Answer:
Values of x are 4i, -4i, 5 and -5
Step-by-step explanation:
[tex]3x^4+27x^2 + 1200[/tex] We need to find all the zeros (roots) of the above equation.
Let assume that x^4 = u^2 and x^2 = u
Putting values of x^4 and x^2 in the above equation and finding the value of u.
[tex]-3u^2 + 27u+1200=0\\Using \,\,quadratic\,\,equation\,\,to\,\,solve:\\u=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\where\,\, a= -3, b= 27 \,\,and\,\, c=1200\\u=\frac{-(27)\pm\sqrt{(27)^2-4(-3)(1200)}}{2(-3)}\\u=\frac{-27\pm\sqrt{729+14,400}}{-6}\\u=\frac{-27\pm\sqrt{729+14,400}}{-6}\\u=\frac{-27\pm\sqrt{15129}}{-6}\\u=\frac{-27\pm123}{-6}\\so, \,\, u = \frac{-27+123}{-6} \,\, and \,\, u \frac{-27-123}{-6}\\u= -16 \,\, and \,\, u = 25[/tex]
So, values of u are -16 and 25
Putting back the value of u i.e, x^2
x^2 = -16 and x^2 =25
solving
Taking square root on both sides:
√x^2 =√-16 and √x^2 = √25
x = ± 4i (as √-1 =i) and x = ±5
So, values of x are 4i, -4i, 5 and -5.
It takes 20 minutes for 5 people to paint 5 walls. How many minutes does it take 9 people to paint 9 walls
5 people , 1 wall ~ 20/5 = 4 minutes
1 person, 1 wall ~ 4/5 minutes
9 people, 1 wall ~ (4/5) x 9 = (36/5) minutes
Therefore 9 people, 9 walls ~ (36/5) x 9
= 64.8 minutes
= 1h 4 min 48 s
Answer:
It takes 20 minutes :)
Step-by-step explanation:
(4x-5x)(x-3) use foil to multiply the binomial
Answer:
-x^2+3x
Step-by-step explanation:
what is the slope,y intercept ,are the lines the same intersecting ,or parallel? What are the number of solutions? Classification ,Consistent-dependent,Consistent-independent,or Inconsistent? use y = mx + b ,m = slope ,b = y-int for y = 2x + 3, 2x - y = 5 and 3x - y = 5 ,2x + y = -3 and y = x + 4 ,y = x + 4. Ive tried posting this question a few times but cannot get the right wording plz help me
Answer:
For equation: y = 2x + 3 , 2x - y = 5 There is no solution to this system of equations.For equation: y = 2x + 3 , 2x - y = 5 There is one solution to the system of equations.For equation: y = x + 4 , y = x + 4 There are infinite solutions to the system.Step-by-step explanation:
The equation of straight line is written as y = m x + c where 'm' is slope. y - intercept of line is value which intersect the point on y-axis.To find y -intercept , put x = 0 in equation.If slope of two lines are equal then lines are parallel.If the lines are not parallel, they will always intersectFor equation: y = 2x + 3 , 2x - y = 5
Compare equation y = 2x + 3 with y = m x + c then we get slope 'm' is 2.
Now, put x = 0 in y = 2x + 3 to get y-intercept
y = 2(0)+ 3
y = 0 + 3
y = 3
so, the y-intercept is 3 .
Re-write this equation 2x - y = 5 in the slope intercept form;
Subtract 2x from both the sides of 2x - y = 5
2x - y - 2x = 5 - 2x
- y = - 2x + 5
Multiply both the sides by '-1'
y = 2x - 5
so, when we compare above equation with y = m x + c then we get slope 'm' is 2 .
Now, put x = 0 in y = 2x - 5 to get y-intercept
y = 2(0) - 5
y = 0 - 5
y = - 5
so, the y-intercept is - 5 .
Equation y = 2x + 3 and 2x - y = 5 are parallel (since there slope are equal 'm = 2').
There is no solution to this system of equations.
For equation: 3x - y = 5 , 2x + y = -3
Re-write this equation 3x - y = 5 in the slope intercept form;
Subtract 3x from both the sides of 3x - y = 5
3x - y - 3x = 5 - 3x
- y = - 3x + 5
Multiply both the sides by '-1'
y = 3x - 5
so, when we compare above equation with y = m x + c then we get slope 'm' is 3 .
