Answer:
Step-by-step explanation:
x-117+120
x+3
Simplify : a) [tex]\sqrt{x} 0.49x^1^8[/tex] when x<0
Simplify : b) [tex]15\sqrt{x} 0.16c^1^2[/tex] x can be anything
(a) The simplified expression is [tex]\[-0.49 \cdot |x|^{18.5} \cdot i\][/tex]. (b) The simplified expression remains [tex]\[15\sqrt{x} + 0.16c^{12}\][/tex].
Let's simplify the given expressions step-by-step.
a) Simplify [tex]\(\sqrt{x} \cdot 0.49x^{18}\) for \(x < 0\)[/tex]
Since [tex]\(x < 0\), \(x\)[/tex] is negative. This affects the interpretation of [tex]\(\sqrt{x}\)[/tex] in the real numbers because the square root of a negative number is not real. However, if we consider complex numbers, we need to include the imaginary unit [tex]\(i\).[/tex]
Given:
[tex]\[\sqrt{x} \cdot 0.49x^{18}\][/tex]
First, let's express [tex]\(\sqrt{x}\)[/tex] in terms of the imaginary unit:
[tex]\[\sqrt{x} = \sqrt{|x|} \cdot i\][/tex]
Next, rewrite \(x^{18}\):
[tex]\[x^{18} = (x^2)^9 \\= |x|^{18} \cdot (-1)^9 \\= -|x|^{18}\][/tex]
Thus, the expression becomes:
[tex]\[\sqrt{|x|} \cdot i \cdot 0.49 \cdot -|x|^{18}\][/tex]
Simplify the coefficients and combine terms:
[tex]\[0.49 \cdot -1 = -0.49\\\sqrt{|x|} \cdot |x|^{18} = |x|^{\frac{1}{2}} \cdot |x|^{18} = |x|^{18.5}\][/tex]
Therefore, the simplified expression is:
[tex]\[-0.49 \cdot |x|^{18.5} \cdot i\][/tex]
b) Simplify [tex]\(15\sqrt{x} + 0.16c^{12}\)[/tex]
Here, [tex]\(x\) and \(c\)[/tex] can be anything.
Given:
[tex]\[15\sqrt{x} + 0.16c^{12}\][/tex]
There are no common factors to combine these terms, so the expression is already simplified. The terms involve different variables and exponents, and cannot be further simplified together.
So the simplified expression remains [tex]\[15\sqrt{x} + 0.16c^{12}\][/tex]
a) The simplified expression is [tex]\[-0.49 \cdot |x|^{18.5} \cdot i\].[/tex]
b) The expression remains as usual given in the question:
[tex]\[15\sqrt{x} + 0.16c^{12}\][/tex]
Pls help me with this!
Step-by-step explanation:
5-in 5-in five interest answer
Write the Contrapositive of the statement Below.⬇
If you have, 400$, then you can afford a new laptop computer.
Answer:
If you can't afford a new laptop computer, then you haven't got 400$.
Step-by-step explanation:
The contrapositive is:
If A implies B then not B implies not A.
Molly is saving money to buy a new bike that costs $189. He has save $99 so far. He plans on saving $10 each week. Write and solve an equations to determine after how many weeks Molly will have enough money to buy the bike.
Answer: Molly will have to save $10 each week for 9 weeks to get $189.
Step-by-step explanation:
Start at $99, count $10 every week until you get $189. Your answer is 9 weeks.
In a certain school 75% of the students in first year chemistry have had algebra if there are 300 students in first year chemistry how many of them have had algebra?
Answer:
225
Step-by-step explanation:
Total number of students =300
75% have had algebra
Number of students that have had algebra will be
= 75%/100% x 300
= 0.75 x 300
= 225
So, 225 of the 300 students have had algebra
Answer:225 students
There are 2 simple ways to get the answer.
A bag contains five white balls and five black balls. Your goal is to draw two black balls.
a) You draw two balls at random. What is the probability that they are both black?
b) You draw two balls at random. Once you have drawn two balls, you put back any white balls, and redraw so that you again have two drawn balls. What is the probability that you now have two black balls? (Include the probability that you chose two black balls on the first draw.)
The probability of drawing two black balls from a bag containing 5 white and 5 black balls is 2/9 (approximately 0.22) if you do not replace balls after drawing them, and 1 if you replace any white balls that are drawn.
Explanation:This question relates to the concept of probability in mathematics. The total number of balls in your bag is 10 (5 white balls and 5 black balls). If you want to draw two black balls, the probability will change based on the conditions of the question.
a) For the first draw, there are 5 black balls out of a total of 10 balls, so the probability is 5/10 or 0.5. If a black ball is drawn in the first draw, there are now 9 total balls and 4 of them are black, so the probability for the second black ball is 4/9. For both balls to be black, multiply the individual probabilities: (5/10) * (4/9) = 20/90 = 2/9 approximately equal to 0.22.
b) If you draw two balls and put back any white balls, then redraw until you have two balls, you are essentially ensuring that white balls are not counted. In this case, every draw will either be a black ball or a redraw with a white ball, so the probability is essentially 1 that you will eventually draw a black ball. Therefore, the probability of drawing two black balls using this method is (1/1) * (1/1) = 1.
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Can anyone help with my math problems because I need help and you need to be quick. I will mark brainliest.
If m (x) = StartFraction x + 5 Over x minus 1 EndFraction and n(x) = x – 3, which function has the same domain as (m circle n) (x)?
Question:
If m (x) = StartFraction x + 5 Over x minus 1 EndFraction and n(x) = x – 3, which function has the same domain as (m circle n) (x)?
h (x) = StartFraction x + 5 Over 11 EndFraction
h (x) = StartFraction 11 Over x minus 1 EndFraction
h (x) = StartFraction 11 Over x minus 4 EndFraction
h (x) = StartFraction 11 Over x minus 3 EndFraction
Answer:
Option C: [tex]h(x)=\frac{11}{x-4}[/tex] has the same domain as [tex]$(m \circ n)(x)$[/tex]
Explanation:
It is given that [tex]m(x)=\frac{x+5}{x-1}[/tex] and [tex]n(x)=x-3[/tex]
Let us find the domain of [tex]$(m \circ n)(x)$[/tex]
[tex]$\begin{aligned}(m \circ n)(x) &=m(n(x))\\&=m(x-3) \\ &=\frac{(x-3)+5}{(x-3)-1} \\ &=\frac{x+2}{x-4} \end{aligned}$[/tex]
Now, let us equate the denominator equal to zero to determine the domain.
[tex]$x-4=0$[/tex]
[tex]x=4[/tex]
Thus, the function becomes undefined at the point [tex]x=4[/tex]
Hence, the domain of [tex]$(m \circ n)(x)$[/tex] is [tex]$(-\infty, 4) \cup(4, \infty)$[/tex]
Now, we shall find the function which has the same domain as [tex]$(m \circ n)(x)$[/tex]
Option A: [tex]h(x)=\frac{x+5}{11}[/tex]
The function h(x) has the domain of set of all real numbers [tex]$-\infty<x<\infty$[/tex]
Thus, the interval [tex](-\infty,\infty)[/tex] is not the same domain as [tex]$(-\infty, 4) \cup(4, \infty)$[/tex]
Hence, Option A is not the correct answer.
Option B: [tex]h(x)=\frac{11}{x-1}[/tex]
Equating the denominator equal to zero, the function becomes undefined at the point [tex]x=1[/tex]
Thus, the function h(x) has the domain of [tex]$(-\infty,-1) \cup(-1, \infty)$[/tex] is not the same domain as [tex]$(-\infty, 4) \cup(4, \infty)$[/tex]
Hence, Option B is not the correct answer.
Option C: [tex]h(x)=\frac{11}{x-4}[/tex]
Equating the denominator equal to zero, the function becomes undefined at the point [tex]x=4[/tex]
Thus, the function h(x) has the domain of [tex]$(-\infty, 4) \cup(4, \infty)$[/tex] is the same domain as [tex]$(-\infty, 4) \cup(4, \infty)$[/tex]
Hence, Option C is the correct answer.
Option D: [tex]h(x)=\frac{11}{x-3}[/tex]
Equating the denominator equal to zero, the function becomes undefined at the point [tex]x=3[/tex]
Thus, the function h(x) has the domain of [tex]$(-\infty,3) \cup(3, \infty)$[/tex] is not the same domain as [tex]$(-\infty, 4) \cup(4, \infty)$[/tex]
Hence, Option D is not the correct answer.
Answer:
It’s C
Step-by-step explanation:
(Easy) help please **attachment**
Answer:
Step-by-step explanation:
Supplementary: ADC
Complementary: AC
Adjacent: ABC
Hope this helps.
If f(1) = 7 and f(n) = f(n − 1) – 4 then find the value of f(6).
Answer:
- 13
Step-by-step explanation:
f(1) = 7
f(n) = f(n − 1) – 4
f(₂) = f(1) – 4 = 7 - 4 = 3
f(₃) = f(₂) – 4 = 3 - 4 = -1
f(₄) = f(3) – 4 = (-1) - 4 = - 5
f(₅) = f(₄) – 4 = (- 5) - 4 = - 9
f(₆) = f(₅) – 4 = (- 9) - 4 = - 13
The value of f(6) is -13, calculated based on the provided recursive formula where each term is four less than the previous.
Explanation:We are given that f(1) = 7, and the recursive equation for n is f(n) = f(n − 1) – 4. Since the equation shows that each next term is four less than the previous one, we can calculate the following iterations:
f(2) = f(2-1) - 4 = f(1) - 4 = 7 - 4 = 3f(3) = f(3-1) - 4 = f(2) - 4 = 3 - 4 = -1f(4) = f(4-1) - 4 = f(3) - 4 = -1 - 4 = -5f(5) = f(5-1) - 4 = f(4) - 4 = -5 - 4 = -9f(6) = f(6-1) - 4 = f(5) - 4 = -9 - 4 = -13So, the value of f(6) is -13.
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cos^2x+sin^2x/cot^2x-csc^2x
[tex]\frac{cos^2x + sin^2x}{cot^2x - cosec^2x} = -1[/tex]
Solution:
Given trignometric expression is:
[tex]\frac{cos^2x + sin^2x}{cot^2x - cosec^2x}[/tex]
We have to evaluate the above expression
Let us use the trignometric identities
[tex]sin^2x + cos^2x = 1[/tex]
Also, use another trignometric identitiy
[tex]1 + cot^2x = cosec^2x[/tex]
Therefore, upon rearranging we get,
[tex]cot^2 x -cosec^x = -1[/tex]
Apply these two identities in given expression
[tex]\frac{cos^2x + sin^2x}{cot^2x - cosec^2x} = \frac{1}{-1}\\\\\frac{cos^2x + sin^2x}{cot^2x - cosec^2x} = -1[/tex]
Thus value of given expression is -1
Please answerrrr I need it desperately and please EXPLAIN how.!!
Answer:
B
Step-by-step explanation:
The opposite of negative one half is the one half and the opposite of 5/2 is -5/2, or -2.5
Check the picture below.
YOU PROBABLY CAN'T ANSWER THIS :/
Using the exponential function 2x + 3, what is the average rate of change between the values 1 ≤ x ≤ 5?
explain your answer step by step
Rate of change of the function: 60
Step-by-step explanation:
The exponential function in this problem is
[tex]f(x)=2^{x+3}[/tex]
The rate of change of a function between a certain interval [tex]x_1 \leq x \leq x_2[/tex] is given by
[tex]r=\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]
where
[tex]f(x_1)[/tex] is the value of the function calculated in [tex]x_1[/tex]
[tex]f(x_2)[/tex] is the value of the function calculated in [tex]x_2[/tex]
In this problem, the interval is
[tex]1\leq x \leq 5[/tex]
So we have:
[tex]f(x_1)=f(1)=2^{1+3}=2^4=16[/tex]
and
[tex]f(x_2)=f(5)=2^{5+3}=256[/tex]
Therefore, the rate of change is:
[tex]r=\frac{256-16}{5-1}=60[/tex]
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If 3/7 of Z is 42, what is 5/7 of Z?
Answer:
x = 70
Step-by-step explanation:
First to make the equation easy, divide 42 by 3 to get what 1/7 of Z equals.
42 / 3 = 14
Now to get 5/7 of Z, just multiply 14 by 5.
14 x 5 = 70
x = 70
Hope this helped.
Answer:
70
Step-by-step explanation:
convert the decimal & solve for Z.
(3/7)Z = 42
(0.4286)Z = 42
Z = 98
Now,
(5/7)Z = ?
putting the value of Z
(0.714) (98) = 70
On the distant plant, Mathology, a sports area covers 7400 yodels2. How many square deckles would this be if 1 deckle = 75.9 yodels?
Answer:
It would be 97.50 square deckles.
Step-by-step explanation:
Given:
On the distant plant, Mathology, a sports area covers 7400 yodels².
1 deckle = 75.9 yodels.
Now, to get the square deckles.
As given, 1 deckle = 75.9 yodels.
So, to get the square deckles by using conversion factor:
75.9 yodels = 1 deckle.
7400 yodels² = [tex]7400\div 75.9[/tex]
= [tex]97.50\ deckels ^2.[/tex]
Therefore, it would be 97.50 square deckles.
The area is approximately 1.286 deckles².
To convert the area from square yodels to square deckles, we need to use the given conversion factor: 1 deckle = 75.9 yodels.
First, we'll find out how many yodels one square deckle is by squaring the conversion factor.
1. Calculate the area of one square deckle in yodels: (75.9 yodels)² = 5752.81 yodels².
2. Convert the given area of the sports area from yodels² to deckles²: 7400 yodels² ÷ 5752.81 yodels²/deckle² ≈ 1.286 deckles².
Therefore, the sports area covering 7400 yodels² is approximately 1.286 square deckles.
Write 5/10 in 3 equivalent forms
Answer:
0.5 50/100 0.50
Step-by-step explanation:
Totsakan's school is selling tickets to a spring musical. On the first day of ticket sales the school sold 1 adult tickets and 8 child tickets for a total of $117. The school took in $182 on the second day by selling 6 adult tickets and 8 child tickets. Find the price of an adult ticket and the price of a child ticket.
Answer:
Each ticket cost $13
Step-by-step explanation:
Day 1-- 1 adult and 8 child ticket= Total of 9 tickets = $117
Day 2--6 adult and 8 child ticket= Total of 14 = $182
Brainliest please :)
A graduated cylinder is filled with 36 cm 3 of liquid the liquid is poured into a different cylinder that has a radius of 3cm , what will the height of the liquid be in the new cylinder ?
The height of the liquid in the new cylinder is about 1.72 cm
Step-by-step explanation:
The formula of the volume of a cylinder is V = πr²h, where
r is the radius of the base of the cylinderh is the height of the cylinder∵ The volume of the liquid = 36 cm³
∵ The liquid is poured into another cylinder with radius 3 cm
∵ The radius of the base = 3 cm
- To find the height of the liquid in the new cylinder equate the rule
of the volume by 36
∵ V = πr²h
∴ π(3)²h = 36
∴ 9πh = 36
- Divide both sides by 9π
∴ h = 1.273239545
The height of the liquid in the new cylinder is about 1.72 cm
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Simplify this algebraic expression completely.
5y- 3(y + 2)
Distributive property: 5y-3y-6
Combine like terms: 2y-6
So there's your answer
To simplify the given expression, distribute the -3 to both terms inside the parentheses, then combine like terms.
Explanation:To simplify the expression 5y - 3(y + 2), we need to follow the order of operations, which is parentheses first, then multiplication and division, and finally addition and subtraction.
First, distribute the -3 to both terms inside the parentheses:
5y - 3 * y - 3 * 2
Now, simplify each term:
5y - 3y - 6
Combine like terms:
2y - 6
This is the simplified form of the given expression.
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5x
4x - 8
Find the value of x.
68 + x
x= 30°
x = 10.4°
x = 12°
x = 24°
Answer:
x = 12
Step-by-step explanation:
Will make brainliest if answered correctly
Answer: Yes it is
Step-by-step explanation: In mathematics, a function is a relation between sets that associates to every element of a first set exactly one element of the second set
Answer:
yes
hope this helps
9. What is the area of the largest square?
A=2
A=36units2
A=64units2
Answer:
If you mean Area=2 and Area=36units times 2 and Area=64units times 2, then the answer is that A = 64units times 2 would be the largest square.
Step-by-step explanation:
The larger the area, the larger the square. The first square has an area of 2. The second square has an area of 72, and the third square has an area of 128, so the third square is the biggest.
Solve the equation 11x + 7 = 73?
Answer:
6
Step-by-step explanation:
ZX is the perpendicular bisector of wY, and YZ = 13.75. Find wz.
The required values are WZ = 13.75 and YZ = 27.
What is a perpendicular bisector?A perpendicular bisector is defined as a line that divides an angle into two equal angles. Draw the given angle first, then cut it in half, and then draw the angle's bisector.
As per question 1,
We have been given that ZX is the perpendicular bisector of WY
YZ = 13.75
13.75 + 13.75 = 27.5
27.5 / 2 = 13.75
WZ = 13.75
As per question 2,
We have been given that ZX is the perpendicular bisector of WY
WZ = 4n - 13 and YZ = n + 17
To find YZ
According to the property of the perpendicular bisector,
WZ = YZ
4n - 13 = n + 17
4n - n = 17 + 13
3n = 30
n = 30/3
n = 10
Substitute the value of n = 10 in YZ = n + 17
So, YZ = 10 + 17 = 27
Thus, the required values are WZ = 13.75 and YZ = 27.
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List the next four multiples of the fraction 3/5
Answer:
6/10,9/15,12/20,15/25
Step-by-step explanation:
Find the area of the shape shown below.
Answer:
936
Step-by-step explanation:
1 x 12 x 13 x 6= 936
Here is some evidence
Answer:36
Step-by-step explanation: L•w/2 = A for triangular
Which of the following numbers is irrational?
Select all that apply.
2.3
n
8/9
1.5
Answer:
N
Step-by-step explanation:
a rectangle has a perimeter of 204 feet. Its length is six feet longer that twice its width. find the dimensions
Answer:
The length of the rectangle is 70 cm
The width of the rectangle is 32 cm
Step-by-step explanation:
Given:
perimeter of the rectangle = 204 feet
Its length is six feet longer that twice its width
To Find:
The dimensions of the rectangle = ?
Solution:
Let the width of the rectangle be x
Then its length is six feet longer that twice its width.
That is length = 6 + 2x
Now we know that the perimeter of the rectangle is
perimeter = 2(length + width)
204 = 2(6+2x+x)
204 = 2(6+3x)
204 = 12 +6x
204 - 12 = 6x
192 = 6x
x =[tex]\frac{192}{6}[/tex]
x = 32
Thus the width is 32 cm
Its length is
=6 + 2x
=6 + 2(32)
=6 + 64
= 70 cm
ida goes to the store to buy groceries. To pay for the groceries, she slides the card through a card reader and puts in a special code. Which payment method is this?
Answer:
Credit Card
Step-by-step explanation:
This is most likely a credit card.
You only need to put a special code in when you're inputting a credit cards pin number.
it is c my dudes yes hes yes
Choose the fraction that goes in the blank. 5/12< _____<3/4
Answer:
All of the following fractions work: 1/2, 7/12, 8/12. There are endless possibilities.
Please mark as Brainliest! :)
Answer:
6/12 ; 7/12 ; 8/12
Step-by-step explanation:
³⁾3/4 = 9/12
5/12 < 6/12 < 7/12 < 8/12 < 9/12