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≠0Solve the equation for y.
4x+6y=12
Answer:
your answer when you solve for y will be: y=-2+ 2x/3
The equation can represent as y = 2 - 2x/3 after solving for y if the equation is 6y = 12 - 4x.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
The equation is:
4x+6y=12
To solve for make the subject as y:
6y = 12 - 4x
Divide by 6 on both sides
y = (1/6)[12 - 4x]
After simplification:
y = 2 - 2x/3
Thus, the equation can represent as y = 2 - 2x/3 after solving for y if the equation is 6y = 12 - 4x.
Learn more about the linear equation here:
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What is the value of (2x)° + 1
Answer:
=2x+1
Step-by-step explanation:
I am pretty sure that is the answer
Twenty-one goats were shown in the county fair. This was seven less than four times the number of horses shown. How many horses were shown? (a) Write an equation that could be used to solve the problem. (b) State the solution.
Answer:
H=horse
H=4(21-7)
Step-by-step explanation:
H=4(21-7)
H=4(14)
There were 56 horses.
Bill purchased x hotdogs and y hamburgers at a baseball game. He spent a total of $10. A hotdog costs 3 dollars and a hamburger costs 4 dollars. Write a linear equation to represent the situation. How many hot dogs and hamburgers did Bill buy?
Answer:
Bill bought 2 hotdogs and 1 hamburger.
Step-by-step explanation:
If Bill spent $10 total, and a hotdog costs $3 while the hamburger costs $4, then find how many times 3 and 4 go into 10. 3 goes into ten 3 times, and 4 also goes into 10 3 times. but if it was 2 hamburgers and a hotdog, Bill would have spent $11. This is because 4+4=8 and if you add 3 you get 11. But if you do it the other way around, 3+3=6, and if you add 4 to 6 you get 10. Son your answer has to be 2 hotdogs and 1 hamburger, or, X=2 and Y=1.
What is the unit rate? 400 m travelled in 50 seconds
Answer:
8 meters per second or 8/1
Step-by-step explanation:
Divide 400 meters by 50
8
So it is 8 meters per second
Hope this helps :)
Please consider Brainliest :)
Answer:
8 meters per 1 second
Step-by-step explanation:
first, do 400m/50sec
then, do 400m/1 divided by 50sec/1
next, do keep change flip so, 400/1 * 1/50=400/50
last simplify so, 400 divided by 50 and 50 divided by 50 equals 8/1
hope this helps
solve for x plsssss help me out
Answer:
-11
Step-by-step explanation:
Triangles have 180 degrees
using the vertical angle theory we know that 80 and 60 are angles
We can subtract them from 180 to get 40 left
this minus 51 is -11
x is -11
helpppppp. (the other one cut out is multiplication property of equality)
Answer:
The second step is Distributive Property and the third is Subtraction Property of Equality
Step-by-step explanation:
The 1/2 is being distributed in the second step making the 8x to 4x and the 6 to 3.
The third step involves the subtraction of "x" from the right hand side and the left hand side.
Rounding Decimals 5.5252; ones
Answer:
6
Step-by-step explanation:
Identify the ones place and check the number to the right.
5.5252
Since we round up if the number to the right is greater than or equal to 5, and the number is a 5, we round up.
Therefore,
5.5252 ≈ 6
Hope this helps.
Form a polynomial whose zeros and degree are given.
Zeros: 6, multiplicity 1; 3, multiplicity 2; degree 3
Type a polynomial with integer coefficients and a leading coefficient of 1 in the box below.
f(x) = (Simplify your answer.)
Answer: (x-6)(x-3)² all multiplied by 3.
Step-by-step explanation: first you will simplify (x-3)² then multiply it by (x-6). Then lastly you will multiply tha entire answer by 3 and simplify.
Hope this helped!!! :))
An online streaming service costs $25 to join. Each gigabyte used costs $2.50. Let g represent the number of gigabytes. Would this situation represent a function?
True False
Answer: 10
Step-by-step explanation:
25 ÷ 2.5 = 10
10 gigabytes
The bottom one Staples has 9 cases of crayons with 1452 boxes in each case
Office Depot has 6 cases of crayons with 504 boxes in each cate
How many total boxes of crayons do both stores hove?
Answer:
d. 16,092
Step-by-step explanation:
Staples: 1452 x 9 = 13,068
Office Depot: 504 x 6 = 3,024
13,068 + 3,024 = 16,092
Samantha claims that 4x + 2 is equivalent to the expression x + 17 + 3x − 15. Check whether Samantha’s equivalent expression is correct using x = 2. Samantha is incorrect because when using x = 2, the resulting values in both expressions are different. Samantha is incorrect because the expressions cannot be checked using x = 2. Samantha is correct because when using x = 2, the resulting values in both expressions are equal.
Answer:
The correct answer is c
Answer:
Answer is c
Step-by-step explanation:
Your welcome
Which of these tables represents a function?
given f(x)=4-3x, what is the value of f(5)?
Answer:
-11
Step-by-step explanation:
Simplify the expression (combine like terms):
6x + 12y + 5 + 2y + 8
Answer:
[tex]6x + 14y + 13[/tex]
Step-by-step explanation:
[tex]6x + 12y + 5 + 2y + 8 \\(6x ) + (12y + 2y) + (5 + 8) \\ 6x + 14y + 13[/tex]
In an inequality, 0.5 is the greater number. What will the position of the other number be in relation to 0.5 on the vertical number line? What is the answer?! Help plz.
Answer:
Closer to 0 than 0.5, or under zero
Step-by-step explanation:
On a vertical number line, anything above zero is positive, and anything under zero is negative. If 0.5 is the greater number, then it has to be closer to zero, or under it.
Answer:
The other number would be located below 0.5 on the vertical number line.
Step-by-step explanation:
10.6n - 45.92 = 18.8 solve for n
Answer:
Step-by-step explanation:
10.6n - 45.92 = 18.8 Add 45.92 to both sides
10.6n = 18.8 + 45.92 Combine like terms on the right
10.6n = 64.72 Divide by 10.6
n = 64.72 / 10.6
n = 6.11
Find the slope of the line -7,-4 and -7,-2
Answer:
slope - x=-7
Step-by-step explanation:
Who can't wait for Cyberpunk to come out
Answer:
i got it, hella good game but reallllyyy buggy
Step-by-step explanation:
feel free to ask questions abt it, I know, lore, controls, gameplay, etc.
What is 3x+1-x=5 answer quick
Answer:
x=2
Step-by-step explanation:
3x+1-x=5
add like terms
2x+1=5
subtract 1 from both sides
2x=4
divide by 2 from both sides
x=2
Answer:
3x+1-x=5
2x+1=5
2x=4
x=2 please give me brainlist
Step-by-step explanation:
y=7-x in standard form please help
Answer:
x + y = 7
Step-by-step explanation:
Can someone please help me ?
Answer:
SAS (unless angle lines are drawn on by you, then it would be not enough info)
Step-by-step explanation:
Two sides both have the tick line to show that they are the same length.
They both share the same side
And if those angle lines were drawn by the question, then it would show that those angles are the same.
Add them all together to get SAS as you have (Side, Angle, Side)
2.3 × 2² ÷ 2- 8·9 help please
Answer:
67.4
Step-by-step explanation:
A large basket of fruit contains 3 oranges, 2 apples and 5 bananas. If a piece of fruit is chosen
at random, what is the probability of getting an orange or a banana?
Answer:
8/10
Step-by-step explanation:
3+2+5=10 options in total. 3 oranges and 5 bananas means 3+5=8 --> 8/10 chance of picking an orange or banana
NEED HELP ASAP WILL GIVE BRAIN
Review the diagram.
On a coordinate plane, a vector labeled 120 meters forms angle 25 degrees with the x-axis. It goes to point mirror 1. Another vector labeled 90 meters goes from point mirror 1 to mirror 2. It forms angle 20 degrees with a horizontal line. Point mirror 2 goes to (0, 0).
A laser beam is aimed 25° from horizontal at a mirror 120 m away. The beam bounces off the mirror and continues for an additional 90 m at 20° above horizontal until it hits a target, mirror 2. What is the distance between the origination point and the target?
approximately 85 m
approximately 122 m
approximately 174 m
approximately 194 m
Answer:
Vectors are usually described in terms of their components in a coordinate system. Even in everyday life we naturally invoke the concept of orthogonal projections in a rectangular coordinate system. For example, if you ask someone for directions to a particular location, you will more likely be told to go 40 km east and 30 km north than 50 km in the direction 37° north of east.
In a rectangular (Cartesian) xy-coordinate system in a plane, a point in a plane is described by a pair of coordinates (x, y). In a similar fashion, a vector
→
A
in a plane is described by a pair of its vector coordinates. The x-coordinate of vector
→
A
is called its x-component and the y-coordinate of vector
→
A
is called its y-component. The vector x-component is a vector denoted by
→
A
x. The vector y-component is a vector denoted by
→
A
y. In the Cartesian system, the x and y vector components of a vector are the orthogonal projections of this vector onto the x– and y-axes, respectively. In this way, following the parallelogram rule for vector addition, each vector on a Cartesian plane can be expressed as the vector sum of its vector components:
Step-by-step explanation:
Answer:
approximately 85 m
Step-by-step explanation:
use the law of cosines
x²=120²+90²-2(120)(90)cos(45)
*120 & 90 are given values
*45 is from 25+20; bcuz of alternate interior angles, the other angle from mirror 1 is 25 degrees, making the total 45 degrees
x=√120²+90²-2(120)(90)cos(45)
x=85, the distance btwn origin point and mirror 2
Can somebody just answer this in simplify form plz!!! Make sure it’s a correct answer :)
(I’m still new to this and idek what “simplify it” means...?
WILL MARK BRAINLIEST
PROMISE!
A player located 18.6 ft from the basket launches a successful jump shot from a height of 10 ft (level with the rim of the basket), at an angle θ = 36º and an initial velocity of v = 25 ft/s. Find the change of distance Δs of the toss if the angle changes by an amount Δθ. Hint: Use the following fact derived from Newton's Laws: An object released at an angle θ with initial velocity v ft/s travels a total distance [tex]s=\frac{1}{32} v^{2} sin(2\theta)[/tex]
Answer:
Step-by-step explanation:
You suck free points
The change of the distance travelled by the ball when the angle of launch
changes can be found by linear approximation.
The change in the distance, Δs, when the angle changes by Δθ in radians is approximately 0.211·Δθ.Reasons:
The distance of the player from the basket = 18.6 ft.
Height from which the jump shot is launched = 10 ft.
Angle of the jump shot = 36°
The initial velocity = 25 ft./s
According to Newton's Law of motion, the distance an object travels when
released at an angle θ, with an initial velocity, v, is given by the following
horizontal range formula equation;
[tex]s = \dfrac{1}{32} \cdot v^2 \cdot sin(2 \cdot \theta)[/tex]
[tex]\dfrac{ds}{d\theta} =\dfrac{d}{d\theta } \left( \dfrac{1}{32} \cdot v^2 \cdot sin(2 \cdot \theta) \right)= \dfrac{v^2 \cdot cos(2 \cdot \theta)}{16}[/tex]
By linear approximation, we have;
[tex]\Delta s = \dfrac{ds}{d\theta} \times \Delta \theta[/tex]
Which gives;
[tex]\Delta s =\dfrac{25^2 \cdot cos(2 \times 36^{\circ})}{16}\times \Delta \theta \approx 12.07 \times \Delta \theta[/tex]
360° = 2·π radians
[tex]12.07 ^{\circ} = \dfrac{2 \cdot \pi}{360} \times 12.07 \approx 0.211 \ radians[/tex]
Δs ≈ 0.211·Δθ
Therefore;
The change in the distance, Δs, when the angle changes by Δθ is 0.211·Δθ.
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Mr. Smith had 262 markers in the art room. He threw away the markers that dried out, and now he has 99 markers. How many markers dried out?
Answer:
163
Step-by-step explanation:
262-99=163
Answer:163
Step-by-step explanation: subtract 262 and 99
Write an equation for the line parallel to the given line that contains C.
y =
Answer:
y=3/7x+46/7
Step-by-step explanation:
Parallel lines have the same slope. This means in the equation y=mx+b, m=3/7 for sure. Then, it gives us the point (1,7). The line has to go through this point so we plug it in: 7=3/7(1)+C. Then, we solve for C using algebra.
7-3/7=C
C=46/7
What is the image of (-4,9) after a dialation by a scale factor of 3 centered at the origin
Answer:
-12,27
Step-by-step explanation: