Answer:
the radius of the pool is 50.025 feet
Step-by-step explanation:
From the information given:
We can have a schematic view of a diagrammatic illustration in our mind where the distance of the pool to Lincy is (20 + r ) and the distance to the tangent is 49.
So; by using pythagoras theorem, since the radius meets the tangent at a right angle; we have:
[tex]r^2 + 49^2 = ( r + 20 )^2[/tex]
[tex]r^2 +2401 = r^2 + 40r + 400[/tex]
[tex]2401 = 40r + 400[/tex]
[tex]2401- 400 = 40r[/tex]
2001 = 40 r
r = 2001/40
r = 50.025 feet
What is the simplified expression for 5 to the power of negative 3 multiplied by 2 to the power of 2 multiplied by 5 to the power of 6 whole over 2 to the power of 3 multiplied by 5 to the power of 2?
Answer
the third(5/2)
Step-by-step explanation:
[(5^(-3))*(2^2)*(5^6)]/[(2^3)*(5^2)]
=[(5^3)*(2^2)]/[(2^3)*(5^2)]
=[5^(3-2)]*[2^(2-3)]
=5*(1/2)
=5/2 or 2.5
Answer:
5/2
Step-by-step explanation:
Hope it helps!!
Btw it was right on the test!!
is this right? i’ll give brainliest :)
It is.
[tex]x-10 \geq 0\\\\x \geq 10\\\\\\-5 +n< -6\\\\n < 5-6\\\\n< -1[/tex]
Answer:
Correctomundo!
Step-by-step explanation:
For x-10 > 0:
1. Add 10 to both sides. x- 10 + 10 > 0 + 10
x > 10
For -5 + n < -6:
1. Simplify both sides of the inequality. n - 5 < -6
2. Add 5 to both sides. n - 5 + 5 < -6 + 5
n < -1
:)
Suppose that a population begins at a size of 100 and grows continuously at a rate of 200% per year. Give the formula for calculating the size of that population after t years. Question 3 options: A) A = 100 + 2et B) A = 100e2t C) A = 100 + te2 D) A = 100 + e2t
The formula for calculating the size of the population after t years using continuous growth is [tex]A = 100e^{2t}[/tex], making option B the right choice.
Continuous growth in the initial amount P, after time period t, and at the rate of r per time period gives the final amount as: [tex]A = Pe^{rt}[/tex]
In the question, we are asked to suppose that a population begins at a size of 100, and grows continuously at a rate of 200% per year, and are asked for the formula for calculating the size of that population after t years.
The given case can be shown as a continuous growth, with:
Initial population, P = 100,
Rate of growth, r = 200% = 2, and,
The time period, t years.
Thus, the formula for calculating the size of that population after t years can be shown using the formula: [tex]A = Pe^{rt}[/tex], as:
[tex]A = 100e^{2t}[/tex].
Hence, the formula for calculating the size of the population after t years using continuous growth is [tex]A = 100e^{2t}[/tex], making option B the right choice.
Learn more about continuous growth at
https://brainly.com/question/20115298
#SPJ1
The outside of this set of four cubic blocks with no space between blocks is painted. What is the number of painted square faces?
Answer:
18
Step-by-step explanation:
There would be four faces on the top, left, bottom, and right. That equals 16. (4x4)
There would also 1 on each end, so you have to add 2. That equal 18.
This is assuming you paint the faces on the bottom. If you didn’t, the answer would be 14. (But it doesn’t say not to paint them.)
I WILL GIVE BRAINLIEST FOR THE CORRECT ANSWER!!! Which equation does the graph below represent? y = −2x y = x y = 2x y = x (click the picture below)
Answer:
y = -2x
Step-by-step explanation:
Some points are (1,-2) , (2, -4), and (3,-6).
From these three points, we can try each of the equations to see what is correct.
If y = -2x
-2 = (-2)1
-4 = (-2)2
-6 = (-2)3
If y = x
-2 ≠ 1
-4 ≠ 2
-6 ≠ 3
If y = 2x
-2 ≠ 2(1)
-4 ≠ 2(2)
-6 ≠ 2(3)
Which inequality is represented by the graph
Answer:
(-2, 5) < x
Step-by-step explanation:
Answer:
2/5x-1.5 > 0
Step-by-step explanation:
Chelsey puts twelve colored pieces of chocolate candy in a bag. Three pieces are green, four pieces are yellow, two pieces are purple, and three pieces are red. She draws one piece of candy from the bag at a time and eats it.
