leg-leg (ll) congruence theorem if the legs of a right triangle are congruent to the legs of a second right triangle, then the triangles are congruent.
Answers
The leg-leg (LL) theorem of congruency states that if the legs of a right triangle are equal to the legs of a second right triangle, then the two triangles are congruent.
We know that two triangles are congruent if and only if they have three pairs of equal sides.
In the case of the LL congruence theorem,
the two triangles have two pairs of equal sides (the legs) and one pair of equal angles (the right angles).
Therefore by the Side-Angle-Side (SAS) congruence criterion, the 2 triangles are congruent.
Alternatively
If the legs are of equal length then
Their squares would be equal to
Hence, the sum of these squares too would be equal.
Now taking a root over these would give us the hypotenuse for these triangles, which in turn should be equal.
Hence, by SSS congruence criteria
the triangles would be congruent.
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Related Questions
What is the result of 36 divided by 3?
6
9
12
18
Answers
Answer:
12
Step-by-step explanation:
The division of 36 and 3 is 12. Therefore, option C is the correct answer.
What is the division?The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.
The given numbers are 36 and 3.
36 divided by 3
Here, 36/3
Where, 36 is dividend and 3 is divisor.
36/3 = 12
So, quotient is 12
Therefore, option C is the correct answer.
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On a number line, point C is at 8, and the midpoint E of CD is at -3.
Point D is at
on the number line.
Answers
Answer: C
Step-by-step explanation:
Point D is at -14 on the number line.
How to determine the midpoint of a line segment?In Mathematics, the midpoint of a line segment with two end points can be calculated by adding each end point on a line segment together and then divide by two (2).
Since E is the midpoint of line segment CD, we can logically deduce the following relationship:
Line segment CD = Line segment C + Line segment D
Midpoint E = (point C + point D)/2
By substituting the given points into the equation above, we have the following:
-3 = (8 + D)/2
-6 = 8 + D
D = -6 - 8
D = -14
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What is the value of y?
Answers
Answer:
Step-by-step explanation:
Remark
The value of the y can be found by using the Geometric Mean. To use the said mean, you must compare parts of one triangle to parts of the second triangle. In this case, the small triangle containing boy 4 and y, must be compared to the triangle use y and 12
Formula
This translates to
4 / y = y/12
Explanation. The two triangles y and 4 and y and 12 are similar. The short side on the small right triangle on the left is 4. The second longest side on the same triangle is y.
In the triangle containing y and 12 The short side is y and the second side length is 12. You have to read this a couple of times to get the meaning of the two ratios.
Solution
4/y = y / 12 Cross multiply
y^2 = 4 * 12
y^2 = 48 Take the square root of both sides.
√y^2 = √48
y = √2 * 2 * 2 * 2 * 3
y = 2 * 2 * √3
Answer
y = 4√3
Answer:
y = 4√3 y = 4√3
Step-by-step explanation:
i hope it's help
Suppose you're making a soup that uses 5 cups of chicken broth for 8 servings. You need to make 12 servings of the soup. How much broth do you need?
A) 7.5 cups
B) 2.5 cups
C) 8.7 cups
D) 10 cups
Answers
A type of glass has a critical angle of 40 degrees for total internal reflection. What is its refractive index?
Answers
The refractive index of the glass is approximately 1.547. This value is obtained using the critical angle of 40 degrees for total internal reflection and the equation sin θc = n2/n1, where n1 is the refractive index of the medium in which the incident ray is traveling.
The critical angle θc for total internal reflection is related to the refractive indices of the two media involved by the equation:
sin θc = n2/n1
where n1 is the refractive index of the medium in which the incident ray is traveling and n2 is the refractive index of the medium in which the refracted ray would travel if it were not totally reflected.
In this case, the incident ray is traveling through the glass and the refracted ray would travel through air (which has a refractive index of approximately 1). Therefore, we have:
sin 40° = 1/n1
Solving for n1, we get:
n1 = 1/sin 40°
Using a calculator, we find:
n1 ≈ 1.547
Therefore, the refractive index of the glass is approximately 1.547.
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Solve each equation -3x + 2 = -1
Answers
-3x=-1-2 - -3x=-3
x=1
2
6. В одном мотке было 75 сантиметров проволоки.
После того как от проволоки отрезали несколько
сантиметров, в мотке осталось 32 сантиметра.
Сколько сантиметров проволоки отрезали от
мотка?
Answers
Answer:
Step-by-step explanation:
После того как от проволоки отрезали несколько
сантиметров, в мотке осталось 32 сантиметра.
