[tex]\large\underline{\sf{Solution-}}[/tex]
We need to solve,
[tex]\dfrac{\sqrt{112}-\sqrt{80}}{\sqrt{20}-\sqrt{28}}[/tex]
We can write the above mentioned expression as,
[tex]\sf\longmapsto\dfrac{\sqrt{2\times2\times2\times2\times7}-\sqrt{2\times2\times2\times5}}{\sqrt{2\times2\times5}-\sqrt{2\times2\times7}}[/tex]
So,
[tex]\sf\longmapsto\dfrac{\sqrt{4\times4\times7}-\sqrt{4\times4\times5}}{\sqrt{2^2\times5}-\sqrt{2^2\times7}}[/tex]
So,
[tex]\sf\longmapsto\dfrac{\sqrt{4^2\times7}-\sqrt{4^2\times5}}{\sqrt{2^2\times5}-\sqrt{2^2\times7}}[/tex]
Hence,
[tex]\sf\longmapsto\dfrac{4\sqrt{7}-4\sqrt{5}}{2\sqrt{5}-2\sqrt{7}}[/tex]
Taking common in respective terms,
[tex]\sf\longmapsto\dfrac{4(\sqrt{7}-\sqrt{5})}{2(\sqrt{5}-\sqrt{7})}[/tex]
On cancelling 4 with 2,
[tex]\sf\longmapsto\dfrac{4\!\!\!/^{\:2}(\sqrt{7}-\sqrt{5})}{2\!\!\!/(\sqrt{5}-\sqrt{7})}[/tex]
[tex]\sf\longmapsto\dfrac{2(\sqrt{7}-\sqrt{5})}{(\sqrt{5}-\sqrt{7})}[/tex]
Taking (-) common,
[tex]\sf\longmapsto\dfrac{-2(\sqrt{5}-\sqrt{7})}{(\sqrt{5}-\sqrt{7})}[/tex]
So, (√5 - √7) gets cut,
Hence,
[tex]\longmapsto\bf\dfrac{\sqrt{112}-\sqrt{80}}{\sqrt{20}-\sqrt{28}}=-2[/tex]
The problem and answer choices are provided. It would be appreciated if I could get an answer as soon as possible.:D
Answer:
4
Step-by-step explanation:
2 + 2 = 4
Look at the arithmetic pattern shown here.
Select the Hint button to view a hint.
Using the variable n for the term, describe the sequence.
Answer:
[tex]a_{n}[/tex] = 10n
Step-by-step explanation:
The nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 10 and d = a₂ - a₁ = 20 - 10 = 10 , then
[tex]a_{n}[/tex] = 10 + 10(n - 1) = 10 + 10n - 10 = 10n
The sequence can be seen to be an arithmetic sequence and the common difference of the sequence is 10.
What is an arithmetic sequence?Arithmetic sequences are an essential concept in mathematics and have applications in various fields, including algebra, physics, computer science, and finance. They are widely used to model patterns and relationships in real-world situations.
Looking at the sequence we can see that the common difference d can be obtained as;
d = S2 - S1
= 20 - 10
= 10
d = S3 - S2
= 30 - 20
= 10
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4. The sum of three consecutive oven integers is 84. What are the three numbers?
Answer:
The required numbers are 26 , 28 and 30
Step-by-step explanation:
Given that the sum of the three even integers is 84.
Multiply (8 + 3i)(3 + 5i).
39 + 49i
9 + 49i
24 + 15i2
24 + 49i + 15i2
Answer:
It's the last option "24 + 49i + 15i^2"
Step-by-step explanation:
To solve you must do FOIL, (First, Outer, Inner, Last). To do this, you must do:
8 × 3 = 24 , 8 × 5i = 40i , 3i × 3 = 9i , and
3i × 5i = 15i^2 .
Don't forget to combine like terms.
Altogether: 24 + 49i + 15i^2 .
Picture does better job at explaining FOIL⤴⤴⤴
Hope this helps :)
Answer: 9+49i
Step-by-step explanation:
answer the question below
Answer:
-6/7
Step-by-step explanation:
maf
Perform the operation. Enter your answer in scientific notation.
9 x 10^*8-5.3 x 10^*8=
Answer:
Not a possible math equation, sorry.
describe a pattern or sequence 5, 3, 1, -1...
Answer:
Step-by-step explanation:
The first member of the pattern is 5
Thereafter, you subtract 2 from the member on the left
5 - 2 = 3
3 - 2 = 1
1 - 2 = - 1
the fastest recorded Hawaiian lava flow moved at an average speed of 6 miles per hour. The function y=6x describes the distance y the lava moved on average in x hours. graph the function. use the graph to estimate how many miles the lava moved after 4.5 hours
Answer:
The answer is 27 6 times 4.5 is 27 Welcome!!!
Step-by-step explanation:
Brainiest ????
Can someone PLEASE tell me the answer to this
Answer:
m /CBA = 82 degree
Step-by-step explanation:
if you want explanation tell me
Use the diagram to find the length
Answer:
25 is the answer.....
25 is the answer
8/3×(−2 1/2) find the product
Step-by-step explanation:
8/3 × -5/2 = -20/3
that is the answer
Sally has a collection of 600 skirts. Of these shirts, 25% are blue, 30% are pink, and the rest are black. How many skirt's in Sally’s collection are black?
Answer:
270
Step-by-step explanation:
because 25% blue 30% pink
so 25+30=55
100-55=45
600×45%=270 shirts
If a toy rocket is launched vertically upward from ground level with an initial velocity of 120 feet per second, then its height h after t seconds is given by the equation h(t) = -16t2 + 120t. How long will it take the rocket to return to the ground?
A) 7.5 seconds
B) 16 seconds
C) 3.75 seconds
D) 120 seconds
Answer:
A) 7.5 seconds
Step-by-step explanation:
Height of the ground is zero
-16t^2 + 120t = 0
Divide both sides by 16
-t^2 + 7.5t = 0
Factor out t
t(-t + 7.5) = 0
From the zero product rule
t = {0, 7.5}
0 would be time of launch
7.5 is time back to the ground
What can be described as “shooting stars” that streak across the sky in a brief flash of light?(1 point)
comets
meteors
meteoroids
meteorites
Answer:
the answers for the quick check:
Step-by-step explanation:
1. d. spiral
2. b stars
3. d. meteors
4. d. as it gets closer to the sun
“Shooting Stars” that streak across the sky in a brief flash of light is Option b) Meteors.
"Shooting stars" are captivating phenomena seen in the night sky. They are commonly mistaken for stars, but they are not stars at all.
Shooting stars, or meteors, are not celestial bodies themselves, but rather the luminous trails created when small space rocks, known as meteoroids, enter Earth's atmosphere at high speeds.
These meteoroids are remnants from comets or asteroids.
When a meteoroid collides with Earth's atmosphere, friction causes it to heat up rapidly.
This intense heat causes the meteoroid to vaporize in a brilliant flash of light, leaving behind a streak across the sky.
This streak is what we commonly refer to as a shooting star or meteor.
Comets, denoted by option (a), are icy bodies that originate from the outer regions of the solar system.
They can produce meteoroids, which in turn create meteors when they enter Earth's atmosphere. However, comets themselves are not what we see as shooting stars.
Meteoroids, as mentioned in option (c), are the actual rocky or metallic fragments that create meteors.
When a meteoroid survives its fiery passage through the atmosphere and lands on Earth's surface, it is referred to as a meteorite, as stated in option (d).
In summary, shooting stars, or meteors, are the dazzling result of meteoroids burning up as they speed through Earth's atmosphere. This captivating display is a reminder of the continuous cosmic activity surrounding our planet, turning the night sky into a canvas of transient and awe-inspiring light shows.
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NOTE: This not a Question of Mathematics, this is a Question from Physics
Complete Question
Choose the correct answer from the given options:
What can be described as “shooting stars” that streak across the sky in a brief flash of light?
a) Comets
b) Meteors
c) Meteoroids
d) Meteorites
find the value of x and y. SHOW WORK
check which of the following numbers are in proportion,10,20,30,40
t2-t1=20-10=10 t3-t2=30-20=10. t4-t3=40-30=10 therefore it is in proportion
Write an equation in slope-intercept form for the line with slope 4/3 and y-intercept -3. Then graph the line.
Answer:
y = 4/3x -3
Step-by-step explanation:
PLEASE HELP THANK YOU AND HAVE A GOOD DAY!
Answer:c
Step-by-step explanation:c because u gotta look closwely
c
George found a job posting on an Internet website. The job pays a yearly salary of $60K. What is the monthly salary based on this annual salary?
plzzzzzzzzzzzzzzzzz help me
Answer:
5k a month
Step-by-step explanation:
Write a complete two-column proof for the following information. Hint: Use the Angle Addition Theorem and the fact that a line is made up of two opposite rays.
Given: m∠1 = 62° and lines t and l intersect
Prove: m∠4 = 62°
Answer:
Hint: Use the Angle Addition Theorem and the fact that a line is made up of two opposite rays. Given: m∠1 = 62° and lines t and l intersect
Step-by-step explanation:
Step-by-step explanation:
Given: m∠1 = 62° and lines t and l intersect
Prove: m∠4 = 62°
Proof:
Statement Reason
m∠1 = 62° Given
m∠1 , m∠2 are supplementary t is a straight line hence linear pair.
m∠4 , m∠2 are supplementary r is a straight line hence linear pair.
Angle 2=180-62 = 118 Definition of supplementary angles
Angle 4 = 180-118 =62 -do-
Angle 1 = Angle 4 Equality property
Hence proved
Olivia started knitting a jumper
4 hours and 43 minutes before 19:13
What time did she start knitting the jumper?
Give your answer in 24 hour time.
Answer: 14:30
Step-by-step explanation:
19:13 - 4.43 looks easy, but time expressed in 24-hour format is a base 60 calculation in the decimal portion. It only contains values between 0 and 59.
I broke it it down to simplify:
1) Take 13 minutes off the 19:13 to make it 19:00.
2) Then take the same 13 minutes off the 4.43, which would make it 4.30 (4 1/2 hours)
3) Now take off the 4.30 from the 19:00. The 4 portion of 4.3 can be removed: 19:00 - 4:00 = 15:00. Then remove the 0:30 portion (1/2 hour), which would leave 14:30.
14:30 plus 4:43 = 18:73, but the 0:73 must convert to 1:13 to account for the 60 minutes/hour format
Olivia started knitting a jumper at 13:30.
What is 24-hour time format?A 24-hour time format is similar regular AM/PM time, except that you keep counting up after you get past 12 PM (noon). So 1 PM in 24-hour format is 13:00, 2 PM is 14:00, and so on. All you need to do is add 12 to any time in the PM to get 24-hour format time.
How to calculate the time?The given time is 19:13 and Olivia started knitting a jumper
4 hours and 43 minutes before the given time.
Then he starts at 13:30 started knitting a jumper.
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Which of the following is a correct conversation factor?
Answer:
B
Step-by-step explanation:
1000mm=1m
Someone help me I will mark you as brain
Answer:did u get it right
Step-by-step explanation:
Please help me! The answer has to be in this form (____,___)
IF U CAN PLEASE SHOW ME WHERE THE LINE MEET ON THE GRAPH
Answer: (2, 4)
Step-by-step explanation:
This is in y=mx+b form
b is the y intercept so the point will be (0, b) for both equations
the m represents the slope to find the x intercept substitute y as 0
Plotting the graph the lines would meet at points (2, 4).
Answer:
Step-by-step explanation:
Can someone please help me !!!!
Answer:
Step-by-step explanation:
i think its the third one..
Helpppppppp please it’s due today
Answer:
Option B, would be the correct option as she sets it in the attic window. I hope this helps you! :)
√80+√20 find it ......
Answer:
Approximately 13.41
Step-by-step explanation:
First do square root of each, which is finding what number multiplies by its self to get the number.
For example: The square root of 80 is approximately 8.94, and the square root of 20 is approximately 4.47.
So: 8.94 + 4.47 = 13.41 (Add normally, but remember to put the decimal in the right place).
Hope this helped :)
[tex]\frac{2}{5}[/tex](6-5p)
Answer: -2x + 12/5
Step-by-step explanation:
In February, 1985, the cost of a gallon of milk was $2.26. In November of 2007, how much would that gallon of milk cost?
Answer:
is this the full question?
can someone help please
Answer:
x=33°
Step-by-step explanation:
(x-1)+x=x+32 (ext angle of a triangle)
x-1+x=x+32
x+x-x=32+1
x=33