Answer:
(a) If r is any rational number and s is any irrational number, then r/s is rational
(b) The statement is false when r is 0
Step-by-step explanation:
Given
[tex]r \to[/tex] rational number
[tex]s \to[/tex] irrational number
[tex]\frac{r}{s} \to[/tex] irrational number
Solving (a): The negation
To get the negation of a statement, we only need to negate the end result
In other words, the number type of r and s will remain the same, but r/s will be negated.
So, the negation is:
[tex]r \to[/tex] rational number
[tex]s \to[/tex] irrational number
[tex]\frac{r}{s} \to[/tex] rational number
Solving (b): When r/s is irrational is false
Given that:
[tex]\frac{r}{s} \to[/tex] irrational number
Set r to 0
So:
[tex]\frac{r}{s} = \frac{0}{s}[/tex]
[tex]\frac{r}{s} = 0[/tex] -- rational
Hence, the statement is false when r is 0
Cary sets up a checking account with an initial balance of $27,700, and the rent for her
apartment is deducted every month for a year. After a year the balance is $7900
(Assume no other transactions occur on the account)
Answer:
$1,650
Step-by-step explanation:
First, we need to find how much she paid the whole year. 27,700-x=7900. If we subtract 7900 from each side and add x to each side, we get 19,800=x. Therefore, she paid $19,800 in rent the whole year. Since there are 12 months in a year, and each month she paid the same, she paid $1,650 in rent each year, for 19800/12=1650
pls help pls help pls help
Which of the following is an example of a quadratic equation?
Answer:
C) any eqaution that has a variable or number squared is a qaudratic equation
2nd one. identify the slope.
Answer:
m = 4 / 5
Step-by-step explanation:
first coordinate : (0,-4)
second coordinate: (5,0)
The formulae for the slope : m=(y2-y1)/(x2-x1)
Substituting,
m = (0 - (-4)) / (5 - 0)
m = 4 / 5
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If 2 to the power of x is 1/32. Find the value of x...
Step-by-step explanation:
2 to the power x =1/32
2 to the power x =1/2 to the power 5
2 to the power x = 2 to the power -5
then,
x = -5
Devon has $200 in his savings account. He has to withdraw $8 every week to pay his friend back for some video games. The video games cost $88. How many weeks will it take to pay his friend back? How much will Devon have left in his savings account?
Answer:
it will tale 11weeks to pay back his friends and he will have $112left after.
Step-by-step explanation:
88÷8=11.
200- 88 =112
Thank you show your work<3
x=
y=
Answer:
[tex]x=-5,\\y=\frac{13}{2}[/tex]
Step-by-step explanation:
[tex]\begin{cases}x+2y=8,\\x=-5\end{cases}[/tex]
Substitute the second equation into the first ([tex]x=-5[/tex]):
[tex]-5+2y=8,\\2y=13,\\y=\boxed{\frac{13}{2}}[/tex]
The second equation already denotes [tex]x=-5[/tex]. Therefore,
[tex]\boxed{x=-5,\\y=\frac{13}{2}}[/tex]
Answer:
x=-5
y=6.5
Step-by-step explanation:
if x=-5 then x+2y=8 could be rewriten as -5+2y=8 then you add 5 on both sides and you get 2y=13 then divide both sides by 2 and you get y=6.5
The LCM of three numbers is 360 and the GCD of the same numbers is 2.If one of the numbers is 40.Find the other 2 numbers
Answer
“The LCM of three numbers is 360“ The prime factors of 360 are 2³×3²×5¹. That means:
At least one of the numbers contains 2³ in its factorization list.
At least one of the numbers contains 3² in its factorization list.
At least one of the numbers contains 5 in its factorization list.
“One of the numbers is 40“ The factorization list of 40 is 2³×5, so 1) and 3) are satisfied.
“The GCD of the same numbers is 2“ This implies that all 3 numbers are even, and that at least one number only has one 2.
The candidates for the 2nd number, that has 3², are: 18, 12, 72 (3²×2³), 120, 180, or 360.
The candidates for the 3rd number depends on how many 2s the 2nd number has.
If more than one: 2, 6, 18, 10, 30, 90
If only 1, those plus 4, 8, 12, 36, 72, 20, 40, 120, 180, 360
Write 1/3 x^2 - 4x + 17 in vertex form
Answer:
f(x)=−4(x+ 41 ) 2 − 4 11
Explanation:
The given function is
f(x) = - 4 {x}^{2} - 2x - 3f(x)=−4x 2 −2x−3
To write the function is vertex form, we need to complete the square.
We first factor -4 to get:
f(x) = - 4 ({x}^{2} + \frac{1}{2} x) - 3f(x−4(x2 + 21 x)−3
Add and subtract the square of half the coefficient of x.
f(x) = - 4( {x}^{2} + \frac{1}{2} x + \frac{1}{16} ) - \frac{1}{4} - 3f(x)=−4(x 2 + 21 x+ 16 1 )− 41 −3
We factor the perfect square trinomial and simplify to get:
f(x) = - 4( {x + \frac{1}{4} )}^{2} - \frac{11}{4}f(x)=−4(x+ 41 ) 2 − 4 11
if you had 12 pieces and cherry has 3 pieces grape has 4 pieces and lemon has 5 pieces What is the probability of selecting a cherry OR grape piece?
Answer:
7 in 12 chance
Step-by-step explanation:
theres 12 pieces and cherry and grape has 7 combined pieces so the chance of you picking a piece that is either cherry or grape is 7/12
Given that cos(θ)= -√3/4 and tan(θ) > 0, find sin(θ)
Answer:
B. -√13/4
Step-by-step explanation:
cos 0 = -√3/4 => x=-√3 , h=4
tan 0 > 0
y should be on quadrant III
y= √4²-3= √16-3=√13 => -√13
so, sin 0 = y/h = -√13/4
Answer:
B. -√13/4
Step-by-step explanation:
:)
Answer this question for me please
Answer:
9-2 = 7
8-3 = 5
[tex]\sqrt{5^{2} +7^{2} \\[/tex]
= 8.602325267
Step-by-step explanation:
55 points:
What is the area of "triangle " XYZ to the nearest tenth of a square inch? Use special right triangles to help find the height. Leave your answer in terms of the radical. Show your work.
Answer:
area of triangle
90⁰+60⁰+x = 180⁰
150⁰ +x = 180⁰
x = 30⁰
Step-by-step explanation:
1/2 × base × heinght
1/2 × 30⁰ × 90⁰
15 × 90
1350 ft² is area of triangle
A factory can make 3,848 pencils in one hour. Which is the best estimate of how many pencils can be made in 4 hours? *
A 160,000 pencils
B 16,000 pencils
C 12,000 pencils
D 1,600 markers
Answer:
B. 16,000 pencils
Step-by-step explanation:
3,848 * 4 is 15,392
Answer:
b
Step-by-step explanation:
bur an
Question 4: Answer the following questions
1)
What percent is 40 of 50?
(2) 4.2)
What percent is 50 of 40?
Answer:
1, 20
2, 20
Step-by-step explanation:
Answer:
your correct answers are
1, 20
2, 20
Step-by-step explanation:
Chris is playing a card game with his friends. The game uses only the four aces from a standard deck of cards. For each move, a player draws one card, replaces it, and then draws the second card.
Answer:
1/4
Step-by-step explanation:
Let's call the aces for hearts, diamonds, clubs, and spades. So, are red and [tex] c, s[/tex] is black.
Since the first card is replaced, the two picks are identical. This means that the sample space is given by all the possible couple
There are 16 such couples (we have four choices for the first card, and the same four choices for the second card). Now let's compute the odds in our favor to deduce the probability of winning:
If we want a player to draw two cards of the same color, the following couples are good:
so 8 possible couples over 16. This means that a player's probability of drawing two cards of the same color is 8/16 = 1/2.
Similarly, the probability of drawing a red ace first and then a black ace is represented by the following couples:
which are 4 over the same 16 as above, thus leading to a probability of 4/16 = 1/4.
BRAINLIEST ASAP PLEASE Write an equation for each translation.
36. y = sin x, Pi/4
units to the right
Answer:
Step-by-step explanation:
y=sin (x-\pi/4)
Solve the equation. 6g = 48 what does g equal?
Answer:
8
Step-by-step explanation:
First we need to figure out what g equals
Since 6 x 8 = 48 your answer would be 8
6 x 8 = 48
~ LadyBrain
The value of g that satisfies the equation is 8.
To solve the equation 6g = 48 and find the value of g, we can isolate the variable g by dividing both sides of the equation by 6:
6g / 6 = 48 / 6
This simplifies to:
g = 8
Therefore, g equals 8. By dividing both sides of the equation by 6, we find that when g is multiplied by 6, it results in 48. Hence, the value of g that satisfies the equation is 8.
To know more about equation:
https://brainly.com/question/10724260
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Jodie ran at an average speed of 6 km/h for 10 minutes.
How far did she run in km?