Now, put x = 0 in y = 3x - 5 to get y-intercept
y = 3(0) - 5
y = 0 - 5
y = - 5
so, the y-intercept is - 5 .
Re-write this equation 2x + y = -3 in the slope intercept form;
Subtract 2x from both the sides of 2x + y = -3
2x - y - 2x = -3 - 2x
- y = - 2x - 3
Multiply both the sides by '-1'
y = 2x + 3
so, when we compare above equation with y = m x + c then we get slope 'm' is 2 .
Now, put x = 0 in y = 2x + 3 to get y-intercept
y = 2(0) + 3
y = 0 + 3
y = 3
so, the y-intercept is 3 .
Equation 3x - y = 5 and 2x + y = -3 are intersecting lines (since their slope are not equal).
There is one solution to the system of equations (since the lines are intersect).
For equation: y = x + 4 , y = x + 4
Compare equation y = x + 4 with y = m x + c then we get slope 'm' is 1.
Now, put x = 0 in y = x + 4 to get y-intercept
y = 0+ 4
y = 4
so, the y-intercept is 4 .
since equation of line are same therefore slopes are also equal
Equation y = x + 4 and y = x + 4 are parallel lines.
There are infinite solutions to the system. ( Since equivalent equation)
Plz help meehhh :(((
A bus travels two different routes: the Green Route and the Blue Route. The routes are different lengths.
• On Monday the bus traveled the Green Route 6 times and the Blue Route 5 times, traveling a total of 52 miles.
• On Tuesday the bus traveled the Green Route 12 times and the Blue Route 13 times, traveling a total of 119 miles.
What is the length of the Green Route in miles?
A) 4.4 mi
B) 4.5 mi
C) 6.4 mi
D) 6.8 mi
Answer:
B
Step-by-step explanation:
Let length of Green Route be g and length of Blue Route be b
From 1st bullet point we can write the equation:
6g+5b = 52
From 2nd bullet, we can write:
12g + 13 b = 119
We can solve for b of the 1st equation as:
[tex]6g+5b = 52\\5b=52-6g\\b=\frac{52-6g}{5}[/tex]
Now we can put this value of b into 2nd equation and solve for g (as shown below):
[tex]12g+13b=119\\12g+13(\frac{52-6g}{5})=119\\12g+\frac{676-78g}{5}=119\\\frac{60g+676-78g}{5}=119\\60g+676-78g=5*119\\60g+676-78g=595\\-18g=-81\\g=\frac{-81}{-18}=4.5[/tex]
Hence, the green route is 4.5 miles, B is right.
A wheel with a dot on its edge rolls on the ground. The radius of the wheel is 15 inches. When the dot is at the position shown below, at an angle of 112°, what is the distance of the dot above the ground, to the nearest tenth of an inch?
Answer:
The distance of the dot above the ground is 28.9 in
Step-by-step explanation:
see the attached figure with letters to better understand the problem
we know that
The triangle ABC is an isosceles triangle
CA=CB=15 in ------> is the radius of the circle
∠ACD+112°=180° ---> because the diameter divide the circle into two equal parts
∠ACD=180° -112°=68°
In the right triangle ACD
Find AD we have sin(68°)=AD/AC AD=AC*sin(68°) substitute the value AD=15*sin(68°)=13.9 in
Find the distance AB
AB=2*AD AB=2*13.9=27.8 in
The diameter is equal to
2*15=30 in
The distance of the dot above the ground is equal to
AB+(30-27.8)/2
27.8+1.1=28.9 in
Choose all the examples that require measuring the area.
Answer options:
A.the space the bottom of a tent takes up
B.the distance around the outside of a tent
C.the measure from the top to the bottom of a tent
D.the measure from the top to the bottom of a flat sleeping bag
E.the space a flat sleeping bag takes up
F.the distance around the outside of a flat sleeping bag
Answer:
A and E
Explanation:
A.the space the bottom of a tent takes up- Area
B.the distance around the outside of a tent- Perimeter
C.the measure from the top to the bottom of a tent- Height
D.the measure from the top to the bottom of a flat sleeping bag-length
E.the space a flat sleeping bag takes up-area
F.the distance around the outside of a flat sleeping bag- perimeter
What is the sum of the first 100 terms of the sequence 4,9,14,19, ...?
