Answer:quadrupled
Step-by-step explanation:
If the radius of a circle is doubled, the area of the circle will be quadrupled and the circumference will also be doubled. This makes sense because the area of a circle is directly proportional to the square of the radius of the circle (if the radius of a circle is increased x times, its area will be increased to x^2 times the original area), whereas the circumference is proportional to the size of the radius (if the radius of a circle is increased x times, its circumference will increase x times).
Two particles are projected simultaneously towards each other from opposite ends of a straight horizontal tube. One particle travels 97 cm in the 1st 2 seconds, 93 cm in next 2 seconds , 89 cm in another next 2 seconds, etc. The other particle travels 49 cm in the 1st 2 seconds, 47 cm in the next 2 seconds , 45 cm in another next 2 seconds, etc. Find how long it takes for the particles to meet and hence, determine the distances travelled by each particle.
This shows that it will take the particle 23 secs to meet.
The distance travelled by each particle is 50cm
If two particles are projected simultaneously towards each other from opposite ends of a straight horizontal tube,
The first particle distances are 97cm, 93cm, 89cm... every 2secs
This form an arithmetic sequence and the nth term is expressed as:
Tn = a + (n - 1)d
a is the first term = 97
d is the common difference = 4
Substitute
Tn = 97+(n - 1)(4)
Tn = 97 + 4n -4
Tn = 4n + 93
Similarly for the distances 49 cm, 47 cm, 45cm .....
This also forms an arithmetic sequence and the nth term is expressed as:
Tn = a + (n - 1)d
a is the first term = 49
d is the common difference = 2
Substitute
Tn = 49+(n - 1)(2)
Tn = 49 + 2n -2
Tn = 2n + 47
For the particles to meet, this means that 4n + 93 = 2n + 47
4n - 2n = 47 - 93
2n = -46
n = -23
This shows that it will take the particle 23 secs to meet.
To get the distance travelled by each particle
Tn = 4n + 93
T2 = 4(2) + 93
T2 = 101
For the other sequence;
Tn = 2n + 47
T2 = 2(2) + 47
T2 = 51
Taking the difference;
D = 101 - 51 = 50cm
Hence the distance travelled by each particle is 50cm
Learn more here: https://brainly.com/question/13989292
Which of the following are perfect squares? 2, 4, 6, 16, 20,25, x², x³, x¹⁵, x²⁰, x²⁵
Answer:
4, 16, 25, [tex]x^{2}[/tex], [tex]x^{20}\\[/tex].
Step-by-step explanation:
Answer:
16, 4, 25, x², x ²⁰
. . . . . . . .
One student solved the inequality -4 > x/-7 and got 28 < x. Another student solved the inequality and got x > 28. Are they both correct? Explain.
Answer: solutions are the same, just written differently, inequality sign is reversed when multiplying. Yes, both students are correct. When multiplying by –7, the inequality symbol+ is reversed. The answers are the same, just written differently.
Step-by-step explanation: Happy to Help. Brainliest Please
The function g(x) = 8|x – 15| - 30 is a transformation of the parent function p(x) = x. Which of the following correctly describes the transformation of function p that generates function g?
A p is translated 30 units down, then has a vertical shrink by a factor of 8, and then is translated 15 units right.
B. p has a vertical shrink by a factor of 8, then is translated 15 units down, and then is translated 30 units left
c. p is translated 15 units left, then has a vertical stretch by a factor of 8, and then is translated 30 units up.
D. p is translated 15 units right, then has a vertical stretch by a factor of 8, and then is translated 30 units down.
Using translation concepts, it is found that the correct option, which represents the transformation made to function [tex]g(x) = 8|x - 15| - 30[/tex], is given by:
D. p is translated 15 units right, then has a vertical stretch by a factor of 8, and then is translated 30 units down.
The parent function is:
[tex]p(x) = |x|[/tex]
The first transformation was [tex]x \rightarrow x - 15[/tex], which means that it was shifted 15 units to the right.
Then, the function was multiplied by 8, which means that it was stretched vertically by a factor of 8.
Finally, 30 was subtracted from the function, which means that it was shifted down 30 units.
Hence, the correct option is given by:
D. p is translated 15 units right, then has a vertical stretch by a factor of 8, and then is translated 30 units down.
A similar problem is given at https://brainly.com/question/18405655
A boat sails directly toward a 250-m skyscraper that stands on the
edge of a harbor. The angular size of the building is the angle
formed by lines from the top and bottom of the building to the
observer (see figure). Complete parts (a) and (b) below.
a) The value of [tex]\theta[/tex] as a function of "x" is [tex]\theta = tan^{-1}\frac{250}{x}[/tex]
b) The rate of change of the angle with respect to x is -0.000308rad/m
Find the complete question and diagram attached
Form the right-angled triangle shown:
Adjacent side = x
Opposite side = 250m
angle of elevation = [tex]\theta[/tex]
Using the SOH CAH TOA identity
[tex]tan\theta = \frac{opposite}{hypotenuse} \\tan \theta = \frac{250}{x} \\\theta = tan^{-1}\frac{250}{x}[/tex]
Hence the value of [tex]\theta[/tex] as a function of "x" is [tex]\theta = tan^{-1}\frac{250}{x}[/tex]
b) If x = 450m
[tex]\theta = tan^{-1}\frac{250}{x}\\tan \theta = \frac{250}{x}\\[/tex]
Differentiate both sides with respect to "x"
[tex]sec^2 \theta \frac{d\theta}{dx} = \frac{-250}{x^2} \\ \frac{d\theta}{dx} = \frac{1}{sec^2\theta} \times \frac{-250}{x^2}[/tex]
Substitute x = 450m and [tex]\theta = 60^0[/tex] into the resulting expression to have:
[tex]\frac{d\theta}{dx} = \frac{1}{sec^260^0} \times \frac{-250}{450^2}\\\frac{d\theta}{dx} = (cos60)^2\times \frac{-250}{202,500}\\\frac{d\theta}{dx} = 0.5^2\times \frac{-250}{202,500}\\\frac{d\theta}{dx} =-0.000308[/tex]
Hence the rate of change of the angle with respect to x is -0.000308rad/m
Learn more here: https://brainly.com/question/15580615
12. Determine the slope of the line having the equation 2x + y = 12
a. 2
b. -2
c. ½
d. -½
Answer:
b. -2
Step-by-step explanation:
Note the slope-intercept form: y = mx + b
Note that:
y = (x , y)
m = slope
x = (x , y)
b = y-intercept
First, isolate the variable, y. Note the equal sign, what you do to one side, you do to the other. Subtract 2x from both sides of the equation:
2x (-2x) + y = (-2x) + 12
y = -2x + 12
Remember, m is the variable for the term that stands for the slope (directly next to the x variable). In this case, your answer will be -2
b. -2 is your answer.
~
Answer:
b. -2
Step-by-step explanation:
2x+y=12
add -2x to both sides
y = -2x + 12
this is in slope intercept form y = mx + b
m meaning the slope
in this case the slope is -2
the answer will be b. -2
The area of a rectangle is x^2-4/2x in.2, and its length is (x + 2)2/2 in. Find the width.
Step-by-step explanation:
the area (length × width) is
A = (x² - 4)/2x in² = (x + 2)(x - 2)/2x
length = (x + 2)²/2 = (x + 2)(x + 2)/2
width = A/length = 2(x+2)(x-2) / 2x(x+2)(x+2) =
= (x-2)/x(x+2) = (x-2)/(x²+2x)
.Factor 20x2 + 68x - 160
Answer:
4(5x-8) (x+5)
Step-by-step explanation:
4(5x^2+17x-40)
4(5x-8) (x+5)
-14 + 6x = 1 - 3x what is x
Answer:
X = 5/3
Step-by-step explanation:
-14 + 6x = 1 - 3x
-14 + 9x = 1
9x = 15
x = 5/3
Hope this helps! Pls give brainliest!
