Answers
The proof of the above parallelogram is given as follows.
What is the proof that shows that AB ≅ CD and BC ≅ DA?Statement Reason
ABCD is a parallelogram. GivenDraw AC (See Attached) Unique Line postulate∠DCA and ∠BCA are alt. Interior angles Def. of Alt. Int. AnglesAB ║ CD Def. of parallelogramBC ║DA Def. of parallelogram∠BCA and ∠DAC are alt. int. angles Def. of Alt. Int. Angles∠BCA ≅ DAC Alt. Int. Angles theorem∠DCA ≅ ∠BAC Alt. Int. Angles theoremAC ≅ AC Reflexive propertyΔABC ≅CDA ASAAB ≅ CD CPCTCBC ≅ DA CPCTCLearn more about Parallelograms:
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Related Questions
two supplementary angles differ by 34. find the angles..
Answers
Answer:
107°
73°
Step-by-step explanation:
Let the two supplementary angles be x° and y°.
x + y = 180....(1)
Since, supplementary angles differ by 34.
Therefore,
x - y = 34....(2)
Adding equations (1) & (2)
x + y = 180
x - y = 34
_________
2x = 214
x = 214/2
x = 107°
Plug x = 107 in equation (1)
107 + y = 180
y = 180- 107
y = 73°
5% of what number is 29?
Answers
Answer:
1,45
Step-by-step explanation:
\( \frac{29 \times 5\%}{100\%} = 1.45\)
Consider the following system of equations given in slope-intercept form.
y = −1
3
x + 17,
y = 5x - 23
Use the graphing calculator to determine the best window range to find the point of intersection.
–10 Less-than-or-equal-to x Less-than-or-equal-to 10, –10 Less-than-or-equal-to y Less-than-or-equal-to 10
–20 Less-than-or-equal-to x Less-than-or-equal-to 0, –20 Less-than-or-equal-to y Less-than-or-equal-to 0
0 Less-than-or-equal-to x Less-than-or-equal-to 20, 0 Less-than-or-equal-to y Less-than-or-equal-to 20
20 Less-than-or-equal-to x Less-than-or-equal-to 40, 20 Less-than-or-equal-to y Less-than-or-equal-to 40
answer: c.0 Less-than-or-equal-to x Less-than-or-equal-to 20, 0 Less-than-or-equal-to y Less-than-or-equal-to 20
Answers
Option c. The range of window for the data is given as 0 Less-than-or-equal-to x Less-than-or-equal-to 20, 0 Less-than-or-equal-to y Less-than-or-equal-to 20
How to solve for the range of the dataWe have the equation to be
y = −3x + 17,
and y = 5x - 23
We have to make the two equations to be equal
This would then give us
−3x + 17 = 5x - 23
The next step is to take the like terms
3x - 5x = -23-17
-2x = -40
From you we have to divide by -2
x = 20
The range would be written as
0 ≤ x ≤ 20, 0 ≤ y ≤ 20
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what is the chemical formula of water.
Answers
Answer:
Guess its H2
Step-by-step explanation:
prove me wrong
Answer: H2O is the answer
If f(x) = 2x - 9, which of the following are correct? Select all that apply. f(-1) = -11 f(2) = 5 f(3) = -3 f(0) = -9 f(-3) = 15
Answers
f(-1) = -11 and f(3) = -3 . these functions are true .
What does a math function mean?
A relationship between a group of inputs and one output each is referred to as a function. A function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. f(x), where x is the input, is a common way to refer to a function.In mathematics, a function is an expression, rule, or law that establishes the relationship between two variables (the dependent variable).given function f(x) = 2x - 9
f(-1) = -11 ⇒ x = -1 put in function
f( -1 ) = 2 * -1 - 9 ⇒ - 11
f(2) = 5 ⇒ x = 2 put in function
f( 2 ) = 2 * 5 - 9 = 1
f(3) = -3 ⇒ x = 3 put in function
f ( 3 ) = 2 * 3 - 9 = -3
f(-3) = 15 ⇒ x = -3 put in function
f( -3) = 2 * -3 - 9 = - 15
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Jimmy works at a carnival to raise money for his church. He sold chips and sodas. Chips were sold for $1.50 each. Sodas were sold for $1.75 each. Jimmy sold 150 items in total. Of the items sold 2/5 were chips and the remaining items were sodas. How much money did Jimmy raise from the sodas that were sold?