Answer:
25150
Step-by-step explanation:
First, we have to see that this is an arithmetic sequence... since to get the next element we add 5 to it. (a geometric sequence would be a multiplication, not an addition)
So, we have a, the first term (a = 4), and we have the difference between each term (d = 5), and we want to find the SUM of the first 100 terms.
To do this without spending hours writing them down, we can use this formula:
[tex]S = \frac{n}{2} * (2a + (n - 1) * d)[/tex]
If we plug in our values, we have:
[tex]S = \frac{100}{2} * (2 * 4 + (100 - 1) * 5) = 50 * (8 + 99 * 5)[/tex]
S = 50 * (8 + 495) = 50 * 503 = 25150
Answer:
Sum of 100 terms = 25150
Step-by-step explanation:
Formula:-
Sum of n terms of an AP
Sₙ = n/2[2a + (n - 1)d]
Where n - number of terms
a - first term and d - common difference
To find the sum of 100 terms
here, n = 100, a = 4 and d = 5
S₁₀₀ = n/2[2a + (n - 1)d]
= 100/2[2*4 + (100 - 1)5]
= 50[8 + 99*5]
= 25150
Which answer describes this type of series 240+144+86.4+51.84
Well this series is neither arithmetic or geometric as said in the other solution but since there are addition signs I will find the sum
The sum is 522.24
Prudence is creating a garden in her backyard. She wants it to be the shape of an equilateral triangle with sides of length 20 feet. What will be the area of this triangular garden? Round your answer to the nearest whole foot.
Answer:
The area of the triangular garden is [tex]173\ ft^{2}[/tex]
Step-by-step explanation:
we know that
The equilateral triangle has three equal sides and three equal internal angles (the measure of each internal angle is 60 degrees)
The area of a triangle applying the law of sines is equal to
[tex]A=\frac{1}{2}(a)(b)sin(C)[/tex]
In this problem we have a equilateral triangle
therefore
[tex]a=b=20\ ft[/tex]
[tex]C=60\°[/tex]
substitute
[tex]A=\frac{1}{2}(20)(20)sin(60\°)[/tex]
[tex]A=\frac{1}{2}(20)(20)\frac{\sqrt{3}}{2} \\ \\A=100\sqrt{3}\ ft^{2}\\ \\A=173\ ft^{2}[/tex]
which answer choice best describes f(x)=x-12
The relationship does not show a direct linear variation best describes f(x)=x−12. Option D is the correct choice.
A function is a specific mathematical relationship with a predefined domain and range, where each value in the domain corresponds to one value in the range.
In the given function, f(x) = x - 12, the slope of the line represents how much 'y' increases as 'x' increases.
A constant slope means that the increase in 'y' is uniform across the entire line. In this case, the slope (m) is 1.
However, this function doesn't exhibit a direct linear variation, as it also has a y-intercept of -12.
The presence of the y-intercept at -12 indicates that the line does not pass through the origin, and therefore, it doesn't show a direct linear variation.
Hence, the linear function f(x) = x - 12 does not display a direct linear variation, making option (D) the correct choice.
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Question:-
Which answer choice best describes f(x)=x−12?
A. The relationship shows a direct linear variation with a constant of variation of −12 .
B. The relationship shows a direct linear variation with a constant of variation of 1.
C. The relationship shows a direct linear variation with a constant of variation of 12.
D. The relationship does not show a direct linear variation
what is the surface area of the rectangular prism below?
A. 423 units squared
B. 630 units squared
C. 1260 units squared
D. 846 units squared
Answer: D. 846 units squared
Step-by-step explanation:
12x9=108
108x2=216
15x9=135
135x2=270
12x15=180
180x2=360
360+270+216=846 units squared
The surface area of the rectangular prism is 846 sq.units
What is a rectangular Prism ?A rectangular prism is a three dimensional figure with rectangle at its base. It can also be called as a Cuboid .
