Can u show me how to simply this step by step please? This is very important. HELP!!!!!
Answers
Given:
[tex]$\frac{\left(\frac{a^{2}-b^{2}}{a b}\right)}{\left(\frac{1}{b}-\frac{1}{a}\right)}[/tex]
To find:
The simplified expression.
Solution:
[tex]$\frac{\left(\frac{a^{2}-b^{2}}{a b}\right)}{\left(\frac{1}{b}-\frac{1}{a}\right)}[/tex]
Apply the fraction rule: [tex]\frac{\frac{y}{z}}{x}=\frac{y}{z \cdot x}[/tex]
[tex]$\frac{\left(\frac{a^{2}-b^{2}}{a b}\right)}{\left(\frac{1}{b}-\frac{1}{a}\right)}=\frac{a^{2}-b^{2}}{a b\left(\frac{1}{b}-\frac{1}{a}\right)}[/tex] ------------ (1)
Let us simplify [tex]\frac{1}{b}-\frac{1}{a}[/tex].
LCM of a and b = ab
Adjacent fraction based on the LCM
[tex]\frac{1}{b}-\frac{1}{a}=\frac{a}{a b}-\frac{b}{a b}[/tex]
[tex]=\frac{a-b}{a b}[/tex]
Substitute this in equation (1).
[tex]$=\frac{a^{2}-b^{2}}{\frac{a-b}{a b} a b}[/tex]
Common factor ab get canceled.
[tex]$=\frac{a^{2}-b^{2}}{a-b}[/tex]
Apply the algebraic formula: [tex]x^{2}-y^{2}=(x+y)(x-y)[/tex]
[tex]$=\frac{(a+b)(a-b)}{a-b}[/tex]
Cancel the common factor a - b, we get
[tex]=a+b[/tex]
The simplified expression is a + b.
Related Questions
earth moves in a orbit that is 585 million miles away from the sun.Write 585 million in scientific notation form.
Answers
Answer: 5.85 x 10 to the power of 6
Step-by-step explanation:
Are the lines 2x+3y=2 and 2x+3y=4 parallel?
Answers
Answer:
Yes.
Step-by-step explanation:
Since the coefficients of x and y, respectively, are equal, the answer is yes. These two lines are two different parallel lines with the same slope and different y-intercepts.
Answer:
2x+3y=2--------(1)
2x+3y=4----------(2)
|d|=|C2-C1|/SQ.RT A SQ.+B SQ.
=4-2/RT.4+9
=2/RT.13 UNITS
In the diagram, the measure of angle 1 is (3x), and the measure of angle 2 is (12x)".
516
87
What is the measure of angle 4?
Answers
Answer:
Angle 4 is 144.
Step-by-step explanation:
Applying the definition of vertical angles, the measure of angle 4 is: 144°.
What are Vertical Angles?Vertical angles are a pair of angles that lie directly opposite each other and are equal in measure to each other.
m∠1 + m∠2 = 180° (linear pair)
Substitute
3x + 12x = 180
15x = 180
x = 12
∠4 and ∠2 are vertical angles, therefore:
m∠4 = m∠2 = 12x
Plug in the value of x
m∠4 = 12(12)
m∠4 = 144°
Therefore, applying the definition of vertical angles, the measure of angle 4 is: 144°.
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For a standard normal distribution, find the approximate value of P(z≤0.42). Use the portion of the standard normal table below to help answer the question.
0.00
0.22
0.32
0.42
0.44
0.64
0.84
1.00
Probability
0.5000
0.5871
0.6255
0.6628
0.6700
0.7389
0.7995
0.8413
O
A. 16%
B. 34%
C. 66%
D. 84%
Answers
We have been given that a z-score table and corresponding probability to each z-score. We are asked to find the probability of a getting a z-score less than or equal to 0.42 that is [tex]P(z\leq0.42)[/tex].
z-score Probability
0.00 0.5000
0.22 0.5871
0.32 0.6255
0.42 0.6628
0.44 0.6700
0.64 0.7389
0.84 0.7995
1.00 0.8413
Upon looking at our given table, we can see that the probability corresponding to z-score of 0.42 is 0.6628.
[tex]P(z\leq0.42)=0.6628[/tex]
Now, we will convert [tex]0.6628[/tex] into percent as:
[tex]0.6628\times 100\%=66.28\%[/tex]
Upon rounding to nearest percent, we will get:
[tex]66.28\%\approx 66\%[/tex]
Therefore, the approximate value of [tex]P(z\leq0.42)[/tex] is [tex]66\%[/tex] and option C is the correct choice.
Answer:
C
Step-by-step explanation:
Evaluate 6²-7²+8²-9²+..+998²-999²
Answers
Answer:
-499,485.
Step-by-step explanation:
We can transform this to an arithmetic series by working it out in pairs:
6^2 - 7^2 = (6-7)(6+7) = -13
8^2 - 9^2 = (8-9)*8+9) = -17
10^2 - 11^2 = -1 * 21 = -21 and so on
The common difference is -4.
The number of terms in this series is (998 - 6) / 2 + 1
= 992/2 + 1 = 497.
Sum of n terms of an A.S:
= n/2 [2a1 + (n - 1)d
Here a1 = -13, n = 497, d = -4:
Sum = (497/2)[-26 - 4(497-1)]
= 497/2 * -2010
= -499,485.
A 45 foot ladder is leaning against a building. The foot of the ladder is positioned 10 feet from the base of the building. Determine the angle at which the ladder meets the ground
Answers
Solution:
Given that,
A 45 foot ladder is leaning against a building
The foot of the ladder is positioned 10 feet from the base of the building
The figure is attached below
Let,
AB = foot of the ladder from the base of the building
AB = 10 feet
AC = length of ladder
AC = 45 feet
Then by definition of cos,
[tex]cos\ \theta = \frac{AB}{AC} \\\\cos\ \theta = \frac{10}{45}\\\\\theta = cos^{-1} 0.222 \\\\\theta = 77.17[/tex]
Thus, the angle at which the ladder meets the ground is 77.17 degree
Antonia bought a set of dishes, a towel, and a candle at a housewares store. The set of dishes cost $35.10, the towel cost $21.28, and the candle cost $9.53 before any coupons or discounts. She used a $0.50-off coupon on the candle, a $2.75-off coupon on the towel, and the set of dishes was on sale for 10% off the regular price. Which of the following best describes the amounts that Antonia saved? a. she saved the greatest percentage on the set of dishes b. she saved the greatest percentage on the towel c. she saved the greatest percentage on the candle d. she saved the same percentage on the towel and the set of dishes.
Answers
Answer:
A
Step-by-step explanation:
Since $2.75 discount is given on towel
$0.5 discount is given on candle
10% discount is given on set of dishes
We will have to calculate the discount for the set of dishes
10% of $35.10
10/100 ×35.10
=35.1
So the discount on the set of dishes is $35.1
When comparing the discount on the three things she bought,it was observed that she gained a lot from the discount given on the set of dishes
So the answer is A
A segment XD is drawn in rectangle QUAD as shown
below.
What are the measures of ZXDQ and ZUXD ?
mZ XDQ=
mZ UXD =
–
–
–
–
–
–
–
–
Answers
Answer:
41 and 139
Step-by-step explanation:
the answers are 41 and 139
HELP PLEASE
Identify a, b, and c in the following quadratic equation 2x2+24=−4x.
Answers
Answer:
term a is 2x²
term b is 4x
term c is 24
Step-by-step explanation:
2x² + 24 = -4x
2x² + 4x + 24 = 0
term a is 2x²
term b is 4x
term c is 24
Tell me if I am wrong.
Can I get brainliest
The following distribution is not a probability distribution because
the probability values are not discrete.
the values of the variable are negative
the probability values are not increasing
the probability values do not add to 1.
Answers
Answer:
Choice 2
Step-by-step explanation:
The following distribution is not a probability distribution because the probability values do not add to 1.
If it were a probability distribution, the sum of all the probability values would be equal to 1.
The sum of the probability values is 0.16 + 0.15 + 0.42 + 0.13 + 0.31,
which is equal to 1.17.
Since the sum is greater than 1, it violates the requirement for a probability distribution.
Hence, the probability values do not add to 1.