*
10 points
$90.00
$157.50
$43.50
$70.50
Answers
Answer:
$ 157.50
Step-by-step explanation:
2/5 of 5 items = 1.50(2) +1.75(3) =3+5.25 = 8.25 150 / 5 Items = 30 of (3) = 90 sodas therefore = 30 *5.25 = 157.5 = $ 157.50
It was 12°C when Preston got home from school.
The weather report shows a storm front moving
in that will drop the temperature by 17°C. What
is the expected temperature
Answers
Answer:
-5 degrees C
Step-by-step explanation:
drop indicates minus
12-17=-5
-5 degrees C
Rationalize the denominator 1/ (5-2√3)
Answers
\(\qquad\)_________________________
\(\bf Multiplying\:by\:\: \purple{ \dfrac{5+\sqrt{3}}{5+\sqrt{3}}}\\\)
\(\qquad\)\( \longrightarrow \bf \dfrac{1}{5 - 2\sqrt{3} } \times \dfrac{5 + 2\sqrt{3} }{5 + 2\sqrt{3} }\\ \)
\(\qquad\)\(\longrightarrow \sf \dfrac{1(5 + 2\sqrt{3}) }{(5 - 2\sqrt{3})(5 + 2\sqrt{3}) } \)
\(\qquad\)\(\longrightarrow \sf \dfrac{5 + 2\sqrt{3} }{ {(5)}^{2} - (2 \sqrt{3})^{2} } \)
\(\qquad\)\( \longrightarrow \sf \dfrac{5 + 2 \sqrt{3} }{(5 \times 5) - (2 \times 2 \times \sqrt{3} \times \sqrt{3} )} \)
\(\qquad\)\( \longrightarrow \sf \dfrac{5 + 2 \sqrt{3} }{(25) - (12)} \)
\(\qquad\)\( \purple{ \longrightarrow \bf \dfrac{5 + 2 \sqrt{3} }{13} } \)
\(\qquad\)_________________________
Answer is 2/(5+√13)
Rationalize the denominator 1/ (5-2√3)
Consider the following series. [infinity] Σ n = 1 2^(n + 1) . 3^−n. Determine whether the geometric series is convergent or divergent. Justify your answer. O Converges; the series is a constant multiple of a geometric series. O Converges; the limit of the terms, an, is 0 as n goes to infinity. O Diverges; the limit of the terms, a, is not 0 as n goes to infinity. O Diverges; the series is a constant multiple of the harmonic series.
Answers
Converges; the series is a constant multiple of a geometric series. Option A.
The given series can be written as:
\(\sum n=1 to \ \infty 2^{(n+1)} * 3^{(-n)\)
= 2 * ∑n=1 to ∞ (2/3)^n
This is a geometric series with first term a=2 and common ratio r=2/3. The series converges if and only if |r| < 1. Here, |r| = 2/3 < 1, so the series converges.
The sum of a convergent geometric series with first term a and common ratio r is given by:
sum = a / (1 - r)
Applying this formula, we get:
sum = 2 / (1 - 2/3) = 2 * 3 = 6
Therefore, the given series converges to 6.
The correct answer is option (a) Converges; the series is a constant multiple of a geometric series.
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Find the fith term in the sequence.. Pls help!
Answers
The fifth term in the sequence is 3
What is a sequence?
Mathematical sequences are lists of elements, usually integers, where the order of the elements is important. Here, the components all fit into a precise pattern. In everyday life, sequences appear frequently. Sequences include, for instance, a row of house numbers, a pay increase each year (by a defined dollar amount or percentage), a book's page numbers, etc.