A rectangular prism is given with
length 12 units
Width 15 units
Height 9 units
The surface area of the rectangular prism is given by
A = 2 * l * w + 2 * l * h + 2 * w * h
A = 2 * 12 * 15 + 2 * 9 * 12 + 2 * 15 * 9
A = 360 + 216 + 270
A = 846 sq.units
Therefore the surface area of the rectangular prism is 846 sq.units
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What should be done to solve the following equation?
d - 8 = 9
Subtract 8 from both sides of the equation.
Add 8 to both sides of the equation.
Add 9 to both sides of the equation.
Subtract 9 from both sides of the equation.
To solve this equation, you need to isolate/get the variable (d) by itself, to do so, you should add 8 on both sides
d - 8 = 9
d - 8 + 8 = 9 + 8
d = 17 The 2nd option is your answer
About 34% of people are expected to be infected by the flu this season. What is the risk that a randomly selected person will be infected by the flu?'a) 34 b) 0.34 c) 0.66 d) 66 e) 1 divided by the population size
Answer:
B 0.34
Step-by-step explanation:
If 34% of all people are expected to get the flu, then that means 34% of any sample size should also expect to be infected. If they choose 1 person at random from either the population or a preselected random sample, then that person has a 34% chance of getting the flu. 0.34 is the decimal corresponding to 34%. So the probability is 0.34
Convert the percentage to a decimal. The answer is 0.34.
Convert 34% to a decimal, which is 0.34.The correct answer is b) 0.34.which of the following functions is nonlinear
Answer:
D.Step-by-step explanation:
The last option, option D is not linear.
In mathematics, linear refer to a proportional behaviour that can be modelled with a line, the functions that model this behaviour are called linear functions, and their graphs are lines.
Now, specifically, in Algebra, a linear expression refers to an expression which has variables with an exponent equal to 1, like option A, B and V. As you can see option D has an expression which variable is squared, that means it's not linear, and its graph is not a line, but a parabola.
The function which is not linear equation is f(x) =x²+ 9.
Thus, option (D) is correct.
A linear equation is an equation that represents a straight line on a graph.
It is an algebraic equation in which the variables are raised to the power of 1, and there are no exponents or radicals involved.
The general form of a linear equation in two variables, x and y, is given by:
ax + by = c
a) f(x) =x have the highest degree 1.
So, it is linear equation.
b) f(x) = 10x + 100 have the highest degree 1.
So, it is linear equation.
c) f(x) = 1/5x - 2 have the highest degree 1.
So, it is linear equation.
d) f(x) =x²+ 9 have the highest degree 1.
So, it is not a linear equation.
Thus, option (D) is correct.
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Max can mow a lawn in 45 minutes. Jan takes twice as long to mow the same lawn. If they work together, how long will it take them to mow the lawn?
a.15.0 minutes
b.22.5 minutes
c.30.0 minutes
d.120.0 minutes
Answer:
c. 30.0 minutes
Step-by-step explanation:
Max mows 1/45 lawns per minute.
Jan takes twice as long (90 minutes per lawn), so mows 1/90 lawns per minute.
Working together, they mow ...
(1/45 + 1/90) lawns per minute = (2/90 +1/90) lawn/min = 3/90 lawn/min
= 1/30 lawn/min
Then for one lawn, it takes ...
(1 lawn)/(1/30 lawn/min) = 30 min
Answer:
A
Step-by-step explanation:
30 min
The area of a rectangular patio is 5 5/8 square yards, and its length is 1 1/2. What is the patio width, in yards
The width is 3 3/4. you just have to divide 5 5/8 by 1 1/2.
let's firstly convert those mixed fractions to improper fractions and then proceed.
[tex]\bf \stackrel{mixed}{5\frac{5}{8}}\implies \cfrac{5\cdot 8+5}{8}\implies \stackrel{improper}{\cfrac{45}{8}}~\hfill \stackrel{mixed}{1\frac{1}{2}}\implies \cfrac{1\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{3}{2}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \textit{area of a rectangle}\\\\ A=Lw~~ \begin{cases} L=length\\ w=width\\ \cline{1-1} L=\frac{3}{2}\\ A=\frac{45}{8} \end{cases}\implies \cfrac{45}{8}=\cfrac{3}{2}w\implies \cfrac{45}{8}=\cfrac{3w}{2}\implies 90=24w \\\\\\ \cfrac{90}{24}=w\implies \cfrac{15}{4}=w\implies 3\frac{3}{4}=w[/tex]
{PLEASE HELP ASAP}
I dont know how to do these very well at all, please help me!
the answer for this question is all are not polynomials
Answer:
The first, second, and last ones are polynomials, the others are not.
