Imaginary Numbers
Simplify
i^9
Answer:
i^9 = i
Step-by-step explanation:
If the price of an item is $34 and the sales tax on it is $1.36, what is the sales-tax rate? You can use the calculator tool.
Answer:
$0.04 per $1
Step-by-step explanation:
If you pay $1.36 for $34, then the tax rate is 1.36/34=0.04
That's for each dollar value of an item, you pay $0.04
The length of a rectangle is 3 meters more than twice its width. the length of this rectangle is 10 meters. write an equation to solve the perimeter of this rectangle
Brandon can paint a fence in 12 hours and Elaine can paint the same fence in 11 hours. How long will they take to paint the fence if they work together?
A) 5 13/24 hr
B) 5 ¾ hr
C) 11 ½ hr
D) 5 17/23 hr
Answer:5 17/23
Step-by-step explanation:
The seats at a local baseball stadium are arranged so that each row has five more seats than the row in front of it. If there are four seats in the first row, how many total seats are in the first 24 rows?
These are the choices
1,476
2,856
2,952
1,428 ...?
What is the domain of the quadratic function graphed below?
Rewrite with only sin x and cos x.
cos 3x
cos x - 4 cos x sin2x
-sin3x + 2 sin x cos x
-sin2x + 2 sin x cos x
2 sin2x cos x - 2 sin x cos x
Final answer:
To rewrite expressions using only sin x and cos x, we can use trigonometric identities like [tex]cos 2x = 1 - 2sin^2 x[/tex] and sin 2x = 2sin x cos x. By applying these identities, we can simplify the given expressions.
Explanation:
To rewrite the given expressions using only sin x and cos x, we can use the following trigonometric identities:
[tex]cos 2x = 1 - 2sin^2 x[/tex]sin 2x = 2sin x cos x[tex]sin 3x = 3sin x - 4sin^3 x[/tex]Using these identities, we can rewrite the expressions as follows:
cos 3x = [tex]4cos^3 x - 3cos x[/tex]cos x - 4cos x sin^2 x = cos x - 4sin x cos x sin x = [tex]cos x - 4sin^3 x cos x[/tex]-sin 3x + 2sin x cos x = [tex]-(4sin^3 x) + 2sin x cos x[/tex] = [tex]-4sin^3 x + 2sin x cos x[/tex]-sin 2x + 2sin x cos x = -2sin x cos x + 2sin x cos x = 0[tex]2sin^2 x cos x - 2sin x cos x[/tex] = 2sin x cos x (sin x - 1)
4x + 5x + 12 = -6 (given)
9x + 12 = -6 (simplify)
9x = -18 (subtraction)
x = -2 (addition)
Which reason is incorrect?
A) addition
B) given
C) simplify
D) subtraction
Answer:
Addition
Step-by-step explanation:
USA Testprep
For tax reasons, I need to create a rectangular vegetable patch with an area of exactly 50 sq. ft. The fencing for the east and west sides costs $4 per foot, and the fencing for the north and south sides costs only $2 per foot. What are the dimensions of the vegetable patch with the least expensive fence? ...?
**^^**
While doing a math problem in class, Jared's answer was different from his teacher's. So she had him come up and work the problem on the board. Here's Jared's work.
36.47
x 12
----------
7294
+ 3647
-----------
109.41
What was his mistake?
A>He multiplied incorrectly.
B>He left out the place holder under the 4.
C>There are not enough numbers after the decimal.
D>The sum of 7,294 and 3,647 is incorrect.
Answer:
The other answer is wrong, actually
Step-by-step explanation:
The real answer is B, He left out the place holder under the 4.
Jared did not multiply incorrectly.
What is 2x-16=90 in Algebra1
One number is 3 less than twice another. If their sum is 39, find the numbers.
Which of the following systems of equations represents the word problem?
A.y = 2x - 3 and y = x + 39
B.y = 2x - 3 and x + y = 39
C.y = 2(x - 3) and x + y = 39 ...?
Let
y------> one number
x-----> another number
we know that
[tex]y=2x-3[/tex] ------> equation A
[tex]x+y=39[/tex] ------> equation B
substitute equation A in equation B
[tex]x+[2x-3]=39[/tex]
[tex]3x=39+3[/tex]
[tex]x=42/3=14[/tex]
Find the value of y
[tex]y=2*14-3=25[/tex]
the numbers are [tex]25[/tex] and [tex]14[/tex]
therefore
the answer is the option B
[tex]y=2x-3[/tex] and [tex]x+y=39[/tex]
Which relation is a function?
I. {(2, 4), (–1, 7), (3, 0), (5, 4)}
II. {(–3, 6), (–3, 6), (8, 6), (8, 10)}
III. {(4, 1), (–2, 5), (–8, 3), (4, 6)}
A. II only
B. I only
C. I and II
D. II and III
Gina works at a diner. She earns $6 each hour plus tips.In one week,she worked 37 hours a week and earned $43 in tips.How much did she make altogether? Write an equation. Use a variable for the unknown.Solve.
each month for 7 months, samuel mows 3 lawns. how many more lawns does he need to mow before he has mowed 29 lawns?
In the diagram below, BC is an altitude of ABD. To the nearest whole unit, what is the length of CD?
Answer:
Actually the answer is 56, so D.
Step-by-step explanation:
To the nearest whole unit, the length of CD is approximately 4 units.
Given Information:
In triangle ABD, BC is an altitude (perpendicular) from point B to side AD.
We need to find the length of CD.
Approach:
Since BC is an altitude, triangle BCD is a right triangle with BC as one of its legs and BD as its hypotenuse.
We can use the Pythagorean theorem to relate the lengths of BC, CD, and BD.
Pythagorean Theorem: The Pythagorean theorem states that in a right triangle:[tex][ \text{Hypotenuse}^2 = \text{Leg}_1^2 + \text{Leg}_2^2 ][/tex]
Application to Triangle BCD:
Let’s denote the length of CD as (x).
BC is given as 30 units.
BD can be expressed as (BD = AB + AD), where AB is the length of the other leg.
Using Triangle ABC:
Triangle ABC is also a right triangle.
We have AC = 16 units (given).
Using the Pythagorean theorem for triangle ABC: [tex][ AB^2 + BC^2 = AC^2 \ AB^2 + 30^2 = 16^2 \ AB^2 + 900 = 256 \ AB^2 = 256 - 900 \ AB^2 = -644 ][/tex]
Since we cannot have a negative side length, we discard this solution.
Using Similar Triangles:
Notice that triangle BCD is mathematically similar to triangle ACE.
The coefficient of similarity is evident from the side CE.
We can set up the following proportion: [tex][ \frac{BC}{CD} = \frac{AC}{CE} \ \frac{30}{x} = \frac{16}{CE} \ CE = \frac{16x}{30} ][/tex]
Finding BD:
We know that (BD = AB + AD).
Since we couldn’t find AB directly, we express it in terms of CE:[tex][ AB = AC - CE = 16 - \frac{16x}{30} = \frac{480 - 16x}{30} ][/tex]
Now, we can find BD: [tex][ BD = AB + AD = \frac{480 - 16x}{30} + 16 = \frac{480 + 480 - 16x}{30} = \frac{960 - 16x}{30} ][/tex]
Applying the Pythagorean Theorem to Triangle BCD: [tex][ BD^2 = BC^2 + CD^2 \ \left(\frac{960 - 16x}{30}\right)^2 = 30^2 + x^2 \ 960^2 - 32x \cdot 960 + 256x^2 = 900x^2 + 900 \cdot 30^2 \ 960^2 - 32x \cdot 960 = 900x^2 - 900 \cdot 30^2 \ 960^2 + 900 \cdot 30^2 = 932x^2 \ x^2 = \frac{960^2 + 900 \cdot 30^2}{932} \ x \approx 3.75 ][/tex]
To the nearest whole unit, the length of CD is approximately 4 units.
When Emma was born, she weighed 3.2 kilograms. In 2 months, she weighed
5.15 kilograms.
How much did Emma gain in her first 2 months?
a dragongfly traveled at a rate of 35 miles per hour for 2.5 hours .what distance did the dragonfly travel?
The GCF of the numbers in the expression (32 + 16) is . The numbers left inside the parentheses after factoring out the GCF are and .
Answer:
The answer is :
2 and 1
Step-by-step explanation:
The GCF means greatest common factor between given numbers.
The GCF of the numbers in the expression (32 + 16) is 16.
Factor each with a common factor of 16:
[tex](16\times2+16\times1)[/tex]
After factoring out 16, we have:
[tex]16(2+1)[/tex]
So the answer is :
2 and 1
Sketch each parabola using the given information.