\(a_{n} = 4 + ( -1 )^n\)
Substitute n=5
\(a_{5} = 4 + ( -1 )^5\)
= 4 + (-1)
= 4 - 1
= 3
So, the fifth term in the sequence is 3
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what percentage of $600 is $30?
Answers
Answer:
5%
hope its help
A business reports a net income of -$2,730 over a 3-month period. What is the average
income per month for that period?
Answers
Answer:
-910
Step-by-step explanation:
Answer:
The answer is $910, all you do is take the income and divide it by the number of months to find the average.
Step-by-step explanation:
Avery has a loyalty card good for a discount at her local pharmacy. The item she wants to buy is priced at $6, before discount and tax. After the discount, and before tax, the price is $5.04. Find the percent discount.
Answers
Answer:
16% is the answer.
Answer:
16%
Step-by-step explanation:
$6 divided by $5.04 = 0.84
0.84 x 100 = 84%
100 - 84 = 16
6 - 5.04 = 0.96
0.96 divided by 6 = 0.16
0.16 x 100 = 16
2 times the radius equals the....
Answers
Answer:
diameter
Step-by-step explanation:
double the radius is the diameter
If 4.5 pounds of cherries cost $10, what is the unit price?
Answers
what is 48,020,000 expressed in scientific notation? I need help i don't understand please
Answers
To put the number in scientific notation must put it between 1 and 10 times 10^x
Where x is the number of decimals
48,020,000 = 4.802 * 10^x
To find x count that we move the decimal point how many places
The decimal point is after the last zero
How many places to be between 4 and 8
There are 7 places between the last 0 and 4
So the answer is
\(4.8020\times10^7\)PLEASE HELP ME
What is the surface area of the cylinder? Approximate using π = 3.14 and round to the nearest square meter.
a cylinder with a radius labeled 2.6 meters and height labeled 6.1 meters
82 square meters
91 square meters
96 square meters
142 square meters
Answers
The surface area of the cylinder, rounded to the nearest square meter, is: D. 142 square meters
What is the Surface Area of a Cylinder?The surface area of a cylinder can be calculated by using the formula expressed as:
SA = 2\(\pi\)r(h + r), where r is the radius and h is the height.
Given the following:
\(\pi\) = 3.14
radius (r) = 2.6 m
height of the cylinder (h) = 6.1 m
Plug in the values:
\(\sf SA = 2 \times 3.14 \times 2.6 \times (6.1 + 2.6)\)
\(\sf SA \thickapprox 142\) square meters (rounded to the nearest square meter)
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of a pizza remains, and Seth and Ethan want to split it evenly. What fraction of the original pizza will each get?
Answers
Answer:
\(\huge\boxed{\text{Multiply the denominator by 2, or}}\\\\\huge{\boxed{\text{divide the percentage by 2}}}}\)
Step-by-step explanation:
Because there is no fraction or percentage given, simply follow this rule to divide a portion by 2.
Hope it helps :) and let me know if you want me to elaborate(solve with fraction)
Bill intends to buy a car from a car dealer for a price of $45,000. He has $5,000 of his own money that he can use to pay for the car and is considering financing the remaining amount by taking out a loan from a bank. The bank that Bill approaches is willing to offer him a 5 -year loan for $40,000 at 6% per annum that has equal monthly payments covering the principal and interest. Payments will be made at the end of the month.
REQUIRED:
What is the monthly payment Bill needs to make to pay off the loan? (2 marks)
Answers
Answer: Approximately $759.96.
Step-by-step explanation:
To calculate the monthly payment for Bill's loan, we can use the formula for calculating the monthly payment of a loan:
Monthly Payment = P * r * (1 + r)^n / ((1 + r)^n - 1)
Where:
P = Principal amount (loan amount)
r = Monthly interest rate
n = Total number of monthly payments
Let's calculate the monthly payment using the given information:
Principal amount (P) = $40,000
Annual interest rate = 6%
Monthly interest rate (r) = Annual interest rate / 12 = 6% / 12 = 0.06 / 12 = 0.005
Total number of monthly payments (n) = 5 years * 12 months/year = 60 months
Plugging these values into the formula, we get:
Monthly Payment = 40,000 * 0.005 * (1 + 0.005)^60 / ((1 + 0.005)^60 - 1)
Calculating this expression gives us the monthly payment Bill needs to make to pay off the loan.
What is the НСF of
4725
5850
Answers
Answer:
433345344 Answer
Step-by-step explanation:
a tunnel is constructed with a semielliptical arch. the width of the tunnel is 60 feet, and the maximum height at the center of the tunnel is 25 feet. what is the height of the tunnel 5 feet from the edge? round your answer to the hundredths place.
Answers
As a result, the tunnel is 13.83 feet high, 5 feet from the edge.
An ellipse is an oval curve on a plane that contains two fixed points called foci. The sum of the distances between the two foci from each point on the ellipse is constant at all points.
Since the tunnel has an arch that is semi-elliptical, we can put the ellipse's center at the center of its 60-foot width.
What is an ellipse?
An ellipse is a two-dimensional shape that is defined by its axes in geometry. When a plane intersects a cone at an angle to its base, it creates an ellipse. It focuses on two things. For each point in the curve, the sum of the two distances to the focal point remains constant.
What are an ellipse and an example?
An ellipse is the locus of points whose sum of their distances from its two foci is constant and has an eccentricity of less than one. The two-dimensional egg shape and the running tracking in a sports stadium are simple examples of the ellipse in our everyday lives.
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The amount of water on barrel deceased 9 5/8 pints in 7 weeks what was the change of water in 12 weeks
Answers
Answer:
To solve this problem, we can use a proportion.
Let x be the change of water in 12 weeks.
We know that in 7 weeks, the water decreased by 9 5/8 pints.
So, we can set up the proportion:
9 5/8 pints / 7 weeks = x / 12 weeks
To solve for x, we can cross-multiply and simplify:
9 5/8 pints * 12 weeks = 7 weeks * x
115 1/2 pints = 7 weeks * x
x = 115 1/2 pints / 7 weeks
x = 16 1/2 pints per 12 weeks
Therefore, the change of water in 12 weeks is 16 1/2 pints.
Step-by-step explanation:
An investor invests $525 in stock. For each month following, the stock increased at a rate of $25 per
month
Identify the slope of the linear relationship. Explain what the slope represents in the context of the
problem
• identify the y-intercept of the linear relationship. Explain what the y-intercept represents in the
context of the problem.
Create a model/build the function/write the equation in slope-intercept form to represent the total
value of the stock, f (2), based on the number of months, I.
Answers
Answer: f(x) = mx+ b
slope = m = $25 / month
This means that for every month (x) that goes by, the total value of the stock (f(x)) will increase by $25.
y-intercept = b = $525
This is the amount of money in the account at time = 0. This will be equal to the original investment of $525.
f(x) = mx+ b = 25x + 525
Step-by-step explanation:
-6 George has a choice of a $7,200, simple interest loan at 3.8% that he has to start paying back after 3 years, or a $7,500, annual compound interest loan at 3.5% that he also has to start paying back after 3 years. Which method should he choose, simple or compound, and how much less interest will he owe using that method? (8.1A, 8.1B, 8.1C, 8.16) F Compound interest; $79.03 G Simple interest; $79.03 H Compound interest; $5.42 J Simple interest; $5.42
Answers
Answer:
Compound interest; $5.42
Step-by-step explanation:
A school survey found that 24 out of 30 students prefer chocolate milk to white milk. If the school has 500 students, which is the best
prediction of the total number of students who prefer chocolate milk?
Answers
Answer:
Around 401 students would prefer chocolate milk.
Step-by-step explanation:
500/30=16.66667...
24*16.7=400.8
you cant have an eighth of a vote so you round to 401
help asap! i realy need help! i will give Who deserves the Brainliest award?!
