Answer:
[tex]x=\frac{2(1\pm i\sqrt{2} )}{3}[/tex]
General Formulas and Concepts:
Pre-Alg
Order of Operations: BPEMDASAlg I
Standard Form: ax² + bx + c = 0Quadratic Formula: [tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]√-1 is imaginary number iStep-by-step explanation:
Step 1: Define
3x² - 4x + 4 = 0
a = 3
b = -4
c = 4
Step 2: Find roots
Substitute: [tex]x=\frac{-(-4)\pm\sqrt{(-4)^2-4(3)(4)} }{2(3)}[/tex]Simplify: [tex]x=\frac{4\pm\sqrt{(-4)^2-4(3)(4)} }{2(3)}[/tex]Evaluate: [tex]x=\frac{4\pm\sqrt{16-4(3)(4)} }{2(3)}[/tex]Multiply: [tex]x=\frac{4\pm\sqrt{16-48} }{6}[/tex]Subtract: [tex]x=\frac{4\pm\sqrt{-32} }{6}[/tex]Factor: [tex]x=\frac{4\pm\sqrt{-1} \sqrt{32} }{6}[/tex]Simplify: [tex]x=\frac{4\pm4i\sqrt{2} }{6}[/tex]Factor: [tex]x=\frac{4(1\pm i\sqrt{2} )}{6}[/tex]Simplify: [tex]x=\frac{2(1\pm i\sqrt{2} )}{3}[/tex]Max pays a flat rate of $85 for his cell phone. He is also charged $0.15 for every text that he sends. His cell phone bill can be no more than the amount he has budgeted for it each month. If x represents the number of texts and y represents his budgeted amount, which inequality represents Max's cell phone budget each month? (3 points)
a $0.15x + $85 ≥ y
b $0.15x + $85 ≤ y
c $0.15x - $85 ≥ y
d $0.15x - $85 ≤ y
How many gallons of a 70% antifreeze solution must be mixed with 100 gallons of 30% antifreeze to get a mixture that is 60% antifreeze?
Answer:
350 gallons
Step-by-step explanation:
Let x = number of gallons of 70% solution
100 = number of gallons of 25% solution
Then, x + 100 = number of gallons of 60% solution
0.70x + 0.25(100) = 0.60(x + 100)
0.70x + 25 = 0.60x + 60
0.10x = 35
x = 350 gal
Mix 350 gal of 70% solution with 100 gal of 25% solution to obtain 450 gal of 60% solution.
Answer: Add 315 gallons of 70% antifreeze to 90 gallons of 25% antifreeze to make a 60% mixture.
can someone help me with this
Answer:
31°
Step-by-step explanation:
If ∠dab=55° and ∠cab=24° and ∠cab+∠dac=∠dab then all you need to do is subtract 55° and 24° to get 31°
Find the slope of the line graphed below.
Answer:
(rise/run) 5/4
decimal ver: 1.25
Answer:
[tex]\frac{5}{4}[/tex]
Step-by-step explanation:
The line passes trough the points (2, 2) and (-2, -3).
[tex]m=\frac{rise}{run}=\frac{-3-2}{-2-2}=\frac{-5}{-4} =\boxed{\frac{5}{4}}[/tex]
Hope this helps.
A river flows due south at 1.4 mi/h. In what direction should the swimmer head, at a velocity of 3 mi/h, in order to arrive at a landing point due east of his starting point? (Round your answer to one decimal place.)
Solution:
It is that a river is flowing in the south direction with a speed of [tex]$v_r$[/tex]1.4 mi/h.
A swimmer wishes to cross the river in a horizontal direction so that he lands at a point which is due east of his starting point.
The speed of the swimmer is [tex]$v_s$[/tex] = 3 mi/h
Therefore he has to swim in such a direction that his resultant is in the direction east to his starting point.
Let this angle be θ.
Therefore, from the figure,
[tex]$\sin \theta = \frac{v_r}{v_s}$[/tex]
[tex]$\sin \theta = \frac{1.4}{3}$[/tex]
[tex]$\theta = \sin^{-1}(0.46)$[/tex]
[tex]$=27.4^\circ[/tex]
Therefore, the swimmer has to swim in the northeast direction making an angle of (90+27.4) = 117.4° with the direction of flow of river (i.e. south).
