Answer: z = 3, -1.5 + 1.5[tex]\sqrt{3}[/tex]i, -1.5 - 1.5[tex]\sqrt{3}[/tex]i
Step-by-step explanation:
A cubic equation will have three solutions. This equatoin will give us one real solution. We will also have two complex solutions. These are solutions that involve "imaginary numbers" and will utilize the value i. We will write the equation in standard form and factor it.
z³ - 27 = 0
(z - 3)(z² + 3z + 9) = 0
The first factor gives us z = 3, because 3 - 3 = 0. Now, we will look at when the second factor equals 0. Let us complete the square.
z² + 3z + 9 = 0
(z² + 3z + 2.25) + 9 - 1.5 = 0
(z² + 3z + 2.25) + 6.75 = 0
(z + 1.5)² + 6.75 = 0
Lastly, we can continue solving. We will subtract 7.5 from both sides of the equation and then take the square root of both sides. Then, we will subtract 1.5 from both sides of the equation and simplify the radical. [tex]i=\sqrt{-1}[/tex].
(z + 1.5)² = -6.75
z + 1.5 = ±[tex]\sqrt{6.75}[/tex]i
z = -1.5 ±1.5[tex]\sqrt{3}[/tex]i
Answer:
z = 3, -1.5+1.5√3i, -1.5-1.5√3i
Step-by-step explanation:
You want the solutions to the equation z³ = 27.
CubicA cubic equation has three solutions. This one has one positive real solution and two complex conjugate solutions.
We can rewrite the equation to standard form, then factor the difference of cubes.
z³ -27 = 0
(z -3)(z² +3z +9) = 0
The first factor will be zero when z = 3, so that is one solution.
The second factor will be zero when ...
(z +1.5)² +6.75 = 0 . . . . . . . complete the square
(z +1.5) = ±√(-6.75) = ±√(-27/4) = ±(3/2)√(-3) . . . subtract 6.75; square root
z = -1.5 ±1.5√3i
The three solutions to the equation are ...
z = 3z = -1.5+1.5(√3)iz = -1.5-1.5(√3)i<95141404393>
Find the equation that has a slope of -1/8 and passes through the point (0,-4)
A. Y= 1/8x
B. Y=1/4x-4
C. Y=-1/8x-4
Answer:
Option C
Step-by-step explanation:
Given :-
The slope of the line is -1/8The line passes through (0,-4) .And we need to find out the equation of the line .We are here given slope and a point . So we can use the slope point form of the line. As ,
[tex]:\sf\implies m ( x - x_1)= y - y_1 \\\\\sf:\implies \dfrac{-1}{8}(x -0)= y - (-4) \\\\\sf:\implies \dfrac{-x}{8}= y +4 \\\\\sf:\implies \boxed{ \sf\red{y = \dfrac{-x}{8}-4}}[/tex]
Hence the option C is correct.
The problem solving is on the image, 6th grade
Amanda is 10 years old. She wants to
start saving for college. She saves $450
this year and wants to double her money every year after. Write an equation to model this situation. How much money will she have when she is 18 years old?
Answer:
7200
Step-by-step explanation:
450 x 2 = 900
900 x 8 =7200
According to the National Association of Colleges and Employers, the mean salary for a new college graduate is $45,327. A small college wants to know if the mean salary of their most recent graduates is greater than $45,327. A random sample of 10 recent graduates from the small college was selected and the mean and standard deviation of the salary for those graduates was found. With all conditions for inference met, a significance test was conducted and a p-value of 0.045 was obtained. Which of the following statements is the most appropriate conclusion using a significance level of a = 0.05?
(A) There is convincing statistical evidence that the mean salary for all recent college graduates from the small college is greater than $45,327.
(B) There is convincing statistical evidence that the mean salary for the sample of 10 college graduates from the small college is greater than $45,327.
(C) There is not convincing statistical evidence that the mean salary for all recent college graduates from the small college is greater than $45,327
(D) There is not convincing statistical evidence that the mean salary for the sample of 10 college graduates from the small college is greater than $45,327.
(E) There is not convincing statistical evidence that the graduates from this college will always eam more than $45,327.
Answer:
(A) There is convincing statistical evidence that the mean salary for all recent college graduates from the small college is greater than $45,327.
Step-by-step explanation:
According to the National Association of Colleges and Employers, the mean salary for a new college graduate is $45,327. A small college wants to know if the mean salary of their most recent graduates is greater than $45,327.
At the null hypothesis, we test if the mean salary is the expected salary of $45,327, that is:
[tex]H_0: \mu = 45327[/tex]
At the alternate hypothesis, we test if the salary is greater than the expected salary of $45,327, that is:
[tex]H_1: \mu > 45327[/tex]
With all conditions for inference met, a significance test was conducted and a p-value of 0.045 was obtained. Which of the following statements is the most appropriate conclusion using a significance level of a = 0.05?
The p-value of the test if 0.045 < 0.05, which means that there is sufficient evidence to accept the alternate hypothesis, that is, to conclude that the mean salary for all recent college graduates from the small college is greater than $45,327.
This means that the correct answer is given by option A.
Marie grew 10 plants with 2 seed packets. How many seed packets does Marie need to have a total of 15 plants in her backyard? Solve using unit rates
Answer:
he need 3 seeds to plant a 15 plant
The diameter of a pipe is 6 cm. If the pipe is 26 cm long, what is its volume?
Use the value 3.14 for π , and round your answer to the nearest whole number.
Be sure to include the correct unit in your answer.
i think this question answer is 734.76cm^3
Parallelogram JKLM shown below is going to be rotated 270° clockwise to create J'K'L'M'. Which rule describes this transformation? K M F. (x, y) = (-y, x)
G. (x, y) = (-x. -Y)
H. (x, y) = (y, -x)
J. (x,y) → (-x, y) c
Answer:
F. (x, y) = (-y, x)
Step-by-step explanation:
270º clockwise transformation:
The 270° clockwise transformation of a point (x,y) is:
(x,y) -> (-y,x)
Thus, as we just apply the rule in this conceptual question, the correct answer is given by:
F. (x, y) = (-y, x)
Which interval is the graph of the parent absolute vale function f(x)=|x| decreasing
Answer:
(-∞,0)
Step-by-step explanation:
The graph of ƒ(x) = |x| is below.
The function is decreasing on (-∞,0) .
A is wrong. The function both decreases and increases on (-∞,∞).
C is wrong. The function is decreasing on (-6,0), but that is only a portion of the interval.
D is wrong. the function is increasing on (o,∞)
A coffee cup keeps coffee at 175 degrees for 2 hours each quarter hour after that the coffee loses 15 degrees of warmth what will the temperature of the coffee be after 4 hours who ever actually helps get brainliest and random answers will be reported.
Answer:
I believe the answer is 55 degrees.
Plz don't report me if i'm wrong.
Step-by-step explanation:
HELP PLZZ TIMED TEST 5 MIN LEFT!
Step-by-step explanation:
answer: 135 degrees for the missing side
Can anyone help ?
Kim rolls a dice and flips a coin.
a) Calculate the probability that she
gets a 2 and a head.
b) Work out the probability that she
gets an even number and a tail.
What would b be
Answer:
a) 1 / 12
b) 1 / 4
Step-by-step explanation:
The events are independent since they do not affect each other. The total probability of two independent events is the product of the probabilities of the two events.
a) When rolling a die, there are 6 outcomes, the numbers 1 - 6. There is only 1 outcome where you can get a 2. Therefore, the probability of rolling a two is 1/6.
When flipping a coin, there are two ways it can land: heads or tails. And there is one outcome with heads. The probability of getting head would be 1 / 2.
To find the the total, you multiply the probabilities of the two events: 1 / 6 * 1 / 2 = 1 / 12
b) As stated before, when rolling a die, there are 6 outcomes, the numbers 1 - 6. There are 3 outcomes where she can roll an even number: the numbers 2, 4, or 6. So, the probability of rolling an even number is 3 / 6 or 1 / 2.
When flipping a coin, there are two ways it can land: heads or tails. And there is one outcome with tails. The probability of getting tails would be 1 / 2.
Now, you multiply the two probabilities to get the total probability: 1 / 2 * 1 / 2 = 1 / 4
There are 4 consecutive integers that sum to 394. What is the least of these integers?
Answer: 97
Step-by-step explanation:
394 / 4 = 98.5, so the 4 numbers must be around 98.5.
97 + 98 + 99 + 100 = 394
PLEASE HELP ALL LINKS GIVEN WILL BE REPORTED
Answer:
- 13
Step-by-step explanation:
[tex]log \frac{ {a}^{6} {b}^{6} }{ {c}^{7} } \\ \\ = log( {a}^{6} {b}^{6} ) - log {c}^{7} \\ \\ = 6log \: a + 6log \: b - 7log \: c \\ \\ = 6(2) + 6( - 3) - 7(1) \\ \\ = 12 - 18 - 7 \\ \\ \therefore \: log \frac{ {a}^{6} {b}^{6} }{ {c}^{7} } = - 13[/tex]
Me puedes ayudar es para hoy porfavor
Answer:
mira a las base de las figuras y busca cual base matchs con la figuras de la figura prinsipal
Step-by-step explanation:
como el cono va con la del toda la izquierda de la de la mitad
Subtract 8−2x from 3−6x .
Answer in this format:
Answer:
[tex]4x + 5[/tex]
Step-by-step explanation:
[tex](8 - 2x) - (3 - 6x)[/tex]
[tex]8 - 2x - 1 \times 3 - (6x)[/tex]
[tex]8 - 2x - 3 + 6x[/tex]
[tex] - 2x + 5 + 6x[/tex]
[tex]4x + 5[/tex]
Hope it is helpful....Pls help I’ll brainlest
▬▬▬▬▬▬▬▬▬▬▬▬▬▬
Law of Exponents ⸔
→ aᵐ × aⁿ = aᵐ＋ⁿ
→ aᵐ ÷ aⁿ = aᵐ－ⁿ
→ (aᵐ)ⁿ = aᵐⁿ
→ aᵐ × bᵐ = (ab)ᵐ
→ a⁰= a¹
→ aᵐ/bᵐ = (a/b)ᵐ
Question's solution ⸔
→ 5⁰
→ 1 [a⁰ = 1]
▬▬▬▬▬▬▬▬▬▬▬▬▬▬
If a circle has an area of 144 sq. cm, what will be its area if the radius is reduced to one third?
Answer:
Step-by-step explanation:
1/3; 33.33 or 0.33
Find the common ratio of the geometrie sequence 6, 24, 96,
Answer:
4
Step-by-step explanation:
To find the common ratio, take the second term and divide by the first term
24/6 = 4
Check by taking the third term and dividing by the second term
96/24 = 4
The common ratio is 4
x = 15, x = 5; (0.75)
Answer:
12
Step-by-step explanation:
12 is 75 of 15 %^%^%^%^^^___<<<7<
how do i do this? i don’t know how
The 3 inside angles of a triangle need to equal 180 degrees.
Add the 3 together to equal 180:
X + 2x + x+ 14 = 180
Combine like terms:
4x + 14 = 180
Subtract 14 from both sides:
4x = 166
Divide both sides by 4
X = 41.5
Answer:
Fraction form: x = 83/2
Decimal form: x = 41.5
Step-by-step explanation:
The 3 angles inside the triangle will always add up to 180 degrees.
So that gives us the equation:
x + 14 + x + 2x = 180
Combine like terms:
4x + 14 = 180
Subtract on both sides:
4x = 166
Divide:
41.5
Kim got a "40" in a class and I make a 70 on a test. How much does the grade goes up?
Answer:
30%
Step-by-step explanation:
The angle of elevation to the top of the Empire State Building in New York is found to be 11° from the ground at a distance of 5281 feet from the base of the building. Using this information, find the height of the Empire State Building in feet. Use the dimensions given in the diagram to give an equation and solve. Round two decimal places.
