Triangles ABC and DEF are shown.
B
25 cm
A
35 cm
Choose
20 cm
D
C
E
28 cm
16 cm
F
20 cm
Select the correct transformations from the drop-down menus to complete the statement below.
Doug shows that ADEF is similar to triangle AABC by using a series of transformations.
First, he Choose....
begin Math ToWeb (your LaTeX) S\triangleDEFS ADEF end
MathToWeb Choose...
✓Then, he Choose...
ADEF
Answers
If the hypotenuse and one leg of one right-angled triangle are equal to the corresponding hypotenuse and leg of another right-angled triangle, the two triangles are congruent.
What is congruent triangle?The SSS congruence theorem tells us that the triangles are congruent because there are three pairs of congruent sides. The corresponding triangle sides are also in proportion, so they are similar according to the SSS similarity theorem.The term “congruent” means exactly equal shape and size. This shape and size should remain equal, even when we flip, turn, or rotate the shapes.If two triangles have the same size and shape they are called congruent triangles. If we flip, turn or rotate one of two congruent triangles they are still congruent. If the sides of two triangles are the same then the triangles must have the same angles and therefore must be congruent.The measurement of side DF is 4cm.If all three corresponding sides are equal and all three corresponding angles are equal in measure, two triangles are said to be congruent.Here in the figure attached below,
Given two triangles ΔABC and ΔDEF
Also given that,
ΔABC and ΔDEF are congruent to each other.
Given AC = 4cm
Since both triangles are congruent ,
Side AC is congruent to DF
Therefore DF = 4cm (based on SSS theorem).
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Related Questions
If f(x)=-2x-3 find the value f(4y)
Answers
Answer:
f(4y) = -8y - 3
Step-by-step explanation:
Step 1: Define variables
f(x) = -2x - 3
f(4y) = x = 4y
Step 2: Plug in x = 4y
f(4y) = -2(4y) - 3
f(4y) = -8y - 3
50 Points!!! Solve each inequality. Then graph the solution set on a number line. Photo attached
Answers
50
Step-by-step explanation:
plot it on the number line
Write a word problem that could be solved with the equation
0.15x + 200 650
Answers
Answer:
13.3
Step-by-step explanation:
For which situation could flipping a coin be used to generate a random sample
A: To predict if a machine will be defective or not. B: To predict student performance on an exam. C: To predict the number of peanuts in a container. D: to predict which of four players will win a gold tournament.
I put A but Im not sure.
Answers
Answer: B
because its 50/50 chance you'll have heads or tails
Which polynomial is prime?
O 3x³ + 3x² - 2x - 2
O 3x³ − 2x² + 3x − 4
-
O
4x³ + 2x² + 6x + 3
O
4x³+4x²-3x - 3
Answers
Answer:
B
Step-by-step explanation:
a prime polynomial is one which does not factor into 2 binomials.
its only factors are 1 and itself
attempt to factorise the given polynomials
3x³ + 3x² - 2x - 2 ( factor the first/second and third/fourth terms )
= 3x²(x + 1) - 2(x + 1) ← factor out common factor (x + 1) from each term
= (x + 1)(3x² - 2) ← in factored form
--------------------------------------------------
3x³ - 2x² + 3x - 4 ( factor the first/second terms
= x²(3x - 2) + 3x - 4 ← 3x - 4 cannot be factored
thus this polynomial is prime
----------------------------------------------------
4x³ + 2x² + 6x + 3 ( factor first/second and third/fourth terms )
= 2x²(2x + 1) + 3(2x + 1) ← factor out common factor (2x + 1) from each term
= (2x + 1)(2x² + 3) ← in factored form
-------------------------------------------------
4x³ + 4x² - 3x - 3 ( factor first/second and third/fourth terms )
= 4x²(x + 1) - 3(x + 1) ← factor out common factor (x + 1) from each term
= (x + 1)(4x² - 3) ← in factored form
--------------------------------------------------
the only polynomial which does not factorise is
3x³ - 2x² + 3x - 4
Which is equivalent to 56c^16/162c^3 squared after it has been simplified completely?
Answers
Answer:
B
Step-by-step explanation:
Just took the test plz mark brainliest
Answer:
B
Step-by-step explanation:
*Edgy 2020*
A golf course rents golf clubs for $10 plus $4 for each hour the golf clubs are rented. An expression for the total cost of renting the golf clubs for h hours is 10 + 4h.
Complete the table by finding the total cost of renting the golf clubs for h hours.
Answers
To complete the table, we can use the expression 10 + 4h to calculate the total cost of renting the golf clubs for different values of h.
Table below:h Total cost
1 14
2 18
3 22
4 26
5 30
For example, if the golf clubs are rented for 1 hour, the total cost is $14 (10 + 4(1) = 14). If they are rented for 2 hours, the total cost is $18 (10 + 4(2) = 18), and so on.
What is the expression for the total cost of renting golf clubs for h hours at a golf course that charges $10 plus $4 for each hour rented?The expression for the total cost of renting golf clubs for h hours at a golf course that charges $10 plus $4 for each hour rented is 10 + 4h.
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Find F2 if FX equals X +1 squared
Answers
Answer:
9
Step-by-step explanation:
f(x) = (x+1) ^2
f(2) = (2+1)^2
f(2) = 3^2 = 9
A triangle has one angle that measures 71° and one angle that measures 19º.
What kind of triangle is it?
OA.
equiangular triangle
ОВ.
isosceles triangle
OC.
right triangle
OD
obtuse triangle
Answers
Step-by-step explanation:
always remember : the sum of all angles in every triangle is always 180°.
therefore, when we get 2 angles, we can calculate the third. in our case
180 - 71 - 19 = 90
so, the third angle is 90°.
and that makes the triangle a right-angled triangle. or short : right triangle.
so, C is the right answer.
