Answer:
Step-by-step explanation:
As seen from the first given equation: x + 1/x = 2
If we think of x as x/1 instead then we get:
x/1 + 1/x = 2.
To combine the fractions we multiply the top and bottom of the first one (x/1) by x to get x^2/x so both have the same denominator so we can combine them which gives us:
(x^2+1)/x=2
Move x to the other side and we get:
x^2+1=2x
Move it back and we get a quadratic equation of
x^2 - 2x + 1
This factors into (x-1)(x-1) meaning x=1
For all the other equations they are equal because x=1.
1 to the power of anything is still one so each of the equations below will result in: 1+1/1 which is 2.
Therefore all of them are equal.
Hope this helped!
x+a=3/4 I don't know how to solve this and I need someone to help explain it to me.
-5 - 1 =
please help me and it isnt -4
Answer:
the answer is -6
Step-by-step explanation:
if you have -5 and you take away another number, you end up with -6
Answer:
-6
Step-by-step explanation:
-5 - 1 ISNT -4
-5 + 1 IS -4
If m 8 =22, m 7=31, and m EAD=102 find m 9
S is the answer
Step-by-step explanation:
Let 3+4+8+9+13+14+18+___ 40 terms=S
Solve for a. 2z=4a/m +3
Answer:
a = (2mz - 3m)/4Step-by-step explanation:
2z = 4a/m +3
-3 -3
2z - 3 = 4a/m
×m ×m
(2z -3)m = 4a
÷4 ÷4
[(2z -3)m]/4 = a
a = (2mz - 3m)/4
Marco arranged the tiles in this way, and then wrote an expression based on his arrangement. What expression do you think Marco might have written?
Answer: 2(2a+b)^2
Step-by-step explanation:
4a+2b then squared which doubles it
What is 4/q as a decimal
Answer:
what is the value of q?
Step-by-step explanation:
3. Given: a+b=12 and ab=9
Use (a + b)2 to find a² +bº. (Do not solve for a and b individually)
Answer:
a²+b²=126
Step-by-step explanation:
(a+b)²=a²+b²+2ab
(12)²=a²+b²+2×9
144=a²+b²+18
a²+b²=144-18=126
please someone help me to prove this...
Answer: see proof below
Step-by-step explanation:
Use the following Power Reducing Identities:
[tex]\cos^2 A = \dfrac{1}{2}(1 + \cos 2A)\\\\\sin^2 A = \dfrac{1}{2}(1 - \cos 2A)[/tex]
Use the following Product to Sum Identity:
[tex]\cos A\cdot \cos B=\dfrac{1}{2}\bigg[\cos(A+B)+\cos(A-B)\bigg][/tex]
Proof LHS → RHS
[tex]\text{LHS:}\qquad \qquad \qquad \cos^2\beta\cdot \sin^4\beta\\.\qquad \qquad \qquad =\cos^2\beta\cdot \sin^2\beta\cdot \sin^2 \beta[/tex]
[tex]\text{Power Reducing:}\qquad \dfrac{1}{2}\bigg(1+\cos 2\beta\bigg)\dfrac{1}{2}\bigg(1-\cos 2\beta\bigg)\dfrac{1}{2}\bigg(1-\cos 2\beta\bigg)\\\\\\.\qquad \qquad \qquad \quad =\dfrac{1}{8}(1+\cos 2\beta)(1-\cos 2\beta)(1-\cos 2\beta)[/tex]
[tex]\text{Expand:}\qquad \qquad \dfrac{1}{8}\bigg(1-\cos 2\beta-\cos^2 2\beta+\cos^3 2\beta\bigg)\\\\.\qquad \qquad \qquad =\dfrac{1}{8}\bigg(1-\cos 2\beta-\cos^2 2\beta+\cos^2 2\beta \cdot \cos \2\beta\bigg)[/tex]
[tex]\text{Power Reducing:}\qquad \dfrac{1}{8}\bigg(1-\cos 2\beta -\dfrac{1}{2}(1+\cos 4\beta)+\dfrac{1}{2}(1+\cos 4\beta)\cos 2\beta\bigg)\\\\.\qquad \qquad \qquad =\dfrac{1}{16}\bigg(2-2\cos 2\beta -1-\cos 4\beta +\cos 2\beta +\cos 4\beta \cdot \cos 2\beta \bigg)\\\\.\qquad \qquad \qquad =\dfrac{1}{16}\bigg(1-\cos 2\beta -\cos 4\beta+\cos 4\beta \cdot \cos 2\beta \bigg)[/tex]
[tex]\text{Product to Sum:}\quad \dfrac{1}{16}\bigg(1-\cos 2\beta -\cos 4\beta +\dfrac{1}{2}[\cos(4\beta+2\beta)+\cos (4\beta-2\beta)]\bigg)\\\\.\qquad \qquad \qquad =\dfrac{1}{32}\bigg(2-2\cos 2\beta -2\cos 4\beta +\cos 6\beta +\cos 2\beta\bigg)\\\\.\qquad \qquad \qquad =\dfrac{1}{32}\bigg(\cos 6\beta-2\cos 4\beta -\cos 2\beta +2 \bigg)[/tex]
[tex]\text{LHS=RHS:}\\ \dfrac{1}{32}\bigg(\cos 6\beta-2\cos 4\beta -\cos 2\beta +2 \bigg)=\dfrac{1}{32}\bigg(\cos 6\beta-2\cos 4\beta -\cos 2\beta +2 \bigg)[/tex]
HELP WILL GIVE BRAILEST AND WILL GIVE 50 POINTS!!!!! (also please tell me how you did it!) Simplify and Solve: 12x + 8 < 116
Answer:
Step-by-step explanation:
1. isolate the variable subtract both sides by 8 (12x+8-8<116-8)
2. Divide both sides by twelve (12x/12<116-8/12)
3. Simplify (x<108/12)
4. Answer (x<9)
=12x+8−8<116−8
=12x<108
Step 2: Divide both sides by 12.[tex] \frac{12x}{12} < \frac{108}{12} [/tex]
Answerx<9
The amount of water in reservoirs is often measured in acre-ft. One acre-ft is a volume that covers an area of one acre to a depth of one foot. An acre is 43,560 ft2. Find the volume in SI units of a reservoir containing 46.0 acre-ft of water.
