Answers
Given the quadratic equation:
[tex]16x^2-24x-27=0[/tex]To find the solutions for the given equation you have to apply the quadratic formula:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]Where
a is the coefficient of the quadratic term
b is the coefficient of the x-term
c is the constant of the equation
For this equation, a= 16, b= -24, and c= -27, replace the values into the formula:
[tex]\begin{gathered} x=\frac{-(-24)\pm\sqrt[]{(-24)^2-4\cdot16\cdot(-27)}}{2\cdot16} \\ x=\frac{24\pm\sqrt[]{576+1728}}{32} \\ x=\frac{24\pm\sqrt[]{2304}}{32} \\ x=\frac{24\pm48}{32} \end{gathered}[/tex]Solve the addition and subtraction separately to determine both possible values of x:
-Addition:
[tex]\begin{gathered} x=\frac{24+48}{32} \\ x=\frac{72}{32} \\ x=\frac{9}{4} \end{gathered}[/tex]-Subtraction
[tex]\begin{gathered} x=\frac{24-48}{32} \\ x=-\frac{24}{32} \\ x=-\frac{3}{4} \end{gathered}[/tex]The solutions of the quadratic equation are x=9/4 and x=-3/4
Related Questions
The following formula is used to calculate the monthly payment on a personal loan.
P= PV.
i
1-(1+i)^-n
In this formula, n represents the
a. number of periods over which interest is calculated on the loan
b.number of applicants for the loan
c.number of years it will take to pay the loan back
d. number of dollars the loan is for
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Stella is a scientist. She observes and counts 210 bacteria in a culture. Later, Stella counts again and finds the number has increased by 30%. How many bacteria are there now? There are bacteria now.
Answers
Answer:
273
Step-by-step explanation:
you just need to find 30% of 210 which is 63
Then you do 210 + 63 which is 273 bacteria
Raios de luz solar estão atingindo a superfície de um lago formando um ângulo x com a sua superfície, conforme indica a figura. Em determinadas condições, pode-se supor que a intensidade luminosa desses raios, na superfície do lago, seja dada aproximadamente por i(x) = k . sen(x) sendo k uma constante, e supondo-se que X está entre 0° e 180°. Quando X = 150°, a intensidade luminosa se reduz a qual percentual de seu valor máximo? A
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sua resposta é a letra b eu não sei se a resposta está certa
Determine whether the given numbers represent the lengths of sides of a right triangle.9,40,41Do the given numbers represent the lengths of the sides of a right triangle?YesNo
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To prove that these numbers form the sides of a right triangle we should do these steps
1. Square the longest side
2. Find the sum of the squares of the other 2 sides
3. If the sum equals the square of the longest side, then the numbers can form a right triangle
Since the longest side is 41, then
[tex](41)^2=1681[/tex]Since the other 2 numbers are 40 and 9, then
[tex](40)^2+(9)^2=1600+81=1681[/tex]From both steps, we can say
[tex](41)^2=(40)^2+(9)^2[/tex]Then the answer is
YES, 9, 40, 41 can form the sides of a right triangle
I know how to do everything except the #1 step
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Answer:
[tex]A^{\doubleprime}(-6,-21),B^{\doubleprime}(6,-15)\text{ and C}^{\doubleprime}(-3,-12)[/tex]Explanation:
Given the coordinates A, B and C as follows:
[tex]A(-3,4),B(1,2)\text{ and C(-2,1)}[/tex]If a point is reflected across the x-axis, we have the transformation rule:
[tex](x,y)\to(x,-y)[/tex]Thus, the image of A are:
[tex]A(-3,-4),B(1,-2)\text{ and C(-2,-1)}[/tex]Next, a translation by <1,-3>:
[tex]\begin{gathered} A(-3+1,-4-3),B(1+1,-2-3)\text{ and C(-2+1,-1-3)} \\ A(-2,-7),B(2,-5)\text{ and C}(-1,-4) \end{gathered}[/tex]Finally, a dilation by K=3 gives the final image required:
[tex]A^{\doubleprime}(-6,-21),B^{\doubleprime}(6,-15)\text{ and C}^{\doubleprime}(-3,-12)[/tex]Find S20 given -4,8,20,32, ... Precalc Series and sequences, will give brainliest.