A. What is the probability that Chelsey will draw out three pieces of candy in this order: red, green, yellow?
B. What is the probability that Chelsey will draw out three pieces of candy in this order: green, yellow, red?
C. What is the probability that Chelsey will draw out three pieces of candy in this order: yellow, red, green? D. Make a conclusion about how the order in which she draws out the red, green, and yellow pieces affects the probability.
The probabilities are as follows A.3/10, B. 1/5, C. 1/10, D. 2/5
What is probability?Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Letitia tells her son, Evan, to close his eyes and pick out one piece of candy from the package. Calculate the probability of selecting each colour of candy.
The probability will be calculated as:-
The probability that Chelsey will draw out three pieces of candy in this order: red, green, yellow
3/10
The probability that Chelsey will draw out three pieces of candy in this order: green, yellow, red
1/5
The probability that Chelsey will draw out three pieces of candy in this order: yellow, red, green
1/10
The order in which she draws out the red, green, and yellow pieces affects the probability.
2/5
To know more about probability follow
https://brainly.com/question/24756209
#SPJ2
What is the sum of x?
Answer:
the answer is 40
Step-by-step explanation:
x+60
x=60-20
x=20
how do i measure the bounce height of a tennis ball released from a height of 150 cm?
Answer:
You can use a slow motion camera and see clearly. You should probably put a meter ruler in the background so you can check the height
Step-by-step explanation:
Does anyone know this one! Thanks
Answer: 22.4 cm!
Step-by-step explanation:
If you have the measurements of one side of an equal sided octagon, then you multiply that number (which in this case is 2.8) by 8. Hope this helps!
The linear combination method gives a solution of (–4, 2) for which of these systems of linear equations?
Answer:
[tex]3x + 13y = 14[/tex]
[tex]6x + 11y = -2[/tex]
Step-by-step explanation:
See Attachment for complete question
To determine which of the options has (-4,2) as its solution; we have to test each linear combination until we arrive at an answer;
Given that
[tex](x,y) = (-4,2)[/tex]
Testing Option A
[tex]3x + 13y = 14[/tex]
[tex]6x + 11y = -2[/tex]
Substitute [tex]x = -4[/tex] and [tex]y = 2[/tex] in [tex]3x + 13y = 14[/tex]
[tex]3(-4) + 13(2) = 14[/tex]
Open Brackets
[tex]-12 + 26 = 14[/tex]
[tex]14 = 14[/tex]
Substitute [tex]x = -4[/tex] and [tex]y = 2[/tex] in [tex]6x + 11y = -2[/tex]
[tex]6(-4) + 11(2) = -2[/tex]
Open Brackets
[tex]-24 + 22 = 2[/tex]
[tex]2 = 2[/tex]
In both cases, the expression on the right hand side equates to that on the left hand side;
Hence, there's no need to check for other options.
If water flows 12 feet in 9 seconds through the turbine, how far will the water flow in 54 seconds? If the water continues to flow at this rate, how long will it take the water to travel 54 feet?
Answer:
40.5 sec
Step-by-step explanation:
The flow rate is (12 ft) / (9 sec), or 4/3 ft/ sec.
In 54 sec, the water will have moved
(4/3 ft/sec)(54 sec) = 72 ft.
If the flow rate is 4/3 ft/sec and the distance covered is 54 ft, we divide
54 ft by (4/3 ft/sec) to determine how long it takes the water to flow 54 ft:
54 ft
---------------- = 40.5 sec
(4/3 ft/sec)
Which formula can be used to describe the sequence? –81, 108, –144, 192, ...
Answer:
a(n) = -81(-4/3)^(n - 1)
Step-by-step explanation:
The first term is -81. From -81 we obtain the next term, 108, by multiplying -81 by -4/3. Note how (-4/3)(108) = -144 as anticipated.
Thus, the common ratio is -4/3.
The explicit function for this geometric series is
a(n) = -81(-4/3)^(n - 1)
Answer:
C
Step-by-step explanation:
PLEASE HURRY! ANSWER ASAP
Which two grids can be combined to get 140%?
Square A) A grid model with 100 squares with 1 square shaded.
Square B) A grid model with 100 squares with 15 squares shaded.
Square C) A grid model with 100 squares with 40 squares shaded.
