Prove the sum of two rational numbers is rational where a, b, c, and d are integers and b and d cannot be zero. Fill in the missing step in the proof.
Answer:
We conclude that the sum of two rational numbers is rational.
Hence, the fraction will be a rational number. i.e.
[tex]\frac{ad+cb}{bd}[/tex] ∵ b≠0, d≠0, so bd≠0Step-by-step explanation:
Let a, b, c, and d are integers.
Let a/b and c/d are two rational numbers and b≠0, d≠0
Proving that the sum of two rational numbers is rational.
[tex]\frac{a}{b}+\frac{c}{d}[/tex]
As the least common multiplier of b, d: bd
Adjusting fractions based on the LCM
[tex]\frac{a}{b}+\frac{c}{d}=\frac{ad}{bd}+\frac{cb}{db}[/tex]
[tex]\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}[/tex]
[tex]=\frac{ad+cb}{bd}[/tex]
As b≠0, d≠0, so bd≠0
Therefore, we conclude that the sum of two rational numbers is rational.
Hence, the fraction will be a rational number. i.e.
[tex]\frac{ad+cb}{bd}[/tex] ∵ b≠0, d≠0, so bd≠0Simplify.
Look at the picture
Answer:
1397.970007
Step-by-step explanation:
[tex]( \frac{3}{5} ) - 2[/tex]
simplify
Oaquin earns 2.00 for each magazine sale. Each time he sells a magizine he also gets a five daller-tip. How much money will he earn after selling x magazines
Answer:
$7 per magazine sale
Step-by-step explanation:
1 magazine = $2
$5 per magazine
$7 per magazine sold
if you get paid semimonthly it means you get paid *
A. less money than someone getting paid weekly because there are more weeks in a
year
B. every other month or 6 times
C. less in February because its a short month
D. twice a month or 24 times per year
Answer:
The answer is D.
Step-by-step explanation:
Semi-monthly means every half month, you will get paid once. So each month you will get paid twice.
Answer:
y=mx+b
Step-by-step explanation:
Please help!!!!!!!!!!!!!!! With all of them.
Answer:
1: SSS
2: SAS
3: SSS
4: SSS
5: SAS
6: SSS
Step-by-step explanation:
When do you need an exponent that is equal to zero? When do you need an
exponent that is negative? What makes these exponents useful?
When an exponent is equal to 0, the whole expression equals one. It does not matter what the base is - the expression will always equal 1. When the exponent is negative, the expression equals 1 over the expression. Here are some examples where this might be useful:
[tex]x^{0} = 1[/tex][tex]x^{-4} = \frac{1}{x^4}[/tex]Hope you found this helpful!
Answer:
first, decay
second, B
third, 0.86
Step-by-step explanation:
edge 2021
2. The envelope below has a mailing label. L(x) = 6x + 5 W(x) = 6x + 5 M(x) = x +4 NOx) = x + 2 MR. AL GEBRA 123 INFINITY WAY POLYNOMIAL, XY 11235 a. Let A(x) = L(x).W(X) - M(x)•N(x). Find A(x).
Answer:
A(x) = 35x² + 54x + 17
Step-by-step explanation:
Relation in the polynomials has been defined as,
A(x) = L(x).W(x) - M(x).N(x)
L(x) = (6x + 5)
W(x) = (6x + 5)
M(x) = (x + 4)
N(x) = (x + 2)
By substituting the polynomials in the expression,
A(x) = (6x + 5)(6x + 5) - (x + 4)(x + 2)
= (6x + 5)² - (x + 4)(x + 2)
= (36x² + 60x + 25) - (x + 4)(x + 2) [Since, (a + b)² = a² + 2ab + b²]
= (36x² + 60x + 25) - [x(x + 2) + 4(x + 2)]
= (36x² + 60x + 25) - [x² + 2x + 4x + 8]
= (36x² + 60x + 25) - [x² + 6x + 8]
= (36x² - x²) + (60x - 6x) + (25 - 8)
= 35x² + 54x + 17
A(x) = 35x² + 54x + 17
Sherlock wants to rent a textbook. He has to pay a fixed base cost plus a daily rate for renting the textbook. The table shows the amount of money, y, in dollars, that Sherlock has to pay for renting the textbook for x days:
Textbook Rental
Number of days
(x) Rent (dollars)
(y)
0 6
1 13
2 20
3 27
4 34
Which equation best shows the relationship between x and y? (1 point)
a
y = x + 13
b
y = 7x + 13
c
y = x + 6
d
y = 7x + 6
Answer:
D
Step-by-step explanation:
Y=kx+n
The table says when x=0 y=6 which means
N=6
Now we need k.
13=k*1+6
K*1=7
K=7
Y=7x+6
need help asap!!!!!!!!!!!!!!!!!!!!
Answer:
really?
Step-by-step explanation:
u better give me brainliest for this:
BAC goes to BAC
BCA goes to BCA
DAC goes to DAC
and suprise suprise
DCA goes to DCA
Can someone please help me with this question?!
Answer:
-5
Step-by-step explanation:
The slope is given by
m= ( y2-y1)/(x2-x1)
= ( 0-10)/(2-0)
= -10/2
= -5
is 3.625 an irrational number? or is it a whole number?
Answer:
It is a rational number
Step-by-step explanation:
Answer:
First, step is what is irrational,
We can't say 3.625 is irrational by observing this.
Irrational is continuously repeating and recurring number
Step-by-step explanation:
I need help with THIS
Answer:
1) 10x
2)360-(5x+20)-10x-(7x-8) (I think?)
3) 7x-8
4) 5x+20
Step-by-step explanation:
Answer:
x=15.8degrees
Step-by-step explanation:
10x+5x+7x+20-8=360
22x+12=360
=22x=360- 12
22x=348
x=15.8 degrees
IM STUCK WITH THIS, ITS BETWEEN 22 OR 12 CAN SOMONE CHECK?
ILL MARK U BRAINIEST
Answer:
12
Step-by-step explanation:
it’s 12 because 4 x 3 = 12
Solve the equation y = ax − b for the variable x.
Answer:
x = y/a + b/a
? is that what you meant
Step-by-step explanation:
Answer:
the answer is d) x = y/a+ b/a
Step-by-step explanation:
brainliest pleasee
what is the answer to this equation ... 3 + 2c + 5c + 2 ??
Answer:
solution:7c+5
A lamppost casts a shadow that is 15 yards long. A 3-foot-tall mailbox casts a shadow that is 5 yards long. How tall is the lamppost?
The lampost is feet tall.
Answer:
I think the answer is 9 feet
Step-by-step explanation:
what the slope of(4,-13) (8,-8)
Answer:
5/4
Step-by-step explanation:
1. -13 - -8 = -5
2. 4-8 = -4
3. -5/-4 = 5/4
plz help
will give brallest
Answer:
your answer is the very first one
Step-by-step explanation:
whats this answer i need it fast uwu
I listen to r & B music but I wanna try another genre. Any music suggestions?
Answer:
rap
Step-by-step explanation:
eminem brainliest pls
Answer:
Maybe try pop or hip-hop? Check out artists similar to Khali Uchis, she has contemporary R&B, pop and hip-hop.
Starting with number 0 on my calculator, I do a calculation in five steps. At each step, I either add 1 or multiply by 2. What is the smallest number that cannot be the final result?
Answer:
assuming only positive integers, the answer is 1
Step-by-step explanation:
the smallest number that you can get by adding is:
start with 0then add 1 = 1add another 1 = 2add another 1 = 3add another 1 = 4add another 1 = 5but you can also multiply, and anything multiplied by 0 is 0:
start with 0multiply by 2 = 0multiply by 2 = 0multiply by 2 = 0multiply by 2 = 0multiply by 2 = 0The question does not say that we need to do any specific calculation, it only gives us 2 options and we can choose them as many times as we want.
(^2 - 9)(x^3 + 3)
Pls someone answer this for me;(
Answer:
x^5-27
Step-by-step explanation:
add the exponents
multiply the rest
Write the linear equation in Slope-Intercept Form y = mx + b of the line that passes through the given points, then graph
the line.
Answer:
y = 3x + 7.
To graph the line mark off the 2 points and draw a line through them.
Step-by-step explanation:
The slope = (-2-7) / (-3-0)
= -9/-3
= 3.
The value of b is found using the point-slope form of a line:
y - y1 = m(x - x1)
using m = 3, (x1, y1) = (0, 7):
y - 7 = 3(x - 0)
y = 3x + 7.
5 students share 2 candy bars what fraction of a candy bar does each student get?
Answer:
2/5
Step-by-step explanation:
Take the number of candy bars and divide by the number of students
2/5
Each will get 2/5 of a candy bar
Answer:
2/5
Step-by-step explanation:
The value of (a+b)sq + (a-b)sq is
Answer:
2asq
General Formulas and Concepts:
Pre-Algebra
Distributive PropertyAlgebra I
Combining Like TermsStep-by-step explanation:
Step 1: Define
(a + b)sq + (a - b)sq
Step 2: Simplify
Distribute sq: asq + bsq + asq - bsqCombine like terms: 2asq33
34
11) If the sales tax rate in NC is 7%, how much tax
would I pay on a $23 pair of boots?
Answer:
$1.61
Step-by-step explanation:
Tax paid = 7% of $23
= 0.07*23
= $1.61
3. Read the conjecture below. Select all of the true statements about this conjecture. If you multiply two numbers, then the product is greater than either number. Select all that apply. a. This conjecture is true. For example, (7)(4) = 28. The product of 28 is greater than 7 and greater than 4. b. This conjecture is false. There is a counterexample that would prove this conjecture false. c. This conjecture is false: . d. There is not enough information.
Answer:
This conjecture is false. There is a counterexample that would prove this conjecture false.
Step-by-step explanation:
Given the conjecture that if you multiply two numbers, then the product is greater than either number is very false. There is a counterexample that would prove this conjecture false.
The counter example is as shown;
Let the two numbers be 1 and 2.
Take their product;
1(2) = 2
We can see that their product which is 2 although greater than 1 is not greater than the other number but equal to it. This example therefore counter the conjecture. This is applicable to numbers with 1 included.
what does 9a-2=12+2a
Answer:
a=2
Step-by-step explanation:
Subtract 2a from both sides.
9a−2−2a=12
Combine 9a and −2a to get 7a.
7a−2=12
Add 2 to both sides.
7a=12+2
Add 12 and 2 to get 14.
7a=14
Divide both sides by 7.
a=[tex]\frac{14}{7}[/tex]
Divide 14 by 7 to get 2.
a=2
Hugo took a math test with 40 questions. If he got 75% of the answers correct, how many did he answer incorrectly?
Answer:\
10
Step-by-step explanation:
25 % correct ie, 40 * 25/100
=10
plz mark as brainliest!!