Answers
Solution
Step 1
Given -4, 8, 20, 32....
Common difference
8- (-4)=12
20 -8= 12
32- 20= 12
The common difference (d) is 12
Step 2
We are finding the sum of the first 20th term
[tex]S_{20}=\frac{n}{2}(2a+(n-1)d)[/tex]where n is 20
d is 12
a is -4
[tex]\begin{gathered} S_{20}=\frac{20}{2}(2\times-4\text{ +(20-1)12)} \\ S_{20}=10(-8+(19)12) \\ S_{20\text{ }}=10(-8+228) \\ S_{20}=10(220) \\ S_{20}=2200 \end{gathered}[/tex]using pascals triangle, find the 5th power of 25
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The image below shows the pascal triangle.
The pascal triangle shows until the fifth power, where a = 25 and b = 0.
[tex]25^5=25^5+5\cdot25^4\cdot0+10\cdot25^3\cdot0^2+10\cdot25^2\cdot0^3+5\cdot25\cdot0^4+0^5=9,765,625[/tex]Hence, the answer is 9,765,625.which which mixture tastes saltier explain how you know. PLEASE HELP ME WITH THIS I'm not good at math sorry
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The saltier mixture will have more teaspoons of salt per cups of water.
For mixure B, we have 2.5 cups of water per teaspoons of salt this is 1/2.5 = 0.4 teaspoons of salt per cups of water.
Now, we need to calculate the relation between teaspoons of salt per cups of water for mixture A, so:
[tex]\begin{gathered} \text{We calculate the relation for the thr}ee\text{ rows in the table:} \\ 1)\frac{4}{5}=0.8\text{ teaspoons of salt/cups of water} \\ 2)\frac{7}{8\frac{3}{4}}=0.8\text{ teaspoons of salt/cups of water} \\ 3)\frac{9}{11\frac{1}{4}}=0.8\text{ teaspoons of salt/cups of water} \end{gathered}[/tex]So, mixture A has the greater relation of teaspoons of salt per cups of water, so it's saltier than mixture B.
Lionfish are considered an invasive species, with an annual growth rate of 65%. A scientist estimates there are 7,000 lionfish in a certain bay after the first year.Write the explicit equation for f (n) that represents the number of llonfish in the bay after in years. Show all necessary math work.
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
Lionfish:
growth rate: 65%
time = 1 year
amount (1) = 7000
Step 02:
explicit equation:
f(1) = 7000
n = time
r = 65% = 0.65
f(n) = f(1) * r ^ (n - 1)
f(n) = 7000 * (0.65) ^ (n - 1)
[tex]f(n)\text{ = 7000 }\cdot(0.65)^{(n-1)}[/tex]The answer is:
f(n) = 7000 * (0.65) ^ (n - 1)
Solve: 1/4 (36x – 16) = 5x – 18
Answers
We must solve for x the following equation:
[tex]\frac{1}{4}(36x-16)=5x-18.[/tex]1) We multiply both sides by 4, and we get:
[tex]\begin{gathered} 36x-16=4\cdot(5x-18), \\ 36x-16=20x-72. \end{gathered}[/tex]2) We pass the -16 at the left side as +16 at the right side:
[tex]\begin{gathered} 36x=20x-72+16, \\ 36x=20x-56. \end{gathered}[/tex]3) We pass the -56 at the right side as +56 at the left side:
[tex]\begin{gathered} 36x-20x=-56, \\ 16x=-56. \end{gathered}[/tex]4) Finally, dividing both sides by 16, we get:
[tex]x=-\frac{56}{16}=-3.5.[/tex]Answerx = -3.5
Use the Law of Sines to find the indicated angle 0. (Assume C = 67º. Round your answer to one decimal place.)
Answers
Answer
40.3º
Explanation
The Sine rule is used to solve angles and sides of triangle.
If a triangle ABC has angles A, B and C at the points of the named vertices of the tringles with the sides facing each of these angles tagged a, b and c respectively, the sine rule is given as
[tex]\frac{\text{ Sin A}}{a}=\frac{\text{ Sin B}}{b}=\frac{\text{ Sin C}}{c}[/tex]For this triangle,
Angle A = ? (Isn't given)
Angle B = θ
Angle C = 67º
Side a = ? (Isn't given)
Side b = 56.3
Side c = 80.2
We are then told to find the Angle B, that is, θ
So, using the later parts of the Sine Rule
[tex]\frac{\text{ Sin B}}{b}=\frac{\text{ Sin C}}{c}[/tex]Substituting the known variables, we have
[tex]\begin{gathered} \frac{\text{ Sin B}}{b}=\frac{\text{ Sin C}}{c} \\ \frac{\text{ Sin }\theta}{56.3}=\frac{\text{ Sin }67º}{80.2} \\ \text{ Sin }\theta=\frac{56.3\times\text{ Sin }67º}{80.2}=\frac{56.3\times0.9205}{80.2} \\ \text{ Sin }\theta\text{ = 0.6462} \\ \theta=Sin^{-1}(0.6462)=40.3º \end{gathered}[/tex]Hope this Helps!!!
I need help in math two please
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a reflection over the y-axis an then a traslation
Follow the instructions below..Write (20)4 without exponents.+(2a)* = 0Х5?Fill in the blanks.(zla)* = 120
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Given the indices expression shown below;
[tex](2a)^4[/tex]This can be simplified as:
[tex]\begin{gathered} (2a)^4=2^4a^4 \\ (2a)^4=2^2\times2^2\times a^4 \\ (2a)^4=4\times4\times a^4 \\ (2a)^4=16a^4 \end{gathered}[/tex]This gives the resulting expression on expansion
A trade magazine routinely checks to drive-through service times of fast food restaurants and 95% confidence interval that results from examining 501 customers in one fast food chains drive-through has a lower bound of 166.2 seconds in an upper bound of 169.6 seconds what does this mean?
Answers
The confidence level of an interval is the probability that the mean of an distribution rest inside this interval.
Then, there is a 95% probability that the mean drive-through service time of this fast-food chain is between 166.2 seconds and 169.6 seconds.
A map of Levi's property is being made with a scale factor of 2 centimeters: 3 meters. Whats the scale factor
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As a result, if 2 centimeters on the map equals 3 meters, you might express that as a fraction and convert it to a standard unit of meters: 0.02 / 3, which you could then multiply by 50 / 50 to get the fraction 1 / 150. The scale factor 1 is 150.
What is Scale Factor?The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller). For instance, we can increase the size of a rectangle with sides of 2 cm and 4 cm by multiplying each side by, let's say, 2. The new figure we receive will resemble the first figure, but every dimension will be double that of the first rectangle. The scale factor in this case will be denoted by the number 2.Scale factor = Dimension of the new shape Dimension of the original shape is the fundamental formula used to calculate it. The formula is expressed as Scale factor = Larger figure dimensions Smaller figure dimensions in the event that the original figure is enlarged.
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10 POINTS
The given table of values represents a linear equation. What is the slope?
x 3 4 5 6
y 1 5 9 13
Responses
2,
3,
5,
4
Answers
The slope of the linear equation is 4.
We are given a table which has the values of the "x" column and the corresponding "y" column.The values in the "x" column are 3, 4, 5, and 6.The values in the "y" column are 1, 5, 9, and 13.The values represent the linear equation as given.We need to find the slope of the linear equation.We can form the data into coordinate form.The points are (3, 1), (4, 5), (5, 9), and (6, 13).Let us consider the first (3, 1) and the last point (6, 13) to cover the whole range of the data that is given to us.The slope is given by the ratio of the change in the y-coordinates to the change in the x-coordinates.The slope is Δy/Δx.The slope is (13 - 1)/(6 - 3).The slope is 12/3.The slope is 4.To learn more about equations, visit :
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solve the literal equation for x.v= x• y•zx=
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v = x• y•z
v/(y•z) = x• y•z/(y•z) (dividing by (y•z) on both sides of the equation)
v/(y•z) = x (simplifying)
The answer is x=v/(y•z)
Calculate the value of the limit to the indicated values of x then draw the graphf (x) = (x² -1 ) / (x-1,) with x = 1
Answers
Given:
The function is,
[tex]\lim _{x\to1}\frac{(x^2-1)}{(x-1)}[/tex]Take the limit as x tends to 1,
[tex]\begin{gathered} \lim _{x\to1}\frac{(x^2-1)}{(x-1)} \\ \text{Applying the limit as x=1 it will give }\frac{0}{0}\text{ form } \\ So,\text{ simplify the function.} \\ \lim _{x\to1}\frac{(x^2-1)}{(x-1)}=\lim _{x\to1}\frac{(x^{}-1)(x+1)}{(x-1)}=\lim _{x\to1}(x+1)=1+1=2 \end{gathered}[/tex]The limit of the function is 2.
The graph of the function is,
Corbin begins calculating the volume of a cylinder, in cubic meters, using the following steps. V = Bh V = (113.04) x 20 Which model could represent Corbin's cylinder? 120 m 113.04 m 20 m 36 m A 20 m 6 m 20 m *50.52 m
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Given the following expression:
[tex]\begin{gathered} V=Bh \\ \Rightarrow V=(113.04)\cdot(20) \end{gathered}[/tex]Notice that the value of the area of the base is the following:
[tex]B=\pi\cdot r^2=113.04[/tex]with pi = 3.14, we can solve for r to find the radius of the cylinder:
[tex]\begin{gathered} 3.14r^2=113.04 \\ \Rightarrow r^2=\frac{113.04}{3.14}=36 \\ \Rightarrow r=\sqrt[]{36}=6 \\ r=6 \end{gathered}[/tex]therefore, the cylinder has radius 6 and height 20 (the correct model is C)
Joseph raced his control car 600 feet in 24 seconds. He said the speed of the remote control car was 20 feet per second during the race. Assuming the car raced at a constant speed. A. Joseph is correct the car was traveling 20 feet per second because 600÷24=20 per second B. Joseph is correct the car traveling 20 feet per second because 600÷25=20 feet per second C. Joseph is incorrect the car was traveling 24 feet per second because 600÷25=24 feet per second D. Joseph is incorrect the car was traveling 25 feet per second because 600÷24=25 feet per second
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D. Joseph is incorrect the car was traveling 25 feet per second because 600÷24=25 feet per second
Explanations:Distance raced in 24 seconds = 600 Feet
Distance raced in 1 second = 600 / 24
Distance raced in 1 second = 25 feet
Therefore, the speed of the car = 25 feet per second
Joseph said the speed = 20 feet per second
Joseph is incorrect because the car was travelling 25 feet per second
A mail order company has a 6% success rate. If it mails advertisements to 538 people, find the probability of getting less than 28 sales. Round z-value calculations to 2 decimal places and final answer to at least 4 decimal places.
Answers
Solution
- This is a binomial probability problem because we have multiple trials.
- The formula for calculating the Z-value is:
[tex]\begin{gathered} Z=\frac{X-\mu}{\sigma} \\ where, \\ \mu=\text{ The mean} \\ \sigma=\text{ The standard deviation} \\ X=\text{ The value we are testing} \end{gathered}[/tex]- This value of Z can be used to calculate the probability we need using a Z-score calculator or a Z-distribution table.
- Before we proceed, we need to find the mean and the standard deviation as follows:
[tex]\begin{gathered} \mu=np \\ n=\text{ Number of subjects} \\ p=\text{ The probability of success} \\ \\ \mu=\frac{6}{100}\times538 \\ \\ \mu=32.28 \\ \\ \sigma=\sqrt{np(1-p)} \\ \sigma=\sqrt{538\times\frac{6}{100}(1-\frac{6}{100})} \\ \\ \therefore\sigma=5.5085 \end{gathered}[/tex]- Now that we have both the mean and the standard deviation, we can proceed to find the value of the Z-score as follows:
[tex]\begin{gathered} Z=\frac{X-\mu}{\sigma} \\ \\ Z=\frac{28-32.28}{5.5085} \\ \\ \therefore Z=-0.78\text{ \lparen To 2 decimal places\rparen} \end{gathered}[/tex]- Now that we have the Z-score value, we can proceed to find the corresponding probability for values less than X = 28 sales using a Z-distribution table or a Z-score calculator.
- Using a Z-score calculator, we have:
- Since we are looking for the probability of having sales lower than 28, we have:
[tex]P(X
A rectangle has vertices at (0, 0), (3,0), and (0,6). What is the area of the rectangle? у 10- 9- 8 ? square units 7 6 DONE 5- 4 3- 2 1 х o i 2 3 4 5 6 ; 8 9 10
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Shawn, this is the solution to the exercise:
Width of the rectangle = 3 units (from 0 to 3)
Length of the rectangle = 6 units (from 0 to 6)
In consequence, the area is:
• Area = Width * Length
,• Area = 3 * 6
,• Area = 18 units²
Find the variance and the standard deviation of the following set,(5,6,7,8,9)
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To find the variance, and standard deviation, calculate first for the mean.
[tex]\begin{gathered} \mu=\frac{\sum x_i}{n} \\ \mu=\frac{5+6+7+8+9}{5} \\ \mu=\frac{35}{5} \\ \mu=7 \end{gathered}[/tex]Now that we have the mean, we can now solve for the variance.
[tex]undefined[/tex]PLEASE HELP IM SICK AND I DONT UNDERSTAND.DUE IN 30 MINS!!!!!!
Answers
Answer:
x = 11
Step-by-step explanation:
all angles in a triangle will add up to 180.
So we can start with the equation:
(19 + x) + (7 + 8x) + angle str = 180.
we are given the angle stv. This angle equals 125.
the angle of a straight line is 180. In order to find the angle next to another angle like angle stv and str are, all you have to do is subtract the angle from 180.
So to find str:
180 - 125 = 55
we already have one of our angles which is 55
so the equation is now:
(19 + x) + (7 + 8x) + 55 = 180
now do some simple simplification:
(19 + x) + (7 + 8x) + 55 = 180
______________ -55_-55
(19 + x) + (7 + 8x) = 125
26 + 9x = 125
-26_____-26
9x = 99
99/9 = 11
x = 11
Therefore, x = 11
Sean has $900 in a savings account that earns 5% annually. The interest is notcompounded. How much will he have in 1 year?Use the formula i = prt, where i is the interest earned, p is the principal (starting amount), ris the interest rate expressed as a decimal, and t is the time in years.Submit
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Answer:
The interest after one year is $45
Explanation:
Principal = $900
Rate = 5%
Time = 1 year
I = P x R x T / 100
I = 900 x 5 x 1 / 100
I = 4500/100
I = $45
Therefore, the interest after one year is $45
3. Which equation correctly shows the relationship between the numbers 4p2,560 and 256?
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748,917 has 8 in the thousands place
The value of the digit in the hundreds place in the number 653,841 is 800
Now, out of the options, we want to get a digit that is multiplied by 10 of this
The digit multiplied will be 8,000
So, we want to select a number out of the options which has a value of 8,000 in the thousands place
The correct number here is 748,917
This is because the digit in the thousands place here is 8,000
Compare 8º and 8 ^-2. Which is greater? Explain
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Note that any number raised to the power of zero is 1.
Therefore:
[tex]8^0=\text{ 1}[/tex][tex]8^{-2}=\text{ }\frac{1}{8^2}=\text{ }\frac{1}{64}=\text{ 0.015625}[/tex]Since 1 > 0.015625:
[tex]8^0>8^{-2}[/tex]Eliminate factors equivalent to 1 and rewrite the right side of this equation
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For his long distance phone service, Bill pays an $8 monthly fee plus 6 cents per minute. Last month, Bill's long distance bill was $13.64. For how many minutes was Bill billed?
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The long distance bill is
Monthly fixed $8
Monthly variable $0.06 per minute
If the cost is c and minutes m, we can write cost as:
[tex]c=8+0.06m[/tex]Given, last month's cost, c, to be $13.64, we want to find the minutes.
We put 13.64 into 'c' of the formula found and find m.
Shown below:
[tex]\begin{gathered} 13.64=8+0.06m \\ 13.64-8=0.06m \\ 5.64=0.06m \\ m=\frac{5.64}{0.06} \\ m=94 \end{gathered}[/tex]Ansswe
Type the correct answer in the box. Use numeral instead of words. If nessary, use / for fraction bar. The data set represents the number of cups of coffee sold in a Cafe
Answers
4, 5, 6, 6, 7, 8, 9, 9, 10, 10, 12, 12, 14, 15,
The first quartile is 6 and the third is 12
So the difference is 12- 6 = 6 (answer)