Сколько сантиметров проволоки отрезали от
мотка?
One reason for using a distribution instead of the standard Normal curve to find critical values when calculating a level C confidence interval for a population mean is that
(a) z can be used only for large samples.
(b) z requires that you know the population standard deviation θ
.
(c) z requires that you can regard your data as an SRS from the population.
(d) the standard Normal table doesn't include confidence levels at the bottom.
(e) a z critical value will lead to a wider interval than a t critical value.
(b) z requires that you know the population standard deviation θ
.
Answers
Therefore , the solution of the given problem of standard deviation comes out to be the group standard deviation in order to use (b) z.
What does standard deviation actually mean?Statistics uses variance as a way to quantify difference. The image of the result is used to compute the average deviation between the collected data and the mean. Contrary to many other valid measures of variability, it includes those pieces of data on their own by comparing each number to the mean. Variations may be caused by willful mistakes, irrational expectations, or shifting economic or business conditions.
Here,
We use the z-distribution if the total standard deviation is known; otherwise, we use the t-distribution.
Additionally, for small sample sizes, the t-distribution is used, whereas for big sample sizes, the z-distribution is used.
The fact that z requires that you know the population standard deviation, and that this is frequently not known in practice, is one reason to use a distribution rather than the traditional .
Normal curve to find critical values when computing a level C confidence interval for a population mean.
You must be aware of the group standard deviation in order to use (b) z.
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The local government is concerned with the population of a new predatory fish, the tiger gar, which was first observed in Lake Richmond about 5 years ago. The following table shows the approximate number of tiger gars living in the lake since 2016:
2016 2017 2018 2019 2020 2021
322 399 507 618 785 975
Using the TI-nspire calculator, write an exponential function that models the population of tiger gar in the lake. (Round all numbers to the nearest hundredth.)
y=blank(blank)x
Answers
The exponential function that models the population of tiger gar in the lake is given as follows:
\(y = 322.63(1.25)^x\)
How to define an exponential function?An exponential function has the definition presented as follows:
\(y = ab^x\)
In which the parameters are given as follows:
a is the value of y when x = 0.b is the rate of change.Considering x as the number of years since 2016, the points are given as follows:
(0, 322), (1, 399), (2, 507), (3, 618), (4, 785), (5, 957).
Inserting these points into an exponential regression calculator, the equation is given as follows:
\(y = 322.63(1.25)^x\)
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Combine the like terms to create an equivalent expression.
7+4c+2d+3=7+4c+2d+3=
Answers
The expression "7 + 4c + 2d + 3" is already in its simplest form, which means that the terms cannot be combined any further.
What is the standard form of the equation?
A standard form is a method of writing mathematical concepts like an equation, expressions, or numbers in standard form. Example: 2.5 billion years is written as 2,500,000,000 years.
This is because the like terms in the expression, which are the terms that have the same variable and exponent, have already been combined.
In this case, there are no like terms with different coefficients that can be combined.
For example, there are no two terms with the variable "c" that have different coefficients that can be combined to simplify the expression further.
Similarly, there are no two terms with the variable "d" that have different coefficients that can be combined.
Therefore, the equivalent expression is "7 + 4c + 2d + 3 = 7 + 4c + 2d + 3".
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How many significant figures are in the number
43.6? 43.6 has [?] significant figures.
Answers
Answer:
43.6 has 3 significant figures.
Express the first quantity as percentage of the second of 45g and 75g
Answers
The first quantity (45g) as 60 percentage of second (75g).
What do you mean by Percentage?A part of whole expressed in Hundredth. Percentage is a fraction of a number out of 100%. It can be in fraction or in decimal.
To convert the given percentage value in decimal, divide the given value by 100.
For example:
1. 50% in decimal or fraction will be 50/100 = 0.5.
2. 20% in decimal or fraction will be 20/100 = 0.2.
How to calculate Percentage?1. Finding the total amount from which we need to find the percent.
2. Dividing the required amount to find the percentage by total amount.
3. Multiply it by 100.
For example:
1. It rained 10 of the 30 days in April.
Percentage will be 10/30 = (1/3) x 100
Percentage = 33.33%
Here, we have given that:
Total amount = 75g
Required amount for percent = 45g
Now, to find the percentage:
Percentage = 45/75
Percentage = 0.6 x 100
Percentage = 60%
Hence,
The first quantity (45g) as 60 percentage of second (75g).
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The polynomial of degree 4, P(x) has a root of multiplicity 2 at x = 4 and roots of multiplicity 1 at = 0 and x = -2. It goes through the point (5, 14). Find a formula for P(x). P(r)
Answers
Answer:
\(\textsf{Factored form}: \quad P(x)=\dfrac{2}{5}x(x-4)^2(x+2)\)
\(\textsf{Standard form}: \quad P(x)=\dfrac{2}{5}x^4-\dfrac{12}{5}x^3+\dfrac{64}{5}x\)
Step-by-step explanation:
Given information:
P(x) = polynomial of degree 4.Root of multiplicity 2 at x = 4.Root of multiplicity 1 at x = 0.Root of multiplicity 1 at x = -2.Passes through point (5, 14).The multiplicity of a root refers to the number of times the associated factor appears in the factored form of the equation of a polynomial.
Therefore:
\(\boxed{P(x)=ax(x-4)^2(x+2)}\)
where a is a constant to be found.
To find the value of a, substitute the given point (5, 14) into the function and solve for a:
\(\begin{aligned}P(5)&=14\\\implies 5a(5-4)^2(5+2)&=14\\5a(1)^2(7)&=14\\5a(1)(7)&=14\\35a&=14\\a&=\dfrac{14}{35}\\a&=\dfrac{2}{5}\end{aligned}\)
Therefore, the formula for P(x) in factored form is:
\(\boxed{P(x)=\dfrac{2}{5}x(x-4)^2(x+2)}\)
Expand the factored form to write the formula in standard form:
\(\implies P(x)=\dfrac{2}{5}x(x+2)(x-4)^2\)
\(\implies P(x)=\left(\dfrac{2}{5}x^2+\dfrac{4}{5}x\right)(x^2-8x+16)\)
\(\implies P(x)=\dfrac{2}{5}x^4-\dfrac{16}{5}x^3+\dfrac{32}{5}x^2+\dfrac{4}{5}x^3-\dfrac{32}{5}x^2+\dfrac{64}{5}x\)
\(\implies P(x)=\dfrac{2}{5}x^4-\dfrac{12}{5}x^3+\dfrac{64}{5}x\)
How do u write Nineteen million three hundred thousand twenty five and twenty two hundredths
Answers
Let's roll two dice and find the probability of rolling a certain sum. Is this a simple or compound event?
Two dice - Red and Blue
Recall that a simple event has one and only one outcome of interest. In this example, we are rolling two dice, but we are only interested in one outcome, the sum of the two dice. This is a simple event.
What is the probability of:
Rolling a sum of 1?
Rolling a sum of 3?
Rolling a sum of 12?
Rolling a sum of 7?
Since we are rolling a pair of dice and looking for the sum, the sample space is a little more complicated than rolling one die. The chart below will help us determine the possible outcomes. The top row indicates the numbers on the sides of the blue die and the first column represents the number on the sides of the red die. The white area indicates the sum of the numbers in the row and column.
# Rolled 1 2 3 4 5 6
1 1+1=2
1
+
1
=
2
1+2=3
1
+
2
=
3
1+3=4
1
+
3
=
4
1+4=5
1
+
4
=
5
1+5=6
1
+
5
=
6
1+6=7
1
+
6
=
7
2 2+1=3
2
+
1
=
3
2+2=4
2
+
2
=
4
2+3=5
2
+
3
=
5
2+4=6
2
+
4
=
6
2+5=7
2
+
5
=
7
2+6=8
2
+
6
=
8
3 3+1=4
3
+
1
=
4
3+2=5
3
+
2
=
5
3+3=6
3
+
3
=
6
3+4=7
3
+
4
=
7
3+5=8
3
+
5
=
8
3+6=9
3
+
6
=
9
4 4+1=5
4
+
1
=
5
4+2=6
4
+
2
=
6
4+3=7
4
+
3
=
7
4+4=8
4
+
4
=
8
4+5=9
4
+
5
=
9
4+6=10
4
+
6
=
10
5 5+1=6
5
+
1
=
6
5+2=7
5
+
2
=
7
5+3=8
5
+
3
=
8
5+4=9
5
+
4
=
9
5+5=10
5
+
5
=
10
5+6=11
5
+
6
=
11
6 6+1=7
6
+
1
=
7
6+2=8
6
+
2
=
8
6+3=9
6
+
3
=
9
6+4=10
6
+
4
=
10
6+5=11
6
+
5
=
11
6+6=12
6
+
6
=
12
How many outcomes are in the sample space? Answer
Answers
Answer:
the answer to your question how many outcomes is really gonn adepend on you you slove you problem but my amswer is gonna be 7.
