(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]
use the net to compute the surface area of three dimensional figure.
Option C:
Surface area of the three dimensional figure is 166 unit².
Solution:
Let us find the area of the net of the figure.
Length = 7, Width = 5, Height = 4
Area of the bottom = length × width
= 7 × 5
= 35 unit²
Area of the Top = length × width
= 7 × 5
= 35 unit²
Area of the left = width × height
= 5 × 4
= 20 unit²
Area of the right = width × height
= 5 × 4
= 20 unit²
Area of the front = length × height
= 7 × 4
= 28 unit²
Area of the back = length × height
= 7 × 4
= 28 unit²
Surface area = 35 + 35 + 20 + 20 + 28 + 28
= 166 unit²
Surface area of the three dimensional figure is 166 unit².
help me plz!!!!!!!!!!!!!!!
Answer: for the third one you use x= 55
so angle = 110
for the fourth one x= 102
angle = 100
Step-by-step explanation:
HELP! I put the formula but I don’t know the radius
Answer:
C. 8,624
Step-by-step explanation:
recall that the formula for circumference is
Circumference = 2πr ( = given as 85 meters)
hence,
85 = 2πr
r = 85/(2π)
given h = 15m
volume of cylinder
= πr²h
= π (85/2π)² 15 (using calculator and assuming π = 3.14)
= 8628.58
Comparing with the choices, the closest choice (within rounding error) is C. 8,624
2x + 3 for x = 3
evaluate each expression for the given value of x
Answer: 9
Step-by-step explanation:
2x + 3 when x = 3
2(3) + 3
2 * 3 = 6
6 + 3 = 9
To evaluate the mathematical expression 2x + 3 for x = 3, substitute x = 3 into the equation to get 2(3) + 3 = 6 + 3, and then add the numbers to get 9.
Explanation:
To evaluate the expression 2x + 3 for x = 3, you would replace x with 3 in the expression, then follow the order of operations (PEMDAS/BODMAS) to solve the expression.
Here is the step-by-step breakdown:
Substitute x = 3 into the expression, this makes the expression: 2(3) + 3 = 6 + 3 Then, you add the numbers together to get: 9
So, when x = 3, the value of the expression 2x + 3 is 9.
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Fully answer BOTH questions a and b below.
On a recent survey, 60% of those surveyed indicated that they preferred walking to running.
a. If 540 people preferred walking, how many people were surveyed?
b. How many people preferred running?
Answer:
a. Number of people surveyed were 900.
b. 360 people preferred running.
Step-by-step explanation:
Given:
On a recent survey, 60% of those surveyed indicated that they preferred walking to running.
If 540 people preferred walking.
Now, to find a. number of people were surveyed. b. number of people preferred running.
a.
Number of people preferred walking = 540.
Percentage of people preferred walking = 60%.
Let the total number of people surveyed be [tex]x.[/tex]
Now, to get the number of people surveyed:
60% of x = 540.
[tex]\frac{60}{100} \times x=540[/tex]
[tex]0.60\times x=540[/tex]
[tex]0.60x=540[/tex]
Dividing both sides by 0.60 we get:
[tex]x=900.[/tex]
Thus, number of people surveyed = 900.
b.
Total number of people surveyed = 900.
People preferred walking = 540.
Now, to get the people preferred running we subtract people preferred walking from total number of people surveyed:
[tex]900-540[/tex]
[tex]=360.[/tex]
Thus, people preferred running = 360.
Therefore, a. Number of people surveyed were 900.
b. 360 people preferred running.
Collin has $500 in his bank account. He starts saving $30.00 per week. Kamryn
has $750 in her bank account, and she is saving $20.00 per week. Assume
neither Collin nor Kamryn make any withdrawals.
After how many weeks will. Collin and Kamryn have the same amount of
money in their accounts?
Answer:
x = 25
Step-by-step explanation:
You would need to start by creating an equation. X would represent the numbers of weeks.
500 + 30x = 750 + 20x
Now get the numbers on one side. To do this subtract 500 form each side.
30x = 250 + 20x
Next, get the variables to one side. This can be done by subtracting 20x from each side.
10x = 250
Finally divide by 10 to get the variable by its self.
x = 25
Hope this helps.
After 25 weeks, Collin and Kamryn have the same amount of
money in their accounts.
What is linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
Let's suppose the after x weeks, Collin and Kamryn have the same amount of money in their accounts:
Then we can frame a linear equation as per the problem:
Collin's amount of money = 500 + 30x
Kamryn amount of money = 750 + 20x
500 + 30x = 750 + 20x
10x = 250
x = 25
Thus, after 25 weeks Collin and Kamryn have the same amount of
money in their accounts.
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Translate the sentence into an inequality.
The product of b and 6 is less than - 16.
The sentence 'The product of b and 6 is less than -16' translates to the inequality '6b < -16' in Mathematics.
Explanation:In mathematics, translating a sentence into an inequality involves identifying the mathematical symbols and operations represented by the words in the sentence. In this case, 'the product of b and 6' translates to '6 * b' and 'is less than' translates to '<'. So, the sentence 'The product of b and 6 is less than -16' translates to the inequality '6 * b < -16' or '6b < -16' in simplified form.
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solve y= 2/3x +7 and 3y= 2x -3
Answer:
The system has no solution
Step-by-step explanation:
we have
[tex]y=\frac{2}{3}x+7[/tex] ----> equation A
[tex]3y=2x-3[/tex]
Isolate the variable y
Divide by 3 both sides
[tex]y=\frac{2}{3}x-1[/tex] ------> equation B
Compare equation A and equation B
Both lines have the same slope and different y-intercept
so
Line A and Line B are parallel lines
The lines do not intersect
therefore
The system has no solution, because both lines are parallel
see the attached figure to better understand the problem
Marcos had 15 coins in nickels and quarters. He had 3 more quarters than nickels. He wrote a system of equations to represent this situation, letting x represent the number of nickels and y represent the number of quarters. What is the solution?
Answer:
Marcos had 6 nickel coins and 9 quarter coins.
Step-by-step explanation:
We are given the following in the question:
Let x be the number of nickel coins and y be the number of quarter coins.
Marcos had 15 coins in nickels and quarters.
Thus, we can write the equation:
[tex]x + y =15[/tex]
He had 3 more quarters than nickels. We can write he equation,
[tex]y = x + 3[/tex]
Solving the two equations, we get,
[tex]2y = 18\\y = 9\\x + 9 = 15\\x = 6[/tex]
Thus, Marcos had 6 nickel coins and 9 quarter coins.
The solution to the system of equations representing Marcos's coins is x = 6 and y = 9. Hence, Marcos had 6 nickels and 9 quarters.
Explanation:This question pertains to creating and solving a system of equations in mathematics. Given Marcos had 15 coins in nickels and quarters and considering the information that he had 3 more quarters than nickels, two equations can be formed from this. The first equation sets up the total number of coins: x + y = 15. The second equation sets ups the difference in quantity of each coin: y = x + 3.
To find the solution, substitute the second equation in for y in the first equation. This gives: x + (x + 3) = 15. Solve the equation and find x = 6. Furthermore, using x in our second equation, we get y = 6 + 3 = 9. Therefore, Marcos had 6 nickels and 9 quarters.
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what does x equal in the function: f(-11)=5x+1
Final answer:
In the equation f(-11)=5x+1, solving for x yields x = -2.4.
Explanation:
To find what x equals in the function f(-11)=5x+1, we start by understanding that the function f(x) identifies the relation between x and f(x). In this case, f(-11) has been given the value of 5x+1. Therefore, we solve for x by setting the expression equal to f(-11).
We have the equation 5x + 1 = f(-11). Since f(-11) is given as a constant, we substitute and solve for x:
5x = -12
x = -2.4
Hence, x equals -2.4 in the function f(-11)=5x+1.
HELP ASAP PLEASE HELP ME
Answer:
She is not correct
x = -9
Step-by-step explanation:
The sum of interior angles in a triangle is equal to 180° therefore if you add all three angles in this triangle it must add up to 180°
50 - 5x + 5 - 4x + 17 - 3x = 180 add/subtract the like terms
72 - 12x = 180
- 12x = 108 divide both sides by 12
-x = 9
x = -9
If a prison deceased by 372 prisoners each month over one year what the monthy decrease
Answer:
31 deaths per month
Step-by-step explanation:
12 months in a year
372 / 12 = 31
The sales tax rate is 8.25%. If Sheila bought a sweater for $35, a pair of jeans for $89, and a handbag for $55, find her total cost including the sates tax. Round your answer to the nearest cent.
Answer:185,422.61
Step-by-step explanation:8.25%/100=0.0825 but since it a sale tax you add a 1 so it would be 1.0825•35=37.88•89= 337.32•55=185,422.61
The measure of angle 1 is 30 degrees less than twice the measure of angle 2. What is the measure of angle 1. What is the measure of angle 2
Answer:
110°
Step-by-step explanation:
the supplement of an angle is 30 degrees less than twice the measure of the angle itself. find the angle and its supplement.
