[tex] d \propto v^2[/tex]
$\implies d=kv^2$
substitute the given values, $5=k(10)^2\implies k=\frac1{20}$
now, $d=\frac{1}{20}\times( 70)^2=\frac{70\times70}{20}=245$
A big blunder from my side, now fixed!
Allison is rolling her hula hoop on the playground. The radius of her hula hoop is 35 \text{ cm}35 cm35, start text, space, c, m, end text. What is the distance the hula hoop rolls in 444 full rotations?
Answer: 880 cm
Step-by-step explanation:
Given: Radius of the hula hoop = 35 cm
Hula hoop is circular in shape
Then, Circumference = [tex]2\pi r[/tex] , where r = radius
Now , Circumference of hula hoop = [tex]2\times \dfrac{22}{7}\times35=220\ cm[/tex]
Now , the distance the hula hoop rolls in 4 full rotations = 4 × (Circumference of hula hoop)
[tex]= 4 \times 220=880\ cm[/tex]
Hence, the required distance = 880 cm
Answer:
880
Step-by-step explanation:
Please help!! Thank you in advance! Will mark Brainliest!
Answer:
F , D, E
Step-by-step explanation:
The smallest angle is opposite the smallest side
The largest angle is opposite the largest side
DE is smallest so F is smallest
Then EF so D
DF is largest so E is the largest angle
Please solve, will give BRAINLIST!!
Answer:
x = 19 1/3
Step-by-step explanation:
6/14 = 7/(x-3)
Using cross products
6 * (x-3) = 7*14
6x -18 = 98
Add 18 to each side
6x-18+18 =98+18
6x = 116
Divide each side by 6
6x/6 = 116/6
x =58/3
x = 19 1/3
Answer= 58/3
Step by Step
Step 1: Cross-multiply.
6*(x−3)=(7)*(14)
6x−18=98
Step 2: Add 18 to both sides.
6x−18+18=98+18
6x=116
Step 3: Divide both sides by 6.
6x /6 = 116 /6
x= 58 /3
Help please!!!! Thank you
Answer:
E) 15pi/2
Step-by-step explanation:
The total circle area is pi*r^2. r = 6. so the total area is 6^2pi, or 36pi.
However, we are dealing with 75/360 of a circle, or 5/24 of a circle. 5/24 * 36pi = 15pi/2.
state the vertical distance and horizontal distance of the two pairs of points given.
Answer:
the horizontal distance is the x-intercept, and the vertical distance is the y-intercept
1) x-int=1, y-int=1
2) x-int=6, y-int=5
HELP ME PLEASE ASAP! Zoe is making a quilt. The ratio of red squares to green squares is 2 to 3. She uses a total of 55 squares. How many green squares does she use?
Answer: 33
First you divide 55 by 5 to get the total number of squares in one part, which equals 11. Then you multiply by 3 since there are 3 parts of green squares to get your answer, 33.
i need help please i give 5 stars ;(
Answer:
D. [tex]\sqrt{\frac{2*2*2*2*3}{5*5*7} }[/tex]
Step-by-step explanation:
48 divided by 2 is 24. Insert the 2.
24 divided by 2 is 12. Insert the 2.
12 divided by 2 is 6. Insert the 2.
6 divided by 2 is 3. Insert the 2 and 3:
[tex]48=2*2*2*2*3[/tex]
175 divided by 5 is 35. Insert the 5.
35 divided by 5 is 7. Insert the 5 and 7:
[tex]175=5*5*7[/tex]
:Done
If you invest $600 at 5% interest compounded continuously, how much would you make after 6 years?
Answer:
809.915$
Step-by-step explanation:
Amount of money = Principal x e^(rate x year)
= 600 x e^(0.05 x 6)
= 809.915$
Answer:
$809.92
Step-by-step explanation:
(see attached for reference)
Recall that the formula for compound interest (compounded continuously) is
A = P e^(rt)
where,
A = final amount (we are asked to find this)
P = principal = given as $600
r = interest rate = 5% = 0.05
t = time = 6 years
e = 2.71828 (mathematical constant)
Substituting the known values into the equation:
A = P e^(rt)
= 600 e^(0.05 x 6)
= 600 (2.71828)^(0.30)
= $809.92
Make the biggest possible number using the digits below only once 4 , 5 , 5 answer
Answer:
554
Step-by-step explanation:
The largest number (5) should go in the hundreds place, the second-largest number (also 5) should go in the tens place and the smallest number (4) should go in the units place so the answer is 554.
A pair of opposite vertices of a square is (1, 2) and (3,4). Find the coordinates of the remaining
vertices of the square.
Answer:
(3, 2) and (1, 4)
Step-by-step explanation:
Plot the two points on a graph.
The other two points are (3, 2) and (1, 4).
To do this with algebra, it takes a few steps.
The diagonals of a square are perpendicular and bisect each other. You are given opposite vertices, so first, find the midpoint of that diagonal.
((1 + 3)/2, (2 + 4)/2) = (2, 3)
The midpoint of the diagonal is (2, 3).
This diagonal has slope 1 and y-intercept 1, so its equation is
y = x + 1
The perpendicular bisector has equation
y = -x + 5
The two vertices we are looking for, lie in a circle whose center is the midpoint of the diagonals, (2, 3), and whose radius is half of the diagonal.
Use Pythagoras to find the diagonal's length.
2^2 + 2^2 = c^2
c^2 = 8
c = sqrt(8) = 2sqrt(2)
Half of the diagonal is sqrt(2). This is the radius if the circle.
The equation of the circle is
(x - 2)^2 + (y - 3)^2 = (sqrt(2))^2
(x - 2)^2 + (y - 3)^2 = 2
The points of intersection of this circle and the second diagonal are the two vertices you are looking for.
System of equations:
(x - 2)^2 + (y - 3)^2 = 2
y = -x + 5
Use substitution and substitute y with -x + 5 in the equation of the circle.
(x - 2)^2 + (-x + 5 - 3)^2 = 2
(x - 2)^2 + (-x + 2)^2 - 2 = 0
x^2 - 4x + 4 + x^2 - 4x + 4 - 2= 0
2x^2 - 8x + 6 = 0
x^2 - 4x + 3 = 0
(x - 3)(x - 1) = 0
x - 3 = 0 or x - 1 = 0
x = 3 or x = 1
Now we find corresponding y values.
y = -x + 5
x = 3
y = -3 + 5 = 2
This gives us (3, 2).
y = -x + 5
x = 1
y = -1 + 5 = 4
This gives us (1, 4).
Answer: (1, 4) and (3, 2)
Which of the following statements about fractions is not true? a. Proper fractions have a greater numerator than denominator b. Improper fractions are percentages greater than 100% c. Mixed fractions can be written as improper fractions d. The product of a fraction and its reciprocal is 1
Answer:
c
Step-by-step explanation:
Answer:
A. Proper fractions have a greater numerator than denominator.
Order the expressions from least to greatest.
2^3 - 2^1 , 2^1 + 3^1 , 3^2
Answer:
2¹ + 3¹, 2³ - 2¹, 3²
Step-by-step explanation:
2³ - 2¹ = 8 - 2 = 6
2¹ + 3¹ = 2 + 3 = 5
3² = 9
URGENTT PLEASE ANSWER
Answer:
Step 2
Step-by-step explanation:
9 was added to both sided so the equation would remain equal and the 9 would be cancelled out on the left side.
Consider f(x) = 3x2 + 4 and g(x) = 2x − 3. Which statements about f + g are true? Select all that apply. A. The domain is all real numbers. B. The range is all real numbers. C. It is a linear function. D. It is a quadratic function.
PLEASE HELP
Answer:
B. The range is all real numbers. D. It is a quadratic function.Step-by-step explanation:
Given the functions f(x) = 3x² + 4 and g(x) = 2x − 3, to know that statements that is true about f+g, we will need to add the functions together first.
f(x)+g(x) = 3x² + 4 + 2x - 3
f(x)+g(x) = 3x²+2x +4 - 3
f(x)+g(x) = 3x²+2x + 1
The highest degree of a quadratic function is 2 and since the highest degree of the resulting function is 2, hence the resulting sum of the equations is quadratic.
Also the range of the values is all real numbers because the presence of x² in the function will always return a positive value greater than x.
Hence the correct statements are 'the range is all real numbers and it is a quadratic function'
Answer:
B AND D
Step-by-step explanation:
What is a 27 of the sequence 15, 10,5,...?
A.O
B. -75
c.
1/625
D. -115
Answer:
B. -75
Step-by-step explanation:
you count backwards from 5, 27 times
0,2,4,0,2,3,2,8,6
What is the mean?
What is the median?!
What is the first quartile (Q1)?!
What is the third quartile (Q3)?
What is the minimum?
What is the maximum?
What is the interquartile range of the data?!
Answer:
LOOK BELOW
Step-by-step explanation:
Mean= add all of the numbers together and divide by total amount of
numbers
aka=3
Median= put all the numbers in order and find the number in the middle
aka=2.5
Minimum=0
Maximum=8
This data can only be found using a Box and Whisker Plot....
I can't really explain a box and whisker plot so you have to look that up to understand that.. SRY!!!
------------------------------------
First Quartile=1
Third Quartile=5
Interquartile Range=4
Answer:
Mean= add all of the numbers together and divide by total amount of
numbers
aka=3
Median= put all the numbers in order and find the number in the middle
aka=2.5
Minimum=0
Maximum=8
This data can only be found using a Box and Whisker Plot....
I can't really explain a box and whisker plot so you have to look that up to understand that.. SRY!!!
------------------------------------
First Quartile=1
Third Quartile=5
Interquartile Range=4
Step-by-step explanation:
x - (-20) = 5 _________________
X - (-20) = 5
When you subtract a negative, change it to addition:
X + 20 = 5
Subtract 20 from both sides:
X = -15
Answer:
[tex]\boxed{x=-15}[/tex]
Step-by-step explanation:
[tex]x-(-20)=5[/tex]
[tex]\sf Distribute \ negative \ sign.[/tex]
[tex]x+20=5[/tex]
[tex]\sf Subtract \ 20 \ from \ both \ sides.[/tex]
[tex]x+20-20=5-20[/tex]
[tex]x=-15[/tex]
Starting at the same spot on a circular track that is 80 meters in diameter, Hillary and Eugene run in opposite directions, at 300 meters per minute and 240 meters per minute, respectively. They run for 50 minutes. What distance separates Hillary and Eugene when they finish
Answer:
143.32 m
Step-by-step explanation:
Given the following :
Diameter of circular track = 80m
Hillary's speed = 300m per minute
Eugene's speed = 240m per minute
Run time = 50 minutes
Note: they both run in opposite direction.
Calculate the Circumference(C) of the circle :
C = 2πr or πd
Where r = radius ; d = diameter
Using C = πd
C = πd
C = π * 80
C = 251.327
Eugene's distance covered = (240 * 50) = 12000
Hillary's distance covered = (300 * 50) = 15000
Number turns :
Eugene = 12000/ 251.327 = 47.746561
Hillary = 15000/251.327 = 59.683201
Therefore ;
48 - 47.746561 = 0.253439
60 - 59.683201 = 0.316799
(0.253439+0.316799) = 0.570238
Distance which separates Eugene and Hillary when they finish :
0.570238 * 251.327 = 143.32 m
Enter the coordinates of the point
on the unit circle at the given angle.
60°
Answer:
(1/2, [tex]\frac{\sqrt{3} }{2}[/tex])
Step-by-step explanation:
Don't totally trust me on this...
Using a table of values, determine the solution to the equation below to the nearest fourth of a unit. 2^x=1-3^x
Answer:
Option (1)
Step-by-step explanation:
Given equation is,
[tex]2^x=1-3^x[/tex]
To determine the solution of the equation we will substitute the values of 'x' given in the options,
Option (1)
For x = -0.75
[tex]2^{-0.75}=1-3^{-0.75}[/tex]
0.59 = 1 - 0.44
0.59 = 0.56
Since, values on both the sides are approximately same.
Therefore, x = -0.75 will be the answer.
Option (2)
For x = -1.25
[tex]2^{-1.25}=1-3^{-1.25}[/tex]
0.42 = 1 - 0.25
0.42 = 0.75
Which is not true.
Therefore, x = -1.25 is not the answer.
Option (3)
For x = 0.75
[tex]2^{0.75}=1-3^{0.75}[/tex]
1.68 = 1 - 2.28
1.68 = -1.28
Which is not true.
Therefore, x = 0.75 is not the answer.
Option (4)
For x = 1.25
[tex]2^{1.25}=1-3^{1.25}[/tex]
2.38 = 1 - 3.95
2.38 = -2.95
It's not true.
Therefore, x = 1.25 is not the answer.
Solve logs (8 - 3x) = log20 for x.
A. X = 14
B. X = -13
C.x = -8
D. X= -4
Answer:
x = -4
Step-by-step explanation:
logs (8 - 3x) = log20
Since we are taking the log on each side
log a = log b then a = b
8 -3x = 20
Subtract 8 from each side
8 -3x-8 =20 -8
-3x = 12
Divide by -3
-3x/-3 = 12/-3
x = -4
Answer:
[tex] \boxed{\sf x = -4} [/tex]
Step-by-step explanation:
[tex] \sf Solve \: for \: x \: over \: the \: r eal \: numbers:[/tex]
[tex] \sf \implies log(8 - 3x) = log 20[/tex]
[tex] \sf Cancel \: logarithms \: by \: taking \: exp \: of \: both \: sides:[/tex]
[tex] \sf \implies 8 - 3x = 20[/tex]
[tex] \sf Subtract \: 8 \: from \: both \: sides:[/tex]
[tex] \sf \implies 8 - 3x - 8 = 20 - 8 [/tex]
[tex] \sf \implies - 3x = 12 [/tex]
[tex] \sf Divide \: both \: sides \: by \: - 3:[/tex]
[tex] \sf \implies \frac{-3x}{-3} = \frac{12}{-3} [/tex]
[tex] \sf \implies x = - 4[/tex]
Line m and point P are shown below. Part A: Using a compass and straightedge, construct line n parallel to line m and passing through point P. Leave all construction marks. Part B: Explain the process that you used to construct line n.
Answer:
The steps to construct a a line parallel to another line from a point includes
1) From the given line draw a transversal through the point
2) With the compass, copy the angle formed between the transversal and the given line to the point P
3) Draw a line through the intersection of the arcs of the angle construction to get the parallel line through the point P
Step-by-step explanation:
What number must be added to the expression for it to equal zero? (–6.89 + 14.52) + (–14.52)
Answer:
The number to be added is 6.89
Step-by-step explanation:
Here, we want to know what number must be added to the expression to make it equal to zero.
Let the number be x
Thus;
-6.89 + 14.52 -14.52 + x = 0
-6.89 + x = 0
x = 6.89
Raj correctly determined that ray LH is the bisector of AngleGLI. A line contains points K, L, M. 4 lines extend from point L. One line extends to point F, another to G, another to H, and another to I. Which information could he have used to determine this? AngleGLH Is-congruent-to AngleILM mAngleKLM = 5mAngleILM mAngleGLI = 2mAngleGLH mAngleGLI = mAngleGLH + mAngleHLI
Answer: C.) mAngleGLI = 2mAngleGLH
Step-by-step explanation:
Hope it helps!!!
For ray LH as the bisector of angle GLI, we can determine that the relation ∠GLI = 2∠GLH holds
What is an angle?An angle is formed from the intersection of two lines. Types of angles are acute, obtuse and scalene.
∠GLI is bisected by LH, hence:
∠GLH = ∠HLI (definition of bisection)
∠GLI = ∠GLH + ∠HLI (angle addition)
∠GLI = 2∠GLH
The information that can be used to determine this is ∠GLI = 2∠GLH
Find out more on angle at: https://brainly.com/question/25770607
Write your answer in scientific notation.
(6.4 x 10^3 ) + (5.2 x 10^4 )
Answer:
5.84 x10.^4
Step-by-step explanation:
Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the
10
If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.
Directions: Using the digits 0 to 9, fill in the boxes so that the chart is accurate. Use each digit only once per blue box and once per red box. Logs are base 10. Please help me out with this would really appreciate it, thanks.
Step-by-step explanation:
log 10 = 1. So if log x < 1, then x < 10. And if log x > 1, then x > 10.
The upper left number is the smallest, and can't be smaller than 1. If the exponent is 0, we can put any number in the red box.
The fractions in the upper right and lower left need to be as large as possible. The denominators will be small, and the numerators will be large.
From there, a little trial and error does the rest. The are many possible answers. I've included one.
asap!!
~~~~~~
A line passes through point (–6, –1) and is parallel to the equation y = –2x – 5. What's the equation of the line?
Question 25 options:
y = –2x – 13
y = 12{"version":"1.1","math":"\(\frac{1}{2}\)"}x + 3
y = –12{"version":"1.1","math":"\(\frac{1}{2}\)"}x – 1
y = 2x + 5
click on picture for a, b, c ,or d
Answer:
y=−2x−13.
Step-by-step explanation:
The equation of the line in the slope-intercept form is y=−2x−5.
The slope of the parallel line is the same: m=−2.
So, the equation of the parallel line is y=−2x+a.
To find a, we use the fact that the line should pass through the given point: −1=(−2)⋅(−6)+a.
Thus, a=−13.
Therefore, the equation of the line is y=−2x−13.
PLEASE ANSWER QUICKLY ASAP
READ THE QUESTIONS CAREFULLY
Answer:
I hope it helps.
The solutions in photo ^_^
What is the domain of F(x) = In(x)?
Answer as an inequality: [tex]x > 0[/tex]
Answer in interval notation: [tex](0, \infty)[/tex]
Answer in words: Set of positive real numbers
All three represent the same idea, but in different forms.
======================================================
Explanation:
Any log is the inverse of an exponential equation. Consider a general base b such that f(x) = b^x. The inverse of this is [tex]f^{-1}(x) = \log_b(x)[/tex]
For the exponential b^x, we cannot have b^x = 0. We can get closer to it, but we can't actually get there. The horizontal asymptote is y = 0.
Because of this, [tex]\log_b(x)[/tex] has a vertical asymptote x = 0 (recall that x and y swap, so the asymptotes swap as well). This means we can get closer and closer to x = 0 from the positive side, but never reach x = 0 itself.
The domain of [tex]\log_b(x)[/tex] is x > 0 which in interval notation would be [tex](0, \infty)[/tex]. This is the interval from 0 to infinity, excluding both endpoints.
------------------------
The natural log function Ln(x) is a special type of log function where the base is b = e = 2.718 approximately.
So,
[tex]\log_e(x) = \text{Ln}(x)[/tex]
allowing all of what was discussed in the previous section to apply to this Ln(x) function as well.
------------------------
In short, the domain is the set of positive real numbers. We can't have x be 0 or negative.
What is another way to write 100,203 in other forms
Answer:
You can write in
Step-by-step explanation:
Lakhs
First write 100,203.
Put ones,tens,hundreds,thousands,ten thousands and lakh on top of each number from the extreme left.
This is how you can write 100,203 in another way. You can't write in any other way than this one.
Hope this helps....
Have a nice day!!!!
