Answer:
a = [tex]\frac{11}{7}[/tex] ; b = [tex]\frac{6}{7}[/tex]
Step-by-step explanation:
[tex]\frac{3 + \sqrt{2}}{3 - \sqrt{2} } = a + b\sqrt{2} \\\\[/tex]
Rationalising [tex]\frac{3 + \sqrt{2}}{3 - \sqrt{2} }[/tex] gives :-
[tex]\frac{3 + \sqrt{2}}{3 - \sqrt{2} } = \frac{(3 + \sqrt{2})(3 + \sqrt{2})}{(3 - \sqrt{2})(3 + \sqrt{2}) } = \frac{(3 + \sqrt{2})^2}{3^2 - (\sqrt{2})^2 } = \frac{11 +6\sqrt{2} }{7}[/tex]
Comparing [tex]\frac{11 + 6\sqrt{2} }{7}[/tex] with [tex]a + b\sqrt{2}[/tex] gives
a = [tex]\frac{11}{7}[/tex] & b = [tex]\frac{6}{7}[/tex]
Answer:
[tex]\frac{11}{7}[/tex] + [tex]\frac{6}{7}[/tex] [tex]\sqrt{2}[/tex]
Step-by-step explanation:
Given
[tex]\frac{3+\sqrt{2} }{3-\sqrt{2} }[/tex]
Multiply the numerator/ denominator by the conjugate of the denominator.
The conjugate of 3 - [tex]\sqrt{2}[/tex] is 3 + [tex]\sqrt{2}[/tex] , thus
= [tex]\frac{(3+\sqrt{2})(3+\sqrt{2}) }{(3-\sqrt{2})(3+\sqrt{2}) }[/tex] ← expand numerator/ denominator using FOIL
= [tex]\frac{9+6\sqrt{2}+2 }{9-2}[/tex]
= [tex]\frac{11+6\sqrt{2} }{7}[/tex]
= [tex]\frac{11}{7}[/tex] + [tex]\frac{6}{7}[/tex] [tex]\sqrt{2}[/tex] ← in the form a + b[tex]\sqrt{2}[/tex]
with a = [tex]\frac{11}{7}[/tex] and b = [tex]\frac{6}{7}[/tex]
-5(k + 6) + 7(k – 4)
Answer:
2k-58
Step-by-step explanation:
-5(k+6) + 7(k-4)
-5k-30+7k-28
2k-48
Abdul wants to hang a square poster that measure 1 1/2 feet on a side in the center of a 12-foot-long wall. How far from the end of the wall should abdul place the side of the poster?
Answer:
5.25 feets
Step-by-step explanation:
Given the question :
Abdul wants to hang a square poster that measure 1 1/2 feet on a side in the center of a 12-foot-long wall. How far from the end of the wall should abdul place the side of the poster?
Length of one side of Square poster = 1 1/2 Feets = 3/2 feets
Length of wall = 12 feets long
Since Abdul wants the poster to be centered in the wall; then the picture should be placed such that there must be equal space left on either side of the wall after hanging.
Hence, (12/2 - 1 1/2) = (6 - 0.75) feets
= 5.25 feets
2(3x” – 2)-(4x? - 4x)
What is this simplified to?
Answer:
6x-4
Step-by-step explanation:
Let's simplify step-by-step.
2(3x−2)−(4x−4x)
Distribute the Negative Sign:
=2(3x−2)+−1(4x−4x)
=2(3x−2)+−1(4x)+−1(−4x)
=2(3x−2)+−4x+4x
Distribute:
=(2)(3x)+(2)(−2)+−4x+4x
=6x+−4+−4x+4x
Combine Like Terms:
=6x+−4+−4x+4x
=(6x+−4x+4x)+(−4)
=6x+−4
Answer:
=6x−4
PLEASE HELP, ITS TIMED HURRY >>>>
Answer:2
Step-by-step explanation:
IM FAST RIGHT???
