Solve and state any extraneous solutions
[tex] \frac{3x}{x - 1} + 2 = \frac{3}{x - 1} [/tex]
[tex] \frac{3x}{x - 1} + \frac{2(x - 1) }{ x - 1} = \frac{3}{x - 1} [/tex]
[tex] \frac{3x}{x - 1} + \frac{2x - 2}{ x - 1} = \frac{3}{x - 1} [/tex]
[tex] \frac{3x + 2x - 2}{ x - 1} = \frac{3}{x - 1} [/tex]
[tex]3x + 2x - 2 = 3[/tex]
[tex]5x - 2 = 3[/tex]
[tex]5x = 3 + 2[/tex]
[tex]5x = 5[/tex]
[tex]x = \frac{5}{5} [/tex]
[tex]x = 1[/tex]
the length of a rectangle is 5 less than twice the width. If the perimeter of the rectangle is 146 centimeters, find the dimensions of the rectangle
Answer:
26x47
Step-by-step explanation:
To calculate the length of the rectangle we would do 2(2x - 5) + 2(x) = 146
We simplify and get 6x - 10 = 146,
then divide both side by 6 and plus 10 both sides,
we will get
x = 26
Now we've found one of the length,
to find the other side we do 26 * 2 = 52, and subtract 52 from 146,
which would get 94, then we divide it by 2
94/2 = 47
The dimensions is 26x47
Which two ratios are equivalent to 10 : 12?
11 : 13 and 20 : 24
10 : 12 and 11 : 13
5 : 6 and 20 : 24
5 : 6 and 11 : 13
Answer:
10 : 12 is equivalent to 5 : 6 and 20 : 24.
Step-by-step explanation:
You can divide and multiply the ratio by 2 to get an equivalent ratio.
The ratio which is equivalent to 10: 12 are 5: 6 and 20: 24 Therefore, option (C) will be correct.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
As per the given ratio, 10:12.
Divide numerator and denominator by 2
(10/2):(12/2) = 5:6.
Multiply the numerator and denominator by 2
(10×2);(12×2) = 20:24
Hence "The ratio which is equivalent to 10: 12 are 5: 6 and 20: 24".
For more information about ratios and proportions,
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To paint a house, a painting company charges a flat rate of $500 for supplies, plus $50 for each hour of labor. a. How much would the painting company charge to paint a house that needs 20 hours of labor?
Answer:
For 20 hours it would be $1,500.
Step-by-step explanation:
The equation for this problem would be Y = 50x + 500.
Y is the total charge and x is the number of hours.
Hope this helps! Sorry if it was not what you were looking for!
Answer: 1500
Step-by-step explanation: 50x20=1,000 plus the addition price of the supplies 1,000+500= $1500
Factorise: (a) 3x2 + 27y2 + z2 - 18xy + 6 √3yz -2 √3zx (b) 27 x3 + 125y3 (c) (2a – 3b + c )2
(d) 1 a3 + b3 + 125 c3 - 15 a b c (e) [x – 1/x y]3 (f) x4 y4 – x y
64^4
(g) 8x3 – (2x – y)3 (h) a6 _ b6
Answer please
Answer:
(a) [tex]3x^2 + 27y^2 + z^2 - 18xy + 6 \sqrt{3} yz -2 \sqrt{3} zx[/tex]
this can be written as
[tex](-x\sqrt{3})^2 + (y3\sqrt{3})^2 + (z)^2 +2 ( -x\sqrt{3} )( y3\sqrt{3}) + 2( y3\sqrt{3})(z) + 2(z)( -x\sqrt{3})[/tex]
which is equivalent to
[tex]a^2+ b^2 + c^2 + 2ab + 2bc + 2ac = (a+b+c)^2[/tex]
[tex](-x\sqrt{3} + y3\sqrt{3} + z)^2 = (-x\sqrt{3} + y3\sqrt{3} + z)(-x\sqrt{3} + y3\sqrt{3} + z)[/tex]
(b)[tex]27 x^3 + 125y^3[/tex] = [tex](3x)^3 + (5y)^3[/tex]
which is same as [tex]a^3 + b^3 = (a+b)(a^2 +b^2 -ab)[/tex]
= [tex](3x + 5y)(9x^2 + 25y^2 -15xy)[/tex]
(c) [tex](2a - 3b + c )^2[/tex] = (2a -3b +c)(2a -3b+c)
(d) [tex]a^3 + b^3 + 125 c^3 - 15 a b c[/tex]
this is same as
[tex]a^3 + b^3 +c^3 - 3abc[/tex] = [tex](a+b+c)( a^2+b^2+c^2 -ab-bc-ac)[/tex]
= [tex](a + b + 5c)(a^2+b^2 +25c^2 -ab -5bc -5ac)[/tex]
(e) [tex](x - 1/x y)^3[/tex] = [tex](x - 1/xy)(x - 1/xy)(x - 1/xy)[/tex]
(f) [tex]x^4 y^4 - x y64^4 = xy( x^3y^3 - 64^4) = xy( x^3y^3 - (256)^3) \\ = xy( xy - 256 )(x^2y^2 + 65536 + 256xy)[/tex]
(using the property of [tex]a^3 -b^3 = (a-b)(a^2+b^2 +ab)[/tex] )
(g) [tex]8x^3 - (2x - y)^3 = (2x)^3 - (2x-y)^3 \\ = (2x - 2x + y)(4x^2 + (2x-y)^2 + 2x(2x-y))\\ = y(8x^2 + y^2 -6xy +4x)[/tex] using the same property above
(h)
[tex]a^6 -b^6 = (a^2)^3 - (b^2)^3 = (a^2-b^2)( a^4+b^4 +a^2b^2)\\ = (a-b)(a+b)( a^4+b^4 +a^2b^2)[/tex]
PLEASE HELP! (don't graph, give me the coordinates and i will graph myself)
Answer:X=3
y= -4
Step-by-step explanation:
If we're solving for x or y, then the intercept we're not solving for is equal to zero. Solving for y means x=0, solving for x means y=0.
so solving for x, 4x=12--> x=3, since y=0 in this scenario.
Solving for y, x=0, so -3y=12--> y=(-4)
9514 1404 393
Answer:
see below for a table
Step-by-step explanation:
You can easily identify intercept points by solving for one variable when the other is zero.
x-intercept (y=0)
4x = 12
x = 12/4 = 3
y-intercept (x=0)
-3y = 12
y = 12/-3 = -4
So, the coordinate pairs of these points are ...
(3, 0) and (0, -4)
__
If you solve for y, you get ...
-3y = 12 -4x
y = (4/3)x -4 . . . . . divide by -3
This suggests that x being a multiple of 3 will be useful for finding integer values of y.
We already have points for x=0 and x=3. We can add points for x=6 and x=-3.
y = 4/3(6) -4 = 4
y = 4/3(-3) -4 = -8
So, the additional points are ...
(6, 4) and (-3, -8)
negative 3 times x equals?
Answer:
-3x
Step-by-step explanation:
Answer:
Step-by-step explanation:
If we multiply any negative number in this case -3 times a POSITIVE we will always get a negative. So the positive we can put as x and multiply -3 times x = -3x.
Hope this helps :D
A basketball team played six games. In those games, the team won by 7 points, lost by 20, won by 8, won by 11, lost by 3, and won by 9. What is the mean amount by which the team won or lost over the six games?
Answer:
the mean of which the team won is 8.75
The mean of which the team lost is 11.5
Step-by-step explanation:
add all the numbers of which the team won by then divide the sum by the number of numbers there are
example:
7+8+11+9=35/4=8.75
Allen earns $260.50
doing yard work. He mows 8
lawns for $25
each and weeds gardens for $5.50
each. What equation can be used to find the number of gardens he weeds, w
?
Need help with this question. Thanks
Answer:
C
Step-by-step explanation:
-18x+2y>=-13
2y>= -13+18x
y>= -6.5+9x
Write the equation of the line that goes through (-2/3, 7/8) and is PARALLEL to 3x + 4y = 7
Answer:
6x+8y = 3
Step-by-step explanation:
we have 3x + 4y = 7
4y = -3x + 7
y = -3/4 x + 7/4
so slope is -3/4
2 parallel lines always have same slope
so the slope of our new line is -3/4
so y = -3/4 x + C
for c,
we have (x,y) = (-2/3,7/8)
7/8 = -3/4 * -2/3 + C
C = 3/8
so equation is
y = -3/4 x + 3/8
simplyfyig,
8y = -6x + 3
or, 6x+8y = 3
ΔZAP has coordinates Z (−1, 5), A (1, 3), and P (−2, 4). A translation maps point Z to Z' (1, 1). Find the coordinates of A' and P' under this translation.
Group of answer choices
A' (−4, 0); P' (−1, −1)
A' (3, −1); P' (0, 0)
A' (−1, −1); P' (−4, 0)
A' (0, 0); P' (3, −1)
Given: Triangle WTR with WT = 25 and WR = 40. Identify all possible lengths for TR.
40
17
15
42
52
67
65
14
Answer:
The possible lengths of TR : TR = 17, 40, 42, 52,
Step-by-step explanation:
Given: Triangle WTR with WT = 25 and WR = 40. Identify all possible lengths for TR.
To find the possible lengths of the third side of a triangle:
c - a< b > a + c
a = WT = 25
c = WR= 40
b = TR = ??
40 - 25 < b < 40 + 25
15 < b < 65
The possible lengths of TR has to be greater than 15 and less than 65, Hence: TR = 17, 40, 42, 52,
Which statement about converting metric units of measurement is true? Use the metric table to help answer the question.
Metric Table
kilo-
hecto-
deka-
unit
deci-
centi-
milli-
1,000
100
10
1
0.1
0.01
0.001
To find the number of hectometers in 87 centimeters, move the decimal point 4 units to the left.
To find the number of meters in 9,382 centimeters, move the decimal point 2 units to the right.
To find the number of kilometers in 6.39 decimeters, move the decimal point 3 units to the left.
To find the number of dekameters in 18 kilometers, move the decimal point 3 units to the right.
Answer:
To find the number of hectometers in 87 centimeters, move the decimal point 4 units to the left.
Mark me brainliest if I am right...PLEASE
Answer:To find the number of hectometers in 87 centimeters, move the decimal point 4 units to the left.
Step-by-step explanation:
Leda makes 73 oatmeal muffins for a bake sale. She accidentally drops five of them and throws them away. She puts as many of the remaining muffins as possible into 13 containers so that each container has the same number of muffins. How many of the remaining muffins does Ieda have left over?
Answer:
She would have 5 muffins left over
Step-by-step explanation:
Do 73-3, because she dropped 3 and threw them awayTake 70 and divide it by 13, there are 70 muffins and 13 containers (I used a calculator)Then you get a decimal (if you use a calculator), look at the whole number which should be 5Next, you multiply 5 by 13, this will allow you to find what you would 'add into' a normal division problem (if you were to do it on paper)Lastly, take 70 and subtract what you got for step for (it should be 65, so the equation would be 70-65)Divide following polynomials 5x2 - 18x-27/x-5
Answer:
[tex]\frac{5x^{3}-18x^{2} -5x-27 }{x}[/tex]
Step-by-step explanation:
Write an expression to find how many times Jason will blink in 60 minutes if he continues to blink 19 times a minute.
rename 4/5 and 5/7 using the least common denominator
Answer:
wh
Step-by-step explanation:
Answer:
4/5 = 28/35 and 5/7 = 25/35
Explanation:
Multiply 5 times 7 to get 35, then multiply 4 times 7 for the numerator of the first fraction and 5 times 5 for the numerator of the second equation.
Solve for r: 7r+ 30 = -65
Answer:
R= - 95/7
Step-by-step explanation:
How would you solve absolute value equations with "or" and "and"? Sometimes even with coefficients.
9514 1404 393
Explanation:
In general, a system of equations has a solution that satisfies all of the equations. That is, the solution set is the intersection (and) of the solution sets of the individual equations in the system. Equations involving the absolute value function are no different.
That being said, you need to consider the meaning of an equation involving the absolute value function.
The function itself is piecewise defined:
[tex]\displaystyle |x|=\left\{ {x, x\ge0} \atop {-x, x<0}} \right.[/tex]
So, any equation involving the absolute value function automatically resolves to two equations, each with its own condition on the function value.
__
Example 1:
|x+1| > 3
is equivalent to the two disjoint conditional equations ...
(x +1) > 3 and (x +1) ≥ 0 . . . . OR
-(x +1) > 3 and (x +1) < 0
the first of these has the solution x > 2; the second of these has the solution x < -4. The solution set of this equation is the OR of the two solution sets:
x < -4 or x > 2
__
Example 2:
|x +1| < 3
is equivalent to the two disjoint conditional equations ...
(x +1) < 3 and (x +1) ≥ 0 . . . . OR
-(x +1) < 3 and (x +1) < 0
The first of these has the solution -1 ≤ x < 2, and the second of these has the solution -4 < x < -1. Again, the solution set of this equation is the OR of the two solution sets. However, we find we can write that union as a single compound inequality:
-4 < x < 2
__
When an absolute value equation involves more than one absolute value function, then the equation will probably resolve into multiple equations, each defined on its own domain. Sometimes keeping those domains straight can be tedious.
Above, we have considered inequalities. If you have an equation, you need to consider that it will likely resolve to two equations. The solution set will be the OR of the solutions to those two equations.
Example 3:
|x +1| = 3
is equivalent to the two conditional equations ...
(x +1) = 3 and (x +1) ≥ 0 . . . . OR
-(x +1) = 3 and (x +1) < 0
The first of these has the solution x = 2; the second has the solution x = -4. The solution set is the OR of these two solutions:
x = -4 or x = 2
__
The "and" condition restricts the domain of each of the individual pieces of the equation. The "or" condition applies to the collection of solutions that may exist in each of those restricted domains.
Anyone????? That can help me answer these
Answer:
5. 3050ft³ (rounded to 3 s.f.)
6. 4190ft³(rounded to 3 s.f.)
7. 4600ft³(rounded to 3 s.f.)
Formulas (For easier reference):
Volume of a cone: pi×r²×[tex]\frac{h}{3}[/tex]
Volume of cylinder: pi×r²×h
Volume of a sphere: [tex]\frac{4}{3}[/tex]×pi×r³
Volume of a hemisphere: [tex]\frac{2}{3}[/tex]×pi×r³
Step-by-step explanation:
You can just apply the formulas to the question:
5. Volume of cone = pi×9²×[tex]\frac{(16-10)}{3}[/tex]
= 162pi
Volume of cylinder = pi×9²×10
= 810pi
Volume of figure = 162pi+810pi
= 972pi
= 3050ft³ (rounded to 3 s.f.)
6. Volume of sphere = [tex]\frac{4}{3}[/tex]×pi×10³
= 1333[tex]\frac{1}{3}[/tex]pi
= 4190ft³(rounded to 3 s.f.)
7. Volume of hemisphere = [tex]\frac{2}{3}[/tex]×pi×(26÷2)³
= 1464[tex]\frac{2}{3}[/tex]pi
= 4600ft³(rounded to 3 s.f.)
HELP PLEASE ILL GIVE BRAINLIEST!!!!!!!!!
Answer:
the first questions answer is yes the seconds is no
HAVE A NICE DAY!!!
-7[-8-4a]=25+a
A. a= -16
B. a=-5
C. a= -11
D. a=-3
Answer:
-1.48148148
Step-by-step explanation:
-7 x -8 = 56
-7 x -4a = 28a
25-56=-31
27a/-31
a=-1.48148148
help me please.
[tex]help \: me[/tex]
The solution is where the two lines cross each other:
(-1,3) and (2,6)
The answer is B.
Gloria’s washing machine is broken. Since her machine is pretty old, she doesn’t want to spend more than $100 for repairs. A service call will cost $35 and the labor will be an additional $20 per hour. There are no other charges. What is the maximum number of hours that the repair person can work without the total cost exceeding $100?
Answer:
The actual answer is 3.25
Step-by-step explanation:
I just took the test
the maximum number of hours that the repair person can work is 3.5 hours
Given :
Gloria doesn’t want to spend more than $100.
A service call will cost $35 and the labor will be an additional $20 per hour
Let 'h' be the maximum number of hours the repair can take.
Lets find out the total cost for 'h' hours
35+ additional 20 per hour
[tex]35+20h[/tex]
The total cost should not exceed 100
[tex]35+20h \leq 100\\20h \leq 100-35\\20h\leq 65\\Divide \; by \; 20\\h\leq 3.5[/tex]
So , the maximum number of hours that the repair person can work is 3.5 hours
Learn more : brainly.com/question/19042935
Please Find 23% of 40
Answer:
9.2
Step-by-step explanation:
THE POWER OF MULTIPLICATION
grabriella volunteers at the hospital every 4th day.she volunteers at the food pantry every 6th day.she volunteered at the hospital and the food pantry both on march 31.On what date will she next volunteer at both?
Answer:
April 12th
Step-by-step explanation:
I need help with number 11 and number 12
Answer:
11) 6
12) 3
Step-by-step explanation:
2 log 2 8
so 2(log2 8)
Base 2 so 2^x=8 so 3.
2*3 is 6.
log a a cubed
base a so a^ x = a^3
x=3
so 3.
Hope this helps ;D
Answer:
6 and 3
Step-by-step explanation:
Using the rules of logarithms
log[tex]x^{n}[/tex] ⇔ n log x
[tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex]
[tex]log_{a}[/tex] a = 1
(11)
let 2 [tex]log_{2}[/tex]8 = n , then
[tex]log_{2}[/tex] 8² = n
[tex]log_{2}[/tex] 64 = n
[tex]log_{2}[/tex] [tex]2^{6}[/tex] = n
[tex]2^{6}[/tex] = [tex]2^{n}[/tex]
Since bases on both sides are equal, equate the exponents, that is
n = 6
(12)
[tex]log_{a}[/tex] a³
= 3 [tex]log_{a}[/tex] a
= 3 × 1
= 3
Which statements about opposites are true?
Select each correct answer.
Answer:
(a) TRUE
(b) TRUE
(c) FALSE
(d) TRUE
Step-by-step explanation:
" The "opposite" of any number is also known as it's " additive inverse" i.e. for any number 'a' the additive inverse is 'a' ".
(a) TRUE
Since let us consider any negative number '-5' then it's opposite is '5' since (-5)+5=0
(b) TRUE
this could be seen clearly from the number line.
(c) FALSE
this statement is false since we can take example of zero.
the opposite of zero is 0 but 0×0≠1.
(d) TRUE
since 0-0=0.Step-by-step explanation:
compared to last year, the population of Boom Town has increased by 10%. The population is now 6,600. What was the population last year?
Answer:
60
Step-by-step explanation:
6600 x 10% = 60&$;#;,$:#&#>$