Answers
Angle Formed by Two Chords = 1/2(Sum of the Intercepted Arcs)
m<JPM = 1/2 (114 + 96) = 1/2 (210) = 105
Answer:
A ) 105
Answer:
C.Apex(105)
Step-by-step explanation:
Related Questions
If three tangents to a circle form an equilateral triangle, prove that the tangent points form an equilateral triangle inscribed in the circle
Answers
Assuming that [tex]FED[/tex] is an equilateral triangle according to the wording of the problem, we have that the angles [tex]\widehat{AFB}=\widehat{BEC}=\widehat{CDA}=60[/tex].
We also know that the circle in green is Inscribed in [tex]FED[/tex].
The following applies to every inscribed circle inside a triangle:
The center of the inscribed circle of a triangle is the intercept of all three angle bisectors of the triangle.
The above theorem implies that the line [tex](FO) [/tex] is an angle bisector because it goes through the vertex F and the center of the inscribed circle.
The previous statement implies that the angle [tex]\widehat{OFB}=30[/tex].
Now let's work on the [tex]OFB[/tex] triangle.
Knowing that [tex]\widehat{OBF}=90[/tex] (because [tex](EF)[/tex] is tangent to the circle at B and [tex]OB[/tex] is a radius of the circle. If you're lost here, remember that a tangent to a circle is always perpendicular to the radius of the circle.) we can then derive that [tex]\widehat{FOB}=180-90-30=60[/tex] (because the sum of the measures of all angles in a triangle is always equal to 180 degrees).
In the same way, we can prove also that:
[tex]\widehat{BOE}=\widehat{EOC}=\widehat{COD}=\widehat{DOA}=\widehat{AOF}=60 degrees[/tex].
Knowing the above we notice that [tex]\widehat{BOC}=\widehat{COA}=\widehat{AOB}=120degrees[/tex].
We're at the last part of our proof here:
Now notice that [tex]\widehat{BOA}[/tex] subtends the same arc on the circle that [tex]\widehat{BCA}[/tex].
According to the inscribed angle theorem, an angle [tex]\theta[/tex] inscribed in a circle is half of the central angle [tex]2\theta[/tex] that subtends the same arc on the circle.
Therefore [tex]\widehat{BCA}=\frac{\widehat{BOA}}{2}=60degrees[/tex]
We can prove in a similar fashion that: [tex]\widehat{CAB}=\widehat{ABC}=60degrees[/tex]
Therefore all the angles of the [tex]ABC[/tex] triangle have a measure of 60 degrees, we conclude then that [tex]ABC[/tex] is equilateral.
Determine the volume of the pencil
Answers
[Volume of the pencil]=[Volume of cylinder]+[volume of cone]
[Volume of cylinder]=pi*(0.5²)*15=11.78 cm³
[volume of cone]=pi*(0.5²)*2/3=0.52 cm³
[Volume of the pencil]=[11.78]+[0.52]=12.30 cm³
the answer is 12.30 cm³
The volume of the pencil is approximately 4.05 cm³.
To determine the volume of the pencil, we need to calculate the volumes of the cylindrical body and the conical tip separately and then add them together.
Volume of the cylindrical body:
The formula for the volume of a cylinder is [tex]V = \pi r^2h[/tex], where r is the radius and h is the height.
[tex]V_{cylinder} = \pi (0.5 cm)^2 * 15 cm[/tex]
Volume of the conical tip:
The formula for the volume of a cone is [tex]V = (1/3)\pi r^2h[/tex], where r is the radius and h is the height.
[tex]V_{cone} = (1/3) * \pi (0.5 cm)^2 * 2 cm[/tex]
Now, we can calculate the volumes:
[tex]V_{cylinder} = \pi * (0.5 cm)^2 * 15 cm = 3.53 cm^3\\\\V_{cone} = (1/3) * \pi * (0.5 cm)^2 * 2 cm = 0.52 cm^3[/tex]
Finally, we can add the volumes of the cylindrical body and the conical tip to get the total volume of the pencil:
[tex]Total\ volume = V_{cylinder} + V_{cone} = 3.53 cm^3 + 0.52 cm^3 = 4.05 cm^3[/tex]
Therefore, the volume of the pencil is approximately 4.05 cubic centimeters ([tex]cm^3[/tex]).
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what is the approximate distance between the points (1 -2) and (-9 3) on a coordinate grid?
Answers
Answer:
11.18
Step-by-step explanation:
The perimeter of an equilateral triangle with a side of 6 inches is
12 in.
18 in.
36 in.
Answers
Find the volume of this square pyramid, given that its height is 8 m.
A) 24 m3.
B) 72 m3.
C) 216 m3.
D) 648 m3.
Answers
Answer:
A) [tex]24\text{ m}^3[/tex].
Step-by-step explanation:
We have been given an image of a square pyramid and we are asked to find the volume of our given pyramid.
[tex]\text{Volume of square pyramid}=\frac{a^2*h}{3}[/tex], where,
a = Base length of square,
h = height of pyramid.
Upon substituting our given values in above formula we will get,
[tex]\text{Volume of square pyramid}=\frac{\text{(3 m)}^2*\text{ 8 m}}{3}[/tex]
[tex]\text{Volume of square pyramid}=\frac{9\text{ m}^2*\text{ 8 m}}{3}[/tex]
[tex]\text{Volume of square pyramid}=\frac{72\text{ m}^3}{3}[/tex]
[tex]\text{Volume of square pyramid}=24\text{ m}^3[/tex]
Therefore, the volume of our given square pyramid is 24 cubic meters and option A is the correct choice.
Answer:
A. 24 m3.
Step-by-step explanation:
Which of the following values is closest to the mean for the set of data shown below?
23, 32, 20, 43, 41, 66, 63, 59, 54, 36, 45, 61, 55, 44, 47
A.45.9 B.50 C.58 D.54.3
Answers
hoped it helped!!!
then divide by how much numbers there are (49.9)
so your answer is b
please mark brainliest!
Solve the system of equations using the linear combination method.
{9x+5y=35
{2x+5y=0
Enter your answers in the boxes.
x =_
y =_
Answers
please mark as brainliest
hope it helps
“How many times did you ride the Ferris wheel today?” Is the question a statistical question? Explain why or why not.
Answers
Lisa made $286 for 13 hours of work. at the same rate, how many hours would she have to work to make $242 ?
Answers
Use k as the constant of proportionality to write the equation expressing the relationship: y varies inversely as x. if y = 10 when x = 5, determine k.
Answers
[tex]y= \dfrac{k}{x} [/tex]
you can solve for k, the constant of variation (or proportionality), by multiply both sides of the function to get [tex]xy=k[/tex]. Substituting 5 for x and 10 for y, you see that k = 50.
y = k/x
Step-by-step explanation:
How do I solve and graph this?
Answers
3x - 6 ⩾ y
now, with inequalities, what we do is, we graph the line of 3x - 6 = y, and then we shade the "true region".
if we pick a point on say hmmm (4, 0), namely x = 4 and y = 0, we can plug that in the inequality and see what we get,
3(4) - 0 ⩾ 6
12 - 0 ⩾ 6
12 ⩾ 6
is 12 really greater or equals to 6? well yes, therefore, the point (4, 0) lies on the "true region", since it's true, 12 is indeed ⩾ 6, so, where that point is, we shade.
now, the ⩾ means equals to or greater, and therefore, since the values could also equal the boundary points, the line is a solid line, because it includes the line itself, as well as the shading.
check the picture below.
Five is a solution of (Y < -3)
A.True
B.False
Answers
The integer '5' has a higher value than -3 as it leans on the right side of a number scale, while -3 sits on the left side.
I hope this helps!
Using radicals , write an equivalent expression for the expression 2 1/3
Answers
If so, then [tex]2^{1/3} = \sqrt[3]{2}[/tex]
Which is the cube root of 2. Raising any value to the 1/3 power is the same as taking the cube root.
I'm assuming that the 1/3 is an exponent.
If so, then
Which is the cube root of 2. Raising any value to the 1/3 power is the same as taking the cube root.
Find the first six terms of the sequence.
a1 = -4, an = an-1 + 7
-4, 3, 10, 17, 24, 31
-4, 7, 14, 21, 28, 35
3, 10, 17, 24, 31, 38
0, 7, 14, 21, 28, 35
Answers
Answer: A) -4, 3, 10, 17, 24, 31
Step-by-step explanation: To solve the given problem we need to calculate the first six terms of the sequence (starting with a1):
a1=-4
a2=a1+7
a2=-4+7
a2=3
a3=a2+7
a3=3+7
a3=10
a4=a3+7
a4=10+7
a4=17
a5=a4+7
a5=17+7
a5=24
a6=a5+7
a6=24+7
a6=31.
Someone please help, with a cherry on top?
View attached graph and find the approx. slope
THANK YOU SOOO MUCH!!!
Answers
The band is selling wrapping paper for a fundraiser. Customers can buy rolls of plain wrapping paper and rolls of shiny wrapping paper. The band sold a total of 55 rolls and made $950. If a roll of plain wrapping paper cost $14 and a roll of shiny cost $20, how many rolls of each did they sell ?
Answers
y= # shiny rolls
QUANTITY EQUATION:
x+y=55
COST EQUATION:
$14x + $20y= $950
SOLVE:
Solve for one variable in quantity equation. Substitute that answer in cost equation.
STEP 1:
x+y=55
subtract y from both sides
x= 55-y
STEP 2:
$14x + $20y= $950
14(55-y) + 20y= 950
multiply 14 by all in parentheses
(14*55)+(14*-y) + 20y= 950
770-14y+20y= 950
combine like terms
770+6y= 950
subtract 770 from both sides
6y= 180
divide both sides by 6
y= 30 shiny rolls
STEP 3:
Substitute y answer in either equation to solve for x.
x+y=55
x+30=55
subtract 30 from both sides
x= 25 plain rolls
Hope this helps! :)
The roll of plain wrapping paper sold is 25.
The roll of shiny wrapping paper sold is 30.
What are the linear equations that represent the question?a + b = 55 equation 1
14a + 20b = 950 equation 2
Where:
a = roll of plain wrapping paper sold
b = roll of shiny wrapping paper sold
What is the roll of shiny wrapping paper sold?Multiply equation 1 by 14
14a + 14b = 770 equation 3
Subtreact equation 3 from equation 2
6b = 180
Divide both sides by 6
b = 30
What is the roll of plain wrapping paper sold?
Subtract 30 from 55
55 - 33 = 25
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Is the expression 2f + 4f + 2 – 3 equivalent to 6f – 1? 6f – 1 evaluated at f = 9 is 53. 2f + 4f + 2 – 3 evaluated at f = 9 is also 53. 6f – 1 evaluated at f = 3 is 17. what is 2f + 4f + 2 – 3 evaluated at f = 3?
Answers
the expression 2f + 4f + 2 – 3-------> we can group it (2f+4f)+(2-3)
(2f+4f)+(2-3)=(6f-1)
therefore
the expression [2f + 4f + 2 – 3] is equivalent to [6f-1]
if the expression [6f-1] for f=3 is 17
then
the expression [2f + 4f + 2 – 3] for f=3 is also 17
let's check it
[2*3 + 4*3 + 2 – 3]--------> [6+12+2-3]=[20-3]=17------> is ok
Answer: 17
Step-by-step explanation:
WORTH 20 POINTS!!
The endpoints of one diagonal of a rhombus are (0, -8) and (8, -4). If the coordinates of the 3rd vertex are (1, 0), what are the coordinates of the 4th vertex? (7, -12)
(7, -8)
(-8, -4)
(-4, -12)
Answers
The rhombus consists of two lines which connecting the endpoints which are intersecting each other. If you have the slopes of these, you can create a relation which says that
[tex]k_1 \cdot k_2 = -1[/tex]
where [tex]k_i[/tex] are the slopes of the lines.
Now you have one slope, which is [tex]k_1 = \frac{-8 - (-4)}{0-8} = \frac{1}{2}[/tex] which means that the slope of the other one has to be
[tex]k_2 = -1 \cdot 2 = -2[/tex]
Given that you have the point (1,0) its trivial to see that this is satisfied by the point (7,-12)[tex]k_2 = \frac{-12-0}{7-1}=\frac{-12}{6} = -2[/tex]
Its worth noting that you want to draw the points, that you have the correct order when you calculate the slope.
The area of a triangle is 1440 cm^2. the base of the triangle is 5 times the height. what is the height of the triangle?
Answers
Triangle Area = .5 * base * height
1,440 = .5 * 5h * h
1,440 = 2.5 h^2
576 = h ^2
height = 24 centimeters
and the base is therefore 120 centimeters
Double Check
base = 120 cm
height 24 cm
area = .5 * 120 * 24
area = 1,440
A test is worth 140 points. Ten percent of those points are from one short-answer question. How many points is the short-answer question worth?
Answers
140 points x 10% = 140 x 0.1 = 14 points for the short-answer quesion.
The short-answer question worth of 14 points.
What is unitary Method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given:
Total points of test =140
and 10 % of those points are from one short-answer question.
So, the points for short-answer question are
=10 % of 140
=10/100 x 140
=1400/100
=14
Hence, short-answer question worth of 14 points.
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Rene has a coupon for $3.25 off a package of name brand cookies that normally costs $7.89. The store brand cookies coats $5.58. How much will Rene save if she uses her coupon and buys the name brand cookies instead of the store brand cookies? HELP
Answers
Rene will save $0.94 if she uses her coupon and buys the name brand cookies instead of the store brand cookies.
Explanation:To find out how much Rene will save if she uses her coupon and buys the name brand cookies instead of the store brand cookies, we have to first determine how much the name brand cookies will cost after applying the coupon. We subtract the value of the coupon i.e. $3.25 from the original cost of name brand cookies which is $7.89. The result comes out to be $4.64.
To calculate the savings, we now have to subtract the cost of name brand cookies after coupon ($4.64) from the original cost of the store brand cookies ($5.58). Hence, the savings amount to $5.58 - $4.64 which equals $0.94
So, if Rene uses her coupon and buys the name brand cookies instead of the store brand cookies, she will save $0.94.
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The half-life of iodine-123 is about 13 hours. You begin with 52 grams of iodine-123. (a) Write an equation that gives the amount of iodine-123, I , remaining after t hours. Write your answer in the form I ( t ) = a ⋅ b t . Round your answer for b to three decimal places.
Answers
Final answer:
The amount of iodine-123 remaining after t hours can be expressed as I(t) = 52 · 0.945^t, where the constant 0.945 is calculated using the half-life of 13 hours.
Explanation:
The half-life of a radioactive isotope is the time it takes for half of the radioactive atoms to decay. For iodine-123, which has a half-life of approximately 13 hours, we can use an exponential decay model to express the amount of iodine-123 remaining after t hours.
The decay formula is generally given by I(t) = I0e-kt, where I0 is the initial amount, k is the decay constant, and t is time. However, the question asks us to express the equation in the form of I(t) = a · bt, which is another common representation for exponential decay.
To find the value of b, we know that after one half-life, b13 = 1/2. Thus, b = (1/2)1/13.
Let's calculate b: b = (0.5)1/13 ≈ 0.945 (rounded to three decimal places).
Since we start with 52 grams of iodine-123, our initial amount (a) is 52. Therefore, the equation for the amount of iodine-123 remaining after t hours is:
I(t) = 52 · 0.945t
The equation to calculate the amount of iodine-123 remaining after t hours is I(t) = a * b^t, where a is the initial amount of iodine-123, b is the decay constant, and t is the time in hours. The decay constant can be calculated using the formula b = 0.693 / t1/2, where t1/2 is the half-life of iodine-123. In this case, the half-life is 13 hours.
Explanation:The equation that gives the amount of iodine-123 remaining after t hours can be written as:
I(t) = a * b^t
Where:
I(t) is the amount of iodine-123 remaining after t hoursa is the initial amount of iodine-123b is the decay constant, which can be calculated using the half-life formulat is the time in hoursTo calculate the decay constant b, we can use the formula:
b = 0.693 / t1/2
where t1/2 is the half-life of iodine-123. In this case, the half-life is 13 hours, so:
b = 0.693 / 13 = 0.053
Therefore, the equation becomes:
I(t) = a * 0.053^t
Round the value of b to three decimal places, so b = 0.053.
Which function is a shrink of the exponential growth function shown on the graph?
A.) f(x) = 2(3)x
B.) f(x) = 1/2(3)x
C.) f(x) = 2(1/3)x
D.) f(x) = 1/2(1/3)x
Answers
Selection B is appropriate.
Which expression can you simplify by combining like terms? Clear Check 6 d 2 +5cd−3dc+8 6d2+5cd-3dc+8 12 c 2 −8 d 2 c+3dc+4 12c2-8d2c+3dc+4 7 d 2 −3 c 2 +6d−c 7d2-3c2+6d-c 16 c 2 +8cd+7c−8d 16c2+8cd+7c-8d
Answers
The expression that can be simplified by combining like terms is 16 c^2 + 8cd + 7c - 8d, where 8cd and -3dc are like terms and can be combined to simplify the expression to 16c^2 + 5cd + 7c - 8d.
Explanation:The expression 16 c2 + 8cd + 7c - 8d can be simplified by combining like terms. Like terms in an algebraic expression are terms that have the same variable raised to the same power. Here, the terms 8cd and -3dc are like terms and can be combined.
Here's the step-by-step simplification:
First, identify like terms in the expression. In 8cd and -3dc, since multiplication is commutative (meaning ab = ba), cd and dc are essentially the same term. So, 8cd and -3dc can be combined.Combine the like terms by adding their coefficients. For 8cd and -3dc, we have 8 - 3 to get 5cd.Now, the simplified expression is 16c2 + 5cd + 7c - 8d.This process of combining like terms helps in simplifying algebraic expressions, making them easier to work with.
After combining like terms, it's important to always check the answer to see if the simplification is reasonable and if there are any other like terms that can be combined.
So, the simplified expressions are:
1. [tex]\(6d^2 + (5c - 3d)d + 8\)[/tex]
2. [tex]\(12c^2 - (c(8d - 3)) + 4\)[/tex]
3. [tex]\(7d^2 - 3c^2 + 6d - c\)[/tex]
4. [tex]\(16c^2 + c(8d + 7) - 8d\)[/tex]
Let's simplify each expression by combining like terms:
1. [tex]\(6d^2 + 5cd - 3dc + 8\)[/tex]
Combine like terms:
[tex]\(6d^2 + (5cd - 3dc) + 8\)[/tex]
[tex]\(6d^2 + (5c - 3d)d + 8\)[/tex]
2. [tex]\(12c^2 - 8d^2c + 3dc + 4\)[/tex]
Combine like terms:
[tex]\(12c^2 - (8d^2c - 3dc) + 4\)[/tex]
[tex]\(12c^2 - (c(8d - 3)) + 4\)[/tex]
3. [tex]\(7d^2 - 3c^2 + 6d - c\)[/tex]
No like terms to combine.
4. [tex]\(16c^2 + 8cd + 7c - 8d\)[/tex]
Combine like terms:
[tex]\(16c^2 + (8cd + 7c) - 8d\)[/tex]
[tex]\(16c^2 + c(8d + 7) - 8d\)[/tex]
If you wanted to predict the value of the y variable when the x variable is 15, you would be _____ the data.
A.) Correlating
B.) Extrapolating
C.) Interpolating
Answers
Answer:
If you wanted to predict the value of the y variable when the x variable is 15, you would be extrapolating the data.
Step-by-step explanation:
If you wanted to predict the value of the y variable when the x variable is 15, you would be Extrapolating the data.
Extrapolation means, estimating the value of a variable beyond its given range.
An initial investment of $200 is now valued at $350. The annual interest rate is 8% compounded continuously. The equation mc022-1.jpg represents the situation, where t is the number of years the money has been invested. About how long has the money been invested? Use a calculator and round your answer to the nearest whole number.
Answers
Answer:
7 years
Step-by-step explanation:
An initial investment of $200 is now valued at $350.
The annual interest rate is 8% compounded continuously.
Formula:
[tex]A=Pe^{rt}[/tex]
Where,
A is amount, A=350
P is principle, P=200
R is rate of interest, r=0.08
t is time, t=?
Substitute the value into formula
[tex]350=200e^{0.08\cdot t}[/tex]
[tex]e^{0.8t}=1.75[/tex]
Taking ln both sides
[tex]0.08t = ln(1.75)[/tex]
[tex]t=6.99\approx 7[/tex]
Hence, 7 years ago money was invested.
Answer:
Its 7 years
Step-by-step explanation:
A farmer has a collection of chickens and dogs. all together there are 120 legs and 43 heads. how many of each animal does he have? answer
Answers
(26*2)+(17*4)=120 legs
26 chickens and 17 dogs
Number of chicken = 26
And, Number of dogs = 17
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
A farmer has a collection of chickens and dogs.
And, all together there are 120 legs and 43 heads.
Hence, Number of chicken = x
And, Number of dogs = y
Thus, We get;
⇒ x + y = 43
⇒ x = 43 - y .. (i)
⇒ 2x + 4y = 120
⇒ x + 2y = 60 .. (ii)
Substitute value of x from (i) to (ii);
⇒ x + 2y = 60
⇒ 43 - y + 2y = 60
⇒ y = 60 - 43
⇒ y = 17
And, From (i);
⇒ x = 43 - y
⇒ x = 43 - 17
⇒ x = 26
Thus, Number of chicken = 26
And, Number of dogs = 17
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Rico travelled from the United States to the United Kingdom. Once Rico arrived, he converted his American dollars into British pounds (the currency in the U.K.). He gave the bank teller $500 and was given back 295 pounds. At the end of his vacation Rico had 75 pounds left over which he converted back into US dollars. How much money (in US dollars ) did Rico have when he got home? Round the answer to the hundredth.
Answers
Consider the diagram. What is the length of segment AB?
Answers
we know that
A median of a triangle is a line segment joining a vertex to the midpoint of the opposing side, bisecting it.
In this problem the line DB is a median of triangle ADC
The line DB is also the altitude of a triangle ADC, because is perpendicular to the side AC
so
AB=BC
we have that
[tex]BC=9\ units[/tex]
therefore
[tex]AB=9\ units[/tex]
the answer is the option
[tex]9[/tex]
PLEASE HELP ASAP!!!