Selma uses a jogging trail that runs through a park near her home. The trail is a loop that is of a mile long. On Monday, Selma ran the loop in of an hour. What is Selma’s unit rate in miles per hour for Monday’s run?
In this activity, you will use the common denominator method to calculate a unit rate that involves fractions. Answer the questions that follow to calculate Selma’s unit rate in miles per hour.
part A. According to the question, the unit rate is to be expressed in which units?
Part B. Now, write Selma’s jogging rate as a complex fraction. A complex fraction is one whose numerator, denominator, or both are fractions. Be sure to include units in your answer.
Part C. Find the least common denominator of the two fractions from part B. To do this, list and compare the first five multiples of the denominators. The smallest number that appears in both lists is the least common denominator. Show your work.
Part D
Answer:
a) Her rate is 1 mile per hour for Monday’s run
b) 0.447 m/second
c) In fraction 20467m/180000 seconds
Step-by-step explanation:
Speed = distance / time = 1 mile/ 1 hour
= 1 mile per hour
Her rate is 1 mile per hour for Monday’s run
part A. According to the question, the unit rate is to be expressed in miles per hour units.
Part B.
Speed = distance / time = 1 mile/ 1 hour
= 1 mile per hour
But 1 mile = 1609.34 m
and 1 hour = 3600 seconds
There fore
1 mile/ 1 hour = 1*1609.34/ 1*3600 seconds
= 0.447 m/second
Part C.
1 mile/ 1 hour =1609.34/ 3600 seconds
= 1609.34 * 100/100 * 1/3600 ( multiplying and dividing by 100 to remove the decimal)
= 160934/360000
= 20467m/180000 seconds
The first five multiples of 1 are 2,3,4,5,6,7,8, 9......
The LCM of 1 and 1 is 1
If you can answer my riddle I will mark as brainlest ok?
RIDDLE: If you give me food I will live but if you give me water I will die. What am I?
Answer:
fire
Step-by-step explanation:
if you give fire food or fuel it will still be alive
but if you give it water it will go out
PLZ GIVE BRAINLEST
Answer:
The answer is a fire because if you put water on a fire, it will die out, but if you put stuff in the fire it will live on.
There are 18 girls and 24 boys who want to participate in a trivia challenge. If each team must have the same ratio of girls and boys, what is the greatest number of teams that can enter? Find how many boys and girls each team would have.
Answer:
4 team could enter 5 people in each team
Step-by-step explanation:
there will be 6 teams, each team having 3 girls and 4 boys
Step-by-step explanation:
6*3=18
6*4=24
What equation shows how to use equivalent fractions to evaluate 2/5 + 3/4
Answer:
Step-by-step explanation:
Exact form: 23/20
Decimal form: 1.15
Find the exact value of tan^-1(1)
A. Pi/4
B. 7pi/4
C. 5pi/4
D. 3pi/4
Mr. Parks spent $96.30 on 3 hats and 6 key chains. a. If each hat cost $15.50, how much did each key chain cost?
Based on the information given the amount that the key chain cost is $8.3
Cost:Let x represent the cost of the key chain
$96.30 = 3($15.50) + x
x = $96.30 - $46.50
x= $49.8
Hence:
Cost per key chain= $49.8/6
Cost per key chain= $8.3
Inconclusion the amount that the key chain cost is $8.3
Learn more about cost here:https://brainly.com/question/1153322
Calculate the insurance costs.
The Greene family obtains bodily injury and property damage automobile insurance in the amount of 50/100/10. The car
that they insure is not driven to work, and no male drivers under twenty-five use the car.
a. What does the Greene family pay as an annual premium?
b. How much would it cost him to purchase insurance in the amount of 100/300/25?
c. What is the difference in cost?
Answer:
a. What does the Greene family pay as an annual premium? $450.60
b. How much would it cost him to purchase insurance in the amount of 100/300/25? $480.70
c. What is the difference in cost? $30.10
(っ◔◡◔)っ ♥here you go♥
What should be subtracted from 538 to get reminder 3 when divided by 11
Answer:
4
Step-by-step explanation:
Answer: 7
Step-by-step explanation: 538÷11=48 + 10
so to get remainder 3 subtract 7 from 538
Use the information mZ1 = (3x + 30), m42 = (5x – 10°, and x = 20, and the theorems you have learned to
show that 1 || m.
Answer:
Step-by-step explanation:
First you have to do 2 + 2=
What does 0.05 x 300 represent?
Answer:
15
Step-by-step explanation:
A fair 66-sided die is rolled 77 times and the resulting sequence of 77 numbers is recorded. A) How many different sequences are possible?B) How many different sequences consist entirely of even numbers? C) How many different sequences are possible if the first, third, and fourth numbers must be the same? D) How many sequences are there where every number is different? E) How many sequences are there where there are at least two numbers that are the same?
Answer: A. 279936 sequences.
B. 2187 sequence.
C. 7776 sequence.
D. 46656 sequence
E. 64 sequence.
Step-by-step explanation:
Given data:
A 6 sided fair die
No of time rolled = 7
Resulting sequence recorded = 7.
Solution.
A.) No of different possible sequence
= 6^7
= 279936 sequences.
B.) Sequence consisting of only even number
= there are 3 even numbers between 1 and 7 ( 2,4,6).
= 3^7
= 2187 sequence.
C.) possible sequences are when the first, third, and fourth numbers must be the same.
= 6* 6 ^n
where n = 4
= 6*6^4
= 7776 sequence.
D.) sequence when every number is different.
There are 6 sides of a die, so when every number is different it is.
= 6^6
= 46656 sequence
E.) sequence when atleast there are two numbers that are the same.
= 2^6
= 64 sequence.
Evaluate the following expression. Express your answer in simplest form.
3
16
+
5
18
1
2
5
16
10
32
Answer:
518125161348
Step-by-step explanation:
316
518125161032
-------------------------
518125161348
In ΔIJK, j = 7.6 cm, k = 7.8 cm and ∠I=27°. Find the length of i, to the nearest 10th of a centimeter.
Answer:
3.6
Step-by-step explanation:
TRUST ME LOL
anyone know thisssss
Area can be defined as the number of square units it takes to cover the inside
of a figure
A. True
B. False
Answer:
A
Step-by-step explanation:
It is making me add 20 characters to my answer so ignore this :)
Answer:
its TRUE
Step-by-step explanation:
Which of the following equations has only one solution?
X( x - 1) = 9
x2 - 6x + 9 = 0
x2 = 9
Answer:
x^2 - 6x + 9
Step-by-step explanation:
x(x - 1) = 9
x^2 - x - 9 = 0
x = 3.54 or x = -2.54 (using quadratic formula)
x^2 - 6x + 9 = 0
(x-3)^2 = 0
x = 3
x^2 = 9
x = ±√3 (any positive number square rooted always have 2 answers)
PLS HELP
4. What does the y-intercept of the graph of Monday's storm mean? Does the y-intercept of the graph of Thursday's storm have the same meaning?
Answer/Step-by-step explanation:
✅The y-intercept of the graph of Monday's storm is the amount of precipitation recorded at the beginning of the tracking or when the tracking started.
✍️The y-intercept of the graph of Monday's storm is 0 mm, when time = 0 min.
✅The y-intercept of the graph of Thursday's storm also has the same meaning as that of Monday's storm.
✍️The y-intercept of the graph of Thursday's storm is 0 mm, when time = 0 min.
Edgardo adquirió un vehiculo a un costo de $23,970. Su vida útil es de 7 años y tiene
un valor residual de $975.
a ¿Cuánto deprecia el vehículo cada año?
b. ¿Cuál será su valor al cabo de 5 años?
c. Haz la tabla de depreciación y valor por año
Responder:
$ 3,285
$ 7545
Explicación paso a paso:
Dado que:
Costo del vehículo = $ 23,970
Valor de rescate = $ 975
Vida útil = 7 años
Depreciación por año = (costo del vehículo - valor residual) / vida útil
Depreciación por año = (23970 - 975) / 7
Depreciación por año = 22995/7
Depreciación por año = $ 3285
Valor del vehículo después de 5 años:
23970 - (3285 * 5)
= $ 7545
Año _____ valor del vehículo
1 ________ 20685
2 ________ 17400
3 ________ 14115
4 ________ 10830
5 ________ 7545
6 ________ 4260
7 ________ 975
The mass of Earth is 5.9722×1024 kg. The mass of Venus is 4.8685×1024 kg. What is the difference between the mass of Earth and the mass of Venus?
Step-by-step explanation:
5.9722x1024 - 4.8685x1024
1130.1888
What is the sum of –356.1 + 258.6? –614.7 –97.5 97.5 614.7
Answer:
The answer is -97.5
Answer:
-97.5
Step-by-step explanation:
um yas
randma has 3 pounds of flour. She uses 1 pounds of flour to make rolls for
hanksgiving dinner. How much flour does Grandma have left over?
Answer:
2 pounds
Step-by-step explanation:
i feel like it's a trick question :/
True or False
Gross income is the amount of money you earn before taxes
________________________
Net income is after taxes.
________________________
There are 24 pay periods in a year if you are paid monthly.
________________________
Regular or straight time pay is calculated by the hourly rate X hours worked.
___________________________
Piecework is when you are paid for each item of work that you do.
__________________________
Fill in the blank
When I earn extra money based on the amount I sell, this is called____________________________.
Overtime begins when a person works more than _____ hours per week.
Social Security, Federal , and ______________ taxes will be deducted from an employee’s paycheck.
Overtime Pay is an Act covered by ______________________________________________________.
Annual salary is calculated by dividing the salary by _____________________________________.
Answer:
True
Step-by-step explanation:
Gross income is prior to any deductions, expenses, or other appropriations have been taken out.
2. True
Net income is after taxes
3. False
This would be biweekly if 24 payperiods
4. True
5. True
Fill in blank
1. Commission (I think)
2. 40
3. State
4. Dept of Labor; act is called Fair Labor Standards Act
5. Fair Labor Standards Act
6. if you need to know annual salary, then mulitply your gross income by the number of payperiods in one year, if you need to know your monthly salary then divide the annual salary by 12 to get monthly.
I will put brainliest
The bowling club at your school had a car wash last week.
They washed 72 cars in 6.5 hours.
About how many cars did they wash per hour?
Answer:
11.077 cars / 11 cars (nearest whole number)
Step-by-step explanation:
6.5 hours → 72 cars
1 hour → 72/6.5 cars = 11.077 cars (5 s.f.)
Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider using it. lim xâ[infinity] x + x2 1 â 5x2
Answer:
[tex]\frac{1}{5}[/tex]
Step-by-step explanation:
Given the expression;
[tex]\lim_{x \to \infty} \dfrac{x+x^2}{5x^2}[/tex]
To find the limit of the function, we need to first divide through by the highest degree if x i.e x² as shown;
[tex]\lim_{x \to \infty} \dfrac{\frac{x}{x^2} +\frac{x^2}{x2}}{\frac{5x^2}{x^2} }\\ \lim_{x \to \infty} \frac{\frac{1}{x}+ 1 }{5}\\As \ x \ tends \ to \ \infty, \ \frac{1}{x} \ tends \ to \ zero. \ Hence;\\ \lim_{x \to \infty} \frac{\frac{1}{x}+ 1 }{5} = \frac{0+1}{5}\\= \dfrac{1}{5}[/tex]
Hence the limit of the function as x tends to infinity is [tex]\frac{1}{5}[/tex]
Which polynomial was factored? x2 – 2x – 8 x2 + 2x – 8 x2 – 2x – 4 x2 + 2x – 4
Answer:
x^2+2x-8
Step-by-step explanation:
x^2+2x-8 = (x+4)(x-2)
Answer: A. x^2 -2x -8
Step-by-step explanation: