Answer:
-3/2 ±1/2 sqrt(5) = x
Step-by-step explanation:
f(x) = 2x^2 + 6x + 2
Set the function equal to 0
0 = 2x^2 + 6x + 2
Factor out 2
0 = 2(x^2 + 3x + 1)
Divide by 2
0 = (x^2 + 3x + 1)
Subtract 1 from each side
-1 = x^2 +3x
Complete the square by dividing the x coefficient by 2 and then squaring
(3/2)^2 = 9/4
-1 +9/4 = x^2 +3x+9/4
-4/4+9/4 = (x+3/2) ^2
5/4 = (x+3/2) ^2
Taking the square root of each side
± sqrt(5/4) = sqrt( (x+3/2) ^2)
±1/2 sqrt(5) = (x+3/2)
Subtract 3/2 from each side
-3/2 ±1/2 sqrt(5) = x
Sudhanshu is solving a system representing a race between two remote control cars. The variable x is defined as time in seconds, and y is the distance in meters from the starting line.
Red car: y = 3 x + 5. Blue car: y = 4 x.
How many solutions should Sudhanshu find?
zero
one
two
infinite
Answer:
One
General Formulas and Concepts:
Algebra I
Slope-Intercept Form: y = mx + b
m - slope b - y-interceptSolving systems of equations
Step-by-step explanation:
Step 1: Define
Identify systems
y = 3x + 5
y = 4x
Step 2: Solve
If we compare the 2 lines, we can see that they both have a different slope. If they had the same slope but different y-intercepts, then they would be parallel and have no solution. We can also see that the 2 lines aren't the same. If they were, then they would have infinite solutions.
∴ the systems should have only one solution.
Answer:
B
Step-by-step explanation:
Determine the value(s) for which the rational expression -3z+6/6z^2+14z-80 is undefined.
Answer:
[tex]z= 2 \ and \ z = \frac{-20}{3}[/tex]
Step-by-step explanation:
For the given expression to be undefined, it means that the denominator of the expression must be equal to zero
Hence;
[tex]6z^2+14z-80 = 0[/tex]
On factorizing:
[tex]6z^2+14z-80=0\\3z^2+7z-40 = 0\\3z^2-6z+20z-40 = 0\\3z(z-2)+20(z-2) = 0\\(3z+20)(z-2) =0\\(z-2)=0 \ and \ (3z+20)=0\\z= 2 \ and \ z = \frac{-20}{3}[/tex]
find all the missing measurement
Answer:
fshscssjjsv 57
Step-by-step explanation:
fsuevwuwhw 58
Please someone help I need help been stuck on this for the longest
Answer:
a.) 16
b.) 8
Step-by-step explanation:
a. how much lower was the 6am temperature in Nome than in Wyoming
Essentially this question is asking us to find the difference of the temperatures of Nome and Wyoming at 6am
Temperature of Nome at 6am: -31
Temperature of Wyoming at 6am: -15
Difference between two temperatures: -31 - (-15)
The two negative signs cancel out and the sign changes to +
-31 + 15 = -16
The temperature in Nome was 16 degrees lower then in Wyoming
b. At noon the temperature of Boston had risen by 14 degrees. what was the temperature of boston at noon.
All we have to do for this one is add 14 to the temperature of Boston at 6am. ( This is because the question tells us the temperature has risen 14 degrees by noon )
-6 + 14 = 8
At noon the temperature would be 8 degrees in Boston.
Help please :) Whoever helps and gets answer correct gets Brainliest!
Answer:
1/8 is the slope
Step-by-step explanation:
Answer:
slope = 8
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{1}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (1, 26) and (x₂, y₂ ) = (2, 34) ← 2 ordered pairs from the table
m = [tex]\frac{34-26}{2-1}[/tex] = [tex]\frac{8}{1}[/tex] = 8
what is proportion as applied in mathematics
Answer:
como se siente el actor al presentar la obra hola
Please Help! What's the rule that represents the sequence 13, 27, 41, 55, ...?