Step-by-step explanation:
PLEASE HELP!!
For the following questions, use Euler's Formula to find the missing number.
1. Faces: 25
Vertices: 17
Edges: ?
43
41
39
40
2. Vertices: 11
Edges: 34
Faces: ?
25
28
26
24
3. Edges: 36
Faces: 22
Vertices ?
19
15
16
17
Answer:
see explanation
Step-by-step explanation:
Using Euler's formula for Polyhedra, that is
F + V - E = 2
where F is faces, V is vertices and E is edges
1
Rearrange formula for E
F + V - E = 2 ( add E to both sides )
F + V = 2 + E ( subtract 2 from both sides )
E = F + V - 2
= 25 + 17 - 2 = 40
-------------------------------------------------
2
Rearrange formula for F
F + V - E = 2 ( add E to both sides )
F + V = 2 + E ( subtract V from both sides ) F = 2 + E - V, so
F = 2 + 34 - 11 = 25
-----------------------------------------------------
3
Rearrange formula for V
F + V - E = 2 ( add E and subtract F from both sides )
V = 2 + E - F
= 2 + 36 - 22 = 16
Answer:
1. use Euler's formula to find the missing number f=25 vertices=17 Edges=?
40
2. Mario's company makes gemstones Faces=12 vertices=? edges=20
10 vertices
3. Pierre built the model shown in the diagram for a social studies project
pentagon
4. A jewelry store buys small boxes find the surface area of the box to the nearest whole number
266 cm^2
5. Find the lateral area of the prism below Round your answer to the nearest whole number
322 m^2
6. Find the surface area of the cylinder in terms of pi
350pi cm^2
7. Allison is planning to cover the lateral surface of a large cylindrical can diameter 3 feet height 3.5 feet
33. ft^2
8. Find the surface area of the regular pyramid shown to the nearest whole number
740 m^2
9. is the figure below drawn in one point or 2 point perspective
Patti went swimming for 1hour 15minutes on monday. On Tuesday she swam twice as long as she swam on Monday. On Wednesday she swam 50minutes less than the time she swam on Tuesday. How much time did she spend swimming during that three day period
Patti swam a total of 5 hours and 25 minutes over the three days—1 hour and 15 minutes on Monday, 2 hours and 30 minutes on Tuesday, and 1 hour and 40 minutes on Wednesday.
Explanation:Patti went swimming for 1 hour and 15 minutes on Monday. To find out how long she swam over the three days, we need to calculate the time for each day and then sum them up.
On Tuesday, she swam twice as long as she did on Monday, which means she swam 2 * (1 hour and 15 minutes) = 2 hours and 30 minutes.
On Wednesday, she swam 50 minutes less than the time she swam on Tuesday, which means she swam (2 hours and 30 minutes) - 50 minutes = 1 hour and 40 minutes.
To find the total time Patti spent swimming during the three days, we add up Monday's, Tuesday's, and Wednesday's swimming times:
Monday: 1 hour and 15 minutesTuesday: 2 hours and 30 minutesWednesday: 1 hour and 40 minutesThe total is 5 hours and 25 minutes.
Solve for x.
A. 12
B. 11
C. 10
D. 9
Answer:
C. 10
Step-by-step explanation:
The values on the left are proportional to the values on the right. You can write the ratios different ways, but the one I chose is ...
6/15 = x/25
6·25/15 = x = 150/15 = 10
The value of x is 10.
A triangle has side lengths:
5,13,12 Is this triangle a right triangle, an acute triangle of an obtuse triangle?
Answer
5^2 + 12^2 = 25 + 144 = 169 = 13^2
Therefore, it is a right triangle.
Step-by-step explanation:
Answer:
5² + 12² = 25 + 144 = 169 = 13²
Therefore, it is a right triangle.
Step-by-step explanation:
A washer and a dryer cost $696 combined. The washer costs $46 more than the dryer. What is the cost of the dryer?
You're buying two items, we can represent them as X. First you set one of the X's to be the dryer, and since we know that the washer costs 46 more than the dryer, that can be represented as X + 46. The equation can be written as follows:
x + (x + 46) = 696
2x + 46 = 696
2x = 650
x = 325
Therefore, the dryer costs $325, and the washer costs $371
The cost of the dryer is found by setting up an equation where x represents the dryer's cost and solving for x. The calculation steps reveal that the dryer costs $325.
The student is asking how to find the cost of a dryer when given the combined cost of a washer and dryer, and that the washer costs $46 more than the dryer. To solve this, we first let the cost of the dryer be x dollars. Therefore, the cost of the washer would be x + $46. We are told that combined they cost $696.
Setting up the equation: x + (x + $46) = $696.
Combine like terms: 2x + $46 = $696.
Subtract $46 from both sides: 2x = $696 - $46.
Calculate the remaining balance: 2x = $650.
Divide both sides by 2 to find the cost of the dryer: x = $325.
Therefore, the cost of the dryer is $325.
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
The results of a survey indicate that between 76% and 84% of the season ticket holders are satisfied with their seat locations.
What is the survey’s margin of error?
Answer:
4%
Step-by-step explanation:
Answer:
+/- 4%.
Step-by-step explanation:
That would be +/- (84-76)/2
= +/- 8/2
= +/-4%.
A circle has its center at (-1, 2) and a radius of 3 units. What is the equation of the circle? (1 point) (x - 1)2 + (y + 2)2 = 3 (x + 1)2 + (y - 2)2 = 3 (x + 1)2 + (y + 2)2 = 9 (x + 1)2 + (y - 2)2 = 9
Answer:
(x + 1)^2 + (y - 2)^2 = 3^2 = 9
Step-by-step explanation:
The standard equation of a circle with center at (h, k) and radius r is
(x - h)^2 + (y - k)^2 = r^2.
Here, h = -1, k = 2 and r = 3, so the equation of this particular circle is
(x + 1)^2 + (y - 2)^2 = 3^2 = 9.
If the mean of a normal distribution is 315 what is the median of the distribution? A.420
B.315
C.105
D.210
The normal distribution is symmetric about its mean. For any symmetric distribution, the mean is the same as the median. So the answer is B.
In a normal distribution, the mean and median are equal due to its symmetrical nature. Therefore, if the mean is 315, then the median is also 315.
Explanation:The question asks about the relationship between the mean and median in a normal distribution. In a normal distribution, the mean, median, and mode are all equal. This is due to the symmetrical nature of the normal distribution around its mean. So, if the mean of the normal distribution is 315, the median is also 315.
The answer to the student's question is: B.315.
Janice swims 450 meters in 5 minutes. Find her swimming speed in meters per minute
90 speed in meters
:explenation step by step
1. 5× =450
2. 450÷5=90
3.5×90=450
Final answer:
Janice's swimming speed is calculated by dividing the distance she swims, 450 meters, by the time it takes, 5 minutes, resulting in a speed of 90 meters per minute.
Explanation:
To calculate Janice's swimming speed in meters per minute, you divide the distance she swims by the time it takes her to swim that distance. Janice swims 450 meters in 5 minutes.
Swimming speed = Distance ÷ Time.
Swimming speed = 450 meters ÷ 5 minutes = 90 meters per minute.
Therefore, Janice's swimming speed is 90 meters per minute.
One of the steps Misaki used to solve an equation is shown below.
Which property justifies the step shown?
2q(q+4)=10 2q^(2)+8q=10
multiplicative identity property
associative property
commutative property
distributive property
inverse property
Answer:
Distributive property
Step-by-step explanation:
The given equation is:
[tex]2q(q+4)=10[/tex]
To solve this equation, we expand the left hand side using the distributive property to obtain:
[tex]2q^2+8q=10[/tex]
That was exactly what Miskai did.
Therefore the property that justifies his step shown is the distributive property.
This property says that, if a, b, and c are real numbers then,
[tex]a(b+c)=ab+bc[/tex]
WILL GIVE THE BRAINLIST !!!!!!!!!!!!!!!!!!!!!!!!!!!!!! I REALLY NEED THIS A.S.A.P !!!write 1/400 as a percent to the nearest hundredth of a percent
Answer:
0.25%
Step-by-step explanation:
To change a fraction to a percentage, we multiply the fraction by 100%.
1/400 = 1/400 x 100 = 0.25%
hope this helps
The value of the Percentage 1/400 as a percent is: 0.25%
How to calculate the percentage?Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100.
Percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".
Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100. It is given by:
Percentage = (value / total value) * 100%
Thus:
1/400 as a percent is calculated as:
1/400 * 100/1
= 100/400
= 0.25%
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Convert 6cis (5pi)/6 to rectangular form.
A. 3 Square root of 3 + 3i
B. -3 Square root of 3 +3i
C. 3 Square root of 3 - 3i
D. -3 Square root of 3 - 3i
E. 3 - 3 Square root of 3 i
Answer:
B
Step-by-step explanation:
I love these! Ok, the expanded formula you need for this is
[tex]6(cos\frac{5\pi }{6}+sin\frac{5\pi }{6}i)[/tex]
From the unit circle we get the cos and sin of that angle and fill them in:
[tex]6(-\frac{\sqrt{3} }{2}+\frac{1}{2}i)[/tex]
Distributing through the parenthesis gives you
[tex]-\frac{6\sqrt{3} }{2}+\frac{6}{2}i[/tex]
which simplifies to
[tex]-3\sqrt{3}+3i[/tex]
To convert 6cis (5pi)/6 from polar form to rectangular form, use the formula r*cos(theta) + r*sin(theta)*i. The magnitude (r) is 6 and the angle (theta) is 5pi/6. The rectangular form results to be B. -3 Square root of 3 +3i.
Explanation:The student is asked to convert the complex number 6cis (5pi)/6 from polar form to rectangle form. In polar form, a complex number can be represented as rcis(theta), where r is the magnitude and theta is the angle. To convert this to rectangular form, we use the formula r*cos(theta) + r*sin(theta)*i. In this case, r=6 and theta=5pi/6. Therefore, the rectangular form of the given number is (6*cos(5pi/6)) + (6*sin(5pi/6))*i which equals -3 +
3 square root
of 3*i. Hence, the correct answer is B. -3 Square root of 3 +3i.
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Help, please Jake has $100 of birthday money in his wallet. He spends $15 at Twistee Treat and $10 at Wawa. While walking home he finds a $20 bill on the ground. His friend borrows $40 from Jake. At home, Jake mows the lawn and earns $35. Evaluate an expression to determine how much money Jake has in his wallet.
Answer:
The expression is [tex]x=100-15-10+20-40+35[/tex]
Jake has in his wallet [tex]\$90[/tex]
Step-by-step explanation:
Let
x-----> the money that Jake has in his wallet
we know that
The expression that represent the situation is equal to
1) Jake has $100 of birthday money in his wallet
so
[tex]x=100[/tex]
2) He spends $15 at Twistee Treat and $10 at Wawa
so
[tex]x=100-15-10[/tex]
3) He finds a $20 bill on the ground
so
[tex]x=100-15-10+20[/tex]
3) His friend borrows $40 from Jake
so
[tex]x=100-15-10+20-40[/tex]
4) At home, Jake mows the lawn and earns $35
so
[tex]x=100-15-10+20-40+35[/tex]
[tex]x=\$90[/tex]
Jake has $90 in his wallet after accounting for all his expenses, earnings, and the money borrowed by his friend. This calculation includes his birthday money, spending, found money, and earnings from mowing the lawn.
To determine how much money Jake has in his wallet, we need to account for all his spending, earnings, and borrowings.
Start with Jake's initial amount: $100Subtract his spending at Twistee Treat: $100 - $15 = $85Subtract his spending at Wawa: $85 - $10 = $75Add the $20 bill he found: $75 + $20 = $95Subtract the $40 borrowed by his friend: $95 - $40 = $55Add the earnings from mowing the lawn: $55 + $35 = $90Therefore, Jake has $90 in his wallet.