tex]$=\frac{1}{2}\times16\times26[/tex]
Area of the triangle = 208 m²
Area of the given shape = area of the square + area of the triangle
= 324 m² + 208 m²
Area of the given shape = 532 m²
Hence area of the figure is 532 m².
Answer: 532 is answer
Hope u get a good grade
A small jar of salsa contains 12 1/2 ounces. A large jar of salsa contains 75 ounces. How many small jars of salsa equal the same number of ounces as 1 large jar of salsa?
We can start off by making 12 1/2 to an improper fraction:
12 1/2 = 25/2
Divide the large jar of salsa by the small jar of salsa: 75 / 25/2.
Reciprocal of second and turn divide to multiply:
75 * 2/25.
150/25 = 6.
So 6 jars of small salsa = 1 large jar of salsa.
What is 5 divided by 25
Answer:
0.2
Step-by-step explanation:
Answer: .2
Step-by-step explanation:
If the question was 25 divided by 5 it'll be 5 but because it's 5 divided by 25 the answer came out as a deciamal.
.2 can also mean it is 2/10 or maybe 20%