The solution to the equation x² + 24 = 0 over the complex numbers is x = ±2√(6)i. After isolating x² on one side, we take the square root of both sides and introduce the imaginary unit i because the number under the square root is negative.
Explanation:To solve the equation x² + 24 = 0 over the complex numbers, we need to find values of x that satisfy the equation. This is a quadratic equation with 'a' as 1 (the coefficient of x²), 'b' as 0 (since there is no x term), and 'c' as 24.
We will first isolate x² by subtracting 24 from both sides of the equation:
x² = -24
Next, to find x, we take the square root of both sides. Remember that when we take the square root of a negative number, we get an imaginary number. The square root of -24 can be expressed as:
x = ±√(-24)
This simplifies to:
x = ±√(24) × ±i
Since √(24) is √(4 × 6), which simplifies to 2√(6), the final solution in terms of complex numbers is:
x = ±2√(6)i
Evaluate
12x−3y
12x−3y
when
x=−
1
4
x=−14
and
y=3
y=3
.
12x - 3y
Put the values of x = -14 and y = 3 to the expression:
12(-14) - 3(3) = -168 - 9 = -177
I'd really appreciate it if anyone could help! :)
Which graph represents a function?
The graphs will be below the question.
C (third graph, the parabola); To find if it is a function or not draw a vertical line on the graph. If the vertical line could never intercept the figure more than once anywhere on the graph then it is a function.
From left to right of the pictures it's the 3rd photo. It's the 3rd photo because it passes the vertical line test witch means if a vertical line was drawn within the middle of the graph it would only pass through one line and not two. The other ones would pass through two lines instead of one. I hope this helped you!
Yolanda spends 8 1/2 hour per month playing soccer how many hrs does she play in a year
A rectangle has perimeter 78 cm and length 34 cm. What is its? width?
The perimeter of a rectangle is twice the sum of the dimensions:
[tex] 2p = 2(w+l) [/tex]
We know two of the three unkowns, so we can solve for w:
[tex] 78 = 2(w+34) \iff 78 = 2w+68 \iff 10=2w \iff w=5 [/tex]
Solve the following multiplication problems.
a. 9 kg 3 hg 1 cg × 9 =
b. 11 dg 4 cg × 12 =
c. 10 g 5 dg × 6 =
d. 5 g 3 dg 4 cg × 8 =
help...
Answer:
Step-by-step explanation:
We convert into decimals and then multiply
Otherwise we can convert everything into one unit and then multiply.
10 hg = 1 kg and 100x1000 cg = 1kg
Using this
a. 9 kg 3 hg 1 cg × 9 = 9.300001x9=83.700009 kg
b. 11 dg 4 cg × 12 = 11.400004x12 =16.8000048kg
c. 10 g 5 dg × 6 = 10.5x6 =63.0 kg
d. 5 g 3 dg 4 cg × 8 =5.300004x8 = 42.400032
HELP PLEASE PLEASE PLEASE
Enter a recursive rule for the geometric sequence.
2, 6, 18, 54, …
a1= ; an=
Answer:
Step-by-step explanation:
Given a geometric sequence.
2, 6, 18, 54, …
We have to find the I and nth term.
A geometric sequence. is one where each term is multiplied by a constant value to get the next term.
In our sequence, we find the pattern as each term is multiplied by 3 to get successive terms.
Hence common ratio r = 3
First term = a = 2
For Geometric sequence nth term = a_n = ar^(n-1)
Hence we get a_1 = 2
and a_n = 2(3)^(n-1)
By substituting for n any natural number we can get that term.
A taxi service charges $1.00 for the first 1/10 mile then $0.10 for each additional 1/10 mile after that.
Answer:
y = 1.00+0.10 x
Step-by-step explanation:
Given that a taxi has a minimum charge of 1 dollar upto 1/10 mile and adds 0.10 for every additional 1/10 mile.
If a person travels <=1/10 miles his charges are 1 dollar
If he travels >1/10 miles charges are 1 dollar +0.10(extra miles 1/10)
Let y be the charges and x be the no of 1/10 miles.
Then the equation for y in terms of x would be
y =1.00 +1/10(x)
y = 1.00+0.10 x
I am F years old and my brother is B years older.What is the sum of our ages?
If you are F years old and your brother is B years older, then your brother is F+B years old. Add your age (F) and your brother's age (F+B) and you get F+(F+B) = 2F+B
The sum of your ages is 2F+B
where F and B are placeholders for numbers.
Which is the correct equation for the following graph?
A.) Y = 3x – 5
B.) Y = -3x + 5
C.) Y = 1/3x – 5
D.) Y = 3x + 5
Twelve skateboards have 48 wheels. What is the value of the ratio of skateboards to wheels, in simplest form?
ratio = 12 : 48 = 1 : 4 = [tex]\frac{1}{4}[/tex] as a fraction in simplest form
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!
Find the value of i77.
A) 1
B) i
C) −1
D) −i
[tex]i^{77}=i^{4\cdot19+1}=(i^4)^{19}\cdot i^1=1^{19}\cdot i= i[/tex]
i^77 = (i^4)^19 * i
= 1^19 * i
= 1 * i
= i
Answer is i
A conjecture and the paragraph proof used to prove the conjecture are shown.
Given: E is the midpoint of segment D F. Prove: 2 D E equals D F. A segment DF is horizontal with endpoints D and F. E is the midpoint of the segment.
Drag an expression or statement to each box to complete the proof.
Answer:
1. DF (option 3)
2. segment addition postulate
3. segment congruence postulate
4. DF (option 5)
Answer with explanation:
Given: E is the mid point of DF.
Prove: 2 DE=D F
Proof with explanation:
It is given that [tex]\Bar{DE}[/tex] is mid point of [tex]\Bar{DF}[/tex].
1.→
So, [tex]\Bar{DE}\cong\Bar{DF}[/tex]
-------------------------By Definition of mid point
2.→ DE=E F----------------Segment Congruence Postulate
3.→DE+E F=D F ----------------Segment Addition Postulate
4.→DE+DE=D F-------------By Substitution
5.→Simplifying gives
2 DE=D F
Mrs. Carson pays kristin $48 for babysitting 6 hours, and mr. Vasquez pats her $67.50 for babysitting 9 hours. Who pays kristin the better salary? Explain your answer.
Find the greatest common factor of 14w^3 and 15w^4
What are the domain and range of the function below?
Answer:
Domain is the set of all real numbers
Range is the set of all real numbers.
Step-by-step explanation:
Given a graph with curve which has y intercept -5, and x intercept 5.
The graph is continuous at all points of x and y
We find that the graph is a straight line with positive slope of the form
x/5 +y/-5=1
Or x-y =5
The graph is defined for all values of x and y.
The domain is the set of values x can take
In the graph horizontal axis is x axis.
Hence from the graph we see that x can take values from -infinity to + infinity
Hence domain is x = R
For range, we consider the values of y as per graph.
WE find that y is taking values in the interval (-infinity, infinity)
Hence Range =R
The term 'domain' in mathematics refers to the complete set of possible values of the independent variable in a function. The 'range' on the other hand, represents the possible results of the function after an experiment or survey. These values are not always numerical but could be a set of words or phrases.
Explanation:The domain of a function is the complete set of possible values of the independent variable. In the context of your question, it can be a list such as X = {English, Mathematics,...} representing all the majors offered at a university, or it can be a numerical set, for example Y = {0, 1, 2,...} representing the integers from zero up to the upper limit of classes. Even functions like Z where the domain includes any amount of money from zero upwards can exist.
Similarly, the range of a function is the set of all possible values that the function can take after the experiment is performed or the question is answered. For instance, if a function has a domain of hair color, its range would be the different hair colors like black, blond, gray, green, orange, etc. This shows that the domain and range of a function are not necessarily numerical.
The specific value x the function takes only becomes known after performing the experiment or survey. However, there might be certain values that are outside the domain of the function and as such, would not give a reliable prediction, just like 90 in the dataset from 65 to 75. Such an occurrence doesn't fall within the domain of the function and can't be accurately predicted.
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Does This. Graph Represent A Function? Why Or Why Not?
Answer: D. Yes because it passes the vertical line test.
Step-by-step explanation
A function cannot have duplicate x-coordinates.
When given a table or a set of coordinates, if there is an x-coordinate that is paired with two different y-coordinates then it is not a function.
When given a graph, the simplest way to determine if it is a function is to use the vertical line test. If you can draw a vertical line anywhere through the graph and it passes through two points, then it is not a function.
In the given graph, it passes the vertical line test so it IS a function.
