Answers
====================================================
Explanation:
Check out the diagram below. I recreated the diagram in your textbook, but I added on a few other points and segments.
Point E is the midpoint of segment AB. Segment OE is perpendicular to AB.
Point F is the midpoint of CD. Segment OF is perpendicular to CD.
Right triangle AOE forms with OA = 10 as the hypotenuse (radius of the circle) and AE = 8, since E cuts AB in half.
Use the pythagorean theorem to find that...
a^2+b^2 = c^2
(AE)^2 + (OE)^2 = (OA)^2
8^2 + (OE)^2 = 10^2
64 + (OE)^2 = 100
(OE)^2 = 100-64
(OE)^2 = 36
OE = sqrt(36)
OE = 6
--------------------
Because chord CD is the same length as chord AB, this means the chords are the same distance from the center point O.
So, OE = OF = 6
Since we have rectangle OEPF, the opposite sides are congruent and we can say OF = EP = 6
Now focus on right triangle OEP. Use the pythagorean theorem again
a^2+b^2 = c^2
(OE)^2 + (EP)^2 = (OP)^2
(6)^2 + (6)^2 = (OP)^2
72 = (OP)^2
(OP)^2 = 72
OP = sqrt(72)
OP = sqrt(36*2)
OP = sqrt(36)*sqrt(2)
OP = 6*sqrt(2)
Related Questions
The following system of equations is shown below.
2x + 3y=4
X-y=-3
Which of the below is the solution to this system?
Answers
Answer:
(-1,2)
Step-by-step explanation:
point form : (-1,2)
Equation form : x = -1, y= 2
If 1 and -2 are zeroes of x^2+ax+b=0. Find a and b. First and correct answer will be marked brainliest.
Answers
Answer:
a = 1, b = -2
Step-by-step explanation:
You are given values of x are 1 and 2 when the equation is 0
To solve the problem substitute the values of x into the equation
For x =1
1^2 + a(1) + b = 0
1 + a + b = 0
a+b = -1(call this equation i)
For x = -2
-2^2 + a(-2) + b = 0
4 - 2a + b = 0
-2a + b = -4 (call this equation ii)
Now solve equation i and ii simultaneously to get values of a and b.
a+b = -1
-2a+b = -4
By elimination method (also you can solve by substitution method) subtract equation ii from equation i, we get
3a = 3
Divide 3 both sides, you get
a = 1
Take the value of a above substitute it into either equation i or ii to get the value of b
Here i considered equation i
a + b = -1
1 + b = - 1
b = - 1 - 1
b = -2
Therefore a = 1, b = -2
find a system of linear equations with three unknowns whose solutions are the points on the line through (1, 1, 1) and (3, 5, 0).
Answers
A system of linear equations with three unknowns whose solutions are the points on the line through (1, 1, 1) and (3, 5, 0) can be found as follows:
Suppose that the line through the points (1, 1, 1) and (3, 5, 0) can be represented by the vector equation (x, y, z) = (1, 1, 1) + t(2, 4, -1), where t is a scalar parameter. Then we have x = 1 + 2t, y = 1 + 4t, z = 1 - t. This vector equation can be rewritten as a system of linear equations by equating each component of the vectors.
We have:
x = 1 + 2t, y = 1 + 4t, z = 1 - t
So, the system of linear equations with three unknowns whose solutions are the points on the line through (1, 1, 1) and (3, 5, 0) is:
x - 2t = 1, y - 4t = 1, z + t = 1.
To find a system of linear equations with three unknowns whose solutions are the points on the line through (1, 1, 1) and (3, 5, 0), we can use the parametric equation of a line in three dimensions. Suppose that the line through the points (1, 1, 1) and (3, 5, 0) can be represented by the vector equation (x, y, z) = (1, 1, 1) + t(2, 4, -1), where t is a scalar parameter.
This vector equation means that the coordinates of any point on the line can be obtained by adding a scalar multiple of the direction vector (2, 4, -1) to the point (1, 1, 1).
In other words, if we let t vary over all real numbers, we obtain all the points on the line. Then we can rewrite the vector equation as a system of linear equations by equating each component of the vectors. We have:
x = 1 + 2t,y = 1 + 4t, z = 1 - t .
This system of equations represents the line passing through (1, 1, 1) and (3, 5, 0) in three dimensions. The first equation tells us that the x-coordinate of any point on the line is 1 plus twice the t-coordinate. The second equation tells us that the y-coordinate of any point on the line is 1 plus four times the t-coordinate.
The third equation tells us that the z-coordinate of any point on the line is 1 minus the t-coordinate. Therefore, any solution of this system of equations gives us a point on the line through (1, 1, 1) and (3, 5, 0). Therefore, the system of linear equations with three unknowns whose solutions are the points on the line through (1, 1, 1) and (3, 5, 0) is:
x =1+ 2t, y - 4t = 1, z + t = 1
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Help please. I need an answer quick please.
“Select all the graphs that show a proportional relationship”
Answers
Answer:
Step-by-step explanation:
The graphs of all proportional relationships go through the origin. The first graph satisfies this criterion; the second does not.
Tom work for a company
hi normal rate of pay i £15 per hour
when tom work for longer than 7 hour per day he i paid for each hour he work more than 7 hour
tom rate of overtime pay per hour i 1 1/3
on monday tom work for 11 hour
work out the total amount of money that tom made on monday
Answers
If on Monday Tom work for 11 extra hours the total amount of money that tom made on Monday is £885.
As per the given data, the extra money he earns can be calculated as,
= [(11 - 7) × 15] × 13 + (7 × 15)]
= (4 × 15 × 13) + 105
= 780 + 105
= £885
Therefore, the amount of money is £885.
Time and work are concerned with how long it takes a person or a group of people to finish a task and how well each of them completes it.
Indirect proportion is related to time and work. In both directions, when one quantity rises, the other falls, and vice versa. It takes less time to finish the same amount of work when people work more hours.
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the angle \theta 1θ 1 theta, start subscript, 1, end subscript is located in quadrant \text{iv}ivstart text, i, v, end text, and \sin(\theta 1)
Answers
The angle θ1 located in quadrant IV and sin(θ1) is negative.
The angle θ1 located in quadrant IV and sin(θ1) is negative. When an angle is located in quadrant IV, it means that the angle is between 270 and 360 degrees (or between -90 and 0 degrees).
The sin function is negative in quadrants III and IV. Since θ1 is in quadrant IV, sin(θ1) will be negative. This is because sin is defined as the ratio of the opposite side to the hypotenuse in a right triangle. In quadrant IV, the x-coordinate (adjacent side) is positive and the y-coordinate (opposite side) is negative, so sin is negative.
Therefore, we can conclude that the angle θ1 located in quadrant IV and sin(θ1) is negative.
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Determine whether the quadrilateral is a parallelogram, answer Yes or No below
Answers
The quadrilateral is a parallelogram so it is Yes.
What are the properties of a parallelogram?If a quadrilateral has a pair of parallel opposite sides, it’s a special polygon called parallelogram .The properties of a parallelogram are as follows:
The opposite sides are parallel and equal
The opposite angles are equal
The consecutive or adjacent angles are supplementary
If any one of the angles is a right angle, then all the other angles will be at right angle.
The quadrilateral is a parallelogram since the adjacent interior angles 75° and 105° are supplementary meaning they sum up to 180°
In conclusion, yes, the figure is a parallelogram.
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A rectangle has a height 3 times the length of its base. If the base increases by 3 cm and the height by 5 cm then the area is 319 2. What are the dimensions of the rectangle?
Answers
Answer:
The length of a rectangle is 3 times the width.The area is 75 cm^2.
True or false: when you combine zero with the set of natural numbers, you get the set of whole numbers
Answers
Answer:
True!!!
Step-by-step explanation:
0 + 500 = 500 which is a whole number
every natural number is a whole one and 0 doens't make a difference at all.
Answer: True
Step-by-step explanation: The set of counting numbers, {1, 2, 3, 4, ...} is called the set of natural numbers.
When we include 0 in the set of natural numbers, the new set,
{0, 1, 2, 3, ...} is called the set of whole numbers.
Notice that all natural numbers are included
within the set of whole numbers.
We can represent the relationship between
these two sets of numbers using a diagram.
The larger circle below represents the set of whole numbers.
Then all natural numbers will appear within the set of whole numbers.
what is 6/45 in simplest form with steps, and ⁻4/36 in simplest form with steps
Answers
Answer:
answer is 2/15
Step-by-step explanation:
simplify it
Answer:
Hope this helped!!
Step-by-step explanation:
6/45 U have to find the common number that both the numbers are divisible by. They are both divisible by 3.
6/3/45/3=
2/15 That is your answer
For 4/26 both the numbers are divisible by 4
So 4/4/36/4=
1/12 That is your answer
Show that if m
∗
(A)=0, then m
∗
(AUB)=m
∗
(B)
Answers
A and B have the same elements, the measure of AUB will be equal to the measure of B.
To show that if m*(A) = 0, then m*(AUB) = m*(B), we need to prove the following:
1. If m*(A) = 0, then A is a null set.
2. If A is a null set, then AUB = B.
3. If AUB = B, then m*(AUB) = m*(B).
Let's break down each step:
1. If m*(A) = 0, then A is a null set:
- By definition, a null set has a measure of 0.
- Since m*(A) = 0, it implies that A has no elements or its measure is 0.
- Therefore, A is a null set.
2. If A is a null set, then AUB = B:
- Since A is a null set, it means that it has no elements or its measure is 0.
- In set theory, the union of a null set (A) with any set (B) results in B.
- Therefore, AUB = B.
3. If AUB = B, then m*(AUB) = m*(B):
- Since AUB = B, it implies that both sets have the same elements.
- The measure of a set is defined as the sum of the measures of its individual elements.
- Since A and B have the same elements, the measure of AUB will be equal to the measure of B.
- Therefore, m*(AUB) = m*(B).
By proving these three steps, we have shown that if m*(A) = 0, then m*(AUB) = m*(B).
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Rotate ΔABC with vertices A(-1, 4), B(2, 1), and C(3, -3) about the origin by 90°.
What are the coordinates of A'?
Answers
Write an algebraic convergence code based on the same format of this geometric convergence code.Image transcription textIdef convergenceGeometric(a, 10=-1, pltx=True, verbose=True, c=!b'):
inputs :
sequence converging to zero at a geometric rate
10
the last point to use in calculating the slope
pltx
Logical variable for show the convergence plot
verbose Logical vorioble for printing information
color of the line to be plotted
outputs:
rho
the order of geometric convergence
S
the asymptotic error constant. If rho=1, 0<S<1. If
rho>1, S=0.
rho = (log10 (a[10]) - Log10(a[10 - 1])) / (log10(a[10 - 1]) - Log10(a[10 - 2]))
rho = fabs (rho)
S = fabs (a [10] / a[10 - 1])
if verbose:
print( 'geometric, rho = (0:1.3f}, S = (1:1.3f} .format(rho, S))
if pltx:
pit. loglog(a[0: -2], a[1:-1], c)
pit. ylabel('S\log(la_{k+1}[)$')
pit .xlabel( ' $\log(la_k[)$:)
pit . show ()
return rho, S... Show more
Answers
We can see here that an algebraic convergence code that follows a similar format to the provided geometric convergence code is seen below:
def convergenceAlgebraic(a, tolerance=1e-6, max_iterations=100, pltx=True, verbose=True, c=1.5):
n = 0
x = a
error = abs(f(x) - x)
How the code runs?Continuation of the code:
while error > tolerance and n < max_iterations:
x_new = f(x) + c
error = abs(x_new - x)
x = x_new
n += 1
if verbose:
print(f"Iteration {n}: x = {x}, Error = {error}")
if pltx:
plot_convergence(x, f)
return x
def f(x):
# Define the algebraic function here
return x**2 - 4*x + 3
def plot_convergence(x, f):
# Plot the convergence here
pass
# Example usage
convergenceAlgebraic(a=10, tolerance=1e-6, max_iterations=100, pltx=True, verbose=True, c=1.5)
In this code, we have a function convergenceAlgebraic that takes an initial value a, a tolerance level tolerance, a maximum number of iterations max_iterations, a flag pltx to control whether to plot the convergence, a flag verbose to control whether to print the iteration information, and a constant c specific to the algebraic convergence.
The f(x) function represents the algebraic function you want to converge towards, and plot_convergence is a placeholder function to visualize the convergence.
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The total amount of kinetic and potential energy in a system is called
Answers
The total amount of kinetic and potential energy in a system is called mechanical energy.
Mechanical energy is the sum of kinetic energy and potential energy within a system. Kinetic energy (KE) is the energy possessed by an object due to its motion, and it is calculated using the formula KE = (1/2)mv², where m is the mass of the object and v is its velocity. Potential energy (PE) is the energy possessed by an object due to its position or condition, and it can be gravitational potential energy, elastic potential energy, or other forms. The total mechanical energy (ME) is obtained by adding the kinetic and potential energy together, so ME = KE + PE.
In summary, the total amount of kinetic and potential energy in a system is referred to as mechanical energy. This energy accounts for both the motion and position-related energies within the system. The calculation of mechanical energy involves summing the kinetic energy, which depends on the mass and velocity of the objects, with the potential energy, which can arise from factors such as gravity or elasticity. Understanding and analyzing the mechanical energy in a system can provide insights into its overall energy distribution and behavior.
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Determine whether each infinite geometric series diverges or converges. 1 - 1/6 + 1/36 - 1/216 + . . . .
Answers
The given infinite geometric series converges.
To determine whether an infinite geometric series converges or diverges, we need to check the common ratio (r) of the series. In this case, the common ratio can be found by dividing any term by its preceding term.
In the given series, the first term is 1, and each subsequent term is obtained by multiplying the preceding term by -1/6. Therefore, the common ratio (r) is -1/6.
For an infinite geometric series to converge, the absolute value of the common ratio (|r|) must be less than 1. In this case, |r| = |-1/6| = 1/6, which is less than 1.
Since the absolute value of the common ratio is less than 1, the given series converges. The specific value of the convergence can be determined using the formula for the sum of an infinite geometric series, which is S = a / (1 - r), where S is the sum, a is the first term, and r is the common ratio.
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a plane leaves chicago and flies 750 miles to new york.
Answers
Answer:
what is ur question exactly, ur question is missing some parts
There was a sample of 350 milligrams of a radioactive substance to start a study. since then, the sample has decayed by 7.3% each year. let t be the number of years since the start of the study. let y be the mass of the sample in milligrams. write an exponential function showing the relationship between y and t .
Answers
Answer:
y = 350*0.927^tStep-by-step explanation:
Initial amount = 350 mgDecay = 7.3% per year or 0.073Time = t yearsFinal mass = yThe equation:
y = 350*(1 - 0.073)^t = 350*0.927^tUse the diagram below. If m∠3 = 60°, find m∠4.
Answers
Answer:
120
Step-by-step explanation:
(b) an experiment involving peas results in 580 offspring, 152 of which peas have yellow pods. mendel claimed that the proportion of peas with yellow pods should be 25%. we want to know if these data are consistent with mendel's hypothesis. which statistical inference procedures should we use?
Answers
As per Mental hypothesis, the statistical inference procedures that we should use Chi-square test for goodness of fit.
Hypothesis
In probability, an idea or explanation that you then test through study and experimentation is known as hypothesis.
Given,
Here we have given that, an experiment involving peas results in 580 offspring, 152 of which peas have yellow pods. Mendel claimed that the proportion of peas with yellow pods should be 25%. we want to know if these data are consistent with Mendel's hypothesis.
And we need to find in which statistical inference procedures should we use.
According to the definition of Chi-square test for goodness of fit, the claim is that the proportion of peas with yellow pods should be 25%. And then here the researcher wants to check that the experimental and observed counts of yellow offspring peas shows significant difference or not.
So, the statistical procedure used to study this case is Chi-square test for goodness of fit . Hence, option (1) is correct.
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it took 4 hours to drive 240 mile. At this rate, how long does it take to drive 90 miles
Answers
Answer:
1 hour and 30 minutes
Step-by-step explanation:
4 hours = 240 miles
1 hour = 240 ÷ 4 = 60 miles
90 ÷ 60 = 1.5 hours =
1 hour and 30 minutes
Mmmm! I love apple cider punch this time of year, and so do all my neighbors. My recipe calls for two quarts of apple cyder, three teaspoon of cinnamon, and one pint of lemon-lime soda. This will make enough for 8 people to share. In my neighborhood, however, there are 36 people. How much do I need for each ingredient to make enough for everyone?
Answers
Answer:
j
Step-by-step explanation:
Which angle must have the same measure as angle x
Answers
Answer:
Two angles that have the same measure are called congruent angles. Here are two angles that both measure 30°. We say that angle x is congruent to angle y.
Step-by-step explanation:
a merchant blends tea that sells for $3 a pound with tea that sells for $2.75 a pound to produce 80 lb of mixture that sells for $2.90 a pound. how many pounds of each type of tea does the merchant use in the blend?
Answers
the merchant uses 48 pounds of the $3 tea and 32 pounds of the $2.75 tea in the blend.
To determine the amount of each type of tea used in the blend, we can set up a system of equations based on the given information. Let's assume x pounds of the $3 tea are used and y pounds of the $2.75 tea are used.
The first equation represents the total weight of the mixture: x + y = 80 (equation 1).
The second equation represents the average price per pound of the mixture: (3x + 2.75y) / 80 = 2.90 (equation 2).
To solve this system of equations, we can use the method of substitution or elimination.
Using substitution, we can solve equation 1 for x: x = 80 - y. Substituting this into equation 2, we have (3(80 - y) + 2.75y) / 80 = 2.90.
Simplifying the equation, we get (240 - 3y + 2.75y) / 80 = 2.90.
Combining like terms, we have (240 - 0.25y) / 80 = 2.90.
Cross-multiplying, we get 240 - 0.25y = 2.90 * 80.
Simplifying further, we have 240 - 0.25y = 232.
Subtracting 240 from both sides, we get -0.25y = -8.
Dividing both sides by -0.25, we find y = 32.
Substituting this value of y into equation 1, we have x + 32 = 80.
Solving for x, we get x = 80 - 32 = 48.
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simplify each expression 3(m-5)+m
Answers
3(m-5) + m
3m - 15 + m
4m - 15
HELP PLS SHJSSJKJS ILL MARK U BRAINLIST
Answers
Answer:
1500
Step-by-step explanation:
To get this, just multiply by 10 or add a 0:
150*10= 1500
Hope this helps!
1) A bowl contains 7 cooked and 5 uncooked In how many ways can: a) 2 cooked or 3 uncooked eggs be selected. B) 2 cooked and 3 uncooked eggs be selected
Answers
a) The number of ways to select 2 cooked or 3 uncooked eggs is 76.
b) The number of ways to select 2 cooked and 3 uncooked eggs is 210.
a) To select 2 cooked or 3 uncooked eggs, we can either choose 2 cooked eggs and 0 uncooked eggs, or 1 cooked egg and 1 uncooked egg, or 0 cooked eggs and 2 uncooked eggs, or 3 uncooked eggs and 0 cooked eggs.
The number of ways to choose 2 cooked eggs and 0 uncooked eggs is given by the combination formula
C(7, 2) = 21
The number of ways to choose 1 cooked egg and 1 uncooked egg is given by
C(7, 1) x C(5, 1) = 35
The number of ways to choose 0 cooked eggs and 2 uncooked eggs is given by:
C(5, 2) = 10
The number of ways to choose 3 uncooked eggs and 0 cooked eggs is given by:
C(5, 3) = 10
Therefore, the total number of ways to select 2 cooked or 3 uncooked eggs is:
21 + 35 + 10 + 10 = 76
b) To select 2 cooked and 3 uncooked eggs, we need to choose 2 cooked eggs from the 7 cooked eggs and 3 uncooked eggs from the 5 uncooked eggs
The number of ways to choose 2 cooked eggs from 7 cooked eggs is given by:
C(7, 2) = 21
The number of ways to choose 3 uncooked eggs from 5 uncooked eggs is given by:
C(5, 3) = 10
Therefore, the total number of ways to select 2 cooked and 3 uncooked eggs is:
21 x 10 = 210
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Harlan is building a fence. After he sets the corner post, he uses 2 eight-foot posts, 4 braces, and 48 feet of paneling for every 12 feet of fence. Harlan needs to build 60 feet of fence today and he has 208 feet of paneling. How many more feet of paneling does he need?
Answers
can yall help and can you show work
Answers
Answer:
-12k+24 is the answer...
Step-by-step explanation:
-12k+24 is the answer...
-4(3k-6)-4k = -8k+24-4k
= -12k+24
5x - Зу = -7
— 2x – 3y = 19
WHICH method would be best to solve these ? Elimination, Graphing, Substitution, or none of these
Answers
Answer:
I think elimination method will the the beat and easiest method we can use in that question,
Hint: Summaries do NOT tell how things look, feel, smell, or taste. A. My sister's wedding was a success. B. I ate yummy salmon at my sister's wedding. C. My dress at my sister's wedding was blue.
Answers
A summary is a brief overview of the main points or important details of a text or event. In the case of the statements provided, option A, "My sister's wedding was a success," is the best example of a summary.
A summary provides a general overview of the event without going into specific details about how things looked, felt, smelled, or tasted, as does option A.
Options B and C, "I ate yummy salmon at my sister's wedding" and "My dress at my sister's wedding was blue," are not summaries because they focus on specific details rather than providing an overview of the event.
In conclusion, alternative A. My sister's wedding was a success is correct.
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