multiply the polynomals (a^2+4a-6) and (3a^2-a+3) simplify the answer. show your work
Answers
Explanation
Step 1
apply distributive property
\(\begin{gathered} (a^2+4a-6)(3a^2-a+3)= \\ a^2(3a^2-a+3)+4a(3a^2-a+3)-6(3a^2-a+3)= \\ 3a^4-a^3+3a^2+12a^3-4a^2+12a-18a^2+6a-18 \\ \end{gathered}\)Step 2
add similar terms
\(\begin{gathered} 3a^4-a^3+3a^2+12a^3-4a^2+12a-18a^2+6a-18 \\ 3a^4+11a^3+-19a^2+18a-18 \\ \end{gathered}\)I hope this helps you
A relation is shown (2,7), (0.1), (8, 9), (12, 18), (?, ?)} Select all ordered pairs that could replace the missing ordered pair to make the relation a function. •(-2,9)•(8,-18)•(7,-2)•(-8,0)•(0,0)
Answers
In order to be a function, the input values (x) must have only one output value (y)
So:
Possible pairs.
(-2,9)
(7,-2)
(-8,0)
the table shows the enrollment in a university class so far, broken down by student type.
adult education 7
graduate 2
undergraduate 9
Considering this data, how many of the next 12 students to enroll should you expect to be undergraduate students?
Answers
Answer:
6
Step-by-step explanation:
The number of students in the next 12 to enroll should you expect to be undergraduate students is 6.
What is Probability?Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.
The value of probability will be always in the range from 0 to 1.
From the table,
Total number of students = 7 + 2 + 9 = 18
Number of undergraduates = 9
Probability of having a undergraduate student to enroll = 9/18 = 1/2
When the next 12 students are enrolled,
Number of undergraduates = 1/2 × 12 = 6
Hence 6 students are expected to be undergraduates in the next 12 students.
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Please help! I don’t know the answer to this.
Answers
Answer:
as we can see b and are reflections as ther are same
8. Bonnie worked for 40 hours each week for 30
weeks. How many hours did she work
altogether? /
Answers
Answer:
1,200 40×30=. h. h= hours
14. Solve 2/3 + 5/6 and put answer in simplest form.
A. 9/6
B.1 1/2
C 2/3
D. 7/6
Answers
Answer:
I believe it is C
Step-by-step explanation:
the answer is supposed to be 3/2 but i dont know
-11f=7(1-2f)+5 solve for f
Answers
Answer:
4
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
f = 4
Answer:
f = 4
Step-by-step explanation:
I got this answer ON Khan Academy.
Hope this helps! :)
Which equation represents a line that is perpendicular to the y-axis?
SEE PIC
Answers
Answer: c
Step-by-step explanation:
y = -8
10 minutes! help!
suppose f(x) is given by following graph
Answers
Answer:
this is hard
Step-by-step explanation:
is it trigonometry?
please answer need help
Answers
PLEASE HELP FAST!!!!!
Answers
Answer:
120 feet is the answer
can't believe that you got me in a suit and tie I had to take a pull so I wouldn't cry
You got a line out the church door sayin' goodbye
Yeah, I believe 'em when they say you're in a better place
NAME THE SONG AND THE SINGER 50 POINTS!!!!!
Answers
Answer:
give heaven some hell by Hardy
Step-by-step explanation:
uhm help pleaseeee <3
Answers
They can buy 20 pumpkins
Answer:
they can buy 20 pumpkin
Step-by-step explanation:
250/12.32=20.29222077922
so 20 pumpkin they can buy
The volume of a cuboid is 540cm³. The length is 6cm and the width is 150mm. Work out the height of the cuboid in cm.
Answers
Step-by-step explanation:
To work out the height of the cuboid, we need to use the formula:
Volume = Length x Width x Height
We have been given the volume and the length, so we can substitute those values into the formula:
540 = 6 x Width x Height
Now we need to convert the width from millimeters to centimeters, so we divide it by 10:
150mm ÷ 10 = 15cm
Substituting this value into the formula:
540 = 6 x 15 x Height
Simplifying:
540 = 90 x Height
Dividing both sides by 90:
6 = Height
Therefore, the height of the cuboid is 6cm.
What is the complementary angle of CFB
Answers
Step-by-step explanation:
CFB reads as twenty five degrees
complementary angle will add to it to sum 90 degrees = sixty five degrees
angle CFD is sixty five degrees