6. Which type of angle pair are LSM and OSN?
A. Adjacent angles
B. Linear pair
C. Complementary angles
D. Vertical angles
7. Which of the following statements are false?
A. LSM and MSN are adjacent angles
B. LSM and MSN form a linear pair of angles
C. LSM and MSN are vertical angles
D. M
8. Which angle is supplementary to LSM?
A. OSN
B. SLM
C. LMS
D. MSN
6. These angles are vertical angles, so D. is the correct answer!
7. These angles are not vertical angles, although I don't know what D. is....
8. D) MSN is the correct answer
Lands mother gave her and her two sisters $21 to spend at the movies.If each girl gets the same amount, how munch do they each spend?
How to say 12079 two different ways using hundred, tens, and ones
The number 12079 could be said two ways in terms of hundreds, tens, and ones. It can be 'twelve thousand, seventy-nine' or 'one hundred and twenty hundred, seven tens and nine ones'
Explanation:The number 12079 can be said in two different ways using hundred, tens and ones. First, you could say it as 'twelve thousand, seventy-nine.' This is because 12 is the thousands component (consisting of hundreds and thousands), and 79 is the ones and tens components. Secondly, you could say it as 'one hundred and twenty hundred, seven tens and nine ones'
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Which of the following is the minimum value of the equation y = 2x^2 + 5?
A) 0
B) 5
C) 2
D) -5
The number 5.003 × 10 -5 written in standard form is _____.
Which of the following is the correct expansion of (x + 5)(x + 3)?
A.x2 + 15x + 8
B.x2 + 8x + 15
C.x2 + 5x + 8
D.x2 + 3x + 5
The answer would be B. x^2+8x+15
(4x^4+34x^3+44x^2+11x-27)/(x+7) dividing polynomials
ANSWER
[tex]\frac{4x^4+34x^3+44x^2+11x-27}{x+7}=4x^3+6x^2+2x-3- \frac{6}{x+7}[/tex]
EXPLANATION
See graph in attachment.
Answer
4x³+6x²+2x-3 remainder -6
Explanation
Find the attached file.
The product of three integers is -3. What is all of the possible values for the three factors?
WILL GIVE FIRST ANSWER BRAINLIEST
Use the substitution method to solve the system of equations. 3x + 7y = 1 y = x – 7
A. (3, –4)
B. (4, –3)
C. (2, –5)
D. (5, –2)
Answer: The correct option is (D) (5, -2).
Step-by-step explanation: We are given to use the method of substitution to solve the following system of equations :
[tex]3x+7y=1~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\y=x-7~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
Substituting the value of y from equation (ii) in equation (i), we get
[tex]3x+7y=1\\\\\Rightarrow 3x+7(x-7)=1\\\\\Rightarrow 3x+7x-49=1\\\\\Rightarrow 10x=50\\\\\Rightarrow x=\dfrac{50}{10}\\\\\Rightarrow x=5,[/tex]
and from equation (ii) again, we get
[tex]y=x-7=5-7=-2.[/tex]
Thus, the required solution is (x, y) = (5, -2).
Option (D) is CORRECT.
Henry can write 5 pages of his novel in 3 hours. At this rate how many pages can Henry write in 8 hours? Please help!
Divide 5 pages by 3 hours to fins how many pages he wrote in 1 hour:
5 pages / 3 hours = 1 2/3 pages per hour.
Multiply 1 2/3 pages per hour by total hours to find total pages.:
1 2/3 x 8 = 13 1/3 pages (13.33)
You earn $9.20 per hour at your summer job. Write and solve an inequality that represents the number of hours you need to work in order to buy a smartphone that cost $299.
What is the slope of the line shown below?
Aurora has a cell phone plan that charges
$65
for phone service plus
$12
for each gigabyte of data used each month. If her bill for September is
$113,
how many gigabytes of data did she use in September?
Aurora used 4 gigabytes of data in September.
Explanation:To determine how many gigabytes of data Aurora used in September, we need to subtract the fixed phone service charge from her total bill. The difference will represent the additional charges for the data usage. Let's say she used x gigabytes. The equation for her bill can be written as: 65 + 12x = 113. To solve for x, we can subtract 65 from both sides and then divide both sides by 12 to isolate x. Solving this equation, we find that x = 4. So, Aurora used 4 gigabytes of data in September.
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Number 4. List all possible rational zeros of g(x)=2x^3 -6x^2 +x-9
Correct answer will get brainliest
The complete solution is in image attached.