Answer:
9 + i
Step-by-step explanation:
You just simplify by combining the real and imaginary parts of each expression.
Hope this helps you!!
If x = 1, y = 7, and z = 15, determine a number that when added to x, y, and z yields
consecutive terms of a geometric sequence. What are the first three terms in the
geometric sequence?
You're looking for a number w such that the numbers
{1 + w, 7 + w, 15 + w}
form a geometric sequence, which in turn means there is a constant r for which
7 + w = r (1 + w)
15 + w = r (7 + w)
Solving for r, we get
r = (7 + w) / (1 + w) = (15 + w) / (7 + w)
Solve this for w :
(7 + w)² = (15 + w) (1 + w)
49 + 14w + w ² = 15 + 16w + w ²
2w = 34
w = 17
Then the three terms in the sequence are
{18, 24, 32}
and indeed we have 24/18 = 4/3 and 32/24 = 4/3.
A hot air ballon is hovering 94 meters above the ground and begins to assend at a rate of 8 meters per second Let y be the height of the balloon in meters seconds after it begins to assend. Write an equation in slope-intercept form that models the height of the balloon. And how high is the ballon after 25 seconds?
Hi
let's call X amount of second going and Y the height reach by the ballon.
so Y=8X+94
f(x) = 8X+94
If you want to know how high will the ballon be in 25 seconds, remplace X by 25 and do the math. Have fun .
8 thousand+7tens=6thiusand+. tens
Answer:
207 tens
Step-by-step explanation:
If you mean
8,000 + 70 = 6000 + X tens
then it should be 207 tens
3 and 4 are complementary
Complementary angles are those whose sum is 90° hence angles 3 and 4 will not be complementary angles but they will have adjacent angles so it will be true.
What is an angle?An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.
The identical endpoint of the two rays—known as the vertex—is referenced as an angle's sides.
In another word, the angle is the measurement of the angular distance for example for linear motion we have a meter inch but for angular rotation, we don't have the measurement so the angle is useful to measure the angular rotation.
Given,
Angle 3 and angle 4 are only two angles of a single line
So,
∠3 + ∠4 = 180°
So they will be supplementary angle not complimentary angle.
Angle 3 and 4 are adjacent angle because they are neighbors of each other.
Hence, they will not be complementary angles but will be the adjacent angle.
For more about the angle
brainly.com/question/13954458
#SPJ5
In a high school graduating class of 300, 200 students are going to college, 40 are planning to work full-time, and 80 are taking a gap year.
a. These are mutually exclusive events.
b. These are not mutually exclusive events.
c. You should add their individual probabilities.
d. None of the above are true.
The problem solving plan identifies steps to organize your information. Which of the following answer choices are included in the steps to organize your information?
A. Organize the problem and find the question.
B. Solve the problem and change your strategy if necessary.
C. Write the facts, organize your thoughts and define your strategy.
D. Organize the steps and underline the question.
c.write the fact,organize your thoughts and define your strategy.
Answer:
c
Step-by-step explanation:
A right triangle has sides 20 and 48. Use the Pythagorean Theorem to find the length of the hypotenuse
Answer: Let the length of the hypotenuse be x
Applying the Pythagorean theorem we have :
x²=20²+48²
⇒x²=2704
⇒x=52( ∀ x >= 0 )
Step-by-step explanation:
Let assume the hypotenuse(longest side of right triangle) be x
By Pythagoras theorem
[tex] \bf \large \longrightarrow \: {c}^{2} \: = \: {a}^{2} \: + \: {b}^{2} [/tex]
c = xa = 20b = 48Applying Pythagoras theorem
[tex] \bf \large \implies \: {x}^{2} \: = \: {20}^{2} \: + \: {48}^{2} [/tex]
[tex]\bf \large \implies \: {x}^{2} \: = \:400 \: + \: 2304[/tex]
[tex]\bf \large \implies \: {x}^{2} \: = \:2704[/tex]
[tex]\bf \large \implies \: \sqrt{x} \: = \: \sqrt{2704} [/tex]
[tex]\bf \large \implies \: \: x \: = \: 52[/tex]
Hence , the length of hypotenuse is 52.
answer no explantion pls i need asap
Answer:
Below.
Step-by-step explanation:
Area = 5(x + 3)
= 5x + 15
Perimeter = 2(x + 3) + 2(5)
= 2x + 6 + 10
= 2x + 16.
Solve the equation.
1. For parentheses:
Distribute
4-2(x+7) = 3(x+5)
2. If necessary:
Combine Terms
3. Apply properties:
Add Subtract
Multiply
Divide
4. To start over:
Reset
Answer:
x = -5
Step-by-step explanation:
4-2(x+7) = 3(x+5)
Distribute
4 - 2x-14 = 3x+15
Combine like terms
-2x-10 = 3x+15
Add 2x to each side
-2x-10 +2x =3x+2x+15
-10 = 5x+15
Subtract 15 from each side
-10-15 = 5x+15-15
-25 = 5x
Divide by 5
-25/5 = 5x/5
-5 =x
a) Show that the equation 2 x + 3 cos x + e^x = 0 has a root on the
interval (-1,0)
b) Use the Bisection method to find the solution of 2 x + 3 cos x +
e^x = 0. accurate with in 10-3. On (-1,0). (Use four digits-Rounding)
a) The equation has a root in the interval (-1,0)
b) The solution of [tex]2x+3cos(x)+e^{x}=0[/tex] by using the Bisection Method is x=0.9977 accurate within [tex]10^{-3}[/tex]
a) The intermediate zero theorem (Bolzano's Theorem) tells us that whenever you have a continuous function in a given interval and the extremes of the functions on this interval have oposite signs, then there must be a zero in between those extreme values.
A formal definition of this theorem is written like this:"If a function f on the closed interval [a,b] is a continuous function and it holds that f(a)>0 and f(b)<0 or f(a)<0 and f(b)>0, then there is at least one x-value such that f(x)=0"
So basically we need to evaluate the given equation for both extremes of the interval x=-1 and x=0, if they return results opposite in sign, then there must be a zero in that interval, so let's evaluate the function for x=-1:
[tex]2x+3cos(x)+e^{x}[/tex]
[tex]2(-1)+3cos(-1)+e^{-1}=-0.0112[/tex]
Let's now test for x=0
[tex]2x+3cos(x)+e^{x}[/tex]
[tex]2(0)+3cos(0)+e^{0}=4[/tex]
So notice we ended up with two values -0.0112 and 4. One is positive and the other is negative, therefore there must be a zero in that interval.
b) The zero is located at x=-0.9977
The idea of the bisection method is to find values for x in the middle of two x-values that return opposite sign answers when evaluated on the given function. So we can start with the extremes of the given interval:
x=-1 and x=0
so we find the value in the middle by using the following formula:
[tex]mid-value=\frac{x_{1}+x_{2}}{2}[/tex]
so we get:
[tex]mid-value=\frac{-1+0}{2}[/tex]
mid-value=-0.5
Next, we evaluate the given function for that value:
[tex]2(-0.5)+3cos(-0.5)+e^{-0.5}=2.2393[/tex]
Since we got a positive answer, we now find the midpoint between -0.5 and -1 (which was the last x-value that returned a negative answer) so we get:
[tex]mid-value=\frac{-1-0.5}{2}[/tex]
mid-value=-0.75
Next, we evaluate the given function for that value:
[tex]2(-0.75)+3cos(-0.75)+e^{-0.75}=1.1674[/tex]
and we repeat the process until que get to the desired accuracy. I uploaded a table that has the corresponding iterations and its answers. There were 14 iterations done until we got to the final answer x=-0.9977.
Learn more about the intermediate zero theorem here:
https://brainly.com/question/13154408?referrer=searchResults
If the white rod is 1/3, what color is the whole??
Answer:
brown
Step-by-step explanation:
it might be brown because it compelled
Find the quotient of 90 over -10
90/-10
= 9/-1
= -9
So, -9 is the quotient.
4) Daily tickets to Six Flags cost $50 each.
Variable #1:
What is the variable
Answer:
Amount of tickets
Step-by-step explanation:
The variable is the amount of tickets purchased because that is the only thing that changes, according to the statement that says that daily tickets are $50.
Use the discriminant to determine the number of real solutions to the equation 3m ^ 2 = - 6
Hi,
no need to use discriminant for that.
3(m)^2 = -6
m^2 = -6/3
m^2= -2
in R, there is no
solution as a square can not be negative.
PLEASE HELP
Identify the first five terms of the sequence in which a, = 3n2 - 1.
Step-by-step explanation:
you cannot just put the actual numbers in and calculate ?
and you can't provide the correct problem statement, as it seems.
I assume you mean
an = 3n² - 1
a sequence starts with a1, so, n>=1
a1 = 3×1² - 1 = 3-1 = 2
a2 = 3×2² -1 = 3×4 - 1 = 12 - 1 = 11
a3 = 3×3² - 1 = 3×9 - 1 = 27 - 1 = 26
a4 = 3×4² - 1 = 3×16 - 1 = 48 - 1 = 47
a5 = 3×5² - 1 = 3×25 - 1 = 75 - 1 = 74
there, that is all there is to it. you really needed help with that ?
Which of the following theorems verifies that A DEF - AXZY?
O A. LL
B. HA
C. HL
D. AA
HA
Step-by-step explanation:See In Triangle DEF and Triangle XZY
[tex]\because\begin{cases}\sf \angle E=\angle Z=90° \\ \sf \ FD\sim XY=Hypotenuse\end{cases}[/tex]
Hence
[tex]\sf \Delta DEF\sim \Delta XZY(Angle-Angle)[/tex]
The theorems that verify that Δ DEF ~ Δ XZY is AA theorem of similarity.
What are similar triangles?Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion.
Given that, two triangles, Δ DEF and Δ XZY, we need to find a theorem that will verify that, Δ DEF and Δ XZY are similar,
So, we have, ∠ X = 40°,
Therefore, ∠ Y = 90°-40° = 50°
Now, we get,
∠ Y = ∠ F = 50°
∠ E = ∠ Z = 90°
We know that,
if two pairs of corresponding angles are congruent, then the triangles are similar.
Therefore, Δ DEF ~ Δ XZY by AA rule
Hence, the theorems that verify that Δ DEF ~ Δ XZY is AA theorem of similarity.
Learn more about Similar triangles click;
https://brainly.com/question/14926756
#SPJ7
(-4/9)*3×(-27/20)*4=
(-4/9)*3×(-27/20)*4= 7.2
Step-by-step explanation:
here's the answer to your question
Payton took a friend for a birthday dinner. The total bill for dinner was $44.85 (including tax and a tip). If Payton paid a 19.5% tip, what was his bill before adding the tip?
(Round your answer to the nearest cent.)
$
Number
Answer:
The answer closest to 36.10425. So 36.10 or 36.1
Step-by-step explanation:
x = 44.85 ( 1 - 0.195) = 36.10425
If this helps, it would be nice if 5 stars are given, and a brainliest :)
The amount of the bill before adding the amount of tip is evaluated being of $37.53 approx.
How to find the percentage from the total value?Suppose the value of which a thing is expressed in percentage is "a'
Suppose the percent that considered thing is of "a" is b%
Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).
Thus, that thing in number is
[tex]\dfrac{a}{100} \times b[/tex]
For this case, we can assume the amount of bill without tip being A.
Then, as given, Payton gave 19.5% tip (tip is given assumingly on A), then:
Total price of the bill = Bill amount before tip + Tip
44.85 = A + (19.5 % of A)
(we don't write symbols like of currency generally in equations, and understand it from context(which is dollars here))
44.85 = A + (19.5 % of A)
or
[tex]44.85 = A + \dfrac{A}{100} \times 19.5\\\\\text{Multiplying 100 on both the sides}\\\\4485 = 100A + 19.5A\\4485 = 119.5A\\\\\text{Dividing both the sides by 119.5}\\\\\dfrac{4485}{119.5} = A\\\\37.53 \approx A\\\\A \approx 37.53 \: \rm \text{(in dollars)}[/tex]
Thus, the amount of the bill before adding the amount of tip is evaluated being of $37.53 approx.
Learn more about percent here:
https://brainly.com/question/11549320
Write down the missing number number 86 493 -...... =8420
Answer:
78,073
Step-by-step explanation:
Subtract 8,420 from 86,493...86,493-8,420=78,073 is the answer
Double check by using inverse operations...78,073+8,420=86,493
It is correct, as I ended up with 86,493, the starting number of the equation.
if f(x)=x+7 and 9(x)=1/x-13 what is the domain of (f•g)(x)
Answer:
The only limitation is x≠0
The interval notation is (-∞,0)∪(0,∞)
Step-by-step explanation:
Set up the expression.
