Answer: x = ¹/₂ ± √⁸¹
------------
2
Step-by-step explanation:
First write out the equation
x² - x - 20
Now we now write the equation by equating to 0
x² - x - 20 = 0
We now move 20 to the other side of the equation. So
x² - x = 20,
We now add to both side of the equation square of the half the coefficient of the (x) and not (x²) which is (1) . So, the equation now becomes
x² - x + ( ¹/₂ )² = 20 + ( ¹/₂ )²
x² - ( ¹/₂ )² = 20 + ¹/₄
( x - ¹/₂ )² = 20 + ¹/₄, we now resolve the right hand side expression into fraction
( x - ¹/₂ )² = ⁸¹/₄ when the LCM is made 4
Taking the square root of both side to remove the square,we now have
x - ¹/₂ = √⁸¹/₄
x - ¹/₂ = √⁸¹/₂
Therefore,
x = ¹/₂ ± √⁸¹
-----------
2
The circle graph shows the percentage of numbered tiles in a box. If each numbered tile is equally likely to be pulled from the box, what is the probability of pulling out a tile with a 6 on it? (Hint: Remember that percents are based out of 100% and probability is represented as a fraction of 100%)
Answer: [tex]\dfrac{1}{5}[/tex]
Step-by-step explanation:
From, the circle graph in the attachment below,
The percentage of portion taken by 6 (dark blue) = 20%
So, the probability of pulling out a tile with a 6 on it = percentage of portion taken by 6 (dark blue) = 20% [Probability can also be written as a percentage]
[tex]=\dfrac{20}{100}\\\\=\dfrac{1}{5}[/tex] [we divide a percentage by 100 to convert it into fraction]
Hence, the probability of pulling out a tile with a 6 on it = [tex]\dfrac{1}{5}[/tex]
3. What is the distance from (−4, 0) to (2, 5)? Round your answer to the nearest hundredth. (4 points)
Answer:
7.81
Step-by-step explanation:
its a triangular shape
let x = 4 + 2 = 6
let y = 5
length between two points = h
h² = x² + y²
h² = 6² + 5²
h = sqrt of 61
h = 7.81
solve for the variable x^2 - 8 = -1 Show all work please
Answer:
x = ±sqrt(7)
Step-by-step explanation:
x^2 - 8 = -1
Add 8 to each side
x^2 - 8+8 = -1+8
x^2 = 7
Take the square root of each side
sqrt(x^2) = ±sqrt(7)
x = ±sqrt(7)
Which equation shows y-5=x converted to slope intercept form.
Answer:
C) y = x + 5
Step-by-step explanation
Add 5 to both sides
NEED HELP THANKLSSSS
Answer:
Side length: 3 cm.
Surface area: 54 cm squared.
Step-by-step explanation:
The formula for a cube is the side length cubed, since the formula for a rectangular prism is length times width times height. Those three measurements are the same for a cube.
So, since the volume is 27 cm cubed, we can say that the side length of the cube is the cube root of 27 cm cubed, or 3 cm.
There are 6 sides on a cube, and every cube has the same area. Since the side length of the cube is 3 cm, the area of one side of the cube is 3 * 3 = 9 cm squared. 9 * 6 = 54 cm squared.
Hope this helps!
I have 5 eggs, I broke 2, I cooked 2 and I ate 2, how many do I have left?
Answer:
Step-by-step explanation:
To decipher how many eggs you have left, we must read the statement well.
I have 5 eggs if I break 2 eggs it is to cook them and when they are cooked they will be eaten, so we simply do the following:
5 -2= 3
Now you only have 3 eggs left.
Step-by-step explanation:
Given:
5 eggs
Required:
Number of eggs after breaking, cooking and eating 2.
Solution:
I won't count the eggs as 6.
Broken=cooked=eaten=2
5-2=3
Hope it helps ;) ❤❤❤
Use a graphing calculator to sketch the graph of the quadratic equation and then give the coordinates for the x-intercepts (if they exist) y=x2+7x+10 A (-2,0),(5,0) B (2,0);(-5,0) C (2,0);(5,0) D (-2,0);(-5,0)
Answer:
Option D.
Step-by-step explanation:
The given quadratic equation is
[tex]y=x^2+7x+10[/tex]
We need to draw the graph of given equation by using graphing calculator as shown below.
From the graph it is clear that the parabola intersect the x-axis at points (-2,0) and (-5,0). So, the x-intercepts are (-2,0) and (-5,0).
Therefore, the correct option is D.
Is this equation linear or nonlinear?
y =x/2
Answer:
linear
Step-by-step explanation:
You are given the following information obtained from a random sample of 5 observations. 20 18 17 22 18 At 90% confidence, you want to determine whether or not the mean of the population from which this sample was taken is significantly less than 21. (Assume the population is normally distributed.) a) State the null and the alternative hypotheses. b) Compute the standard error of the mean. c) Determine the test statistic. d) Test to determine whether or not the mean of the population is significantly less than 21.
Answer:
a
The null hypothesis is
[tex]H_o : \mu = 21[/tex]
The Alternative hypothesis is
[tex]H_a : \mu< 21[/tex]
b
[tex]\sigma_{\= x} = 0.8944[/tex]
c
[tex]t = -2.236[/tex]
d
Yes the mean population is significantly less than 21.
Step-by-step explanation:
From the question we are given
a set of data
20 18 17 22 18
The confidence level is 90%
The sample size is n = 5
Generally the mean of the sample is mathematically evaluated as
[tex]\= x = \frac{20 + 18 + 17 + 22 + 18}{5}[/tex]
[tex]\= x = 19[/tex]
The standard deviation is evaluated as
[tex]\sigma = \sqrt{ \frac{\sum (x_i - \= x)^2}{n} }[/tex]
[tex]\sigma = \sqrt{ \frac{ ( 20- 19 )^2 + ( 18- 19 )^2 +( 17- 19 )^2 +( 22- 19 )^2 +( 18- 19 )^2 }{5} }[/tex]
[tex]\sigma = 2[/tex]
Now the confidence level is given as 90 % hence the level of significance can be evaluated as
[tex]\alpha = 100 - 90[/tex]
[tex]\alpha = 10[/tex]%
[tex]\alpha =0.10[/tex]
Now the null hypothesis is
[tex]H_o : \mu = 21[/tex]
the Alternative hypothesis is
[tex]H_a : \mu< 21[/tex]
The standard error of mean is mathematically evaluated as
[tex]\sigma_{\= x} = \frac{\sigma}{ \sqrt{n} }[/tex]
substituting values
[tex]\sigma_{\= x} = \frac{2}{ \sqrt{5 } }[/tex]
[tex]\sigma_{\= x} = 0.8944[/tex]
The test statistic is evaluated as
[tex]t = \frac{\= x - \mu }{ \frac{\sigma }{\sqrt{n} } }[/tex]
substituting values
[tex]t = \frac{ 19 - 21 }{ 0.8944 }[/tex]
[tex]t = -2.236[/tex]
The critical value of the level of significance is obtained from the critical value table for z values as
[tex]z_{0.10} = 1.28[/tex]
Looking at the obtained value we see that [tex]z_{0.10}[/tex] is greater than the test statistics value so the null hypothesis is rejected
Add (7.8x10^5+(2.4x10^5)
answer: 1020000
step-by-step explanation:
(7.8*10^5+(2.4*10^5) given expression
(7.8*10^5)+(2.4*10^5) group with parenthesis
(7.8+2.4)*10^5 combine like terms
10.2*10^5 preform addition
10.2*100000 evaluate the exponent
1020000 multiply out
How can I factor these complex conjuages? a^2 + b^2 and a^2 - b
Answer:
1) [tex](a+ib)(a-ib)[/tex]
2) [tex]a^2+i^2b[/tex]
Step-by-step explanation:
1) [tex]a^2+b^2[/tex]
=> [tex]a^2 - (-1)b^2[/tex] (We know that -1 = [tex]i^2[/tex] )
=> [tex]a^2-i^2b^2[/tex]
=> [tex](a)^2-(ib)^2[/tex]
Using Formula [tex]a^2 -b^2 = (a+b)(a-b)[/tex]
=> [tex](a+ib)(a-ib)[/tex]
2) [tex]a^2-b[/tex]
=> [tex]a^2+(-1)b[/tex] (We know that -1 = [tex]i^2[/tex] )
=> [tex]a^2+i^2b[/tex] (It cannot be simplified further)
Answer:
[tex]\boxed{(a+ib)(a-ib)}[/tex]
[tex]\boxed{a^2+i^2b}[/tex]
Step-by-step explanation:
[tex]a^2 + b^2[/tex]
Rewrite expression.
[tex]a^2- (-1)b^2[/tex]
Use identity : [tex]-1=i^2[/tex]
[tex]a^2- i^2 b^2[/tex]
Factor out square.
[tex]a^2-(ib)^2[/tex]
Apply difference of two squares formula : [tex]a^2-b^2 =(a+b)(a-b)[/tex]
[tex](a+ib)(a-ib)[/tex]
[tex]a^2-b[/tex]
Rewrite expression.
[tex]a^2+(-1)b[/tex]
Use identity : [tex]-1=i^2[/tex]
[tex]a^2+i^2b[/tex]
Solve for X in the equation, where 4B = −2X − 2A
Answer:
X = [tex]\left[\begin{array}{ccc}2&-7&3\\13&0&2\end{array}\right][/tex]
Step-by-step explanation:
4B = -2X - 2A
Dividing both sides by -2
=> -2B = X + A
Subtracting A to both sides
=> X = -2B-A
Now, Let's Solve:
=> X = [tex]-2\left[\begin{array}{ccc}0&2&-2\\5&0&3\end{array}\right] -\left[\begin{array}{ccc}-2&3&1\\-3&0&4\end{array}\right][/tex]
=> X = [tex]\left[\begin{array}{ccc}-2*0&-2*2&-2*-2\\-2*5&-2*0&-2*3\end{array}\right] - \left[\begin{array}{ccc}-2&3&1\\-3&0&4\end{array}\right][/tex]
=> X = [tex]\left[\begin{array}{ccc}0&-4&4\\10&0&6\end{array}\right] - \left[\begin{array}{ccc}-2&3&1\\-3&0&4\end{array}\right][/tex]
=> X = [tex]\left[\begin{array}{ccc}0-(-2)&-4-3&4-1\\10-(-3)&0-0&6-4\end{array}\right][/tex]
=> X = [tex]\left[\begin{array}{ccc}2&-7&3\\13&0&2\end{array}\right][/tex]
A lottery ticket has a grand prize of $31 million. The probability of winning the grand prize is .000000018. Determine the expected value of the lottery ticket.
Answer:
$0.558
Step-by-step explanation:
The expected value is the sum of the value of each outcome times the chance that it happens. In this case, there are two outcomes:
Win $31 millionWin $0Then our expected value can be calculated as:
[tex]EV=(31,000,000)(0.000000018)+(0)(1-0.000000018)=0.558[/tex]
from $2003$ onward, the number of daily visitors to a website increased by $200\%$ every two years. So, for example, the number of visitors in $2011$ was $200\%$ more than the number of visitors in $2009$.
In what year was the number of daily visitors $800\%$ more than the number of daily visitors in $2003$? Explain, in words, why your answer is correct.
Answer:
2007
Step-by-step explanation:
If the number of visitors was, say, 100 people in 2003, then in 2005 that number would have gone up to 300 people, which is a 200% increase. And that number would have gone up to 900 people in 2007, which is an 800% increase.
Answer:
2007
NOT YOU TRYING TO GET THE AOPS PREALGEBRA 2 ANSWER
I stan though :D
Duane is making cookies. The recipe calls for two times as many cups of sugar as butter, two times as many cups of oats as sugar, and two times as many cups of flour as oats. If Duane puts in one cup of butter, how many cups of flour does he need to add? (also this is from MobyMax)
Answer:
Step-by-step explanation:
Let b represent the number of cups of butter needed.
Let s represent the number of cups of sugar needed.
Let o represent the number of cups of oat needed.
Let f represent the number of cups of flour needed.
The recipe calls for two times as many cups of sugar as butter. It means that
s = 2b
Two times as many cups of oats as sugar. It means that
o = 2s
Two times as many cups of flour as oats. It means that
f = 2o
If Duane puts in one cup of butter, it means that b = 1
Therefore,
s = 2 × 1 = 2 cups
o = 2s = 2 × 2 = 4 cups
f = 2o = 2 × 4 = 8 cups
Therefore, he needs to add 8 cups of flour
Answer: Let b represent the number of cups of butter needed. Let s represent the number of cups of sugar needed. Let o represent the number of cups of oat needed. Let f represent the number of cups of flour needed. The recipe calls for two times as many cups of sugar as butter. It means that s = 2bTwo times as many cups of oats as sugar. It means that o = 2sTwo times as many cups of flour as oats. It means that f = 2oIf Duane puts in one cup of butter, it means that b = 1Therefore, s = 2 × 1 = 2 cupso = 2s = 2 × 2 = 4 cupsf = 2o = 2 × 4 = 8 cups Therefore, he needs to add 8 cups of flour
Step-by-step explanation:
The Highway Safety Department wants to study the driving habits of individuals. A sample of 121 cars traveling on the highway revealed an average speed of 60 miles per hour with a standard deviation of 11 miles per hour. Determine a 95% confidence interval estimate for the speed of all cars.
Answer:
{58.02007 , 61.97993]
Step-by-step explanation:
Data are given in the question
Sample of cars = n = 121
Average speed = sample mean = 60
Standard deviation = sd = 11
And we assume
95% confidence t-score = 1.97993
Therefore
Confidence interval is
[tex]= [60 - \frac{1.97993 \times 11}{\sqrt{121} }] , [60 + \frac{1.97993 \times 11}{\sqrt{121} }][/tex]
= {58.02007 , 61.97993]
Basically we applied the above formula to determine the confidence interval
Line segment TS is tangent to circle O at point N.
Circle O is shown. Line segment Q N goes from one side of the circle to the other side. Tangent T S intersects the circle at point N. Point P is on the circle between points Q and N. Point R is on the circle between points Q and N. Angle Q N T is 74 degrees.
If the measure of Angle Q N T is 74°, what is the measure of Arc Q P N?
37°
74°
148°
212°\
Answer:
148°
Step-by-step explanation:
The measure of the intercepted arc QN is twice the measure of inscribed angle QNT.
arc QN = 2(74°) = 148°
_____
Comment on the question and answer
Your description "on the circle between points Q and N" is ambiguous. You used the same description for both points P and R. The interpretation we used is shown in the attachment. If point P is on the long arc NQ, then the measure of arc QPN will be the difference between 148° and 360°, hence 212°. You need to choose the answer that matches the diagram you have.
__
We call angle QNT an "inscribed angle" because it is a degenerate case of an inscribed angle. The usual case has the vertex of the angle separate from the ends of the arc it intercepts. In the case of a tangent meeting a chord, the vertex is coincident with one of the ends of the intercepted arc. The relation between angle measure and arc measure remains the same: 1 : 2.
Answer:
148
Step-by-step explanation:
Edge 2020
Winston and Alice are taking a trip. Winston left at 8 am and traveled an average of 50 miles per hour. Alice left at 10 am and traveled an average of 70 miles per hour. At what time are they at the same place at the same time? Write a system of equation to represent this situation. Then use the substitution method with that system to determine at the time they will be in the same location. How many miles away from home will they be at that time?
Answer:
3 PM
350 miles
Step-by-step explanation:
Let's say t is the number of hours since 8 AM.
The distance traveled by Winston is:
w = 50t
The distance traveled by Alice is:
a = 70(t−2)
When w = a:
50t = 70(t−2)
50t = 70t − 140
140 = 20t
t = 7
Winston and Alice will be at the same place 7 hours after 8 AM, or 3 PM.
The distance they travel is 350 miles.
Help ASAP!!!
Find the given angle, to the nearest degree.
Answer:
[tex]\boxed{\mathrm{x = 43.8 \ degrees}}[/tex]
Step-by-step explanation:
Let the angle be x
Tan x = [tex]\frac{opposite}{adjacent}[/tex]
Where opposite = 48, Adjacent = 50
Tan x = [tex]\frac{48}{50}[/tex]
Tan x = 0.96
x = [tex]Tan ^{-1}0.96[/tex]
x = 43.8 degrees
Answer:
[tex]\boxed{43.8 \°}[/tex]
Step-by-step explanation:
Use tangent since hypotenuse length is not given.
[tex]tan \theta = \frac{opposite}{adjacent}[/tex]
[tex]tan(x)=\frac{48}{50}[/tex]
[tex]x=tan^{-1}(\frac{48}{50} )[/tex]
[tex]x=43.8[/tex]
What are the positive and negative square roots of 1?
Answer:
Positive is 1
Negative is-1
Step-by-step explanation:
(25 points) PLEASE HELP, I gotta get this done or my mom will beat the hell out of me
Solve
x + y = 2
4y = -4x + 8
by elimination (not Gaussian!)
Thanks!
(also, please show work!)
Answer:
x=1
y=1
Step-by-step explanation:
Please look at the image below for solutions⬇️
Answer:
Step-by-step explanation:
Add the equations in order to solve for the first variable . Plug this value into the equations in order to solve for the remaining variables.
Point form
(x, 2-x)
A copy machine makes 153 copies in 4 minutes 15 seconds how many copies does it make per minute
Answer:
36 copies.
Step-by-step explanation:
4mins 15 seconds is the same as 4+1/4 minsutes. Since 1 minute is less than 4+1/4minutes and 4+1/4 minutes produces 153 copies. 1 minute will produce less.
(1÷4+1/4)×153
= 36 copies.
What is the image of (-8, 10) when reflected in the y-axis?
Answer:
if you're just reflecting the point over the y-axis it just becomes (8,10)
Answer: (8, 10)
Explanation and Example:
I have a trick that I use. I'm not sure if it will make sense to you but I'll explain it. When the question asks you to reflect over the x-axis, then keep the x in (x,y) the same and just flip the sign for the y. If the question asks you to reflect over the y-axis, then keep y the same and flip the sign for x.
Reflect over x-axis:
(-2, 6) -----> (-2, -6)
Reflect over y-axis:
(-4, -8) -----> (4, -8)
Six years ago, an investor purchased a downtown apartment complex and an adjacent piece of land. The current value of the property is $850,000. Of the total, the current value of the apartment complex is $710,000 and the current value of the land is $140,000. Using the straight-line method, assuming an average appreciation of 6% on the land and an average depreciation of 3% on the apartment complex, what was the original value of the property? Round your answer to the nearest dollar.
Answer: $951,064.06 would be your answer.
Step-by-step explanation: Hope that helped!
Jeremy's father drives him to school in rush hour traffic in 20 minutes. One day there is no traffic, so his father can drive him 18 miles per hour faster and gets him to school in 12 minutes. How far (in miles) is it from Jeremy's home to school?
Answer:
9 miles
Step-by-step explanation:
Let's say that the speed that Jeremy's father drives Jeremy through traffic is x. When there is no traffic, Jeremy's father drives 18 miles per hour faster than his speed in traffic, x. This would make the speed that Jeremy's father drives Jeremy to school without traffic, 18 / 60 + x. This is as it is 18 miles per hour faster, not 18 miles per minute faster.
Now recall the formula Speed = Distance / Time, or S = D / T. We want the distance here ( How far (in miles) from Jeremy's home to school ) so let's isolate D here in this formula,
S = D / T ⇒ D = S [tex]*[/tex] T - and as you know, the distance from Jeremy's home to school is the same, with or without traffic. So, we can consider case 1 : Jeremy's " distance traveled " in traffic, and case 2 : Jeremy's " distance traveled " without traffic, and make them equal to one another.
20 [tex]*[/tex] x = 12 [tex]*[/tex] ( 18 / 60 + x ),
20x = 3.6 + 12x,
8x = 3.6,
x = 0.45 - Now the distance is 20 [tex]*[/tex] x, and hence 20 [tex]*[/tex] 0.45 = 9 miles
6th grade math , help me please :)
Answer:
a= 7/20
b=35
Step-by-step explanation:
A was simple because 7 people with blue eyes for every 20 people written in fraction form. For b they say what if it was 100 total people so 20 x 5 = 100 so 7 x 5= 35 so your answer to b is 35
The formula relating linear velocity v and angular velocity ω for a circle of radius r is______ , where the angular velocity must be measured in radians per unit time.
Answer:
[tex]v=wr[/tex]
Step-by-step explanation:
The formula relating linear velocity v and angular velocity ω for a circle of radius r is
[tex]v=wr------1[/tex]
where v = linear velocity in m/s
w= angular velocity in rad/s
r= radius of curve
Both linear and angular velocity relates to speeds of objects, while linear velocity is to objects that moves, angular velocity is to objects that turns
please help me please!!!
Answer:
she has covered 6 miles in 1 ½ hours
Step-by-step explanation:
you need to learn how to read a graph.
it quite easy actually.
just look where the line on the graph is on 1.5 hours ( you can count the boxes if you don't know where 1.5 or 1 ½ is)
someone could help me?
Answer:
[tex]B= 3.14 * 4^4 = 50.24cm^2\\h = 16cm\\V=B*h=50.24*16=803.84cm^3[/tex]
Step-by-step explanation:
The area of the base is the area of a circle with a radius equal to 4 cm. It means that the area can be calculated as:
[tex]B = 3.14 * r^2\\B= 3.14 * 4^4 = 50.24cm^2[/tex]
The height of the cylinder is shown in the picture, it is equal to 16 cm.
Finally, the volume of the cylinder can be calculated as:
[tex]V = B*h=50.24*16 = 803.84cm^3[/tex]
Where B is the base and h is the height of the cylinder.
Victor is in the 28% tax bracket.
a. How much will a $900 tax credit save him?
b. how much will a $900 charitable contribution save him if he itemized his deductions?
Incomplete question. I've made some assumptions to provide clarity.
Answer:
a. $45,743.07
b. $44,843.07
Step-by-step explanation:
Let's assume Victor is a single filer with an income of $100,000.
Using the 2017 tax bracket rates for single filers, Victor would be expected to pay:
- 10 percent on the first $9,325 = 10% x 9525 =$932.5
- plus 15 percent of the amount between $9,326 and $37,950 (37950-9326) x 15% = $4293.6
- plus 25 percent of the amount between $37,951 and $91,900 (91900-37,951 ) x25% = $13487.25
- plus 28 percent of the amount over $91,901-$191,650 (191650-91901) x 28% = 27929.72
Total= $46,643.07
Minus $900 tax credit= $46,643.07-$900= $45,743.07
Minus $900 charitable contribution = $45,743.07-$900= $44,843.07