![Add Or Subtract.[tex] \binom{7 \sqrt{2} }{2} - \binom{ \sqrt{8} }{2} [/tex]](https://i5t5.c14.e2-1.dev/c-qa-images/contents/attachments/SlRUarJdVbUOkufk03XMWudVwkvXp7Or.jpeg)
Answers
This is the fraction of 5*sqrt(2) all over 2
"sqrt" is shorthand for "square root"
--------------------------------------------
Work Shown:
[tex]\frac{7\sqrt{2}}{2}-\frac{\sqrt{8}}{2}[/tex]
[tex]\frac{7\sqrt{2}}{2}-\frac{\sqrt{4*2}}{2}[/tex]
[tex]\frac{7\sqrt{2}}{2}-\frac{\sqrt{4}*\sqrt{2}}{2}[/tex]
[tex]\frac{7\sqrt{2}}{2}-\frac{2*\sqrt{2}}{2}[/tex]
[tex]\frac{7\sqrt{2}-2*\sqrt{2}}{2}[/tex]
[tex]\frac{5\sqrt{2}}{2}[/tex]
Related Questions
alvin's age is two times elga's the sum of their ages is 87 what is elga's age?
Answers
87= 2x+x <== let x equal Elga's age.
Since Alvin's is 2 times Elga's, then you can represent that by 2x. They add up to 87.
87= 2x+x
87= 3x
Divide both sides by 3.
x=29
Elga is 29.
I hope this helps!
~kaikers
By forming an algebraic equation based on the given information, we find that Elga's age is 29 years.
Explanation:This question belongs to the category of Algebraic equations. We know that Alvin's age is two times Elga's, so we could represent Alvin's age as 2E, where E represents Elga's age.
The problem also tells us that the sum of their ages equals 87. That means we can form this equation: E + 2E = 87.
Combining like terms, we get 3E = 87. Finally, dividing each side by 3, we find the value of E (Elga's age).
So, Elga's age is 87 / 3, which equals 29 years.
Learn more about Algebraic equations here:https://brainly.com/question/32183344
#SPJ2
I am an odd number. I am less than 100. The sum of my fights is 12. I am a multiple of 15. What number am I?
Answers
1. Odd numbers, which are multiple of 15 and less then 100, are: 15, 45 and 75.
2. the sums of digits are: for 15 is 6, for 45 is 9, for 75 is 12.
3. this number is 75.
How do I double the volume of a pyramid
Answers
1) double the height, or any other single dimension
2) multiply the base edge lengths, or any other pair of dimensions, by √2
3) multiply every dimension by ∛2
4) multiply the dimensions by any combination of numbers whose product is 2.
Write an expression using variables for the sum of two consecutive numbers
Answers
Then the second one will be n+1
The sum will be n + n+1 = 2n + 1
Question is 2n + 1 always odd or always even?
The answer is always odd.
you are starting your own small business in Albuquerque. you borrow $10,000 from a bank at 9% rate for 5 years find the interest you will pay on this loan
Answers
10,000(1+0.09.5) = 14,500
=$4,500 interest
I will have to pay $4500 interest for the loan I have taken to start a small business.
What is simple interest?We know simple interest (SI) is given by SI = (p×r×t)/100, where
p = principle, r = rate in percentage, and t = time in years.
Given, P = $10,000, r = 9% and t = 5.
∴ SI = (10000×9×5)/100.
SI = 100×45.
SI = 4500.
So, I need to pay $4500 for the loan.
learn more about simple interests here :
https://brainly.com/question/25845758
#SPJ2
What is the length of YX¯¯¯¯¯¯? Enter your answer as a decimal in the box. Round your final answer to the nearest hundredth. m_https://static.k12.com/nextgen_media/assets/8107298-NG_GMT_SemB_10_UT_06.png'
Answers
YX²=(YZ)(YV)
YX=√(YZ)(YV)
YZ=9+19
YV=9
2. When you substitute the values of YZ and YV into YX=√(YZ)(YV), you obtain:
YX=√(YZ)(YV)
YX=√(9+19)(9)
YX=√(28)(9)
YX=√252
YX=15.87
What is the length of YX?
