=========================================================
Explanation:
We can prove this by contradiction.
Let's say
A = some rational numberB = some irrational numberC = some other rational numberand
A+B = C
We'll show that a contradiction happens based on this.
If A is rational, then A = p/q where p,q are two integers. The q cannot be zero.
If C is rational, then C = r/s for some other integers. We can't have s be zero.
Note the following
A+B = C
B = C - A
B = r/s - p/q
B = qr/qs - ps/qs
B = (qr - ps)/qs
B = (some integer)/(some other integer)
This shows B is rational. But this is where the contradiction happens: We stated earlier that B was irrational. A number cannot be both rational and irrational at the same time. The very definition "irrational" literally means "not rational".
In short, I've shown that if A+B = C such that A,C are rational, then B must be rational as well.
The template is
rational + rational = rational
Therefore, we've shown that if A is rational and B is irrational, then C cannot possibly be rational. C is irrational.
Another template is
rational + irrational = irrational
Which equation is equivalent to x^2 +24-8=0?
A.(x+12)^2 =152
B.(x-12)^2=136
C.(x+8)^2=144
D.(x+12)^2 =144
Answer:
D) is your correct answer
40÷1+3‐(3×7)+7-5 use pedams to answer the following question
Hey there!
40 / 1 + 3 ‐ (3 * 7) + 7 - 5
= 40 + 3 - (3 * 7) + 7 - 5
= 43 + 7 - 5 - 3 * 7
= 50 - 5 - 3 * 7
= 45 - 3 * 7
= 45 - 21
= 24
Answer: 24
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
help me with the picture please
=====================================================
Explanation:
Refer to the diagram below. I've drawn diagonal that slopes upward. This diagonal cuts the quadrilateral into two triangles: One is equilateral and the other is isosceles.
The equilateral triangle marked in blue has all three angles 60 degrees each.
Note that the 60 and y angles combined to form 130, so,
60+y = 130
y = 130-60
y = 70
Then focus on the isosceles triangle (angles y, w and w). These three interior angles must add to 180
y+w+w = 180
70+2w = 180
2w = 180-70
2w = 110
w = 110/2
w = 55
This adds onto its adjacent neighbor of 60 to get w+60 = 55+60 = 115 degrees which is the value of x.
You run 24 steps integer practice
9514 1404 393
Answer:
+24
Step-by-step explanation:
The number of steps run can be represented by the integer +24.
Type the correct answer in the box. Use numerals instead of words.
Betty sets up a lemonade stand and charges $1 per glass. It cost her $50 to set up the stand. Which function gives the profit, p, she makes by selling g glasses of lemonade?
The number of glasses of lemonade, g, that Betty needs to sell to make a profit, p, if the setup cost her $50 is given by the function p(g) =
.
Answer:
1g - 50 = p(g)
Step-by-step explanation:
The profit function is,
⇒ p(g) = g - 50
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Betty sets up a lemonade stand and charges $1 per glass.
It cost her $50 to set up the stand.
And, We have to find the function gives the profit, p, she makes by selling g glasses of lemonade.
Now, The number of glasses of lemonade sold = g,
And, A profit, p by function p(g)
Setup cost = $50
Since, Charges for 1 glass = 1 $
Hence, Charges for g glasses = 1.g = $g
Here, The cost = $50
Hence, Profit = $g - 50
⇒ p(g) = g - 50
Therefore, The profit function is,
⇒ p(g) = g - 50
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(4a)^2 without the exponents
Answer:
16 a*a
Step-by-step explanation:
(4a)^2
(4a) (4a)
16 a*a
Answer:
16a²
Step-by-step explanation:
(4a)²
=>(4)² x (a)²
=> 16 x a²
=>16a²
5x = -y + 6 solve for y
-5y + 10x = 5 solve for y
6y = -3x + 12 solve for y
Step-by-step explanation:
a)-5x+6=y
b)2x-1=y
c) -3/6x+2=y
Step-by-step explanation:
5x = -y + 6
y = 6-5x
-5y +10x = 5
5y = 10x -5
y = 10x-5/5
y = 2x -1
6y = -3x+12
y = -3x+12/6 = -1/4x +2
URGENT HELP 20 POINTS
Answer:
-5.6666.... is a rational number and 3.25 is a rational number but not integer too. the rest you got all right, good job.
hope that answers your question
dont hesitate to comment if you need some explanation about this topic
2x+5
---------
x+1
hãy giupd tôi
2x+5
x+1
2+3.......
x+1
Answer:
ask your teachehope help
and search on somewhere I search it there is so many answer
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!
In December, Doug's guitar store sold 10 acoustic guitars and 12 electric guitars. In January, they sold 13 acoustic guitars and 16 electric guitars. During which month did the guitar store sell a lower ratio of acoustic guitars to electric guitars?
A. not enough information
B. January
C. neither, the ratios are equivalent
D. December
Answer:
December
Step-by-step explanation:
December: acoustic/ electric =10/12 = 5/6
January : 13/16
Get a common denominator of 48
5/6 *8/8 = 40/48 for December
13/16 * 3/3 =39/48 for January
December has a higher ratio
who will give my answer I will mark them as brainliest
Answer:
41+-3=38
the rule in exponent says to subtract and take higher no. sign in addition
If you know the answer please let me know
PLEASE HELP ME I NEED HELP
Answer:
V = 1/32 yd^3
Step-by-step explanation:
To find the volume
V= l*w*h where l is length, w is width, and h is height
V = 1/4 * 1/4 * 1/2
V = 1/32 yd^3
Please help I if you can thank you do much
Answer:
A. (Pay as you go) $120 B. (Regular deal) $90 C. (All-in-one price!) $100 D. The "Regular deal" option would be the least expensive for Carl.
Step-by-step explanation:
If Carl does the "Pay as you go" option he would be charged $6 each time. If he works out 20 times a month, we can multiply 20 by 6 to get a total of $120 for that option.
If Carl does the "Regular deal" option he would be charged $50 + an additional $2 for each time he works out. From there, we can get the equation 2x + 50 where x is the amount of time he works out. If we plug in 20 for x (as he works out 20 times a month), we get 2(20) + 50 which equals a total of $90 for that option.
If Carl does the "All-in-one Price!" option he would be charged $100 for the whole month meaning he has unlimited use of the gym with no extra charge besides the $100.
The cheapest option is the "Regular deal" option as it charges $90 compared to the $100 for the "All-in-one Price!" option & the $120 for the "Pay as you go" option.
Narasimha, Madhu and Pavan started a business by investing Rs. 120,000, Rs. 135,000 and Rs. 150,000 respectively. Find the share of Pavan, out of an annual profit of Rs. 56,700.
Answer:
1.
= Here,
Narasimha invest = 120,000
Madhu 135,000
pavan =
a baker is building a rectangular solid box from cardboard to be able to safely deliver a birthday cake. The baker wants the volume of the delivery box to be 224 cubic inches. If the width of the delivery box is 3 inches longer than the length and the height is 4 inches longer than the length, what must the length of the delivery box be?
3 inches
7 inches
8 inches
4 inches
The length of the rectangular delivery box must be equal to 4 inches.
Let the length of the box be L.
Let the width of the box be W.
Let the height of the box be H.
Given the following data:
Volume of box = 224 cubic inches.Translating the word problem into an algebraic expression;
[tex]W = 3 + L[/tex] ......equation 1
[tex]H = 4 + L[/tex] ......equation 2.
Mathematically, the volume of a rectangular solid is given by the formula;
[tex]Volume = length * width * height[/tex] .....equation 3.
Substituting the values into equation, we have;
[tex]224 = L * (3 + L) * (4 + L)\\\\224 = (3L + L^{2})* (4 + L)\\\\224 = 12L + 3L^{2} + 4L^{2} + L^{3} \\\\224 = 12L + 7L^{2} + L^{3}[/tex]
Rearranging the polynomial, we have;
[tex]L^{3} + 7L^{2} + 12L - 224 = 0[/tex]
We would apply the remainder theorem to solve the polynomial.
According to the remainder theorem, if a polynomial P(x) is divided by (x - r) and there is a remainder R; then P(r) = R.
When x = 3
[tex](x - 3) = 0\\x = 3[/tex]
[tex]P(3) = 3^{3} + 7(3^{2}) + 12(3) - 224\\\\P(3) = 27 + 7(9) + 36 - 224\\\\P(3) = 27 + 63 + 36 - 224 = -98 \neq 0[/tex]
We would try with 4;
[tex]P(4) = 4^{3} + 7(4^{2}) + 12(4) - 224\\\\P(4) = 64 + 7(16) + 48 - 224\\\\P(4) = 64 + 112 + 48 - 224\\\\P(4) = 224 - 224 = 0[/tex]
Therefore, 4 is one of its roots.
Hence, the length of the rectangular delivery box must be equal to 4 inches.
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I need help ASAP!!!Please explain you answer
Answer:
Step-by-step explanation:
The body of the Cylinder.
Formula
Area of the body = circumference * length
circumference = 2*pi * r
r = 6 m
Circumference = 2 * 3.14 * 6
Circumference = 12 * pi
Area of body = 12*pi * length
area of body = 12*9 * pi
Area of body = 108* pi
Two ends
The diagram is not complete enough to know whether or not there are 2 ends or one. I'll assume 2.
Area = 2 * pi r^2 For both
Area = 2 * pi * 6^2
Area = 72 pi
Total Area
Total area = 72 pi +108 pi
Total area = 180 pi
Total Area = 180 * 3.14
Total Area = 565.2
Can anyone help?
For what values of K does the equation (2k+1)x^2 +2x= 10x - 6 have two real and equal roots?
For the equation (2k + 1)x² + 2x = 10x - 6 to have two real and equal roots, the value of k = 5/6.
Since the equation is (2k + 1)x² + 2x = 10x - 6, we collect subtract 10x from both sides and add 6 to both sides.
So, we have (2k + 1)x² + 2x - 10x + 6 = 10x - 6 - 10x + 6
(2k + 1)x² - 8x + 6 = 0
For the equation, (2k + 1)x² + 2x = 10x - 6 to have two real and equal roots, this new equation (2k + 1)x² - 8x + 6 = 0 must also have two real and equal roots.
For the equation to have two real and equal roots, its discriminant, D = 0.
D = b² - 4ac where b = -8, a = 2k + 1 and c = 6.
So, D = b² - 4ac
D = (-8)² - 4 × (2k + 1) × 6 = 0
64 - 24(2k + 1) = 0
Dividing through by 8, we have
8 - 3(2k + 1) = 0
Expanding the bracket, we have
8 - 6k - 3 = 0
Collecting like terms, we have
-6k + 5 = 0
Subtracting 5 from both sides, we have
-6k = -5
Dividing through by -6, we have
k = -5/-6
k = 5/6
So, for the equation (2k + 1)x² + 2x = 10x - 6 to have two real and equal roots, the value of k = 5/6.
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I need help ASAP!!People that now what there doing
[2] (c) Another bag contains 15 red beads and 10 yellow beads. Ariana picks a bead at random, records its colour and replaces it in the bag. She then picks another bead at random. (1) Find the probability that she picks two red beads. [2] (ii) Find the probability that she does not pick two red beads. (0)
Answer:
(c)
Total number of beads:
15 + 10 = 25(i)
Probability of 2 red:
P(RR) = 15/25*15/25 = 9/25(ii)
Probability of no 2 red:
P(R'R') = 1 - 9/25 = 16/25There are 9 classes of 25 students each, 4 teachers, and 2 times as many parent volunteers as teachers.
Each bus holds a total of 45 people.
What is the least number of buses needed for the field trip?
the answer Is found in the question
The least number of buses required for the trip will be 5 buses.
What is the Unitary method?It is a method where we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.
First, let us make a note of the information we have. There are 5 ice-creams. 5 ice-creams cost $125.
Step 1: Let’s find the cost of 1 ice cream. In order to do that, divide the total cost of ice-creams by the total number of ice-creams. The cost of 1 ice-cream = Total cost of ice-creams/Total number of ice-creams = 125/5 = 25. Therefore, the cost of 1 ice cream is $25.
Step 2: To find the cost of 3 ice creams, multiply the cost of 1 ice cream by the number of ice-creams. The cost of 3 ice-creams is cost of 1 ice-cream × number of ice-creams = 25 × 3 = $75. Finally, we have the cost of 3 ice-creams i.e. $75.
Total number of classes = 9
Number of students in each class = 25
Number of teachers = 4
Number of chaperones = Double of teacher
Bus hold = 45 people
A total number of students.
= 9 × 25
= 225
A number of chaperones.
= 4 × 2
= 8
Total people = 225 + 8 + 4 = 237
Least number of buses required for trip = Total people / Bus hold
= 237 / 45
= 5.266
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 A Popsicle store at the beach is comparing their monthly revenue with the sunglasses store next door. The shop owners find that their monthly revenue is positive correlated. This means that eating Popsicles causes people to buy sunglasses.
True or false?
Answer:
false
Step-by-step explanation:
correlation doesn't mean causation-
one doesn't necessarily affect the other, can just be conditions (such as weather) or coincidence
The estimate obtained from a sample of which of the following sizes would most likely be closest to the actual parameter value of a population?
To obtain an estimate of a parameter of a population, we use confidence intervals.
Confidence intervals:
The larger the sample size, the closest the parameter estimate is to the value of the population, as the margin of error of confidence intervals is inversely proportional to the sample size, that is, a greater sample leads to a smaller margin of error.
Thus, you should select the highest sample size in the options.
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Help anyone can help me do this question,I will mark brainlest.
side of cube=5
We know
[tex]\boxed{\sf Side=\dfrac{Diagonal}{\sqrt{2}}}[/tex]
[tex]\\ \sf \longmapsto Diagonal =sude\times \sqrt{2}[/tex]
[tex]\\ \sf \longmapsto Diagonal=5\sqrt{2}[/tex]
[tex]\\ \sf \longmapsto Diagonal=5\times 1.4[/tex]
[tex]\\ \sf \longmapsto Diagonal=7cm[/tex]
Answer:
Hello,
Step-by-step explanation:
[tex]Using\ the\ Pythagorian's\ theorem,\\\\EC^2=EA^2+AC^2\\\\=EA^2+AB^2+BC^2\\\\=3*5^2\\\\EC=5\sqrt{3} \approx{8,660...}[/tex]
Violet is playing a board game with her friends. She earns 78 points during the game, and she receives a game-end bonus for achieving her secret objective. With her bonus, Violet came in second place with 91 points. Let b be the number of points Violet earned for the game-end bonus. Write and solve an equation for b.
Answer:
13
Step-by-step explanation:
78 + b = 91 Equation: Subtract 78 from both sides.
b = 91 - 78
b = 13
You don't need her position in the game or the fact that 91 placed her second.
Madeline is renting bowling shoes for $3.50 every time she goes bowling. She could get a good pair of bowling shoes for $68.
If she goes once every two weeks during the year, would it be less expensive to rent or buy?
A Buy
B Rent
Answer:
rent would be cheaper
Step-by-step explanation:
1.50 x 26 = $39 or $48 for a pair
it would be nine dollars cheaper to rent than to buy
Iit would be less if she rent the shoes.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that Madeline is renting bowling shoes for $3.50 every time she goes bowling.
she goes once every two weeks during the year.
In a year there are 52 weeks.
As she is going once every two weeks during the year, so let us divide 52 by 2, 52/2=26
Rent for each bowling is 3.50
So for 26 times it would be 26×3.50
If she goes once every two weeks during the year, then the rent amount will be $91.
As She could get a good pair of bowling shoes for $68.
91 is greater than 68
So, it would be less expensive if she rent the shoes.
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pls help me asap !!!!
Answer:
9--7
Step-by-step explanation:
Moly completes 3/10 of her science project in 4/5 hour
Answer:
1.5 per hour
Step-by-step explanation:
Add.
(4x2 – 2x) + (5x - 7)
O A. 9x2 - 9x
B. 4x2 + 3x-7
C. 20x3 - 38x2 + 14x
O D. 4x2 - 7x+7
SUBMIT
Answer:
4x^2 +3x -7
Step-by-step explanation:
(4x^2 – 2x) + (5x - 7)
Combine like terms
4x^2 -2x+5x -7
4x^2 +3x -7
( 4x² - 2x ) + ( 5x - 7 )
Now , adding like terms.
4x² - 2x + 5x - 7
4x² + 3x -7
Option ( B ) is the correct answer.
14) A contractor estimated that her expenses for a construction project would be between $700,000 and
$750,000 She has already spent $496.000 How much more can she spend and remain within her
estimate?
Write as an inequality!
Answer:
204000 < x < 254000
Step-by-step explanation:
700000 < 496000 + x < 750000
Solve for x by subtracting 496000 from both sides
204000 < x < 254000 ----> so we can conclude that she can spend between $204,000 and $254,000 more and remain within her estimate.
