The values for the length of the similar triangles are: (a). AE = 10 (b). DE = 17.1
What are similar trianglesSimilar triangles are two triangles that have the same shape, but not necessarily the same size. This means that corresponding angles of the two triangles are equal, and corresponding sides are in proportion.
Given that the triangle ∆BAC is similar to the triangle ∆DAE, then AC correspond to AE, and AB correspond to AD. So;
(a). AC/AE = AB/AD
AC/(AC + 2.5) = 6/(6 + 2)
AC/(AC + 2.5) = 6/8
8AC = 6AC + 15 {cross multiplication}
8AC - 6AC = 15 {collect like terms}
2AC = 15
AC = 15/2 {divide through by 2}
AC = 7.5
AE = 7.5 + 2.5 = 10
(b). 12.8/DE = 6/8
DE = (8 × 12.8)/6
DE = 17.0667
Therefore, the values for the length of the similar triangles are: (a). AE = 10 (b). DE = 17.1
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HELP PLEASE ILL MARK BRAINLIST HELP ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
1. RTS
2. RTS
3. 85, 180
4. 19
Step-by-step explanation:
1. The vertical angles are equal to each other.
2. The sum of the interior angle in a triangle is always 180 degrees.
Let f be the function defined by f(x) = 4x^3 - 5x + 3. Which of the following is an equation of the line tangent to the graph of f at the point where x = -1 ?
The equation of the line tangent to the graph of f defined by g(x) = 4x^3 - 5x + 3 at the point where x = -1 is y = 7x + 11
Given the function of the graph defined as gx) = 4x^3 - 5x + 3.
If x = -1
f(-1) = 4(-1)^3 - 5(-1) + 3.
f(-1) = 4(-1) + 5 + 3
f(-1) = -4 + 8
f(-1) = 4
Hence the coordinate point on the line will be (-1, 4)
Get the slope of the line at x = 1
\(m=\frac{dy}{dx} = 12x^2-5\\m=12(-1)^2-5\\m=12-5\\m=7\)
Get the required equation. The equation of the line in point-slope form is expressed as \(y-y_0=m(x-x_0)\)
\(y-4=7(x+1)\\y-4=7x+7\\y=7x+7+4\\y=7x+11\\\)
Hence the equation of the line tangent to the graph of f at the point where x = -1 is y = 7x + 11
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Jane, kevin, and hans have a total of in their wallets. kevin has less than jane. hans has times what jane has. how much does each have?
Based on the given conditions, Jane has $31, Kevin has $25, and Hans has $50 in their wallets.
Let's solve the problem step by step.
First, let's assume that Jane has X dollars in her wallet. Since Kevin has $6 less than Jane, Kevin would have X - $6 dollars in his wallet.
Next, we're given that Hans has 2 times what Kevin has. So, Hans would have 2 * (X - $6) dollars in his wallet.
According to the information given, the total amount of money they have in their wallets is $106. We can write this as an equation:
X + (X - $6) + 2 * (X - $6) = $106
Simplifying the equation:
4X - $18 = $106
4X = $124
X = $31
Now we know that Jane has $31 in her wallet.
Substituting this value into the previous calculations, we find that Kevin has $31 - $6 = $25 and Hans has 2 * ($25) = $50.
To find the total amount they have, we sum up their individual amounts:
Jane: $31
Kevin: $25
Hans: $50
Adding these amounts together, we get $31 + $25 + $50 = $106, which matches the total amount stated in the problem.
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The complete question is:
Jane, kevin and hans have a total of $106 in their wallets. kevin has $6 less than Jane. hans has 2 times what kevin has. how much do they have in their wallets?
which of the following are characteristics of frequency tables? multiple select question. they can be used for quantitative data. they can be used for qualitative data. an observation can fit into more than one class. no observation can fit into more than one class.
This two are characteristics of frequency tables
1. They can be used for quantitative data.
2. They can be used for qualitative data.
Frequency tables have the following characteristics:
1. They can be used for quantitative data:
Frequency tables display the number of occurrences of each value in a dataset, which is particularly useful when dealing with numerical or quantitative data.
2. They can be used for qualitative data:
Frequency tables can also be used for non-numerical or qualitative data, such as categories or groups, by counting the number of occurrences for each category.
4. No observation can fit into more than one class:
In a frequency table, each observation or data point is assigned to only one class or category, ensuring that there is no overlap between classes.
