What is the name of a number that can be written in the form a+bi where a and b are nonzero real numbers?
Answer:
We are talking about Complex numbers.
Considering [tex]\mathbb{C}[/tex] as the set of Complex numbers, we have
[tex]\Bbb{C}=\{a+bi\ : a, b \in\ \Bbb{R}\}[/tex]
A complex number is a number of the form [tex]a+bi[/tex]
as [tex]i^2=-1[/tex]
please help me find the nth term of this sequence 0, 3, 8, 15, 24
Answer:
80
Step-by-step explanation:
0, 3, 8, 15, 24, 35, 48, 63, 80 which is the nth term
first step you have to find how many steps the sequence was going with.
examples= from 0 to 3 the steps were 3
=from 3 to 8 the steps were 5
= from 8 to 15 the steps were 7
you will recognize that the steps the sequence is going with is odd numbers.
so you will use the odd numbers until you find what you need. which leads you to 80 which is the nth number in the sequence.
Answer:
80
Step-by-step explanation:
Which expression can be used to find the surface area of the following triangular prism? *picture of a triangular prism* Choose 1 answer: (Choice A) 24+24+ 120+160+20024+24+120+160+20024, plus, 24, plus, 120, plus, 160, plus, 200 (Choice B) 24+20024+20024, plus, 200 (Choice C) 24+24+200+120+12024+24+200+120+12024, plus, 24, plus, 200, plus, 120, plus, 120 (Choice D) 48+48+120+160+20048+48+120+160+200
Answer:
A. 24+24+120+160+200
Step-by-step explanation:
Surface area of the triangular prism= addition of the area of each shape that forms the prism
There are two triangles
Area of a triangle=1/2*base*height
=1/2*8*6
=1/2*48
=24
Area of two triangles=24+24
There are 3 rectangles with different dimensions
Back rectangle=length×width
=20×6
=120
Bottom rectangle=length ×width
=20x8
=160
Top rectangle=length × width
=20×10
=200
Surface area =Area of two triangles + Back rectangle + Bottom rectangle + Top rectangle
=24+24+120+160+200
Please help me with this.
Answer:
h(3)=20
Step-by-step explanation:
h(3)=h(3-2)*h(3-1)=h(1)*h(2)=-10*-2=20
Answer:
20
Step-by-step explanation:
h(1) = -10
h(2) = -2
h(n) = h(n-2) * h(n-1)
Let n=3
h(3) = h(3-2) * h(3-1)
= h(1) * h(2)
= -10 * -2
= 20
- The water rate for Columbus Ohio
is $1.98 per 750 gallons of water.
What is the water bill for a resident
who used 27,000 gallons?
Divide total amount used by the amount in the rate:
27,000 / 750 = 36
Multiply that number by the rate:
36 x 1.98 = 71.28
The bill is $71.28
If f(x) = x2 – 2x and g(x) = 6x + 4, for which value of x does (f+g)(x) = 0?
O -4
O-2
O 2
O 4
Answer:
x = -2
Step-by-step explanation:
If you have any questions about the way I solved it, don't hesitate to ask ;)
The value of the function (f+ g)(x) = 0 then x = -2.
What is Function?A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
Given:
f(x) = x² - 2x and g(x) = 6x + 4
As, (f+g)(x) = 0
x² - 2x + 6x + 4 = 0
x² + 4x + 4 =0
x² + 2x + 2x + 4 = 0
x(x+2) + 2 (x +2 )= 0
(x + 2)(x+2) = 0
(x+ 2)²= 0
x+ 2= 0
x = -2
Learn more about function here:
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How does it do? thank you very much
sorry this subject is physic.
Find the first, fourth, and eighth terms of the sequence. A(n) = −5 ∙ 2x − 1
Answer:
The answer is option AStep-by-step explanation:
The rule for the sequence is
[tex]A(n) = 5. {2}^{x - 1} [/tex]
where x is the number of terms
For the first term
x = 1
That's
[tex]A(1) = 5. {2}^{1 - 1} [/tex]
[tex]A(1) = 5. {2}^{0} [/tex]
A(1) = 5(1)
A(1) = 5For the fourth term
x = 4
[tex]A(4) = 5. {2}^{4 - 1} [/tex]
[tex]A(4) = 5. {2}^{3} [/tex]
A(4) = 5(8)
A(4) = 40For the eighth term
x = 8
[tex]A(8) = 5. {2}^{8 - 1} [/tex]
[tex]A(8 ) = 5. {2}^{7} [/tex]
A(8) = 5(128)
A(8) = 640Hope this helps you
Answer:
The first option.
Step-by-step explanation:
The first term of the sequence would be...
A(1) = -5 * 2^(1 - 1)
= -5 * 2^0
= -5 * 1
= -5
The fourth would be...
