Answers
Based on the angle-angle similarity theorem (AA), the similar triangles in the image given can be named as: ΔBAC ~ ΔEDF.
What are Similar Triangles?When two triangles have the same shape but have different sizes, it means the triangles have corresponding pairs of congruent angles and corresponding pairs of sides that are proportional to each other. The triangles are said to be similar.
The image given show two set of triangles that have two corresponding pairs of congruent angles, based on the angle-angle similarity theorem, it means that they are similar to each other.
Therefore, the similar triangles are:
ΔBAC ~ ΔEDF.
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Related Questions
Find the reciprocal of the number. Check that the product of the number and its reciprocal is 1.
-7
Answers
The calculated value of the reciprocal of the number -7 is -1/7
Finding the reciprocal of a numberFrom the question, we have the following parameters that can be used in our computation:
Number = -7
As a general rule, the reciprocal of a number x is 1/x
Using the above as a guide, we have the following:
Reciprocal = -1/7 given that Number = -7
To check, we have
-1/7 * -7
Evaluate
Result = 1
Hence, the reciprocal is 1
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hello, pls help
The distance AB is divided in the specified ratio. Calculate the coordinates of the division point T. A=(3|2|-1), B=(-6|1|-2), 1:2 Please help me because i am not sure if i did it right: T=A+r*(B-A) T=(3,2,-1)+1/3*(-9,-1,-1) T=(0,5/3,-4/3) Is it right? Pls help me
Answers
Yes, your answer is correct.
The coordinates of the division point T are indeed (0, 5/3, -4/3).
We have,
To find the coordinates of the division point T, we use the formula:
T = A + r(B - A)
where r is the ratio in which AB is divided.
In this case, the ratio is 1:2, so r = 1/3 (since 1 + 2 = 3).
Substituting the given values.
T = (3, 2, -1) + (1/3)(-9, -1, -1)
T = (3, 2, -1) + (-3, -1/3, -1/3)
T = (0, 5/3, -4/3)
Thus,
The coordinates of the division point T are indeed (0, 5/3, -4/3).
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An employee started a new job and must enroll in a new family health insurance plan. One of the options involves prescription drug coverage. The employee estimates that the entire family will fill 6 prescriptions per month, totaling $850. The monthly premium for the plan is $48, with 90% coverage for the first $450 in prescription costs, then 80% coverage for all prescription costs over $450. What is the total out-of-pocket expense for one month?
$173
$125
$773
$677
Answers
The total out-of-pocket expense for one month is $677. The correct option is D.
The first step is to calculate the amount of the prescription costs that will be covered by the insurance plan.
Since the family will fill 6 prescriptions per month and the total cost is $850, the average cost per prescription is $850/6 = $141.67 per prescription.
The insurance plan covers 90% of the first $450 in prescription costs, which is $450 * 0.9 = $405.
The remaining $141.67 - $405 = -$263.33 of the first prescription is not covered, since it is below the $450 threshold. This means that the family will have to pay the full cost of the first prescription, and the insurance will not contribute anything to it.
For the remaining 5 prescriptions, the insurance will cover 80% of the cost, since they are over the $450 threshold. The remaining 20% will be the family's responsibility.
The cost of the remaining 5 prescriptions is $141.67 x 5 = $708.35.
The insurance will cover 80% of this amount, which is $708.35 x 0.8 = $566.68.
The family will be responsible for the remaining 20% of the cost, which is $708.35 x 0.2 = $141.67.
Adding up all the costs, the total out-of-pocket expense for one month is:
$405 (first prescription) + $141.67 (20% of remaining prescription costs) + $48 (monthly premium) = $594.67
Therefore, the correct answer is option D: $677.
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What is the sample space Aryonna rolls a standard number cube once
Answers
S = {1, 2, 3, 4, 5, 6} is the sample space Aryonna rolls a standard number cube once
The sample space for rolling a standard number cube once consists of all the possible outcomes or numbers that could appear on the face of the cube.
Since a standard number cube has six faces, numbered 1 through 6, the sample space is:
S = {1, 2, 3, 4, 5, 6}
Each element in this set represents a possible outcome of rolling the number cube once.
Therefore, S = {1, 2, 3, 4, 5, 6} is the sample space Aryonna rolls a standard number cube once
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Choose the equation for the graph.
a) y = 2x - 3| +1
b) y = -2|x - 3| +1
c) y = 2x - 3| - 1
d) y = -2|x + 3| -1
e) y = 2x + 3| +1
Answers
The calculated equation for the graph is y = -2|x + 3| - 1
Choosing the equation for the graph.From the question, we have the following parameters that can be used in our computation:
The absolute value graph
An absolute value function is represented as
y = a|x - h| + k
Where
Vertex, (h, k) = (-3, -1)
So, we have
y = a|x + 3| - 1
The graph faces down
So, a is negative
Possible value is a = -2
So, we have
y = -2|x + 3| - 1
Hence, the function is y = -2|x + 3| - 1
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John has 4 liters of water on his counter. How many milliliters of water does John have on his counter?
Answers
Answer: 4000 millilitres
Step-by-step explanation:
One liter is equal to 1000 millilitres.
So since to get 4 from one, you multiply 1 x 4.
To get to the number of millilitres, you multiply 1000 x 4.
1000 x 4 is 4000.
Question
Construct the exponential function that contains the points (0, 3) and (2, 75).
Provide your answer below:
f(x) = 0
Answers
The exponential function described is f(x) = 3*(5)^x
How to find the exponential function?A general exponential function can be written as:
f(x)= A*(b)^x
Where A is the initial value and b is the base.
Here we know that the function contains the point (0, 3), then:
f(0) = 3 = A*(b)^0
3 = A
We also know that the function contains (2, 75), then:
f(2) = 75 = 3*(b)^2
75/3 = b^2
25 = b^2
√25 = b = 5
The exponential function is.
f(x) = 3*(5)^x
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please answer this question
Answers
The measure of the angle m∠RTS in the circle is drives to be equal to 105°.
What are angles on same segment of a circleAny two angles that have the same endpoint that lie on the same segment of the circle, that is the region between the chord joining the endpoints of the angle and the arc not containing the angle are said to be equal in measure.
Thus;
m∠QPT = m∠RST
so; m∠RST = 34°
Considering the triangle RST, we can solve for m∠RTS as follows:
m∠RTS = 180° - (34 + 41)° {sum of interior angles of a triangle}
m∠RTS = 180° - 75°
m∠RTS = 105°
Therefore, the measure of the angle m∠RTS in the circle is drives to be equal to 105°
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What percent larger is 20.49 trillion to 13.4 trillion
Answers
The answer of the given question based on the percent is , 20.49 trillion is about 52.84% larger than 13.4 trillion.
What is Percentage?Percentage is a way of expressing a quantity or value as a fraction of 100. It is a widely used method for describing proportions, rates, changes, and comparisons in various fields such as mathematics, economics, statistics, science, and everyday life. The term "percent" literally means "per hundred", and it is represented by the symbol "%". To convert a number to a percentage, we multiply it by 100 and add the symbol "%".
To find the percent larger that 20.49 trillion is to 13.4 trillion, we can use the following formula:
Percent change = (New value -Old value) /Old value * 100%
Plugging in the values we have:
Percent change = (20.49 trillion - 13.4 trillion) / 13.4 trillion * 100%
= 7.09 trillion / 13.4 trillion * 100%
= 52.84%
Therefore, 20.49 trillion is about 52.84% larger than 13.4 trillion.
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Statistics help!!!
I chose B and got it wrong, I still don’t understand how to get the correct answer or what that answer is, but I want to understand how to do it right !
What is the probability of rolling a single 6 sided dice three times and getting the following outcomes: 4, a number greater than two, and an
even number.
a) 4/9
b) 21/54 (wrong answer)
c) 1/27
d) 12/216
Answers
Answer:
I am not sure but I will say A I guess.
Find the measure of A and B.
Answers
The measure of sides a and b are 10 and √116 respectively.
What are similar triangles?Similar triangles are triangles that have the same shape, but their sizes may vary. The ratio of corresponding sides of Similar triangles are equal.
This means for two triangles to be similar the corresponding angles of the triangles must be equal.
Therefore;
b/29 = 4/b
b² = 29 × 4
b² = 116
b = √116
using Pythagorean theorem,
b² = a²+4²
116 = a² +16
a² = 116-16
a² = 100
a = 10
therefore the measure of both sides a and b are 10 and √116 respectively.
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23. As long as supplies last, the local animal shelter will give customers a free collar and name tag for each dog or cat
adopted this month. The shelter has the following collars: 5 blue, 8 green, 2 purple, and 5 brown. The name tags that
are available are 10 plastic, 4 leather, and 6 metal.
What is the probability that the first customer will randomly be given a brown collar?
Answers
The probability that the first customer will randomly be given a brown collar is given as follows:
0.25 = 25%.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
The total number of collars is given as follows:
5 + 8 + 2 + 5 = 20 collars.
5 of these collars are brown, hence the probability that the first customer will randomly be given a brown collar is given as follows:
p = 5/20 = 1/4 = 0.25 = 25%.
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Enter a number for y. Approximate to THREE decimal places (last digit should be 8). Thanks in advance!
Answers
Answer: 15.888
Step-by-step explanation:
You should use SOH CAH TOA or 30-60-90 rules. Since they are asking for approximate they probably want you to use SOH CAH TOA
They have given you the opposite of the angle and hypotenuse. The hypotenuse is always across from the right angle
You will use SOH
Sin 60 =y/18 mult both sides by 18
18 sin 60 =y
y=15.588
Line xy is parallel to line segment ac as shown in the figure below.
Answers
Yes, students are correct. By AA similarity criterion, triangle XBY and triangle ABC are similar.
Given that, line XY is parallel to line segment AC.
Consider triangle XBY and triangle ABC,
∠X=∠A (Corresponding angles are equal)
∠Y=∠C (Corresponding angles are equal)
By AA similarity, triangle XBY and triangle ABC are similar.
Yes, students are correct. By AA similarity criterion, triangle XBY and triangle ABC are similar.
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Prove that ABC AADC.
51
51
2
B
Statement
D
1 m/BAC = m_DAC = 51
AB = AD=4
Pick statement
AABCEAADe
Reason
Pick statement
Given
Segments are the same length as themselves,
Pick congruence criterion
a hint
congruence
Answers
ΔABC and ΔADC are congruent by SAS
We have,
From the figure,
We have,
ΔABC and ΔADC
∠BAC = ∠DAC = 51 ( given )
AB = AD = 4 ( given )
AC = AC ( common length )
This means,
ΔABC and ΔADC are congruent by SAS
Thus,
ΔABC and ΔADC are congruent by SAS
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Which of the following is the distance between the two points shown?
A graph with the x-axis starting at negative 4, with tick marks every one-half unit up to 4. The y-axis starts at negative 4, with tick marks every one-half unit up to 4. A point is plotted at negative 3, 0 and at 0.5, 0.
2.5 units
3.5 units
−3.5 units
−2.5 units
Answers
The correct answer for the distance between two points is 3.5 units.
To find the distance between two points on a coordinate plane, we can use the distance formula:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
The two points given are (-3,0) and (0.5,0). Plugging these values into the formula, we get:
distance = sqrt((0.5 - (-3))^2 + (0 - 0)^2)
Simplifying the expression inside the square root:
distance = sqrt(3.5^2)
distance = sqrt(12.25)
distance = 3.5
Therefore, the distance between the two points is 3.5 units.
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Giovanna deposited
5
$1600 into two different savings accounts.
She deposited half of the money at First Oak and the other half at West United.
How much interest will she have earned from both accounts at the end of 5 years?
(Round to the nearest cent)
Answers
Answer:
Since Giovanna deposited half of the money into each account, she deposited $1600 / 2 = $800 into each account.
Let's assume that First Oak offers an annual interest rate of r1, and West United offers an annual interest rate of r2. The amount of interest earned on each account after 5 years would be:
Interest earned on First Oak = $800 * r1 * 5
Interest earned on West United = $800 * r2 * 5
The total interest earned from both accounts would be the sum of these two amounts:
Total interest earned = $800 * r1 * 5 + $800 * r2 * 5
Total interest earned = $4000 * (r1 + r2)
We are not given the interest rates, so we cannot calculate the exact amount of interest earned. However, we can use the given information to make some observations.
Since we are looking for the total interest earned from both accounts, we can simplify the problem by assuming that the interest rates for both accounts are the same. In this case, we have:
Total interest earned = $4000 * 5 * r
Total interest earned = $20000 * r
To find the interest earned, we need to know the value of r. If, for example, the annual interest rate is 4%, then:
r = 0.04
Total interest earned = $20000 * 0.04
Total interest earned = $800
Therefore, if the interest rates for both accounts are the same and equal to 4%, Giovanna would have earned $800 in interest from both accounts at the end of 5 years. However, if the interest rates are different, the total interest earned would be different as well.
Without knowing the interest rates for the two accounts Giovanna deposited her money in, it's not possible to calculate the total interest she'd earn in 5 years. Normally, you would need to use the Simple Interest formula for each account and then add the two results together.
Explanation:This is a Mathematics question about simple interest, which can be solved using the formula: Interest = Principal × Rate × Time. Given that Giovanna divided her money equally into two accounts at First Oak and West United, she put $800 into each account. However, without information about the annual interest rates for both accounts, we can't calculate the amount of interest Giovanna would earn after 5 years. Once the specific interest rates for the two accounts are provided, one could use the Simple Interest formula for each account and then add the interest from both to get the total.
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A company estimates that 0.8% of their products will fail after the original warranty period but within 2 years of the purchase, with a replacement cost of $200.
If they offer a 2 year extended warranty for $30, what is the company's expected value of each warranty sold?
Answers
Step-by-step explanation:
The expected value of each warranty sold can be calculated using the following formula:
Expected Value = (Probability of Failure without warranty x Replacement Cost without warranty) + (Probability of Failure with warranty x Replacement Cost with warranty) - Cost of Warranty
Probability of Failure without warranty = 0.8% or 0.008 (given)
Replacement Cost without warranty = $200 (given)
Probability of Failure with warranty = 0% (since the product is covered under warranty)
Replacement Cost with warranty = $0 (since the cost of replacement is covered under warranty)
Cost of Warranty = $30 (given)
Expected Value = (0.008 x $200) + (0 x $0) - $30
Expected Value = $1.60 - $30
Expected Value = -$28.40
The company's expected value of each warranty sold is -$28.40, which means that on average, the company can expect to lose $28.40 for every warranty sold. This is because the cost of the warranty ($30) is greater than the expected cost of replacement without the warranty ($1.60). Therefore, it is not beneficial for the company to offer the extended warranty.
Irma has $41,000 in a savings account that earns 2% interest per year. The interest is not compounded.To the nearest cent, how much will she have in total in 4months?
Answers
Interest = Principal x Rate x Time
Interest = $41,000 x 0.02 x (4/12) (4 months is one-third of a year)
Interest = $273.33
Therefore, the total amount Irma will have in 4 months is the sum of her initial savings and the interest earned:
Total = $41,000 + $273.33
Total = $41,273.33
Rounding to the nearest cent, Irma will have $41,273.33 in total in 4 months.
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The graph below
Which equation matches the graph?
Answers
Answer:
D
Step-by-step explanation:
What is the term-to-term rule for this sequence? 64, 32, 16, 8, 4
Answers
Answer:
Divide by two is the term-to-term rule.
Step-by-step explanation:
64/2=32
32/2=16
16/2=8
8/2=4
Find the coordinate of point m
that partitions the segment Ab
In the ratio 3:4 if A 7,-3 and b -7,4
Answers
The coordinates of point M divides the line segment AB int he ratio 3 : 4 is given by ( 1, 0).
Ratio in which line segment AB divides m : n = 3 : 4
Let us consider the coordinates of A be ( x₁ , y₁ ) = ( 7, -3 )
Let us consider the coordinates of B be ( x₂ , y₂ ) = ( - 7 , 4)
Let us consider the coordinates of M be ( x , y )
Using the formula of line segment divides in the ration m: n we have,
x = ( mx₂ + nx₁ ) / ( m + n )
y = ( my₂ + ny₁ ) / ( m + n )
Substitute the values we have,
x = ( 3 × (-7) + 4 × 7 ) / ( 3 + 4 )
= ( -21 + 28 ) / 7
= 1
y = ( 3 × (4) + 4 × -3 ) / ( 3 + 4 )
= ( 12 - 12 ) / 7
= 0
Therefore, the coordinates of point M which partition the line segment AB is equal to ( 1, 0).
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The above question is incomplete, the complete question is:
Find the coordinate of point M that partitions the segment AB in the ratio 3:4,if A (7,-3) and B (-7,4).
Solve the following equation for the unknown quantity x.
[tex]\mathrm{9^x=40}[/tex]
*Round to the nearest hundredth as needed*
Answers
Answer:
[tex]x = 1.68[/tex]
Step-by-step explanation:
We have the equation
9ˣ = 40 and we have to solve for x
Take logs on both sides
[tex]\ln(9^x) = \ln(40)\\\\\ln(9^x) = x ln(9) \\\\\therefore x \ln(9) = \ln(40)\\\\x = \dfrac{\ln(40)}{\ln(9)}\\\\\text{Using a calculator, this works out to: }\\\\x=1.67888139\dots \\\\\text{Rounded to the nearest hundredth, }\\x = 1.68\\\\[/tex]
Katie's middle school graduation party will be at the skating rink. The cost for each person is $15. The cost of the room for the party's $80 katies parents have set a budget of $470.
Answers
26 kids can come on the budget of 470.
first subtract the 80 for the room then divided the rest by 15
There were 8 cows and 12 horses at a farm. 5 horses ran away. How many horses were left?
Answers
Answer:
Step-by-step explanation:
7 horses were left
I need help with this problem if do thank you a lot
Answers
The area of the sector is 229.92 square inches and the length of the arc is 32.99 inches.
How to find area of the sector?
Follow is the formula of area of the sector,
Area of sector = [tex] \frac{θ}{360} \times πr²[/tex]
where θ is the angle of the sector in degrees, r is the radius of the circle, and π is a mathematical constant approximately equal to 3.14159.
Substituting the given values,
Area of sector
[tex]= \frac{135}{360} \times π \times 14² \\ = 0.375 \times π \times 196 \\ = 73.0875π[/tex]
≈ 229.92 square inches (rounded to two decimal places)
How To find the length of the arc?
The formula for the arc is [tex]Length \: of \: arc = \frac{θ}{360} \times 2πr[/tex]
Substituting the given values,
Length of arc = (135/360) × 2π × 14
= 0.375 × 2π × 14
= 32.9856
≈ 32.99 inches (rounded to two decimal places)
Therefore, the area of the sector is approximately 229.92 square inches and the length of the arc is approximately 32.99 inches.
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The bar graph shows the number of Asturian households, in thousands, living in poverty from 1999 to 2004. The table holds a quadratic function for the data, where y is the number of households, in thousand living in poverty × years after 1999. 10. 10 1999 2000 2001 2002 2003 2004 QuadReg y = ax2 + bx + c a = 0.2299729818 b = - 0.4599459636 c = 7.5426446323 a. Use the table to express the model in function notation, with numbers rounded to two decimal places #(x) = 0.23x2 + - 0.46x + 7.54 b. According to the function in part (a), in which year was the number of households living in poverty at a minimum? 2000 (Round to the nearest year as needed.) c. Use the model to find the number of households, in thousands, for that year. 7400 (Round to one decimal place as needed.)
