Answer:
1. Assume the contrary, namely that √2 + √3 + √5 = r, where r is a rational number.
Square the equality √2 + √3 = r − √5 to obtain 5 + 2
√6 = r2 + 5 − 2r
√5. It follows
that 2√6 + 2r
√5 is itself rational. Squaring again, we find that 24 + 20r2 + 8r
√30
is rational, and hence √30 is rational, too. Pythagoras’ method for proving that √2 is
irrational can now be applied to show that this is not true. Write √30 = m
n in lowest
terms; then transform this into m2 = 30n2. It follows that m is divisible by 2 and because
2( m
2 )2 = 15n2 it follows that n is divisible by 2 as well. So the fraction was not in lowest
terms, a contradiction. We conclude that the initial assumption was false, and therefore
√2 + √3 + √5 is irrational.
Step-by-step explanation:
Write the word sentences as an inequality.
A number k is less than 10.
An inequality that represent this word sentences is?
Answer:
k<10
Step-by-step explanation:
Which sentence from the text best supports the narrator’s view of Paul as a giant of a man?
A.
“Feeding Bunyan’s crews of ravenous loggers was a big job.”
B.
“Paul dealt with the challenge by digging down to find the tops of the tall pine trees and lowering his loggers to chop logs.”
C.
“Driving logs upstream is impossible, but an impossible job never stopped Paul.”
D.
“To his surprise, when he tried to move the logs, he discovered the lake had no outlet to the river.”
Answer:
The answer is B
Step-by-step explanation:
I did the test and got it right
Crystal receives a monthly salary of $3,980. Find her earnings per year and earnings per week.
Answer:
per year: $47,760 per year
per week: $918.46 per week
Step-by-step explanation:
$3980 per month x 12 months = $47,760 per year
$47,760 per year divided by 52 weeks = $918.4615384615
Since we're talking money, let's round off our answer to the hundredths place ($918.46 per week)
Double check our answer (918.46 x 52 = 47,760) great!
Answer:
47760 per year
918.46154 per week
Step-by-step explanation:
$3,980 x 12= $47760
$47760/52= $918.46154
A birdwatcher on a cliff saw a eagle 70 feet above him. Earlier, he had spotted the eagle 30 feet above him. Which integer represents the eagle's change in altitude?
The integer that represents the altitude change is -40
How to determine the integer that represents the altitude change?From the question, the positions of the eagle are
70 feet above him and 30 feet above him
Rewrite the positions of the eagle properly
This is done as follows
Position 1 = 70
Position 3 = 30
The expression of the altitude change in the position of the eagle is then calculated as
Change = Position 2 - Position 1
Substitute the known values in the above equation
So, we have the following equation
Change = 30 - 70
Evaluate
Change = -40
Hence, the altitude change is -40
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10 + 25
The expression represents a quadraticy polynomial with
terms. The constant
term is
the leading term is
and the leading coefficient is
Answer:
(x+5)^2
Step-by-step explanation:
(x+5)^2 Using the foil method 5+5=10 and 5x5=25
Which fraction represents the shaded part of the grid?
Answer:
30%
Step-by-step explanation:
Answer:
3 tenth or 3/10 or 30%
Step-by-step explanation:
all works :)
The cook took out 54.8 grams of butter, she then found out that she took out 6.9 grams of butter more than she need. How much butter did she need?
Equivalent expression of d+0.38d
Answer:
0.38 x d + d
Step-by-step explanation:
the answer for ur question is
d+0.38d
1.38d
Can you help me do this or you can write it on a piece of paper to help as well!
-90 is greater than or equal to -5(k-3)
Answer:
Step-by-step explanation:
equal
Determine whether each statement below is true or false. Justify each answer. a. The equation Axb is referred to as a vector equation. Choose the correct answer below. A. False. The equation Axb is referred to as a matrix equation because A is a matrix. B. True. The equation Axb is referred to as a vector equation because A is constructed from column vectors. C. True. The equation Axb is referred to as a vector equation because it consists of scalars multiplied by vectors. D. False. The equation Axb is referred to as a linear equation because b is a linear combination of vectors.
What is the volume of the prism?
Answer:
VOLUME OF PRISM = L X W X H (or) LWH
so, L = 2 in
W = [tex]2\frac{1}{4}[/tex] in (or) [tex]\frac{9}{4}[/tex] in
H = 4 in
volume = 2 x [tex]\frac{9}{4}[/tex] x 4 = 18 in³
Joey has 10 packs of gum. 1/5 of his pack are spearmint. How many of his packs are spearmint?
A. 2 packs
B. 10 packs
C. 1 pack
D. 5 packs
Answer:
A. 2 packs
Step-by-step explanation:
Lincoln told his mother that 4 5/10
represents his height, in feet. Which decimal measurement represents Lincoln's height?
Answer:
[tex]4.5[/tex]
Step-by-step explanation:
In order to find the answer to this question you will first need to convert Lincolns height into a improper fraction and then convert the improper fraction into a decimal number.
[tex]L =4\frac{5}{10}[/tex]
Convert into improper fraction
[tex]4\frac{5}{10} =10 \times4=40+5=45=\frac{45}{10}[/tex]
Convert into decimal by dividing the numerator by the denominator:
[tex]45\div10=4.5[/tex]
[tex]L=4.5[/tex]
Hope this helps.
50 points!
a. Use the Point-Slope form to find the equation of the line through the points (-5, 2) and (-2, 6).
b. Write the equation from part (a) above into the General as well as the slope-intercept form showing every step.
c. Find the x and y-intercepts of the equation above.
Answer:
a) y = 4/3x + 26/3
b) 4x - 3y + 26 = 0
c) x-int: (-6 1/2, 0)
y-int: (0, 8 2/3)
Step-by-step explanation:
a) to get points into the point-slope form you first find the slope by taking the difference of the y-values over the difference of the x-values;
slope (m) = (6 - 2) / (-2 - -5) = 4/3
plug 4/3 into 'm' and select one of the two points to plug in their 'x' and 'y' values so you can find 'b' (the y-intercept)
y = mx + b
6 = 4/3(-2) + b
6 = -8/3 + b
b = 6 + 8/3 = 18/3 + 8/3 or 26/3 (or 8.67)
so, put it all together to get the p-s form of y = 4/3x + 26/3
b) general equation is Ax + By + C = 0
take y = 4/3x + 26/3 and multiply each side by 3 to remove denominators
you get: 3y = 4x + 26; rearrange to get 4x - 3y + 26 = 0
c) y-intercept is (0, 8 2/3); derived during step (a)
to get x-intercept, plug zero in for 'y' and solve for 'x':
0 = 4/3x + 26/3
-4/3x = 26/3
cross-multiply and get 12x = -78
x = -78/12 or -39/6 or -6 1/2
A menu has three meat choices, three vegetable choices and two
desserts. How many ways can you choose your dinner?
Answer:
18 ways
Step-by-step explanation:
The computation of the number of ways that could be choose your dinner as follows:
= 3 meat choices × 3 vegetable choices × 2 desserts
= 18 ways
By multiplying all the three things we can determined the number of ways
you deposit 3,800 in an account with an annual interest of 5.2% for 20 years
help me with this question amigos
Answer:
-3 and 1
Step-by-step explanation:
(x+3)(x-1)=0
x+3=0
x-1=0
x=-3
x=1
Use a system of linear equations with two variables and two equations to solve. A number is 9 more than another number. Twice
the sum of the two numbers is 30. Find the two numbers. Let the two numbers be represented by x and y. Let y represent the
larger number. Write your answer as an ordered pair (x, y).
9514 1404 393
Answer:
(x, y) = (3, 12)
Step-by-step explanation:
Using the given variable definitions, we can write the equations ...
y = x + 9
2(x +y) = 30
__
Solving the second equation for y, we have ...
y = 15 -x
Substituting this into the first equation gives ...
15 -x = x +9
6 = 2x . . . . . . . . . add x-9
3 = x . . . . . . . . . . divide by 2
y = 3+9 = 12 . . . . substitute into the first equation
The numbers are (x, y) = (3, 12).
For each part, write the equation that represents the line in slope-intercept form (y = mx + b) and standard form (ax + by = c where a, b, and c are integers and a is not negative).
Answer:
The equation of a line is typically written as y=mx+b where m is the slope and b is the y-intercept
Step-by-step explanation:
Answer:
Step-by-step explanation:
slope-intercept equation for graph a: y = -x + 1
standard-form equation for graph a: x + y = 1
:::::
Slope of line through (0,-2) and (3,4) = (4-(-2))/(3-0) = 2
Slope-intercept equation for graph b: y = 2x-2
Standard form: 2x-y = 2
Graph a solution of x - 6 > 3
In the figure below, if sin x= 5/13, what are cos x and tan x? PLZ HELP FOR THE LOVE OF GOD AND WHTS GOOD IN THE WORLD HELPPP
Answer:
Step-by-step explanation:
cos²x = 1-sin²x = 1-(5/13)² = 144/169
cosx = √(144/169) = 12/13
tanx = sinx/cosx = (5/13)/(12/13) = (5/13)×(13/12) = 5/12
In an urban area, 31% of dog owners pay for someone to walk their dogs. Morgan asks a random sample of 50 dog owners in this urban area if they pay for someone to walk their dog. What is the probability that more than 30% of the owners in the sample pay for someone to walk their dog?
A. 0.439
B. 0.519
C. 0.561
D. 0.586
Answer:
c 0.561
Step-by-step explanation:
did the test on edge
The probability that more than 30% of the owners in the sample pay for someone to walk their dog is option c. 0.561.
Calculation of the probability:Since 31% of dog owners pay for someone to walk their dogs. Morgan asks a random sample of 50 dog
So
= P> ( 0.30 - 0.31) / √0.31 (1 - 0.31)/ 50
= P(z > - 0.1530)
= 0.5608
= 0.561
Hence, the option c is correct.
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you buy 4 pounds of beef at a price of $5.89 per pound. select the two expressions that you could use to determine the total cost you paid.
Answer: plus and times
Step-by-step explanation: You can do 5.89x 4 or
5.89+5.89+5.89+another 5.89 so thoes are your two answers
please help meeeeeeeeeee
Answer:
check explanation for answers
Step-by-step explanation:
ratios are pretty much just simplified fractions
so just turn the numbers into a fraction and simplify them!
trumpets/violins are 5:3
flutes/clarinets are 17:13
trombones/trumpets are 2:5
violins/total instruments are 12:85
please help me with this
a . 18
b . 16
c . 12
d . 9
Round 138.867545518 to 4 decimal places.
The Answer will be 138.8675
Which fraction equals 4
A-8/2
B-8/4
C-2/8
D-4/8
Answer:
it would be A
Step-by-step explanation:
divide it and that is -4 im not sure if u meant -4 or positive 4 other than that you cant get any other 4
Answer:
A-8/2
Step-by-step explanation:
X f(x)
-2 -1/200
-1 -1/20
0 -1/2
1 -5
2 -50
9514 1404 393
Answer:
f(x) = -1/2·10^x
Step-by-step explanation:
The y-intercept is -1/2.
The common ratio is (-1/20)/(-1/200) = 10, so the exponential function can be written as ...
f(x) = -1/2·10^x
determine the relationship between the measures of the given angles
∠PTV > ∠VPT. This is because the angle opposite to the larger side is greater.
What are angles and dihedral angles? What is equation modelling? In Euclidean geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays lie in the plane that contains the rays. Angles are also formed by the intersection of two planes. These are called dihedral angles.Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.Given is a 2 - D image as shown in the question.
It can be concluded that ∠PTV > ∠VPT. This is because the angle opposite to the larger side is greater.
Therefore, ∠PTV > ∠VPT. This is because the angle opposite to the larger side is greater.
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