Answer:
[tex]x = 1\frac{2}{3} [/tex]Step-by-step explanation:
To find:Value of x
Equation:-14 + 6x = 1 - 3x
=> 6x + 3x = 1 + 14
=> 9x = 15
[tex] = > x = \frac{15}{9} [/tex]
[tex] = > x = \frac{5}{3} [/tex]
[tex] = > x = 1 \frac{2}{3} (ans)[/tex]
Erin ran 5 km in 25 minutes. What is her speed in km per minute? (Answer as a decimal)
Answer:
what what what what what what what what
Jimin wants to know whether if there is a difference in proportion of people who like mint chocolate chip-flavored ice cream between Americans and Koreans. She takes a random sample of 46 Americans and find that 30 of them like the flavor, and then she takes a random sample of 53 Koreans and find that 24 of them like the flavor. For a 95% confidence interval of the true difference in proportion of people who like this ice cream flavor, what is the margin of error (MOE)
Answer:
5hj
m5Step-by-step explanation:
Carson has a smart phone data plan that costs $35 per month that includes 10 GB of data, but will charge an extra $15 per GB over the included amount. How much would Carson have to pay in a month where he used 3 GB over the limit? How much would Carson have to pay in a month where he used went over by x GB?
Answer:
3 GB over: $80 x GB over: $35+$15x
Step-by-step explanation:
3 GB over is 3 times 15 plus 35, which equals 80, x GB over is x times 15 plus 35. Boom, answer.
Your welcome!
Answer:
$80
Step-by-step explanation:
Helppppppppppppppppppppppppppppppppppp
Answer:
The answer would be 7 I hope this helps! : )
Answer:
it's 2
Step-by-step explanation:
if we solve 3×2×1/3
then we will get 2 .
"The quotient of five less than a number and 6, is -4."
Answer:
The number is 20
Step-by-step explanation:
x represents the missing number
The equation would be:
[tex]\frac{x-5}{6} =-4[/tex]
Then isolate the variable and solve,
First multiply both sides by 6...
[tex]x-5=-25[/tex]
Add 5 to both sides.
x=20
(0,3) and (2,4) are on the line
(I NEED THE ANSWER FAST PLS) Explain how to use place value and the distributive property to find the product of 828 and 9. (also, please do not give the edge sample answer)
Answer:
7452
Step-by-step explanation:
Answer:
Sample Response: First, write 828 as a sum of 800 + 20 + 8. Next, multiply each number by 9. Add the products to get 7,452.
Step-by-step explanation: edge 2021
_+_+_+_+_+_=300,684 how could I do this with 6 digits to equal 300,684 .?
Answer:
Number 300,684 spell , write in words: three hundred thousand, six hundred and eighty-four . Ordinal number 300684th is said and write: three hundred thousand, six hundred and eighty-fourth. Color #300684. The meaning of number 300684 in Maths: Is Prime? Factorization and dividers. The square root and cube root of 300684. The meaning in computer science, numerology, codes and images, writing and naming in other languages, other interesting facts.
hop it helps:) :(Please answer this question
Answer:
See explanation below:
see attached file below
Helppp I’m in class and need answers
Answer:
Need answers for what? I would LOVE to help you hun but I cant help because there is nothing to answer.
Step-by-step explanation:
Which word is a synonym of verify?
consent or confirm
Answer:
confirm is the correct answer
Plz mark as Brainliest
please help me with this sum
Answer:
391 × 5 = 1955
621 × 3 = 1863
481 × 7 = 3367
531 × 6 = 3186
981 × 2 = 1962
761 × 9 = 6849
581 × 8 = 4648
431 × 3 = 1293
271 × 4 = 1084
821 × 4 = 3284
TIME REMAININO
58:40
Which graph could represent a constant balance in a bank account over time?
Daily Balance
Daily Balance
Daily Balance
de
10
$
1378
Time (day)
1 2 3 4 5
Time day)
O
Daily Balance
35
Save and Exit
NE
Suband
Mark this and return
How to solve x/m = n/p. Solve for x. Please include steps for solving. Thank you
Answer:
[tex]x=\frac{n}{p}m[/tex]
Step-by-step explanation:
Since we have two variables on the left side (x and p), and they are being divided, we need to do the opposite in order to get it to the other side. Therefore, we multiply both sides of the equation by m.
Doing that, we get
[tex]\frac{x}{m} m=\frac{n}{p}m\\\\\\So,x= \frac{n}{p}m\\[/tex]
What is the distance from (-4, 0) to (2, 5)? Round your answer to the nearest hundredth.
Answer:
7.81
Step-by-step explanation:
Step-by-step explanation:
[tex]distance = \sqrt{(x2 - x1) ^{2} + (y2 - y1) ^{2} } [/tex]
Now, substitute the numbers into the equation,
[tex] \sqrt{(2 + 4) ^{2} +( 5 - 0)^{2} } [/tex]
distance = 7.81
brianlist me??
20000 divided by 2 x 56 x 7898 - 100
First to Answer gets brainliest!!!
NO LINKS PLEASE!!!!
Answer:
0.0226122585576093
what should she do next?
Answer:
(-2) *6 = -12
Step-by-step explanation:
4 + (2-4) *6 , solve the subtraction in parenthesis
4 + (-2)*6, solve the multiplication of (-2) *6
4 - 12, solve the subtraction
-8
Can someone please help me with this problem
Answer:
A is the right one
Step-by-step explanation:
if not I'm sorry I'm here to help
What is the distance between the points (7, 8) and (-8, 0) on a coordinate grid?
Answer:
17 units
Step-by-step explanation:
Answer:
17
Step-by-step explanation:
Two particles are projected simultaneously towards each other from opposite ends of a straight horizontal tube. One particle travels 97 cm in the 1st 2 seconds, 93 cm in next 2 seconds , 89 cm in another next 2 seconds, etc. The other particle travels 49 cm in the 1st 2 seconds, 47 cm in the next 2 seconds , 45 cm in another next 2 seconds, etc. Find how long it takes for the particles to meet and hence, determine the distances travelled by each particle.
This shows that it will take the particle 23 secs to meet.
The distance travelled by each particle is 50cm
If two particles are projected simultaneously towards each other from opposite ends of a straight horizontal tube,
The first particle distances are 97cm, 93cm, 89cm... every 2secs
This form an arithmetic sequence and the nth term is expressed as:
Tn = a + (n - 1)d
a is the first term = 97
d is the common difference = 4
Substitute
Tn = 97+(n - 1)(4)
Tn = 97 + 4n -4
Tn = 4n + 93
Similarly for the distances 49 cm, 47 cm, 45cm .....
This also forms an arithmetic sequence and the nth term is expressed as:
Tn = a + (n - 1)d
a is the first term = 49
d is the common difference = 2
Substitute
Tn = 49+(n - 1)(2)
Tn = 49 + 2n -2
Tn = 2n + 47
For the particles to meet, this means that 4n + 93 = 2n + 47
4n - 2n = 47 - 93
2n = -46
n = -23
This shows that it will take the particle 23 secs to meet.
To get the distance travelled by each particle
Tn = 4n + 93
T2 = 4(2) + 93
T2 = 101
For the other sequence;
Tn = 2n + 47
T2 = 2(2) + 47
T2 = 51
Taking the difference;
D = 101 - 51 = 50cm
Hence the distance travelled by each particle is 50cm
Learn more here: https://brainly.com/question/13989292
Pls help and answer the question in the photo
Answer:
Cam
Step-by-step explanation:
Cam first multiplied both sides by 3 which removed the fraction on the left. They then correctly added 5 to both sides to get x on its own.
Hope this helps!