Answers
Answer:
a. The quadratic function for the data can be expressed in function notation as follows, rounding the coefficients to two decimal places:
#(x) = 0.23x^2 - 0.46x + 7.54
b. To find the year when the number of households living in poverty was at a minimum, we need to find the vertex of the parabola given by the quadratic function. The x-coordinate of the vertex is given by:
x = -b/(2a)
Substituting the values for a and b given in the problem, we get:
x = -(-0.4599459636)/(2*0.2299729818) ≈ 1
This means that the minimum occurs one year after 1999, i.e., in the year 2000.
c. To find the number of households living in poverty in the year 2000, we can substitute x = 1 in the function:
#(1) = 0.23(1)^2 - 0.46(1) + 7.54 ≈ 7.4
This means that there were about 7,400 households living in poverty in Asturias in the year 2000.
Step-by-step explanation:
A flower bed has the shape of a rectangle 5yards long 4 yards wide what is its area in square ft
Answers
The area of the flower bed is 180 square feet.
Area refers to the amount of space occupied by a two-dimensional shape or surface. It is measured in square units, such as square meters, square inches, or square centimeters. The area of a shape can be calculated by multiplying the length and width of the shape (in the case of a rectangle or square), or by using more complex formulas for other shapes, such as triangles or circles.
To convert yards to feet, we multiply by 3 since 1 yard = 3 feet.
The length of the rectangle in feet is 5 yards × 3 feet/yard = 15 feet.
The width of the rectangle in feet is 4 yards × 3 feet/yard = 12 feet.
The area of the rectangle in square feet is length × width = 15 feet × 12 feet = 180 square feet.
Therefore, the area is 180 square feet.
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Solve the following system of equations:
y=6−x
y=x2−6x+6
A. (1, 0), (-4, 1)
B. (0, 6), (5, 1)
C. (5, 8), (3, 6)
D. (-4, 12)
Answers
Answer:
B. (0, 6), (5, 1)
Step-by-step explanation:
y=6−x
y=x2−6x+6
6 - x = x² - 6x + 6
x² - 5x = 0
x(x - 5) = 0
x = 0 or x = 5
x = 0; y = 6 - 0; y = 6
x = 5; y = 6 - 5; y = 1
Answer: (0, 6), (5, 1)
A small manufacturing company makes $125 on each stereo sound bar produces, and $100 profit on each flatscreen TV it makes. Each sound bar and TV must be processed by cutting machine (A), a fitting machine (B), and a polishing machine(C). Each sound bar must be processed on machine A for one hour, machine B for one hour, and machine C for four hours. Each TV must be processed or machine A for two hours, Machine B for one hour, and machine C for one hour. Machine A is available for 16 hours machine B 49 machine C for 24 hours.
Answers
x = number of sound bars
y = number of flatscreen TVs
According to the problem, the profit on each sound bar is $125, so the total profit from producing x sound bars is 125x. Similarly, the profit on each flatscreen TV is $100, so the total profit from producing y flatscreen TVs is 100y.
Each sound bar requires one hour on machine A, one hour on machine B, and four hours on machine C. Therefore, the total time required to produce x sound bars is 6x hours on machine A, 6x hours on machine B, and 4x hours on machine C. Similarly, each flatscreen TV requires two hours on machine A, one hour on machine B, and one hour on machine C. Therefore, the total time required to produce y flatscreen TVs is 2y hours on machine A, y hours on machine B, and y hours on machine C.
The problem also gives us information about the available time on each machine:
Machine A is available for 16 hours
Machine B is available for 49 hours
Machine C is available for 24 hours
We can use these constraints to set up the following system of linear inequalities:
6x + 2y ≤ 16 (machine A)
6x + y ≤ 49 (machine B)
4x + y ≤ 24 (machine C)
x ≥ 0, y ≥ 0 (non-negativity)
We want to maximize the total profit, which is given by P = 125x + 100y. This is our objective function.
We can use graphical methods or linear programming software to find the optimal solution to this problem. One possible optimal solution is x = 3 and y = 10, with a total profit of $1,375.
Note that there may be other optimal solutions, and the optimal solution may depend on the specific values of the profit margins and machine availability.