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Jimmy earns a gross income of $2,500 every two weeks. deductions from each paycheck include insurance, retirement, and taxes, which total $1,000. starting with his next paycheck, his insurance will increase by $50. what conclusion can be drawn about his income with this change?
The conclusion that can be drawn from Jimmy's income with the change in insurance is that Jimmy's net income would decrease.
What happens to net income when expenses rise ?When expenses rise, net income will decrease. Net income is calculated by subtracting expenses from gross income, so if expenses increase, the amount of net income will decrease.
This means that with the increase in insurance by $ 50, Jimmy can expect that his net income would decrease by a total amount of $ 50 which is the amount the insurance increased by.
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what information is needed to prove the triangles are congruent using the Hypotenuse-Leg theorem
5. and 6.
The required triangle KLM and triangle QPR has been proved congruent with Hypotenuse-Leg theorem.
What are Pythagorean triplets?In a right angled triangle, its side, such as hypotenuse, perpendicular and base is Pythagorean triplets.
From triangle KLM and QPR,
KM = QR
LK = PQ
Square and subtract above equations,
KM² - LK² = QR² - PQ² - - - - - (1)
From Pythagoras theorem,
hypotenuse ² = perpendicular² + base square,
For triangle KLM
KM² = LK² + LM²
KM² - LK² = LM² - - - - -(2)
For triangle QPR,
QR² = PQ² + PR²
QR² - PQ² = PR² - -- - - - (3)
From equation 2 and 3 put value in equation 1
LM² = PR²
LM = PR
Thus, triangle KLM and triangle QPR proved to be congruent. And the theorem is Hypotenuse-Leg theorem.
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when conducting a hypothesis test concerning the population mean, and the population standard deviation is known, the value of the test statistic is calculated as
We need to know about test statistic to solve the problem. The formula we will need to calculate test statistic is (sample mean- population mean)/(standard deviation/\(\sqrt{size of sample}\))
Test statistic is a number calculated by a statistical test. It describes how far the observed data is from the null hypothesis of no relationship between variables or no difference among sample groups. The test statistic can be calculated using the sample mean, the population mean and population standard deviation.
test statistic= (sample mean- population mean)/(standard deviation/\(\sqrt{size of sample}\))
Therefore the formula to calculate the test statistic will be (sample mean- population mean)/(standard deviation/\(\sqrt{size of sample}\))
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a point is reflected on the x-axis. the reflected point is (4,-3) what is the original point
The original point was before reflection was (4,3)
What is reflection?Reflection is a geometrical transformation of a shape where by the coordinates of points that make the shape are moved over a line of reflection.
The resultant effect of reflection is always a mirror image of what the shape was before.
If the reflected point of the shape is (4, -3) and it is reflected over the x-axis, then the line of reflection is x = 0
When a point is reflected over the x -axis, the x-coordinated is unaffected only the y-coordinate will change.
The direct opposite of -3 reflected over x= 0 is 3.
Therefore the coordinates of the point reflected over the x-axis are (4, 3)
In conclusion, the reflected point(4,-3) was originally at the point(4,3)
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Marsha Bought a Birthday Card for $2.86 And a Pen for $1.57 She paid with a 20 dollar bill. How much change should marsha have received. A $15.57B $24.43C $17.77D $16.57
Answer: The answer is D. 16.57
Step-by-step explanation:
First, you do 2.86+1.57 = 4.43. Then you do 20-4.43. You then get the answer. P.S this is answered by a 7th grader so my step-by-step explanation is kinda bad.
Find the length of side x to the nearest
tenth.
The length of x in the isosceles right triangle is 15.6 units.
How to find the side of an isosceles triangle?An isosceles triangle is a triangle that has two sides equal to each other and two angles congruent to each other.
The triangle above is an isosceles triangle. The triangle is also a right angle triangle. A right angle triangle is a triangle that has one of it's angles as 90 degrees.
Using Pythagoras's theorem, let's find the side x
c² = a² + b²
where
c = hypotenusea and b are the legsTherefore,
11² + 11² = x²
121 + 121 = x²
x = √242
x = 15.5563491861
Therefore,
x = 15.6 units
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What is the goal of solving equations?
At which points are the equations y = x- + 3x + 2 and y = 2x + 3 approximately equal?
Select all the correct locations on the graph. At which points are the equations y = x2 + 3x + 2 and y = 2x + 3 approximately equal? 2.
Answer:
The equations are approximately equals at the points (0.618,4.236)(0.618,4.236) and (-1.618,-0.236)(−1.618,−0.236)
What is the statistical procedure that is used to determine whether a significant difference exists between any numbers of group means?
A)
t-test
B)
ANOVA
C)
Correlation coefficient
D)
Mann Whitney U test
B) ANOVA (Analysis of Variance) is the statistical procedure that is used to determine whether a significant difference exists between any numbers of group means.
Analysis of Variance (ANOVA) is the statistical procedure used to determine whether a significant difference exists between any numbers of group means.
It is commonly used when comparing means across multiple groups or conditions to assess whether there is a statistically significant difference between them. ANOVA analyzes the variance between groups and within groups to make inference about the population means.
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In the diagram c || d identify three numbered angles that have a measure of 70°
Answer:
∠1, ∠5 and ∠8 (a)
Step-by-step explanation:
∠1 because vertical angles are congruent
∠5 because opposite interior angles are congruent
if ∠5 = 70° then ∠8 also equals 70° because of vertical angles
what shape is both a parallelogram and a rhombus (I ready btw)
Answer:
square
Step-by-step explanation:
a square is a quadrilateral which means it has four sides
Answer:
square
Step-by-step explanation:
15% of 140 students=??????
Answer: 21
Step-by-step explanation:
To find this value, we first convert the percentage to a decimal by dividing it by 100: 15/100 = 0.15. We then multiply this decimal by the given number, 140, to find the value of 15% of 140: 0.15 * 140 = 21.
Quadrilateral WXYZ is a rectangle. Find each measure if m<1 = 30 . (Lesson 6-4 )
m<8
In a rectangle WXYZ, if the measure of angle 1 is 30 degrees, then the measure of angle 8 can be determined.
A rectangle is a quadrilateral with four right angles. In a rectangle, opposite angles are congruent, meaning they have the same measure. Since angle 1 is given as 30 degrees, angle 3, which is opposite to angle 1, also measures 30 degrees.
In a rectangle, opposite angles are congruent. Since angle 1 and angle 8 are opposite angles in quadrilateral WXYZ, and angle 1 measures 30 degrees, we can conclude that angle 8 also measures 30 degrees. This is because opposite angles in a rectangle are congruent.
Since angle 3 and angle 8 are adjacent angles sharing a side, their measures should add up to 180 degrees, as they form a straight line. Therefore, the measure of angle 8 is 180 degrees minus the measure of angle 3, which is 180 - 30 = 150 degrees.
So, if angle 1 in rectangle WXYZ is 30 degrees, then angle 8 measures 150 degrees.
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-What is the midpoint between the points (7, 3) and (-5, 5)?
Answer:
The midpoint is ( 1,4)
Step-by-step explanation:
To find the x coordinate of the midpoint add the x coordinates of the endpoint and divide by 2
( 7+-5)/2 = 2/2 =1
To find the y coordinate of the midpoint add the y coordinates of the endpoint and divide by 2
( 3+5)/2 = 8/2 =4
The midpoint is ( 1,4)
Drew practices piano at least 45 minutes per day. He has already practiced 18.5 minutes today. Determine how much longer he will have to practice. Then interpret the solution
So, if they plan to practice a total of 45 minutes and have only completed 18.5 minutes that means they have 26.5 minutes of practice remaining (45-18.5).
Answer:
Step-by-step explanation:
Bessel polynomials are defined recursively as B(0, x) = 1, B(1, x) = x + 1, and for n > 1 : B(n, x) = (2n − 1)xB(n − 1, x) + B(n − 2, x). Use memoization to define a recursive function B which takes on input an int n and a double x. B(n, x) returns a double, the value of the n-th Bessel polynomial at x.
The function checks if the result for the current inputs has already been computed and stored in the `memo` cache. If so, it returns the cached result, otherwise it calculates the result using the recursive definition of the Bessel polynomials and stores the result in the `memo` cache for future use.
Memoization is a technique where we store the results of expensive function calls and return the cached result when the same inputs occur again. Here's a recursive function that uses memoization to calculate the n-th Bessel polynomial at x:
```
memo = {} # Memoization cache
def B(n, x):
if n == 0:
return 1
elif n == 1:
return x + 1
elif (n, x) in memo:
return memo[(n, x)]
else:
result = (2 * n - 1) * x * B(n - 1, x) + B(n - 2, x)
memo[(n, x)] = result
return result
```
The function checks if the result for the current inputs has already been computed and stored in the `memo` cache. If so, it returns the cached result, otherwise it calculates the result using the recursive definition of the Bessel polynomials and stores the result in the `memo` cache for future use. This approach avoids redundant calculations and can significantly speed up the computation of Bessel polynomials for large values of n.
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Find max, min of f(x)=|x^2+4x-5| (x∈[-3;0])
Bilbo found a great deal on rings. He bought a ring for 70% of the original price. If he saved $45, what was the original price?
Answer: $150
Step-by-step explanation:
If Bilbo bought the ring for 70% of the original price, this means that he saved:
= 100% - 70%
= 30%
$45 is therefore 30% of the original price.
Assuming the original price is x:
30% * x = 45
x = 45/30%
x = $150
A scientist measured the growth rate of a bamboo plant at 6 inches in 12 hours. What is the growth rate of the Bamboo? (in inches/hr)
Growth rate
\(\\ \sf\longmapsto Distance/Time\)
\(\\ \sf\longmapsto 6/12\)
\(\\ \sf\longmapsto 0.5in/h\)
What happens to ena if the extracellular concentration of sodium ([na]o) is increased by a factor of 10? factor of 100? decreased by a factor of 10?
Equilibrium potential increases by 2.303 times when Na is increased by factor 10.
Equilibrium potential increases by 4.606 times Na is increased by factor 100.
Equilibrium potential decreases by 4.606 times Na is decreased by factor 100.
Given,
Sodium ion
Here,
Using nernst equation,
E = RT/nF \(ln\frac{Na_{ex} }{Na^+_{in} }\)
E = 58mV
When \({Na_{ex}\) increased by a factor of 10,
E' = RT/nF ln(10 Na)/Na
E/E' = 1/ln(10)
E/E' = 1/2.303
E' = 2.303E
Thus equilibrium potential increases by 2.303 times.
Now when Na is increased by a factor of 100
E' = 4.606E
Equilibrium potential increases by 4.606 times.
Now when Na is decreased by a factor of 100
E' = 4.606E
Equilibrium potential decreases by 4.606 times.
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Complete question is attached below.
a numerical measure of linear association between two variables is the . a. standard deviation b. covariance c. coefficient of variation d. variance
option b is correct - covariance
The correlation coefficient (r ) is a numerical measure that measures the strength and direction of a linear relationship between two quantitative variables.
Covariance
A numerical measure of linear association between two variables.
Covariance is a measure of how changes in one variable are associated with changes in a second variable. Specifically, covariance measures the degree to which two variables are linearly associated. However, it is also often used informally as a general measure of how monotonically related two variables are. It is similar to variance, but where variance tells you how a single variable varies, covariance tells you how two variables vary together.
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which of the three curves drawn matches the graph of y = 2x 2 + x
Mrs. Fulcher had 14 gallon of milk, and she bought 12 gallon more. Her family then drank 58 gallon of milk. How much milk does Mrs. Fulcher have left?
Answer:
Mrs. Gallon is left with -22 gallon of milk
Step-by-step explanation:
Mrs. Fulcher had 14 gallon of milk
She brought 12 gallon of more milk
Milk consumed by her family - 58 gallon
Milk left with Mrs. Fulcher = 14 + 12 -58 = -22
G(Q) = 5 + 3Q + 202 - Q2 C2(Q) = 3 + 4Q + 2 1. Find the MC function for both C1(Q) AND C2(Q). 2. Find AVC function for both Ci(Q) AND C2(Q). 3. Find AFC function for both C1(Q) AND C2(Q). 4. Find AC function for both Ci(Q) AND C2(Q). 5. Find ATC function for both Ci(Q) AND C2(Q).
For C1(Q) = 3 - 2Q.
For C2(Q) = 4.
2. The AVC function
For C1(Q) = 5/Q + 3 + 20/Q - Q.
For C2(Q) = 3/Q + 4 + 2/Q.
3. The AFC function
For C1(Q)= 5/Q - 20/(5 + 3Q + 20/Q - Q)
For C2(Q) = 0.
4. To find the AC function
For C1(Q) = (5 + 3Q + 202 - Q^2)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q).
For C2(Q) = (3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q.
5.To find the ATC function
For C1(Q)= 5/Q² + 3/Q + 20/Q² - Q/Q + 5/Q - 20/(5Q + 3Q² + 20 - Q²)
For C2(Q)= 3/Q² + 4/Q + 2/Q² + 3/Q + 4/Q + 2/Q.
Find the ATC functions for C1(Q) and C2(Q) given the provided cost functions?
1. To find the MC function, we take the derivative of the cost functions with respect to Q.
For C1(Q) = 5 + 3Q + 202 - Q^2, MC1(Q) = 3 - 2Q.
For C2(Q) = 3 + 4Q + 2, MC2(Q) = 4.
2. To find the AVC function, we divide the cost functions by Q.
For C1(Q), AVC1(Q) = (5 + 3Q + 202 - Q^2)/Q = 5/Q + 3 + 20/Q - Q.
For C2(Q), AVC2(Q) = (3 + 4Q + 2)/Q = 3/Q + 4 + 2/Q.
3. To find the AFC function, we subtract the AVC function from the ATC function.
For C1(Q), AFC1(Q) = (5 + 3Q + 202 - Q^2)/Q - (5 + 3Q + 202 - Q^2)/(5 + 3Q + 20/Q - Q)
= 5/Q - 20/(5 + 3Q + 20/Q - Q).
For
C2(Q), AFC2(Q) = (3 + 4Q + 2)/Q - (3 + 4Q + 2)/(3/Q + 4 + 2/Q) = 0.
4. To find the AC function, we add the AVC function to the AFC function.
For
C1(Q), AC1(Q) = (5 + 3Q + 202 - Q^2)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q).
For
C2(Q), AC2(Q) = (3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q.
5. To find the ATC function, we divide the AC function by Q.
For
C1(Q), ATC1(Q) = [(5 + 3Q + 202 - Q²)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q)]/Q
= 5/Q² + 3/Q + 20/Q² - Q/Q + 5/Q - 20/(5Q + 3Q² + 20 - Q²).
For
C2(Q), ATC2(Q) = [(3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q]/Q
= 3/Q² + 4/Q + 2/Q² + 3/Q + 4/Q + 2/Q.
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Rayann walked 26,027,626 millimeters from camp to get to the jungle, and then 66,928,181 more millimeters looking for zebras in the jungle. How many millimeters did she travel in all?
The distance covered by Rayann in millimeters in all is 92,955,807 millimeters
To determine how many millimeters she traveled in all, we will simply add the distance she traveled at first (from camp to the jungle) to the distance she traveled at the second time (looking for Zebras in the jungle).
From the question, the distance Rayann walked from camp to get to the jungle = 26,027,626 millimeters
and the distance she walked looking for Zebras = 66,928,181 millimeters
∴ The distance she traveled in all = 26,027,626 millimeters + 66,928,181 millimeters
The distance she traveled in all = 92,955,807 millimeters
Hence, Rayann traveled 92,955,807 millimeters in all
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Which measurements could represent the side lengths of a right triangle?
4 m, 6 m, 10 m
5 ft, 8 ft, 9 ft
O 16 cm, 30 cm, 34 cm
o 18 in., 24 in., 42 in.
Answer:
16 cm, 30 cm, 34 cm
Step-by-step explanation:
I got this answer simply by plugging each number into my calculator with the following equation:
\(\sqrt{x^{2} +y^{2} }\)
When you the lower numbers into the equation, if the lengths really do give you a triangle, then you should get the largest number as your output. This can help you with any of the other questions that you may have to answer.
Only the measurements of 16 cm, 30 cm, and 34 cm could represent the side lengths of a right triangle.
What are Pythagorean triplets?In a right-angled triangle, its sides, such as hypotenuse, and perpendicular, and the base is Pythagorean triplets.
Here,
The side lengths of a right triangle must satisfy the Pythagorean theorem, which states that the sum of the squares of the two shorter sides (the legs) is equal to the square of the longest side (the hypotenuse). Therefore, we need to check which sets of measurements satisfy this condition.
Only the measurements of 16 cm, 30 cm, and 34 cm could represent the side lengths of a right triangle.
For the first set of measurements, we have:
a = 16 cm, b = 30 cm, c = 34 cm
a² + b² = 256 + 900 = 1156
c² = 1156
Since a² + b² = c², these measurements do represent the side lengths of a right triangle.
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