Final answer:
To calculate i^3, we use the powers of i, where i = √-1. We find that i² = -1, and thus i³ = i² × i = -1 × i = -i.
Explanation:
The value of i to the power of 3, denoted as i3, can be determined by understanding the fundamental properties of the imaginary unit i, where i is defined as i = √-1. To find i3, we start by considering the powers of i:
i1 = i,
i2 = -1,
i3 = i2 × i = -1 × i = -i,
i4 = (i2)2 = (-1)2 = 1.
Therefore, the value of i3 is -i.
What are the roots of the polynomial equation x^3-6x= 3x^2-8? Use a graphing calculator and a system of equations.
–40, –4, 5
–5, 4, 40
–4, –1, 2
–2, 1, 4
x^3 -6x = 3x^2 -8
x^3 - 3x^2 -6x = -8
x^3 - 3x^2 -6x +8 = 0
now factor:
(x-4) (x^2+x-2) = 0
(x-4) (x-1)(x+2) = 0
the roots are 4, 1, -2
answer is the last one
Make a general statement about information is revealed by an unfactored polynomial compared to a factored polynomial
Please find the function rule and explain how you got it so it helps me understand better. I am SO bad with function rules. ;-;
What is the volume of this square pyramid?
384 cm³
288 cm³
192 cm³
96 cm³
The required volume of the square pyramid is 3[tex]84 cm$^3$[/tex]. The answer is option A.
What is volume?Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.
Here,
The formula for the volume of a square pyramid is:
[tex]$V = \frac{1}{3}Bh$[/tex]
Where B is the base area and h is the pyramid's height.
In this case, the base is a square with a side length of 12 cm, so its area is:
[tex]B = 12^2 = 144cm$^2$[/tex]
The height of the pyramid is 8 cm.
Plugging these values into the formula, we get:
[tex]V = \frac{1}{3}(144)(8) = 384$ cm$^3[/tex]
Therefore, the volume of the square pyramid is 3[tex]84 cm$^3$[/tex]. The answer is option A.
Learn more about Volume here:
https://brainly.com/question/1578538
#SPJ2
Determine whether the given triangles are similar. Justify your answer. If they are similar write a similarity statement. How do you do this?
Similar shapes may or may not have equal lengths
Triangles ABC and PRQ are similar by SSS
The corresponding sides on both triangles are:
AB = 8, and PQ = 6
AC = 12, and PR = 9
BC = 12, and QR = 9
Divide the corresponding sides, to determine the scale factor (k)
[tex]k = \frac{6}{8} = \frac{9}{12} = \frac{9}{12}[/tex]
Evaluate the quotients
[tex]k = 0.75 = 0.75 = 0.75[/tex]
Given that the scale factors are equal.
Hence, both triangles are similar by SSS
Read more about similar triangles at:
https://brainly.com/question/2644832
the equation of a quadratic function represented by the graph is y=a(x-3)^2-1. what is the value of a?
Bryan cuts a piece of cardboard in the shape of a trapezoid. The area is 43.5 square centimeters. If the bases are 6 centimeters and 8.5 centimeters long, what is the height of the trapezoid?
To find the height of the trapezoid, use the formula for the area of a trapezoid: A = ((b1 + b2) * h) / 2. Plug in the given values and solve for h.
Explanation:To find the height of the trapezoid, we can use the formula for the area of a trapezoid: A = ((b1 + b2) * h) / 2, where A is the area, b1 and b2 are the lengths of the bases, and h is the height. In this case, the area is given as 43.5 square centimeters, and the lengths of the bases are 6 centimeters and 8.5 centimeters. Plugging in these values, we get:
43.5 = ((6 + 8.5) * h) / 2
Simplifying the equation, we have:
87 = 14.5h
Dividing both sides by 14.5, we find:
h = 6 centimeters
Learn more about Finding the height of a trapezoid here:https://brainly.com/question/27831303
#SPJ12
Height of the trapezoid is 6 centimeters.
Area = (1/2) × (Base1 + Base2) × Height
Given the following values:
Area = 43.5 square centimetersBase1 = 6 centimetersBase2 = 8.5 centimetersWe can plug these values into the formula and solve for the height:
43.5 = (1/2) × (6 + 8.5) × Height
43.5 = (1/2) × 14.5 × Height
43.5 = 7.25 × Height
To isolate the height, divide both sides by 7.25:
Height = 43.5 / 7.25
Height = 6 centimeters
So, the height of the trapezoid is 6 centimeters.
Which is a correct classification for the triangle?
A. Acute triangle
B. Obtuse triangle
C. Equiangular triangle
D. Right angle
while on vacation, Erika bought 6 postcards, which was twice as many postcards as Nathan bought. Samantha bought 4 times as many postcards as Nathan. how many postcards did Samantha buy?
The number of postcards Samantha bought is 12.
