Why is triangle DFC congruent to triangle AEB?
By Side - Angle - Side congruency (SAS) rule, ΔDFC is congruent to ΔAEB as shown below.
What are Congruent triangles?Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure.
Given is a geometrical diagram as shown in the image.
We can prove ΔDFC ≅ ΔAEB as follows -
AE = CF [Given]
Add length EF on both sides of the equation, we get
AE = CF ...[1]
∠ 1 = ∠ 2 [Given] ...[2]
Given is ∠ 1 = ∠ 2. Than the tangent of both angles will be same. On solving the tangent ratio, we get -
BE = FD ...[3]
From equation 1, 2 and 3, we can say that
ΔDFC ≅ ΔAEB
Therefore, by Side - Angle - Side congruency (SAS) rule, ΔDFC is congruent to ΔAEB.
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What are precise definitions of perpendicular and parallel lines
Answer:
Perpendicular lines: When a line intersects another line at exact 90 degrees the lines are said to be perpendicular to each other.
Parallel lines: When two lines are formed such that the two lines are never intersecting and no angle is formed is known as parallel lines.
100 points give me an explanation.
Dont lie or I will report you.
Answer:
Both ans are attached
What is the solution to |2x - 8| ≤ 6?
5x4 6/11 give your answer in simplest form
The answer in simplest form is [tex]20\frac{30}{11}[/tex] .
What is fraction in simplest form?When the numerator (top) and denominator (bottom) of the fraction do not have any common factors, the fraction is said to be in its simplest form. When the top and bottom of a fraction are whole numbers that are coprime to one another, the fraction is said to be in its simplest form.Any fraction can be easily found in its simplest form. By dividing both the numerator and denominator by the greatest common factor that entirely divides them, we need to simplify the fraction's numerator and denominator. Both the numerator and the denominator should still be whole numbers after division. Reducing fractions is another name for this process of simplifying fractions.Given fraction is [tex]5*4\frac{6}{11}[/tex].
So we convert the mixed fraction into an improper fraction to calculate further.
[tex]4\frac{6}{11} =\frac{50}{11}[/tex]
Next, we calculate the above fraction given in the question
[tex]5*\frac{50}{11}[/tex] = [tex]\frac{250}{11}[/tex]
So now we convert obtained improper fraction to mixed fraction which is its simplest form,
[tex]\frac{250}{11} = 20\frac{30}{11}[/tex]
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professor moore forgets to set his alarm with a probability of 0.10. if he sets the alarm, it will wake him on time to make his first class with a probability of 0.95. if he forgets to set the alarm, he wakes up in time for his first class with a probability of 0.25. professor moore was late to his first class. what is the probability that professor moore set his alarm given this information?
Answer: -The probability of setting his alarm is 1-0.1=0.9
-The probability of being in time is therefore calculated as:
0.9 x 0.95 + 0.1 x 0.25
= 0.88
Hence, the probability that the professor shows up in time is 0.88
Step-by-step explanation:
Read through the solution below. Then, answer
the questions that follow.
16
6 + d =
[box]*
d
ad=b(de-c)
b
=
ad
de
=e
-C
= b
In the line marked *, what strategy was used?
The expression
fills in the orange box.
Determine the rate of change of the graph (HELP PLEASE)
this past semester, a professor had a small business calculus section. the students in the class were . suppose the professor randomly selects two people to go to the board to work problems. what is the probability that is the first person chosen to go to the board and is the second?
Given : Professor randomly selects two people to go to board to work on problems.
To find: Probability of chosen first or second person to go to the board.
Let [tex]x[/tex] be the total no. of students.
After the first student is chosen, no of students left = [tex]x[/tex] - 1
Therefore,
the required probability = 1 / total no. of students x no. of students left
⇒ 1 / [tex]x[/tex] ([tex]x[/tex]- 1 )
= 1 / ([tex]x^{2} - x[/tex])
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a foot ball team lost 4 yards, lost 3 yards and then gained 10 yards in three subsequent plays. what was their net change in yards after those three plays
PLISS HELP
Why is diffusion considered a form of passive transport?
Responses
It requires no energy from the cell.
It requires no energy from the cell.
It's a process that occurs automatically.
It's a process that occurs automatically.
It has no effect on the health of the cell.
It has no effect on the health of the cell.
It's carried out while the cell does other things.
Answer:
It requires no energy from the cell.
Step-by-step explanation:
select the correct answer. a 500-gallon water tank drains at a rate of 50 gallons per minute. the amount of water left in the tank depends on the number of minutes it has been draining. what is the range of this relation? 0 ≤ y ≤ 500 0 ≤ y ≤ 10 y ≤ 500 y ≥ 0
Our range is 0 x 10, We could also graph this with x along with the x-axis and w along the y-axis then every minute 50x gallons are gone
We have 500 gallons of the water tank and it drains at the rate of 50 gallons per minute,
.Let's suppose after 5 minutes,
W = 500 - 50 * 5W = 500 - 250W = 250
After 5 minutes, 250 gallons are left in the water tank.
Here the lowest value is 0 so our maximum time is once the tank emptied, or when w is equal to 0.
0 = 500 - 50x
50x = 500X = 500/50X = 10
So, our range is 0 x 10
We could also graph this with x along with x-axis and w along the y-axis, in the graph the x- intercept where the tank is empty
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Round 387.869911589 to 3 decimal places.
\Big(\frac{1}{6}-0.5\Big) \div\frac{5}{11}
(
6
1
−0.5)÷
11
5
387.869911589 to 3 decimal places is 387.870.
What is the number rounded to 3 decimal placesA decimal is a number that is made up of integers and non-integers. The integers are separated from the non-integers by a decimal point.
In order to round off a number to 3 decimal places, there must be 2 numbers to the right of the decimal point.
In order to round off a number to 3 decimal places, if the ten thousandth figure is equal to five or greater than 5, one is added to the thousandth figure. If the ten thousandth figure is less than 5, there is no change in the thousandth digit.
The ten thousandth is greater than 9, so one is added to the thousandth digit. The number becomes 387. 870
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A seafood market sells Maryland crabs for $10.50 per Ib and Alaskan crabs for $8.50 per lb. The owner can bring 500 lbs of crabs to sell at a weekend seafood festival. How much
money can the owner earn at the festival? Show your work and explain your reasoning.
Provided the owner can bring 500 lbs of crabs to sell at the weekend seafood festival, they can earn between $4,250 and $5,250, depending on which type of crabs or their different combinations.
How are the total earnings determined?The total earnings can be determined using mathematical operations of multiplication, division, addition, and subtraction.
The total earnings are the products (multiplication results) of the units of each type of crab and their selling prices.
The selling price of Maryland crabs per Ib = $10.50
The selling price of Alaskan crabs per lb = $8.50
The total quantity of crabs the owner can bring to the seafood festival = 500 lbs
If the owner decides to bring in Maryland crabs, they can earn $5,250 ($10.50 x 500)
If the owner decides to bring in Alaskan crabs, they can earn $4,250 ($8.50 x 500)
If the owner decides to bring a combination of Maryland and Alaskan in the ratio of 50:50, they can earn $4,750 ($10.50 x 250) + $8.50 x 250)
Thus, if the owner sells Maryland crabs, the total earnings are $5,250, but if they sell Alaskan crabs, they earn $4,250.
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The graph of y = 2x^2 - 8x + 7 is identical to the graph of y = a(x-h)^2 + k$ for some real numbers $a, h, k$.
What is the value of $k$?
The form:
y = a(x-h)^2 + k
Is the vertex form of the quadratic equation, by finding the vertex, we conclude that k = -1.
How to get the value of k?For any quadratic equation of the form:
y = a*x^2 + b*x + c
With a vertex (h, k), we can rewrite the equation as:
y = a*(x - h)^2 + k
And the value h of the vertex is given by:
h = -b/(2a)
In this case, the quadratic equation is:
y = 2x^2 - 8x + 7
Then the value h of the vertex is:
h = -(-8)/(2*2) = 2
Evaluating the quadratic equation in x = 2 we will get the value of k, so we have.
y = 2*(2)^2 - 8*2 + 7 = -1
Then the vertex is (2, -1), which means that the value of K is -1.
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Find a point-slope form for the line with slope = 1/5 and passing through the point
(- 6, -7).
The equation of the line in point-slope form is…
Answer:
y+5 = 1/5 (x+6)
Step-by-step explanation:
The point slope form looks like this.
y - y1 = m (x - x1)
the m represent slope and (x1, y1) are the coordinates of the point that the line passes through.
[5*(54-:6-3)]+6*2-60
i need help?
Answer:
177
Step-by-step explanation:
5(54 − 6 − 3) + (6)(2) − 60
= 177
One pound of apples costs $3.25. Five pounds of apples costs $16.25.
Answer:
what do you mean?
Step-by-step explanation:
PLEASE help! 20 points!
There is a 6% sales tax on your clothing purchase.
You pay $1.80 in tax.
What is the total amount you pay?
well, the amount paid was "x", which oddly enough is 100%, but we also know that 6% of that is $1.80, so
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 1.80& 6 \end{array} \implies \cfrac{x}{1.80}~~=~~\cfrac{100}{6} \implies 6x=180\implies x=\cfrac{180}{6}\implies x=30[/tex]
HELP
What is the slope of the line?
Answer:
y= 1/2x+3.5
Step-by-step explanation:
Answer:
y= 1/2x+3.5
I took the test this is right
Step-by-step explanation:
Round 0.699 to the nearest hundredth.
Answer: 0.700
0.699 is the closest to 0.700, the hundredth would go up by one creating 0.700 hope this helps
The 89 members of the Taft School Band spend
a total of $4,628 for tickets to Hammond's
Amusement Park. What is the cost of each
amusement park ticket?
By using division, if 89 members of the Taft school band spend a total of $4628 for tickets to Hammond's amusement park, The the cost of each amusement park ticket is $52
The total number of members of the Taft school = 89 members
The total cost for the ticket to Hammond's amusement park = $4628
The cost of each amusement park ticket = The total cost for the ticket to Hammond's amusement park ÷ The total number of members of the Taft school
Substitute the values in the equation
The cost of each amusement park ticket = 4628/89
= $52
Hence, by using division, if 89 members of the Taft school band spend a total of $4628 for tickets to Hammond's amusement park, The the cost of each amusement park ticket is $52
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which answer?
pls help
Answer:
1. C: y = 3x - 5
2. B: y = -3x - 9
Step-by-step explanation:
1.
y = 3x + 9; (2, 1) (parallel)
(x₁, y₁)
y - y₁ = m(x - x₁)
y - 1 = 3(x - 2)
y - 1 = 3x - 6
+1 +1
-------------------
y = 3x - 5
----------------------------------------------------------------------------------------------------------
2.
y = (1/3)x - 6 ; (-3, 0) (perpendicular)
(x₁, y₁)
y - y₁ = m(x - x₁)
y - 0 = -3(x - (-3))
y - 0 = -3(x + 3)
y - 0 = -3x - 9
+0 +0
----------------------
y = -3x - 9
I hope this helps!
I dont know what im doing Help Meeee
Answer:
the x = 0 and y = 1
so start off at the zero on the x-axis, and move up to the 1 on the y- axis
A factory adds three red drops and two blue drops of coloring to white paint to make each pint of purple paint. The factory will make 50 gallons of the purple paint.
How many drops of red and blue coloring will the factory need in the 50-gallon batch of purple paint?
Answer: 1200 red and 800 blue
a function is graphed below. on which interval of c is the average rate of change of the function the greatest?
1. x=0 to x=2
2. x=12 to x=18
3. x=2 to x=12
4. x=18 to x=24
A cat can jump eight times as high as it is tall. How high could a cat jump if it is 5.6 inches tall?
Answer:
44.8 inches
Step-by-step explanation:
5.6x8
need to write something to let me answer
Answer:
44.8 inches
Step-by-step explanation:
Hope this helps
The graph of y = f(x) is shown below. Find all values of x where f(x) = 0
The values of x when f(x) = 0 are 2 and 8
Graphs are used mostly to show the relationship between two variables (usually x and y).
The graph of y = f(x) is attached
To get the values of x when f(x) = 0 , we consider where the line of the graph crosses the x-axis.
The graph crosses the x-axis at:
x = 2
x = 8
This means that the values of x when f(x) = 0 are 2 and 8
Therefore, in the graph of y = f(x), the values of x where f(x) = 0 are 2 and 8
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Disclaimer : The question mentined is not provided with a graph, the above solution is done as per the graph attached.
The population of a city decreases by 1.7% per year. If this year's population is 366,000, what will next year's population be, to the nearest individual?
The population of the city next year, after decreasing, will be 359,778
Here, we are given that the population of a city decreases by 1.7% per year.
This, means that the city's population will decrease by 1.7% in 1 year, (1.7 × 1.7)% in 2 years and so on.
The population of the city this year is given to be 366,000.
Thus, next year, the population will decrease by-
1.7% of 366,000
= 1.7/100 × 366,000
= 17/10 × 3,660
= 17 × 366
= 6,222
Thus, the city's total population next year will be-
366,000 - 6,222
= 3,59,778
Hence, the city's population to the nearest individual comes out to be 359,778.
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is 5 square root-2 square root rational?
5 square root - 2 square root is 0.821854415 and it is rational.
Given,
5 square root - 2 square root
That is,
√5 - √2
We have to find this is rational or not.
First we have to solve the equation:
√5 - √2 = 0.821854415
Irrational numbers cannot be stated as a fraction, although rational numbers can be expressed as ratios (such as P/Q and Q0). However, both of the numbers are genuine and can be shown on a number line.
So, here 0.821854415 is a rational number.
That is, 5 square root - 2 square root is rational.
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