Answers
Answer:
[tex]-\sqrt{2}[/tex]Step-by-step explanation:
Make the following operations:
a² + b² = 6aba² + 2ab + b² = 8ab(a + b)² = 8aba + b = [tex]2\sqrt{2ab}[/tex]and
a² + b² = 6aba² - 2ab + b² = 4ab(a - b)² = 4aba - b = [tex]-2\sqrt{ab}[/tex], since a < bThe required value is:
[tex]\cfrac{a+b}{a-b} =\cfrac{2\sqrt{2ab} }{-2\sqrt{ab} } =-\sqrt{2}[/tex]Answer:
[tex]\dfrac{a+b}{a-b}=-\sqrt{2}[/tex]
Step-by-step explanation:
Given:
[tex]a^2+b^2=6ab[/tex]
[tex]0 < a < b[/tex]
Add 2ab to both sides of the given equation:
[tex]\implies a^2+b^2+2ab=6ab+2ab[/tex]
[tex]\implies a^2+2ab+b^2=8ab[/tex]
Factor the left side:
[tex]\implies (a+b)^2=8ab[/tex]
Subtract 2ab from both sides of the given equation:
[tex]\implies a^2+b^2-2ab=6ab-2ab[/tex]
[tex]\implies a^2-2ab+b^2=4ab[/tex]
Factor the left side:
[tex]\implies (a-b)^2=4ab[/tex]
Therefore:
[tex]\implies \dfrac{(a+b)^2}{(a-b)^2}=\dfrac{8ab}{4ab}[/tex]
[tex]\implies \dfrac{(a+b)^2}{(a-b)^2}=2[/tex]
[tex]\textsf{Apply exponent rule} \quad \dfrac{a^c}{b^c}=\left(\dfrac{a}{b}\right)^c:[/tex]
[tex]\implies \left(\dfrac{a+b}{a-b}\right)^2=2[/tex]
Square root both sides:
[tex]\implies \sqrt{\left(\dfrac{a+b}{a-b}\right)^2}=\sqrt{2}[/tex]
[tex]\implies \dfrac{a+b}{a-b}=\pm\sqrt{2}[/tex]
As 0 < a < b then:
a + b > 0a - b < 0Therefore:
[tex]\implies \dfrac{a+b}{a-b}=\dfrac{+}{-}=-[/tex]
So:
[tex]\implies \dfrac{a+b}{a-b}=-\sqrt{2}[/tex]
Related Questions
Gavin is selling water bottles at a baseball game to help raise money for new uniforms. Before the game, he buys 48 water bottles for a total of $18.50. At the game, he sells all of the bottles for $1.25 each. How much profit does Gavin make?
$
Answers
Answer: $41.50 41 dollars and 50 cents in profit
Step-by-step explanation:
First, 1.25x48=60
Second, 60-18.50=41.50
Answer:
$41.50
Step-by-step explanation:
So we know that Gavin bought 48 water bottles before the game for $18.50. We also know that he sold the water bottles for $1.25 each.
If we want to know how much profit he made, we first have to find the amount of money he received.
To find this, we need to multiply the number of water bottles by the price for each bottle;
48 × $1.25
This gives us a total of $60.
Now to find the profit, we have to subtract the amount he paid for the water bottles by the total he made;
$60 - $18.50
This means he made a profit of $41.50.
hope this makes sense! <3
the shorter leg of a right triangle is 8 less than the hypotenuse. the longer leg is one less than the hypotenuse. find the perimeter
Answers
The perimeter of the right triangle is 30 units.
How to find the perimeter of a right triangle?The shorter leg of the right triangle is 8 less than the hypotenuse. The longer leg is one less than the hypotenuse.
Let's break the information into smaller chunk.
The shorter leg of a right triangle is 8 less than the hypotenuse.
The longer leg is one less than the hypotenuse.
The hypotenuse is the longest side of a right triangle.
Therefore,
let
the hypotenuse = x
short leg = x - 8
long leg = x - 1
Applying Pythagorean theorem in the given right triangle.
c² = a² + b²
where
c = hypotenusea and b are the other legs.(x - 1)² + (x - 8)² = x²
(x - 1)(x - 1) + (x - 8)(x - 8) = x²
x² - x - x + 1 + x² - 8x - 8x + 64 = x²
2x² - 18x + 65 = x²
x² - 18x + 65 = 0
(x - 13)(x - 5) = 0
Therefore,
x = 5 and x = 13
13² - 5² = a²
169 - 25 = a²
a = √144
a = 12
So, the hypotenuse is 13, the shorter leg is 5 and the longer leg is 12.
perimeter of the right triangle = 13 + 5 + 12 = 30
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if marks age is represented by m and hatch is age is represented by h then which of the following expression represents five less than the sum of marks and hatchi ages
Answers
The expression that represents five less than the sum of mark's and hatch's ages is ( h + m ) - 5
Given,
Mark's age is represented by m
Hatch's age is represented by h
To find an expression that shows the required relation, that is, five less than the sum of mark's and hatch's ages, we need to establish a relation between the given variables.
Sum of mark's and hatch's ages can be represented as ( m + h )
Five less than the sum of mark's and hatch's ages can be represented as ( m + h ) - 5.
Therefore, by establishing a relation between the given variables, we get the expression that represents five less than the sum of mark's and hatch's ages as ( h + m ) - 5.
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How many fish caught in this study had lengths between 45 cm and 90 cm
Answers
Answer:
number of fish caught between 60 and 75 cm =40
Step-by-step explanation:
What is the value of the function f(x) = 8x when x = 0.25?
f(x) =
Answers
Answer:
f(x) = 2
Step-by-step explanation:
What is the value of the function f(x) = 8x when x = 0.25?
substitute in 0.25 for x to get:
f(x) = 8(0.25)
f(x) = 2
A can of Campbell's soup has a diameter of 4 inches and a height of 6 inches.
What is the volume of the soup in the can?
Answers
Answer: V = 75.4
Step-by-step explanation: Assuming this is a cylinder we can use the formula πr^2*h. All we have to do is plug in the numbers for the equation. Since we know radius is half of the diameter we can set radius to 2. h represents height.
So since the formula is saying we need to square the radius. We multiply 2*2=4
We can then plug this in for r squared.
Making our equation= π*4*6 = 75.4
x and y intercept of 7x-9y=35
Answers
The x intercept and y intercept of 7x-9y=35 is (5,0) and (0,-35/9) respectively .
X Intercept is defined as the point where the line crosses the X axis .
For Example : if the line x+y=2 crosses the x axis at 2 , then it's x intercept will be (2,0).
Y Intercept is defined as the point where the line crosses the Y axis.
For Example ; if the line x+y=2 crosses the y axis at 2 , then it's Y intercept will be (0,2) .
In the given question
7x-9y=35
To find the x intercept we substitute the value of y=0,
On substituting y=0 we get
7x=35
x=5
The x intercept is (5,0).
To find the y intercept we substitute the value of x=0,
On substituting x=0 we get ,
-9y=35
y=-35/9
The y intercept is (0,-35/9) .
Therefore , the x intercept and y intercept of 7x-9y=35 is (5,0) and (0,-35/9) respectively .
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Given m||n, find the value of x
Answers
Answer:
[tex]x = 61[/tex]
Step-by-step explanation:
See the attached image for explanation
Hope it helpsCheck the picture below.
Which mapping represents a rotation of 270 degrees clockwise about the origin?
Answers
The mapping representing a rotation of 270 degree clockwise about the origin is (x, y) -----> (-y, x)
We use the rotation of 90 degree to find the mapping of 270 degrees.
The rotation of 270 degree clockwise is same as the anticlockwise rotation of 90 degrees about the origin.
So the mapping of 270 degree clockwise rotation is exactly the mapping of 90 degree anti clockwise rotation.
Now the mapping of 90 degree anti clockwise rotation is (x, y) -----> (-y, x).
So the mapping representing a rotation of 270 degree clockwise about the origin is (x, y) -----> (-y, x)
This implies that a point (x, y) on the co-ordinate plane becomes (-y, x) after a clockwise 270 degree rotation.
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to determine her blood sugar level, charlotte divides up her day into three parts: morning, afternoon, and evening. she then measures her blood sugar level at 3 randomly selected times during each part of the day.
Answers
According to the given statement this is a type of stratified sampling.
What is a Stratified random sampling?Stratified random sampling is often when researchers want to know about different subgroups or based on the entire population being studied. For instance, if one is interested in differences between groups based on race, gender, or gender.
Briefing:she measures her blood sugar level at 3 randomly selected times during each part of the day.
Stratified is defined as taking samples from a group that has been partitioned or divided into multiple pieces.The lady has organized her day into three sections here: morning, afternoon, and evening.This is a method for randomly selecting a sample from a population. therefore, charlotte took 3 random sample from each part of the day.So,
This is a type of stratified sampling.
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I understand that the question you are looking for is :
To determine her blood sugar level, charlotte divides up her day into three parts: morning, afternoon, and evening. She then measures her blood sugar level at 3 randomly selected times during each part of the day.
What type of sampling is used?
What is the answer to this problem ?
Answers
Answer:
191+192
Step-by-step explanation:
to determine customer opinion of their safety features, daimler−chrysler randomly selects 140 service centers during a certain week and surveys all customers visiting the service centers.
Answers
cluster sampling is the type of sampling is used.
What do you mean by cluster sampling?In cluster sampling, a population is divided into clusters, which are smaller groups. They then choose a sample at random from these clusters. Often employed to investigate huge populations, particularly those that are extensively geographically distributed, cluster sampling is a probability sampling technique. Typically, clusters used by researchers are already-existing groups like cities or schools. Clusters are frequently more homogeneous than the population as a whole since they are typically naturally occurring groups, such as schools, cities, or houses. When conducting your study, you should be aware of this as it might compromise the validity of your findings.
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ind both the vector equation and the parametric equations of the line through in the direction of the vector , where t0 corresponds to the given point.
Answers
The parametric equations are line through (0,0,0) in the direction of the vector v=uxw=(1,2,1).
The line through (0,0,0) and perpendicular to both U=(-2,1,0) and
w=(-1,0,1)
Therefore the line through (0,0,0) and parallel to (-2,1,0)
[tex]*10919-1-2, î+1=3618 = (1) ņ - (-2)5+ (1)a • Î +21 + û[/tex]
=(1,2,1)
Therefore direction ratio of the line through (0,0,0) is (1,2,1) Therefore for equation of the line through (0,0,0) and perpendicular to both (-2,1,0) and [tex]w=(-1,0,17 is (0,, z) = (0,0,0) + x (1,2,1),[/tex] & is constant.
[tex].: X (1,4,2)= (0, 1, 0)+ [1,2,1][/tex]
Therefore parametric of the line through (0,0,0) in the direction of the vector v=uxw=(1,2,1)
How do you find a vector?Equivalent Equation of a Plane in Vector Form
The equation for a plane in the real number system R, where r is the position vector of any point on the plane and n is either a normal vector perpendicular to the plane or a parallel vector.
The normal vector must be perpendicular to both as the vectors are both parallel to the plane. Recall that a vector that is perpendicular to both vectors is created by taking the cross product of two vectors. This cross product's characteristic can be used to compute a normal vector to the plane, which results in the normal vector.
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f a person's eye level is h meters above sea level and she can see d kilometers to the horizon, then d=3.57\sqrt(h). Suppose the person's eye level is 7.84 meters above sea level. How far can she see to the horizon? Round your answer to the nearest tenth.
Answers
A function assigns the value of each element of one set to the other specific element of another set. The person can see upto 9.996 meters.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Given that a person's eye level is h meters above sea level and she can see d kilometers to the horizon, then d=3.57√(h).
Now, using the same given function we can find the distance up to which the person will be able to see to the horizon. Therefore, we can write,
d=3.57√(h)
d = 3.57 √(7.84)
d = 3.57 × 2.8
d = 9.996
Hence, the person can see upto 9.996 meters.
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There are 8 guests at lincoln's party. if each guest will be served exactly 1/4 pint of ice cream, how many pints of ice cream will he need? express your answer in simplest form.
Answers
Answer:
2 pints
Step-by-step explanation:
if you add all of it up you get 2 pints.
1/4*8 = 2 pints
14a - (2a +9)=2/3 (12a-18)
Answers
Answer: a=-0.75
Step-by-step explanation:
14a - (2a +9)=2/3 (12a-18)
14a - 2a -9=2/3 * 6(2a-3)
12a-9=2*6/3 (2a-3)
12a-9=2*2(2a-3)
12a-9=4(2a-3)
12a-9=8a-12
4a-9=-12
4a=-3
a=-3/4
a=-0.75
Hope this helped :)
Find x. (Hint: Draw an auxiliary line.)
Answers
The angle x will be 98 ⁰
What are alternate interior angle ?
An alternate interior angle is one formed on the inside side of two parallel lines and opposite on the outer side of the transversal when those two parallel lines are intersected by a transversal and they are equal.
Alternate angles between a transverse and parallel lines are equal .
Let the lines are AB and CD and let us draw a transverse line HI parallel to AB and CD, then the angle FEI will be 62 degree as alternate interior angle are equal. and also angle EPC will be supplementary angle of 144 degree that is 36 degree thus forming angle GEI to be 36 degree also as shown in figure below :
Now calculating angle x :
x = 62+ 36
x = 98 ⁰
Therefore, the angle x will be 98 ⁰
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A print shop borrows $5700 from a credit union for 193 days. The credit union charges simple interest at an annual rate of 12% for this loan. Assume 1/365 each day is
of a year. Answer each part below.
Do not round any intermediate computations, and round your final answers to the nearest cent. If necessary, refer to the list of financial formulas.
Answers
The amount borrowed by the print shop: $5700
Time for which loan is taken: 193 days
Rate of interest: 12%
Day in terms of year is given by: 1/365
The formula for simple interest:
Simple interest = P*R*T/100
where P = principal amount invested
R = rate of interest
T = time in years
Solving the question using the formula we have:
Simple interest = (5700*12*193)/(100*365)
= 13201200/36500
= 361.67 or $362
Interest that will be owed after 193 days will be $362
Amount owed after 193 days will be $5700 + $362 = $6062
Although a part of your question is missing, you might refer to this full question: A print shop borrows $5700 from a credit union for 193 days. The credit union charges simple interest at an annual rate of 12% for this loan. Assume 1/365 each day of a year. Find the interest that will be owed after 193 days. If no payments are made on the loan find the amount owed after 193 days.
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I need help thank you
Answers
Answer:
3
Step-by-step explanation:
[tex]\sqrt[3]{27}[/tex]
= [tex]\sqrt[3]{3^3}[/tex]
= 3
Convert 10 centimeters into yards. Round your answer to the nearest hundredth.
Answers
Answer:
0.11 yards
Step-by-step explanation:
To convert centimeters to yards, find the needed unit conversions:
[tex]cm(\frac{in}{cm})(\frac{ft}{in})(\frac{yd}{ft})[/tex]
Convert centimeters to inches, inches to feet, then feet to yards!
Now replace the values with the correct quantities:
[tex]10cm(\frac{1in}{2.54cm})(\frac{1 ft}{12 in})(\frac{1 yd}{3 ft})[/tex]
Finally, simplify and cross-cancel the units:
[tex]0.10936... yd[/tex]
Round to the nearest hundredth:
[tex]0.11 yd[/tex]
Bonjour,
Quelqu'un pourrait m’aider svp.
Answers
a-/ |-5-10| = 15 ; |-2√2-√12|=2√3+√12 ; |-π-4π|=5π
THIS IS FOR ALEGBRA 2 AND NO TUTOR CAN HELP ME I NEED HELP PLEASE
Answers
The number of hours to operate the mines to minimize cost are Mine 1 hour = 25 hours and Mine 2 hour = 10 hours
How to determine the number of hours?The given parameters can be represented using the following table of values
Mine 1 (x) Mine 2 (y) Available
Regular grade 5 20 325
Low grade 18 9 540
Operating cost 16000 12000
Time 37 34
From the table, we understand that we are to minimize cost
This means that:
Objective function: C = 16000x + 12000y
Subject to:
5x + 20y >= 325
18x + 9y >= 540
Next, we plot the constraints on a graph (see attachment)
From the graph, we have
(x, y) = (25, 10)
This means that
Mine 1 hour = 25 hours
Mine 2 hour = 10 hours
Hence, the number of hours to operate the mines to minimize cost are Mine 1 hour = 25 hours and Mine 2 hour = 10 hours
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Use the below diagram to find the area of the shaded region if the radius of the circle is 92 inches and the measure of angle ABC is 7pi/15
Answers
The area of the shaded region of the circle is 10.972 square inches.
What is the Area of the Sector?
The formula for area of a circle sector is;
A = (θ/360) * πr²
We are given;
Radius of circle = 92 inches
Central angle = 7π/15
Thus;
Area of given sector = (7π/15)/360 * π * 92²
Area of given sector = 7π/15 * 1/360 * π * 92²
Area of given sector = 10.972 square inches
Thus, we can conclude that the area of the shaded region of the circle is 10.972 square inches.
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Darius designed a billboard. The
billboard is 480 inches long by 144
inches high. Darius uses a
computer to design the billboard.
Determine the height for the
computer design that maintains
the same scale and has a length of
12 inches.
Answers
To start, because the figures are proportional, we need to setup some proportions:
480/12=144/x
We do this to divide the length of the original figure by 12, and we set them equal because their quotient should remain constant or the same. Now, we use the cross product property to solve:
480•x=144•12
480x=1728
x=3.6
Therefore, substitute x back into the proportional equation:
480/12=144/3.6
40=40
So, the height is 3.6in. This means the new figure is 1/40 of the original.
5.9 divided by 35.4 yeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answers
Answer: 0.16666
Step-by-step explanation:
You need to move the decimal point over
[tex]\frac{5.9}{35.4} \\ \\ \frac{59}{354}=\frac{59.0}{354} =\frac{0.16666}{554}[/tex]
The sum of 5 and c is greater than or equal to - 28.
Answers
Answer:
C is greater than or equal to -23
Step-by-step explanation:
- 28 + 5 = -23
Simplify the expression to a single power of x. Open parentheses x to the power of begin display style bevelled 1 half end style end exponent over x to the power of begin display style bevelled 1 fifth end style end exponent close parentheses to the power of bevelled 1 fourth end exponent
Answers
The simplified form of the given expression is x raise to the power of one-thirty.
Simplifying indices expressionsGiven the indices expression (x^1/2/(x^1/3)^1/5
Using the indices law below:
a^m/a^n = a^m-n
(a^m)^n
Applying the law above to the given equation
(x^1/2/(x^1/3)^1/5 = (x^1/2-1/3)^1/5
(x^1/2/(x^1/3)^1/5 = (x^1/6)^1/5
(x^1/2/(x^1/3)^1/5 = x^1/30
Hence the simplified form of the given expression is x raise to the power of one-thirty.
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HEY I NEED HELP ASAP CAN YOU HELP? WILL GIVE BRAINLYIST
show your work or explain your reasoning in mathematical terms. Be specific. Draw a picture if you need to.
Question:
Abdul wants to put a rug in a square room that has an area of 775 square feet. He wants to leave a 3-foot border of bare floor on each side. What are the dimensions of the rug rounded to the nearest hundredth?
Answers
The dimensions of the rug which Abdul would use in discuss as described in the task content are; 21.84 ft by 21.84 ft.
What are the dimensions of the rug rounded to the nearest hundredth?It follows from the task content that the dimensions of the rug which Abdul would use in the room in discuss are to be determined.
Since the room Abdul wants to put a rug on is; 775 ft² and the room is a square room.
It follows that all sides of the room are equal and the length of each side can be determined as;
s = √Area; since Area = s².
s = √775
s = 27.839 ft.
Hence, the dimensions of the room is; 27.839 ft by 27.839 ft.
However, since he wants to leave a 3-foot border of bare floor on each side, it follows that the dimensions of the rug on each axis would be;
= 27.839 - 3 -3 = 21.839 ft on all sides.
Consequently, the dimensions of the rug rounded to the nearest hundredth are; 21.84 ft by 21.84 ft.
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A pool measuring 18 meters by 20 meters is surrounded by a path of uniform width, as shown in the figure. If the area of the pool and the
path combined is 1520 square meters, what is the width of the path?
18
20
20+ 2x
18+2x
Answers
By solving a quadratic equation we can see that the width of the path measures 20 meters.
How to find the width of the path?
We know that the pool measures 18 meters by 20 meters, then the area of the pool alone is:
A = 18m*20m = 360 m^2
Now, if the path has a width x, then the rectangle that includes the path and the pool has dimensions:
(18m + 2x) and (20m + 2x)
And its area is given by:
(18m + 2x)*(20m + 2x)
And we know it is equal to 1520 m^2, then (i'm not writting the units in the computation):
(18 + 2x)*(20 + 2x) = 1520
360 + 4x^2 + 76x = 1520
Now we just need to solve that quadratic equation:
4x^2 + 76x - 1520 + 360 = 0
4x^2 + 76x - 1160 = 0
The solutions are:
x = (-76 ± √(76^2 - 4*4*(-1160))/(2*4)
x = (-76 ± 156)/4
We only care for the positive solution, which gives:
x = (-76 + 156)/4 = 20
We conclude that the width of the path measures 20 meters.
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just random question te get points ;)
Answers
Answer:
450 eggs
Step-by-step explanation:
if an egg box can hold 10 eggs
then 45x10=450
if each box has 10 eggs and theres 45 then
10 times 45 is 450