Answer:
56740.15908m³
Approximately to the nearest whole number, the volume of 46 acre-ft of reservoir = 56740m³
Step-by-step explanation:
1 meter = 3.28084ft
1 acre = 43,560 ft²
Therefore, using our unit conversion, the volume in S.I units of a reservoir containing 46 acre- ft of water is calculated as :
46 acre - ft × (1 meter/3.28084ft) × (43,560ft²/1 acre) × (1 meter/3.28084ft)²
= 2003760/35.314670112
= 56740.15908m³
Approximately to the nearest whole number, the volume of 46 acre-ft of reservoir = 56740m³
what should be added m(m-n) to get square ofm(m-n)
Answer: m²-mn
Explanation: multiply the letter outside the brackets by everything inside the brackets, so, m×m = m² and m×n = mn, altogether it is m²-mn.
Mr. Green's lawn mower holds 600 milliliters of gasoline in the tank. He just filled his 6 liter gas can at the station. How many times will he be able to fill his lawn mower tank from the gas can?
Answer:
10 times.
Step-by-step explanation:
Since 1 liter = 1000 milliliters, we can say that 600 milliliters is equal to 0.6 liters because 600/1000 = 0.6
Since the gas can holds 6 liters, and the lawn mower holds 0.6 liters, 6/0.6 = 10.
So, he can fill his lawn mower 10 times with the gas can
Mr Green can fill his lawn 10 times
the first step is to convert the milliliters to liters
600 milliliters to liters
= 600/1000
= 0.6 liters
the number of times can be calculated as follows
= 6/0.6
= 10
hence it will take Mr. Green 10 times to fill his lawn mower
please see the link below for more information
https://brainly.com/question/632986?referrer=searchResults
what is the constant for -9x^3+12p+6
A constant is any numbers in an equation that don't have any variable connected to it.
-9x^3 and 12p are not constants since they are connected to variables.
6 is a constant because its not connected to any variable.
Best of Luck!
Dose every positive real number
also have both a positive and negative cube root?
Answer:
Any real number will have only one real cube root. Hence the technicalities associated with the principal root do not apply.
Step-by-step explanation:
i need help finding the range
Answer:
I think it's -1, 4. But i'm not a 100% sure.
Step-by-step explanation:
Answer:
To find the range, first order the data from least to greatest. Then subtract the smallest value from the largest value in the set.
Step-by-step explanation:
This is how you solve for Range; I can't view the image on my chromebook.
5/8-(1/4) to the 2 power
Answer:
0.5625
Step-by-step explanation:
unit rate 232 miles in 4 hours
Answer:
58 miles per hour
Step-by-step explanation:
leave a heart please :D
36. Find the circumference of a circle with a radius of 8 kilometers. Use 3.14 or for T.
37.Find the area of a circle with a diameter of 26 inches. Use 3.14 or for T.
Answer:
36. 58.34
37. 530.66
Step-by-step explanation:
36. 2x3.14x8=7.28x8=58.34
so 36=58.34
37.
3.14x26/2=3.14x13x13=530.66
please brainly
Point N is between M and R. If MN = 25 in, and NR = 12 in, then what is the length of MR?
If the cost, C, for manufacturing x units of a certain product is given by C=x2+10x+45, find the number of units manufactured at a cost of $ 10,020.
Answer: 95 units.
Step-by-step explanation:
The cost of making x units is:
C(x) = x^2 + 10*x + 45.