Answer:
B
Step-by-step explanation:
an = a+(n-1)d
an=13+(n-1)14
d=14
Subtract 7 pounds 3 ounces from 10 pounds
Find m These questions getting hard
Answer:
the
Step-by-step explanation:
it's fairly easy actually. You just have to use sin
please help, will give brainliest!!!
Answer:
f^-1(x) = sqrt(x+4)
Step-by-step explanation:
y = x^2 -4
Exchange x and y
x = y^2 -4
Add 4 to each side
x+4 = y^2
Take the square root of each side
sqrt(x+4) = y
f^-1(x) = sqrt(x+4)
Answer:
f^-1(x) = sqrt(x+4)
Step-by-step explanation:
SAT scores are normally distributed with a mean of 1,500 and a standard deviation of 300. An administrator at a college is interested in estimating the average SAT score of first-year students. If the administrator would like to limit the margin of error of the 82% confidence interval to 25 points, how many students should the administrator sample
Answer:
The appropriate solution is "259".
Step-by-step explanation:
According to the question,
[tex]\sigma = 300[/tex]
[tex]M.E=25[/tex]
At 82% CI,
[tex]\alpha = 0.18[/tex]
Critical value,
[tex]Z_c=1.341[/tex]
Now,
The sample size will be:
⇒ [tex]n=(Z_c\times \frac{\sigma}{E} )^2[/tex]
By substituting the values, we get
[tex]=(1.341\times \frac{300}{25} )^2[/tex]
[tex]=(1.341\times 12)^2[/tex]
[tex]=259[/tex]
Multiply the complex numbers: (1∕2 + 4i)2
Question 10 options:
A)
–153∕4 + 4i
B)
153∕4 + 8i
C)
–153∕4 + 8i
D)
153∕4 + 4i
Step-by-step explanation:
153∕4 + 8i is the correct answer
[I'm supposing that you have to find the value of (1/ 2 + 4i)²]
Answer:
[tex] = \frac{ - 63}{4} + 4i[/tex]
Step-by-step explanation:
we must know that
(a + b)² = a² + b² + 2ab[tex] {( \frac{1}{2} + 4i) }^{2} = { (\frac{1}{2} })^{2} + {(4i)}^{2} + 2 . \frac{1}{2} . 4i[/tex]
[tex] = \frac{1}{4} + 16 {i}^{2} + 4i[/tex]
since i²= -1[tex] = \frac{1}{4} - 16 + 4i[/tex]
[tex] = \frac{1 - 64}{4} + 4i[/tex]
[tex] = \underline{ \frac{ - 63}{4} + 4i} [/tex]
[I'm also assuming that instead of -153/4 + 4i option A says -63/ 4 + 4i.]
so the answer is option A.
...............................................................
I need help with this please need to turn this in today
Answer:
a) 75 m lower
b) 308 m
Step-by-step explanation:
a) -131 - -206 = 75
b) -206 + 514 = 308
Let sin A = -5/13 with 270 degrees < A < 360 degrees and cos B = -15/17 with 90 degrees < B < 180 degrees find sin (A+B)
Answer:
Step-by-step explanation:
Put the following equation of a line into slope-intercept form, simplifying all
fractions.
9x – 15y = 135
Answer:
y=3/5x-9
Step-by-step explanation:
9x – 15y = 135
Subtract 9x from each side
9x -9x – 15y =-9x+ 135
-15y = -9x +135
Divide each side by -15
-15y/-15 = -9x/-15 +135/-15
y=3/5x-9
Need help with the answers that have been left Blank don’t understand how to do them
Step-by-step explanation:
d=20 J.
E=2,N,J
this is your answer
2-[6÷2+{6×1/2+(7/2-3/2)}]
Answer:
-6
Step-by-step explanation:
2 - [6 ÷ 2 + {6 × 1/2 + (7/2 - 3/2)}] =
Follow the correct order of operations.
Do one step at a time and copy everything else each time, so you don't lose track of any operation.
= 2 - [6 ÷ 2 + {6 × 1/2 + 4/2}]
= 2 - [6 ÷ 2 + {6 × 1/2 + 2}]
= 2 - [6 ÷ 2 + {3 + 2}]
= 2 - [6 ÷ 2 + 5]
= 2 - [3 + 5]
= 2 - 8
= -6
Answer:
-6
hope this helps
Step-by-step explanation:
2_(6÷2+(6*1/2+(7/2-3/2))) solve the ones in bracket first
(7/2-3/2)=2
2-(6÷2+(6×1/2+2))
6×1/2+2
6×1/2=3
3+2=5
2-(6÷2+5)
6÷2=3
3+5=8
2-8
=-6
The circumference of a circle with radius r can be found using the formula C=2πr
Find the circumference of a circle with radius 15.4 feet . Round your answer to two decimal places.
----------------------ft
Answer:
96.72
Step-by-step explanation:
Answer:
96.77
Step-by-step explanation:
pi is 3.142
radius = 15.4ft
c = 2*3.142*15.4
The total bill for repairing Mark’s TV was $211. The repair shop charges $25 an hour for labor plus $16 for parts. How many hours of labor did it take to repair Mark’s TV? Write it in an equation.
Refer to the values described below, then identify which of the following is most appropriate: discrete random variable, a. Responses to the survey question "How many pets do you have?" b. Exact heights of the next 100 babies born in a region c. Responses to the survey question "What is your eye color?" d. Exact foot length of humans e. Number of people in families a. Since the outcomes are b. Since the outcomes are countable, this is this is a discrete random variable. random variable.
Answer:
Exact heights of the next 100 babies born in a region.
Step-by-step explanation:
A discrete random variable involves two key factors ; discrete and randomness ; Hence, a discrete random variable should have a finite or countable Number of outputs or values. It should also stem from a random procedure. Here, the height of the next hundred babies is a random procedure as the next 100 babies in the region are unknown until Given birth too and as such all pregnant women have the chance of having their babies among. Since, we are dealing with exact height values which are countable (100), then we this is a discrete random variable.
The California State University (CSU) system consists of 23 campuses, from San Diego State in the south to Humboldt State near the Oregon border. A CSU administrator wishes to make an inference about the average distance between the hometowns of students and their campuses. Describe and discuss several different sampling methods that might be employed. (Select all that apply.) There are no potential problems with self reporting of distances.
Answer:
1)The sample could be generated by taking a stratified random sample by taking a simple random sample from each of the 23 campuses and again asking each student in the sample to report the distance from their hometown to campus.
2)One could take a simple random sample of students from all students in the California State University system and ask each student in the sample to report the distance from their hometown to campus.
3)Certain problems arise with self reporting of distances, such as recording error or poor recall.
Step-by-step explanation:
1)The sample could be generated by taking a stratified random sample by taking a simple random sample from each of the 23 campuses and again asking each student in the sample to report the distance from their hometown to campus.
2)One could take a simple random sample of students from all students in the California State University system and ask each student in the sample to report the distance from their hometown to campus.
3)Certain problems arise with self reporting of distances, such as recording error or poor recall.
Use the limit comparison test to determine whether ∑n=19∞an=∑n=19∞8n3−2n2+196+3n4 converges or diverges.
(a) Choose a series ∑n=19∞bn with terms of the form bn=1np and apply the limit comparison test. Write your answer as a fully simplified fraction. For n≥19,
limn→∞anbn=limn→∞
(b) Evaluate the limit in the previous part. Enter ∞ as infinity and −∞ as -infinity. If the limit does not exist, enter DNE.
limn→∞anbn =
(c) By the limit comparison test, does the series converge, diverge, or is the test inconclusive?
Answer:
Diverges
General Formulas and Concepts:
Algebra I
Exponential Rule [Dividing]: [tex]\displaystyle \frac{b^m}{b^n} = b^{m - n}[/tex]Calculus
Limits
Limit Rule [Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to c} x = c[/tex]Series Convergence Tests
P-Series: [tex]\displaystyle \sum^{\infty}_{n = 1} \frac{1}{n^p}[/tex]Direct Comparison Test (DCT)Limit Comparison Test (LCT): [tex]\displaystyle \lim_{n \to \infty} \frac{a_n}{b_n}[/tex]Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \sum^{\infty}_{n = 19} \frac{8n^3 - 2n^2 + 19}{6 + 3n^4}[/tex]
Step 2: Apply DCT
Define Comparison: [tex]\displaystyle \displaystyle \sum^{\infty}_{n = 19} \frac{n^3}{n^4}[/tex][Comparison Sum] Simplify: [tex]\displaystyle \displaystyle \sum^{\infty}_{n = 19} \frac{1}{n}[/tex][Comparison Sum] Determine convergence: [tex]\displaystyle \displaystyle \sum^{\infty}_{n = 19} \frac{1}{n} = \infty , \ \text{div by P-Series}[/tex]Set up inequality comparison: [tex]\displaystyle\frac{8n^3 - 2n^2 + 19}{6 + 3n^4} \geq \frac{1}{n}[/tex][Inequality Comparison] Rewrite: [tex]\displaystyle n(8n^3 - 2n^2 + 19) \geq 6 + 3n^4[/tex][Inequality Comparison] Simplify: [tex]\displaystyle 8n^4 - 2n^3 + 19n \geq 6 + 3n^4 \ \checkmark \text{true}[/tex]∴ the sum [tex]\displaystyle \sum^{\infty}_{n = 19} \frac{8n^3 - 2n^2 + 19}{6 + 3n^4}[/tex] is divergent by DCT.
Step 3: Apply LCT
Define: [tex]\displaystyle a_n = \frac{8n^3 - 2n^2 + 19}{6 + 3n^4}, \ b_n = \frac{1}{n}[/tex]Substitute in variables [LCT]: [tex]\displaystyle \lim_{n \to \infty} \frac{8n^3 - 2n^2 + 19}{6 + 3n^4} \cdot n[/tex]Simplify: [tex]\displaystyle \lim_{n \to \infty} \frac{8n^4 - 2n^3 + 19n}{6 + 3n^4}[/tex][Limit] Evaluate [Coefficient Power Rule]: [tex]\displaystyle \lim_{n \to \infty} \frac{8n^4 - 2n^3 + 19n}{6 + 3n^4} = \frac{8}{3}[/tex]∴ Because [tex]\displaystyle \lim_{n \to \infty} \frac{a_n}{b_n} \neq 0[/tex] and the sum [tex]\displaystyle \sum^{\infty}_{n = 19} a_n[/tex] diverges by DCT, [tex]\displaystyle \sum^{\infty}_{n = 19} \frac{8n^3 - 2n^2 + 19}{6 + 3n^4}[/tex] also diverges by LCT.
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Convergence Tests (BC Only)
Book: College Calculus 10e
a truck rental company rents a moving truck for one day by charging $20 plus $0.05 per mile. Write a linear equation that relates the cost C, in dollars, of renting the truck to the number x of miles driven. waht is the cost of renting the truck if the truck is driven 107 miles
Answer:
The linear equation that relates the cost C, in dollars, of renting the truck to the number x of miles driven is 0.05*x + 20 and the cost of renting the truck if the truck is driven 107 miles is 25.35.
Step-by-step explanation:
A linear function is a polynomial function of the first degree that has the form:
f (x) = y = m*x + b
where m is the slope of the function and b is the y-intercept.
The graph of a linear function is always a line.
A truck rental company rents a moving truck for one day by charging $20 plus $0.05 per mile. So, the number of miles travel is represented by "x" and the cost per mile is represented by "c". The y-intercept is the starting cost at zero miles or $20. The slope is the rate per mile or $0.05. Then:
c= 0.05*x + 20
If the truck is driven 107 miles, then:
c= 0.05* 107 + 20
Solving:
c= 25.35
So, the linear equation that relates the cost C, in dollars, of renting the truck to the number x of miles driven is 0.05*x + 20 and the cost of renting the truck if the truck is driven 107 miles is 25.35.
Put the following equation of a line into slope-intercept form, simplifying all
fractions.
5x – 4y = -4
Answer:
[tex]\boxed {\boxed {\sf y= \frac{5}{4}x+1}}[/tex]
Step-by-step explanation:
We are given the equation of a line and asked to put it into slope-intercept form.
Slope-intercept form is:
[tex]y=mx+b[/tex]
Where:
m= slope b= y-interceptIn order to put the equation into slope-intercept form, we have to isolate the variable y by performing the inverse operation.
[tex]5x-4y= -4[/tex]
5x is being added to -4y. The inverse of addition is subtraction, so subtract 5x from both sides of the equation.
[tex]5x-5x-4y=-4-5x[/tex]
[tex]-4y=-4-5x[/tex]
The variable y is being multiplied by -4. The inverse of multiplication is division. Divide both sides of the equation by -4.
[tex]\frac {-4y}{-4}=\frac{-4-5x}{-4}[/tex]
[tex]y= \frac{-4}{-4}+\frac{-5x}{-4}[/tex]
[tex]y=1+\frac{5}{4}x[/tex]
Rearrange the equation.
[tex]y= \frac{5}{4}x+1[/tex]
The fractions are completely simplified, so this is our final answer.
The equation of the line in slope-intercept form is [tex]\bold {y= \frac{5}{4}x+1}}[/tex].
The slope is 5/4 and the y-intercept is 1.
What is the constant of variation k of the direct variation y=KP through (-3, 2)
Answer:
isisis
Step-by-step explanation:
ISO’s
Answer:
-2/3
Answer: The constant of variation k for y = kx through (-3, 2) is k = -2/3.
Each month, Terrance spends $128.00 on his car payment, $63.00 for car insurance, and $45.00 on gas. Round each amount to the nearest ten and estimate the amount of money Terrance spends each month to own a vehicle. $240.00 $220.00 $230.00 $210.00 which one is it
Answer:
$240
Step-by-step explanation:
Rounding each amount to the nearest 10
Car $128 = $130
Insurance $63 = $60
Gas $45 = $50
130 + 60+ 50 = $240
Malingo read 3/8 of a book on Friday, 1/4 on Saturday and the rest on Sunday. what fraction did he read on Sunday?
Answer:
3/8
Step-by-step explanation:
We can write the entire book with the number 1. Now we can write this operation
3/8 + 1/4 + x = 1
3 + 2 + 8x = 8
5 + 8x = 8
8x = 3
x = 3/8
Slope=6and passes through (4,-1)
Answer:
Step-by-step explanation:
If you need the equation:
point slope form is:
y-y1 = m(x-x1)
m is the slope and (x1,y1) is a point on the line.
y- (-1) = 6(x-4)
If you want standard form:
y= 6x -24 -1
y=6x-25
You have 8 quarts of milk. You need 1.25 cups to make one serving of deep fried chicken. How many servings can you make?
Answer: 25.6 servings (partial serving) / 25 servings (whole serving)
Step-by-step explanation:
Concepts:
As we can see from the question, there are two units applied. [Quarts] and [cups]; therefore, we need to do the unit conversion.
1 quart = 4 cups
Solve:
Step one: Convert quarts into cups
1 quart = 4 cups8 quarts = 4 × 8 = 32 cupsStep two: Divide the cups to find the number of servings
32 cups / 1.25 cups = 25.6 servings**Disclaimer** I am not sure about the rules that you apply in mathematics. Here, the answer is not an integer. I am concerned whether you would allow partial servings. In my understanding, the servings shall be a whole, thus should be rounded. However, if you are fine with decimals, then you have the choice.
Hope this helps!! :)
Please let me know if you have any questions
