Answer:
b = - 1 ± [tex]\sqrt{\frac{10}{3} }[/tex]
Step-by-step explanation:
Given
6b² + 12b - 14 = 0 ( add 14 to both sides )
6b² + 12b = 14
To complete the square the coefficient of the b² term must be 1
Factor out 6 from the 2 terms on the left side
6(b² + 2b) = 14
To complete the square
add/subtract ( half the coefficient of the b- term)² to b² + 2b
6(b² + 2(1)b + 1 - 1) = 14
6(b + 1)² + 6(- 1) = 14
6(b + 1)² - 6 = 14 ( add 6 to both sides )
6(b + 1)² = 20 ( divide both sides by 6 )
(b + 1)² = [tex]\frac{20}{6}[/tex] = [tex]\frac{10}{3}[/tex] ( take the square root of both sides )
b + 1 = ± [tex]\sqrt{\frac{10}{3} }[/tex] ( subtract 1 from both sides )
b = - 1 ± [tex]\sqrt{\frac{10}{3} }[/tex] ← exact solution
Answer:
x = -1 ± √(10/3) = (-3 ± √30)/3
Step-by-step explanation:
Steps to complete this process:
ax² + bx + c = 0
Divide by the co-efficient of x² i.e. 'a'=> (ax² + bx + c)/a = 0/a
=> x² + (b/a)x + (c/a) = 0
=> x² + 2x(b/2a) + (c/a) = 0
Now it seems somewhat like a square (x² + 2x(b/2a), in order to complete:
Add (b/2a)² to both sides=> x² + 2(b/2a) + (b/2a)² + (c/a) = (b/2a)²
=> (x + b/2a)² + (c/a) = b²/4a²
=> (x + b/2a)² = (b² - 4ac)/4a²
So on & you can derive quadratic formula.
In the given question:
=> 6b² + 12b - 14 = 0
=> (6b² + 12b - 14)/6 = 0/6
=> b² + 2b - 7/3 = 0
=> b² + 2(1)b + 1² - (7/3) = 1²
=> (b + 1)² - (7/3) = 1
=> (b + 1)² = 10/3 or 30/9
=> b + 1 = ±√(30/9)
=> b = -1 ± √(30)/3
=> b = (-3 ± √30)/3
*this is the rationalized form(rational-denominator), exact answer:
=> (b + 1)² - (7/3) = 1
=> (b + 1) = ± √(10/3)
=> b = -1 ± √(10/3)
You can take LCM, and even rationalize it to (-3 ± √30)/3.
Find the length of the line segment in decimal form.
Answer:
Step-by-step explanation:
(2 , 4) ; ( -1 , -1)
[tex]Distance = \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]
why can u write both addition expression and subtraction expression for the situation
Answer:
It depends if the number is an integer {-1,+7,-7}
e.g -7+4
these numbers are integers that is why you can write both addition and subtraction expressions
Calculus (yet again)!
The water level of a certain body of water is changing at a rate of [tex]W(t) = \frac{1}{2}cos(3 - \frac{t}{2})[/tex] inches per hour, where t represents hours since 12 a.m.
What is the average hourly number of inches that the water level changes for this lake in one day?
I'm pretty sure that the number of inches that the water changes in one day would be represented by [tex]\int\limits^2_0 {W(t)} \, dt[/tex] (where the number on top of the integral is a 24), but how would I set up an integral for the average hourly number of inches? Thank you so much!
Answer:
The average hourly number of inches that the water level changes per day is about 0.0231 inches per hour.
Step-by-step explanation:
The water level of a certain body of water is changing at a rate represented by the function:
[tex]\displaystyle W(t) = \frac{1}{2}\cos \left( 3- \frac{t}{2}\right)[/tex]
Where W is measured in inches per hour and t represents hours since 12 A.M.
And we want to determine the average hourly number of inches that the water level changes for the lake in one day.
Recall that the average value of a function is given by:
[tex]\displaystyle f_\text{avg} = \frac{1}{b-a} \int_{a}^{b} f(x) \, dx[/tex]
Hence, the find the average hourly number of inches that the water level changes in one day, we simply need to find the average value of W from t = 0 to t = 24.
Substitute:
[tex]\displaystyle W(t)_{\text{avg}} = \frac{1}{(24)-(0)} \int_{0}^{24} \frac{1}{2}\cos \left(3 - \frac{t}{2}\right) \, dt[/tex]
Simplify:
[tex]\displaystyle W(t)_{\text{avg}} = \frac{1}{24} \int_{0}^{24} \frac{1}{2}\cos \left(3 - \frac{t}{2}\right) \, dt[/tex]
Evaluate using u-substitution. We can let:
[tex]\displaystyle u = 3 - \frac{t}{2} \Rightarrow du = -\frac{1}{2}\, dt\Rightarrow -2\, du = dt[/tex]
Hence:
[tex]\displaystyle W(t)_{\text{avg}} = -\frac{1}{24} \int_{3}^{-9} \cos u \, du[/tex]
Evaluate:
[tex]\displaystyle \begin{aligned} W(t)_{\text{avg}} &= \frac{1}{24}\int_{-9}^{3} \cos u\, du \\ \\ &= \frac{1}{24}\left(\sin u\Big|_{-9}^{3}\right) \\ \\ &= \frac{1}{24}\left(\sin3 - \sin -9\right) \\ \\ &=\frac{1}{24}\left(\sin 3 + \sin 9\right) \\ \\ &\approx0.0231 \end{aligned}[/tex]
In conclusion, the average hourly number of inches that the water level changes per day is about 0.0231 inches per hour.
Which statement is supported by the graph?
The bicycle has speed but not velocity.
The bicycle is moving at a constant velocity.
The bicycle has a displacement of 3 m.
The bicycle is not in motion.
Answer:
The correct answer is D. The bicycle is not in motion.
Step-by-step explanation:
In the position-time graph we can see that the position of the cycle hasn't changed when the time has changed (e.g. when time changes from 2s to 3s, the position remains 3m). Therefore, we can conclude that the cycle is not moving, and therefore answer D. is correct.
Answer:
its d
Step-by-step explanation:
WHATS 9+10??????????????
I need the volume of part f in this question and please show the working if you do solve it !!
Answer:
10 x 4 x 3=120
4 x 3 x 3=36
4 x 3 x 3=36
120+48+48=192
im sorry....i don't know the proper working>_<
look at the adjoining figure and write 2 pairs of intersecting lines.
Answer:
Line AB and Line GHLine CD and Line FFConcept:
Intersecting lines are lines that overlap upon only one point. The number of lines can be two or more.
Intersecting lines can intersect at any angle.
Solve:
There are in total four intersecting points in the given figure.
As we can see from the figure, any two lines would intersect each other
Therefore, 2 pairs of intersecting lines can be any pairings of lines that are not in the same orientation.
Line AB and Line GHLine CD and Line FFHope this helps!! :)
Please let me know if you have any questions
When the sum of the internal angles of a polygon is 10 right angles, then how
many sides does it have?
Answer:
7 sides
Step-by-step explanation:
formula for sum of interior angles
(n-2)× 180= 10 right angles
(n-2)× 180 = 900
n-2= 900÷180
n= 5+2
n= 7
how do you solve sin(x) + cos(x) * tan(x)
Step-by-step explanation:
[tex] \sin(x) + \cos(x) \times \tan(x) \\ = \sin(x) + \cos(x) \times \frac{ \sin(x) }{ \cos(x) } \\ = \sin(x) + \sin(x) \\ = 2 \sin(x) [/tex]
Step-by-step explanation:
sin(x) + cos(x) = sin x ÷cos x
sin(x) + cos(x) sin(x) ÷ cos (x)
join cos x and sin x
sin x + sin x
cancel cos x with cos x
The answer is 2 sin x
How can a frequency table or histogram help you organize and analyze data?