What is an Equation?An equation is a mathematical statement that is formed when two algebraic expressions are equated using an equal sign.
Erika bought 6 postcards
Let the number of postcards Erika bought is given by x
Erika bought twice as many postcards as Nathan bought
Let the number of postcards Nathan bought is given by y
x = 2y
Samantha bought 4 times as many postcards as Nathan
Let the number of postcards Samantha bought is given by z
z = 4y
The value of x = 6, so
6 = 2y
y = 3
z = 4y
z = 12
Postcards bought by Samantha is 12.
To know more about Equation
https://brainly.com/question/10413253
#SPJ2
A single gram of a certain metallic substance has 0.52 gram of copper and 0.26 gram of zinc. The remaining portion of the substance is nickel. Ben estimated that 0.2 gram of nickel is in 1 gram of the substance. He used this to estimate the amount of nickel in 35 grams if substance. Find the result of Bens estimation strategy. Then find the exact amount of nickel in 35 grams of the substance.
In one gram of substance 0.22 grams of nickel is present. Then the amount of nickel in the 35 grams of the substance is 7.7 grams.
What are ratio and proportion?A ratio is an ordered couple of numbers a and b, written as a/b where b can not equal 0. A proportion is an equation in which two ratios are set equal to each other.
A single gram of a certain metallic substance has 0.52 grams of copper and 0.26 grams of zinc.
The remaining portion of the substance is nickel.
Let the gram of nickel be x. Then we have
x + 0.52 + 0.26 = 1
x = 0.22
0.22 grams of nickel.
Ben estimated that 0.2 gram of nickel is in 1 gram of the substance.
He used this to estimate the amount of nickel in 35 grams of the substance.
Then we have
→ 35 × 0.2 = 7
We know that in 1 gram the amount of nickel is 0.22 gram. Then er have
→ 35 × 0.22 = 7.7
The amount of nickel in the 35 grams of the substance is 7.7 grams.
More about the ratio and the proportion link is given below.
https://brainly.com/question/14335762
A monument in the shape of a right triangle sits on a rectangular pedestal that is 5 meters high by 11 meters long. The longest side of the triangular monument measures 61 meters.
Answer:65
Step-by-step explanation:
60 + 5 is 65
a 6lb watermelon costs $2.40 before a 30% discount. Which equation would allow you to find the discounted price of the watermelon?
The following circle graph represents how the Townsends spend their monthly income. What is the central angle measure of the section that represents "Savings"?
18°
36°
5°
9°
The circle graph represents how the Townsends spend their monthly income.
Total central angle of the circle is 360°
Townsend saves 5% of the monthly budget.
Therefore, the central angle measure of the section that represents "Savings" is 5% of the total central angle
= 5% of 360°
= 18°
The central angle measure of the section that represents "Savings" is 18°
Hope this helps ..!!
Thank you :)
Answer:
18˚
Step-by-step explanation:
The total amout is 360˚ and this small ooprtion is 18˚.
how do you solve u/6 > (with an underline underlining it) 3
plz help
its due tomorrow
There are 160 people in a grade. The ratio of boys to girls is 3 to 5. Which proportion can you use to find the number x of boys?
To find the number of boys, we can use the proportion 3/8 = x/160. Solving the equation, we find that the number of boys is 60.
Explanation:To find the number of boys, we can use the proportion:
3/8 = x/160
We know that the ratio of boys to girls is 3 to 5, which is equivalent to 3/8. Cross-multiplying the proportion, we get x = (3/8) * 160. Solving the equation, we find that the number of boys is 60.
Learn more about Finding the number of boys in a given grade here:https://brainly.com/question/34102719
#SPJ3
A cylinder has a radius of 12.2 inches and a height of 6.1 inches.
What is the approximate volume of the cylinder?
Use 3.14 for pi.
74.4 in³
148.8 in³
2850.9 in³
4961.2 in³
Answer:
It's C. 2850.8 in3
Step-by-step explanation:
A square with an area of 4 in² is dilated by a factor of 7. What is the area of the dilated square?
Which Value of t makes the following true -16+t<-32
Mr.holms used 4/5 of a carton of orange juice.he used equal amounts of leftover juice for two servings what fraction of the whole carton of juice did he use for each serving
What is the difference from 6z to z6
PLEASSSEEE HELPPPP BRAINLIEST REWARDED
Jordana drew the function below. Which statement correctly explains whether or not her function is linear?
Answer and step-by-step explanation:
The function is not linear because the graph is not a straight line.
A linear function has a graph that is a straight line; the rate of change is the same between consecutive points.
In this graph, the rate of change is different between different pairs of points. This is a parabola; this is not a linear function.
Answer:
it is not linear because its not a straight line
Step-by-step explanation:
gimme brainliest
A certain recipe calls for 2 1/3 cups of sugar, how much sugar is needed to make 1/3 of the recipe?