vertex (3, 6), y-intercept 2
Use the substitution method to solve the system of equations. 2x - y = 10 3x - 2y = 8
Answer:
x=12, y=14
Step-by-step explanation:
[tex]2x - y = 10[/tex]
Solve the equation for y. Subtract 2x from both sides
[tex]- y = -2x+10[/tex]
Divide both sides by -1
[tex]y=2x-10[/tex]
Substitute 2x-10 for y in the second equation
[tex]3x - 2(2x-10)= 8[/tex]
[tex]3x - 4x+20= 8[/tex]
[tex]-1x+20= 8[/tex]
Subtract 20 from both sides
[tex]-1x= -12[/tex]
Divide both sides by -1
x= 12
[tex]y=2x-10[/tex]
Substitute 12 for x
[tex]y=2(12)-10=14[/tex]
y=14
$800,000 if your rate of return is 5.3% compounded monthly
If you deposit the amount you need to achieve your goal in 20 years, how much will your savings be worth after 10 years?
the ordered pair for an x-intercept has an x-value of 0 A.True or False
The ordered pair for an x-intercept has an x-value of 0 has some value of x and it has zero value for y, So it is a False statement.
What is the equation of line?The equation of a straight line is a relationship between x and y coordinates, The general equation of a straight line is y = mx + c, where m is the slope of the line and c is the y-intercept.
Given statement,
the ordered pair for an x-intercept has an x-value of 0
we can see in graph that when line intersect the x axis, the x coordinate of that point is known as x-intercept,
suppose, we have one line , y = 3x+3
so when we draw graph for it,
and if we see x-intercept
it will come out as, 0 = 3x+3 ⇒ x = -1
It is clear that value of x is not zero
hence, the given statement is false
To know more about Line check:
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7x-5y=4; what does x and y equal
How many grams are in 40 hectograms
There are 4000 grams in 40 hectograms.
To convert from hectograms to grams, you need to know that there are 100 grams in 1 hectogram.
Therefore, to find out how many grams are in 40 hectograms, you can use the conversion factor:
40 hectograms * 100 grams/hectogram = 4000 grams
So, there are 4000 grams in 40 hectograms.
To learn more about `hectograms; -
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Camille Keegan sells lamps for $105.55 that cost her $75.00. Camille's percent of markup based on the selling price is:
Markup = $105.55 - $75 = $30.55. Percentage markup based on selling price = $30.55 / $105.55 * 100% = 28.94%
Camille's percent of markup based on the selling price is calculated by finding the difference between the selling price and the cost price, dividing by the selling price, and then multiplying by 100. The calculation reveals that the markup percentage is approximately 28.94%.
Explanation:The question asks us to calculate Camille Keegan's percentage of markup based on the selling price of the lamps. The markup is the difference between the selling price and the cost price. To find the percentage of markup based on the selling price, we use the formula: (Markup / Selling Price) × 100. First, we find the markup by subtracting the cost price from the selling price, which is $105.55 - $75.00 = $30.55. Then we divide the markup by the selling price: $30.55 / $105.55. Finally, we multiply the result by 100 to get the percentage of markup based on the selling price.
Step-by-step calculation:
Therefore, Camille's percent of markup based on the selling price of the lamps is approximately 28.94%.
if the point (x, –1) is on the unit circle, what is the value of x?
Answer:
0^2 (–1)2 = 1.
Step-by-step explanation:
Can a cubic equation have 3 complex roots? 3 real roots? ...?
Final answer:
A cubic equation can have either three real or three complex roots (including a real root and a pair of complex conjugate roots), determined by its discriminant. Complex roots arise in pairs due to the conjugate root theorem, ensuring that the coefficients of the equation remain real.
Explanation:
A cubic equation, which is an equation of the form ax^3 + bx^2 + cx + d = 0, can indeed have 3 complex roots or 3 real roots, depending on the discriminant and the nature of the coefficients. According to the Fundamental Theorem of Algebra, every cubic equation has three roots in the complex number system, which includes real numbers as a subset.
If the discriminant is positive, the cubic equation has three distinct real roots. If the discriminant is zero, the equation has a multiple root and all its roots are real.
Equilibrium problems in mathematics may require using cube roots when finding the solution, and utilizing the correct functions on a calculator is vital for these calculations. This could be in applied sciences like chemistry or physics, where cubic equations may arise.
Eric sells shirts. It costs him $100 to buy all the shirts and $10 to print designs on the shirts. Eric sells each shirt for $4. So far Eric has sold 20 shirts. Eric uses an equation to calculate his total profit.
What is the slope of the equation modeling this situation?
To find the slope of the equation modeling Eric's situation, subtract the total cost from the selling price per shirt, resulting in a loss of $106 per shirt sold.
The slope of the equation modeling Eric's situation can be calculated as follows:
Profit per shirt = Selling price per shirt - Total cost per shirtProfit per shirt = $4 - ($100 + $10)Profit per shirt = $4 - $110 = -$106The slope, which represents the profit per shirt, is -$106, indicating a loss of $106 for each shirt sold.
square root of 85 is between what two consecutive number