Answers
radius = length of BC = x
Triangle ABC is a right triangle. The right angle (aka 90 degree angle) is at angle B as shown by the square marker.
Because we have a right triangle, we can use the pythagorean theorem
(leg1)^2 + (leg2)^2 = (hypotenuse)^2
(AB)^2 + (BC)^2 = (AC)^2
(22)^2 + (x)^2 = (x+14)^2
484 + x^2 = x^2 + 28x + 196
484 + x^2-x^2 = x^2 + 28x + 196-x^2
484 = 28x+196
484-196 = 28x+196-196
288 = 28x
28x = 288
28x/28 = 288/28
x = 72/7
x = 10.285714
The exact value of x, as a fraction is 72/7
Using a calculator, the approximate value of x is roughly 10.285714
So the radius is exactly 72/7 units long.
The radius is approximately 10.285714 units long.
The radius of a circle in Euclidean geometry is the distance from its center to any point on the circumference, and it can be calculated by dividing the circumference by 2π. In physics, the radius is also the radius of curvature for an object's circular path, determined by position data and the Pythagorean theorem.
Explanation:In mathematics, especially in Euclidean geometry, the radius of a circle is a fundamental concept that refers to the distance from the center of the circle to any point on its circumference.
Referring to the examples provided, one method to find the radius (r) is by understanding the relationship between the circumference of a circle (C) and its radius. In a flat, Euclidean space, the ratio C/r is a constant 2π, where π (pi) is approximately 3.14159. Therefore, if you know the circumference, you can calculate the radius by rearranging the formula to r = C/(2π).
In one of our more practical examples, the radius of curvature is used in the context of circular motion. When dealing with the path of an object in a circular trajectory, the radius of the circle also represents the radius of curvature. For instance, using position data where x = 3 m and y = 4 m, we can use the Pythagorean theorem to find the radius, r = √(3² + 4²) = 5 m.
Understanding these principles is crucial in fields such as physics, where the radius is directly related to calculating velocities and accelerations in circular motions as seen with centripetal acceleration.
Related Questions
How do I do these only need to do 1 I just need to see how to do it!
Answers
y = 7x + b
Because we need (5,8) to be an intersections, lets substitute these values in.
8 = 7(5) + b
8 = 35 + b
-27 = b
Now that we know the y-intercept, lets make our equation.
y = 7x - 27
Hope this helps!
The distance around the outside of Cedar Park is 0.8 mile. Joanie ran 0.25 of the distance during her lunch break. How far did she run?
Answers
Hope I helped!
Answer: 0.2
Step-by-step explanation:
To calculate the distance that Joanie run during her lunch break is necessary to multiply the total distance around the outside of Cedar Park (0,8) by the 1/4 of the total distance that she ran (0,25).
So, the expression is:
0,25 . 0.8 = 0,2
Joanie run 0,2 miles during her lunch break.
Mr woods is going to fence his garden, His garden is rectangular shaped with the length being 13 1/2 feet and the width 8 1/4 feet how many feet of the fence should mr woods buy to fence in his garden?
Answers
=2(13 1/2 + 8 1/4)
=2 (21 3/4)
=43 1/2 feet
MATH HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
__________________________________________________________
"It travels for 2 hours, then stops for 1 hour, and finally travels again for 2 hours."
_____________________________________________________________
round to the nearest hundred 5,503,569
Answers
Final answer:
To round 5,503,569 to the nearest hundred, observe the hundreds and the following digit. Since the following digit is a 9, round the hundreds digit up to 7 and zeros follow. The rounded number is 5,503,600.
Explanation:
To round the number 5,503,569 to the nearest hundred, we need to look at the digit in the hundreds place and the digit following it. In 5,503,569, the hundreds digit is 6, and the digit to its right is 9. According to rounding rules, if the digit right after the one we are rounding is 5 or greater, we round up. Since 9 is greater than 5, we round the hundreds place up from 6 to 7 and change all the digits to the right of the hundreds place to zero.
The final answer, therefore, is 5,503,600 when 5,503,569 is rounded to the nearest hundred.
Brody is purchasing some tools for his workshop. He has a budget of $120 and needs to buy at least 14 tools. Each hammer costs $10, and each wrench costs $6.
Answers
Answer:
The graph in the attached figure
Step-by-step explanation:
Let
x------> the number of hammers
y------> the number of of wrenches
we know that
[tex]10x+6y\leq 120[/tex] -----> inequality A
[tex]x+y\geq 14[/tex] -----> inequality B
using a graphing tool
The solution of the system of inequalities is the shaded area
see the attached figure
complete a prime factorization of 54 and write it as a product of primes
Answers
2 * 27
2 * 3 * 9
2 * 3 * 3 * 3 or 2 * 3^3 <==
30 increased by 3 times the square of a number
Answers
30 + 3(y x y), let say y is 2
30 + 3(2 x 2)
30 + 3(4)
30 + 12 = 42
The number is 30+ 3x².
What is square of a number?When an integer is multiplied by itself, the resultant number is known as its square number. Basically, a square number is a number that is obtained by the product of two same numbers. In geometry, the area of a square with 'n' as the side length (where n is an integer) is the finest example of a square number.
When an integer is multiplied by the same integer, the resultant number is known as a square number. For example, when we multiply 5 × 5 = 52, we get 25. Here, 25 is a square number. Square numbers are always positive, they cannot be negative because when a negative number is multiplied by the same negative number, it results in a positive number.
let the number be x
Now, 3 times square of a number
3x²
and, 30 increased
=30+ 3x²
Hence, the number is 30+ 3x².
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Luis can spend up to $240 buying men’s and women’s shirts for his club. Men’s shirts cost $8 each and women’s shirts cost $12 each. He needs to buy at least 3 men’s shirts and at least 8 women’s shirts. Also, the women’s shirts must be at least twice the number of men’s shirts.
The graph shows the feasible region, where x represents the number of men’s shirts and y represents the number of women’s shirts.
Which ordered pairs meet all the constraints and make sense in context of the situation?
Select each correct answer.
(4, 9)
(7, 13)
(2, 15)
(5,12)
(6, 15)
Answers
Let
x------> the number of men’s shirts
y-----> the number of women’s shirts
we know that
[tex]8x+12y \leq 240[/tex] ----> constraint A
[tex]x\geq 3[/tex] ----> constraint B
[tex]y\geq 8[/tex] ----> constraint C
[tex]y\geq 2x[/tex] ----> constraint D
using a graphing tool
see the attached figure N[tex]1[/tex]
The solution is the shaded area
Remember that
if an ordered pair meets all restrictions and makes sense in the context of the situation, then the ordered pair is a system solution
we're going to proceed to verify each pair ordered
case A) [tex](4,9)[/tex]
Substitute the value of x and y in each constraint
[tex]x=4\\y=9[/tex]
Verify constraint A
[tex]8*4+12*9 \leq 240[/tex]
[tex]140 \leq 240[/tex] -------> is true
Verify constraint B
[tex]4\geq 3[/tex] -------> is true
Verify constraint C
[tex]9\geq 8[/tex] ------> is true
Verify constraint D
[tex]9\geq 2*4[/tex]
[tex]9\geq 8[/tex] -----> is true
therefore
the ordered pair [tex](4,9)[/tex] is a system solution
case B) [tex](7,13)[/tex]
Substitute the value of x and y in each constraint
[tex]x=7\\y=13[/tex]
Verify constraint A
[tex]8*7+12*13 \leq 240[/tex]
[tex]212 \leq 240[/tex] -------> is true
Verify constraint B
[tex]7\geq 3[/tex] -------> is true
Verify constraint C
[tex]13\geq 8[/tex] ------> is true
Verify constraint D
[tex]13\geq 2*7[/tex]
[tex]13\geq 14[/tex] -----> is not true
therefore
the ordered pair [tex](7,13)[/tex] is not a system solution
case C) [tex](2,15)[/tex]
Substitute the value of x and y in each constraint
[tex]x=2\\y=15[/tex]
Verify constraint A
[tex]8*2+12*15 \leq 240[/tex]
[tex]196 \leq 240[/tex] -------> is true
Verify constraint B
[tex]2\geq 3[/tex] -------> is not true
Verify constraint C
[tex]15\geq 8[/tex] ------> is true
Verify constraint D
[tex]15\geq 2*2[/tex]
[tex]15\geq 4[/tex] -----> is true
therefore
the ordered pair [tex](2,15)[/tex] is not a system solution
case D) [tex](5,12)[/tex]
Substitute the value of x and y in each constraint
[tex]x=5\\y=12[/tex]
Verify constraint A
[tex]8*5+12*12 \leq 240[/tex]
[tex]184 \leq 240[/tex] -------> is true
Verify constraint B
[tex]5\geq 3[/tex] -------> is true
Verify constraint C
[tex]12\geq 8[/tex] ------> is true
Verify constraint D
[tex]12\geq 2*5[/tex]
[tex]12\geq 10[/tex] -----> is true
therefore
the ordered pair [tex](5,12)[/tex] is a system solution
case E) [tex](6,15)[/tex]
Substitute the value of x and y in each constraint
[tex]x=6\\y=15[/tex]
Verify constraint A
[tex]8*6+12*15 \leq 240[/tex]
[tex]228 \leq 240[/tex] -------> is true
Verify constraint B
[tex]6\geq 3[/tex] -------> is true
Verify constraint C
[tex]15\geq 8[/tex] ------> is true
Verify constraint D
[tex]15\geq 2*6[/tex]
[tex]15\geq 12[/tex] -----> is true
therefore
the ordered pair [tex](6,15)[/tex] is a system solution
therefore
the answer is
[tex](4,9)[/tex]
[tex](5,12)[/tex]
[tex](6,15)[/tex]
see the attached figure N[tex]2[/tex] to better understand the solution
Answer:
(4,9) (5,12) (6,15)
Step-by-step explanation:
Those were the correct options.