Answer:
Distance cover by Jodie = 1 kilometer
Step-by-step explanation:
Given;
Speed of Jodie = 6 kilometer/ hour
Total time Jodie ran = 10 minutes
Find:
Distance cover by Jodie
Computation:
Total time Jodie ran = 10 minutes = 10 / 60 = 0.1667 hour
Distance = Speed x time
Distance cover by Jodie = Speed of Jodie x Total time Jodie ran
Distance cover by Jodie = 6 x 0.1667
Distance cover by Jodie = 1.002
Distance cover by Jodie = 1 kilometer
What is the slope of (6,-2) and (-3,1)
Answer:
slope = 1
Step-by-step explanation:
We have two points which are (6,-2) and (-3,1).
and we need to find slope
use the slope formula
m = ( y² - y1 ) / ( x² + x¹)
Where,
m is the slope( y² - y1 ) = ( 1 - 6 )( x² + x¹) = ( -3 -2)substitute the values
m = ( 1 - 6 ) / ( - 3 -2)
m = -5 / -5
divide we get
m = 1
Answer:
slope = - [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (6-2) and (x₂, y₂ ) = (- 3, 1)
m = [tex]\frac{1-(-2)}{-3-6}[/tex] = [tex]\frac{1+2}{-9}[/tex] = [tex]\frac{3}{-9}[/tex] = - [tex]\frac{1}{3}[/tex]
i need to know the answer
Answer:
Option A is correct
Step-by-step explanation:
Please Mark me brainlist
Find the unit rate for the number of parts manufactured per hour if 1380 parts are made in 4 hours. Round to the nearest integer. Group of answer choices
Answer:
345
Step-by-step explanation:
The answer is 345 because you divide 1380 by 4 which is 345.
The total number of students in the seventh grade is 9 more than 4 times as many students as are in the art class. If there are 101 students in the seventh grade, how many students are in art class?
Answer:
I think there are 23 students in the art class.
Step-by-step explanation:
You first subtract 9 from 101. Then, you divide by four to get 23.
A man was 62 years 18 years ago. what will be his age in 6 years time
Answer:80 and a half years old
Step-by-step explanation:62+18=80 6 months=1/2 of 1 year
80+1/2 = 80 1/2 years old
Which range of y values makes
this inequality true?
0.6y < 15
Pls help
Answer:
yes this is true helpful answer
Gabe went to the florida mall. He bought k model planes and spent 24 on books.Then he another 25 at another store
Answer:
[tex]Amount = 49 + 14.99k[/tex]
Step-by-step explanation:
Given
[tex]Books = 24[/tex]
[tex]Another\ Store = 25[/tex]
[tex]Model = k[/tex]
Cost of [tex]Model = 14.99[/tex] --- Missing from the question
Required
Represent the amount spent
The amount is calculated as:
[tex]Amount = Books + Another\ Store + Model * Cost[/tex]
[tex]Amount = 25 + 24 + k * 14.99[/tex]
[tex]Amount = 49 + 14.99k[/tex]
which of the following statement is true?
The terminal side of θ in standard position contains the point (3, 0). Find the exact values of the six trigonometric functions of θ
[tex]\textit{we know that }\theta \textit{ contains the point }(\stackrel{x}{3}~~,~~\stackrel{y}{0})\textit{, let's find the hypotenuse} \\\\\\ \textit{using the pythagorean theorem} \\\\ r^2=a^2+b^2\implies r=\sqrt{a^2+b^2}\implies r=\sqrt{3^2+0^2} \qquad \begin{cases} r=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ r=\sqrt{3^2}\implies r=3[/tex]
[tex]\rule{34em}{0.25pt}\\\\ sin(\theta)=\cfrac{opposite}{hypotenuse} =\cfrac{y}{r}\implies \cfrac{0}{3}\implies 0 \\\\\\ cos(\theta)=\cfrac{adjacent}{hypotenuse} =\cfrac{x}{r}\implies \cfrac{3}{3}\implies 1 \\\\\\ tan(\theta)=\cfrac{opposite}{adjacent} =\cfrac{y}{x}\implies \cfrac{0}{3}\implies 0[/tex]
[tex]cot(\theta)=\cfrac{adjacent}{opposite} =\cfrac{x}{y}\implies \cfrac{3}{0}\implies und efined \\\\\\ csc(\theta)=\cfrac{hypotenuse}{opposite} =\cfrac{r}{y}\implies \cfrac{3}{0}\implies und efined \\\\\\ sec(\theta)=\cfrac{hypotenuse}{adjacent} =\cfrac{r}{x}\implies \cfrac{3}{3}\implies 1[/tex]
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Find the sum of 1+2+3+4...19
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Answer:
190
Step-by-step explanation:
1+2+3+4......19=210-20
=190
find the eighth term of an arithmetic sequence if the first term is 5 and the common difference is 6
Answer:
47
Step-by-step explanation:
Formula for finding nth term of an arithemetic sequence is:
tn = t1 + (n-1) d
Where t1 is the first term, n is the specific term, and d is the common difference.
Plug numbers into the formula and solve:
t8 = 5 + (8-1)6
t8 = 47