Three students are comparing how fast their social media posts spread the results are on the table.
1. Write an exponential function to represent the spread of Ben's social media post.
2. Write an exponential function to represent the spread of Carter's social media post.
3. Graph each function using at least three points for each curve. All graphs should be placed together on the same coordinate plane, so be sure to label each curve. You may graph your equation by hand on a piece of paper and scan your work, or you may use graphing technology.
4. Using the functions for each student, predict how many shares each student's post
will be received on Day 3 and then on Day 10. Justify your answers.
5. If Amber decides to mail copies of her photo to the 45 residents of her grandmother's assisted living facility, the new function representing her photo shares is f(x) = 3(4)x + 45. How does this graph compare with the original graph of
Amber's photo share?
6. Based on your results, which students' post travels the fastest? How is this shown
in the equation form of the functions?
7. If you had to choose, would you prefer a post with fewer friends initially but more
shares, like Amber, or more friends initially but fewer shares? Justify your answer with your calculations from
previous questions.
Answers
The spread of Carter's social media post is f(x) = 3(3)x. On Day 3, Ben's post will be received 8 shares and Carter's post will be received 27 shares. On Day 10, Ben's post will be received 524 shares and Carter's post will be received 729 shares.
What is exponential function?Amber's new function of f(x) = 3(4)x + 45 will produce a graph with a steeper slope than the original graph of Amber's photo share. Carter's post travels the fastest, as his equation form has the highest exponential rate. Depending on the goal of the post, one might prefer a post with fewer friends initially but more shares, such as Amber, or more friends initially but fewer shares, such as Ben.
Exponential function is a mathematical function that increases or decreases exponentially. It is an equation of the form y = ax^b, where a is the base and b is the exponent, and x is the independent variable.
1. The exponential function to represent the spread of Ben’s social media post is f(x) = 3(2)x.
2. The exponential function to represent the spread of Carter’s social media post is f(x) = 3(3)x.
3. The graph of Ben’s post will have a curve that increases exponentially as the x-values increase, while the graph of Carter’s post will have a curve that increases exponentially faster than Ben’s as the x-values increase. Three points that can be used to graph each curve are (0, 3), (1, 9), and (2, 27) for Ben’s post and (0, 3), (1, 9), and (2, 27) for Carter’s post.
4. On Day 3, Ben’s post will have 81 shares (f(3) = 3(2^3) = 81), and Carter’s post will have 243 shares (f(3) = 3(3^3) = 243). On Day 10, Ben’s post will have 59049 shares (f(10) = 3(2^10) = 59049), and Carter’s post will have 59049 shares (f(10) = 3(3^10) = 59049). This is shown in the equation form of the functions because each function is in the form of a(b^x). For Ben’s post, a = 3, b = 2, and for Carter’s post, a = 3, b = 3. As the x-values increase, the value of b increases exponentially and so the total number of shares increases exponentially.
5. Amber’s new function representing her photo shares is f(x) = 3(4)x + 45. The graph of this function will be different from the original graph of Amber’s photo share because it is no longer an exponential function - it is a linear function. The graph will have a constant rate of increase as the x-values increase, reflecting that the number of shares is increasing by a constant number with each additional day.
6. Based on the results, Carter’s post travels the fastest. This is shown in the equation form of the functions because Carter’s post has a larger value of b (3) than Ben’s post (2), indicating that Carter’s post is increasing exponentially faster than Ben’s post.
7. It would depend on the situation, but generally speaking it would be preferable to have more friends initially and fewer shares, like Amber. This is because if a post has few friends initially and more shares, the post will spread faster, but there is no guarantee that the post will continue to spread after it reaches its peak. If a post has more friends initially and fewer shares, the post will spread more slowly, but it is more likely to continue to spread for a longer period of time.
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Related Questions
I need this asap I need to turn it in like an hour 25points
Answers
Answer:
c. 36 people
pls mrk me brainliest
Answer:
The answer would indeed be C. 36 people.
a rectangular pizza, 35 cm by 70 cm, is cut into 24 square pieces. two round pizzas, each cut into 12 slices, also give 24 pieces. so that the pizza slices are the same size, what must be the diameter of the round pizzas? round to the nearest tenth. don't include units.
Answers
The diameter of each round pizza should be approximately d ≈ 2r ≈ 39.6
Rounding to the nearest tenth, we get a diameter of 39.6 cm.
The rectangular pizza has an area of:
35 cm x 70 cm = 2450 [tex]cm^2[/tex]
Dividing the area by 24 gives us the area of each square piece:
[tex]2450 cm^2 / 24 = 102.08 cm^2[/tex]
For the round pizzas, each slice is a sector of the circle, and the area of each sector is given by:
[tex]A = (θ/360)\pi r^2[/tex]
where θ is the angle of the sector in degrees, and r is the radius (half the diameter) of the circle.
Since each round pizza is cut into 12 slices, each slice covers an angle of:
θ = 360/12 = 30 degrees
We want the area of each slice to be equal to the area of each square piece from the rectangular pizza, which is 102.08 [tex]cm^2[/tex]. Therefore, we can set up the equation:
[tex](30/360)\pi r^2 = 102.08[/tex]
Simplifying, we get:
[tex]\pi r^2/12 = 102.08[/tex]
[tex]\pi r^2 = 1224.96[/tex]
[tex]r^2[/tex] ≈ 391.2
r ≈ 19.8
Therefore, the diameter of each round pizza should be approximately:
d ≈ 2r ≈ 39.6
Rounding to the nearest tenth, we get a diameter of 39.6 cm.
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how do you calculate volume
Answers
Answer:
Height*width*depth= volume
Identify the number as prime, composite or neither. If the number is composite, write it as the product of prime factors 360
Answers
Step-by-step explanation:
To determine whether 360 is prime, composite, or neither, we need to check if it has any factors other than 1 and itself.
We can start by finding the prime factorization of 360:
First, we can divide 360 by 2 to get 180:
360 ÷ 2 = 180
Next, we can divide 180 by 2 to get 90:
180 ÷ 2 = 90
We can continue dividing by 2 until we can no longer divide evenly:
90 ÷ 2 = 45
45 ÷ 3 = 15
15 ÷ 3 = 5
5 is a prime number, so we have found the prime factorization of 360:
360 = 2 × 2 × 2 × 3 × 3 × 5
Therefore, we can see that 360 is composite because it has more than two factors. We can write it as the product of its prime factors as shown above.
In summary, the number 360 is composite and its prime factorization is:
360 = 2 × 2 × 2 × 3 × 3 × 5
The CPI basket price for two consecutive years in five different economies are given. Determine the rate of inflation for each economy. Then
order the tiles from least to greatest inflation rate.
Answers
The greatest inflation rate was 1.78% in year1 and year2
When you have a lot of repetitive calculations to do, it is convenient to let a spreadsheet do it. Copying the given data to the spreadsheet ensures we have made no data entry errors.
The inflation rate is calculated as ...
(year 2 price)/(year 1 price) -1 . . . . . expressed as a percentage
[tex]\frac{74.30}{73.00}=1.0178\\\\\frac{76.015}{75}=1.0135\\\\\frac{89.25}{88}=1.0142[/tex]
The attachment shows the results of this calculation as applied to the economies in the order shown. The least-to-greatest order is shown in the right-most column.
The complete question is-
The CPI basket price for two consecutive years in five different economies are given. Determine the rate of inflation for each economy. Then order the tiles from least to the greatest inflation rate.
Year 1 = $73.00
Year 2 = $74.30
Year 1 = $75.00
Year 2 = $76.15
Year 1 = $88.00
Year 2 = $89.25
Year 1 = $72.50
Year 2 = $73.75
Year 1 = $79.00
Year 2 = $80.25
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The length of a rectangle is 11 cm more than twice its width. If the area of the rectangle is 6 cm", what
are the dimensions of the rectangle?
The width of the rectangle is
cm.
ation
The length of the rectangle is
cm
Answers
The width of the rectangle is 3/2 cm and the length is 17 cm.
The formula for the area of a rectangle is A = L x W, where A is the area, L is the length, and W is the width. To solve this problem, we can rearrange the formula to solve for W: W = A / L. In this case, A = 6 cm and L = 2W + 11 cm. Substituting these values, we get W = 6 / (2W + 11). We can solve this equation by dividing both sides by 2W to get 1/W = 6 / (2W + 11) * 1/2W. Simplifying, we get 1/W = 3 / (11 + 2W). Subtracting 3/11 from both sides, we get -2/11 W = -3/11. Finally, we can solve for W by dividing both sides by -2/11 to get W = 3/2 cm.
Therefore, the width of the rectangle is 3/2 cm, and the length of the rectangle is 2W + 11 = 11 + 6 = 17 cm.
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12 ft by 21 ft rectangle. How much carpeting does she need to buy to cover her entire family room?
Answers
Answer:
144 feet²
Step-by-step explanation:
12 x 12 = 144
The initial population of a town is 15 000, and it grows with a
doubling time of 10 years. What will the population be in 12 years?
24 years?
Answers
The population of the town after 12 years Aand in 24 years will be approximately 34,461 and 79,171 respectively.
What will the population be in 12 years and in 24 years?If the population doubles every 10 years, then we can use the formula for exponential growth to find the population after a certain number of years:
P = P₀ x 2^(t/T)
where:
P₀ = initial population = 15,000
P = population after t years
T = doubling time = 10 years
t = number of years
Using this formula, we can find the population after 12 years:
P = 15,000 × 2^(12/10)
P = 34,461
Therefore, the population of the town after 12 years will be approximately 34,461.
Similarly, we can find the population after 24 years:
P = 15,000 × 2^(24/10)
P = 79,171
Therefore, the population of the town after 24 years will be approximately 79,171.
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please help i have until saturday
Answers
The distance between the two points from the geometrical formula for that purpose is 6.2.
What is distance between two points in geometry?The distance between two points in geometry is the length of the straight line segment that connects the two points. It is calculated using the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse.
Using the formula;
d= √(x2 - x1)^2 + (y2 - y1)^2
d = √(7.5 - 3)^2 + (6.25 - 2)^2
d = √20.25 + 18.06
d = 6.2
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HELP NEEDED QUICK!!
Directions: Calculate the following simple interest problems. Write your answers in the space provided. Use the formula I = P × R × T and round your answers to the nearest cent or the nearest tenth of a percent. Use four decimal places for fractions of time.
(a) I = ?, P = $500, R = 8%, T = 3 months (3/12)
simple interest: $
(b) I = ?, P = $50, R = 12%, T = 1 month (1/12)
simple interest:
cents
(c) I = ?, P = $1,000, R = 18%, T = 24 months (24/12)
simple interest: $
(d) I = ?, P = $600, R = 15%, T = 60 days (60/360)
simple interest: $
(use .1667)
Answers
(a) The simplest interest is $12.
(b) The simplest interest is 5 cents.
(c) The simplest interest is $360.
(d) The simplest interest is $15.
What is the interest rate?
In relation to the amount lent, deposited, or borrowed, the amount of interest due each period is expressed as an interest rate. The total interest on a sum lent or borrowed is determined by the principal amount, the interest rate, the frequency of compounding, and the period of time over which it is lent deposited, or borrowed.
The formula of simple interest is I = P × R × T
(a) Given that P = $500, R = 8% = 0.08, T = 3 months = (3/12) years = 1/4 years
The simple interest is
500 × 0.08 × (1/4)
= $12
(b) Given that P = $50, R = 12% = 0.12, T = 1 months = (1/12) years
The simple interest is
50 × 0.12 × (1/12)
=$0.5
= 5 cents
(c) Given that P = $1,000, R = 18% = 0.18, T = 24 months = (24/12) years = 2 years
The simple interest is
1000 × 0.18 × 2
=$360
(d) Given that P = $600, R = 15% = 0.15, T = 60 days = (60/360) years
The simple interest is
600 × 0.15 × (60/360)
=$15
P is principal, R is known as rate of interest.
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An outdoor racetrack is shaped like an ellipse. The equation of the inner lane is x^2/6241 + y^2/1296=1. Each lane is approximately 1 meter apart. Find the length and width of the second lane, as indicated in the figure. Assume that the center is located at (0,0), that the track is a horizontal ellipse, and that one meter is equivalent to one coordinate unit.
ANSWER CHOICES:
A.
length = 79 m
width = 36 m
B.
length = 81 m
width = 38 m
C.
length = 158 m
width = 72 m
D.
length = 160 m
width = 74 m
Answers
The length οf the secοnd lane is apprοximately 160 meters, and the width is apprοximately 74 meters. Sο the cοrrect οptiοn is D.
We can start by nοticing that the given equatiοn [tex]x^2/6241 + y^2/1296 = 1[/tex]is the equatiοn οf an ellipse cantered at the οrigin, with a majοr axis οf length 2a = 279 = 158 and a minοr axis οf length 2b = 236 = 72. This is the equatiοn οf the innermοst lane.
Tο find the equatiοn οf the secοnd lane, we need tο add 1 meter tο bοth sides οf the equatiοn, since each lane is apprοximately 1 meter apart. This gives:
[tex]x^2/6241 + y^2/1296 = 2^2[/tex]
Simplifying, we get:
[tex]x^2/6241 + y^2/1296 = 4[/tex]
This is the equatiοn οf an ellipse with the same center as the first ellipse, but with a majοr axis οf length 2(a+1) = 280 = 160 and a minοr axis οf length 2(b+1) = 237 = 74.
Therefοre, the length οf the secοnd lane is apprοximately 160 meters, and the width is apprοximately 74 meters. Sο the cοrrect οptiοn is D.
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Theorem: For any real number x, x+∣x−5∣≥5 In a proof by cases of the theorem
A. x≤0 B. x≤5 C. x<5 D. x<0
Answers
The theorem holds for all real numbers x and the other case is that x < 5.
option C.
What is a real number?A real number is a value that represents a quantity along a continuous number line. Real numbers can be either rational or irrational. Rational numbers are numbers that can be expressed as a ratio of two integers, such as 1/2, 3/4, or -7/8.
For the given question, if one of the cases is that x > 5, we can determine the other case by considering the definition of absolute value:
If x > 5, then ∣x-5∣ = x-5 (since x-5 is positive),
so x + ∣x-5∣ = x + (x-5) = 2x - 5
which is clearly greater than or equal to 5.
If x < 5, then ∣x-5∣ = -(x-5) (since x-5 is negative),
so x + ∣x-5∣ = x - (x-5) = 5,
which is also greater than or equal to 5.
Therefore, the theorem holds for all real numbers x.
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The complete question is below:
Theorem: For any real number x, x+∣x−5∣≥5. In a proof by cases of the theorem, there are two cases. One of the cases is that x > 5.
What is the other case?
A. x≤0
B. x≤5
C. x<5
D. x<0
A statistics student wants to determine if there is a relationship between a student's number of absences, x, and their
grade point average (GPA), y. The given data lists the number of absences and GPAs for 15 randomly selected
students.
Number of
Absences
GPA
15 1 0
9
12
3
3
2.1 4.3 4.5 3.2 4.0 1.7 3.8 2.9
6
1
3.6
2 7
3.4
2.6
Using technology, the y-intercept is
O4.5, which means a student with no absences has a GPA of 4.5.
O 4.5, which means a student with no absences is predicted to have a GPA of 4.5.
O 3.79, which means a student with no absences is predicted to have a GPA of 3.79.
O 3.79, but it does not make sense to interpret the y-intercept in this context.
0 4
3.1
2.8
9 10
2.8
4.1
Answers
Answer: The correct answer is:
The y-intercept is 3.79, which means a student with no absences is predicted to have a GPA of 3.79.
Explanation:
To determine the relationship between the number of absences and the GPA, the student can use linear regression analysis. The regression line can be obtained using software such as Excel or R. The y-intercept of the regression line represents the predicted value of the response variable (GPA) when the predictor variable (number of absences) is zero.
Using technology, the y-intercept for this data set is found to be 3.79. This means that a student with zero absences is predicted to have a GPA of 3.79. Therefore, the correct answer is that the y-intercept is 3.79 and it does make sense to interpret it in this context.
Step-by-step explanation:
What is -37/76 simplified
Answers
Answer:
Already in simplest form. -37/76
Step-by-step explanation:
Nothing changes, it's the most simplified it can be.
answer #
you can't simplify the answer
Points A, B, and C are collinear. Point B is the midpoint of AC. Find the length of AB.
AB = 3x
BC = 4x − 6
Answers
Answer:
18 unitsStep-by-step explanation:
As per question, point B is the midpoint of AC.
According to definition of midpoint, AB = BC:
3x = 4x - 64x - 3x = 6x = 6The length of AB is:
AB = 3*6 = 18Answer:
AB = 18
Step-by-step explanation:
To find:-
The length of AB .Answer:-
We are here given that points A , B and C are collinear and B is the midpoint of AC . From the data provided in the question we have;
AB = 3x BC = 4x - 6 .Since B is the midpoint of AC, it will divide AC into two equal parts namely AB and BC. And these parts will be equal to one another. ( By Euclid's first axiom, Things which are half of the same thing are equal to one another.)
So we have;
[tex]\sf:\implies AB = BC \\[/tex]
[tex]\sf:\implies 3x = 4x - 6 \\[/tex]
[tex]\sf:\implies 3x -4x = -6 \\[/tex]
[tex]\sf:\implies -x = -6 \\[/tex]
[tex]\sf:\implies\red{ x = 6} \\[/tex]
Finally plug in the value of x, in the given expression of AB as ,
[tex]\sf:\implies AB = 3(x) \\[/tex]
[tex]\sf:\implies AB = 3(6) \\[/tex]
[tex]\sf:\implies \red{AB = 18} \\[/tex]
Hence the value of AB is 18 .
Add. Express your answer in standard form. (Highest exponent first and then descending order)
[tex](2x^{4} -5x^{3} -7) + (-5x^{5} -5x^{2} +9x+17)[/tex]
Answers
Answer:
The answer would be -5x^5 + 2x^4 - 5x^3 - 5x^2 + 9x + 10.
Name the type of angle indicated
Answers
Answer: Acute
Step-by-step explanation:
Acute - Less than 90 degress
Straight - Exactly 180 degrees
Obtuse - More than 90 degrees
Right - Exactly 90 degrees
Solve for x. Type your answer as a number
Answers
The numerical value of x is 3.
What is the numerical value of x?The Midsegment Theorem states that the segment joining the midpoints of two sides of a triangle is parallel to and half the length of the third side.
This simply means that:
The middle segment = half the third side
From the image:
The middle segment = x + 10The third side = x + 23Using the Midsegment Theorem
x + 10 = 1/2 × (x + 23)
Solve for x
Multiply both sides by 2
2( x + 10 ) = 1/2 ×2 (x + 23)
2( x + 10 ) = x + 23
2x + 20 = x + 23
2x - x = 23 - 20
x = 3
Therefore, the value of x is 3.
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8 to 2 but double the equivalent ratio
Answers
Answer:
Step-by-step explanation:
8:2 doubled is 16:4
When you are factoring a polynomiat and the signs of the polynomial are as follows: a x 2
+bx⋅c, the factors will have the following signs: a (t)(t) b (x) (+x) one of each d none of the above Question 2 (1 point) Give one of the prime factors of: x 2
−4x+12 a. (x−4) b (x+4) c) (x−6) d (x+6)
Answers
However, the response would be (x - 2 + 2i2)(x - 2 - 2i2) if you are searching for factors with real coefficients.
what is polynomial ?A polynomial is a mathematical expression made up of variables, factors, one or more terms, and non-negative integer exponents used in addition, subtraction, multiplication, and multiplication. Any mathematical object, including numbers, variables, and even functions, can be represented by the variables in a polynomial. In the polynomial equation 3x2 + 2x - 5 as an illustration, the coefficients are 3, 2, and -5, the variable is x, and the exponent is 2. This polynomial has the terms 3x2, 2x, and -5, each of which is denoted by a plus or negative sign. Monomials have one term, binomials have two terms, trinomials have three terms, and so on. Polynomials can be categorized based on how many terms they contain.
given
The solution to the first question is "none of the above," as the signs of the terms in a polynomial are not what determine the signs of the factors.
(x - 2i)(x + 2i) is one of the prime factors of x2 - 4x + 12, where I is the imaginary number.
However, the response would be (x - 2 + 2i2)(x - 2 - 2i2) if you are searching for factors with real coefficients.
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PLS HELP!!!!!
Find area and perimeter.
Answers
Answer:
I think it has an area of 4 and a perimeter of 8, i'm not totally sure but I thought I'd try to help
Answer:
area:4
perimeter:8ft
Step-by-step explanation:
when doing the area, you have to MULTIPLY the length by the width. For example, length:5ft width:7ft so to find the area you have to multiply both and get the answer of 35. so for the sum you have is 2 × 2 = 4
for perimeter, you have to ADD all the sides so if you have a square with all sides of 4 you add them all up which = 16. so for your sum, add them all up = 8ft
Hope it helps I'm not that good at explaining :)
Colby is making a home video consisting of a 5-minute introduction followed by several short skits. Each skit is 6 minutes long. If Colby's video is 143 minutes long, how many skits are in his video?
Answers
answer: 23
explanation - 143 - 5 = 138
(total time - the intro)
138 / 6 = 23
(remaining time divided by skit time)
A circular fountain has a radius of 11 feet. Find the area in terms of pi
Answers
[tex]\mathcal{A} = \pi r^{2} = \pi (11^{2}) = 121 \pi \ ft^{2}[/tex]
Answer:
121 pi divide to 4
Step-by-step explanation:
the answer is 121 pi divide to 4. please see it on the picture.
70.61% of 736.97cm
Give your answer rounded to 2 DP.
Answers
Answer:
520.37 cm
Step-by-step explanation:
apply equation:
x = 736.97(0.7061) = 520.374517
Notice 70.61% is the same as 0.7061 (just divide by 100)
now you need to round to 2 DP
x ≈ 520.37
so the 70.61% of 736.97cm is 520.37 cm
Philip's meal costs $14.50 at a local restaurant. The server did their job very well and Philip would like to a 20% tip. What amount of money should he leave as a tip?
Answers
Answer:
$2.90
Step-by-step explanation:
We know
Philip's meal costs $14.50 at a local restaurant. Philip would like to a 20% tip
20% = 0.2
14.50 x 0.2 = $2.90
So, he should leave $2.90 as a tip.
Find the values of p
for which the integral converges. And evaluate the integral for those values of p
.
a
)
∫
1
0
3
1
x
p
d
x
b
)
∫
[infinity]
e
25
x
(
ln
x
)
p
d
x
Answers
a) For the integral ∫01^3 1/x^p dx to converge, p > 0. Evaluating the integral for those values of p gives ∫01^3 1/x^p dx = -1/(p-1).
b) For the integral ∫[infinity]^e 25/x^(lnx)^p dx to converge, p > 1. Evaluating the integral for those values of p gives
∫[infinity]^e 25/x^(lnx)^p dx = -25/(p-1).
Convergence and divergence. The improper integral is said to converge if the limit is both real and a limited integer.
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A school supplier sells boxes of A4 paper for £4, and offers a £2 discount on any order paid for in advance. Write the formula the supplier would use for calculating what to charge for any order paid in advance. Use n to represent the number of boxes purchased.
Answers
When calculating the price of an order that has been paid in advance, the school supplier will use the following formula:
4n - 2
The ordering cost formula is useful for calculating the economic order quantity and gives businesses insight into how
much of an item is necessary to meet customer demand and fulfill sales goals.
These ordering costs can include shipping fees, unexpected transportation costs, inspection fees and other expenses
necessary to acquire inventory products. Essentially, any money your company spends to place and receive inventory
orders accounts for the purchasing and ordering costs.
Where n represents the number of boxes purchased.
The school supplier sells boxes of A4 paper for £4, and a £2 discount is given on any order paid for in advance.
Formula for calculating what to charge for any order paid in advance:
To calculate the price for an order paid in advance, the formula 4n - 2 should be used.
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prove that the altitude to the base of an icosceles triangle is also the following. The median to the base please dont make it to much of a crazy explanation i need to copy and paste it lol.
Answers
We οbserve that the line segment AM frοm vertex A tο midpοint M οf base BC alsο bisects BC, since M is the midpοint οf BC. Therefοre, we have AM = BM = MC = BC/2.
What is Isοsceles triangle?An isοsceles triangle is type οf triangle that has the twο sides οf equal length. In isοsceles triangle, angles οppοsite equal sides are alsο equal in measure. The third side οf isοsceles triangle is called base.
Tο prοve this, we can cοnsider the fοllοwing diagram οf an isοsceles triangle ABC with base BC:
A
/ \
/ \
/ \
/ h \
B------------C
where h is the altitude tο the base BC and M is the midpοint οf the base BC. We want tο shοw that the line segment AM is alsο the median tο the base BC.
First, we οbserve that the triangle ABC is isοsceles, sο the twο legs AB and AC are cοngruent. Therefοre, the altitude h frοm vertex A tο base BC bisects BC, which means that BM = MC = BC/2.
Secοnd, we οbserve that the line segment AM frοm vertex A tο midpοint M οf base BC alsο bisects BC, since M is the midpοint οf BC. Therefοre, we have AM = BM = MC = BC/2.
Thus, we have shοwn that the altitude tο the base and the median tο the base οf an isοsceles triangle are the same line segment, which cοmpletes the prοοf.
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What is the area of a sector with a central angle of 90° and a diameter of 20.6 mm?
Use 3.14 for and round your answer to the nearest hundredth.
Enter your answer as a decimal in the box.
mm²
Answers
Answer:
37.03 sq. mm.
Step-by-step explanation:
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The ratio of 2 institutions is 7 : 3 and their sum is 630. Find the number
Answers
the first institution has 441 and the second institution has 189.
We can use algebra to solve the problem. We can start by assigning variables to represent the two institutions:
Let x be the multiplier of the ratio.
Then, we have:
7x is the first institution.
3x is the second institution.
From the problem, we know that the sum of the two institutions is 630:
7x + 3x = 630
Simplifying the left side, we get:
10x = 630
Dividing both sides by 10, we get:
x = 63
Now that we know the value of x, we can find the number of each institution:
First institution = 7x = 7(63) = 441
Second institution = 3x = 3(63) = 189
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