A coffee shop uses 4 liters of milk every day.If there are 15 liters of milk in the refrigerator, after how many days will more milk need to be purchased?
Answers
2m - nx = x + 4 with description
Answers
Since 2m does not contain the variable to solve for, move it to the right side of the equation by subtracting 2m from both sides.nx-x=-2m+4Factor x out of −nx−xx(−n−1)=−2m+4Divide each term by −n−1-n-1 and simplify.x=2(m−2)/n+1
The equation 2m - nx = x + 4 is a linear equation solvable for x using algebraic manipulation. The solution is x = (2m - 4)/(nx + 1), requiring values for m and n to find x's specific value.
The given equation 2m - nx = x + 4 is a linear equation and can be solved for x by applying algebraic techniques. The question indicates that there is an element of differential equations involved, suggesting that it might be related to more advanced topics such as linear differential equations or characteristics equations. However, the provided context also mentions concepts like probability with positive and negative jumps, quadratic equations, and principles from physics, but these do not directly apply to the initial linear equation provided.
To solve for x in the given equation, we would rearrange the terms to isolate x:
2m - nx = x + 4
2m - 4 = x(nx + 1)
x = (2m - 4)/(nx + 1)
The solution for x is now expressed in terms of m and n. To find the specific value of x, values for m and n must be known.
The value of the expression (2x^2)/(x) + x(100-15x) when x = 5 is
Answers
Answer:
[tex]\dfrac{2x^2}{x} + x(100-15x)[/tex] at x=5
135
Step-by-step explanation:
Given: The expression [tex]\dfrac{2x^2}{x} + x(100-15x)[/tex]
This is rational expression of variable x.
Put x=5 into the expression and then simplify
[tex]\Rightarrow \dfrac{2\cdot 5^2}{5} + 5(100-15\cdot 5)[/tex]
[tex]\Rightarrow 2\cdot 5 + 5(100-75)[/tex]
[tex]\Rightarrow 2\cdot 5 + 5\cdot 25)[/tex]
[tex]\Rightarrow 10+125[/tex] (Addition of two integer)
[tex]\Rightarrow 135[/tex]
Hence, The value of given expression is 135
Find f(2) and f(a+h) when f(x)=3x^2+2x+4
Answers
= 3(4) + 4 + 4
= 12 + 8
f(2) = 20
f(a+h) = 3(a+h)^2 + 2(a+h) + 4
= 3(a^2 + 2ah + h^2) + 2a + 2h + 4
f(a+h) = 3a^2 + 6ah + 3h^2 + 2a + 2h + 4
For a large cooking project, Arthur needs to put 18 cups of water into a large pot. He can transport a maximum of 4 cups from the sink in a single trip. The pot already contains 5 cups of water. How many trips are required for Arthur to fill the pot to 18 cups?
Answers
18-5=13
step 2 divide 13 by 4 to figure the number of trips
13/4=3.25
step 3 you cant make a quarter trip and you still need that quarter cup so you round up
3.25 = 4 trips
step 4 finished
Each side of this pentagon is the same length.
How many lines of symmetry does this pentagon have?
A.
0
B.
2
C.
3
D.
5
Answers
Lixin intends to buy either Gift A, which costs $10 or Gift B, which costs $8, as Christmas gifts for each of her parents, 2 siblings, 13 relatives and 10 friends. Given that she intends to spend $230, find the number of each gift she should buy
Please help !! I need someone
Answers
a + b = (2 + 2 + 13 + 10)...a + b = 27 (this is the number of gifts to buy)
a = 27 - b
10(27 - b) + 8b = 230
270 - 10b + 8b = 230
-10b + 8b = 230 - 270
-2b = -40
b = -40/-2
b = 20 <=== she bought 20 eight dollar gifts
a = 27 - b
a = 27 - 20
a = 7 <=== she bought 7 ten dollar gifts
Determine if conjecture: True or False
The difference between two negative numbers is always negative
Answers
-4-(-2)=-4+2=-2, true
-2-(-4)=-2+4=2, not negative, that's our counterexample
false, the question sais 'always' but we found at least 1 instance where it is false and therfor it is a false statement
False, because the difference between two negative numbers is not always negative.
Here,
Given that, The difference between two negative numbers is always negative.
We have to prove this statement is true or false.
What is Negative number?
In the real number system, a negative number is a number that is less than zero.
Now,
We can prove it false with a counter example.
Let two negative number -6 and -8.
Hence, difference between -6 and -8 is,
⇒-6 - ( -8 )
⇒-6 + 8
⇒2
it is not negative number.
Hence, the difference between two negative numbers is not always negative.
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How to find instantaneous and average velocity?
Answers
v(avg) = s / t
that's the average distance, but at some point the object could have moved faster / slower and we want to see the instantaneous velocity. The principal is the same. You take a a little piece of the road for a little piece if time and get the avg velocity of the tiny part of the road. But this way it will be not the exactly speed at that moment, it will be just the avg speed in the little fragment. So we must add limits. What will be the velocity for so tiny part of time that it approaches zero?
We get :
lim s/t = ds/dt
t->0
Instantaneous velocity is found by taking the derivative of the position function with respect to time, giving the velocity at a specific moment. Average velocity is calculated by dividing the total displacement by the total time elapsed.
To find instantaneous velocity, we take the derivative of the position function x(t) with respect to time t. This provides the velocity at any given moment. Mathematically, if the position x is a function of time t, then the instantaneous velocity v at time t is defined as:
v = lim_(Δt→0) (x(t + Δt) - x(t)) / Δt
For average velocity, we simply take the total displacement (the change in position) and divide it by the total time elapsed. Suppose we have an object that moves from position x1 to x2 over a time period from t1 to t2, the average velocity ū is:
ū = (x2 - x1) / (t2 - t1)
When the time interval becomes very small, the average velocity approaches the instantaneous velocity.
The sum of two trinomials ________.
Answers
The equation 1.5r+15=2.25r1.5r+15=2.25r represents the number rr of movies you must rent to spend the same amount at each movie store. How many movies must you rent to spend the same amount at each movie store?
Answers
Combine like terms: 1.5r+15-1.5r=2.25r-1.5r
15=0.75r
Get the unknown alone: 15/.75=.75/.75r
20=r or r=20 :)
HELP!! Given f(x)=5x squared and g(x) = x squared + 2x squared - 5x, what is F (x) * g(x)?
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A+b
A*b
A-b
A *divide sign*
Which one isn't closed
Answers
michael found a job listed in the classified ads that pays a yearly salary of $57.3k what is the weekly salary based on this annual salary
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57.3*1000 (k means 1,000) = 573,000/1 year. Multiplying it by 1 year/52 weeks (to cancel the years), we get 573000/52=around $11019.23 as our answer
CHECK MY ANSWERS PLS!!
Answers
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Problem 2 is correct. The rates of change for f(x), g(x) and h(x) respectively are: 16, -0.5, 12 (in that order)
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Problem 3 is correct. The function f(x) has at most 3 x intercepts. The function g(x) visually is showing 4 x intercepts. For h(x), we have 2 x intercepts on the interval [0,2pi].
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Problem 4 is incorrect. The answer is actually choice D) f(x) and h(x) since they are both trig functions with the same min and max (they hit the peaks and valleys at the same y values). Note how one function is merely a phase shift of the other. See figure 2 (attached).
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Problem 5 is incorrect. The answer is h(x) because the lowest point is (1,-6). See figure 3 (attached). The point D = (1,-6) is the lowest point.