A(4) = -5 * 2^(4 - 1)
= -5 * 2^3
= -5 * 8
= -40
The eighth would be...
A(8) = -5 * 2^(8 - 1)
= -5 * 2^7
= -5 * 128
= -640
So, the correct answer is the first option.
Hope this helps!
can somewon help i need help
Answer:
1875 cm3
Step-by-step explanation:
20 * 20 * 5 - (5 * 5 * 5) = 1875 cm3
Answer:
1,875
Step-by-step explanation:
Help, please show work
Answer:
132
Step-by-step explanation:
If US bisects the angle then
BUS = SUL
2x+10 = 3x-18
Subtract 2x from each side
2x+10 -2x = 3x-18-2x
10 = x-18
Add 18 to each side
10+18 =x
28 =x
We want to find BUL
BUL = BUS + SUL
2x+10 + 3x-18
5x-8
5*28 -8
140-8
132
Answer:
m<BUL=132
Step-by-step explanation:
Since US bisects <BUL, we know that <BUS ≅ <SUL
This is based on the angle bisector definition.
Hence, we can set up an equation to solve for x.
<BUS≅<SUL
2x+10=3x-18
Subtract 10 from both sides
2x+10-10=3x-18-10
2x=3x-28
Subtract 3x from both sides
2x-3x=3x-3x-28
-x=-28
Divide both sides by -1
x=28
m<BUL is the sum of m<BUS and m<SUL
m<BUL=m<BUS+m<SUL
m<BUS=2x+10
m<SUL=3x-18
Plug it in
m<BUL=2x+10+3x-18
Combine like terms
m<BUL=5x-8
Plug in 28 for x
m<BUL=5(28)-8
m<BUL=140-8
m<BUL=132
Directions: Calculate the percent increase or decrease between the starting and ending
quantities below. Round your answer to one decimal place.
1. Start: 3
End: 10
Answer:233.333%
Step-by-step explanation:
1. 10-3=7 subtract end by start
2.7/3=2.333 divide difference by absolute value of start
32.333x100=233.333% multiply by 100 if negative its decreasing if positive it increasing
hoped this helped
Find the volume. Show work plz
Answer:
[tex]93\frac{1}{3}[/tex] [tex]yd^{3}[/tex]
Step-by-step explanation:
The volume of a pyramid is:
[tex]V=\frac{lwh}{3}[/tex] (basically saying that you multiply the length, width, and the height together and then you divide that by 3)
Now, let's do the first part.
8 × 5 × 7 = 280
Now, let's divide.
280 ÷ 3 = 93 1/3
That's your answer!
Hope that helps and maybe earns a brainliest!
Have a great day! :)
PLEASE HELP ME WITH THIS DS-9JF-9EJFWEF
Trish entered a problem on her calculator that gave her this result on the screen: “0.1894528...”. Would this decimal be considered a repeating decimal? Why or why not?
The decimal 0.1894528 is not a repeating decimal.
What is the decimal number?The accepted method for representing both integer and non-integer numbers is the decimal numeral system. Decimal notation is the term used to describe the method of representing numbers in the decimal system. The numbers are first in fractions and then divided by the number to give a decimal number.
The given decimal number is “0.1894528. In the decimal number if the numbers are repeating then it is called the repeating decimal number if the numbers are not repeating then it is called a nonrepeating decimal number. Here the given decimal is nonrepeating decimal.
Therefore, the decimal 0.1894528 is not a repeating decimal.
To know more about decimal numbers follow
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The hanger image below represents a balanced equation. Find the value of r that makes the equation true.
Step-by-step explanation:
R is 4 times so the equation will be
32 = 4r
32/4 = r
8 = r
I know how to find the distance of two coordinates but not three could someone help me on this??
What is the equation that is perpendicular to the line y=2x-3 and passes through the point (-6,5)? Show all of your work.
Answer: y=(-1/2)x+5.5
Step-by-step explanation:
y=2x+3
This equation is in the slope-intercept form y=mx+b
m is the slope.
b is the y-intercept, the value of y when x=0.
m=2
The slope of the perpendicular line is -1/2.
(y-y1)=m(x-x1)
(y-4)=(-1/2)(x-3)
y-4=(-1/2)x+1.5
add 4 to both sides
4+y-4=(-1/2)x+1.5+4
y=(-1/2)x+5.5
Answer:
y = -1/2x + 2
Step-by-step explanation:
The slope of a perpendicular line will be the opposite reciprocal (opposite sign, and reciprocal)
The line's slope is 2, so the perpendicular line's slope will be -1/2.
