Answer:
[tex]\boxed{\sf a=\cfrac{\sqrt{15i} }{3}}[/tex]
[tex]\boxed{\sf a=-\cfrac{\sqrt{15i} }{3}}[/tex]
Step-by-step explanation:
[tex]\sf 6a^2 + 10 = 0[/tex]
We'll solve this equation using The Quadratic Formula:
[tex]\boxed{\sf \frac{-b\pm \sqrt{b^2-4ac} }{2a} }[/tex]
[tex]\sf 6a^2 + 10 = 0[/tex]
Substitute 6: a, 0: b, 10: c
[tex]\longmapsto\sf a=\cfrac{0\pm\sqrt{0^2-4\times 6\times 10} }{2\times 6}[/tex]
→ Square 0
→ Multiply -4 * 6= -24
→ Multiply -24 * 10 = -240
[tex]\longmapsto\sf a=\cfrac{0\pm\sqrt{-240} }{2\times 6}[/tex]
→ Take the square root of -240:
→ Multiply 2 * 6= 12
Now, Separate solutions:
[tex]\longmapsto\sf a=\cfrac{0\pm 4\sqrt{15i} }{12}[/tex]
Now, Separate solutions:
First, solve the equation when ± is plus:
[tex]\longmapsto \boxed{\sf a=\cfrac{\sqrt{15i} }{3}}[/tex]
___
Now, solve it when ± is minus:
[tex]\longmapsto \boxed{\sf a=-\cfrac{\sqrt{15i} }{3}}[/tex]
__________________________________________
[tex]\sf\longmapsto 6a^2+10=0[/tex]
a=6b=0c=10[tex]\sf\longmapsto a=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex](This a is root of equation)
[tex]\sf\longmapsto a=\dfrac{-0\pm\sqrt{0^2-4(6)(10)}}{2(6)}[/tex]
[tex]\sf\longmapsto a=\dfrac{\pm\sqrt{-240}}{12}[/tex]
[tex]\sf\longmapsto a=\dfrac{\pm\sqrt{240}i}{12}[/tex]
[tex]\sf\longmapsto a=\dfrac{\pm 4√15i}{12}[/tex]
[tex]\sf\longmapsto a=\dfrac{\pm √15i}{3}[/tex]
[tex]\sf\longmapsto a=\dfrac{\pm √3√5i}{3}[/tex]
[tex]\sf\longmapsto a=\pm\dfrac{√5i}{\sqrt{3}}[/tex]
[tex]\sf\longmapsto a=\pm\sqrt{\dfrac{5}{3}}i [/tex]
What is i?i stands for iota.
[tex]\sf\longmapsto i=\sqrt{-1}[/tex]
what is -3 (x+2) = 16 -x
Answer:
x = -11
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Algebra I
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityTerms/Coefficients
Step-by-step explanation:
Step 1: Define
Identify.
-3(x + 2) = 16 - x
Step 2: Solve for x
[Distributive Property] Distribute -3: -3x - 6 = 16 - x[Addition Property of Equality] Add x on both sides: -2x - 6 = 16[Addition Property of Equality] Add 6 on both sides: -2x = 22[Division Property of Equality] Divide -2 on both sides: x = -11Each container on a cargo ship holds 60 boxes of furniture.
Which table shows the values for 60c, the number of boxes
in c containers?
4
5
6
Number of Containers, C
Number of Boxes, 60c
240 300 360
4
5
6
Number of Containers, C
Number of Boxes, 60c
240 280 320
B.
4
5
6
Number of Containers, C
Number of Boxes, 60C
240 350 460
C
Answer:
imagine cheating on your star assessment but same tho the answer is c
Step-by-step explanation:
because i solved it on paper
Answer:
Step-by-step explanation:
C
( ꈍᴗꈍ)
introduction to algebra explain
Answer:
Algebra is the branch of Maths that uses alphabetical letters to find unknown numbers. These letters are also called variables. ... Algebra involves the simple operation of mathematics like addition, subtraction, multiplication, and division involving both constant as well as variables. For example, x+10 = 0.
Step-by-step explanation:
In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics. It includes everything from elementary equation solving to the study of abstractions such as groups, rings, and fields.
Hiiii!
Here's what algebra is:
Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols. In elementary algebra, those symbols (today written as Latin and Greek letters) represent quantities without fixed values, known as variables. ... The letters x and y represent the areas of the fields.
In simple words: a generalization of arithmetic in which letters representing numbers are combined according to the rules of arithmetic.
Hope it helps! ( ꈍᴗꈍ)
-Nezuko
What’s that answer please
4-0,9+(-0,11)-(-1,3) PLEASE HELP
Answer:
-20
Step-by-step explanation:
PEMDAS
Keisha bought seventy-two trading cards for her and her eleven friends. If Keisha and her friends get an equal amount, how many cards does each person receive?
Answer: 6
Step-by-step explanation: You might think the answer is 72/11 but you must realize that keisha counts as a person too. Thus, the answer is 72/12 or 6 cards for each person :)
Would appreciate brainly <3
72 trading cards
11 friends
to find:how many cards each of her friend receives.
solution:[tex] \frac{72}{11} [/tex]
[tex] = 6.5454545455[/tex]
[tex]nearest \: whole \: number = 7[/tex]
so, approximately each of her friend will get 7 cards.
answer= option C
SUPER EASY! FRACTIONS PLS HELP!
a kindergraten teacher has a bucket of 51 crayons and another bucket of 5 redpencils,14 blue pencils and 6 green pencils.the bucket of crayons contains 19 red crayons ,17 blue crayons 9 green crayons and 6 yellow crayons.
1.what is the fraction of green crayons to the total number of crayons written in simplest form
2.the teacher places the crayons and pencils in one bucket what is the fraction of yellow crayons and green pencils wriiten in simplest form
3.penicls come in boxes of 6 the number of boxes of blu pencils in the bucket can be represented by the mixed numeral 2 2/6 what is the number of boxes in simplest form?
Answer:
1: 1/3
2: 3/19
3: 7/3
Step-by-step explanation:
The maximum land speed of a cheetah is about 120km/hour.
What is this speed limit, rounded to the nearest whole number, in m/s?
Answer:
33 m/s
Step-by-step explanation:
120 km/h × (1 h)/(3600 s) × (1000 m)/(1 km) ≈ 33 m/s
_____
Additional comment
In general, units conversion is done by multiplying by a factor whose numerator and denominator have equal values, but different units. The units in that fraction need to be arranged to cancel the units you don't want and leave the units you do want.
If h(x) = 15x - 171, find h(3)
H(3) means to replace x in the equation with 3 and then solve:
15(3) - 171
45-171
-126
Answer: -126
helpppp
simplify √5 × √3
Answer:
√15
Step-by-step explanation:
When you multiply surds:
multiply the numbers inside the square roots i.e. √(5 × 3) = √15simplify if possible (not possible in this case)Hope this helps!
Please help and explain. You don't understand it very well.
Answer:
y = (-1/2)x + 2
Step-by-step explanation:
The black line slopes down as we move from left to right, so we conclude that the slope is negative. From (0, 2) to (4, 0), y drops by 2 units (the rise) and x increases by 4 units (run).
Thus the slope is m = rise / run = -2/4, or m = -1/2.
The y-intercept is (0, 2), so the value of b in the equation y = mx + b is 2.
Thus the equation of this line is y = mx + b => y = (-1/2)x + 2
here is a screenshot please help 15 points
GIVING BRAINLIEST!!!
A pole is being decorated with 15-meter ribbons that are strung from the top of the 7.2-meter pole to a point on the ground. Which is the approximate measure of the angle formed by the ribbon and the pole?
The angle formed by the ribbon and the pole is 29°
Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.
Let θ represent the angle formed by the ribbon and the pole.
Hence:
[tex]sin(\theta)=\frac{7.2}{15} \\\\\theta=sin^{-1}0.48\\\\\theta=29^o[/tex]
The angle formed by the ribbon and the pole is 29°
Find out more on Trigonometric ratio at: https://brainly.com/question/1201366
The sum of two numbers is 110.The larger number is 2 less than 7 times the smaller.Find the Large number
Answer:
The larger number is 96.
Step-by-step explanation:
[tex]let \: the \: two \: numbers \: be \: a \: and \: b \\ a + b = 110 \\ let \: a \: be \: the \: larger \: number \\ a = 7b - 2 \\ we \: can \: get \: the \: value \: of \: b \: by \: substituting \: the \: value \: above \: for \: a \: in \: eq \: 1 \\ 7b - 2 + b = 110 \\ 8b - 2 = 110 \\ 8b = 110 + 2 \\ 8b = 112 \\ b = \frac{112}{8} \\b = 14\\ calculate \:the \: value \: of \: a \: using \: the \: equation \: above \\ a + b = 110 \\ a = 110 - 14 \\ a = 96 \\ hence \: the \: large \: number \: is \: 96[/tex]
A painter checks a canvas to be sure it is rectangular. One of the canvas’ diagonals measures 48 inches. If the canvas is a rectangle, what is the measure, in inches, of the other diagonal?
A.)24
B.)12
C.)96
D.)48
Answer:
D)48
Step-by-step explanation:
need help ASAP its due tonight
Answer:
Step-by-step explanation:
15/3 + 3 =
15/3 + 9/3 =
24/3 =
8
2(15) + 3 30 + 3 33
------------- = -------------- = ----------------
3 3 3
33/ 3 =
11
mark me brainliest :D
Whats 16 x 32 what does it equal
Pls help this is due today and i have no idea
Answer:
x=38°
Step-by-step explanation:
sinx/21 =sin(38°)/21
sinx=21Sin(38°)/21
x = arcsin(21Sin(38°)/21)
x=38°
Which of the following is the difference of two squares

4g-16h
16a^2-4y^2
2x^2-4y^2
25m^3+100n^2
Answer:
2nd option
Step-by-step explanation:
A difference of squares has the general form
a² - b²
where the terms on either side of the subtraction ( the difference ) are both perfect squares.
The only one fitting this description is
16a² - 4y²
= (4a)² - (2y)² ← difference of squares
The standard diameter of a golf ball is 42. 67 mm. A golf ball factory does quality control on the balls it manufactures. Golf balls are randomly measured to ensure the correct size. One day, an inspector decides to stop production if the discrepancy in diameter is more than 0. 002 mm. Which function could represent this situation?.
The absolute value function that could represent this situation is:
[tex]|D - 42.67| = 0.002[/tex]
The absolute value function is defined by:
[tex]|x| = x, x \geq 0[/tex]
[tex]|x| = -x, x < 0[/tex]
It measures the distance of a point x to the origin.The diameter should be of 42.67 mm with an allowance of 0.002 mm. Thus, the absolute value of the difference between the diameter and of 42.67 should be of 0.002, that is:
[tex]|D - 42.67| = 0.002[/tex]
A similar problem is given at https://brainly.com/question/24514895
a certain store is selling packages of 10 pencils and 4 pens. the manager wants to make a larger package in the same ratio. if the large package has 10 pens, how many pencils are in the large package?
Answer: 25 pencils
Step-by-step explanation:
2 × 5 = 10
5 × 5 = 25
Mr. Walker asked his students to use the associative property to find an expression that is equivalent to (13 + 15 + 20) + (20 + 47 + 18). The expressions that four students created are shown in the table below.
Expressions Generated by Students
Student
Expression
Jeremy
(20 + 13 + 15) + (20 + 47 + 18)
Layla
(20 + 47 + 18) + (13 + 15 + 20)
Keith
(13 + 20) + (20 + 47 + 18) + 15
Melinda
(13 + 15 + 20 + 20) + (47 + 18)
How many of the students correctly applied only the associative property to rewrite the expression?
one
two
three
four
Mark this and return
Answer:
Jeremy
Step-by-step explanation:
You need to add 20+13+15=48 Then you add 20+47+18=85.
Out of 1700 people 49% were females how many more males than females were at the concert?
Pls explain how
Answer: 51% were males
Which means that there were 1% more males than females = 34 more males than Females
Step-by-step explanation:
100%-49%=51%
51%-49%=1%
1700x49%=833 females
1700x51%=867 males
867 Males -833 Females = 34 more Males
Evaluate the expression below.
5^{0}5
0
The 5-0-5 Agility Test is one of the most commonly recognised agility tests, despite its inability to actually measure agility. Instead, this is a change of direction speed test, which contrary to common belief, may not be capable of distinguishing between dominant and non-dominant leg performances.
Can someone help please no links
Answer:
-4 or 4 I would have to go with-4!!
Step-by-step explanation:
I hope this helps in any way!!
Ari needs to mix 3 tablespoons of dish soap with 6 tablespoons of vinegar to make a cleaning solution. How many tablespoons of vinegar are needed for each tablespoon of dish soap?
Answer:1 tablespoon of dish soap to 2 tablespoons of vinegar
Step-by-step explanation:
Answer:
1 tablespoon of dat soap to 2 table spoons of dat vinegar.
Step-by-step explanation:
So imagine. If 3 tablespoons of dish soap is to 6 table spoons of vinegar then 3 goes into 6 twice. So, 1 tablespoon of dish soap is it 2 table spoons of vinegar.
another way to look at it:
1tbs dish soap = 2tbs vinegar
2tbs dish soap = 4tbs vinegar
3tbs dish soap = 6tbs vinegar
Simplify this expression:
[tex]7xy - x^{2}t+4xy+5x^{2}t[/tex]
Answer:
[tex]11xy+4x^{2} t[/tex]
Step-by-step explanation:
1. Collect Like Terms
[tex](7xy+4xy)+(-x^{2} t+5x^{2} t)\\[/tex]
2. Simplify.
[tex]11xy+4x^{2} t[/tex]
What is the median of 8,19,36,46,56
Answer:
median = 36
Step-by-step explanation:
The median is the middle value of the data arranged in ascending order.
8 19 36 46 56
↑ middle value
median = 36
The FM radio station KAMB broadcast from an antennae atop a 150 meter tall radio tower at a frequency of 90 MHz with a total radiated power of 40 kilowatts. Neighbors have complained about problems they attribute to excessive radiation from the tower, but the city engineer who measured the radiation level near the base of the tower found it to be well below the accepted standard. You have been hired by the HOA to assess the engineer's report. You know a few things about electromagnetic radiation and therefore conclude that we must find the optimum place on the ground to measure the maximum radiation emitted from the antennae. From your extensive knowledge in physics, you know that the intensity of radiation, I, is given by the formula:
I=12/32π*Psin2(θ)/r^2
where P is the power output, r is the distance from the top of the tower to the point on the ground, and θ is the angle measured from the tower to r.
Find the distance R from the base of the tower to the optimum location for taking the radiation reading. (m)
What is the maximum radiation reading from the ground in kw/m^2
If the city code requires that electromagnetic radiation be under 200 microwatts per square meter, is this antenna operating within city code? Yes or No
Answer: 150 m, 5.305*10^-5 kW/m^2, No
Step-by-step explanation:
See attachment, hope this helps
Using the radiation intensity formula we will have to:
a) [tex]150 m[/tex]
b) [tex]5.305*10^{-5} kW/m^2[/tex]
c)No
From the data informed, we have:
[tex]h=150m\\P=40KW[/tex]
Using the given formula and performing some mathematical operations:
[tex]I=\frac{12Psin^2(\theta)}{32(\pi)r^2} \\I= \frac{12(40)(R/r)^2}{32(\pi)r^2} \\= \frac{15R^2}{r^2\pi } \\= \frac{15R^2}{(R^2+150^2)^2\pi} \\[/tex]
deriving the given equation, we will have:
[tex]=\frac{(R^2+150^2)^22R-R^2(2(R^2+150^2))2R}{(R^2+150^2)^2}[/tex]
So from this equation we have that the answer of the letter A corresponds:
[tex]R=150[/tex]
For letter B we will have to develop this equation:
[tex]I= 5.30X10^{-5}[/tex]
As for the letter C, when converting the value found, it should give 200 microwatts, which is false.
Learn more: brainly.com/question/10148635
Clarke earns
2.5
%
interest a savings account each year. If Clarke deposits
$
2
,
000.00
into a savings account, how much interest will Clarke earn during the first year?
Answer:
$ 50.00
Step-by-step explanation:
Hope this helps!