The answer is: The lenght of YX is 15.87
Final answer:
To find the actual length represented by YX, we set up a proportion using the given scale length and solve for the unknown length x. Using one of the provided scale ratios, such as 0.5 inches representing 2000 miles, we perform cross-multiplication to solve for x and determine the accurate length after calculations.
Explanation:
The student is asked to find the actual length represented by the segment YX on a map or a diagram when given a scale length. To solve the problem, we set up a proportion based on the scale provided and solve for the unknown length x. There are different given scales in the prompts such as 0.5 inches representing 2000 miles, 8 inches representing an unknown number of miles, and 3 inches also representing an unknown number of miles.
Example with a Scale Ratio of 0.5 inches to 2000 miles
To solve for x when the scale is 0.5 inches on the map corresponds to 2000 miles in reality, we use a proportion: 1 inch/2000 miles = 0.5 inches/x miles. After cross-multiplication, we get x = 0.5 inches * 2000 miles, which after calculation will give us the value of x rounded to the nearest hundredth.
Example with a Scale Ratio of 0.25 inches to 2000 miles
Similar steps are taken if the scale is 0.25 inches. We set up the proportion 1 inch/2000 miles = 0.25 inches/x miles and solve for x after cross-multiplication.
The area of a rectangle is 30 sq meters. The perimeter is 26 feet. What are the dimensions of the rectangle?
Answers
Answer:
The given rectangle is not possible.
Step-by-step explanation:
The minimum perimeter of such a rectangle is 4√30 meters, about 21.9 meters. That is about 71.9 feet. The largest rectangle with a perimeter of 26 feet will have an area of about 3.93 square meters.
The rectangle described cannot exist.
ordered: 0.5 mg
Available: 2 mg/ml
how many mls should be given?
Answers
Final answer:
The patient should be given 0.25 mls of the medication.
Explanation:
To calculate the volume of medication a patient should be given, we can use a basic formula that relates the ordered dose, the concentration of the medication available, and the volume required to deliver the ordered dose. In this case, the student has been asked to determine how many milliliters (mls) of medication to administer when 0.5 mg is ordered and the medication concentration available is 2 mg/ml.
The formula to use is:
Dose ordered (mg) / Concentration of medication (mg/ml) = Volume to administer (ml)
So for this problem:
0.5 mg / 2 mg/ml = 0.25 ml
Therefore, the patient should be given 0.25 mls of the medication.
Can you please help me out ?
Answers
ratio
leg:leg:hypo = x : x : x√2
hypo = 22√2 (x = 22)
so leg = 22
answer
22 units
Where,
a: side of the triangle.
h: hypotenuse.
We then have to clear the value of a:
a = sine (45) * h
Substituting:
a = sine (45) * (22 * root (2))
a = (root (2) / 2) * (22 * root (2))
a = 22
Answer:
22 (option 3)
The functions f and g are defined as follows f(x)=5x+3/6x+7 and g(x)= square root sign x^2-4x
find f(6/x) and g(x-4)
Answers
This means that f(6/x) = [5(6/x)+3] / [6(6/x)+7] = [ 30/x +3 ] / [36/x +7]
If we assume x≠0 , f(6/x) = [30 +3x]/ [36 + 7x]
g(x)=√ [ x^2-4x ]
g(x-4) = √ [ (x-4)^2-4(x-4) ] = √ [ x² -8x +16 -4x +16 ] = √ [ x^2-12x +32]
Maya added 10 grams of salt to 40 grams of water.
She made ___ grams of ___% solution.
Please help
*show work*
Answers
She made __50__ grams of __20__% solution
-------------------------------------------------------------------
Work Shown:
There's 10+40 = 50 grams of stuff overall (that "stuff" being salt and water). Of this total, 10 grams are salt so 10/50 = 1/5 = 0.20 = 20% is salt. Therefore this is a 20% salt solution.
We can say "20% solution" or "20% salt solution" to be more specific of what kind of chemical mix it is.
Answers:
She made __50__ grams of __20__% solution
-------------------------------------------------------------------
Work Shown:
There's 10+40 = 50 grams of stuff overall (that "stuff" being salt and water). Of this total, 10 grams are salt so 10/50 = 1/5 = 0.20 = 20% is salt. Therefore this is a 20% salt solution.
We can say "20% solution" or "20% salt solution" to be more specific of what kind of chemical mix it is.
David and Josh are both practicing for an upcoming swim tournament. Every week, David swims for 3x hours at an average speed of x laps per hour. Josh swims 5 more hours per week than David, but at an average speed that is 4 laps per hour less than David's average speed.
Which of the following functions will give the total distance, in laps, that Josh swims each week?
Answers
Explanation:
This questions has 4 answer choices to select the right one.
These are the answer choices:
A) f(x) = 3x^2 - 17x + 20
B) f(x) = 3x^2 + 7x - 20
C) f(x) = 3x^2 - 7x - 20
D) f(x) = 3x^2 + 17x + 20
Solution:
Translate the given word statements into algebraic expressions:
1) Every week, David swims for 3x hours at an average speed of x laps per hour =>
time = 3x
speed = x
2) Josh swims 5 more hours per week than David =>
time = 5 + 3x
speed that is 4 laps per hour less than David's average speed =>
speed = x - 4
3) distance, in laps, that Josh swims each week, equal time * speed
=> distance = (3x + 5) (x - 4)
4) Expand the parenthesis:
a) distributive property: (3x)(x) + (3x)(-4) + 5(x) + 5(-4) = 3x^2 - 12x + 5x - 20 =
= 3x^2 - 7x - 20
Answer: 3x^2 - 7x - 20 (option C)
Complete the table of values for the linear equation -2x-5=30 brainly. Enter your answers in the boxes.
Answers
-2x=30+5
-2x/-2=35/-2
X=-17.5
The value of x is x = -17.5.
The linear equation in question is -2x - 5 = 30. To complete a table of values for this equation, solve for x first:
Add 5 to both sides of the equation to isolate the term with x: -2x = 35.
Divide both sides by -2 to solve for x: x = -17.5.
Now that you have the value of x, you can fill in the table with x = -17.5, since a table of values typically includes various values for x and the corresponding values for the equation. However, in this case, the equation is simply solved for a single value of x without needing different values for it.
Which of the following statements is true about lines 3y + 2x - 9 = 0 and 12y + 8x - 5 = 0? They are parallel They are perpendicular They are parallel to the x-axis They are parallel to the y-axis
Answers
Answer:
The statement "They are parallel" is true.
Step-by-step explanation:
The general form of the equation of a straight line is:
[tex]Ax+By+C=0[/tex]
where A, B, and C are three real numbers.
A line parallel to the x-axis has this form [tex]y=C[/tex] where C is a real number.
A line parallel to the y-axis has this form [tex]x=C[/tex] where C is a real number.
From the lines given none of these have the form of a line parallel to the x-axis or the y-axis. Therefore the statements "They are parallel to the x-axis" and "They are parallel to the y-axis" are false.
Two non-vertical lines in a plane are parallel if they have both:
the same slopedifferent y-interceptsTwo non-vertical lines are perpendicular if the slope of one is the negative reciprocal of the slope of the other.
To check if the lines are parallel of perpendicular you must transform these lines into the slope/intercept form
[tex]y=mx+b[/tex]
where m represents the slope and b represents the y-intercept.
