Problem 4:
The hypotenuse of a right angled triangle is 20 cm. The difference between its other two sides is 4 cm. Find the length of the sides.
Answers
Answer:
12cm and 16cm
Step-by-step explanation:
The hypotenuse of the right angle triangle = 20cm
let the other two sides be x and y;
The difference;
x = y - 4
Problem:
Find x and y;
Solution:
According to the pythagoras theorem;
x² + y² = 20² ------ i
x² + y² = 400 ----- i
and x - y = 4 ---- ii
So; x = 4 + y
Now input the value into equation (i);
(y + 4)² + y² = 400
(y+4)(y+4) + y² = 400
y² + y² + 4y + 4y + 16 = 400
2y² + 8y + 16 = 400
2y² + 8y + 16 -400 = 0
2y² + 8y - 384 = 0;
y² + 4y - 192 = 0
Factorize the equation;
y² + 16y - 12y - 192 = 0
y(y + 16) - 12(y + 16) = 0
(y-12)(y + 16) = 0
y -12 = 0 or y+ 16 = 0
y = 12 or -16
It is not realistic for the length of a body to be a negative value, so y= 12;
since;
x - y = 4,
x = 4 + 12
x = 16
Related Questions
Given: AB=AC, AD=AE and DC=EB
Prove: <1 is equal to <2
PLEASE HELP! Thank you!
Answers
The prove of ∠1 equal to ∠2 is shown below.
What is mean by Triangle?
A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
⇒ AB = AC, AD = AE and DC = EB
Now,
In ΔDBC and ΔEBC;
⇒ DC = EB (Given) ..(i)
Since, AB = AC
So, the ΔABC is a isosceles triangle.
Hence, ∠DBC = ∠ ECB ..(ii)
Here, AB = AC and AD = AE
So, BD = EC ..(iii)
Hence, By the condition (i), (ii) and (iii);
By SAS condition,
⇒ ΔDBC ≅ ΔEBC
Hence, We get;
⇒ ∠1 = ∠2
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Can someone please help?
The temperature in a room is controlled by an electronic thermostat. The temperatures vary according
to the sinusoidal function: = 6 sin[90( − 11)] + 19, where y is the temperature (°C) and x is the
time in hours past midnight.
a) What are the maximum and minimum temperatures in the room?
b) At what time does the temperature first hit 13 °C?
Answers
Answer:
a. max. 25c. min.13c
b. 2:00
Step-by-step explanation:
Cara is standing on the edge of a 15 foot high diving board. Her friend Sierra is Treading Water 45 feet from the spot in the pool directly below Cara. What is the angle of depression from the edge of the diving board to the surface of the water where Sierra is located?
Answers
Using the information given in the exercise, you can draw the following diagram:
Where β is the angle of depression (in degrees) from the edge of the diving board to the surface of the water where Sierra is located.
In order to find the measure of the angle of depression, you need to use the following Inverse trigonometric function:
\(\beta=arc\tan (\frac{opposite}{adjacent})\)In this case, you can identify that:
\(\begin{gathered} opposite=15 \\ adjacent=45 \end{gathered}\)Therefore, substituting the values, you get the following result:
\(\begin{gathered} \beta=arc\tan (\frac{15}{45}) \\ \\ \beta=18.43\degree \end{gathered}\)The answer is:
\(18.43\degree\)
Gasoline is pouring into a vertical cylindrical tank of radius 55 feet. When the depth of the gasoline is 66 feet, the depth is increasing at 0.30.3 ft/sec. How fast is the volume of gasoline changing at that instant
Answers
The volume of gasoline in the cylindrical tank is increasing at 23.56 ft.³/sec when the depth of the gasoline in the tank is 6 feet. Computed using differentiation.
Since the tank is cylindrical in shape, its volume can be written as:
V = πr²d,
where V is its volume, r is the radius, and d is the depth.
The radius is constant, given r = 5ft.
Thus the volume can be shown as:
V = π(5)²d,
or, V = 25πd.
Differentiating this with respect to time, we get:
δV/δt = 25πδd/δt ... (i),
where δV/δt, represents the rate of change of volume with respect to time, and δd/δt represents the rate of change of depth with respect to time.
Now, we are given that when the depth increases at 0.3 ft./sec when the depth of the gasoline is 6 feet.
Thus, we can take δd/δt = 0.3 ft./sec, in (i) to get:
δV/δt = 25πδd/δt = 25π(0.3) ft.³/sec = 23.56 ft.³/sec.
Thus, the volume of gasoline in the cylindrical tank is increasing at 23.56 ft.³/sec when the depth of the gasoline in the tank is 6 feet. Computed using differentiation.
The question written correctly is:
"Gasoline is pouring into a vertical cylindrical tank of radius 5 feet. When the depth of the gasoline is 6 feet, the depth is increasing at 0.3 ft./sec. How fast is the volume of gasoline changing at that instant?"
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(1 point) because of an economic slump, a company finds that its annual profits have dropped from 800 thousand dollars in 2006 to 200 thousand dollars in 2009. if profit follows an exponential decline, what's the expected profit in 2010? hint: your calculations will be easier if you let ????
Answers
The expected profit in 2010 is 50,000 dollars. This means that the company's annual profits are projected to decrease further due to the economic slump. It is important to note that this calculation assumes that the exponential decline will continue at the same rate in the future.
The expected profit in 2010 can be calculated using exponential decay. By using the given information, we can find the decay factor. We can then apply the decay factor to the 2009 profit to find the expected profit in 2010.
1. To calculate the expected profit in 2010, we need to determine the decay factor. The decay factor can be found by dividing the profit in 2009 by the profit in 2006.
Decay factor = 200,000 / 800,000 = 0.25
2. Now, we can use the decay factor to calculate the expected profit in 2010. We multiply the 2009 profit by the decay factor.
Expected profit in 2010 = 200,000 * 0.25 = 50,000 dollars
Therefore, the expected profit in 2010 is 50,000 dollars. This means that the company's annual profits are projected to decrease further due to the economic slump. It is important to note that this calculation assumes that the exponential decline will continue at the same rate in the future.
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You and a friend go out to eat and spend $130 on dinner. In addition to the cost of the meal you must pay a 89 sales tax and leave a 20% tip. How much will each of you spend on dinner after you include the tax and tip?
Answers
Answer:
$167.57
Step-by-step explanation:
"In addition to the cost of the meal you must pay a 89 sales tax:" don't you mean a 8.9% sales tax?
Tax: 8.9% of $130 = %11.57
Tip: 20% of $130 = 26.00
Total: meal, tax and tip: $130 + $11.57 + $26 = $167.57
suppose that a particular item is class 200 according to the national motor freight classification (nmfc). what is the relationship between this item's rate and the rate for an item in class 100?
Answers
The relationship between this item's rate and the rate for an item in class 100 is that the rate for a class 200 item will be at least 1.001 times higher than the rate for a class 100 item.
A system used by carriers to categorize items based on their density, stowability, handling, and liability is called the National Motor Freight Classification (NMFC). Each class indicates a range of CWT prices that the carrier will impose on the shipment of the goods.
The NMFC predicts that the rate for a class 200 item will be higher than the rate for a class 100 item. This is because class 200 objects tend to be denser and require more handling and space, which raises the cost of transportation. Carriers therefore charge more for class 200 items to be transported than for class 100 items.
To give you an idea of the range of rates per CWT, class 100 items have a rate of $5 or less, while class 200 items have a rate of $5.01 to $7.00 per CWT. Therefore, the rate for a class 200 item will be at least 1.001 times higher than the rate for a class 100 item.
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Identify the area of a regular decagon with side length 5 m rounded to the nearest tenth.
THE RED IS THE ONE I GOT WRONG
Answers
Answer:
192.4 m^2
Step-by-step explanation:
See the attached image.
The area of a regular polygon is \(A=\frac{1}{2}ap\) where p is the perimeter and a is the apothem (the distance from the center to the midpoint of a side).
The perimeter is p = 10(5) = 50m. This is a huge decagon!
Calculate the measure of angle KGL. In a decagon, the total of all interior angles is 180(10-2) = 1440 degrees. That makes one of the interior angles 1440 / 10 = 144, and angle KGL is half of that, 72 degrees.
To find a, use a trigonometric ratio in right triangle GKL. GL = 2.5, half the length of side GH.
\(\tan{72^\circ} = a/2.5\\\\a=2.5\tan{72^\circ} \approx 7.6942\)
The area of the decagon is
\(A=\frac{1}{2}(7.7.6942)(50) \approx 192.4\)
amy bill and cara each played a game
amys score was 10 times bills score
caras score was half of amys score
write down the ratio of amys score to bills score to caras score
give your answer in simplest form
Answers
Amy = 10
Amy:Bill = 10:1,
Bill = 1
Cara =1/2 Amy’s
Cara = 1/2 x 10
Cara= 5
Amy:Bill:Cara = 10:1:5
Please help thank you so much in advance
Answers
Answer:
Its 70º
Step-by-step explanation:
Find the Fourier series of f on the given interval. solve each problem in detail. 16. f(x)={0,ex−1,−π
Answers
The Fourier Series is a mathematical method of expressing a periodic function as a sum of simple sine waves or cosine waves, or as an exponential function.
Fourier series have numerous applications in engineering, physics, and other fields. The function f(x)={0,ex−1,−π belongs to a class of functions that are periodic over 2π and piecewise smooth. Thus, the Fourier Series can be used to represent this function.
In order to find the Fourier series of f(x)={0,ex−1,−π , we first need to find the coefficients a_n and b_n. These coefficients are defined by the following integrals:
\(a_n = \frac{1}{\pi} \int_{-\pi}^{\pi} f(x) \cos(nx) dx and \\b_n = \frac{1}{\pi} \int_{-\pi}^{\pi} f(x) \sin(nx) dx.\)
Using these equations, we can find the coefficients for our function. Since f(x) is an odd function, all the coefficients a_n are zero.
The integral for b_n can be evaluated as follows:
\(b_n = \frac{1}{\pi} \int_{-\pi}^{\pi} f(x) \sin(nx) dx b_n = \frac{1}{\pi} \int_{0}^{\pi} (e^{x}-1)\sin(nx) dx \\b_n = \frac{1}{\pi} \left[ -\frac{1}{n}\cos(nx) (e^x-1) + \frac{1}{n} \int_{0}^{\pi} e^{x}\cos(nx) dx \right]\)
The first term in the square brackets is zero, because \cos(n\pi) = (-1)^n, and n is odd.
The second term can be evaluated using integration by parts:
\(b_n = \frac{1}{\pi} \left[ -\frac{1}{n}\cos(nx) (e^x-1) + \frac{1}{n} \left( e^{x}\frac{\sin(nx)}{n} + \frac{1}{n}\int_{0}^{\pi} e^{x}\sin(nx) dx \right) \right] \\b_n = \frac{1}{\pi} \left[ \frac{e^{\pi}}{n}\sin(n\pi) - \frac{1}{n} \int_{0}^{\pi} e^{x}\sin(nx) dx \right]\)
Since \sin(n\pi) = 0, the first term is zero. The second term can be evaluated using integration by parts again:
\(b_n = \frac{1}{\pi} \left[ -\frac{e^{\pi}}{n^2}\cos(n\pi) + \frac{1}{n^2} \int_{0}^{\pi} e^{x}\cos(nx) dx \right] \\b_n = \frac{1}{\pi} \left[ \frac{e^{\pi}}{n^2} - \frac{1}{n^2} \int_{0}^{\pi} e^{x}\cos(nx) dx \right]\)
The integral for the cosine term is the same as before, except with cosine instead of sine:
\(a_n = \frac{1}{\pi} \int_{0}^{\pi} (e^{x}-1)\cos(nx) dx a_n \\= \frac{1}{\pi} \left[ \frac{1}{n}\sin(nx) (e^x-1) + \frac{1}{n} \int_{0}^{\pi} e^{x}\sin(nx) dx \right] a_n \\= \frac{1}{\pi} \left[ \frac{e^{\pi}}{n}\sin(n\pi) - \frac{1}{n} \int_{0}^{\pi} e^{x}\sin(nx) dx \right]\)
The first term is zero, since \(\sin(n\pi) = 0\).
The second term is the same as the integral for \(b_n\), except with cosine instead of sine:
\(a_n = \frac{1}{\pi} \left[ -\frac{e^{\pi}}{n^2}\cos(n\pi) + \frac{1}{n^2} \int_{0}^{\pi} e^{x}\cos(nx) dx \right] \\a_n = \frac{1}{\pi} \left[ -\frac{e^{\pi}}{n^2} + \frac{1}{n^2} \int_{0}^{\pi} e^{x}\cos(nx) dx \right]\)
Finally, we can use these coefficients to find the Fourier series of f(x).
The series is defined as:
\(f(x) = \frac{a_0}{2} + \sum_{n=1}^{\infty} \left[ a_n\cos(nx) + b_n\sin(nx) \right] where a_0 = \frac{1}{\pi} \int_{-\pi}^{\pi} f(x) dx.\)
In this case, a_0 = 0, since f(x) is an odd function.
The Fourier series for f(x) is therefore:
\(f(x) = \sum_{n=1}^{\infty} \left[ \frac{1}{\pi n^2} \left( e^{\pi} - 1 \right) \left( 1 - \cos(nx) \right) + \frac{1}{\pi n} \sin(nx) \right]\)
The Fourier series of f(x)={0,ex−1,−π can be determined by using the formulas for the coefficients and evaluating the integrals. In this case, since the function is odd, only the sine coefficients are non-zero. The Fourier series can then be expressed as a sum of sine and cosine terms, and used to approximate the function f(x) over the interval [-π,π].
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In mrs kuliks class there are 20 female students and 8 male students what is the percent of male students
Answers
Answer:
About 29%
Step-by-step explanation:
Nathan has a very nice aquarium. 2/3 of his fish have stripes 3/7 of the striped fish are over 6 inches long. What fraction of the fish in his aquarium are striped fish over 6 inches in length.? Group of answer choices
Answers
Step-by-step explanation:
To find the fraction of fish in Nathan's aquarium that are striped fish over 6 inches in length, we need to multiply the fractions representing the proportions of striped fish and the proportions of those over 6 inches long.
Given information:
- 2/3 of Nathan's fish have stripes.
- 3/7 of the striped fish are over 6 inches long.
To calculate the desired fraction, we multiply these two fractions:
(2/3) * (3/7) = 6/21
The resulting fraction is 6/21. This fraction represents the proportion of fish in Nathan's aquarium that are both striped and over 6 inches long. However, we can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 3:
(6/3) / (21/3) = 2/7
Therefore, the fraction of fish in Nathan's aquarium that are striped and over 6 inches in length is 2/7.
Edward runs around the park trail 4 times in 1 day. He knows that the trail is 2414 meters long. Which equation will give Edward the best estimate of how many total meters he runs in 1 day? CLEAR CHECK 4+2400=2404 meters, 4×2300=9200 meters, 4+2300=2304 meters, 4×2400=9600 meters
Answers
The equation for the total distance that he runs in one day is:
total dsitance = 4*2414 m = 9656m
Which equation gives the best estimate of how many total meters he runs?So, here we know that Edward uns around the park trail 4 times in one day.
So, if D is the total distance of the trail, then the total distance that Edward runs in one day is 4 times D, then the equation is:
total distance = 4*D
Here we know that the trail is 2414 meters long, then the equation will be:
total dsitance = 4*2414 m = 9656m
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Tessa has a coin jar full of dimes and pennies. When she took the coin jar to the bank, she was told that it contained exactly $27.34. Give three different combinations of the number of dimes and pennies that could have been in the coin jar.
Answers
Answer:
Step-by-step explanation:
Note: In solving our problems below, we will use the value of the coins in dollars which are listed under the third column in the table above. As you can see, the penny has a value of 0.01, the nickel has a value of 0.05, the dime has a value of 0.10, and the quarter has a value of 0.25
Select the correct answer from each drag-drop menu.
I’m triangle ABC m
The side lengths, in order from greatest to least, are __________(Ab, Ac, or Bc) for all 3 blanks.
Answers
Answer:
I think the answers bc, ab, and ac
Step-by-step explanation:
Sorry if it ends up being wrong i had the question before but im pretty sure that's the answer.
ERADES
4
Declan is training to take part in a 10 km race.
He runs the same distance every day for 30 days. A
For the first 20 days, his mean running time was 56.2 minutes.
His mean running time for all 30 days was 54.4 minutes.
Work out Declan's mean running time for the last 10 days of his training.
unning time for first 20
Answers
Answer: 54.5
Step-by-step explanation: 54.5
WILL MARK BRAINLIEST!!! Please solve the whole page with work!! It will be very much appreciated and I will heart the correct comment and give it 5 stars
Answers
Answer:
its only 5 points tho :c
Step-by-step explanation:
HURRY PLEASE
What is the end behavior of the polynomial function?
Answers
I need help with this one it does not make scene
Answers
Step-by-step explanation:
\( {x}^{2} - 3x + 4 + 4 {x}^{2} - (x + 12)\)
\(5 {x}^{2} - 4x - 8\)
100 POINTS PLS HELP ASAP
Mullet fish are known to jump out of the water when being pursued by predators. The height in inches of one mullet fish can be described by the function f (x) = 2sin2x − 1, where x represents the time in seconds. Another mullet fish's height from the water level can be represented by the equation g(x) = cos x. At which values on the interval [0, 2π) will the two fish be at the same height above the water? (2 points)
a. open bracket pi over 3 comma 5 times pi over 3 close bracket
b. open bracket pi over 3 comma pi comma 5 times pi over 3 close bracket
c. open bracket pi over 4 comma 3 times pi over 4 comma 5 times pi over 4 comma 7 times pi over 4 close bracket
d. {π}
Answers
The values on the interval [0, 2π) where the two fishes will be at the same height above the water is
d. {π}How to find when the fishes have the same height
To find the values on the interval [0, 2π) where the two fish will be at the same height above the water, we need to find the values of x that satisfy the equation f(x) = g(x).
Given:
f(x) = 2sin(2x - 1)
g(x) = cos(x)
We can solve this by plotting the two equations and the point of intersections denotes the points of equal height
Therefore, the values from the graph, on the interval [0, 2π) where the two fish will be at the same height above the water are:
x = 0.581, 1.194, and π.
The correct answer choice is d. {π}.
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please help ASAP!!!!!
Answers
Answer:
that would be 26
Step-by-step explanation:
you got this!
NEED HELP
A. 7 inches
B. 49 inches
C. 91 inches
D. 119 inches
Answers
Answer:
cute ko hahahahahahahahahahahahahaha
Beth is making a garden plot which measures 6 open parentheses square root of x plus 2 end root close parentheses units in length and open parentheses 5 square root of x plus 2 end root close parentheses units in width. What is the area of the garden?
Answers
The area of the garden whose length and width as given in the task content is; 30 (x + 2) square units.
What is the area of the garden plot whose length and width are as described?It follows from the task content that the expression which represents the area of the garden plot whose dimensions are as given.
Recall that Area, A = length × width.
Therefore, since length = 6 (√(x + 2)) units
The width = (5 √(x + 2) ) units
Hence, the area of the garden plot as required in the task content is; 6 (√(x + 2)) × ( 5 √(x + 2) )
= 30 (x + 2) square units
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Use Pythagorean Theorem to solve for x.
HELP ME PLZZZZ!!!! ASAP
Answers
Answer: \(2\sqrt{22}\)
Step-by-step explanation:
Pythagorean theorem: \(a^{2} +b^{2} = c^{2}\), where a and b are the legs and c is the hypotenuse.
We can solve for x by only using the left side of the triangle. Since we're only using the left side of the triangle, we can reduce 18 by 2 to get 9. Now we plug in our information to the equation.
\(9^{2} +b^{2} = 13^{2}\)
\(81 +b^{2} = 169\)
Since we don't know what \(b^{2}\) is, we're going to isolate it by subtracting 81 on both sides
\(b^{2} = 88\)
We have to square root both sides in order to find out b (or x in the problem).
\(\sqrt{b^{2}} = \sqrt{88}\)
When you put this on a calculator it would result in \(2\sqrt{22}\) which is the answer d in the problem.
plz help
solve for q
Answers
Answer: -3
Step-by-step explanation:
-3^2=-3*-3=-9
Because the square of q is equal to -9, the square root of -9 is equal to q.
Because of this fact, we can find the square root of -9 to get our answer.
\(\sqrt{-9}\) = 3 i.
Therefore, q is equal to 3 i or \(\sqrt{-9}\).
Hope this helped! :)
You are in a satellite orbiting a moon of Saturn. By measuring the acceleration due to gravity of the moon, and knowing how far away you are from the surface of the moon, what can you calculate?
Answers
By measuring the acceleration due to gravity of a moon of Saturn and knowing the distance from the satellite to the moon's surface, you can calculate the mass of the moon.
The acceleration due to gravity of a celestial body is determined by its mass. By measuring the acceleration due to gravity of the moon while in orbit and knowing the distance from the satellite to the moon's surface, you can use Newton's law of universal gravitation to calculate the mass of the moon. The equation for calculating the mass involves the gravitational constant, the acceleration due to gravity, and the distance from the satellite to the moon's center. With these values, you can solve for the mass of the moon, providing valuable information about its size and composition.
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The table shows the ratio between the number of tickets ordered and their cost: Number of Tickets Cost (dollars) 5 20 7 28 9 36 Find equivalent ratios when the number of tickets ordered is 1, 2, and 3. Write them as ordered pairs in the form (x-coordinate, y-coordinate). Starting from the origin, explain how to plot the three equivalent ratios on a coordinate grid. (10 points)
Answers
9514 1404 393
Answer:
(1, 4)(2, 8)(3, 12)Step-by-step explanation:
The ratios all have ...
first number : second number = 1 : 4
Using first numbers of 1, 2, 3, the second numbers can be found by multiplying these by 4. (1, 4), (2, 8), (3, 12)
__
You plot these (x, y) points the same way you plot any point on a coordinate grid. The first (x) value is the horizontal distance from the vertical axis. Positive is to the right. The second (y) value is the vertical distance from the horizontal axis. Positive is up.
__
Of course, the origin is where the horizontal and vertical axes meet. It can be convenient to find one of the coordinates on its respective axis, then use the other coordinate to find the point at the desired distance from that axis.
Usually, you would choose the axis on the basis of how easy it is to determine exactly where the coordinate lies. If the y-axis is marked every 5, for example, it might be hard to determine where a multiple of 4 will lie. Locating the x-coordinate on the x-axis may be an easier way to start.
x2 + 5x - 36 which binomial is a factor of the polynomial?
Answers
Thus, the two binomials that are factor of the polynomial are $(x + 9)$ and $(x - 4)$.
Which graph represents y=1/2x+2
please help!!
Answers
Answer:
B
Step-by-step explanation:
Let’s first look at the y-intercept. Since the equation is in y = mx + b form, we know that m is the slope and b is the y-intercept, so the slope is 1/2 and the y-intercept is 2, or (0,2). We can narrow down our search by noticing that C and D don’t intersect (0,2). That leaves A and B.
The slope is calculated by (y_1 - y_2)/(x_1 - x_2) given points (x_1, y_1) and (x_2, y_2). The slope for A is (4-0)/(2-(-2)) = 4/4 = 1 and the slope for B is (2-0)/(0-(-4)) = 2/4 = 1/2. The slope of B matches the slope that we are looking for. So, the answer is B.