Now, if the cost is $10,020, then we can solve this for x as:
C(x) = 10,020 = x^2 + 10*x + 45
x^2 + 10*x + 45 - 10,020 = 0
x^2 + 10*x - 9,975 = 0
Now, remember that for a quadratic equation:
a*x^2 + b*x + c = 0
the solutions are:
[tex]x = \frac{-b +-\sqrt{b^2 - 4*a*c} }{2*a}[/tex]
In this case the solutions are:
x = [tex]x = \frac{-10 +-\sqrt{10^2 - 4*1*(-9,975)} }{2*1} = \frac{-10 +- 200}{2}[/tex]
Then we have two solutions, one for each sign:
x = (-10 -200)/2 = -110
x = (-10 + 200)/2 = 95
Here we must choose the positive option, as x represents a positive quaintity.
Then the number of units manufactured is 95.
Can someone please help to explain this?
Answer:
[tex]\frac{PQ}{DE}[/tex] = [tex]\frac{4}{6}[/tex]
Step-by-step explanation:
Given
Δ PQR ~ Δ DEF
Then the ratio of corresponding sides are equal
The corresponding letters in the names of the triangles gives the corresponding sides.
Thus PQ/DE, QR/EF, PQ/DF
In this case
[tex]\frac{PQ}{DE}[/tex] = [tex]\frac{4}{6}[/tex]
what is 3,393 divided by 13
Answer:
261
I hope this helps!
The level of various substances in the
blood influences our health. Here are
measurements of the level of phosphate
in the blood of a patient, in milligrams of
phosphate per deciliter of blood, made
on 6 consecutive visits to the clinic:
5.6, 5.2, 4.6, 4.9, 5.7, 6.4
What is the standard deviation for these
data?
A. .642
B. 5.4
O. 32.4
D. 177.02
Answer:
A
Step-by-step explanation:
Owen made 60% of the shoys he attempted during his hockey practice he made 18 shots how many shots did owen attempt during hocjey pratice
The world's largest ocean, the Pacific ocean, has an area of about 200,000,000 km^(2) , which can be written as 2 x 10 ^(n) km^(2). What is n?
Answer:
n = 8
Step-by-step explanation:
:)
A farmland is 30cm long and 15cm wild what is the area of the farmland
Suppose you have 20 coins that total $3.00. Some coins are nickels and some are quarters. Which of the following pairs of equations would you use to find out how many of each coin you have?
Answer:
Step-by-step explanation:
n + q = 20
.05n + .25q = 3.00
5n + 25q = 300
n + q = 20
5n + 25q = 300
-5n - 5q = -100
20q = 200
q = 10 quarters
n + 10 = 20
n = 10 nickels
(10 nickels, 10 quarters)
Select the correct answer.
Which graph represents the solution to this inequality?
-(127 + 8) < -21 + 11
OA. tt
-17
-15
-13
-11
-9
7
-5
+
-17
- 15
- 13
-11
-9
-7
-5
Oc.
+
-17
- 15
-13
- 11
-9
7
-5
C
-17
-15 -13
-11
-9
-7
-5
Answer:
C
Step-by-step explanation:
Given
- [tex]\frac{1}{4}[/tex] (12x + 8) ≤ - 2x + 11 ← distribute parenthesis on left side
- 3x - 2 ≤ - 2x + 11 ( add 3x to both sides )
- 2 ≤ x + 11 ( subtract 11 from both sides )
- 13 ≤ x , thus
x ≥ - 13
Since x can equal - 13 then a solid circle at - 13 represents the solution
Since x greater than - 13 then the arrow is facing to the right of - 13 on the number line.
Then the graph representing the solution is C
Find sets of three consecutive odd integers whose sum is between 100 and 115
Answer:
33, 35, 37
Step-by-step explanation:
Consecutive: in a row
Odd: any number not evenly divisible by 2
Integers: Whole numbers
Sum: the answer to an addition problem
So, 100 is close to 30*3, so start there and move on. It has to be a little more, so start at 31, 33, and 35, but it's only 99, so you need something a little more. Check 33, 35, and 37 to be sure, and you've got your answer!
What is 3X to the second power plus 4X -3+ negative 4X to the second power minus 2X -4 in polynomial form
Answer:
The polynomial form of the expression is: 25·X² + 2·X + 2.
Step-by-step explanation:
The expression that can be formed using the provided data is:
[tex](3X)^{2}+(4X-3)+(-4X)^{2}-(2X-4)[/tex]
Simplify the expression to get a result in polynomial form as follows:
[tex](3X)^{2}+(4X-3)+(-4X)^{2}-(2X-4)[/tex]
[tex]=9X^{2}+4X-3+16X^{2}-2X+5\\\\=(9+16)X^{2}+(4-2)X+(5-3)\\\\=25X^{2}+2X+2[/tex]
Thus, the polynomial form of the expression is: 25·X² + 2·X + 2.