The slope/intercept form for the first line is:
[tex]3y+2x-9=0\\\\3y+2x-9-2x=0-2x\\\\3y-9=-2x\\\\3y-9+9=-2x+9\\\\3y=-2x+9\\\\y=\frac{-2x+9}{3}\\\\y=\frac{-2}{3}x+3[/tex]
The slope/intercept form for the second line is:
[tex]12y+8x-5=0\\\\12y+8x-5-8x=0-8x\\\\12y-5=-8x\\\\12y-5+5=-8x+5\\\\12y=-8x+5\\\\y=\frac{-8x+5}{12}\\\\y=\frac{-2}{3}x+\frac{5}{12}[/tex]
We can see that the lines have the same slope and different y-intercepts. Therefore the statement "They are parallel" is true.
We can check our work with the graph of the lines.
3(p+8) = -6 ( p + 6 )
Answers
P= -20
-----
3
Hope this helps:)
*GilmoreGirl01*
what is the radius and center of this circle?
[tex] {x}^{2} + {y}^{2} + 2x - 4y - 2 = 0[/tex]
Answers
the radius is
[tex] \sqrt{7} \: or \: 2.646[/tex]
It took the race car 22 minutes to travel 114.4 kilometers. At what rate did the car travel?Use the formula r = d/t, where r is the rate, d is the distance, and t is the time. Round your answer to the nearest tenth.
Answers
T=22 minutes
R= 114.4 km /22 min
R= 5.2 km/min
The total land area of the United stated is about 3483511 square miles more than the total land area of Tennessee, which is about 53927 square miles. Write and solve an equation to find the total land area of the United stayed.
Answers
Let us denote the total land area of Tennessee by [tex] T [/tex].
Now, It has been given to us that the total land area of Tennessee is about 53927 square miles.
Therefore, [tex] T=53927 [/tex]
It has also been given to us that the total land area of the United States is about 3483511 square miles more than the total land area of Tennessee.
Let us denote the total land area of the United States by [tex] U [/tex].
Now, if the total land area of the United States (denoted by [tex] U [/tex]) is 3483511 square miles more than the total land area of Tennessee (which is 53927 square miles and is denoted by [tex] T [/tex]), then that means that we have to add 3483511 square miles to the total land area of Tennessee to get the total land area of the United States. This can be written in the equation form as:
[tex] U=3483511+T=3483511+53927=3537438 [/tex]
Thus the total area of the United States is 3537438 square miles.
Final answer:
The total land area of the United States is calculated by adding the land area of Tennessee to the difference given in the question. The equation is US Area = 53,927 + 3,483,511. Solving this equation, the total land area of the United States is approximately 3,537,438 square miles.
Explanation:
To find the total land area of the United States, we can use the given information and set up an equation. The total land area of Tennessee is about 53,927 square miles. The question states that the total land area of the United States is about 3,483,511 square miles more than Tennessee's land area. We can express this relationship with the following equation:
Total land area of the United States = Land area of Tennessee + 3,483,511 square miles
US Area = 53,927 + 3,483,511
Solving for the total land area of the United States:
US Area = 3,537,438 square miles
Therefore, the total land area of the United States is approximately 3,537,438 square miles.
A new car is purchased for 20700 dollars. The value of the car depreciates at 13.75% per year. What will the value of the car be, to the nearest cent, after 12 years?
Answers
Answer:
y≈3508.16
Step-by-step explanation:
3/10n = 4/5
what value of n will make this equation correct?
Answers
Answer:
the answer is 2 and 2/3 if that doesn't pop up then 8/3 also works.
Step-by-step explanation:
For each pair of numbers, tell: By what percent of the first number is the second number larger? By what percent of the second number is the first number smaller? 15 and 20
Answers
Reason: The second number (20) is larger than the first number (15) by 5 and 5 is 33.33% the first number.
.
The answer for the second question is 25%, also.
Reason: The first number (15) is smaller than the second number (20) by 5 and it is 25 percent of the second number.
:)
By using a rule of 3, we will see that:
The second number is 33.33% larger than the first one.The first number is 25% smaller than the second one.How to find the percentages?
In the first case, we want to know by what percent of the first number is the second larger.
Then the 100% will be taken as the first number, so we have the relation:
100% = 15
And the other number will represent a percentage X, so we write:
X = 20
By taking the quotient of these two equations, we get:
X/(100%) = 20/15
Solving this for X, we get:
X = (20/15)*100% = 133.33%
We can conclude that the second number is 33.33% larger than the first number.
For the second part, we take 20 as our 100%, and we do the same thing:
X = (15/20)*100% = 75%
Then 15 is (100% - 75% = 25%) 25% smaller than 20.
As you can see the percentages are different. Why does this happen? because in each case the 100% represents a different number.
Finally, we can conclude that:
The second number is 33.33% larger than the first one.The first number is 25% smaller than the second one.If you want to learn more about percentages, you can read:
https://brainly.com/question/843074
A: 2x + 8y = 5 B: x + 9y = 10 To solve this system of equations by elimination, what could you multiply equation B by if you want to add the equations together and have a resulting equation with only the y-variable (the x-variable is eliminated)?
Answers
A: 2x + 8y = 5
B: x + 9y = 10
B x (-2) : -2x - 18y = -20
A + B:
8y - 18y = 5 - 20
- 10y = -15
y = 1.5
To solve for x
B: x + 9y = 10
x + 9(1.5) = 10
x + 13.5 = 10
x = 10 - 13.5
x = -3.5
B: x + 9y = 10
You can multiply equation B by -2 to be able to eliminate the x variable in both equations when you add them together.
B) -2(x + 9y)= 10
-2x - 18y= -20
Add both equations together:
2x + 8y = 5
+(-2x - 18y= -20 )
the x variable is eliminated
-10y= -15
divide both sides by -10
y= -15/-10
y= 1 1/2
Solve for x:
x + 9y= 10
x + 9(1 1/2)= 10
x + 13.5= 10
x= -3.5
ANSWER: multiply equation B by -2
Hope this helps! :)
Quadrilateral ABCD is inscribed in this circle.
What is the measure of ∠A ?
Enter your answer in the box.
____°
Answers
Answer:
Measure of ∠A is 106°
Step-by-step explanation:
We are given that, 'Quadrilateral ABCD is inscribed in the circle'.
So, we get that,
'ABCD is a cyclic quadrilateral' i.e. The sum of the opposite interior angles is 180°.
Thus, we have,
∠A +∠C = 180°
i.e. ∠A + 74° = 180°
i.e. ∠A = 180° - 74°
i.e. ∠A = 106°
Thus, the measure of ∠A is 106°.
which equation can be solved to find x, the measure of BD in the diagram below?
Answers
Angle formed outside=1/2(difference of intercepted arcs)
∠ACE=1/2(AE-BD)
∠ACE=53°
AE=233°
BD=x
Hence the formula for obtaining BD will be:
53=1/2(233-x)
The correct answer is A
Answer:
A. [tex]\frac{1}{2} (233^{o}-x)=53^{o}[/tex]
Step-by-step explanation:
Let x be the measure of arc BD.
Since we know that an angle formed by two intersecting tangents equals one-half the difference of the measures of the intercepted arcs (the major arc-minus the minor arc).
[tex]\text{ Measure of tangent-tangent angle}=\frac{1}{2} (\text{measure of major arc-measure of minor arc})[/tex]
We can see from our given graph that the tangent-tangent angle's measure is 53 degree. The measure of its intercepting major arc equals 233 degrees and minor arc equals x.
Upon substituting our given values in above formula we will get,
[tex]53^{o}=\frac{1}{2} (233^{o}-x)[/tex]
[tex]\frac{1}{2} (233^{o}-x)=53^{o}[/tex]
Therefore, the equation that can be solved to find x (the measure of arc BD) will be [tex]\frac{1}{2} (233^{o}-x)=53^{o}[/tex] and option A is the correct choice.
What are the solutions of the equation x4 + 95x2 – 500 = 0? Use factoring to solve.
Answers
set u=x^2, and substitute
u^2+95u-500=0
Since -5*100=-500, and -5+100=95, we factor equation as
(u-5)(u+100)=0
=> u=5 or u=-100
Back-substitute,
u=5 => x= ± √ 5
u=-100 => x= ± 10i (if you work with complex roots)
So
answer: the real roots of given equation are ± √ 5
the complext roots are: x= ± 10i
Using factorization, the factors of the given equation are; ±√5 and ±10i.
What is Factorization?In mathematics, factorization or factoring consists of writing a number or any mathematical item as a product of several factors, typically small or easier objects of the same.
we have been given the equation:
x⁴ + 95x² – 500 = 0
Factorizing the above equation,
x⁴ + 100x² - 5x² - 500 = 0
x²(x² + 100) - 5(x² + 100) = 0
(x² - 5)(x² + 100) = 0
Solving further:
x² = 5
x² = -100
x = ±√5
x = √-100
Factors : ±√5 and ±10i
Therefore, we know that the factors of the given equation are; ±√5 and ±10i.
Know more about Factorization here:
brainly.com/question/25829061
#SPJ2
What is the general term for the sequence 1, 6, 11, 16
Answers
The general term of the sequence is an = 5n - 4
Among 81678167 cases of heart pacemaker malfunctions, 457457 were found to be caused by firmware, which is software programmed into the device. if the firmware is tested in 33 different pacemakers randomly selected from this batch of 81678167 and the entire batch is accepted if there are no failures, what is the probability that the firmware in the entire batch will be accepted? is this procedure likely to result in the entire batch being
Answers
Part a)
Total number of cases = 8167
Number of Malfunctions due to firmware = 457
Probability that a malfunction is because of firmware = [tex] \frac{457}{8167}[/tex]
Probability that the malfunction is not because of firmware = 1 - Probability that a malfunction is because of firmware = [tex]1- \frac{457}{8167}= \frac{7710}{8167} [/tex]
Probability of selecting 3 pacemakers without a malfunction because of firmware = [tex] ( \frac{7710}{8167} )^{3} = 0.841[/tex]
Part b)
The probability of selecting 3 pacemakers without any malfunction because of firmware is 0.841, which is a high probability. So we can say, yes this procedure is very likely to result in entire batch being accepted. The probability near 1 is considered a very higher probability for an event and the probability near 0 is considered a very lower probability for an event.
The ice rink sold 95 tickets for the afternoon skating session, for a total of $828. answer General admission tickets cost $10 each and youth tickets cost $8 each. How many general admission tickets and how many youth tickets were sold?
I think it is 34 general and 61 youth
Answers
yes, you are right
a rectangle is 1/3 yards long and 2/3 yards wide.
what is the area of the rectangle?
enter your answer in the box as a fraction in simplest form
[tex] \frac{?}{?} \: {yd}^{2} [/tex]
Answers
Area = Length x Width
Length of rectangle = 1/3 yards
Width of rectangle = 2/3 yards
So, the area A of the rectangle will be:
[tex]A = \frac{1}{3}* \frac{2}{3} = \frac{2}{9} [/tex]
So, the Area of rectangle will be [tex] \frac{2}{9} [/tex] square yards.
Final answer:
The area of a rectangle with dimensions of 1/3 yards by 2/3 yards is calculated using the formula length × width, resulting in an area of 2/9 square yards. This value is already in simplest form.
Explanation:
The question asks us to find the area of a rectangle that is 1/3 yards long and 2/3 yards wide. The formula to calculate the area of a rectangle is length × width. Therefore, to find the area, we multiply 1/3 yards by 2/3 yards.
Area = (1/3) yd × (2/3) yd = 2/9 yd²
This calculation shows that the area of the rectangle is 2/9 square yards. It is important to express the answer in simplest form, as the question requests, and 2/9 is already in its simplest form.
Which of the following is a perfect square?
A. 127
B. 100
C. 13
D. 102
Answers
We can find the perfect square by taking the square root of each number. The number that reduces to a whole number when the square root is taken is your answer.
sqrt(100) = 10 so B. 100 is your answer.