Write an expression that has four terms and simplifies to 16x+15
An expression that has four terms is equal to [tex]8(2x+1) +7[/tex] and simplifies to [tex]16x+15.[/tex]
What is an expression?" An expression is defined as the statement which relates the variable and the number using mathematical operation."
According to the question,
Given a simplified expression,
[tex]16x +15[/tex]
An expression that has four terms
[tex]8(2x +1) +7[/tex]
Four terms are [tex]8, 2x , 1, 7[/tex]
Simplify the expression we get,
[tex]8\times 2x + 8\times 1+ 7\\\\= 16x + 8 +7\\\\= 16x +15[/tex]
Hence, an expression that has four terms is equal to [tex]8(2x+1) +7[/tex] and simplifies to [tex]16x+15.[/tex]
Learn more about expression here
https://brainly.com/question/14083225
#SPJ2
Simplify the expression
To simplify this expression, you have to remember that when a number or a variable is raised to the negative exponent you have to reciprocate the number. In this expression, c^-8 will be reciprocated so it will become part of the numerator. Therefore, the final answer would be 12c^8/d^2.
Which of these best describes an undefined term?
A. A term that is a building block for other definitions in geometry
B. A clause in a conditional statement that begins with "then"
C. A statement that has already been proven to be true
D. A statement that is the opposite of an original statement
Answer:
A. A term that is a building block for other definitions in geometry.Step-by-step explanation:
In Geometry, undefined terms refer to concepts like point, line and plane. Which are concepts that cannot be defined, they are too intuitive. Undefined terms are always true, they cannot be prove because those concepts are too primitive.
It's important to know that Geometry develops another complex defintions from these undefined terms, beacuse point, line and plane are the fundamentals of Geometry.
Therefore, the right answer is A.
Other choices are just wrong, because undefined terms aren't condition statments, they cannot be proven and they aren't oppsite of an original statement.
The regular price of a smart phone is represented by x. When an upgraded phone is released, the new price is 25% more than the older model. The upgraded phone's price can be represented by which expression?
Answer:
1.25x
Step-by-step explanation:
Rotate the parallelogram 180° clockwise about point Q.
A.
Answer with explanation:
Given : A Parallelogram A B CD.
When the Parallelogram is rotated by an angle of 180° through point Q,
⇒The Answer can be explained in this way, when you rotate by an angle of 90° the two corresponding sides of Pre-Image and Image will be Perpendicular to each other , while you rotate by an Angle of 180°, the two corresponding sides of Pre-Image and Image will be Anti-Parallel to each other.
⇒By looking at the four options , the option in which Corresponding side of Preimage that is Parallelogram ABCD and after rotating through an angle of 180°,and Corresponding Side of Image that is Parallelogram A'B'C'D' are Anti-parallel to each other.
⇒Point Q , will lie on line joining from D to D'.
Option D
a product cost 48.50 for 75 feet was is my cost per inch
A school baseball team earned $3416.90 from selling 5716 tickets to their game. If grandstand tickets sold for 65 cents each and bleacher tickets sold for 40 cents each, how many of the bleacher tickets were sold?
find the missing number
9/10 minus blank = 1/5
The missing number in the equation 9/10 minus blank = 1/5 is 7/10. To find this, we converted 1/5 to the common denominator of 10, resulting in 2/10, and subtracted it from 9/10.
Explanation:To find the missing number in the equation 9/10 minus blank = 1/5, we need to subtract 1/5 from 9/10. To do calculations with fractions, it's essential to have a common denominator. In this case, the least common denominator for 10 and 5 is 10. We need to express 1/5 as 2/10 to match the denominator of 9/10.
Next, we subtract the two fractions:
9/10 - 2/10 = 7/10So, the missing number is 7/10, because 9/10 minus 7/10 equals 1/5. This result becomes clear with the common denominators, as we are able to subtract the numerators directly while keeping the denominator.
Final answer:
To solve for the missing number in the equation 9/10 minus blank equals 1/5, we find a common denominator, move like terms, and solve for x, yielding the missing number 7/10.
Explanation:
To find the missing number in the equation 9/10 minus blank equals 1/5, we need to isolate the blank (let's call it x). To do this, we'll move all known values to one side of the equation.
Start with:
9/10 - x = 1/5
Add x to both sides:
9/10 = x + 1/5
Now, find a common denominator which is 10 in this case, to combine the fractions. This gives us:
9/10 = (x ⋅ 10/10) + (2/10)
Keep in mind, the arithmetic of common denominators to simplify the equation.
Combine like terms:
9/10 = (10x + 2)/10
Multiply both sides by 10 to get rid of the denominator:
9 = 10x + 2
Subtract 2 from both sides:
7 = 10x
Finally, divide by 10:
x = 7/10
So, the missing number is 7/10.