Andrea should show that c = 2 so ΔABC = ΔRTS and ∡C = ∡S hence ∡C may be a right angled triangle since it's the angle opposite to the hypotenuse c and so, ΔABC could be a trilateral.
According to the statement
We have to prove that the ABC is a right triangle.
So, For this purpose, we know that the
A right-angled triangle is a type of triangle that has one of its angles equal to 90 degrees.
From the given information:
Andrea should show that c = 2, so: ∡ABC = ∡RTS and ∡C = ∡S. Hence, ∡C could be a right angled triangle, hence ΔABC could be a trilateral.
And
In this question, we are told that the given sides of the Triangle are a, b and c. Now, Andrea is in a position to draw the 2 sides of the correct triangle with sides = a and b and therefore the third, hypotenuse capable 2. Since the length of the hypotenuse = 2, then we have;
2² = a² + b²
However, we are told that c² = a² + b²
Therefore, c = 2
Hence, Andrea should show that c = 2 so ΔABC = ΔRTS and ∡C = ∡S hence ∡C may be a right angled triangle since it's the angle opposite to the hypotenuse c and so, ΔABC could be a trilateral.
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Find the exact value of the following expression
The exact value of the expression is -1/2
Trigonometry identityGiven the following trigonometry value
sin 5π/3
Since the value of π is 180 degrees, hence;
sin 5(180)/3
sin 5(60)
sin 300
This can be written as;
sin(360 - 30) = -sin30
sin(360 - 30) = -(1/2)
Hence exact value of the expression is -1/2
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An elite private college receives large donations from successful alumni. The account that holds these donations now has $955 million.
How much would the account earn in 1 year of simple interest at a rate of 2.33%? Round to the nearest dollar.
Answer
$22,251,500
How much would the account earn in 1 year at 2.33% if the interest was compounded daily? Round to the nearest dollar.
Answer
$22,512,028
How much more interest is earned by compounding daily as compared to simple interest?
Answer
$260,528
If the money is used to pay full scholarships, and the price of tuition is $61,000 per year, how many more students each year can receive full 4-year scholarships if the interest were compounded daily rather than using simple interest?
Answer
One, since each 4-year (full) scholarship is worth $244,000.
1. The private college's tuition account can earn $22,251,500 in simple interest at 2.33% in one year.
2. The account would earn $22,512,028 in one year at 2.33% interest compounded daily.
3. The difference between daily compound interest and simple interest is $260,528.
4. If the money is used to pay full scholarships, and the tuition price is $61,000 per year, 4 more students can receive full 4-year scholarships with daily compounding instead of simple interest.
What is the difference between simple interest and compound interest?Compound interest adds the earned interest to the principal and periodically compounds the new total, unlike simple interest.
Data and Calculations:1) Simple Interest:
Principal = $955 million
Period = 1 year
Interest rate = 2.33%
Simple Interest = $22,251,500 ($955,000,000 x 2.33% x 1)
2) N (# of periods) = 365 days
I/Y (Interest per year) = 2.33%
PV (Present Value) = $955,000,000
PMT (Periodic Payment) = $0
Results:
FV = $977,512,028.18
Total Daily Compound Interest = $22,512,028.18
3) The difference between daily compound interest and simple interest is $260,528 ($22,512,028 - $22,251,500).
4) Price of tuition per year = $61,000
Additional earnings from compounding interest = $260,528
Additional students to sponsor for tuition each year = 4.27 ($260,528/$61,000).
Thus, compound interest earns more for the investor than simple interest.
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Shauna drove 75 miles in 3 hours at a constant speed. How many miles did she drive in 2 hours?
f. 2.5 miles
g. 50 miles
h. 75 miles
i. 100 miles
The total distance traveled in 2-hour time is 50 miles. (option g)
Shauna drove 75 miles in 3 hours at a constant speed, so the total distance covered in 3 hours is 75 miles to find the distance covered in 2 hours, we first need to find the distance or miles covered in 1 hour
To find the distance Shauna traveled in 2 hours, use the following formula: –
Speed = distance/time
Total distance traveled = 75 miles
Total time = 3 hours = 3 hours
Speed = 75/3
Speed = 25 miles per hour
Distance traveled in 2-hour time is 50 miles.
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please help if you can, vv appreciated!!
Answer:
I believe 72
Step-by-step explanation:
Write the equation of the circle that passes through the given point and has a center at the origin. (Hint: You can use the distance formula to find the radius.) (0,4)
The equation of the circle that passes through the point (0 , 4) and has a center at the origin is x^2 + y^2 = 16.
Using the distance formula, get the radius of the circle by solving for the distance between the center and the point (0 , 4).
radius = distance = √(x2 - x1)^2 + (y2 - y1)^2
radius = √(0 - 0)^2 + (4 - 0)^2
radius= √0 + 16
radius = 4
The standard form of the equation of the circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.
Given the radius and center of the circle, substitute these values to the standard form of the equation of the circle.
(x - h)^2 + (y - k)^2 = r^2
where (h , k) = (0 , 0)
r = 4
(x - 0)^2 + (y - 0)^2 = 4^2
x^2 + y^2 = 16
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Rotation 90° counterclockwise around the
origin of the point (-8, 3)
(8,3)
(3,8)
(-8,-3)
(-3,-8)
The answer is (-3.-8)
When we rotate a point 90° counterclockwise around the origin, it's the same as rotating it 270° clockwise around the origin.
When we rotate something 270° clockwise around the origin, the original coordinates (x, y) becomes (-y, x).
Clockwise Rotations (CW) follow the path of the hands of a clock. These rotations are denoted by negative numbers. Counterclockwise Rotations (CCW) follow the path in the opposite direction of the hands of a clock. These rotations are denoted by positive numbers.
The angle of rotation between the two points or vertices is the number of central angles times the measure of a single central angle: angle of rotation =m×α = m × α .
y is 3, and -(3) is just -3, since multiplying negatives make a negative.
x just remains x, but it's in a different position.
This makes the new coordinate (-3, -8)
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the 4th and 5th terms of a GP are -13.5 and 40.5 find the first term and the sum of the first five terms
Answer:
First term: 0.5
Sum of the first give terms: 30.5
Step-by-step explanation:
General form of a geometric sequence:
[tex]a_n=ar^{n-1}[/tex]
where:
[tex]a_n[/tex] is the nth terma is the first termr is the common ratioGiven terms:
[tex]a_4=-13.5[/tex][tex]a_5=40.5[/tex]To find the common ratio r, divide consecutive terms:
[tex]\implies r=\dfrac{a_5}{a_4}=\dfrac{40.5}{-13.5}=-3[/tex]
To find the first term, substitute the found value of r and one of the terms into the general formula:
[tex]\begin{aligned}\implies a_5 =a(-3)^4 & = 40.5\\81a & = 40.5\\a & = \dfrac{40.5}{81}\\a & = 0.5 \end{aligned}[/tex]
Sum of the first n terms of a geometric series:
[tex]S_n=\dfrac{a(1-r^n)}{1-r}[/tex]
To find the sum of the first 5 terms of the geometric sequence, substitute n = 5 and the found values of a and r into the formula:
[tex]\begin{aligned}\implies S_5 & =\dfrac{0.5(1-(-3)^5)}{1-(-3)}\\\\& =\dfrac{0.5(1+243)}{1+3}\\\\& =\dfrac{0.5(244)}{4}\\\\& =\dfrac{122}{4}\\\\ & = 30.5\end{aligned}[/tex]
Therefore, the sum of the first 5 terms is 30.5.
Solve for y in terms of x
5x+y=31
Answer: y=31-5x
Step-by-step explanation:
subtract the 5x to the other side to get y.
A certain days plant grows 1 1/6 inches every week.how long will it take the plant to grow 6 1/6 inches
Answer: The amount of long will it take the plant to grow is [tex]5\frac{2}{7}[/tex] weeks.
Step-by-step explanation:
Given data,
A certain days plant grows 1 1/6 inches
It take the plant to grow 6 1/6 inches
Let us assume,
A certain days plant grows = x
It take the plant to grow = y
So ,
we can write,
x = 1 and 1/6
x = 1*1/6
L.C.M is '6',
Then,
x = (6+1) / 6
x = 7/6
Then,
y = 6 and 1/6
y = 6*1/6
y =(1+36) / 6
y = 37/6
So, divide y/x = (37/6) / (7/6)
= 37/6 * 6/7
L.C.M is 42
= 222/42
= 5 12/42
= 5 2/7 weeks
Therefore,
The amount of long will it take the plant to grow is [tex]5\frac{2}{7}[/tex] weeks.
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REASONING If an exterior angle adjacent to \angle A is acute, is Δ A B C acute, right, obtuse, or can its classification not be determined? Explain your reasoning
The exterior angle is acute, the sum of the farthest interior angles must also be acute, implying that the third angle is obtuse. As a result, every triangle should be obtuse.
What exactly is indeed an obtuse-angled triangle?An obtuse-angled triangle has one of its interior provides a clear view than 90°.. If one angle in an obtuse triangle measures upwards of 90°, the combination of the remaining two angles is a little less than 90°.
Briefly:if the exterior angle is acute, this same sum of something like the remote interior angles must also be acute, implying that the third angle is obtuse. As a result, the triangle must be obtuse. Furthermore, because the exterior angle and A form a linear pair, A must be obtuse because consecutive acute angles cannot form a linear pair.
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How do i do this problem
Identify the hypothesis and conclusion of conditional statement.
If three points lie on a line, then they are collinear.
The hypothesis is the phrase following the word if = " three points lie on a line"
The conclusion is the phrase following the word then = "they are collinear."
What is hypothesis?A specific, verifiable prediction of what the researcher(s) believe the study's results will be is known as a hypothesis (plural: hypothese). It is stated at the outset of the investigation.
Most often, this entails speculating on a potential correlation between two variables: the independent variable (what the researcher modifies) and the dependent variable (what the research measures).
The null hypothesis and the alternative hypothesis (known as the experimental hypothesis when the technique of examination is an experiment) are traditionally written as two separate forms of the hypothesis in research.
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Find an equation doe the line that is tangent to the curve y=3x^3-3x at the point (-1,0)
The tangent to the given curve at the point (1,0) is: y=6x-6.
What is tangent?The straight line that "just touches" the curve at a given location is referred to as the tangent line to a plane curve in geometry. It was described by Leibniz as the path connecting two points on a curve that are infinitely near together.When you ride a bicycle, every point on the wheel's circumference forms a tangent with the road, providing a practical illustration of a tangent.When you ride a bicycle, every point on the wheel's circumference forms a tangent with the road, providing a practical illustration of a tangent.A straight line that only touches a circle once is said to be tangent to it. The term "point of tangency" refers to this location.The first derivative f'(x), the slope (tangent) of the original curve, may be obtained at every point (x,y) on the curve because the supplied curve is a continuous function, making Eq. 1 differetiable at every x.
The slope of the tangent at x=1 is given by the first derivative of Eq. 1: f'(1)=9(1)2-3=6.
A line that passes through the point (x1, y1) and has a slope of m has the equation:
(y-y1)=m(x-x1) ··· Eq.2 (the point- slope form of linear function)
Here, x1=1, y1=0, and m=f'(x1)=6. Add these numbers to Eq. 2. It is possible to repeat and simplify Eq. 2 as follows: y-0=6(x-1) ⇒ y=6x-6
Consequently, y=6x-6 is the tangent to the given curve at position (1, 0).
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Solve each equation. 3(2-c)=-(c+4)
The solution of the given equation 3(2-c)=-(c+4) is c = 5.
According to the given question.
We have an equation
3(2 - c ) = -( c + 4)
Since, we have to solve the above equation for c.
Therefore, the solution of the above equation is gievn by
3(2 - c) = -( c + 4)
⇒ 3(2) -3(c) = -c -4 (by distributive law)
⇒ 6 -3c = -c - 4
⇒ 6 + 4 -3c = -c (adding 4 both the sides)
⇒ 10 -3c = -c
⇒ 10 = -c + 3c ( adding 3c both the sides)
⇒ 10 = 2c
⇒ 10/2 = c (multiply both the sides by 2)
⇒ 5 = c or c = 5
Hence, the solution of the given equation 3(2-c)=-(c+4) is c = 5.
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Which of the following statements describe the steps to copy XY? Select all that apply.
X
OA. Use a ruler to draw line and label point M.
OB. Use a straightedge to draw line and label point M.
OC. Place a compass point at X and open the compass to length XY.
OD. Using the same setting, place the compass point at M, draw an arc through line , and mark point N as t
If the arithmetic mean of 6 x, 3 x , and 27 is 18, then what is the value of x?
A. 2
B. 3
C. 5
D. 6
According to the given data" the arithmetic mean of 6 x, 3 x , and 27 is 18" the value of x = 3.
What exactly does arithmetic mean?The arithmetic mean or average, or simply the mean or average, is indeed the sum of a set of numbers multiplied by the number of numbers in the set.
How can we find the arithmetic mean?One approach is to compute the arithmetic mean. To do this, add all of the values together and divide the total by the number pf values. For example, if you have a set of "n" numbers, add them together as follows: a + b + c + d, and so on. Then divide the total by "n."
According to the given data:If the arithmetic mean of 6 + x, 3 + x , 27 = 18
So value of x will be as follows:
(6x + 3x + 27)
(6x + 3x + 27)/3 = 18
9x+27/3 = 18
9x +27 = 54
x = (54-27)/9
x = 27/9
x = 3
According to the given data the value of x = 3.
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In China, the highest elevation is Mount Everest and the lowest elevation is Turpan Pandi. Mount Everest is located at 8850 m above sea level. Turpan Pandi is located at -154 m. What is the distance between the highest and the lowest points of elevation?
PLEASE I NEED HELP GREATLY APPRECIATE IT!
The distance between the highest and the lowest points of elevation is 9904 meters.
What is the distance?In order to determine the distance between the highest and the lowest points of elevation, subtract the heights of both places from each other.
Subtraction is a mathematical operation that is used to determine the difference between two or more numbers. The sign used to denote subtraction is -.
Height of mount Everest - height of Turpan Pandi
8850 - (-154)
8850 + 154 = 9004m
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The sum of four consecutive is 490. What are the four consecutive integers
The four consecutive integers are 121, 122, 123, 124.
We have the sum of four consecutive integers equals to 490
We have to determine those integers.
What are Integers?An integer is a number with no decimal or fractional part. It includes negative and positive numbers, including zero.
Assume the first integer is x. Then, the other integers will be -
x + 1 , x + 2 , x + 3.
Therefore -
x + (x + 1) + (x + 2) + (x + 3) = 490
4x + 6 = 490
4x = 484
x = 121
So -
x = 121
x + 1 = 122
x + 2 = 123
x + 3 = 124
Hence, the four consecutive integers are 121, 122, 123, 124.
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Mike sold 5,640 chickens and 5,732 ducks from his farm. He
made $79,696. If he sold 5,640 chickens and 5,640 ducks, he
would get $78,960. How much money did he make from
selling the 5,732 ducks?
$
The number of money farmers made by selling 5732 ducks will be $45856.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that Mike sold 5,640 chickens and 5,732 ducks from his farm. He made $79,696. If he sold 5,640 chickens and 5,640 ducks, he would get $78,960.
Form two equations to get the amount:-
5640c + 5732d = 79696
5640c + 5640d = 78960
Solve both the equations by elimination method:-
5640c -5640c + 5732d - 5640d = 79696 - 78960
92d = 736
d = 736 / 92
d = $8
Total amount = $8 x 5732 = $45856
Therefore, the money farmers made by selling 5732 ducks will be $45856.
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Write each arithmetic series in summation notation. 5+8+11+ . . . . . . +38
Using the summation notation, the series 5+8+11+ . . . . . . +38 can be written as
[tex]\sum\limits^{12}_{n=1} {(3n+2)}[/tex] or [tex]24+3\sum\limits^{12}_{n=1} {n}[/tex]
Given an arithmetic series:
5+8+11+ . . . . . . +38
The common difference (d) of each term is:
d = 8 - 5 = 3
The first term, a(1) = 5.
Hence, using the formula for the nth term of an arithmetic sequence:
a(n) = a(1) + (n-1) . d
a(n) = 5 + (n-1) . 3
a(n) = 3n + 2
Let us find n that result in a(n) = 38
a(n) = 3n + 2
38 = 3n + 2
3n = 36
n = 12
We can, then, conclude that the series 5+8+11+ . . . . . . +38 has 12 terms.
Therefore, the summation notation is:
[tex]\sum\limits^{12}_{n=1} {a(n)} = \sum\limits^{12}_{n=1} {(3n+2)}[/tex]
[tex]= \sum\limits^{12}_{n=1} {3n}+ \sum\limits^{12}_{n=1} {2}[/tex]
[tex]= 3\sum\limits^{12}_{n=1} {n}+ 2\times 12[/tex]
[tex]= 24+3\sum\limits^{12}_{n=1} {n}[/tex]
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Simplify each expression by rationalizing the denominator.
3√5/√11
The simplified expression after rationalizing the denominator is [tex]3\sqrt{55} / 11[/tex].
The given expression is,
[tex]3\sqrt{5} /\sqrt{11}[/tex] equation 1
Name the given expression as equation 1.
To simplify the given expression first we need to rationalize the denominator that is [tex]\sqrt{11}[/tex] .
To rationalize the denominator we need to multiply and divide the given equation 1 by [tex]\sqrt{11}[/tex] . On multiplying and dividing the given equation 1 by [tex]\sqrt{11}[/tex], we will get
[tex]3\sqrt{5} /\sqrt{11}[/tex] = ( [tex]3\sqrt{5}[/tex] ×[tex]\sqrt{11}[/tex])/([tex]\sqrt{11}[/tex] ×[tex]\sqrt{11}[/tex])
On further simplifying the expression , we will get
= ([tex]3\sqrt{5}[/tex] × [tex]\sqrt{11}[/tex])/11 = [tex]3\sqrt{55} / 11[/tex]
So, we can conclude that the simplified expression after rationalizing the denominator is [tex]3\sqrt{55} / 11[/tex].
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What is the radius of a table with a circumference of 10 feet?
A. 1.6 ft B. 2.5 ft
C. 3.2 ft D. 5 ft
The radius of a table with a circumference of 10 feet is A. 1.6 ft .
What is circumference of circle?A circle's outside boundary is called the circumference and can be measured, or calculated, by using
Circumference = 2πr
where r is the radius of circle.
Now it is given that,
Circumference of table = 10 feet
Since, Circumference = 2πr
⇒ 2πr = 10
⇒ r = 10/2π
⇒ r = 10/6.28
⇒ r = 1.59
⇒ r ≈ 1.6 feet
Thus, the radius of a table with a circumference of 10 feet is A. 1.6 ft
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b. Is there a pattern in the table? Explain.
Answer:
no photo
Step-by-step explanation:
we need a photo to decide if answer is correct or not
Let f(x)=2x-1, g(x)=3x, and h(x) = x² + 1. Compute the following:
f(g(-3)) =
Answer:
Step-by-step explanation:g(-3) = 3(-3) = -9
f(g(-3)) = f(-9) = 2(-9) -1 = -18 -1 = -19
Function his a transformation of the parent exponential function, f(2)= 2º.
h(z)=-3-2²
Which statement is true?
A. Function h is a horizontal translation of function f
OB.
Function h is a reflection and a translation of function f
OC. Function h is a vertical translation of function f
OD. Function his a reflection and a dilation of function
According to the question, the true statement is the function 'h' is a vertical translation of a function ''f.
What is exponential function?
The exponential function can be defined as the base of two with the integer powers. The base can be represented as common factors as well as common multipliers. The graph representation of the exponential function can be called as "rate of change". It either increases or decreases or constant with respect to another functions.
The transformation of a function can be performed either with translation, reflection, vertical sliding or horizontal sliding. It can be done with the help of the calculated values known as asymptotic. And the end behavior of the function is always consistent.
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1/2(12x+10)+2×
simplify
Simplify each expression.
3 . (4-8) / 2
3 . (4-8) / 2
= 3. (-4) /2
= 3. ( -2)
= -6
What is algebric equation?In algebraic equation or polynomial equation is an equation of the frame P=0 where P could be a polynomial with coefficients in a few field, regularly the field of the rational numbers.
algebraic equation, statement of the equality of two expressions defined by applying to a set of factors the algebraic operations, namely, expansion, subtraction, increase, division, raising to a control, and extraction of a root.
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Find the sum of each infinite geometric series. 0.5+0.05+0.005+ . . . .
The sum of the infinite geometric series 0.5+0.05+0.005+ . . . is S = 0.55556
The given geometric series is:
0.5 + 0.05 + 0.005 + . . .
The common ratio (r) of a geometric series is given by:
r = a(n) / a(n - 1)
Notice that in the given series:
a(1) = 0.5
a(2) = 0.05
a(3) = 0.005
Hence, the common ratio is
r = a(2) / a(1) = 0.05/0.5 = 0.1
Since 0 < r < 1, the series is convergent and the sum exists.
Use the sum formula:
S = a(1) / (1 - r)
Substitute a(1) = 0.5 and r = 0.1 into the formula:
S = 0.5 / (1 - 0.1)
= 0.5 / (0.9)
= 0.55556
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Consider flipping coins until either two heads hh or heads then tails ht first occurs. by conditioning on the first coin toss, find the probability that ht occurs before hh.
The probability that ht occurs before hh IS 1/3
Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.
P(HH)=1/4
P(HT)=1/4
p(HT) = ½×p(TH) + ½×1 = p(TH)/2 + 1/2.
p(HH) = p(HH)/2
p(HT) = p(TH)/2 + 1/2
p(TH) = p(HH)/2 + p(HT)/2
p(TT) = p(TH)/2 + p(TT)/2
p(HH) = 0.
p(TH) = p(HT)/2
p(HT) = p(HT)/4 + 1/2
p(TH) = 1/3
p(TT) = p(TH) implies p(TT) = 1/3
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Sora Nakai had sales of $67,264.
Answer:
Could you explain the problem a bit more?
Step-by-step explanation:
