Answers
The match each pair of rational numbers with their sum is:
[tex]\frac{2*(a-b)}{a^2b^2} = \frac{-2}{a^2b}+\frac{2}{ab^2}[/tex]
[tex]\frac{a-b^2}{a^2b^3} }=\frac{1}{ab^3} +\frac{-1}{a^2b}[/tex]
[tex]\frac{2ab-1}{4a^2b^2} }=\frac{1}{2ab} +\frac{-1}{4a^2b^2}[/tex]
[tex]\frac{2*(1-ab^2)}{a^2b^3} =\frac{2}{a^2b^3}+\frac{-2}{ab}[/tex]
FactoringIn math, factoring or factorization is used to write an algebraic expression in factors. There are some rules for factorization. One of them is a factor out a common term for example: x²-x= x(x-1), where x is a common term.
When you factor an expression using the rule a factor out a common term, it is possible simplify an expression
Then, you should factor and simplify each given algebraic expression.
[tex]\frac{2*(a-b)}{a^2b^2} =\frac{2a-2b}{a^2b^2}=\frac{2a}{a^2b^2} -\frac{2b}{a^2b^2} =\frac{2}{ab^2} +\frac{-2}{a^2b}[/tex][tex]\frac{a-b^2}{a^2b^3} }=\frac{a}{a^2b^3} -\frac{b^2}{a^2b^3} =\frac{1}{ab^3} +\frac{-1}{a^2b}[/tex][tex]\frac{2ab-1}{4a^2b^2} }=\frac{2ab}{4a^2b^2} -\frac{1}{4a^2b^2} =\frac{1}{2ab} +\frac{-1}{4a^2b^2}[/tex][tex]\frac{2*(1-ab^2)}{a^2b^3} =\frac{2-2ab^2}{a^2b^3}=\frac{2-2ab^2}{a^2b^3}=\frac{2}{a^2b^3}+\frac{-2}{ab}[/tex]
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Related Questions
Find the mean and median of the data. 31, 14, 18, 26, 17, 32
Answers
Answer:
The mean is 23
The median is 22
Step-by-step explanation:
To find the mean you have to do 2 steps:
Step 1: Add up all your numbers:
31 + 14 + 26 + 17 + 32 + 18
= 138
Step 2: Divide you answer by how many numbers there are(6):
138 ÷ 6
= 23
Now to find you median
First put the numbers in order:
14, 17, 18, 26, 31, 32
Now grab the middle number and since there are an even amount of numbers grab the 2 middle numbers:
14, 17, 18, 26, 31, 32
Now add the 2 numbers:
18 + 26
= 44
The last step is to divide your answer by 2:
44 ÷ 2
= 22
Susan collects softball cards in her collection she had 128 she decides to gives 3 eights
Answers
Answer:
need more information to answer for you.
Step-by-step explanation:
A. The graph is translated 2units down.
B. The graph is translated 2 units left.
C. The graph is translated 2 units right.
D. The graph is translated 2 units up.
Answers
Answer:
c
Step-by-step explanation:
the -2 causes a shift 2 units right
HELP with this please!!
Answers
[tex]~~~~\dfrac{12}{x^2 -49} \cdot \dfrac{x^2+9x+14}{9}\\\\\\=\dfrac{4}{x^2 -7^2}\cdot \dfrac{x^2 + 7x +2x +14}{3}\\\\\\=\dfrac{4}{(x+7)(x-7)} \cdot \dfrac{x(x+7)+2(x+7)}{3}\\\\\\=\dfrac{4}{(x+7)(x-7)}\cdot \dfrac{(x+7)(x+2)}{3}\\\\\\=\dfrac{4(x+2)}{3(x-7)}[/tex]
Answer:
[tex]\frac{4(x + 2)}{3(x - 7)}[/tex]
Step-by-step explanation:
Hello!
We can simplify this by factoring, and cross reducing.
Simplify[tex]\frac{12}{x^2 - 49} * \frac{x^2 + 9x + 14}{9}[/tex][tex]\frac{12}{(x+7)(x - 7)} * \frac{(x + 2)(x + 7)}{9}[/tex][tex]\frac{12(x + 2)}{9(x - 7)}[/tex][tex]\frac{4(x + 2)}{3(x - 7)}[/tex]The final simplified form is [tex]\frac{4(x + 2)}{3(x - 7)}[/tex]
State the various transformations applied to the base function f(x)=|x| to obtain a graph of the function g(x) = |x| − 2.
Horizontal shift of 1 unit to the right and a vertical shift upward of 2 units.
Horizontal shift of 1 unit to the right and a vertical shift downward of 2 units.
Horizontal shift of 1 unit to the left and a vertical shift downward of 2 units.
Horizontal shift of 1 unit to the left and a vertical shift upward of 2 units.
Answers
Horizontal shift of 1 unit to the left and a vertical shift downward of 2 units.
Transformation of functionTransformation technique is a way of changing the position of an object on an xy-plane.
Given the parent function of a modulus function f(x) = |x|, the graph of the function g(x) = |x| - 2 shows a vertical translation of the parent function down by 2 units.
The resulting graph of the translated function is as shown below
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How does the volume of the larger cube compare to the volume of the smaller cube? Use pencil and
paper. Use this and other examples to describe what happens to the volume of a cube if you triple the length
of the edges.
Answers
Answer:
Option C, The volume of the length cube is 3 times the volume of the smaller cube
Step-by-step explanation:
21.8 / 7.8 = 2.8
the volume of the larger would be 21.8^3 = 10360.23
the volume of the larger would be 7.8^3 = 474.55
53° 44°
xº
X=
46°
degrees
Answers
X = 53° + 44° + 46° = 143°
In triangle RTS △RTS shown below, point U is on
ST, and point V is on RT so that angle RST UVT∠RST≅∠UVT. If ST=13 VT=5, and RV=13.2, find the length of TU. Figures are not necessarily drawn to scale.
Answers
Answer: 7
Step-by-step explanation:
As [tex]\angle T \cong \angle T[/tex] by the reflexive property, we know that [tex]\triangle RST \sim \triangle UVT[/tex] by AA.
Since corresponding sides of similar triangles are proportional,
[tex]\frac{UT}{5}=\frac{13.2+5}{13}\\UT=(5)\left(\frac{13.2+5}{13} \right)=\boxed{7}[/tex]
20 POINTS + BRAINLY Complete the table.
52, 54, 55, 55, 57, 58, 59, 59, 61, 61, 61, 62, 63, 63, 64, 65, 65, 68, 70, 72
Interval Frequency
50-54 2
55-59
60-64
65-69
70-74
Answers
The frequency of the data set that matches with the interval stated are:
50 - 54: 2
55 - 59: 6
60 - 64: 7
65 - 69: 3
70 - 74: 2
What is a Frequency?Frequency is the number of times a data point or a set of points within an interval appears often in a data set.
The corresponding frequency to each of the interval given for the data would be as follows:
50 - 54: 2
55 - 59: 6
60 - 64: 7
65 - 69: 3
70 - 74: 2
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Write the product using exponents.
(-6)x(-6)x(-6)
The expression is
Answers
Answer:
(-6)³z² or -6³z²
Step-by-step explanation:
An exponent is used to signify the number of times a factor appears in a product.
__
In the expression (-6)·(-6)·(-6)·z·z, the factor (-6) appears 3 times, and the factor z appears 2 times. Written with exponents, this could be ...
(-6)³z²
_____
Additional comment
We can simplify this by realizing the product of the constant factors will be negative. (There is an odd number of minus signs.) The expression can also be written as ...
-6³z²
The version with (-6) being cubed is a more direct translation to the use of exponents.
question 3 help me please
Answers
Answer:
3x+(4x-1)+90°=180°{sum of angles in a triangle}
3x+4x-1+90°=180°
7x+89°=180°
7x=180°-89°
7x=91°
divide both sides by 7
x=13
Answer:
The answer is x=13
Isabel says that 0.02 can be expressed as 20%. Is she correct? Explain why or why not.
Answers
[tex]\text{She is not correct because}\\\\20\% = \dfrac{20}{100} = \dfrac 2{10} = 0.2 \neq 0.02[/tex]
The median of the values:29,24,30,23,28,18,
Answers
Answer:
26
Step-by-step explanation:
18,23,24,28,29,30
(6 in total + 1)/2=3.5.
- the number which is 3.5 is between 24 and 28.
- middle number between these two is 26.
Look at the photo and answer the question.
Please don’t just put the answer at the top of the text and don’t make it hard to find.
Answers
Answer:
second option
Step-by-step explanation:
5 newton pushing it to the right
while a mere 4 newton pushing it to the left
more force pushing towards right
This would be the answer because there are 5 newtons forcing the given object to the right while there are 4 newtons forcing the object to the left. Because 5 is greater than 4, the object would accelerate to the right in this model with 1 newton more of force than it would to the left.
whitch of the following is closest to 8 62 61 65 66
Answers
Answer:
If the question is which is closest to 8, the answer is 61
Step-by-step explanation:
can someone help with this please
Answers
Answer:
Step-by-step explanation:
PLEASE HELP URGENTLY! RIGHT ANSWERS ONLY!
Answers
Answer:
Hi! The answer is B!
I would suggest using a graphing calculator to compare all the lines. You can use this free one called Desmos, sorry i was not able to attach a link :)
What is Parabola?
What is the transformation of parabolas?
Answers
Answer:
What is Parabola:
a symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side. The path of a projectile under the influence of gravity ideally follows a curve of this shape.
What is the transformation of parabolas?
The function y=x2+b has a graph which simply looks like the standard parabola with the vertex shifted b units along the y-axis. Thus the vertex is located at (0,b). If b is positive, then the parabola moves upwards and, if b is negative, it moves downwards. Similarly, we can translate the parabola horizontally
Step-by-step explanation:
the gas tank in minas car holds 15 gallons. Her car gets between 25 and 30 miles to the gallon. If Mina fills up the gas tank and then drives until she runs out of gas, what is the least number of miles she can drive?
A. 300mi
B. 375mi
C. 405mi
D. 450mi
Answers
the lowest mileage rate is 25 miles per gallon.
Multiply 25 by 15 gallons
25 x 15 = 375 miles
Answer: B. 375 miles
if the area of a square is 32ft how long is the diagonal?
Answers
A square has the same length all 4 sides, therefore in order to find the length of the sides, you would need to find the square root of 32, which would be 5.66 or 4 radical 2. Then to find the diagonal length you would need to split the square diagonally resulting in 2 triangles. We know the side lengths of the triangles but not the hypotenuse( longest side of triangle), which is the diagonal length. To figure this out we would use the Pythagorean theorem a^2 + b^2 = c^2. We know what a and b are so we substitute, do basic algebra, and find that c is equal to 8
Answer: 8
Step-by-step explanation:
To find the diagonal, we need to use two formulas:
Area of a square: [tex]A = s^{2}[/tex] (Area = side * side)
Pythagorean Theorem: [tex]a^{2} +b^{2} =c^{2}[/tex]
Since every side of a square is the same:
[tex]a^2 = b^2\\a = b = \sqrt{32} \\a^{2} = 32\\b^2 = 32[/tex]
Our equation:
[tex]32 + 32 = c^2\\64 = c^2\\8 = c[/tex]
The picture below visually explains the problem
Hope this helps!
0.510 (3+0.2) x -1.6
-
Answers
Answer:
-2.6112
Step-by-step explanation:
= 0.510 (3+0.2) x -1.6
= 0.510 x 3.2 x -1.6
= -2.6112
hence answer is -2.6112.
answer is 8.99, but how tho
Answers
Answer:
x ≈ 8.99
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you of the relationship between trig functions and sides in a right triangle. Here, the geometry of the problem can be modeled by a right triangle. We are given one side and want to find the difference in lengths of the other side for two different angles.
__
setupThe tower height is the side opposite the angle of elevation. The distance from the tower to the end of the shadow is the side adjacent to the angle of elevation, so the relevant trig relation is ...
Tan = Opposite/Adjacent
tan(angle of elevation) = (tower height)/(length of shadow)
Solving for the length of shadow, we have ...
length of shadow = (tower height)/tan(angle of elevation)
The difference in shadow lengths is 2x for the two different angles, so we have ...
2x = 24.57/tan(30°) -24.57/tan(45°)
__
solutionDividing by 2 and factoring out the tower height, we have ...
x = 12.285(1/tan(30°) -1/tan(45°)) = 12.285(√3 -1)
x ≈ 8.993244
The value of x is about 8.99.
LL
F
C
9
5
D
2x+3
E
What is the value of x and the length of segment DE?
1 5
9
9
2x + 3
2. 10x+15=9(9)
Length of DE=
units
Answers
Answer:
[tex]x=\boxed{6.6}[/tex]
[tex]\overline{\sf DE}=\boxed{13.2}\:\:\sf units[/tex]
Step-by-step explanation:
Geometric Mean Theorem - Altitude Rule
The altitude drawn from the vertex of the right angle perpendicular to the hypotenuse separates the hypotenuse into two segments. The ratio of one segment to the altitude is equal to the ratio of the altitude to the other segment:
[tex]\sf \dfrac{segment\:1}{altitude}=\dfrac{altitude}{segment\:2}[/tex]
From inspection of the given diagram:
altitude = FD = 9segment 1 = CD = 5segment 2 = DE = [tex]2x+3[/tex][tex]\begin{aligned}\sf \dfrac{segment\:1}{altitude} & = \sf \dfrac{altitude}{segment\:2}\\\\\implies \dfrac{5}{9} & = \dfrac{9}{2x+3}\\\\5(2x+3) & = 81\\\\10x+15 & = 81\\\\10x & = 66\\\\ \implies x & = 6.6\end{aligned}[/tex]
Substitute the found value of x into the expression for DE:
[tex]\begin{aligned}\sf \overline{DE} & = 2x+3\\\implies \sf \overline{DE} & = 2(6.6)+3\\& = 13.2+3\\& =16.2\:\: \sf units\end{aligned}[/tex]
Given that the expression x³_ ax² + bx+c leaves the same remainder when divided by x + 1 or x-2, find 'a' in terms of 'b'.
Answers
Answer:
Hi,
a=b+3
Step-by-step explanation:
[tex]\begin{array}{c||c|c|c|c}&x^3&x^2&x&1\\---&---&---&---&---\\&1&-a&b&c\\x=-1&&-1&a+1&-a-b-1\\---&---&---&---&---\\&1&-a-1&a+b+1&c-a-b-1\\\end{array}[/tex]
[tex]\begin{array}{c||c|c|c|c}&x^3&x^2&x&1\\---&---&---&---&---\\&1&-a&b&c\\x=2&&2&4-2a&2b+8-4a\\---&---&---&---&---\\&1&2-a&b+4-2a&c+2b+8-4a\\\end{array}[/tex]
Thus:
c+2b+8-4a=c-a-b-1
3b-3a=-9
a=b+3
A wire goes from the top of a 55 ft pole to the ground. It makes a 70
o angle with the ground. How long is the wire? NEEDN ASAP!!! ill give 20 points for this
Answers
Answer:
58.5 ft
Step-by-step explanation:
sin 70=55/length
length=58.5 ft
Please help me with this
Answers
Answer:
42
Step-by-step explanation:
6 times 7 is 42
a line contains the point (2,3) and has a slope of 1/2 What is the point-slope form of the equation for the line
Answers
The point-slope form of the equation for the line is y - 3 =1/2(x - 2)
Point-slope formFrom the question, we are to determine the point-slope form of the equation for the line
The point-slope form of the equation of a line is given by
y - y₁ = m(x - x₁)
Where (x₁, y₁) is a point on the line
and m is the slope of the line
From the given information,
Slope, m = 1/2
and we have the point (2,3)
∴ The point-slope form of the equation for the line is
y - 3 =1/2(x - 2)
Hence, the point-slope form of the equation for the line is y - 3 =1/2(x - 2)
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If f(x) and f¹(x) are inverse functions of each other and f(x) = 2x+ 5, what is ƒ˜¹ (8) ?
Answers
If f(x) and f¹(x) are inverse functions of each other then value of ƒ˜¹ (8) = 3/2.
What is Function?In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
We have,
f(x) = 2x + 5
Let us consider f(x) as y
So, y= 2x + 5
Now replace x to y and y to x
x= 2y+ 5
Solving for y we get
2y = x - 5
y = (x - 5)/2
[tex]f^{-1[/tex](x) = (x - 5)/2
Now, [tex]f^{-1[/tex](8) = (8 - 5)/2
[tex]f^{-1[/tex](x) = 3/2
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Is LMN = OPQ? If so, name the congruence postulate that applies. N Given: LM = OP PQ = MN P M = 00 O A. Congruent - SAS O B. Congruent - SSS O C. Might not be congruent O D. Congruent - ASA
Answers
Based on the sides of LMN and OPQ, the congruence postulate that applies is B. Congruent - SSS.
When is the SSS rule used?It is used when the two triangles given have three equal corresponding sides which also have equal angles.
All three sides of LMN and OPQ are equal sides and have equal angles and so the SSS rule applies.
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help me pleaseeeeeeeeeeeeeee
Answers
Answer:
C
Step-by-step explanation:
Evaluating the options :
Option A
⇒ 5/2x + 7/2 = 3/4x + 14
⇒ 2.5x - 0.75x = 14 - 3.5
⇒ 1.75x = 10.5
⇒ x = 6
⇒ No ×
===========================================================
Option B
⇒ 5/4x - 9 = 3/2x - 12
⇒ 1.5x - 1.25x = -9 + 12
⇒ 0.25x = 3
⇒ x = 12
⇒ No ×
=========================================================
Option C
⇒ 5/4x - 2 = 3/2x - 4
⇒ 1.5x - 1.25x = -2 + 4
⇒ 0.25x = 2
⇒ x = 8
⇒ Yes √
C is the right answer.