If the area of the triangle is 50m² the length of it's other two sides is 10m each and hypotenuse is 14.1m
What is area of a triangle?A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices. A triangle is also a polygon.
A right angled triangle is a triangle with 90°. Since of one of the angle is 45° , this means that the triangle is isosceles and the other two sides will be equal. This means a= b
Area of triangle = 1/2absinC
50 = 1/2 b²sin90
50× 2 = b²× 1
b² = 100
b = √ 100
b =10m
b = 10m
a= 10m
using Pythagoras theorem
c² = 10²+10²
c² =100+100
c²= 200
c =√200
c = 14.1m
therefore the measure of the other two sides is 10m each and the hypotenuse is 14.1m
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Can someone solve this step by step and with a graph?
An ellipse has foci (0, – 2) and (0, 2) and a minor axis of length 6. What is the equation in standard form of the ellipse?
Length of major axis using formula of eccentricity is √2,2
How to find the length?Given that foci of the ellipse is at (0,2) & (0,−2)
⇒Major axis of ellipse is along y-axis.
So, equation of ellipse can be taken as: x²/a² +y/b² = 1 where a<b
Length of minor axis, 2a=4 (Given)
⇒a=2 ....(1)
and b=2 ....(2)
e = √(1-a²/b²)
⇒a²=b²-b²e²
b²=8
Therefore b=2√2 .....3
Find equation of ellipse using above result
x²/4 + y²/8 = 1
Checking options, we have ( 2,2) satisfying the equation of ellipse above.
Hence the length of the is √2,2
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An object travels along a horizontal path at a constant rate. The object travels 1/20 of the length of the path in 3/4 seconds. At that rate, how many seconds does it take the object to travel the entire length of the path?
Number of seconds it takes the object to travel the entire length of the path is 15 seconds.
What is the speed?The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.
Given that, the object travels 1/20 of the length of the path in 3/4 seconds.
1/20 is a tiny portion of the length that needs to be traveled.
20/20 is the whole length.
If 1/20 gets traveled in 3/4 of a second, multiply 3/4 by 20.
That is, 20(3/4) = 15 seconds
Therefore, number of seconds it takes the object to travel the entire length of the path is 15 seconds.
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For which function is the average rate of change over the interval 1 < x < 5 greater than the average rate of change over the same interval for the function g(x) = 1. 8x2?
A. F(x) = x2 B. G(x) = 1. 2x2 C. H(x) = 1. 5x2 D. K(x) = 2x2
The average rate of change over for the interval 1 < x < 5 k(x) greater than the average rate of change over of g(x)
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
We have,
g(x) = 1.8 [tex]x^{2}[/tex]
The average rate of change of g(x) over the interval 1 < x < 5:
= [tex]$\frac{g(5)-g(1)}{5-1}[/tex]
= [tex]$\frac{1.8 \times (5)^{2} -1.8 \times(1)^{2} }{5-1}[/tex]
= [tex]$\frac{43.2}{4}[/tex]
= 10.8..............(1)
The average rate of change of f(x) = [tex]x^2[/tex] in the interval 1 < x < 5:
= [tex]$\frac{25-1}{4}[/tex]
= [tex]$\frac{24}{4}[/tex]
= 6..............(2)
The average rate of change of g(x) = 1.2 [tex]x^2[/tex] in the interval 1 < x < 5:
= [tex]$\frac{28.8}{4}[/tex]
= 7.2.................(3)
The average rate of change of h(x) =1.5 [tex]x^2[/tex] in the interval 1 < x < 5:
= [tex]$\frac{36}{4}[/tex]
= 9...........(4)
The average rate of change of k(x) = 2 [tex]x^{2}[/tex] in the interval 1 < x < 5:
= [tex]$\frac{48}{4}[/tex]
= 12.........(5)
From (1), (2), (3), (4), and (5) we see that,
The average rate of change of [tex]$\mathbf{k}(x)=2 x^2$[/tex] is larger than the average rate of change of [tex]$g(x)=1.8 x^2$[/tex].
12 > 10.8
Thus,
Option D is the correct answer.
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A bus company uses a grid to locate bus stops. The bus station is at (3, 4). The point (7, 6) represents the first bus stop. The location of the second bus stop is determined using the same relationships as those between the coordinates of the bus station and the first bus stop. A coordinate plane is titled Use the drop-down menus to describe the relationships between the coordinates of the first and second bus stop. The Choose... increases by 4, and the Choose... increases by 2.