[tex](x+7)*(\frac{1}{x}-13)[/tex]
Multiply using FOIL.
[tex](x*\frac{1}{x})+(x*-13)+(7*\frac{1}{x})+(7*-13)[/tex]
[tex]1-13x+\frac{7}{x}-91[/tex]
[tex]-13x+\frac{7}{x}-91[/tex]
Find the Domain.
The only limitation is x≠0
The interval notation is (-∞,0)∪(0,∞)
what is the importance of mathematics?
hurry
What is the measure of the unknown angle?
Image of a straight angle divided into two angles. One angle is forty two degrees and the other is unknown.
Answer:
x = 138
Step-by-step explanation:
A straight line is 180
x+ 42 = 180
X = 180-42
x = 138
The domain of a function is always equal to which one of the following options?
A. all possible output values of the function
B. the range of the function
C. all possible input values of the function
D. all real numbers
Answer:
C. all possible input values of the function
Step-by-step explanation:
Answer:
C is right
Step-by-step explanation:
domain is f(x)=x^2 is all real numbers but domain g(x)=1/x is all real numbers except for 0 which is x but domains and the rang can be the same also
Use the properties of exponents to simplify the expression: y^(y3)2
please explain in detail!! ty
because y^3 is raised to the power of two, we will have to multiply the exponents rather than adding them.
By distributing the power of 2, we will get y^2(6).
Because now the exponents are being multiplied, we can just add them to get y^8. The other y has a power of 1, so we'll just add the power of that y as well to get y^9.
summary:
multiply exponents if they are being raised to a power.
add exponents if they are being multiplied, and only add them if they have the same base (in this case, both the bases of the exponents are y, so we can add them)
I need help answering this question thank guys
Answer:
b
Step-by-step explanation:
the square root of 8 is 2 and the square root of 18 is 4.5 and both simplified is 4/9.
Aslo did this last week.
3. Solve the system of equations using the elimination method.
5x + 2y = 9
-5x + 4y = 3
please give detailed steps!!
Answer:
x = 1
y = 2
Step-by-step explanation:
5x + 2y = 9
-5x + 4y = 3
==> 6y = 12 ==> y = 12/6 ==> y = 2.
we replace y by its value in the first or the second equation, so will have:
5x + 2×2 = 9
5x + 4 = 9
5x = 5
x = 1
Mr. Jerome has an outstanding balance of $12000 on his credit card. The interest rate on the card is 12% he intends to pay off
the card in 2 years. Find the APR on the card.
The price of an item has been reduced by 70%. The original price was $30. What is the price of the item now?
Answer:
$9
Step-by-step explanation:
30*(100%-70%)=9
Answer:
9
Step-by-step explanation:
Take the original price
Multiply by the discount percent
30 *70%
30 *.70
21
The discount is 21 percent
Subtract this from the original amount
30-21
9
Plz help and explain if this is a parallelogram
Answer:
It is a parallelogram!
Step-by-step explanation:
This is because it has four sides and all the sides have parallel lines if that makes sence.
What is the common ratio between successive terms in the sequence?
1.5, 1.2, 0.96, 0.768,...
0 0.8
-0.3
0 0.3
O 0.8
Answer:
[tex]1.5,1.2,0.96,0.768[/tex]
Common ratio between successive terms
[tex]=\frac{1.2}{1.5}[/tex]
[tex]=0.8[/tex]
OAmalOHopeO
The value of the common ratio between successive terms in the sequence is,
⇒ 0.8
What is Geometric sequence?An sequence has the ratio of every two successive terms is a constant, is called a Geometric sequence.
Given that;
The sequence is,
⇒ 1.5, 1.2, 0.96, 0.768,...
Hence, The value of the common ratio between successive terms in the sequence is,
⇒ 1.2 / 1.5
⇒ 12/15
⇒ 0.8
Thus, The value of the common ratio between successive terms in the sequence is,
⇒ 0.8
Learn more about the geometric sequence visit:
https://brainly.com/question/25461416
#SPJ7