Answer:
The height of the building is of 1026.52 feet.
Step-by-step explanation:
This situation is modeled by a right triangle, in which the length of the opposite side to the angle of 11º is the height of the building, while the length of the adjacent side is of 5281 feet.
Tangent:
In a right triangle, the tangent of an angle is the length of the opposite side divided by the length of the adjacent side.
In this question:
[tex]\tan{(11)} = \frac{x}{5281}[/tex]
[tex]x = 5281*\tan{(11)}[/tex]
Using a calculator, we have that the tangent of 11 degrees is: 0.1944. Thus:
[tex]x = 5281*\tan{(11)} = 5281*0.1944 = 1026.52[/tex]
The height of the building is of 1026.52 feet.
I own 1 mini fish and 2 giant fish each giantfish weighs 3 times as much as minfish. If my mini fish eats my two giantfish, then how many times more weight will my mini fish have now than before
Answer: 6 pounds
Step-by-step explanation:
Answer:
The mini fish would weigh 6 times its original amount hypothetically but if we were talking realistically then you would need more information to figure that out. But even then there's no way of determining the specific weight.
Step-by-step explanation:
what is the value of x ?
Answer:
x = 19
Step-by-step explanation:
The two angles form a right angle
A right angle has a measure of 90 degrees
Thus, x + 14 + 3x = 90
^This is the equation we will use to solve for x
x + 14 + 3x = 90
step 1 combine like terms
x + 3x = 4x
we now have 4x + 14 = 90
step 2 subtract 14 from each side
90 - 14 = 76
14 - 14 cancels out
we now have 76 = 4x
step 3 divide each side by 4
4x / 4 = x
76 / 4 = 19
we're left with x = 19
How are these triangles congruent ?
- HL
- AAA
- ASA
Question 17 (1 point)
Bicycle, a company that makes dice, is looking to change the size of the dice they produce. The current dice have edge lengths of 5mm, and the company wants to increase them to 15mm. How will the volume of the dice be effected if this change is made?
Question 17 options:
30x larger
3x larger
10x larger
27x larger
Answer:
3x
Step-by-step explanation:
If a fair coin is tossed 4 times, what is the probability, to the nearest thousandth, of getting exactly 3 tails?
Answer:
000.3
Step-by-step explanation:
The probability of getting exactly 3 tails is 0.25 If a fair coin is tossed 4 times, what is the probability.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
We have a coin if it is tossed 4 times.
Then the probability of getting exactly 3 tails is:
[tex]=\rm 4 C_3(\frac{1}{2} )^3\times (1-\frac{1}{2} )^1[/tex]
[tex]=\rm 4\times \frac{1}{16}[/tex]
= 1/4
= 0.25
Thus, the probability of getting exactly 3 tails is 0.25 If a fair coin is tossed 4 times, what is the probability.
Learn more about the probability here:
brainly.com/question/11234923
#SPJ2
A soccer ball is kicked from the top of a 64 ft building into the air at an initial speed of 48 ft/sec. Its flight as a functions of time can be modeled by: h(t)=−16t2+48t+64. After how many seconds, will the soccer ball hit the ground (h=0)?
Answer:
t = 4 seconds
Step-by-step explanation:
The height of a soccer ball as a function of time is given by :
[tex]h(t)=-16t^2+48t+64[/tex]
We need to find the time when the ball hit the ground i.e. h = 0
Put h = 0 in above equation. So,
[tex]-16t^2+48t+64=0\\\\16(-t^2+3t+4)=0\\\\-t^2+3t+4=0[/tex]
It is a quadratic equation such that,
t = -1 s and t = 4 s
Neglecting -1 s, the ball will hit the ground after 4 seconds.
A marathon had 567 runners registered. Of these runners, about 0.7% completed the race in under 2 h 12 min. How many runners completed the race in this time?
Answer:
3
Step-by-step explanation:
Can somebody help me seriously
Answer: b
Step-by-step explanation:
I don't know but i am right