Angle ABE & angle DBC are right angles then ∠ABE≅ ∠EBC
What is complementary angle theorem?
If two angles are complementary to the same angle, then they are congruent.
1.∠ABE and ∠DBC are right angles(Given)
2. m∠ABE=90⁰
m∠DBC=90⁰
By definition of right angles
3.∠ABE and ∠DBE are complementary.
∠DBE and ∠EBC are complementary.
(By complementary theorem)
two angles are complementary to the same angle, then they are congruent.
4. ∠ABE≅ ∠EBC (is complementary to same)
Hence ∠ABE≅ ∠EBC.
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The graph of a function g is shown below.
Find g (-2)
1. Squares with side lengths 6, 8, and 10 meters?2. Squares with areas 64 in?, 100 in?, 144 in2? 3. Two squares with side length 5 feet and a square with area 50 square feet?4. Explain how you know whether three squares will join at their corners to form a right triangle.
In order to know if 3 squares will form a right triangle,
a. The sum of the length of two of the squares must be greater than the length of the last square.
b. The lengths of the squares (if they are integers) must form a Pythagorean triple.
Pythagorean triples are:
3, 4, 5
5, 12, 13
8, 15, 17
9, 40, 41
there are more triples but we only need these for this question
c. They must conform to the Pythagoras Theorem.
[tex]\begin{gathered} \text{Pythagoras theorem is:} \\ c^2=a^2+b^2 \\ \text{where c is the largest side of the right angled triangle or hypothenus} \\ \text{while a and b are adjacent and opposite of the right angled triangle} \end{gathered}[/tex]Now we can proceed with these points at hand.
1. Squares with side lengths 6, 8, 10 can be written as:
2(3), 2(4), 2(5).
Ignoring the "2", we can see that this follows the Pythagorean triple.
therefore, 6, 8, 10 can form a right-angled triangle
2. 64, 100, 144 can be written as:
4(16), 4(25), 4(36)
Ignoring the "4", we can see that this does not follow the Pythagorean triple.
If we input the values into the Pythagoras theorem, we shall have:
[tex]\begin{gathered} 64^2+100^2\text{ = 4096 + 10000 = 14096} \\ 144^2=\text{ 20736} \\ \text{Therefore, we can s}ee\text{ that:} \\ 64^2+100^2\text{ }\ne\text{ }144^2 \end{gathered}[/tex]Therefore, 64, 100, 144 cannot form a right-angled triangle
3. Two squares with lengths 5 and a Square with an area of 50 square feet:
We need to find the length of the square with an area of 50 square feet.
[tex]\begin{gathered} \text{Area of square = l}^2 \\ \text{where l is the length of the side} \\ 50=l^2 \\ \text{square root both sides} \\ l\text{ = }\sqrt[]{50\text{ }}\text{ = 5}\sqrt[]{2} \end{gathered}[/tex]Now that we know the length of the 3rd and largest side of this triangle, we can now determine whether it is a right-angled triangle.
This case has a non-integer as part of the sides of the triangle, thus, condition b does not apply.
We must check via Pythagoras theorem:
[tex]\begin{gathered} By\text{ pythagoras:} \\ 5^2+5^2=25+25=50 \\ \text{while,} \\ (5\sqrt[]{2})^2=5^2\times(\sqrt[]{2})^2=25\times2=50 \\ \text{Thus we can s}ee\text{ that:} \\ 5,5,5\sqrt[]{2}\text{ can form a right-angled triangle} \end{gathered}[/tex]Therefore, the final answer: 1 and 3 can form a right-angled triangle but 2 cannot
4. I have given the reasons why they form a right-angled triangle above. But let me restate them:
In order to know if 3 squares will form a right triangle,
a. The sum of the length of two of the squares must be greater than the length of the last square.
b. The lengths of the squares (if they are integers) must form a Pythagorean triple.
Pythagorean triples are:
3, 4, 5
5, 12, 13
8, 15, 17
9, 40, 41
there are more triples but we only need these for this question
c. They must conform to the Pythagoras Theorem.
[tex]\begin{gathered} \text{Pythagoras theorem is:} \\ c^2=a^2+b^2 \\ \text{where c is the largest side of the right angled triangle} \\ \text{while a and b are adjacent and opposite of the right angled triangle} \end{gathered}[/tex]
Arc length s. Central Angle 36 feet. π/2 radiansFind the radius r of a circle with an arc length s and a central angle 0.
The formula for determining the length of an arc is expressed as
length of arc = #/360 * 2 * pi * radius
where
# represents the central angle
From the information given
length of arc = 36
We would convert from radians to degree
1 pi rad = 180 degrees
pi/2 rad = 180/2 = 90 degrees
Thus, # = 90 degrees
The equation becomes
36 = 90/360 * 2 * pi * radius
36 = 0.25 * 2 * 3.14 * radius
36 = 1.57 * radius
radius = 36/1.57
radius = 22.93 feet
Given f(x)=cosxf(x)=cosx, which function below doubles the amplitude and has a period of 3π3π?g(x)=3cos2xg of x is equal to 3 cosine 2 xg(x)=12cos2xg of x is equal to 1 half cosine 2 xg(x)=2cos2x3g of x is equal to 2 cosine 2 x over 3g(x)=3cos3x2g of x is equal to 3 cosine 3 x over 2
Answer:
[tex]g(x)=2\cos \frac{2x}{3}[/tex]Explanation:
A cosine function is generally given as;
[tex]\begin{gathered} y=a\cos (b) \\ \text{where Amplitude }=|a| \\ \text{ Period }=\frac{2\pi}{|b|} \end{gathered}[/tex]Given the below function;
[tex]f(x)=\cos x[/tex]If we compare both functions, we'll see that a = 1 and b = 1.
If we need another function with double the amplitude, then the value of a in that function will be (a = 2 x 1 = 2).
If we're to have another function g(x), with a period of 3 pi, let's go ahead and determine the value of b in the second function;
[tex]\begin{gathered} \frac{2\pi}{b}=3\pi \\ 3\pi\cdot b=2\pi \\ b=\frac{2\pi}{3\pi} \\ b=\frac{2}{3} \end{gathered}[/tex]Since we now have that for the second function g(x), a = 2 and b = 2/3, therefore g(x) can be written as below;
[tex]g(x)=2\cos \frac{2x}{3}[/tex]
Answer:
The derivation that correctly uses the cosine sum identity to prove the cosine double angle identity is A. A 2-column table with 3 rows. Column 1 has entries 1, 2, 3. Column 2 is labeled Step with entries cosine (2 x) = cosine (x + x), = cosine (x) cosine (x) minus sine (x) sine (x), = cosine squared (x) minus sine squared (x)
Step-by-step explanation:
It should be noted that the cosine difference identity is found by simplifying the equation by first squaring both sides.
Therefore, the derivation that correctly uses the cosine sum identity to prove the cosine double angle identity is that a 2-column table with 3 rows. Column 1 has entries 1, 2, 3. Column 2 is labeled Step with entries cosine (2 x) = cosine (x + x), = cosine (x) cosine (x) minus sine (x) sine (x), = cosine squared (x) minus sine squared (x).
In conclusion, the correct option is A.
The height of a sand dune (in centimeters) is represented by cm, where is measured in years since . Find and , and determine what each means in terms of the sand dune. Give the values of and below, including units.
The height of the sand dune after 13 years is 324 cm. The rate of change height of sand dunes is - 8t.
Given the equation is -
f(t)=1000-4t²
f(13) = 1000 - 4 (13)²
= 1000 - 676
= 324 cm
f'(t) = - 8t
f'(13) = - 8(13)
= -104cm
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Complete Question -
The height of a sand dune (in centimeters) is represented by f(t)=1000-4t2 cm, where t is measured in years since 1995. Find f(13) and f'(13), and determine what each means in terms of the sand dune. Give the values of f(13) and f'(13) below, including units.
[tex](a - \frac{95 }{5} )^{2} - \frac{36}{25} m^{2} [/tex]
Please Evaluate
A college believes that 22% of applicants to that school have parents who have remarried. How large a sample is needed to estimate the true proportion of students who have parents who have remarried to within 5 percentage points with 99% confidence?
Use the following expression for the number of elements of a sample, related to a certain proportion a Z-score:
[tex]n=(\frac{Z}{E})^2\cdot p\cdot q[/tex]where,
p: percentage of applicants in decimal form = 0.22 (28%)
q = 1 - p = 1 - 0.22 = 0.78
E: percentage margin = 0.05 (5%)
Z-score for 99% confidence = 2.576 (found in a Z-score table)
Replace the previous values of the parameters into the formula for n and simplify:
[tex]n=(\frac{2.576}{0.06})^2\cdot0.22\cdot0.78\approx316[/tex]Hence, approximately 316 students are needed for the sample.
Question
Solve.
−6.6x=−4
What is the solution to the equation?
Enter your answer as a simplified fraction in the box.
The solution to the equation would be 20/33 as a simplified fraction.
What is the solution for an equation?The solution of an equation refers usually to the values of the variables involved in that equation which if substituted in place of that variable would give a true mathematical statement.
We have been given an equation as; −6.6x=−4
Thus we need to solve the equation to find the solution.
-6.6x = -4
Then Divide both sides by -6.6.
x = -4/(-6.6)
x = 40/66
x = 20/33
Hence, the solution to the equation would be 20/33 as a simplified fraction.
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Help Me Please..!
[1st Person That Answer Will Get Brainlyest.]
List A i.e. |-6(5/7)|, |-6(3/7)|, |5(2/7) shoe the absolute value in order from greatest to the lowest.
What is absolute value?Without taking direction into account, absolute value defines how far away from zero a certain number is on the number line. A number can never have a negative absolute value.
By deducting 1, you may determine the numbers' decreasing order. To write the numbers 10 to 6 in descending order, for instance, we would start with 10, the greatest number in the preceding series, and continue taking away 1 until we reached the lowest number.
There are 4 lists given from which it is obtained only list A is only in which the numbers are in descending order,
|-6(5/7)| = +6.71
|-6(3/4) = +6.42
|-5(2/7)} = +5.28
The numbers are in decreasing order as,
+6.71 > +6.42 > +5.28
Thus, list A i.e. |-6(5/7)|, |-6(3/7)|, |5(2/7) shoe the absolute value in order from greatest to the lowest.
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[tex] \rm\int_{0}^{ \frac{\pi}{2} } \frac{1}{ \sqrt{1 - {sin}^{2} ( \frac{1}2) {sin}^{2} \varphi } } d \varphi \\ [/tex]
This is an another elliptical integral, but of the first kind:
[tex]\displaystyle F(k) = \int_0^{\pi/2} \frac{dx}{\sqrt{1-k^2\sin^2(x)}}[/tex]
[tex]\implies \displaystyle \int_0^{\pi/2} \frac{d\varphi}{\sqrt{1-\sin^2\left(\frac12\right)\sin^2(\varphi)}} = \boxed{F\left(\sin\left(\frac12\right)\right)}[/tex]
can you help me i have to see if it is a direct variation
a direct variation is a relationship between two variables that can be expressed by an equation in which one variable is equal to a constant times the other. For instance,
[tex]y=mx[/tex]in which variables x and y are related by a constant m. A numerical examples of a Direct variations are:
[tex]\begin{gathered} y=-5x \\ y=\frac{2}{3}x \\ y=-\frac{7}{6}x \end{gathered}[/tex]etc. In our case, the figure shows a line. The general equation of a line is in the form
[tex]y=mx+b[/tex]This is almost the same a direc variation, however it has the y-intercept b. In our case, form the graph, we can see that
b=4. In other words, b is the point in which the lines cross y-axis.
Hence, our line doesnt represent a Direct variation since there is a y-intercept b=4.
A company sells sneakers and has a revenue that can be represented by the function R(s) = 90s – s2, where s represents the number of pairs of sneakers sold. The sneaker company has a fixed cost of $1,500, and each pair of sneakers costs $30 to manufacture. Which of the following functions represents the profit P(s) of the sneaker company?
P(s) = – s2 + 120s + 1,500
P(s) = – s2 + 60s + 1,500
P(s) = – s2 + 120s – 1,500
P(s) = – s2 + 60s – 1,500
The function that can represent the profit P(s) of the sneaker company is D. P(s) = – s2 + 60s – 1,500.
What is a function?Mathematically, a function shows a set of inputs that produce one output.
Functions have the domain (independent variable) and the codomain or range (dependent variable).
The domain is always the set of input values, while the range is the output value of the function.
Revenue function R(s) = 90s – s2
Fixed cost = $1,500
Variable cost per unit = $30
Profit = Revenue - Variable and Fixed Costs
Profit function P(s) = 90s – s2 - 30s - 1,500
= 60s - s2 - 1,500
or -s2 + 60s - 1,500
Thus, the correct profit function is Option D.
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Pre calc, easy answer, not the best WiFi sorry if I get disconnected
So,
First of all, we should remember the following:
In this case, we have the following transformation:
[tex]f(x)=\sqrt[]{x}\to g(x)=3\sqrt[]{x}[/tex]As you can see, we're multiplying the function f by 3. So, this is an example of a vertical stretch of the function f by a factor of 3. So the answer is B.
Write the correct equation for the following statement and then solve for the given number of
miles.
You decide to rent a limo for prom. The rate is $200 plus $5 per mile
traveled. Write an equation to calculate your total cost (c) at the end of
the evening for a given number of miles (m).
If you travel 45 miles what will be your total bill at the end
of the evening?
Answer:
$425
Step-by-step explanation:
You want the cost of a 45 mile trip in a limo that costs $200 plus $5 per mile.
Mileage costThe cost of each mile is $5, so the cost of 45 of them will be ...
45 × $5 = $225
Total costThere is a one-time charge of $200 added to the mileage charge, so the total cost will be ...
total bill = $200 + mileage bill
total bill = $200 +225 = $425
The total bill will be $425.
Enter the answer in the space provided.Consider the functionWhat is the average rate of change of f(z) from z = 6toz=6?
To find the average rate of ch
What whole number of 2 is 1024?
Step-by-step explanation:
?????
what are you trying to ask ?
2 × 512 = 1024
2¹⁰ = 1024
what exactly do you need ?
Write the equation of a line in slope intercept form that has a
slope of
2/3 and has a
y-intercept of 10.
Answer:
y = 2/3 x + 10
Step-by-step explanation:
In the slope-intercept form, the equation for a line is expressed as follows: y = mx + b, where m represents the slope and b the y-intercept.
Hope this helps! \( ﾟヮﾟ)/
-10x - 2y = 28
y = -5x - 14
Answer:
parallel
(0, 0)
Step-by-step explanation:
I have no clue how to answer this so I'll do my best.
-10x - 2y = 28 y = -5x - 14
-2y = 10x = 28
÷-2 ÷-2 ÷-2
--------------------
y = -5x - 14
The lines are parallel
----------------------------------------------------------------------------------------------------------
I hope this helps!
Find the distance between the pair of points (-10,-3) and (6,-3)
we know that
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]In this problem we have
(x1,y1)=(-10,-3)
(x2,y2)=(6,-3)
substitute in the formula
[tex]d=\sqrt{(-3+3)^2+(6+10)^2}[/tex][tex]d=\sqrt{(0)^2+(16)^2}[/tex]d=16 units
the distance is 16 units
Fowler inc, just paid a dividend of 2.55 per share on its stock. The dividends are expected to grow by 3.9% per year indefinitely. If investers require a 10.4% return on this stock what will the price be in 3 years, what will the price be in 15 years?
When Fowler inc, just paid a dividend, the price in 15 years for the share is $72.36.
How to calculate the price?This will be illustrated as:
P0 = D1 / (Ke - g)
P0 = Current Price
D1 = Expected Dividend after 1 Year
Ke = COst of Equity
g = Growth Rate
Dividend for first year will be:
D1 = D0(1+g)
= $ 2.55 (1+0.039)
= $ 2.55(1.039)
= $ 2.6495
Current price will be:
P0 = D1 / (Ke - g)
= $ 2.6495 / (0.104-0.039)
= $ 2.6495 / 0.065
= $ 40.76
Price in 15 years will be
P15 = D16 / (Ke - g)
P15 = Price after 15 Years
D16 = Expected Div after 16 Years
Ke = COst of Equity
g = Growth Rate
D16 = D0(1+g)^16
= $ 2.55 (1+0.039)^16
= $ 2.55(1.039)^16
= $2.55 * 1.8444
= $ 4.7031
P15 = D16 / (Ke - g)
= $4.7031 / (0.104-0.039)
= $4.7031 / 0.065
= $72.36
The price is $72.36
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graph (-3,2)(1,2)(8,2)(12,4)
The graph for the given points is as below:
What is graph?
The link between lines and points is described by a graph, which is a mathematical description of a network. A graph is made up of some points and the connecting lines. It doesn't matter how long the lines are or where the points are located. A node is the name for each element in a graph.
The graph for the given points attached below.
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Find the measure of the missing angle. *Don't worry about the degree symbol
this is an ange formed by two intersecting chords
then the missing angle is given by
[tex]\theta=\frac{1}{2}(arcCB+arcSD)[/tex][tex]\theta=\frac{1}{2}(191+55)[/tex][tex]\theta=\frac{1}{2}(246)[/tex][tex]\theta=123\degree[/tex]the missing angle is 123°
Is the comparison true
8•1/11>8
Comparison of the given inequality ( 8.1 /11 ) > 8 is not true.
As given in the question,
Given inequality is :
( 8.1 /11 )> 8
Simplify the given inequality ( 8.1 /11 ) > 8 to check the comparison is true or not.
(8.1 /11)> 8
Multiply both the sides of the given inequality by 11 we get,
( 8.1/11 ) × 11 > 8× 11
⇒ (8 .1) × ( 11/ 11) >88
(8.1 ) × 1 > 88
⇒ ( 8. 1) > 88
For the above inequality, it is not possible as 8 .1 is smaller than 88.
Therefore, comparison of the given inequality ( 8.1 /11 ) > 8 is not true.
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Suppose that the annual rate of return for a common biotechnology stock is normally distributed with a mean of 5% and a standard deviation of 6%. Find the probability that the one-year return of this stock will be negative. Round to four decimal places.
===================================================
Work Shown:
Compute the z score for x = 0.
z = (x - mu)/sigma
z = (0 - 0.05)/(0.06)
z = -0.83333 approximately
Then use a calculator to find that P(Z < -0.83333) = 0.2023
There's about a 20.23% chance of getting negative returns, i.e. the person will lose money on the investment.
A travel agent arranged a payment plan for a client. It required a down payment of $150 and 15 monthly payments of $657. What was the total cost of the plan?
Answer:
$10,005
Step-by-step explanation:
We need to find the total cost of the plan and we already know that the client need to pay $150 for downpayment and 15 monthly payments of $657.
So all we need to find is the 15 monthly payments of $657. (Which we could found with multiplying $657 with 15)
$657×15 = $9,855
Now we just add it with the downpayment ($150) to find the total cost of the plan.
$9,855+$150 = $10,005
You could write the steps like this:
$150+($657×15)=$10 005
a hybrid car can travel 45 miles on one gallon of gas. determine the amount of gas needed for a 500 miles trip
We have the following:
[tex]r=45\frac{m}{g}[/tex]now, for 500 miles
[tex]\frac{500m}{45\frac{m}{g}}=11.11g[/tex]therefore about 11.11 gallons of gas is needed
Answer: roughly 12 gallons or exactly 11.11111111111111111 etc
Step-by-step explanation:
Solve the equation below and find the variation constant, Find y when x=18, if y varies directly as x, and y=50 when x=13.
Answer:
• k=50/13
,• y=69.231 (to the nearest 1000th)
Explanation:
If y varies directly as x, the equation of variation is:
[tex]y=kx,\text{ k=variation constant}[/tex]When x=13 and y=50
[tex]\begin{gathered} 50=13k \\ k=\frac{50}{13} \end{gathered}[/tex]Substituting k into the equation above, we have:
[tex]y=\frac{50}{13}x[/tex]Therefore, when x=18
[tex]\begin{gathered} y=\frac{50}{13}\times18 \\ y\approx69.231 \end{gathered}[/tex]When Mr. Jackson got in his car yesterday, the odometer read 187,198.9 km. When he got home, the reading was 187,399.4 km. How far did Mr. Jackson drive?
Answer:
200.5
Step-by-step explanation:
reading of odometer at beginning = 187,198.9 km
reading of odometer after reaching home = 187,399.4
distance travelled = 187,399.4 - 187,198.9 = 200.5 km
juans dog Stan's two feet and 3 inches tall Peters dog stands 9 in tall how much taller is juans dog than Peters dog
To answer this question, we need to transform all the values into one type of measure. In this case, we can work with inches. Then, we have:
[tex]2ft\cdot\frac{12in}{1ft}=24in[/tex]Then, we have that in two feet we have 24 inches. Then, we have:
Juan's dog: 24 inches + 3 inches ---> 27 inches tall.
Peter's dog: 9 inches tall.
Now, how much taller is Juan's dog than Peter's dog is:
[tex]\frac{\text{Juan's dog}}{\text{Peter's dog}}=\frac{27in}{9in}=3[/tex]Therefore, Juan's dog is 3 times taller than Peter's dog.
24. If a ream of paper (500 sheets) is 2.125 inches thick, how thick is one sheet of paper? Give your answer in scientific notation. (1) 1.0625 x 103 (2) 42.5 x 103 (3) 4.25 x 103 (4) 4.25 x 10-3 (5) 4.25 x 10-2