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Which could be the length of BC?
11 ft
13 ft
15 ft
18 ft
Answers
Answer:D
Step-by-step explanation: Got it right on the test
what is the distance between ( 4, 7 ) and ( 2, 2 )
Answers
Answer:
it would be [tex]\sqrt{29}[/tex]
Step-by-step explanation:
To calculate the distance between (4, 7) and (2, 2), we use the distance formula, derived from the Pythagorean theorem: d = √[(x₂ - x₁)² + (y₂ - y₁)²]. Substituting our values into the equation gives a final answer of √29 units.
Explanation:
The subject of your question pertains to the calculation of distance between two points in a two-dimensional space, which is a concept in Mathematics. The points given are (4, 7) and (2, 2). To find the distance between these points, we can use the distance formula, derived from the Pythagorean theorem. The formula is d = √[(x₂ - x₁)² + (y₂ - y₁)²].
Here, (x₁,y₁) is (4, 7) and (x₂,y₂) is (2, 2). By substituting these values into the formula, we get
d = √[(2 - 4)² + (2 - 7)²]
= √[(-2)² + (-5)²]
= √[4 + 25]
= √29.
Therefore, the distance between (4, 7) and (2, 2) is √29 units.
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Based on the scale drawing, what is the length, in feet, of the actual parking lot?
Answers
Answer:
No one can help
Step-by-step explanation:
You did not provide the scale drawing
Find x in the right triangle.
A) 63
B) 175
C) 147
D) 324
Answers
Answer: C
Step-by-step explanation:The solution is 7
3
. This problem can be solved using the Pythagorean Theorem leg2 + leg2 = hyp2. 142 - 72=147,
147
Final answer:
The value of x squared is 147, leading to the answer choice C for the value of x in the right triangle.
Explanation:
To find the value of x in a right triangle where the hypotenuse = 14, and the length of the other side = 7, we will use the Pythagorean Theorem.
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
This can be written as c² = a² + b², where c is the length of the hypotenuse and a and b are the lengths of the other two sides.
Using the given values we have: 14² = 7² + x².
Simplifying this, we get 196 = 49 + x2, and then 196 - 49 = x², which leads to 147 = x².
Therefore, x = √147.
After calculating, we find that x = √147, which simplifies to x = 12.124 (rounded to three decimal places).
However, the answer choices seem to require the square of x, in which case the answer would be 147, which is option C.
Mikiah must choose between a pack of four 6.5-ounce containers of ice cream for $3.77 or a pack of three 8-ounce containers for $3.87. Which is the better buy? Why?
Answers
Answer:
a pack of three 8-ounce containers his is a better purchase
Step-by-step explanation:
In this case, what we must do is calculate the price per ounce and the one with the best value is the best purchase:
option 1: a pack of four 6.5-ounce containers of ice cream for $ 3.77
3.77 / (4 * 6.5) = 0.145
option 2: a pack of three 8-ounce containers for $ 3.87
3.87 / (3 * 8) = 0.161
The value of the price per ounce is less in option 1, therefore, this is a better purchase
What is the minimum amount of information you need in
order to calculate the slope of a line?
A. The x and y intercepts of the line.
B. Any two points along the line.
C. The length of the line.
D. The endpoints of the line,
NEED THIS BY TODAY PLZZZZ!!!!! BE SURE OF YOU ANSWER
Answers
To calculate the slope of a line we require any two points along the line.
Explanation:
suppose two points are given that is (x1,y1) (x2, y2) . The equation of a line is y-y1=m(x-x1) , where m is referred to as the slope of the line .
To find m,
m= y2-y1/x2-x1 . Hence this way of finding slope is known as point- slope form. Another form is there known as slope- intercept form
y=mx+c.
But to find a slope , minimum amount of information that we require is points along the line.
Final answer:
To calculate the slope of a line, only two points on the line are needed. Slope is computed as the difference in y-coordinates divided by the difference in x-coordinates of these points.
Explanation:
To calculate the slope of a line, the minimum amount of information needed is any two points along the line. The slope is the rate of change between two points on a line and can be calculated using the formula slope (m) = (Y₂ - Y₁) / (X₂ - X₁), where Y₂ and Y₁ are the y-coordinates and X₂ and X₁ are the x-coordinates of the two points. It is not necessary to know the length of the line, the endpoints specifically, or the x and y intercepts separately.
The slope-intercept form of a linear equation, y = mx + b, shows that m is the slope and b is the y-intercept. Here, the y-intercept is simply the point where the line crosses the y-axis, but it is not required for calculating the slope when you have two points on the line.
Use the original price and the markdown to find the retail price.
Original price: $40; Markdown: 16%
Answers
Answer:
$33.6.
Step-by-step explanation:
40 x .16 = 6.4
40 - 6.4 = 33.6.
Feel free to let me know if you need more help. :)
if it takes 20 farmers 36 days to harvest their fruits, how long would it take 30 farmers to harvest the same amount of fruit ?
Answers
Answer:
24 days
Step-by-step explanation:
the information we have is:
Farmers Days
20 ⇒ 36
30 ⇒ x
the table describes that 20 farmers harvest the fruits in 36 days, and the x represents the quantity of days that will take 30 farmers to harvest the fruits.
since the amount of farmers and the amount of days are inversely proportional (if we have more farmers they will need less days, and the other way around) we use the inverse rule of three to solve this problem: multiply the quantities at the top of the table (20 and 36) and divide the result by the remaining amount (30).
we get the following:
x = 20 * 36 / 30
x = 720 / 30
x = 24
It will take 24 days for the 30 farmers to harvest the same amount of fruit
what is the domain for y=3
Answers
Answer:
The domain is all real numbers
Step-by-step explanation:
The domain is the input values
y= 3 is a horizontal line across all x
The domain is all real numbers
The domain is all real numbers.
The domain is the possible values for x that result in a valid equation, no dividing by zero or any of that stuff. Here there's no x in the formula, y=3 is a horizontal line, f(x)=3 for all x. No x in the formula means it works for all x; nothing to go wrong.
Explain to me the strategy that you use to order a group of numbers that may be written in different forms, for example percentages, decimals, and fractions.
Answers
Answer:
Convert fractions, decimals, and percents to the same form to compare the values. Convert Percent to Decimal or Fraction. Convert Decimal to Percent or Fraction. Convert Fraction to Decimal or Percent. Then figure out which is greater or lesser. Use this information to write a set of numbers or quantities in order from least to greatest or from greatest to least.
Step-by-step explanation:
Ordering numbers mean plan of numbers either from little to enormous or from huge to little. At the point when the numbers are orchestrated in an expanding order, it is known as Ascending Order, and when the numbers are organized in a diminishing order, and afterward they are known as Descending Order. For ascending, check the most modest number from the given rundown and spot it first and afterward put the numbers as indicated by the expanding order. For descending check the greatest number from the given rundown and spot it first and afterward put the numbers as per the diminishing order.
A percentage is a part of an entire communicated as a number somewhere in the range of 0 and 100 instead of as a portion. All of something is 100 percent, half of it is 50%, none of something is zero percent.
A decimal is a part written in an extraordinary structure. Rather than composing 1/2, for instance, you can communicate the division as the decimal 0.5, where the zero is during the ones spot and the five is in the tenths spot.
A fraction just discloses to us what number of parts of an entire we have. You can perceive a fraction by the slice that is composed between the two numbers. We have a top number, the numerator, and a base number, the denominator. For instance, 1/2 is a fraction. You can compose it with an inclined slice like we have or you can compose the 1 on the 2 with the slice between the two numbers. The 1 is the numerator, and the 2 is the denominator.
simplify. Write the answer with positive exponents. (3x^4y^5) / (21xy^5) (14x^3y^3)/(2xy^8) someone help please
Answers
x^5/y^5
explanation:
3x^4y^5/21xy^5•14x^3y^3/2xy^8
x^3/7•7x^2/y^5
x^3•x^2/y^5
x^5/y^5
A circular plate has circumference 21.4 inches. What is the area of this plate? Use 3.14 for pi.
Answers
Answer:
The area of this plate is [tex]36.31\ \text{inches}^2[/tex].
Step-by-step explanation:
We have,
Circumference of a circular plate, C = 21.4 inches
The circumference of a circular shape is given by :
[tex]C=2\pi r[/tex]
r is radius of circular shape
[tex]r=\dfrac{C}{2\pi}\\\\r=\dfrac{21.4}{2\times 3.14}\\\\r=3.4\ \text{inches}[/tex]
Area of this plate is given by :
[tex]A=\pi r^2\\\\A=\pi (3.4)^2\\\\A=36.31\ \text{inches}^2[/tex]
So, the area of this plate is [tex]36.31\ \text{inches}^2[/tex].
Need help..................
Answers
Answer:
(4-7x)(4+7x)
Step-by-step explanation:
This is a difference of squares. (16 is the square of 4, 49x^2 is the square of 7x.)
The formula for difference of squares is a^2 - b^2 = (a-b)(a+b)
16 - 49^2 = (4-7x)(4+7x)
Given: F(x) = 2x - 1; G(x) = 3x + 2; H(x) = x2
Find F{G[H(2)]}
Answers
Answer:
Step-by-step explanation:
hello :
Given: F(x) = 2x - 1; G(x) = 3x + 2; H(x) = x2
Find F{G[H(2)]}
calculate : H(2) =2² =4
G[H(2)] =G[4]= 3(4)+2 =14
F{G[H(2)]} = F{14}=2(14) =28
Greg sells magazine subscriptions. He earns $.50 for every subscription he sells. He sold 200 magazine subscriptions. How much money did he earn?
Answers
Answer:
100 dollars 0.50x200=100
Step-by-step explanation:
Answer:
He made 100 dollars
Step-by-step explanation:
If he makes half a dollar for every one sold, and he sold 200, then you just do 200 times .50 and you get 100
What is (3 - 3i)(-5 - 4) in the form a + bi?
Answers
Answer:
Hey
Step-by-step explanation:
Answer:
-27+27i
Step-by-step explanation:
you are trying to simplify this and have to follow pemdas and rearrange it into a+bi form
A playground 96 ft long and 48 ft wide is to be resurfaced at a cost of $4.75 per sq ft. What will the resurfacing cost?
Answers
Answer:
$21888
Step-by-step explanation:
96*48=4608
4608*$4.75=21888
The cost to do the resurfacing of the playground can be found to be $21, 888.
How to find the cost ?To find the cost of resurfacing the playground, you need to calculate the total area of the playground and then multiply it by the cost per square foot.
The playground is 96 feet long and 48 feet wide, so its area is:
Area = Length × Width
Area = 96 ft × 48 ft
Area = 4,608 square feet
Multiply the area by the cost per square foot:
Resurfacing Cost = Area × Cost per square foot
Resurfacing Cost = 4,608 sq ft × $4.75/sq ft
Now, calculate the resurfacing cost:
Resurfacing Cost = $ 21,888
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!!!!20 POINTS PLZ HELP!!!
A scale drawing of a rectangular garden has a length of 5 inches and a width of 3.5 inches. If the scale is 1-inch colon 3 feet, what is the area of the actual garden?
Answer options with 5 options
A.10.5 square feet
B.15 square feet
C.17.5 square feet
D.52.5 square feet
E.157.5 square feet
Answers
Answer:
E
Step-by-step explanation:
map scale: actual scale
= 1 inch: 3 feet
Area scale
= (1 in)²: (3 ft)²
= 1 in²: 9 ft²
This means that 1 in² of the drawing represents an actual area of 9 ft².
Area of garden in the drawing
= 5(3.5)
= 17.5 in²
Area of actual garden
= 17.5 ×9
= 157.5 ft²
Thus, the answer is E.
What is the slope of a line that passes through the points
(-2, -7) and (-6, -2)?
Answers
Hope this will help u...
Look at the attached picture ⤴⤴
Rebecca is making bracelets to sell at a charity event. Each bracelet takes 1 1/4 of a foot of embroidery floss to make.If Rebecca has five yards of embroidery floss,how many bracelets can she make?
Answers
Answer:
12
Step-by-step explanation:
She has 15 feet of floss. 15/1.25 is 12.
Hope this helps!!
Answer:
15
Step-by-step explanation:
She has 15 feet of floss