Square D) A grid model with 100 squares with 100 squares shaded
A and B
A and C
B and D
C and D
9. Find P(rolling 1 or 5) with one number cube.
Answer:
1/3
Step-by-step explanation:
There are 6 possible outcomes when rolling 1 die
1,2,3,4,5,6
P ( 1 or 5) = number of times 1 or 5 happens / total outcomes
= 2/ 6
= 1/3
There were some people on a train. 19 people got off the train at the first stop. 17 people get on the train. Now there is 63 people on the train. How many people were on the train to begin with?
Answer:
65 people.
Step-by-step explanation:
We have to work backwards.
We end with 63 people, and at the stop we lost 19 people and gained 17.
[tex]x - 19 + 17 = 63\\[/tex]; if x = # people at the beginning
[tex]x - 19 + 17 = 63\\x - 2 = 63\\x = 65[/tex]
There were 65 people on the train to begin with.
Answer:
65 people
Step-by-step explanation:
Well, we need to work backward,
63 on the train and 17 got on so we do 63 - 17 = 46
Then 19 got off so 46 + 19 = 65
Hence, 65 people were on the train on the first stop.
On the graph of an exponential function representing growth what happens to the slope of the graph as X increases
Answer:
The slope of the graph will increase and get steeper.
Step-by-step explanation:
As x increases in an exponential growth graph, f(x) will have a larger value because the exponent value increases.
So, the graph will become steeper due to a larger slope.
The slope of the graph will increase and get steeper.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the
change in y coordinate with respect to the change in x coordinate as,m = Δy/Δx where, m is the slope
Given:
As we know that, all points on an exponential curve are always at a constant distance from one another because the slope of an exponential curve equals the constant rate of expansion.
The graph is not exponential if the slope is not constant.
So, In an exponential growth graph, f(x) will have a greater value as x grows as the exponent grows.
Consequently, a larger slope will cause the graph to grow steeper.
Learn more about Slope here:
https://brainly.com/question/3605446
#SPJ6
let f(x)= 8x³ + 16x² -15 and g(x) = 2x+1. f(x)/g(x).
4x²+6x-3+12/2x+1. 4x²+6x+3+12/2x+1. 4x²+6x-3-12/2x+1. 4x²+6x+3-12/2x+1
Answer:
f(x)/g(x) = 4x^2+6x-3 remainder -12
or
f(x)/g(x) = (4x^2+6x-3)/(2x+1) + (-12)/(2x+1)
or
((4x²+6x-3)-12)/(2x+1)
Step-by-step explanation:
f(x)= 8x³ + 16x² -15
g(x) = 2x+1.
Using long division,
f(x)/g(x) = 4x^2+6x-3 remainder -12
A taxi driver charges a flat rate of $3.50 plus an additional $1.65 per mile. If Mohammad wants to spend, at most, $60, how far can he travel in the taxi cab?
Round your answer to the nearest mile.
O A. 34 miles
OB. 17 miles
C. 35 miles
D. 16 miles
Answer:
A. 34 miles
Step-by-step explanation:
First, you want to subtract $3.50 from $60. Now you have $56.50. Now you want to divide that by $1.65, to see how many miles you can achieve with your price limit. So, now you have a grand total of 34.24. You round that, and you finally have your answer.
The answer to this problem is A. 34 miles
The number of miles that he can travel in the taxi cab will be 17 miles. Then the correct option is B.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
A cab driver charges a level pace of $3.50 in addition to an extra $1.65 per mile.
Let 'y' be the total amount and 'x' be the number of miles. Then we have
y = 3.50x + 1.65
If Mohammad wants to spend, at most $60. Then the number of miles is given as,
60 = 3.50x + 1.65
3.50x = 58.35
x = 16.67
x ≈ 17 miles
The number of miles that he can travel in the taxi cab will be 17 miles. Then the correct option is B.
More about the linear equation link is given below.
https://brainly.com/question/11897796
#SPJ2
Answer pls I can answer ur question maybe
Answer:
[tex]C=5\pi \approx15.71[/tex]
Step-by-step explanation:
The arc length of the semicircle is basically the circumference of it. Therefore, we can use the circumference formula.
The circumference of a full circle is:
[tex]C=2\pi r[/tex]
Therefore, the circumference of a semicircle is half of that (ignoring the diameter):
[tex]C=\pi r[/tex]
The radius is 5.
[tex]C=\pi (5)=5\pi \approx15.71[/tex]
The arc length is around 15.71 units.
Answer:
39.25
Step-by-step explanation:
5^2=25
25x3.14=78.5
78.5/2=39.25
HURRY FIRST GETS BRAINLLEST The diagram below shows a circular pizza with a diameter of 14 inches. The pizza is in a square box with side lengths of 16 inches. In square inches, how much of the box is empty? Use π = 3.14 and round your answer to the nearest hundredth.
Answer:
pls do mark my answer as the brainliest..........
Step-by-step explanation
portion of square empty = 256 - 153.86 = 102.14cm^2
Scanning the road can be thought of as a
A. way to improve your mileage
B. way to reduce your mileage
C. comprehensive drive test
D. systematic search process
Answer:
D
Step-by-step explanation:
Well scanning the road for mileage wouldn't be the correct formula for "scanning" but looking for a gas station sounds more right.
Answer: d
Step-by-step explanation: i did it and got it right
Isabella filled her pool with water at a constant rate. The table compares the remaining volume of water left to fill the pool (in liters) and the time since Isabella started filling the pool (in minutes).
Time (m) Remaining Volume (L)
4 148
6 112
8 76
What is the size of her pool?
Answer:
It was kinda hard to really understand your question but as of all the information that I received the answer is 220 liters
Step-by-step explanation:
Based on the tables, what is the solution to the equation 2(3)X = 3x + 3? (4 points)
x = -1
x = 0
x = 1
X = 6
Answer: x=1
Step-by-step explanation:
When solving for x you must isolate the terms. In order to isolate the terms divide both sides by 3 in order to break up the 3x. that way you should have 2x=x+1 from there i will subtract the x from both sides, so i receive x=1.
Point A is (-6,-5) Point C is (4,0) Find the coordinates of point B on AC such that the ratio of AB to BC is 2:3.
Answer:
(-2, -3)
Step-by-step explanation:
x coord. from -6 to 4 is 10 units / 5 parts = 2
point B is 2 units * 2 from point A, so x = -2
y coord. from -5 to 0 is 5 units / 5 parts = 1
point B is 2 units * 1 from point A, so y = -3
Answer:
(-2,-3)
Step-by-step explanation:
khan acdemy
The interior ages of a triangle have measure
55,25", and x find the value of
these 3 problems ty
Answer:
See below in bold.
Step-by-step explanation:
1. The 3 angles in a triangle add up to 180 degrees.
So x = 180 - (55 + 25)
= 180 - 80
= 100 degrees.
2. The 4 angles in a quadrilateral add up to 360 degrees,, so
3x + 127 + 54 + 119 = 360
3x + 300 = 360
3x = 360 - 300
3x = 60
x = 20 degrees.
3. Exterior angle
= 94 + 42
= 136 degrees.
What is the volume of the cylinder below?
1
1
4
5
A. 4577 units 3
B. 90 units
C. 367 units 3
D. 727 units 3
Answer:
36pi Units^3
Step-by-step explanation:
Slanted (oblique) cylinders have the same volume as standard (right) cylinders.
V=pi r-squared h
V=pix3x3x4
V=36 pi Units cubed
Answer:
The correct answer is 36 pi units^3
Step-by-step explanation:
Which of the following theorems verifies that WXY=PME?
A. HA
B. HL
C. LA
D. AA
HL = hypotenuse leg
We see that WX = PM are the congruent legs (they are the same length due to the similar single tickmark). Also, XY = ME is the congruent pair of hypotenuses. The HL rule only works for right triangles, as the term "hypotenuse" would not apply for a non-right triangle.
The theorem used is HL.
What is theorem?
A theorem is a statement which has been proved true by a special kind of logical argument called a rigorous proof.
Given:
In both triangles
XW = MP (given)
XY = ME (given)
As, hypotenuse of both triangle is equal and leg of one right triangle are congruent to the hypotenuse.
Learn more about this concept here:
https://brainly.com/question/16967523
#SPJ2
Given: P∈ BC , Pabc = 45, Pabp = 30, Papc = 35. Find AP.
Answer:
10
Step-by-step explanation:
Pabp = AB +BP +AP
Papc = AP +PC +CA
So the sum of perimeters of the two smaller triangles is ...
Pabp +Papc = AB +BP +AP + AP +PC +CA
= (AB +BP +PC +CA) +2AP
= Pabc +2AP
Filling in numbers, we have ...
30 +35 = 45 +2AP
20 = 2AP . . . . subtract 45
10 = AP . . . . . . divide by 2
The length of AP is 10 units.
Please hurry!
Which best explains whether a triangle with side lengths 5 cm, 13 cm, and 12 cm is a right triangle?
Answer: the first one I’m pretty sure! Due to the hypotenuse being the longest length (13) and you would use the Pythagorean theorem
Step-by-step explanation: