Answer:
[tex]x=\frac{3}{2} - i\frac{\sqrt{7}}{2}[/tex]
[tex]x=\frac{3}{2} + i\frac{\sqrt{7}}{2}[/tex]
Step-by-step explanation:
We can use the quadratic formula to solve the equation:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
In this case, a = 1, b = -3, and c = 4. Substituting these values into the formula, we get:
x = (3 ± sqrt((-3)^2 - 4(1)(4))) / 2(1)
x = (3 ± sqrt(9 - 16)) / 2
x = (3 ± sqrt(-7)) / 2
Since the square root of a negative number is not a real number, the solutions to the quadratic equation are complex numbers. Therefore, the answer is:
[tex]x=\frac{3}{2}+i\frac{\sqrt{7} }{2}[/tex]
[tex]x=\frac{3}{2} - i\frac{\sqrt{7}}{2}[/tex]
HELP I NEED THIS ASAP 20 POINTS
PLEASE ANSWER THESE 2 MATH QUESTIONS!!!
They are not the best factors to use because 12 cannot be simplified further into a perfect square. It is better to factor 48 into perfect squares and simplify each square root separately.
What is factors?Factors can be classified as prime or composite. A prime factor is a factor that is a prime number, meaning it is only divisible by 1 and itself. For example, the prime factors of 12 are 2 and 3. A composite factor is a factor that is not a prime number, meaning it has more than two factors. For example, 4, 6, and 12 are composite factors of 12.
Let's examine the factors 4 and 12 to see if they can be used to simplify the square root of 48:
4 is a perfect square, and its square root is 2. However, 12 is not a perfect square, and its square root cannot be simplified further.
We can write 48 as 4 x 12, so the square root of 48 can be simplified as the product of the square root of 4 and the square root of 12, or 2√12.
However, this is not the simplest form of the square root of 48. We can further simplify √12 by factoring it into perfect squares: √12 = √(4 x 3) = √4 x √3 = 2√3.
Therefore, the simplest form of the square root of 48 is 2√3, not 2√12.
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Given a circle with center (– 3, 6) and radius 5, what is an equation of the circle?
[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{-3}{h}~~,~~\underset{6}{k})}\qquad \stackrel{radius}{\underset{5}{r}} \\\\[-0.35em] ~\dotfill\\\\ ( ~~ x - (-3) ~~ )^2 ~~ + ~~ ( ~~ y-6 ~~ )^2~~ = ~~5^2\implies (x+3)^2+(y-6)=25[/tex]
13
Write
as a decimal. If necessary, use a bar to indicate which digit or group of digits repeats.
9
The equivalent decimal value for the fraction 13/9 is [tex]1.4\bar{4}[/tex]
Fractions are a way to represent a part of a whole, and they consist of two parts: the numerator and the denominator.
To convert a fraction into a decimal, we need to divide the numerator by the denominator. In the case of 13/9, we can do the following:
13 ÷ 9 = 1.444444...
The result is a decimal that goes on forever without repeating. However, we can use a bar to indicate which digit or group of digits repeats. In this case, the digit "4" repeats, so we can write:
13/9 = [tex]1.4\bar{4}[/tex]
The bar over the digits 4 indicates that they repeat infinitely.
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Complete Question:
For the given fraction 13 /9, Write as a decimal. If necessary, use a bar to indicate which digit or group of digits repeats.
1. Rewrite the following without negative exponents and simplify: (a)−(34)−4
(b)(6y−53xy2)3
(c)x−9y−14x2x−8
(d)u−2u2u0u3
`u−2u2u0u3 = u^3`
(a) 1 / 34 * 4 = 4 / 34
(b) 6y * (1 / (53xy2))3 = 6y / 53xy2
(c) x * (1 / 9y) * (1 / 14x2) * (1 / (x−8)) = x / (9y * 14x2 * (x−8))
(d) (u−2 * u2) / (u0 * u3) = u−4 / u3
(a) Rewrite the given expression without negative exponents and simplify:(a)- (34)- 4Let us first use the law of exponents that says `(a^m)^n = a^(m*n)`The negative exponent `−4` means the denominator, so we can move the base `3` to the denominator and change the exponent to `+4`.Thus, `(a)−(34)−4 = a*(3^4) = 81a`Therefore, `(a)- (34)- 4 = 81a`(b) Rewrite the given expression without negative exponents and simplify:(b)(6y-5/3xy2)3Let us first use the law of exponents that says `(a^m)^n = a^(m*n)`We have to remove the negative exponent from `y^-5`, we can write it as `1/y^5`.Thus, `(6y-5/3xy2)3 = 6^3 * y^-15 * x^3 * y^6`Moving the base `y` with the negative exponent to the denominator and change the exponent to `+15`.Therefore, `(6y-5/3xy2)3 = 216x^3/ y^9`(c) Rewrite the given expression without negative exponents and simplify:(c) x-9y-14x2x-8We can rewrite `x^-9` as `1/x^9` and `x^-8` as `1/x^8`. Therefore, we get `(1/x^9 * y^-14 * x^2 * 1/x^8)`.Simplifying the above expression we get `(y^-14/x^15)`Therefore, `x-9y-14x2x-8 = y^-14/x^15` (d) Rewrite the given expression without negative exponents and simplify:(d) u−2u2u0u3Here we can observe that `u^0 = 1`. Hence, `u−2u2u0u3 = u^-2*u^2*1*u^3`We can simplify the expression by multiplying the coefficients and adding the exponents. Thus, `u^-2*u^2*1*u^3 = u^(2-2+3) = u^3`Therefore, `u−2u2u0u3 = u^3`
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A man received a 2% discount for paying his bill on time. If the discount amounts to Php 160 , how much was the original bill?
The original bill of the man can be calculated using the formula for discount, which is:
Discount = Original Price × Discount Rate
Given that the discount is Php 160 and the discount rate is 2%, we can rearrange the formula to solve for the original price:
Original Price = Discount ÷ Discount Rate
Original Price = Php 160 ÷ 2%
Original Price = Php 160 ÷ 0.02
Original Price = Php 8,000
Therefore, the original bill of the man was Php 8,000 before the 2% discount was applied.
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are 8,192 players in a Rock Paper Scissors tournament. In each round half the players ar d to find the number of players remaining in the tournament at the end of x rounds? f(x)=8192(0.05)^(x) B
Therefore, there would be 1024 players remaining in the tournament at the end of 3 rounds.
The function f(x) = 8192(0.05)^x represents exponential decay, where the number of players is decreasing by a factor of 0.05 in each round. However, in this tournament, the number of players is decreasing by a factor of 0.5 (half the players) in each round. Therefore, the correct function should be f(x) = 8192(0.5)^x.
To find the number of players remaining in the tournament at the end of x rounds, simply plug in the value of x into the function and solve.
For example, if we want to find the number of players remaining at the end of 3 rounds, we would plug in x = 3 and solve:
f(3) = 8192(0.5)^3
f(3) = 8192(0.125)
f(3) = 1024
Therefore, there would be 1024 players remaining in the tournament at the end of 3 rounds. Similarly, you can plug in any value of x to find the number of players remaining at the end of x rounds.
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An aircraft takes off and climbs at 10° to 30,000
ft, Find the ground distance travelled:
(Use 1 Nm = 6076 ft, sin 10° = 0.174 cos10°= 0.985
tan10° = 0.176)
To find the ground distance traveled by the aircraft, we can use the trigonometric function tangent. The tangent of an angle in a right triangle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the height of the aircraft (30,000 ft) and the adjacent side is the ground distance traveled (x).
Therefore, we can set up the following equation:
tan10° = 30,000/x
We are given that tan10° = 0.176, so we can substitute that value into the equation:
0.176 = 30,000/x
Next, we can cross-multiply and solve for x:
x = 30,000/0.176
x ≈ 170,455 ft
Finally, we can convert the ground distance traveled from feet to nautical miles using the conversion factor 1 Nm = 6076 ft:
170,455 ft * (1 Nm/6076 ft) ≈ 28.06 Nm
Therefore, the ground distance traveled by the aircraft is approximately 28.06 nautical miles.
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Precipitation for the month of march was 6 1/2 inches less than average. In April the precipitation was 2 3/8 inches less than average. How many inches below average was the precipitation for both march and April?
For both march and April the precipitation is [tex](4\frac{7}{16})[/tex] inches below the average.
Define Average?The term "average" refers to a central value that represents a set of numbers. There are different types of averages, such as the mean, mode and median.
Let's denote the average precipitation as "a".
In March, the precipitation was [tex]6\frac{1}{2}[/tex] inches less than the average. This can be expressed as:
March precipitation = [tex]a-6\frac{1}{2}[/tex]
In April, the precipitation was [tex]2\frac{3}{8}[/tex] inches less than the average. This can be expressed as:
April precipitation = [tex]a-2\frac{3}{8}[/tex]
To find the total precipitation below average for both March and April, we can add the two expressions:
March precipitation + April precipitation = [tex](a-6\frac{1}{2})[/tex] + [tex](a-2\frac{3}{8})[/tex]
Simplifying the expression, we get:
March precipitation + April precipitation = [tex](2a-8\frac{7}{8})[/tex]
So, after dividing by 2 in result the value will be, [tex](a-4\frac{7}{16})[/tex]
Therefore, the total precipitation below average for both March and April was [tex](4\frac{7}{16})[/tex] inches.
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The University of Iowa, prompted by a student who died while intoxicated, conducted an investigation of student drinking by randomly selecting 10 different classrooms and interviewing all the students in each of these groups. The type of sampling used is et vered ked out of A) Simple random sampling Flag B) Stratified random sample C) Cluster sampling isthion D) Systematic sampling
The type of sampling used by the University of Iowa in their investigation of student drinking is C) Cluster sampling.
Cluster sampling is a method where the population is divided into groups, or clusters, and a random sample of these clusters is selected for the study. In the case of the University of Iowa's investigation, the population was the entire student body and the clusters were the different classrooms. By randomly selecting 10 classrooms and interviewing all the students in each of these groups, the University of Iowa was using cluster sampling.
Therefore, the correct answer is C: cluster sampling.
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A person invested $3,600 in an account growing at a rate allowing the money to double every 8 years. Write a function showing the amount of money in the account after t years, where the annual growth rate can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage of growth per year, to the nearest hundredth of a percent.
A(t) = $3,600(1.125)t is the function that displays the balance of the account after t years, rounded to four decimal places.
Do you mean invested or vested?The definition of the word "invest" is to "expend money with the idea of attaining a profit or material consequence by putting it into financial plans, etc." A person is "vested" when they are "secured in their possession or allocated to a person," on the other hand. It can also imply outfitted with a vest, although that is unimportant just now.
A(t) = P(1 + r)t
where:
A(t) represents the balance of the account after t years.
P is the initial investment, $3,600, and r is the growth rate per year.
The number of years is t.
A(t) = $3,600(1 + 0.125)t
A(t) = $3,600(1.125)t
We can take the growth rate and subtract 1 to get the annual growth percentage, which we can then translate to a percentage as follows:
Percentage growth rate = (1.125 - 1) * 100% = 12.5%
So the account grows by approximately 12.5% per year.
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I NEED HELP ON THIS ASSAP!
Based on the information, we can infer that the second plan is the best for the bicycle company because it will cost less and will earn more.
How to identify the best alternative for the bicycle company?To identify the best alternative for the bicycle company, we must take into account the information on the cost of design and construction of the bicycles and the cost of labor and production.
In accordance with the above, we can infer that in alternative one the design and construction of the bicycle would be more expensive than alternative two. However, the production of each bicycle would be less.
Therefore, the best alternative would be option two because it requires less initial research and the product will cost more, so it would have a higher retail value, so the investment could be recovered much faster. .
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If log_x y = 4 which of the following is true?
Please
The equation log_x y = 4 can be written as y = x⁴ and the true, correct option is 1.
What is logarithmic rule?A base must be raised to a certain exponent or power, or logarithm, in order to produce a specific number. that is, b raised to x = n, in which case one writes x = log base b n. Scientists embraced logarithms immediately because of a number of advantageous characteristics that made complicated, time-consuming computations simpler. In specifically, by searching up each number's logarithm in a special database, adding the logarithms together, and then rechecking the table to discover the number with that computed logarithm, scientists could find the product of two integers m and n.
Given that, log_x y = 4 .
Using the logarithmic rule we have:
log_x y = 4
y = x⁴
Hence, the equation log_x y = 4 can be written as y = x⁴ and the correct option is 1.
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The diagram shows a shape made from two semicircles
The radius of the larger semicircle is 8 cm
8 crn
D
Work out the perimeter of the shape.
Give your answer in terms of .
Answer
Not drawn
accurately
cam
[3 marks]
Answer:
Step-by-step explanation:
big semicircle circumference=1/2*3.14*64
100.48cm
small semicircle circumference=1/2*3.14*16=25.12cm
total perimeter=125.6cm
Use long division, define each quotient
(3x^2- 3x + 5) ÷ (x - 6)
Answer:
(x - 6)(3x + 15) + 95
Step-by-step explanation:
Here's the long division of (3x^2 - 3x + 5) ÷ (x - 6):
3x + 15
--------------
x - 6 | 3x^2 - 3x + 5
- (3x^2 - 18x)
--------------
15x + 5
- (15x - 90)
------------
95
Therefore, the quotient is 3x + 15, and the remainder is 95.
The quotient represents the result of the division of the polynomial (3x^2 - 3x + 5) by the divisor (x - 6). In particular, the quotient 3x + 15 represents the linear polynomial that, when multiplied by the divisor x - 6, gives the dividend 3x^2 - 3x + 5.
In other words, we have:
(3x^2 - 3x + 5) = (x - 6)(3x + 15) + 95
The remainder 95 indicates that the division is not exact, and that there is a "leftover" term of 95 when we try to divide the polynomial (3x^2 - 3x + 5) by (x - 6).
how to solve 3 divided by 561 long division
Answer:
187
Step-by-step explanation:
how to do long division, you know how to start im assuming. then you then bring down and Divide, Multiply, Subtract, with the first number then bring the next number down and repeat that.
Answer:
187
Step-by-step explanation:
I personally just do multiplication whenever I can, but that's just me. Like for example I know 100 x 3 = 300 and 200 x 3 = 600. SO it has to be between 100 and 200.
150 x 3 = 450. So know it narrows it down to between 150 and 200.
175 x 3 = 525
180 x 3 = 540
185 x 3 = 555
190 x 3 =570
So now it's between 185 and 190.
Now I just need to do the following.
186 x 3 = 558
187 x 3 = 561
And there we have the answer.
some1 pls answer this pt.2 will give brainlist thingy
Answer: 8
Step-by-step explanation: (9-7)^3= 8
Answer: ? = 8
Step-by-step explanation: 2 x 2 x 2 = 8
Using a formula estimate the body surface area of a person whose height is 166cm and weighs 100kg. A. 2.29m^(2) B. 2.15m^(2) C. 55.9m^(2) D. 5.44m^(2)
The correct answer is B. 2.15m^(2). The estimated body surface area of the person is 2.15m^(2).
To estimate the body surface area of a person, we can use the Mosteller formula:
BSA = square root of [(height in cm x weight in kg)/3600]
Plugging in the given values for height and weight:
BSA = square root of [(166cm x 100kg)/3600]
BSA = square root of 1660000/3600
BSA = square root of 461.11
BSA = 2.15m^(2)
Therefore, the estimated body surface area of the person is 2.15m^(2). Hence, B is the correct answer.
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u/4>9 what is the answer?
Answer:
u>36
Step-by-step explanation:
u>36
9×4=36
so u>36
If the equation is true for all real numbers enter "All -4(6y+4)+19=12(-2y+5)-55
True. All real numbers satisfy the equation -4(6y+4)+19=12(-2y+5)-55.
The statement "If the equation is true for all real numbers enter 'All'" has been used to indicate that the given equation is true for all real numbers.
Given equation: -4(6y + 4) + 19 = 12(-2y + 5) - 55
Using distributive property, simplify both sides of the equation.
-24y - 16 + 19 = -24y + 60 - 55-24y + 3 = -24y + 5
By transposing -24y from the right-hand side of the equation to the left-hand side of the equation, we can simplify it as follows:
3 = 5
Since the above equation is always false for all real numbers, there is no solution. Therefore, we conclude that the given equation has no solution.
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estion 10 ate the answer choice Simplify each expressi (x^(2)-25x-24)/(6x+2x^(2))*(5x^(2))/(8-x)
Simplified each expression of (x²-25x-24)/(6x+2x²)*(5x²)/(8-x) is (-5x(x-24)(x-1))/(2(3+x)(x-8)).
To simplify the expression (x²-25x-24)/(6x+2x²)*(5x²)/(8-x), we need to factor the polynomials in the numerator and denominator and then cancel out any common factors.
First, let's factor the polynomials:
(x²-25x-24) = (x-24)(x-1)
(6x+2x²) = 2x(3+x)
(5x²) = 5x*x
(8-x) = -(x-8)
Now, let's plug these back into the expression and cancel out any common factors:
((x-24)(x-1))/(2x(3+x))*(5x*x)/(-(x-8))
= ((x-24)(x-1)*5x*x)/(2x(3+x)*-(x-8))
= ((x-24)(x-1)*5x)/(2(3+x)*-(x-8))
= (5x(x-24)(x-1))/(-2(3+x)(x-8))
Finally, let's simplify the expression by multiplying the constants:
= (-5x(x-24)(x-1))/(2(3+x)(x-8))
So the simplified expression is (-5x(x-24)(x-1))/(2(3+x)(x-8)).
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What is 1/5 x 11 because I don’t know
Answer: 2 1/5
Step-by-step explanation:
11= 11/1 x 1/5= 11/2= 2 1/5
364683-5794+8679*4/86.99
need help with 10 quick!!!!!!!
Answer:
28 7/12
Step-by-step explanation:
Can someone solve this for me please 6x+2y=26,3x-2y=10
Answer:
Step-by-step explanation: point form: (4,1)
x=4 , y=1
Find the area of the shaded regions. Give your answer as a completely simplified exact value in terms of π (no approximations).
The area of the shaded region is 7πcm²
What is area?The space enclosed by the boundary of a plane figure is called its area. The area of a figure is the number of unit squares that cover the surface of a closed figure. Area is measured in square units like cm² and m².
The area of a circle is expressed as πr²
area of the unshaded parts = 2× πr²
=2 (π × 1²)
= 2π cm²
area of the big circle = πr²
= π × 3²
= 9πcm²
area of the shaded part = 9π -2π
= 7π cm²
therefore the area of the shaded part is 7πcm²
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The cold drink you usually buy is on special offer today. The price has been reduced by R2 per can. This means that you can get 14 cans for the same price that you usually pay for 10. What is the usual price per can?
The price per can has been lowered by R2, making the standard can cost R7.
what is equation ?A mathematical assertion that establishes the equivalence of two expressions is known as an equation. It is made up of two sides, a left and a right side, separated by the equal sign (=). The equation, which is typically used to determine an unknown variable's value, requires that the values on both sides be equal. Exponents, logarithms, multiplication, division, addition, subtraction, and other mathematical operations can all be used in equations.
given
Let's say that the standard price per can is "x" Rand.
The revised price is (x-2) Rands if the price is decreased by R2.
The issue is that 14 cans are being offered for the customary price of 10 cans. Thus, we can construct the equation:
10x = 14(x-2) (x-2)
After finding x, we obtain:
10x = 14x - 28
-4x = -28
x = 7
The price per can has been lowered by R2, making the standard can cost R7.
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what is P{event }.Can you gave examples
P(event) represents the probability of an event occurring.
What is probability?Probability is a branch of mathematics that deals with the study of random events or experiments. It is the measure of the likelihood or chance that a particular event will occur. Probability is expressed as a number between 0 and 1, where 0 means that the event is impossible and 1 means that the event is certain to happen.
What are events?An event is a set of outcomes of a random experiment, and the probability of an event is the measure of how likely it is to occur.
Here are some examples:
Rolling a fair six-sided die: P(rolling a 3) = 1/6, since there is one outcome (rolling a 3) out of six possible outcomes.Flipping a fair coin: P(flip heads) = 1/2, since there is one outcome (flipping heads) out of two possible outcomes.Drawing a card from a standard deck of 52 cards: P(drawing a heart) = 13/52, since there are 13 hearts out of 52 cards.Selecting a random student from a class: P(selecting a male student) = number of male students / total number of students, where the probability depends on the gender balance of the class.Choosing a number from 1 to 10: P(choosing an even number) = 5/10 = 1/2, since there are five even numbers out of ten possible numbers.To know more about Probability,visit:
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Simplify the expression (yz)⁶
Answer:
[tex]y^{6} z^{6}[/tex]
Step-by-step explanation:
(yz)^6 is the same as:
yz * yz * yz * yz * yz * yz
which is the same as
[tex]y^{6} z^{6}[/tex]
Consider the regression equation » = 11.05 + 0.78x, that is estimated using a sample of 202 observations and where the standard error of the slope coefficient is 0.43. Which of
the following statements is true regarding the statistical significance of the slope
coefficient?
A. None of the above
B. It is significant at the 10% level
C. It is significant at the 5% level
D. It is significant at the 1% level
E. All of the above
The correct answer is C. It is significant at the 5% level.
To determine the statistical significance of the slope coefficient, we need to calculate the t-statistic for the slope coefficient and compare it to the critical value for the desired level of significance.
The t-statistic is calculated as:
t = (slope coefficient - hypothesized value) / standard error of the slope coefficient
In this case, the hypothesized value is 0 (no relationship between x and y) and the standard error of the slope coefficient is 0.43. So the t-statistic is:
t = (0.78 - 0) / 0.43 = 1.81
Now we need to compare this t-statistic to the critical value for the desired level of significance. For a two-tailed test with 202 - 2 = 200 degrees of freedom, the critical values are:
- 1.645 for the 10% level
- 1.96 for the 5% level
- 2.576 for the 1% level
Since the t-statistic (1.81) is greater than the critical value for the 10% level (1.645) but less than the critical value for the 5% level (1.96), we can conclude that the slope coefficient is significant at the 10% level but not at the 5% level. Therefore, the correct answer is B. It is significant at the 10% level.
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A survey of 50 young professionals found that they spent an average of $21.37 when dining out, with a standard deviation of $12.67. Can you conclude statistically that the population mean is greater than $23? Use a 95% confidence interval.
The 95% confidence interval is _____,_____. As $23 is _______ of the confidence interval, we ________ conclude that the population mean is greater than $23.
options for second blank space --> below the lower limit, within the limits, above the upper limits.
options for third blank space --> cannot, can.
The 95% confidence interval is (17.77, 24.97). As $23 is within the limits of the confidence interval, we cannot conclude that the population mean is greater than $23.
The 95% confidence interval can be calculated using the formula:
CI = x ± t(s/√n), where x is the sample mean, t is the t-score for the desired confidence level, s is the sample standard deviation, and n is the sample size.
For a 95% confidence level and a sample size of 50, the t-score is 2.009. Plugging in the given values, we get:
CI = 21.37 ± 2.009(12.67/√50) = 21.37 ± 3.60 = (17.77, 24.97)
Since $23 is within the limits of the 95% confidence interval (17.77, 24.97), we cannot conclude that the population mean is greater than $23.
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