Answer:
A
Step-by-step explanation:
Hopefully this helps you
pls give me brainlest :)
The quotient of 2 and 9
In survey of 200 game lovers, it was found that 130 like football, 90 like cricket and 20 did not like both games.how many persons were there who liked both games? *
Answer:
There are 10 of them like both games.
10-4x= -9x
I need help quick
Answer:
x = -2
Step-by-step explanation:
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
PEMDAS is the order of operation, and =
Parenthesis
Exponents (& Roots)
Multiplication
Division
Addition
Subtraction.
~
First, add 4x to both sides:
10 - 4x (+4x) = -9x (+4x)
10 = -9x + 4x
10 = -5x
Isolate the variable, x. Divide -5 from both sides:
-5x = 10
(-5x)/-5 = (10)/-5
x = 10/-5
x = -2
x = -2 is your answer.
~
What is the value of 5k + m when k = -3 and m = -
-9?
A. -60
B. -30
C.-24
D. -6
Answer:
C. -24
Step-by-step explanation:
[tex]5k + m \\ k = - 3 \\ m = - 9[/tex]
Plug in values into the given equation
[tex]5( - 3) + ( - 9) \\ - 15 - 9 \\ = - 24[/tex]
Answer:
-24 C.
Step-by-step explanation:
I took the test and got it right
HELP!! The side of a square is 3 raised to the 5/2 power inches. Using the area formula A = s squared, determine the area of the square.
Answer:
3^5/2 is 15.5885.
Step-by-step explanation:
This is plug in math! I'd recommend to get a Ti-84 (makes math like this so much easier)
Answer:
243 square inches
Step-by-step explanation:
The area is the square of the side length:
A = s^2
A = (3^(5/2))^2 = 3^(5/2*2) = 3^5 = 243
The area of the square is 243 square inches.
_____
The relevant rule of exponents is ...
(a^b)^c = a^(bc)
describe fully the single transformation that maps traingle a to triangle b
Answer:
it is a reflection
Answer:
reflection y=x
Step-by-step explanation:
evaluate -40 divided by 5
Answer:
-9
Step-by-step explanation:
Since 5 can go into 40 9 times, the answer would be nine, but by following negative rules, since we have an odd amount of negative numbers in this equation, the answer is -9
Answer:-8
Step-by-step explanation:
5 goes into -40 8 times. 5 goes into 45 9 times.
can i have help on step to -2(8m+8)=-16
Answer:
m = 0
Step-by-step explanation:
[tex]-2(8m+8)=-16\\\\\frac{-2(8m+8)=-16}{-2}\\\\ 8m+8=8\\\\8m+8-8=8-8\\\\8m=0\\\\\frac{8m=0}{8}\\\\ \boxed{m=0}[/tex]
Hope this helps.
find the area of the figure
Answer:
90 inches squared
Step-by-step explanation:
To do this you would first find the area of the 2 triangles shown on the side so we would do 5 times 2 divided by 2 since that is how we solve this problem so we would get 5 inches squared for the 2 triangles then we would find the area of the square which is 100 since it is a 10 by 10 then you would subtract 5+5 by 100 which is 90 so 90 inches squared would be the answer
Answer:
Your correct answer is 90 sq. in.
Step-by-step explanation:
Find the area of the 2 triangles that are shown on the side.
5 x 2 divided by 2 = 5 sq. in.
Now, find the area of the square
The answer for this is 100 because it is a 10 x 10
Next, subtract
5 + 5 by 100 = 90
Which equation matches the graph shown?
A.y=(x-2)(x-1)
B.y=-(x-2) (x+1)
c y= -( x+2) ( x*1)
D. y= ( x-2) (x+1)
Answer:
B. v = - (x - 2)(x + 1)Step-by-step explanation:
The parabola opens downward so a<0
zeros are: x₁=-1 and x₂=2, so the factors are:
(x - x₁) = [x - (-1)] = (x + 1)
(x - x₂) = (x - 2)
which gives: - (x + 1)(x - 2)
For every pound a company spends on advertising it spends £.0.49 on it website express the amount spent on advertising to it website as a ratio in it simplest form
Answer:
1/0.49
Step-by-step explanation:
Every pound = 1 pound
And for every one of this company spends 0.49pound
To express this in a ratio is 1:0.49
Which is also 1/0.49 in fraction.
A ratio tells us how many times a number contains another number. It compares two numbers in relation to each other.
Therefore 1/0.49 expresses the amount spent on advertising as a ratio
Consider a function that describes how a particular car’s gas mileage depends on its speed. What would be an appropriate domain for this function? 0 to 100 miles per hour 0 to 50 miles per gallon times from 0 to 10 minutes times from –10 to 10 minutes
Answer:
0 to 100 miles
Step-by-step explanation:
Trust me I know say thanks ppl
An altitude of a three-dimensional object is best described as option D, "a segment that is perpendicular to the planes containing the two bases."
What is 3d geometry?3D geometry is the study of shapes in 3D space using three coordinates: x-coordinate, y-coordinate, and z-coordinate. To discover the exact location of a point in 3D space, three criteria are required.
An altitude is a line segment drawn from a vertex of a three-dimensional object (such as a pyramid or cone) that is perpendicular to the plane including the base of the object. The altitude can be used to find the height of the object, which is the distance from the vertex to the base along the altitude.
For example, in a pyramid, the altitude is a line segment drawn from the apex (the top vertex) to the center of the base that is perpendicular to the base. In a cone, the altitude is a line segment drawn from the apex to the center of the circular base that is perpendicular to the base.
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The set of irrational numbers is the set of numbers whose decimal representations are neither (blank) nor (blank).
Answer:
neither terminating nor repeating.
Step-by-step explanation:
The set of irrational numbers is the set of numbers whose decimal representations are neither terminating nor repeating.
What are rational numbers and irrational numbers?Rational numbers are numbers which can be written in the form of [tex]\dfrac{a}{b}[/tex]where a and b are integers. Example: 1/2, 3.5 (which is writable as 7/5) etc.
Integer numbers are: ...., -2, -1, 0, 1, 2, ... (so it includes positive and negative natural number, and 0 )
Irrational numbers are those real numbers, which are not rational numbers.
Know that all natural numbers are integers, all integers are rational numbers means, natural numbers are not irrational.
The set of irrational numbers is the set of numbers whose decimal representations are neither terminating nor repeating.
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A scuba diver was 53 below the oceans surface. If he rises 25 feet, what is hte new depth?
Answer:
28 ft below the surface.
Step-by-step explanation:
A scuba diver was 53 below the oceans surface. If he rises 25 feet, what is the new depth?
You subtract 25 ft from 53 ft leaving you with 28 ft.
53 ft
- 25 ft
28 ft below the surface
Hope this helps.
Identify the property that justifies the statement: If 3x=-21, then x=-7.
What is the best solutionto this equation?
x+8= -2
A.-10
B.-6
C.6
D.10
Answer:
Step-by-step explanation:
x + 8 = -2
x = -10
the answer is a
y=3x+12 positive or negative
Answer:
x = -4 thus negative
Step-by-step explanation:
Solve for x:
3 x + 12 = 0
Hint: | Isolate terms with x to the left hand side.
Subtract 12 from both sides:
3 x + (12 - 12) = -12
Hint: | Look for the difference of two identical terms.
12 - 12 = 0:
3 x = -12
Hint: | Divide both sides by a constant to simplify the equation.
Divide both sides of 3 x = -12 by 3:
(3 x)/3 = (-12)/3
Hint: | Any nonzero number divided by itself is one.
3/3 = 1:
x = (-12)/3
Hint: | In (-12)/3, divide 12 in the numerator by 3 in the denominator.
12/3 = (3×4)/3 = 4:
Answer: x = -4
1. A taxicab ride costs $1.30 plus $0.85 per mile. If the total cost of the trip
is $11.50, how many miles did the passenger travel?
Answer:
Step-by-step explanation:
the answer is 12 miles okay so subtract $1.30 from the $11.50 because that is the prize pf being in the car then the pries of a mile is $0.85 if that the case $11.50 -$1.30 would equal $10.2 and $10.2 divide $0.85 is 12 hopefully this helps
If x-(-15)=23, what is the value for x?
Answer:
8
Step-by-step explanation:
When there are 2 minuses, they convert into + so that the ewuation turns into:
x+15=23
Then you move the +15 after the = sign
Now that you changed the side, you have to change sign so :
x= 23-15
x=8
find the distance between each pair of points. round to the nearest tenth (-8,-2) and (6,-1)
Answer: 14
Step-by-step explanation:
To find the distance, find the difference in the x and y values,square them and add them. Then finally find the square root of the number you got after adding them together.
-2-(-1)= -1
-8 -6 = -14
-14^2 + -1^2 = d^2 where d is the distance
196 + 1 = d^2
197 = d^2
d= [tex]\sqrt{197}[/tex]
d= 14.0356 rounded to the nearest tenth is 14.
Bernie is making monthly payments of $300 for a computer coding course that costs $2,500. He doesn’t need to pay any interest on the cost of the course. He started with $200 in his bank account. He plans to add $100 to his savings account every month. How many months will it take Bernie to pay off the total cost of the course using his savings?
Answer:
i believe it is 5.75 months
Step-by-step explanation:
It would take Bernie 23 months to pay off the total cost of $2500 for the course using his savings
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let y represent the amount of money in Bernie account after x months. Hence:
y = 100x + 200
To make $2500:
2500 = 100x + 200
x = 23 months
It would take Bernie 23 months to pay off the total cost of $2500 for the course using his savings
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What is this I need help
Answer:
B. No solution
Step-by-step explanation:
[tex]2y-7\left(y+8\right)=1-5y\\\\\mathrm{Expand}\:-7\left(y+8\right):\quad -7y-56\\2y-7y-56=1-5y\\\\\mathrm{Add\:similar\:elements:}\:2y-7y=-5y\\-5y-56=1-5y\\\\\mathrm{Add\:}56\mathrm{\:to\:both\:sides}\\-5y-56+56=1-5y+56\\\\Simplify\\-5y=-5y+57\\\\\mathrm{Add\:}5y\mathrm{\:to\:both\:sides}\\-5y+5y=-5y+57+5y\\\\Simplify\\0=57[/tex]
Answer:
2y-7(y+8)=1-5y ///// y=B
Step-by-step explanation:
the sides are unequal, therefore, y cannot be found
let a and b be positive integers. 23^a x 23^b
Answer:
23 ^ ( a+b)
Step-by-step explanation:
23^a *23^b
Since the bases are the same, we can add the exponents
23 ^ ( a+b)
Answer:
23^(a+b)
Step-by-step explanation:
A^x*A^y = A^(x+y)
you can think of it like this
A^x = A*A*A*.......*A x times
A^y = A*A*A*....*A y times
therefore A^x * A^y = A*A*A*...*A (x+y) times
=A^(x+y),
so in our case A = 23, and x and y were a and b, so 23^a * 23^b = 23^(a+b)
HELP ME
Bob's Bagels sells 10 bagels for $11.00, and Donny's Bagels sells 4 bagels for $3.00. Which is the better deal?
Answer the questions to find out.
1. Will the better deal have a lower or higher ratio of dollars per bagel?
Write your answer in the space below.
2. What fractions do you compare to find the better deal?
Write your answer in the space below.
3. Which store has the better deal, Bob's Bagels or Donny's Bagels? Explain.
Write your answer in the space below.
Answer:
4 bagels for $3
Step-by-step explanation:
10 bagels for 11 = 1.10 and 4 bagels for $3 = 0.75
Answer:
i would say the first one because you get 10 bagels for 11 $ because 1.50 cents per bagel
select all equations that have the same solution as 3x - 12=24
Answer:
4
Step-by-step explanation:
3x-12=24
-12 to both sides
3x-12-12=24-12
3x=12
3x/3=12/3x
x=4
0.00365 in scientific notation