Answer:
[tex]\red{{\sf{NONSENSE=}}}[/tex]
[tex]\blue{{\sf{REPORT}}}[/tex]
[tex]\color {red}{•}\color {orange}{•}\color {yellow}{•}\color {lime}{•}\color {green}{•}\color {cyan}{•}\color {aquamarine}{•}\color {indigo}{•}\color {blue}{•}\color {violet}{•}\color {blueviolet}{•}\color {pink}{•}\color {magenta}{•} \color {brown}{•}\color {gray}{•}\color {black}{•}[/tex]
What is the length of the altitude of the equilateral triangle below?
Answer:
B
Step-by-step explanation:
Using the sine ratio in either of the 2 right angles and the exact value
sin60° = [tex]\frac{\sqrt{3} }{2}[/tex] , then
sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{a}{4\sqrt{3} }[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )
2a = 4[tex]\sqrt{3}[/tex] × [tex]\sqrt{3}[/tex] = 12 ( divide both sides by 2 )
a = 6 → B
Find the equation of the line that is perpendicular to y=-2x+1 and contains the point (8, 2).
Answer:
y = 1/2x - 2
Step-by-step explanation:
In order for a line to be perpendicular to another, the lines must have opposite reciprocal slopes.
Example of an opposite reciprocal slope: -2 ⇒ 1/2
Insert the information into the point-slope formula:
[tex]y-y_1=m(x-x_1)\\\\y-2=\frac{1}{2}(x-8)\\\\y-2=\frac{1}{2}x-4\\\\y=\frac{1}{2}x-2[/tex]
calculate the area of the classroom.area =l×b
answer it plz
step by step plz
Answer:
I HOPE IT WILL HELP YOU A LOT.
Have a great day ahead.
You use a crowdfunding website to raise money. the website keeps 5% of each donation. Five of your friends each donate the same amount.e total funding you receive is $47.50. How much does each friend donate?
Answer:
Step 1:
Let x represent the amount of each friend donate
Website keeps = 5%
Total funding I receive = $ 47.50
4.75x = $47.50
Step 2:
4.75 = $47.50 - Write the equation
[tex]\frac{4.75x}{4.75}[/tex] = [tex]\frac{47.50}{4.75}[/tex] - Divide both sides of the equation by 4.75
The solution is x = 10
ANSWER: Each friend donates $10
hope this helps Have a good day.
Each friend donates $10.
It is required to find How much does each friend donate.
What is arithmetic?The branch of mathematics dealing with the properties and manipulation of numbers. a science that deals with the addition, subtraction, multiplication, and division of numbers. Fractions, decimals, percentages, fractions, square root, exponents, and other arithmetic operations are used to achieve mathematical simplifications.
Given :
The website keeps 5% of each donation.
Five of your friends each donate the same amount.
Total funding receive is $47.50.
Let x represent the amount of each friend donate
According to question we have,
4.75x = $47.50
Divide both sides of the equation by 4.75 we get,
x = 10
Therefore, each friend donates $10.
Learn more about arithmetic here:
brainly.com/question/24423838
#SPJ2
n the expression below, the letters A,B, C, D and E represent the numbers 1, 2, 3, 4
and 5 in some order.
A×B +C ×D +E
What is the largest possible value of the expression?
Answer:
A × B + C × D + E
1 × 2 + 3 × 4 + 5
= 19
Solve for x: |4x + 12| = 16 (5 points)
Group of answer choices
x = 7, x = −7
x = 1, x = −1
x = 1, x = −7
x = −1, x = 7
X= 1 , X= –7
I hope I helped you^_^
-5.025, -square root of 25, -5 1/2, -11/2 least you greatest
answer =-51/2,-11/2,-5.025,-✓25
-✓25=-5
-11/2=-5.5
-51/2=-25.5
-5.025
In the diagram, bisects FGI.
Angle FGI is formed from angles FGH and HGI. Angle FGH measures 4 x minus 7 degrees. Angle HGI measures 5 x minus 14 degrees.
a.
Solve for x and find mFGH.
b.
Find mHGI.
c.
Find mFGI.
a. x
nothing (Simplify your answer.)
Answer:
C 100%
Step-by-step explanation:
Select the coff
A company that bottles mustard is allowed to advertise their bottle size as 21 ounces as long as the actual amount in the bottle is within
0.15 ounces of that amount. Which inequality shows all the possible actual bottle volumes (1) that the manufacturer would be able to advertise
as 21 ounces?
Answer:
d
Step-by-step explanation:
v+21
[tex]v + 21 \leqslant 0.15[/tex]
The inequality is v+ 21 ≤ 0.15
What is inequality?A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
Given:
A company that bottles mustard is allowed to advertise their bottle size as 21 ounces as long as the actual amount in the bottle is within 0.15 ounces of that amount.
So,
if the volume is v then the situation can be represented as
v+ 21 ≤ 0.15
As, the actual amount is within 0.15 ounces of that amount.
Learn more about inequality here:
https://brainly.com/question/20383699
#SPJ2
Write 8-to 10 sentences about how math can make you a good leader/worker?
^^i didn't really understand that one and yes ill give brainliest and yes I will report your answer if you put absurd stuff
Step-by-step explanation:
Mathematics is a methodical application of matter. ... Mathematics makes our life orderly and prevents chaos. Certain qualities that are nurtured by mathematics are power of reasoning, creativity, abstract or spatial thinking, critical thinking, problem-solving ability and even effective communication skills.pls make me the brainliest
Answer:
Math can make you a good leader and worker in many ways. Math is a subject that usually includes lots of problem-solving and critical thinking skills. When taking a math class you acquire lots of experience with those. Some areas of math such as Calculus, can be very difficult and take lots of determination to learn. People that are able to effectively solve problems are very valuable to businesses as workers and will often be hired and promoted before others who don't posses the same problem-solving skills. Knowing how to make basic calculations without a calculator can also be very useful in any field of work.
The product of 4 and a number x
Answer:
you can`t multiply an integer with a variable unless the variable represents something
ex: if x = 10 then the product of 4 and x is 40
Answer:
4x
Step-by-step explanation:
'Product' refers to multiplication.
Solve the following problem. Round to one decimal place if necssary.
Answer:
x = 16.1051577
Step-by-step explanation:
tan0 = opp/adj
tan0 = 14/x
tan(49)× 14 = 16.1051577
The domain for f(x) and g(x) is the set of all real numbers
Let f(x) = 3x + 5 and g(x) = x^2
Find (f + g)(x).
Answer:
3x square + 5 is your answer
marginal relative frequency example?
Answer:
Marginal relative frequency is the ratio of the sum of the joint relative frequency in a row or column and the total number of data values. Remember, the marginal frequency numbers are the numbers on the edges of a table, kind of like the margins are the areas on the edge of a paper.
Write an equation in slope-intercept form of a line that passes through the point (-4,9) and has a slope of 1/2.
Answer:
y = 1/2x + 11
Step-by-step explanation:
y = 1/2x + b
9 = 1/2(-4) + b
9 = -2 + b
b = 11
please help asap show work and dont put links
Answer:
square root of x. so just find the square roots of all the inputs. you can tell its square root of x cuz all of things where both boxes are fille in each side have the same patter. square root of 1 is 1 square root of 49 is 7 square root of 25 is 5
Step-by-step explanation:
2sinx/2cosx-secx=tan2x
Answer:
hope it help u
Step-by-step explanation:
2sinx/(2cosx – secx)
=2 sinx/(2cosx–1/cosx)
as secx = 1/ cosx
multiplying both the denominator and numerator by cost,we get
2sinxcosx/( 2cos^2x –1) =cos2x
since,2sinxcosx = sin2x and 2cos^2 –1=cos2x
2sinxcosx/(2cos^2x– 1)= sin2x/ cos2x = tan2x
10q - 20 is equivalent to _____.
2(q - 10)
10(q - 20)
10(q - 2)
is 3.4567, 3.4567... irrational or rational
Answer:
Irrational
Step-by-step explanation:
Because irrational this number do not repeat so there for it is not rational.