A function, h(x), is defined as shown.
h(x) =
Which graph represents h(x)? {image Attached)
Answers
Answer:
option B
Step-by-step explanation:
We have three different function for h(x)
[tex]h(x)= \frac{1}{4}x-4, x<=0[/tex]
WE have x<=0, so the graph starts at x=0 and goes down
Plug in 0 for x
[tex]h(0)= \frac{1}{4}(0)-4[/tex]
So h(0)= -4
When x=0, y= -4
The graph starts at (0,-4) and goes down
[tex]h(x)= \frac{1}{3}x-3, 0<x<=3[/tex]
x lies between 0 and 3, so the graph starts at x=0 and ends at x=3
Plug in 0 for x
[tex]h(0)= \frac{1}{3}(0)-3[/tex]
So h(0)= -3
When x=0, y= -4
Plug in 3 for x
[tex]h(3)= \frac{1}{3}(3)-3=-2[/tex]
When x=3, y= -2
The graph starts at (0,-4) and ends at (3, -2)
[tex]h(x)= \frac{1}{2}x-2, x>=4[/tex]
WE have x>=4, so the graph starts at x=4 and goes to the right
Plug in 4 for x
[tex]h(4)= \frac{1}{2}(4)-2[/tex]
So h(4)= 0
When x=4, y= 0
The graph starts at (4,0) and goes to the right.
SEcond graph is correct
Answer:
B
Step-by-step explanation:
In the diagram, m < ACB = 65.
m < ECA =
A. 180
B. 115
C. 65
D. 90
Answers
m < ECA = 180 - 65 = 115
answer
m < ECA = 115
B. 115
The measure for <ECA is 115 degree.
What is Linear Pair?When two lines cross at one point, a linear pair of angles is created. If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°. These are also referred to as additional angles.
Given:
m <ACB = 65 degree
m <ECA = ?
As. <ACB and <ECA forms a linear pair.
So, m<ACB + m<ECA = 180
64 + m <ECA = 180
m <ECA = 180 - 65
m <ECA = 115
Hence, the measure of <ECA = 115 degree.
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The table shows the steps for solving the given inequality for x.
7x + 16 < −5(4 − 5x)
Select the reason for each step from the drop-down menus.
7x + 16 < − 5(4 − 5x) - Given
7x + 16 < −20 + 25x - Distributive Property
16 < −20 + 18x - (Choose)
36 < 18x - (Choose)
2 < x - (Choose)
Answers
Answer:
Subtraction (addition) property of inequalityAddition property of inequalityDivision property of inequalityStep-by-step explanation:
You want the reasons for each of the final three steps in the solution of the inequality 7x +16 < -5(5 -5x).
Steps2. 7x +16 < -20 +25x . . . . . . . given step 2
3. 16 < -20 +18x . . . . . Subtraction property of inequality
7x was subtracted from both sides4. 36 < 18x . . . . . . . . . Addition property of inequality
20 was added to both sides5. 2 < x . . . . . . . . . . . . Division property of inequality
both sides were divided by 18__
Additional comment
Subtraction of 7x is the same as adding -7x, so you can say the reason for step 3 is either of "subtraction property" or "addition property" The same would be true of step 4.
To figure this out, you compare the inequality on each line with the one before, and determine what was changed. If the same thing is done to both sides of the inequality (addition, subtraction, multiplication, division), the reason is the corresponding property of inequality.
The multiplication and division properties of inequality tell you to reverse the comparison symbol when the factor used is negative. Here, the factor is 18, a positive number, so the inequality symbol remains untouched.
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Mario has a number cube with sides numbered 1 through 6. He rolls the number cube twice. He rolls an odd number on the first roll. What is the probability that Mario will roll an even number on the second roll?
Answers
hope this helps
Therefore, the chance of getting an even on the second roll is simply just the chance of getting an even on any roll;
We know a cube has six sides and assuming it is a fair cube, this means the chance of any given side facing upwards is 1/6;
There are 3 numbers which are even between 1 and 6 and 3 that are odd;
So, the chance of an even number facing upwards is:
3 * 1/6 = 3/6 = 1/2
In this case, this would also be the probability that the dice would give an odd number.
how do I factor (x^2 + 1)^1/2 +2(x^2 + 1)^1/2
Answers
This is what I would think to do with such an expression;
It should be alright to leave it as it is on the last line as this should be its simplest form;
But, you could write it out as:
[tex]\frac{(x^{2} \ + \ 3)}{(x^{2} \ + \ 1)^{ \frac{1}{2}}} \\\\ = \frac{(x^{2} \ + \ 3)}{ \sqrt{(x^{2} \ + \ 1)}}[/tex]
O coarda a unui cerc pentru O si raza r=20 cm, are lungimea de 32cm. DIstanta de la centru cercului la coarda este: