Answer:
-2i - 3
I can't see a simpler way to explain it. You just have to work your way through each step.
Step-by-step explanation:
The question is what is i^303?
Remember that when the power is divisible by 4 the expression changes to 1
i^1 = i
i^2 = i * i = sqrt(-1)*sqrt(-1) = - 1
i^3 = i^2 * i = - i
i^4 = i^2 * i^2 = -1 * - 1 = 1
So what does i^303 =
i^300 * i^3
But 300 is evenly divisible by 4. (300 / 4 = 75) so i^300 = 1^75
i^3 = -i
So now you are ready to do the question
(2 - 3i) * -i
2*-i - 3i(-i)
-2i - 3(i^2 * - 1)
-2i - 3(-1 * - 1)
-2i - 3(1)
-2i - 3
Triangle PQR has vertices P(3, 5), Q(-2, 6) and R(8, -1). Give the translation rule (x, y) → (x + 4, y – 5). What will P’ (__, __) be
=======================================================
Explanation:
The rule [tex](x,y) \to (x+4, y-5)[/tex] means we add 4 to the x coordinate and subtract 5 from the y coordinate.
The point (3,5) becomes (3+4, 5-5) = (7,0)
This shifts the point 4 units to the right and 5 units down.
Ben sold his small online business for $100,000. The purchaser will pay him $20,000 today, then $20,000 every year for the next four years. Assume that Ben could invest a lump-sum payment today in an account yielding an interest rate of 4% annually. Find the total present value of all five payments.
A.
$87,096
B.
$88,384
C.
$92,598
D.
$93,964
Answer:
c. 92,598
Step-by-step explanation:
20000 + 20000/1.04 + 20000/(1.04^2) + 20000/(1.04^3) + 20000/(1.04^4)= 20000 + 19230.77 + 18491.12 + 17779.73 + 17096.08
= 92597.
= 92,598
a mixture of 40 liters of paint is 25% red tint, 30% yellow tint and 45% water. 6 liters of yellow tint are added to the original mixture. the percent of yellow tint in the new mixture is?
If a 32-gram serving of pasta contains 4g of protein, how many grams of protein are in a 908-gram box of the pasta ?
Step-by-step explanation:
This is my solution you honestly just need to cross multiply
Answer:
113.5
Step-by-step explanation:
32 : 4 = 908 : X
X = (4 * 908) / 32
X = 113.5
The graph of y = RootIndex 3 StartRoot x minus 3 EndRootis a horizontal translation of y = RootIndex 3 StartRoot x EndRoot. Which is the graph of y = RootIndex 3 StartRoot x minus 3 EndRoot?
On a coordinate plane, a cube root function goes through (negative 8, negative 2), has an inflection point at (2.5, 0), and goes through (10, 2).
On a coordinate plane, a cube root function goes through (negative 10, negative 2), has an inflection point at (negative 3, 0), and goes through (4, 2).
On a coordinate plane, a cube root function goes through (negative 10, 1), has an inflection point at (0, 3), and goes through (8, 5).
On a coordinate plane, a cube root function goes through (negative 8, negative 5), has an inflectoin point at (0, negative 3), and goes through (8, negative 1).
Answer:
Its AAAAAAAAAAA
Step-by-step explanation:
The graph of y = RootIndex 3 StartRoot x minus 3 EndRoot the A is correct
We have given that,
The graph of y = RootIndex 3 StartRoot x minus 3 EndRootis a horizontal translation of y = RootIndex 3 StartRoot x EndRoot.
On a coordinate plane, a cube root function goes through (negative 8, negative 2), has an inflection point at (2.5, 0), and goes through (10, 2).
What is the coordinate plane?A coordinate plane is a two-dimensional plane formed by the intersection of a vertical line called the y-axis and a horizontal line called the x-axis. These are perpendicular lines that intersect each other at zero, and this point is called the origin.
On a coordinate plane, a cube root function goes through (negative 10, negative 2), has an inflection point at (negative 3, 0), and goes through (4, 2).
On a coordinate plane, a cube root function goes through (negative 10, 1), has an inflection point at (0, 3), and goes through (8, 5).
On a coordinate plane, a cube root function goes through (negative 8, negative 5), has an inflection point at (0, negative 3), and goes through (8, negative 1).
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A rope with a length of 3.5 meters is tied from a stake in the ground to
the top of a tent. It forms a 17 degree angle with the ground. How tall
is the tent?
Answer: Approximately 1.0233 meters
Round this however you need to
====================================================
Work Shown:
Refer to the drawing below.
sin(angle) = opposite/hypotenuse
sin(17) = x/3.5
3.5*sin(17) = x
x = 3.5*sin(17)
x = 1.02330096652958
x = 1.0233
Be sure that your calculator is in degree mode.
Use f(x) = 3x - 4 and g(x) = 5 - x2 to evaluate the expression.
(a)
(f of)(x)
(b)
(go g)(x)
Answer:
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
Angle A??
Ch.7.1 trig
9514 1404 393
Answer:
m∠A =86°
Step-by-step explanation:
The sum of angles in a triangle is 180°
A + B + C = 180°
A + 51° + 43° = 180°
A = 86° . . . . . . . . . . . . . subtract 94° from both sides
ASAP! see the picture please!!
Answer:
the second one
function A has a slope of 3
function B has a slope of 5
Can y’all help me on question 32?!
Answer:
b. 96
Step-by-step explanation:
triangle area= b x h / 2
5 x 6 /2= 15
15 x 4 (4 triangles)= 60
square area= b x h
6x6=36
36 + 60 = 96
Write the following percents as both fractions and decimals.
Fraction Decimal
1. 25% ? ?
2. 32.5% ? ?
3. 4% ? ?
4. 75% ? ?
5. 6.5% ? ?
6. 125% ? ?
7. 12.5% ? ?
8. 0.2% ? ?
9. 0.75% ? ?
10. 107% ? ?
11. 210% ? ?
12. 22.5% ? ?
Answer:
1/4, 0.25
13/40, 0.325
1/25, 0.04
3/4, 0.75
13/200, 0.065
1 1/4, 1.25
1/8, 0.125
1/500, 0.002
3/400, 0.0075
107/100, 1.07
21/10, 2.10
9/40, 0.225
A sample of 260 students enrolled at a university were asked what they intended to do after graduation. The results are shown below.
Bar Graph of Type of Employment
What percentage of students intend to go into state or local government after graduation?
Hi my name is Fabian and 69% because 69 is a man which is multi colour hair
Miguel went shopping for a new phone. Sales tax where he lives is 4%. What number should he multiply the price of the phone by to find the total plus tax in one step?
Answer:
miges fue y no me compro el celu
Step-by-step explanation:
mal migel
por culpa de brailyn reverg
What is the similarity
statement for the triangle
pair?
Answer:
side-side-side
Step-by-step explanation:
If two pairs of corresponding angles in a pair of triangles are congruent, then the triangles are similar. We know this because if two angle pairs are the same, then the third pair must also be equal. When the three angle pairs are all equal, the three pairs of sides must also be in proportion.
The similarity statement for the pair of triangles is triangle XYZ similar triangle ENW by AA similarity criterionand mathematically represented as: [tex]\Delta XYZ \, \sim \, \Delta ENW\\[/tex]
Given: In the figure, the angle YXZ is equal to angle NEW and the angle XZY is equal to angle ENW are marked in the corresponding triangles.
To prove triangle XYZ similar triangle ENW by following steps:
Step 1: Consider the triangle XYZ and triangle ENW.
Compare the angle in both the triangles.
[tex]\Delta XYZ \, and\, \Delta ENW\\[/tex][tex]\angle YXZ = \angle NEW\\[/tex][tex]\angle XZY = \angle NWE[/tex]Step 2: Applying the AA similarity criterion:
The Angle-Angle AA similarity criterion states if two angles of one triangle is equal to the corresponding triangle, then two triangles are similar,
This implies triangle XYZ and triangle ENW by AA similarity criterion.
Therefore, the triangle XYZ and triangle ENW by AA similarity criterion. That is [tex]\Delta XYZ \, \sim \, \Delta ENW\\[/tex]
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Two roots of a third degree polynomial function f(x) are -4 and 4. Which statement describes the number and nature of all
roots for this function?
* f(x) has three imaginary roots.
* f(x) has three real roots.
* f(x) has two real roots and two imaginary roots.
* f(x) has three real roots and one imaginary root.
Answer:
f(x) has three real roots.
Step-by-step explanation:
f(x) has three real roots.
A third degree polynomial function with real coefficients has exactly 3 roots.
Furthermore, all complex roots come in pairs, either there is none, or there are exactly two conjugates, which are in the form e1+i(e2) and e1-i(e2) where e1 and e2 are polynomial expressions.
This also means that a third degree polynomial with real coefficients has at least one real root, or three.
Since we are given two real roots for the given polynomial, the third root cannot be complex alone, so the only possibility is that there are three real roots.
If b is real, then all three roots are real.
If b is not real, then two of the roots are real (-4 and 4) and one is imaginary.
What is a polynomial?Polynomial is an equation written with terms of the form kx^n.
where k and n are positive integers.
There are quadratic polynomials and cubic polynomials.
Example:
2x³ + 4x² + 4x + 9 is a cubic polynomial.
4x² + 7x + 8 is a quadratic polynomial.
We have,
The polynomial function f(x) has degree 3 and two roots -4 and 4, we know that (x + 4) and (x - 4) are factors of the function.
To see why, note that when x = -4, the factor (x + 4) becomes zero, making the function zero.
Similarly, when x = 4, the factor (x - 4) becomes zero, making the function zero.
Now,
Since the function has degree 3 and two factors of degree 1, we can conclude that the third factor is also of degree 1.
This means that the function can be written in the form:
f(x) = a (x + 4) (x - 4) (x - b)
where a and b are constants.
We don't know the value of b, but we know that it is a real number (since the other two roots are real).
Thus, the three roots of the function are -4, 4, and b.
Now,
To determine whether the roots are all real or some are imaginary, we need to know the value of b.
If b is real, then all three roots are real.
If b is not real, then two of the roots are real (-4 and 4) and one is imaginary (b).
Thus,
If b is real, then all three roots are real.
If b is not real, then two of the roots are real (-4 and 4) and one is imaginary.
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is it 8%? i think but i just wanna make sure.
Answer:
Yeah, you're right!
Step-by-step explanation:
For 1/6 it's 17%, so just divide by two and you get 8% (rounded).
Answer:
thats right 8%
Step-by-step explanation:
numbers of samples = 6×2 = 12
6 for a cube , and 2 for a fair coin
numbers of event (5, H) is 1
so, the probability is 1/12 = 1/12 × 100%
= 8.33% => rounded => 8%
I need help with #2. Please help. I have to show all work so please explain
Answer:
b = 18 in.
Step-by-step explanation:
Since the triangle given is a right triangle, we can use Pythagorean Theorem to solve for b.
[tex]a^2+b^2=c^2\\7.5^2+b^2=19.5^2\\56.25+b^2=380.25\\b^2=324\\\sqrt{b^2}=\sqrt{324}\\b=18[/tex]
Therefore, b is 18 inches.
Me ayudan por favor ♡?
Answer:
Yes of course I would like to help u.
help? i mark brainlist :)
Answer:
There are 25 students in the class.
Step-by-step explanation:
In order to find the number of students in the class, you can add the number of data points together. Because the name of each person will only be recorded once and only to one data value, that means by adding the total number of data points collected, you can find out the number of students in the sixth-grade class. There are three data points on 3, two data points on 4, five data points on 5, eight data points on 6, two data points on 7, one data point on 8, and four data points on 9, this means the total number of students will be 3 + 2 + 5 + 8 + 2 + 1 + 4 = 25 students, so this will be your answer.
Hey can somebody help me
Answer:
x^2/3
Step-by-step explanation:
Exponent properties!
x^4*x^9 for example,
we add the exponents because the base of the exponents is the same.
now back to the question
x^4/3 * x^2/3
we add those exponents!
6/3 or 2
so we have( x^2)^1/3
^2 and ^1/3 multiply!
we have x^2/3
Soda is often sold in 20 ounce bottles. A pack of sugar (the kind they have at restaurants for your coffee or tea) typically contains 4 grams of sugar. If an 8 ounce bottle of cream soda has 30 grams of sugar, then drinking a 20 ounce bottle of cream soda would be equivalent to eating how many packets of sugar?
Answer:
18.75 packs of sugar
Step-by-step explanation:
20/8 = 2.5 (how many 8 ounce bottles in 20 oz)
2.5 * 30 = 75 (to find how many grams of sugar in the 20 oz bottle)
75/4 = 18.75 (how many packs of sugar it's equal to)
you can also use a ratio to solve:
8/30 = 20/x; cross multiply
600 = 8x; divide 8 on both sides
x = 75
75/4 = 18.74 (how many packs of sugar it's equal to)
- 9 times the difference between a number and 86 is equal to the number plus – 48.
Answer and Step-by-step explanation:
The equation should look like this:
-9(x - 86) = x - 48
Distribute the -9.
-9x + 774 = x - 48
Add 48 and 9x to both sides of the equation.
822 = 10x
Divide both sides of the equation by 8.
82.2 = x
[tex]\frac{411}{5}[/tex] = x -- Fraction Form
#teamtrees #PAW (Plant And Water)
Emilia is painting a triangular picture frame. The perimeter is 30 inches. If one side is 13 inches long and another side is 5 inches long, what is the length of the other side of the picture frame?
Answer:
12 inches
Step-by-step explanation:
30-13=17
17-5= 12
Use information about the triangle's perimeter, to find the side length of C.
If the triangle frame is a right triangle, than you could use the Pythagorean Theorem and use the following formula, a^2 + b^2 = c^2, to find the measure of side c.
Have a great rest of your day, and I hope this helps!
-kiniwih426
Please answer the question below 15 points for answering!
Box Y has edges that are the length of the edges of box X
Box X
Box Y
Which statement is true?
O A. The volume of box Y is of the volume of box X
OB. The volume of box Y is
of the volume of box X
O c The volume of box Y is to of the volume of box X.
OD. The volume of box Y is of the volume of box X.
E. The volume of box Y is 256 of the volume of box X.
Answer:
The volume of box Y is 1/64 of the volume of box X
Step-by-step explanation:
Since. The edge of a box Y is 1/4 the lengtj of box X ;
The volume is 3 dimensional and each dimension of Y is 1/4th the dimension of X
The volume of Y will be (1/4)^3 the volume of Y
(1/4)^3 = 1/4 * 1/4 * 1/4 = 1/64
For instance, if edge of X = 8
Edge of Y which is 1/X ; edge Y = 1/4(8) = 2
Volume, X 8^3 = 512
Volume Y = 2^3 = 8
8/512 = 1 / 64
Xác suất thống kê: Người ta tổng kết các phương pháp chẩn đoán dạ dày tá tràng. Trên lâm sàng chẩn đoán đúng 60%; X-quang 70%; nội soi 80%. Kết hợp cả 3 phương pháp thì khả năng chẩn đoán đúng là bao nhiêu?
Answer:
Step-by-step explanation:
iam a gay 345366e2673
Can someone help me with this one?
Answer:
answer is C
Step-by-step explanation:
y intercept = -3
Answer:
ejjejjeheyreyyeueuuueuuu
!uueueuueu
Step-by-step explanation:
jejjejeujejsjjdjsjjsjsjsjsjjjjejjjejejjjjejeje
HELP PLEASE!!! HELP HELP
Answer:
f(-3) = -1/3
Step-by-step explanation:
-3 is less than -2 so we use the first function 1/x
f(-3) = 1/-3
Answer:
-1/3
Step-by-step explanation:
-3 is less than -2, so use the first one, 1/x and substitute -3 in
1/(-3)=-1/3
Use differentials to estimate the amount of metal in a closed cylindrical can that is 10 cm high and 6 cm in diameter if the metal in the top and the bottom is 0.1 cm thick and the metal in the sides is 0.05 cm thick. (Round your answer to two decimal places.)
Answer:
14/5 cm3 ??
Step-by-step explanation:
2 times the sum of a number and 9 equals 4
Answer
Step-by-step explanation: