Answer: v = -3
=========================================
Work Shown:
[tex]5 = \sqrt{-2-6v}+1\\\\5-1 = \sqrt{-2-6v}\\\\4 = \sqrt{-2-6v}\\\\4^2 = \left(\sqrt{-2-6v}\right)^2 \ \text{ .... square both sides}\\\\16 = -2-6v\\\\16+2 = -6v\\\\18 = -6v\\\\-6v = 18\\\\v = 18 \div (-6)\\\\v = -3[/tex]
As you can see, we don't square both sides until the square root portion is fully isolated or on its own side. So it happens after we subtract 1 from both sides.
Technically, you are able to square both sides without first isolating the square root. But that would mean you'd have to use the FOIL rule and things would get a bit messier than they have to be. Not to mention that the square root term wouldn't fully go away (so you'd have to square again later down the line).
------------------
Checking the answer:
Replace every copy of v with -3. Simplify both sides. We should end up with the same number on each side
[tex]5 = \sqrt{-2-6v}+1\\\\5 = \sqrt{-2-6(-3)}+1\\\\5 = \sqrt{-2+18}+1\\\\5 = \sqrt{16}+1\\\\5 = 4+1\\\\5 = 5\\\\[/tex]
The answer is confirmed.
Adante begins to evaluate the expression 3 and one-third times 5 and one-fourth using the steps below.
Answer:
(3)(5) + (1/3)(5) + (3)(1/4) + (1/3)(1/4)
Step-by-step explanation:
I'm pretty sure that's the correct answer..
As per the following steps the expression [tex]3\frac{1}{3}+5\frac{1}{4}[/tex] has the solution 18.
The question is incomplete I provided the complete problem in the image below.
What is a fraction?A fraction is a number that in mathematics represents a portion of a whole. There are two parts: a numerator and a denominator. The denominator is the total number of pieces that make up the whole, while the numerator is the number of equally sized portions of the whole.
How to solve it?[tex]3\frac{1}{3}\times 5\frac{1}{4}\\=3\frac{1}{3}\times(5+\frac{1}{4})\\=3\frac{1}{3}\times5+3\frac{1}{3}\times\frac{1}{4}\\=(3+\frac{1}{3})\times 5+(3+\frac{1}{3})\times \frac{1}{4}\\=3\times5+\frac{1}{3}\times 5+3\times\frac{1}{4}+\frac{1}{3}\times\frac{1}{4}\\=15+\frac{5}{3}+\frac{3}{4} +\frac{1}{12}[/tex]
In this manner, we solve our problem.
We find the solution to the expression [tex]3\frac{1}{3}\times 5\frac{1}{4}[/tex] and get
[tex]15+\frac{5}{3}+\frac{3}{4} +\frac{1}{12}\\= 15+\frac{20+15+1}{12}\\=15+\frac{36}{12}\\[/tex]
= 15+3= 18
Hence, the solution of the expression is 18.
Learn more about fractions here-
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help ASAP Please show working
Answer:
(a) -1
(b) -2
Step-by-step explanation:
(a) Replace the a's with 1 and the b's with 3 to get 1*3 = 1-3+1 = -1
(b) We already figured out that (1*3) equals -1 so we just need to find -1*2. Using same strategy as part a, replace a and b with -1 and two, respectively. -1*2 = -1-2+1= -2. Hope this helps and sorry if I made a mistake. :)
Given the equation sqrt(x+1)+3=0, explain how to and solve this equation. Is the solution extraneous? Explain
√(x + 1) + 3 = 0 ==> √(x + 1) = -3
has no real solutions, since the square root cannot be a negative number. But if we were to ignore that for the moment, one might try taking the square of both sides, which gives
(√(x + 1))² = (-3)² ==> x + 1 = 9 ==> x = 8
But this is not a valid solution, since
√(8 + 1) = √9 = 3 ≠ -3
While -3 is a square root of 9, we had started off with the *positive* square root of x + 1.
A parabola intersects the x- axis at x=3 and x=9
Step-by-step explanation:
To find the equation of a parabola we need to have 3 points. The intercept of the X axis is the X intercept. The definition of an intercept is when the other value is equal to zero. (3,0) and (9,0)
There appears to not be enough points to answer your question. we also need a vertex
What is the surface area of a cube in which each face of the cube has an area of 7 cm^2?
Answer:
In a cube, the length and width are the same, so both sides will be 7 cm, yielding an area of 49 square centimeters. The surface area of a 7 cm cube will be 294 cm2 . Hope this helps!
THE PROBABILITY OF A FOOTBALL TEAM WINNING A MATCH IS 0.3 THE PROBABILTITY OF THE SAME FOOTBALL TEAM LOSING IS 0.55 WHAT IS THE PROBABILITY OF THE SAME FOOTBALL TEAM WINNING THE MATCH?
Answer:
[tex]P(Win) = 0.30[/tex]
Step-by-step explanation:
Given
[tex]P(Win) = 0.30[/tex]
[tex]P(Lose) = 0.55[/tex]
Required
[tex]P(Win)[/tex]
This is already stated in the question as:
[tex]P(Win) = 0.30[/tex]
Need help ASAP !!!!!
Answer:
Option A is correct answer
hear is explaination
[tex]\longrightarrow{\blue{a.\:90}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
[tex] - 3xy[/tex]
Plugging in the values "[tex]x = 5[/tex]" and "[tex] y = -6[/tex]", we have
[tex] = - 3(5)( - 6)[/tex]
[tex] = - 3( - 30)[/tex]
[tex] = 90[/tex]
[tex]\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘[/tex]
Brian and Hayden go out for dinner and the bill comes to $120.00. Hayden usually tips more than 20% of the bill and Brian usually tips at most 25% of the bill. Given Brian and Hayden's tipping habits, what graph below best represents the range for a tip (d) that the server should expect to see?
Answer:
There are no graphs
Step-by-step explanation:
"what graph below best represents the range for a tip "
Brian
120 * .2 = 24
24 < d
Hayden
120 * .25 = 30
d ≤ 30
24 < d ≤ 30
Which product results in x^2-1
a rational number between -2/3 and 1/4 is
Answer:
[tex]\frac{-7}{12} , \frac{-6}{12} , \frac{-5}{12},\frac{-4}{12} ,\frac{-3}{12} ,\frac{-2}{12} ,\frac{-1}{12},\frac{1}{12} ,\frac{2}{12}[/tex]
Step-by-step explanation:
Given :
To find rational number between -2/3 and 1/2
Firstly need to equate their denominator
[tex]\frac{-2(4)}{3(4)} =\frac{-8}{12} \\\frac{1(3)}{4(3)} =\frac{3}{12}[/tex]
Now,
Rational number between these two numbers will be :
[tex]\frac{-7}{12} , \frac{-6}{12} , \frac{-5}{12},\frac{-4}{12} ,\frac{-3}{12} ,\frac{-2}{12} ,\frac{-1}{12},\frac{1}{12} ,\frac{2}{12}[/tex]
The amount of taxes on a chair was $3.60 the text is the tax rate was 5% find the original price of the chair??
Answer:
Original Price = $72.
Step-by-step explanation:
You first need to know that $3.60 is 5% of the original price.
Then you need to multiply by 20, because 100/5 is 20, meaning that the price multiplied is $72.
The answer is $72.
HELP FAST I NEVER SAW THIS BEFORE IN MY LIFE
I'll mark brainliest for the best answer!!
Answer:
GIRL NO WAY IM LITTERALY TAKING THAT TEST RN AND IM TRYING TO FIGURE OUT THAT SAME QUESTION LOL
Step-by-step explanation:
BUT I THINK ITS -0.5 DONT TAKE MY WORD FOR IT IM JUST ASSUMING ITS THE ANSWER BC ITS THE ONLY ONE THAT MAKES SENSE
The diagram shows triangle ABC.
A = 81°
AB = 8.2 cm
BC = 13.5 cm
Calculate the length of AC.
Answer:
The length of AC is 12.08 cm.
Step-by-step explanation:
Given:
In triangle ABC, AB = 8.2 cm, C = 13.5 cm and angle A = 81 degrees.
Solution:
https://brainly.com/question/21977218
This is erinna's answer, no need to thank me, thank her instead
Using Law of Sines, we get
Using angle sum property, we get
Now,
Therefore, the length of AC is 12.08 cm.
The length of the side AC of the triangle ABC whose side AB is of 8.2 cm and side BC is of 13.5 cm length with angle A of 81° is 12.1 cm approx.
What is law of cosine?Let there is triangle ABC such that |AB| = a units, |AC| = b units, and |BC| = c units and the internal angle A is of θ degrees, then we have:
[tex]a^2 + b^2 -2ab\cos(\theta) = c^2[/tex]
(c is opposite side to angle A)
When one angle and two sides of a triangle are known, and we want to know the length of the remaining third side, then we can use the law of cosines.
We're specified that:
Length of AB = |AB| = c = 8.2 cm|BC| = a = 13.5 cmm∠A = 81°Let the third side's length = |AC| = b cm (don't mix this notation with the notation of the formula said above. We just used notation such that its the smaller case version of the vertex opposite to that side, for example, opposite to AC lies b).
For using formula, we just need to take care that the angle θ is the angle opposite to the side which is going to be on one side (the notation c^2 in the formula given and here since we know the angle A, so the side opposite to A which is BC will be used in one side of the cosine rule, as shown below).
The side opposite to the angle A is BC, thus, we get:
[tex]|BC|^2 = |AB|^2 + |AC|^2 -2|AB||AC| \cos(m\angle A)\\\\13.5^2 = 8.2^2 + b^2 -2(8.2)b \cos(81^\circ)\\\\b^2 - 2.566 b - 115.01 \approx 0\\\\b \approx \dfrac{2.566 \pm \sqrt{2.566^2 - 4(-115.01)}}{2}\\\\b= 12.0835, -9.5175[/tex]
b represents side length, therefore positive. Thus, we obtained the length of the side |AC| approximately 12.1 cm
Thus, the length of the side AC of the triangle ABC whose side AB is of 8.2 cm and side BC is of 13.5 cm length with angle A of 81° is 12.1 cm approx.
Learn more about law of cosines here:
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Solve the system using substitution. Please write the solution in the form of a coordinate pair ( x, y ) SHOW YOUR
WORK!
15x = 30
y + 3x = 12
GIVING BRAINIEST TO WHOEVER HELPS ME AND GETS IN RIGHT!!!
18 km
12 km
20 km
or
14 km
Answer:
20 km
Step-by-step explanation:
Circumference is given by
C = pi*d
20 pi = pi *d
Divide each side by pi
20 =d
I dkabouthtisoneiuisrhihurg
Can someone help me? It's urgent and thank you!
Answer:
B. [tex]\frac{x + 6}{10x}[/tex]
Complete the table to show a proportional relationship,
Write the constant of proportionality, Number of Yoga Classes
Cost (5)
constant of proportionality
Answer:
Step-by-step explanation:
constant of proportionality : 60/4 = 15
Number : 2
Cost : 15 * 2 = $30
Number 6
Cost = 15 * 6 = $90
Number 8
Cost = 15 * 8 = $120
What is the perimeter in terms of x, of the rectangle shown here (x^2+7x-9) (3x^2-2x)
Given:
Consider the dimensions of the rectangle are [tex](x^2+7x-9)[/tex] and [tex](3x^2-2x)[/tex].
To find:
The perimeter in terms of x, of the rectangle.
Solution:
Let the length of the rectangle be [tex](x^2+7x-9)[/tex] and the width of the rectangle is [tex](3x^2-2x)[/tex] units.
The perimeter of a rectangle is:
[tex]P=2(l+w)[/tex]
Where, l is the length and w is the width of the rectangle.
Substituting [tex]l=(x^2+7x-9)[/tex] and [tex]w=(3x^2-2x)[/tex] in the above formula, we get
[tex]P=2((x^2+7x-9)+(3x^2-2x))[/tex]
[tex]P=2(4x^2+5x-9)[/tex]
[tex]P=2(4x^2)+2(5x)+2(-9)[/tex]
[tex]P=8x^2+10x-18[/tex]
Therefore, the perimeter of the rectangle is [tex]8x^2+10x-18[/tex] units.
Hello please help me with this! :D
Based on these segment lengths, which group of segments can form a triangle?
A. 3, 10, 14
B. 8, 7, 13
C. 3, 2, 5
D. 20, 7, 13
Which transformation is not isometric?
(Help fast plz)Which of these tables represents a linear function
Answer:
Step-by-step explanation:
3rd one
A pet store has 115 fish that need to be placed into fish tanks. Each tank can hold 6 fish. How many tanks does the store need for the fish?
Answer:19
Step-by-step explanation: draw the tanks put 6 fish in each tank until you get all 115 in each tank
A furnace was originally priced at $907.07 but went on sale for 33% off. If Omar bought the furnace and paid 9%
sales tax, how much did he pay in total?
PLZ HELP I’LL MAKE YOU A BRAINLEST
Answer:
662.44 total paid
Step-by-step explanation:
907.07X.33(33% off)=299.33 discount
907.07-299.33=607.74 sales price
607.74+.09=54.70 sales tax
607.74+54.70=662.44 sales price including sales tax
A mixture of concrete is made up of sand and cement in the ratio of 5:3.How many cubic centimeters of sand is needed to make 160 cubic centimeters of concrete mix?
Answer: [tex]100\ cm^3[/tex]
Step-by-step explanation:
Given
The ratio of mixture of sand and cement is 5:3
If the total volume of mixture is [tex]160\ cm^3[/tex]
Suppose there is 5x and 3x cubic centimeter of sand and cement respectively i.e.
[tex]\Rightarrow 5x+3x=160\\\Rightarrow 8x=160\\\Rightarrow x=20\ cm^3[/tex]
Sand [tex]5x=5\times 20=100\ cm^3[/tex]
So, there is [tex]100\ cm^3[/tex] of sand in the mixture
select the correct answer
Ans
i cant see the pic
Step-by-step explanation:
Answer:
B) 45°
Step-by-step explanation:
Because we are dealing with a right triangle, we have one angle which is a right angle and 2 angles that are the same measure since sinA=sinB. Since all the interior angles of a triangle must add up to 180°, then m∠A=45° because 2(45°)+90°=180°.
which of the following is the equation of a line perpendicular to the line y+-3/2 x+4
Answer:
The answer is (-2/3)x + 4.. I have added a picture with the solution
I need help solving these problems
Answer:
question one:
x = 6.018150231520483
adjacent angle = 7.986355100472928
Step-by-step explanation:
i have no links, but try to search triginometry calculator and pick carbide calculator for fast trigonometry calculations
it automaticly does sin, cos, and tan for you.
Find the sum of this series \displaystyle \log\left(\frac{1}{2}\right)+\log\left(\frac{2}{3}\right)+\log\left(\frac{3}{4}\right)+\log\left(\frac{4}{5}\right)+...+\log\left(\frac{98}{99}\right) +\log\left(\frac{99}{100}\right)log( 2 1 )+log( 3 2 )+log( 4 3 )+log( 5 4 )+...+log( 99 98 )+log( 100 99 )
Answer:
[tex]\log\left(\frac{1}{2}\right)+\log\left(\frac{2}{3}\right)+\log\left(\frac{3}{4}\right)+\log\left(\frac{4}{5}\right)+...+\log\left(\frac{98}{99}\right) +\log\left(\frac{99}{100}\right) = \log(\frac{1}{100})[/tex]
Step-by-step explanation:
Given
[tex]\log\left(\frac{1}{2}\right)+\log\left(\frac{2}{3}\right)+\log\left(\frac{3}{4}\right)+\log\left(\frac{4}{5}\right)+...+\log\left(\frac{98}{99}\right) +\log\left(\frac{99}{100}\right)[/tex]
Required
The sum
Using the laws of logarithm, we have:
[tex]\log(a) + \log(b) = \log(ab)[/tex]
Take the first two terms of the series
[tex]\log(\frac{1}{2}) + \log(\frac{2}{3}) = \log(\frac{1}{2} * \frac{2}{3})[/tex]
[tex]\log(\frac{1}{2}) + \log(\frac{2}{3}) = \log(\frac{1}{3})[/tex]
Include the third term
[tex]\log(\frac{1}{2}) + \log(\frac{2}{3})+ \log(\frac{3}{4}) = \log(\frac{1}{3} * \frac{3}{4})[/tex]
[tex]\log(\frac{1}{2}) + \log(\frac{2}{3})+ \log(\frac{3}{4}) = \log(\frac{1}{4})[/tex]
Include the fourth term
[tex]\log(\frac{1}{2}) + \log(\frac{2}{3})+ \log(\frac{3}{4}) + \log(\frac{4}{5}) = \log(\frac{1}{4} *\frac{4}{5})[/tex]
[tex]\log(\frac{1}{2}) + \log(\frac{2}{3})+ \log(\frac{3}{4}) + \log(\frac{4}{5}) = \log(\frac{1}{5})[/tex]
Notice the following pattern
[tex]\log(\frac{1}{2}) + \log(\frac{2}{3}) = \log(\frac{1}{3})[/tex] ---------------- n =2
[tex]\log(\frac{1}{2}) + \log(\frac{2}{3})+ \log(\frac{3}{4}) = \log(\frac{1}{4})[/tex] -------------- n = 3
[tex]\log(\frac{1}{2}) + \log(\frac{2}{3})+ \log(\frac{3}{4}) + \log(\frac{4}{5}) = \log(\frac{1}{5})[/tex] ----------- n = 4
So the sum of n series is:
[tex]\log(\frac{1}{2}) + \log(\frac{2}{3})+ ............ + \log(\frac{n}{n+1}) = \log(\frac{1}{n+1})[/tex]
So, the sum of the series is:
[tex]\log\left(\frac{1}{2}\right)+\log\left(\frac{2}{3}\right)+\log\left(\frac{3}{4}\right)+\log\left(\frac{4}{5}\right)+...+\log\left(\frac{98}{99}\right) +\log\left(\frac{99}{100}\right)[/tex]
[tex]\log\left(\frac{1}{2}\right)+\log\left(\frac{2}{3}\right)+\log\left(\frac{3}{4}\right)+\log\left(\frac{4}{5}\right)+...+\log\left(\frac{98}{99}\right) +\log\left(\frac{99}{100}\right) = \log(\frac{1}{99+1})[/tex]
[tex]\log\left(\frac{1}{2}\right)+\log\left(\frac{2}{3}\right)+\log\left(\frac{3}{4}\right)+\log\left(\frac{4}{5}\right)+...+\log\left(\frac{98}{99}\right) +\log\left(\frac{99}{100}\right) = \log(\frac{1}{100})[/tex]
APQR and ARST are shown.
S
R
R
Р
+
H
440
T
What is m TSR?
mZTSR = [1]
Answer:
∠ RST = 68°
Step-by-step explanation:
Since RT = ST then the triangle is isosceles with 2 base angles congruent
∠ RST = [tex]\frac{180-44}{2}[/tex] = [tex]\frac{136}{2}[/tex] = 68°