Now, we know part of the equation: y = -1/2x + b
Plug in the point given:
5 = -1/2(-6) + b
5 = 3 + b
2 = b
Now, we can plug in b into the equation:
y = -1/2x + 2
Vince and 11 of his friends went out for pizza on Saturday night to celebrate Vince’s birthday. The cost of the pizza and soft drinks before sales tax and tip was $47.96. What is the amount of sales tax for the bill if the rate is 7%? Show your work.
Step-by-step explanation:
Since the original price is $47.96 and bill rate is 7%, $47.96 × 1.07 ≈ $51.32
Answer:
$51.32
The amount of sales tax for the bill if the rate is 7% will be $3.36.
What is the percentage?The quantity of anything is stated as though it were a fraction of a hundred.
Vince and 11 of his friends went out for pizza on Saturday night to celebrate Vince’s birthday.
The cost of the pizza and soft drinks before sales tax and tip was $47.96.
Then the amount of sales tax for the bill if the rate is 7% will be
⇒ $47.96 x 0.07
⇒ $3.36
More about the percentage link is given below.
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Maria’s office is located at (–7,–5) on the coordinate plane. Her home is located at (4,–6) and the supermarket is located at (–2,–6). When returning back from the office, she first goes to the supermarket to buy some groceries, and then goes back home. Find the total distance she traveled from her office to home. A. 146−−−√+6 units B. 26−−√+6 units C. 82−−√+6 units D. 202−−−√+6 units
Answer:
B. 6 + √26
Step-by-step explanation:
1. Make a right triangle using the line that goes from office to supermarket.
2. Use pythagorean thereom to find the distance of the longest side.
3. FInd the distance of the line segment going from supermarket to Marias House.
4. Add them together to get 6 + √26.
Answer:
B.
Step-by-step explanation:
1. Make a right triangle using the line that goes from office to supermarket.
2. Use Pythagorean theorem to find the distance of the longest side.
3. Find the distance of the line segment going from supermarket to Maria's House.
4. Add them together to get 6 + √26.
PLEASE HELP! Will mark brainliest! Find the slope of each line:
Answer:
6/7
Step-by-step explanation:
First, find two points that fall on the line and are coordinates on the graph.
The two points I found were (3,5) and (10,11).
Use the slope formula to come up with the slope.
[tex]slope = \frac{change in y}{change in x}[/tex]
slope = [tex]\frac{11-5}{10-3}[/tex] = [tex]\frac{6}{7}[/tex]
Two joggers start from different locations and simultaneously begin heading toward each other. One of the joggers jogs 19mph, while the other jogs 17mph. If the two joggers are 324 miles apart how many hours will it take before they meet?
Answer:
errror
Step-by-step explanation:
Find an equation of the line passing through the pair of points. Write the equation in the form Ax+By = C.
(-4,7), (-5,-2)
Choose the equation of the line in the form Ax + By = C.
Answer:
-9x + y = 43
Step-by-step explanation:
We can put the equation into y = mx + b form first, then change it to Ax + By = C
First, we can find the slope by doing rise/run (y2 - y1) / (x2 - x1)
(-2 - 7) / (-5 + 4)
-9/-1 = 9
We can put this into the equation y = mx + b, along with another point, to find b:
y = mx + b
7 = 9(-4) + b
7 = -36 + b
43 = b
Now, we know the equation will be y = 9x + 43, and we can rearrange this:
Subtract 9x from both sides:
-9x + y = 43 will be the equation of the line
The parallelogram shown below has an area of 120 units^2 . Find the missing height.
Answer:
Step-by-step explanation:
133
What are the solutions of the equation x4 – 5x2 – 14 = 0? Use factoring to solve.
Answer:
[tex]x=\pm 7\text{ or } x=\pm i\sqrt{2}[/tex]
Step-by-step explanation:
We have the equation:
[tex]x^4-5x^2-14=0[/tex]
Since this is in quadratic form, we can consider using u-substitution. Thus, we will let:
[tex]u=x^2[/tex]
Then by substitution:
[tex]u^2-5x-14=0[/tex]
Now we can solve normally. Factor:
[tex](u-7)(u+2)=0[/tex]
Zero Product Property:
[tex]u=7\text{ or } u=-2[/tex]
Back-substitute:
[tex]x^2=7\text{ and } x^2=-2[/tex]
Take the square root of both sides. Since we are taking an even-root, we will need to add plus-minus:
[tex]x=\pm 7\text{ and }x=\sqrt{-2}[/tex]
Therefore, our solutions are:
[tex]x=\pm7\text{ and } x=\pm i\sqrt{2}[/tex]
Determine whether each sequence is a geometric sequence. If yes, then state the common ratio.
1, -4, 16, -64, ...
Answer:
This is a geometric sequence with a common ratio of -4
Step-by-step explanation:
Take the second term and divide by the first term
-4/1 = -4
Take the third term and divide by the second term
16/-4 = -4
Take the fourth term and divide by the third
-64/16 = -4
This is a geometric sequence with a common ratio of -4
what is the right answerrrr??
Answer:
C. Two lines are perpendicular if they have opposite slopes
Step-by-step explanation:
Hey there!
Well 2 lines that are perpendicylar have reciprocal slopes for example,
2 and 1/2 are 2 slopes that are perpendicular.
Hope this helps :)
Graph the solution of 7x+3<−4 or 2x−3≥9
Answer:
Step-by-step explanation:
To do this you would simplify both sides.
For the first one:
[tex]7x+3<-4[/tex]
[tex]7x<-7[/tex] (subtract 3 from both sides)
[tex]x<-1[/tex] (divide 7 from both sides)
and for the second one:
[tex]2x-3\geq 9[/tex]
[tex]2x\geq 12[/tex] (add 3 to both sides)
[tex]x\geq 6[/tex] (divide 2 from both sides)
When you graph these they will look like these pictures
Answer:
[tex]x<-1[/tex] and [tex]x\geq6[/tex]
Step-by-step explanation:
[tex]\bf 7x+3<-4[/tex]
You must subtract 3 from both sides.
[tex]7x+3-3<-4-3\\[/tex]
After subtracting, we got
[tex]7x<-7[/tex]
Let's make it into a fraction and divide
[tex]\frac{7x}{7}<\frac{-7}{7}[/tex]
Now we got the answer
[tex]x<-1[/tex]
[tex]\bf 2x-3\geq 9[/tex]
You must add 3 to both sides.
[tex]2x-3+3\geq 9+3[/tex]
After adding, we got
[tex]2x\geq 12[/tex]
Let's make it into a fraction and divide
[tex]\frac{2x}{2} \geq \frac{12}{2}[/tex]
Now we got the answer
[tex]x\geq 6[/tex]
Your answer is [tex]\bf x<-1[/tex] or [tex]\bf x\geq 6[/tex].
In a certain country, the heights and depths of a road are measured in relation to sea level. Sea level has a value of 0. The lowest point of the country lies at −8 feet. The highest point of the country lies at +107 feet. Which of the following statements best describes the lowest and the highest points?
The lowest point is 8 feet above sea level, and the highest point is 107 feet below sea level.
The lowest point is 8 feet below sea level, and the highest point is 107 feet above sea level.
The lowest point is 8 feet below sea level, and the highest point is 107 feet above the lowest point.
The lowest point is 8 feet above sea level, and the highest point is 107 feet below the lowest point.
A negative value would mean it is below sea level. A positive value would be above sea level.
-8 is 8 feet below sea level
+107 is 107 feet above sea level.
The answer Is:
The lowest point is 8 feet below sea level, and the highest point is 107 feet above sea level.
Answer:
Step-by-step explanation:
The lowest point is 8 feet below sea level, and the highest point is 107 feet above sea level.
Explain how to solve 5x2-3x = 25 by completing the square. What are the solutions?
Answer:
x= 3 +√509/10
Or
x= 3 - √509/10
Step-by-step explanation:
Given:
5x2-3x = 25
Using completing the square method of solving quadratic equation
Step 1: Factor out the coefficient of the x^2 term.
5(x^2 - 3x/5) = 25
Step 2: Add a number that would complete the square inside the parenthesis and also add this to the other side of the equation.
Take (1/2) of (3/5)
1/2 × 3/5
= 3/10
Square 3/10
We have, 9/100
We have,
5(x^2 - 3x/5 + 9/100) = 25 + 9/100
Step 3: Simplify
x^2 - (3/5)x + 9/100 = 25 + 9/100
5(x^2 - 3x/5 + 9/100) = 5 + 9/20
Step 4:
factor the right side
(x - 3/10)^2 = 509/100
Take both roots
√ (x - 3/10)^2 = √509/100
x - 3/10 = ±√ [509/100]
x = [ 3 ±√509 ] / 10
x= 3+√509/10
Or
x= 3 - √509/10
Jen go to the skate park every other day Terry go to skate park every third date Carlos goes to the skate park only on Mondays and Tuesdays today is Monday, June 3 and all the kids are at the skate park on what day would they all be at the skate park again
Answer: Tuesday, July 9 (correct me if I'm wrong)
Step-by-step explanation:
Jen goes every other day, so she goes every odd day.
Terry goes every third day, so Jen and Terry go together every six days.
Six days later is Sunday June 9, then Saturday June 15, then Friday Jun 21, then Thursday June 27, then Wednesday July 3.
Carlos only comes Mondays and Tuesday, so the next six days would be Tuesday July 9.