The location of the second bus stop is given as follows:
(10, 8).
The relationship is described as follows:
When x increases by 4, y increases by 2.
What are the translation rules?The four translation rules are defined as follows:
Left a units: x -> x - a.Right a units: x -> x + a.Up a units: y -> y + a.Down a units: y -> y - a.The change in x is given as follows:
7 - 3 = 4.
The change in y is given as follows:
6 - 4 = 2.
Hence, starting from the first bus stop, the coordinates of the second bus stop are given as follows:
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For what value of a does 9= [1/27]^a+3?
Answer:
The answer is a = -11/3.
6 1/2 divided by 2 1/4
Answer:
26/9 or 2 8/9
Calculate the measures of spread for Mrs. Hampton’s class data. Justify your response by describing the process used to find each measure. 20 points for who ever answers
To calculate the measures of spread for Mrs. Hampton's class data, you need to calculate the range, interquartile range (IQR), variance, and standard deviation.
The range is the difference between the highest and lowest values. To calculate the IQR, you must first find the quartiles of the data set.
The variance is the sum of the squared difference between each data value and the mean, divided by the number of data values. Finally, the standard deviation is the square root of the variance. To justify your response, you can explain how each of these measures of spread can provide insight into the data set, such as showing the spread of values or the degree of variation.
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A package containing 12 electrical locks, each with a unique key, must be delivered to 16 job
site superintendents. How many unique keys will result from the distribution?
180
The total number of unique keys after the distribution will be 48.
When the package containing 12 electrical locks is delivered to 16 job site superintendents, each superintendent will receive 3 locks. This means that the total number of locks will be 16 * 3 = 48
When the locks are distributed, each superintendent will receive 12/16 = 3/4 of a lock. This means that each superintendent will receive 3 locks.
Since each lock comes with a unique key, the total number of unique keys after the distribution will also be 48.
It is important to note that each lock is unique and comes with its own key, so even though the locks are being distributed among 16 superintendents, the number of unique keys will remain the same, which is 48.
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there are 7 people from the computer science (cs) department and 5 people from the math (m) department that could serve on a 4-person committee. a. find the number of different combinations if there are no restrictions on whom could serve on the committee. b. find the probability that the only people serving on the committee are from the cs department.
Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.The probability is equal to the variety of possible outcomes. the total number of outcomes that could occur. For instance, there is only one way to receive a head and there are a total of two possible outcomes, hence the probability of flipping a coin and getting heads is 1 in 2. (a head or tail). P(heads) = 12 is what we write.Given data :
a )
There are 7 people from the CS department and 5 people from the math (M) department who could serve on the committee, so there are a total of 12 people.
department that could serve on a 4-person committee
b) probability that the only people serving on the committee are from the cs department :
The general probability formula can be expressed as: Probability = Number of Favorable Outcomes / Total Number of Outcomes. or. P(A) = f / N
= 5 / 7
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What is the derivative of the natural log of y?
The derivative of the natural log of y is (1/y)(dy/dx). The derivative is performed with respect to x.
What is a natural logarithm?
A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equal to 2.718281828459.
Given function is log y.
The derivative of a function of a real variable in mathematics assesses how sensitively the function's value changes in response to changes in its argument. Calculus's fundamental tool is the derivative.
Generally derivative or the changes of the function is found with respect to x.
Assume that
z = log y
Differentiate with respect to x:
dz/dx = d(log y)/dx
Applying the formula of drivative d(ogx)/dx = 1/x:
dz/dx = (1/y)(dy/dx)
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Triangle PQR is similar to Triangle XYZ. What is the perimeter of Triangle XYZ?
[tex]\cfrac{PQ}{XY}=\cfrac{QR}{YZ}\implies \cfrac{5}{30}=\cfrac{6}{YZ}\implies 5YZ=180\implies YZ=\cfrac{180}{5}\implies YZ=36 \\\\\\ \cfrac{PQ}{XY}=\cfrac{PR}{XZ}\implies\cfrac{5}{30}=\cfrac{10}{XZ}\implies 5XZ=300\implies XZ=\cfrac{300}{5}\implies XZ=60 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{Perimeter of }XYZ}{30~~ + ~~36~~ + ~~60}\implies \text{\LARGE 126}[/tex]
it is known that the average number of pushups a u.s marine does daily is 300 with standard deviation of 50. a random sample of 49 marines is selected. a) the population of interest is [ select ] the parameter of interest is [ select ] the value of the parameter is [ select ] b) if is the sample mean number of pushups a u.s. marine does, since [ select ] , the central limit theorem holds and [ select ] , [ select ] ) c) the probability that the sample mean is less than 292 is [ select ] .
To solve we need to calculate the z-score, but since we are given the sample size then we shall begin as follows:
The z-score is calculated as (320 - 300)/(50/6) = 2.4, which means that the value of 320 is 2.4 standard deviations above the population mean of 300. Using a standard normal table or calculator, we can find the probability that a standard normal random variable is less than 2.4, which is approximately 0.9918.
This means that the probability that the sample mean is greater than 320 is approximately 0.9918. In other words, there is a 99.18% chance that a randomly selected sample of 36 U.S. Marines will have a mean number of pushups greater than 320.
μ=300, σ=50, n=36, x=320
So,
σ/√n
= 50/√36
= 8.33333
z=(320-300)/8.33333
z=2.4
Therefore,
P(x>320)=P(z<2.4)=0.9918.
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-36 = 3/4n and 2/3h + 14 = 18 I don’t know how to solve
Answer: n= -48 and h=6
Step-by-step explanation:
For the first one,
-36=3/4 n.
So, divide both sides by 3/4.
-36/(3/4)= -48.
Plug into original equation to double check the answer is -48.
3/4(-48)= -36
For the second one, 2/3h +14= 18
subtract 14 from both sides.
2/3h= 4
Now, divide both sides by 2/3 to get you h=6.
Same as the first one, plug into the original equation. h is in fact 6! yay!
Consider a random sample of size 32 from a distribution with mean 40 and variance 8. find the (approximate) probability that the sample mean is between 39.75 and 41.25.
The probability that the sample mean is between 39.75 and 41.25 is approximately 0.5987.
The probability that the sample mean is between 39.75 and 41.25 can be calculated using the Central Limit Theorem. This theorem states that the distribution of the sample means will be normally distributed with a mean equal to the population mean (μ = 40) and a standard deviation equal to the population standard deviation divided by the square root of the sample size (σ = 8/√32).
Using this information, we can calculate the probability that the sample mean is between 39.75 and 41.25, which will be the area under the normal curve between those two points. This area can be calculated using the z-score formula, which is (x-μ)/σ = (41.25-40)/(8/√32). This gives us a z-score of 0.25. The probability can then be calculated using a z-table, which is approximately 0.5987. Therefore, the probability that the sample mean is between 39.75 and 41.25 is approximately 0.5987.
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Which theorem or postulate proves that △ABC and △DEF are similar? SSS Similarity Theorem AA Similarity Postulate SAS Similarity Theorem Two triangles with the same shape. In the first triangle, the vertices are labeled as A, B, and C. Base is B C and the top vertex is A. Side A B is labeled 3. Side B C is labeled 7. Side A C is labeled 6. In the second triangle, the vertices are labeled as D, E, and F. Base is E F and the top vertex is D. Side D E is labeled 18. Side E F is labeled 42. Side D F is labeled 36
The theorem that proves that the two triangles are similar is the SAS Similarity Theorem. The theorem states that if two sides of one triangle are proportional to two sides of another triangle, and the included angle between these sides is the same in both triangles, then the two triangles are similar.
In this case, the ratio of the corresponding sides of the two triangles are:
AB/DE = 3/18 = 1/6
BC/EF = 7/42 = 1/6
Since the ratio of corresponding sides is equal, and the included angle between them (angle B and angle E) is the same, the two triangles are similar by the SAS Similarity Theorem.
help this is urgent hurry pls
Answer:
Step-by-step explanation:
You're right; it's 97 degrees. The angles of a triangle add up to 180, so to solve for each triangle's unknown angle value, subtract the known angles from 180. For the left triangle, that's 33 and for the right triangle it's 50. Those missing angles plus the one the question is asking for should add up to 180 degrees as well. Hence, 180 - 33 - 50 = 97.
Which led most directly to the Roman Republic's demise and its transition to an empire?
A) Consuls staying in power too long.
B) War with the Etruscans.
C) The growing divide between the rich and the poor.
D) The failure of direct democracy.
The failure of direct democracy most directly led to the Roman Republic's demise and its transition to an empire. That is option D.
What brought about the Roman Republic's demise?Democracy is defined as the government by the people for the people and based of the will of these people.
In the first part of ancient Rome (509-27 BC), the people were governed by elected officials. This is democracy as we understand it today.
But things began to change, people became less interested in the affairs of government, and the failure of democracy led directly to the rise of one-man empires. The Roman Empire lasted from 27 BC to 476 BC.
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Solve this trigonometry problem
How do you write 37% as a decimal?
Answer:
0.37
Step-by-step explanation:
37% = 37/100 = 0.37
a jar contains three red, five green, two blue, and six yellow marbles. what is the ratio of red to green to blue to yellow marbles?
The ratio of red to green to blue to yellow marbles is, 3 : 5 : 2 : 6
What is the ratio?A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, while the divisor or number that is dividing is referred to as the consequent.
Give that,
A jar contains,
three red, five green, two blue, and six yellow marbles
the ratio of red to green to blue to yellow marbles = ?
The ratio can be written as,
⇒ 3 : 5 : 2 : 6
Hence, the ratio of balls is 3 : 5 : 2 : 6
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Find the area of the shaded region. Round your answer to the nearest tenth.
The area of the shaded region is 17.4 rounded up to the nearest tenth.
How to evaluate for the area of the shaded regionThe unshaded region forms a circle with a radius of 9/2, so to get the area of the shaded region, we subtract the area of the circle from the area of the square as follows:
area of square = 9 m × 9 m = 81 m²
area of the circle = 22/7 × 9/2 × 9/2
area of the circle = 891/14 m²
area of the shaded region = 81 m² - 891/14 m²
area of the shaded region = (1134 - 891)/14
area of the shaded region = 243/14
area of the shaded region = 17.3571
Therefore, the area of the shaded region is 17.4 rounded up to the nearest tenth.
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HELP 20 BRAINLY!!<33
The table should be completed as follows;
Object Radius Circumference
ceiling fan 2.8 ft 17.584 ft.
water bottle cap 13 mm 81.64 mm.
bowl 9.0 cm 56.5 cm.
drum 12.0 in 75.4 in.
How to calculate the circumference of a circle?Mathematically, the circumference of a circle can be calculated by using this mathematical expression:
C = 2πr
Where:
C represents the circumference of a circle.r represents the radius of a circle.For the ceiling fan, the circumference is given by:
C = 2πr
C = 2 × 3.14 × 2.8
C = 17.584 ft.
For the water bottle cap, the circumference is given by:
C = 2πr
C = 2 × 3.14 × 13
C = 81.64 mm.
For the bowl, the radius is given by:
C = 2πr
56.5 = 2 × 3.14 × r
56.5 = 6.28r.
Radius, r = 56.5/6.28 = 8.9968 ≈ 9.0 cm.
For the drum, the radius is given by:
C = 2πr
75.4 = 2 × 3.14 × r
75.4 = 6.28r.
Radius, r = 75.4/6.28 = 12.0 in.
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9. Construct Arguments Katya measured
the growth of a plant seedling. The
seedling grew inch by the end of the
first week and another inch by the end
of the second week. About how much did
6
the seedling grow in the first 2 weeks?
Explain how you made your estimate.
The total growth of the plant in 2 weeks is 7/6 inches.
What are fractions?A fraction is defined as a piece of a whole. The complete could be a single thing or a group of objects. The component reflects the percentage of the cake when we really cut a slice of cake from the whole cake. Latin is where the word "fraction" originates.
Given plant grew in the first week = 1/3 inch
the plant grew in the second week = 5/6 inch
total growth in 2 weeks = 1/3 + 5/6
1/3 is equivalent to 2/6 with same diameter,
total growth in 2 weeks = 2/6 + 5/6
total growth in 2 weeks = 7/6 inches
Hence the total growth is 7/6 inches.
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The correct question is,
Katya measured the growth of a plant seedling. The seedling grew 1/3 inch by the end of the first week and another 5 / 6 inch by the end of the second week. About how much did the seedling grow in the first 2 weeks? Explain how you made your estimate.
determine the equation of each radical function which has been tranformed
The equation of a radical function can be determined by using the transformation rules for x- and y- shifts, stretches/compressions, reflections, and rotations.
The equation of a radical function can be determined by applying various transformation rules. The most common transformations are shifts, stretches/ compressions, reflections, and rotations. For example, a radical function that is shifted left two units would have an equation of y = sqrt(x + 2). This is because the function is shifted two units to the left of the origin, so the equation must include an x + 2 term. Similarly, if the function is reflected in the x-axis, the equation would be y = -sqrt(x). This is because the reflection inverts the sign of the y-coordinate, so the equation must include a negative sign in the radical. For stretches and compressions, the equation must include a coefficient in front of the radical. For example, if the function is stretched horizontally by a factor of 3, then the equation would be y = 3 sqrt(x). This is because the function is stretched by a factor of three, so the equation must include a coefficient of 3 in front of the radical. Finally, for rotations, the equation must include a term for the angle of rotation. For example, if the function is rotated counterclockwise by 45 degrees, then the equation would be y = sqrt(x + y/tan45). This is because the angle of rotation is 45 degrees, so the equation must include a tan45 term.
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A buhel of apple weight about 42 pound there are four pack in a buhel it take 2 lb of apple to make one pie how many pie can you make with one pack of apple
The number of pies made by 1 peck of apples is 5.25.
What is the Unitary method?
A quantity's unit value must first be determined in order to solve a problem for two different quantities of the quantity. The unitary approach is the name of this technique.
Due to that,
One bushel of apples weighs 42 pounds.
There are four pecks in a bushel.
Additionally, two pounds of apples are needed to produce one pie.
The following unitary method can be used to tackle the provided problem:
One peck weighs 42/4, or 10.5 pounds.
Since one pie only requires two pounds.
Pie can be made from 1 pound.
Therefore, 10.5 pounds or one peck can yield 5.25 pies (10.5 0.5).
Thus, 5.25 pies can be made from one peck of apples.
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rosie sold 19 catendars.Suzy sold 26 jaun sold 4 times as many calenars as rosie and sulzy combined how many calendars did juan sell
First, we can find the total number of calendars sold by Rosie and Suzy combined:
19 (calendars sold by Rosie) + 26 (calendars sold by Suzy) = 45 calendars
Next, we can find the number of calendars sold by Juan:
Juan sold 4 times as many calendars as Rosie and Suzy combined, so Juan sold 4 * 45 = 180 calendars.
45°
11√2
11
y
45°
(11√2)/2
022
Find y.
11√2
Answer:
Step-by-step explanation:
it is the pink one
You decide to invest in government bonds to save money for your eventual wedding. You have an
initial investment of $7,000 and when you choose to invest for 14 years you get a 10% rate
of return.
What will be the value of your investment at maturity?
Round off to nearest whole number
The value of your investment at maturity is $16,800. The interest is $9,800.
What is the meaning of initial investment?
The initial sum of money required to open an account or start a buy-in relationship is known as an initial investment. The two distinct but related industries of banking and long-term investment brokering are the main uses of the term "initial investment."
Given that the initial investment is $7,000. The rate of interest is 10% = 0.10. The number of years of investment is 14 years.
The formula of simple interest is
I = Prt
I = interest, P = principal, r = rate of interest, t = time.
Putting P = 7000, r = 0.10, t = 14 in I = Prt:
I = 7000 × 0.10 × 14
I = 9,800
The amount will be interest + principal = 9800+ 7000 = 16,800.
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A hiker on the Appalachian Trail planned to increase the distance covered by 10% each day. After 7 days, the total distance traveled is 75.897 miles.
Part A: How many miles did the hiker travel on the first day? Round your answer to the nearest mile and show all necessary math work. (4 points)
Part B: What is the equation for Sn? Show all necessary math work. (3 points)
Part C: If this pattern continues, what is the total number of miles the hiker will travel in 10 days? Round your answer to the hundredths place and show all necessary math work. (3 points)
a) The hiked 8 miles on first day.
b) The Equation is [tex]S_7 = a_1(r^7 -1)[/tex]/(r -1)
c) 127.49 miles the hiker will travel in 10 days
What is Sequence?A sequence is defined as an arrangement of numbers in a particular order. On the other hand, a series is defined as the sum of the elements of a sequence.
Given:
The sequence of distances is a geometric sequence with first term a1 and common ratio (1 +10%) = 1.10.
and, The sum of 7 terms of the sequence is ...
So,
[tex]S_7 = a_1(r^7 -1)[/tex]/(r -1)
75.897= [tex]a_1(1.1^7 -1)[/tex]/(1.1 -1)
[tex]a_1[/tex]= 7.99999
[tex]a_1[/tex]= 8
So, hiker hiked 8 miles on first day.
b) The Equation is of the form of Geometric Sequence
[tex]S_7 = a_1(r^7 -1)[/tex]/(r -1)
c) For n= 10 days
[tex]S_{10}= a_1(r^{10} -1)[/tex]/(r -1)
= [tex]8(1.1^{10} -1)[/tex]/(1.1 -1)
= 127.49 miles
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