Answers
The absolute value function that matches the graph is given as follows:
y = |x|
How to define the absolute value function?An absolute value function of vertex (h,k) is defined as follows:
y = a|x - h| + k.
The vertex of the function in this problem is at the origin, hence:
(h,k) = (0,0).
The leading coefficient is of a = 1, as when x = 1, y = 1.
Hence the absolute value function that matches the graph is given as follows:
y = |x|
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<1 is a complement of <2, and m<1=66. find <2
Answers
Answer: 24 degrees
Step-by-step explanation: Complementary angles are when two angles add up to 90 degrees. Just do 90-66=24. The answer is 24 degrees. Hope that helped!
Solve for c. -8c=-24
Answers
Answer:
c=3
Step-by-step explanation:
find the solution of the system of equations
Answers
\(\begin{array}{cllll} -6x+5y&=&34\\ -6x-10y&=&4 \end{array} \\\\[-0.35em] ~\dotfill\)
\(\stackrel{ \textit{using elimination method} }{\begin{array}{cllll} \text{\LARGE -1}(-6x+5y&=&34)\\ -6x-10y&=&4 \end{array}}\implies \begin{array}{clclll} 6x ~~ -5y&=&-34\\ -6x-10y&=&4\\\cline{1-3} 0 ~~ -15y&=&-30 \end{array} \\\\\\ -15y=-30\implies y=\cfrac{-30}{-15}\implies y=2 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{substituting on the 1st equation}}{-6x+5(2)=34\implies} -6x+10=34\implies x=\cfrac{24}{-6}\implies x=-4 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill (-4~~,~~2)~\hfill\)
find the macluaring series for both f(x)( and g(x) using the definition of maclaurin series. use basis of your solution ln(1 2x)
Answers
The Maclaurin series for g(x) is ln(1+2x)\(.^{2}\) = -8\(x^2\) - 128ln(2)\(.^{2}\)\(x^{4}\)
To find the Maclaurin series for a function f(x) using the definition of Maclaurin series, we need to express f(x) as a power series centered at x=0, which is given by:
f(x) = Σ[ n=0 to infinity ] (\(n^{2}\)(0)/n!) * \(x^{n}\)
where \(f^n\)(0) is the nth derivative of f(x) evaluated at x=0.
Using the definition of Maclaurin series, we can find the Maclaurin series for f(x) and g(x) as follows:
f(x) = ln(1+2x)
First, we find the derivatives of f(x) with respect to x:
f'(x) = 2 / (1+2x)
f''(x) = -4 / (1+2x)
f'''(x) = 16 / (1+2x)
f''''(x) = -64 / (1+2x)
Next,
We evaluate the derivatives at x=0 to find the coefficients of the Maclaurin series:
f(0) = ln(1) = 0
f'(0) = 2
f''(0) = -4
f'''(0) = 16
f''''(0) = -64
Substituting these coefficients into the formula for the Maclaurin series, we get:
f(x) = 2x - 2x + (8/3)x - (32/3)x + ...
Therefore, the Maclaurin series for f(x) is:
ln(1+2x) = 2x - 2x + (8/3) - (32/3) + ...
g(x) = ln(1+2x)
Using the chain rule, we can find the derivatives of g(x) as:
g'(x) = 4ln(1+2x) / (1+2x)
g''(x) = -8[ln(1+2x) + 1] / (1+2x)
g'''(x) = 32[ln(1+2x) + 2] / (1+2x)
g''''(x) = -128[ln(1+2x) + 3] / (1+2x)
Evaluating these derivatives at x=0, we get:
g(0) = ln(1)\(.^{2}\) = 0
g'(0) = 0
g''(0) = -8
g'''(0) = 0
g''''(0) = -128*ln(2)\(.^{2}\)
Therefore, the Maclaurin series for g(x) is:
ln(1+2x)\(.^{2}\) = -8\(x^2\) - 128ln(2)\(.^{2}\)\(x^{4}\)
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