Let the angle be A, then its supplement = (180 - A)
Now, since the supplement is 30 degrees less than twice the measure of the angle itself, then we'll have:
180 - A = 2A - 30
-3A = - 210
A, or the angle = [tex]\frac{-210}{-3}[/tex]= 70 °
Its supplement, (180 - A) = 180 - 70 = 110°
Perform the following multiplication. 4.7314 × 10 = 47.314 0.47314 473.14 4,731.4
Answer:
47.314
Step-by-step explanation:
We want find the results of the multiplication,
[tex]4.7314 \times 10[/tex]
When we multiply by 10, we move the decimal point forward once.
When we divide by 10, we move the decimal point backwards once.
In this case, we are multiplying, so
[tex]4.7314 \times 10 = 47.314[/tex]
Find an equation for the line with the given properties.
Parallel to the line x = -5; containing the point (6, 2)
Raymond has a set of 57 toy cars and decides to sell 19 of them to Joey. About how many toy cars does Raymond have left
Answer:
raymond has about 38 cars left
Step-by-step explanation:
Because raymond started off with 57 cars and he got rid of( take away) 19 you must use subtraction. 57 - 19 =38
11/4 + 2 1/8 = solve this?
Answer:
4.875
Step-by-step explanation:
A cabin has a room for 7 campers and 2 counselors. How many cabins are needed for a total of 49 campers and 14 counselors?
Answer:
7 cabins
Step-by-step explanation:
So with division, we can find out
49 campers / 7 per cabin = 7
14 counselors / 2 per cabin = 7
As we can see, both problems equal 7, which lets us see that the camp needs 7 cabins to hold all the campers and counselors
A company provides bus trips to various events for a adults and c children. The company charges $18 for each adult and $8 for each child for a trip to an upcoming play. The bus has a maximum capacity of 40 people and the school can only spend $400 dollars on the trip. Write and solve a system of equations to determine the maximum number of adults and children that can attend the play that will satisfy these constraints.
Final answer:
To determine the maximum number of adults and children that can attend the play without exceeding the bus capacity of 40 people and the $400 budget, set up and solve a system of equations representing the capacity and budget constraints. The solution is 8 adults and 32 children.
Explanation:
We are given a situation where a company charges $18 for each adult (a) and $8 for each child (c) for a bus trip to an upcoming play, with the constraints that the bus holds a maximum of 40 people and the available budget is $400. To find the maximum number of adults and children that can attend under these constraints, we need to set up a system of equations:
For the capacity constraint: a + c = 40
For the budget constraint: 18a + 8c = 400
We can solve this system using substitution or elimination. Let's use elimination. Multiply the first equation by -8 and add it to the second equation to eliminate c:
-8a - 8c = -320
18a + 8c = 400
Adding these two equations together gives us:
10a = 80
Thus, a = 8. Plugging a = 8 back into the first equation, we get c = 32.
The maximum number of adults and children that can attend the play is 8 adults and 32 children.
Madison went to the grocery store and purchased cans of soup and frozen dinners. Each can of soup has 500 mg of sodium and each frozen dinner has 700 mg of sodium. Madison purchased 2 more frozen dinners than cans of soup and they all collectively contain 7400 mg of sodium. Determine the number of cans of soup purchased and the number of frozen dinners purchased.
Madison purchased 5 cans of soup and 7 frozen dinners.
Step-by-step explanation:
Given,
Quantity of sodium in each soup can = 500 mg
Quantity of sodium in each frozen dinner = 700 mg
Total quantity = 7400
Let,
Number of soup cans purchased = x
Number of frozen dinners purchased = y
According to given statement;
500x+700y=7400 Eqn 1
y = x+2 Eqn 2
Putting value of y from Eqn 2 in Eqn 1
[tex]500x+700(x+2)=7400\\500x+700x+1400=7400\\1200x=7400-1400\\1200x=6000[/tex]
Dividing both sides by 1200
[tex]\frac{1200x}{1200}=\frac{6000}{1200}\\x=5[/tex]
Putting x=5 in Eqn 2
[tex]y=5+2\\y=7[/tex]
Madison purchased 5 cans of soup and 7 frozen dinners.
Keywords: linear equation, substitution method
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Answer:
Madison purchased 5 cans of soup and 7 frozen dinners
Step-by-step explanation:
A triangle has side lengths of 3 feet and 9 feet.which is the greatest possible perimeter of the triangle
A triangle has sides with lengths of 58 feet, 62 feet, and 84 feet. Is it a right triangle
Answer:
NO
Step-by-step explanation:
84*84=7056
62*62= 3844
58*58=3364
3844+3364=7208
7208 is not equal to 7056
Ben’s living room is a rectangle measuring 10 yards x 168” by how many feet does the legs of the room exceed the width
Answer:
16 feet.
Step-by-step explanation:
Given:
Ben’s living room is a rectangle measuring 10 yards x 168.
Question asked:
How many feet does the legs of the room exceed the width ?
Solution:
By applying unitary method:
Length of rectangle = 10 yards = 30 feet (1 yard = 3 feet)
(10 yard = [tex]3\times10 = 30)[/tex]
Breadth of rectangle = 168 inch = 14 feet (12 inch = 1 feet)
(1 inch = [tex]\frac{1}{12}[/tex])
( 168 inch = [tex]\frac{1}{12}[/tex][tex]\times168 = 14 feet)[/tex]
By subtracting the breadth from the length of rectangle,
30 feet - 14 feet = 16 feet
Therefore, by 16 feet, length of the room exceed the width.
If 5(3x-5) = 20, then
what is 6x -8?
Answer:
10
Step-by-step explanation:
5(3x-5)=20
3x-5=20/5
3x-5=4
3x=4+5
3x=9
x=9/3
x=3
6x-8=6(3)-8=18-8=10
solve 1/8 + 6a/5 = 3/8 + 2a/5 + 7/8
Answer:
no6666//7
Step-by-step explanation:
88../6
m×n, when m=13 and n=12
Answer:
156
Step-by-step explanation:
13 × 12
13
×
12
=
26
130
=
156
Answer:
Step-by-step explanation:
m*n
m=13
n=12
13 * 12
156
Make a math problem for the problem 4 divided by 1/2= 8
Answer:
if Jara has [tex]\$4[/tex] and she wants to buy pen the Prince of each pen is [tex]\$\frac{1}{2}[/tex].
How many pens she can buy.
Step-by-step explanation:
If Jara has [tex]\$4[/tex] and she wants to buy pen the wants to buy pen the Prince of each pen is [tex]\$\frac{1}{2}[/tex] .
How many pen she can buy.
[tex]Let\ Jara\ can\ buy=x\ pens\\\\each\ pen\ cost=\$\frac{1}{2}\\\\Then\ Jara\ can\ buy\ pens=\$\frac{1}{2}x\\\\\frac{1}{2}x=4\\x=8\\Jara\ can\ buy\ =8\ pens[/tex]
Describe and correct the error(s) made in each of the problems below.
1−x / (5−x)(−x)=x−1 / x(x−5)
5/s+2/5=2/s
Answer:
[tex]\displaystyle \frac{1-x}{(5-x)(-x)} =-\frac{x-1 }{ x(x-5)}[/tex]
[tex]\displaystyle \frac{5}{s}\times \frac{2}{5} =\frac{2}{s}[/tex]
Step-by-step explanation:
Errors in Algebraic Operations
It's usual that students make mistakes when misunderstanding the application of algebra's basic rules. Here we have two of them
When we change the signs of all the terms of a polynomial, the expression must be preceded by a negative sign When multiplying negative and positive quantities, if the number of negatives is odd, the result is negative. If the number of negatives is even, the result is positive. Not to confuse product of fractions with the sum of fractions. Rules are quite different
The first expression is
[tex]1-x / (5-x)(-x)=x-1 / x(x-5)[/tex]
Let's arrange into format:
[tex]\displaystyle \frac{1-x}{(5-x)(-x)} =\frac{x-1 }{ x(x-5)}[/tex]
We can clearly see in all of the factors in the expression the signs were changed correctly, but the result should have been preceeded with a negative sign, because it makes 3 (odd number) negatives, resulting in a negative expression. The correct form is
[tex]\displaystyle \frac{1-x}{(5-x)(-x)} =-\frac{x-1 }{ x(x-5)}[/tex]
Now for the second expression
[tex]5/s+2/5=2/s[/tex]
Let's arrange into format
[tex]\displaystyle \frac{5}{s}+\frac{2}{5} =\frac{2}{s}[/tex]
It's a clear mistake because it was asssumed a product of fractions instead of a SUM of fractions. If the result was correct, then the expression should have been
[tex]\displaystyle \frac{5}{s}\times \frac{2}{5} =\frac{2}{s}[/tex]
The measures of two angles in a triangle are 48° and 71°. What is the measure of the third angle?
The sum of the 3 angles needs to be 180.
To find the third angle subtract to the known angles from 180.
180 - 48 - 71 = 61
The third angle is 61 degrees.