Suzi starts her hike at 285 feet below sea level. When she reaches the end of the hike, she is still below sea level at −140 feet. What was the change in elevation from the beginning of Suzi's hike to the end of the hike?
Answers
Answer:
• Elevation is the difference between original length and final length
\( = 285 - 140 \\ \\ = { \underline{ \: \: 145 \: \: feet \: \: }}\)
Answer:
140 ftStep-by-step explanation:
Start point = -285 ftEnd point = - 145 ftChange in elevation:
End point - Start point = -145 - (-285) = 140 ftFor any positive integer n, the value of n! is the product of the first n positive integers. For example, 4! = 4 * 3 * 2 * 1 =24. What is the greatest common divisor of 5! and 7! ?
Answers
The GCD of 5! and 7! is 2^3 * 3^1 * 5^1 = 120.
the greatest common divisor of 5! and 7! is 120.
To find the greatest common divisor (GCD) of 5! and 7!, we need to factorize both numbers and identify the common factors.
First, let's calculate the values of 5! and 7!:
5! = 5 * 4 * 3 * 2 * 1 = 120
7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5,040
Now, let's factorize both numbers:
Factorizing 120:
120 = 2^3 * 3 * 5
Factorizing 5,040:
5,040 = 2^4 * 3^2 * 5 * 7
To find the GCD, we need to consider the common factors raised to the lowest power. In this case, the common factors are 2, 3, and 5. The lowest power for 2 is 3 (from 120), the lowest power for 3 is 1 (from 120), and the lowest power for 5 is 1 (from both numbers).
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Comparing Absolute Values
A student said that since -9 is less than 4, then |-9| is
less than |4|. Is the student correct? Explain why or why
not.
Answers
Answer:
i don not know this. but I think
Step-by-step explanation:
Absolute value depends on the distance from zero, -9 is 9 values from zero as 4 is 4 values from zero
9 is greater than 4; the answer is false
X pitchers of lemonade and y number of lemons.Paula can make 3 pitchers of lemonade with 12 lemons. Write an equation for the relationship between x and y.
Answers
Answer:
y=4x is the first answer
second answer id you will need 16 lemons
Step-by-step explanation:
The ratio is 3:12
if you divide 3 by 3 you will 1
and i you divide 12 by 3 you will get 4
keep in mind this is direct proportion whatever you do to one side you must do to the other
now that i have divided the ratio you get 1:4
meaning 1 pitcher for every 4 lemons that the relationship between x and y
y=4x
and if you make 4 pitchers you will need 16 lemons
hope this helped xx
help me pls with this
Answers
Answer:
1 cup of lemon = 3 cup of apple
Step-by-step explanation:
it is a proportion
Calculate the area under the graph of f(x) = 1/xlnx from x = e to x = e^e
Answers
Using integration, it is found that the area under the graph of f(x) in the desired interval is of 1 unit squared.
How is the area under a graph found?The area under the graph of a curve f(x) between x = a and x = b is given by the following integral:
\(A = \int_{a}^{b} f(x) dx\)
In this problem, the function and the limits of integration are given by:
\(f(x) = \frac{1}{x\ln{x}}\)
\(a = e, b = e^e\)
Hence:
\(A = \int_{e}^{e^e} \frac{1}{x\ln{x}} dx\)
Using substitution:
\(u = \ln{x}\)
\(du = \frac{1}{x} dx\)
\(dx = x du\)
Hence:
\(\int \frac{1}{x\ln{x}} dx = \int \frac{1}{u} du = \ln{u} = \ln{\ln{x}}\)
Applying the Fundamental Theorem of Calculus:
\(A = \ln{\ln{e^e}} - \ln{\ln{e}} = \ln{e\ln{e}} = \ln{\ln{e}} = \ln{e} - \ln{1} = 1\)
Hence, the area under the graph of f(x) in the desired interval is of 1 unit squared.
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A woman’s store sells the following categories of clothing for the following prices blouse Ghc14 each, skirt Ghc16 each, dress Ghc25 each, pantyhose 2 pair for Ghc3 , socks Ghc7
A lady goes to the store on a day when the store has a 20% off sale on all skirts. If yaa buys 2 skirt, 1 dress, 4 pairs of 7 pantyhose, how much money does the lady have to pay
Answers
\(\huge\colorbox{red}T\colorbox{orange}h\colorbox{yellow}a\colorbox{green}n\colorbox{blue}k\colorbox{purple}s\)
Which expression is equivalent to 6y?
6+y
7y - 1
y x y x y x y x y x y
y+y+y+y+y+y
Answers
Answer:
y + y + y + y + y + y
Step-by-step explanation:
6y =
6 * y = ==> add y 6 times
Hence, 6 * y = y + y + y + y + y + y
If m = 34 and n = 5, what is the value of the following expression?
m - 5 • n + 2
A.
145
B.
7
C.
147
D.
11
Answers
\(\large\text{Hey there!}\)
\(\mathsf{m - 5\times n +2}\\\mathsf{= 34 - 5 \times 5+2}\\\mathsf{= 34 - \bold{25} + 2}\\\mathsf{= \bold{9} + 2}\\\mathsf{= \bf 11}\\\\\large\text{Therefore, your answer is:\huge \boxed{\textsf{Option D. 11 }}}\huge\checkmark\)
\(\large\text{Good luck on your assignment \& enjoy your day!}\\\\\frak{Amphitrite1040:)}\)
Calculate the probability for the following situation, then select the correct answer:
You are tossing a coin, then rolling a die, then drawing a card from a deck of cards. What is the probability that you will get: a head AND an odd number on the die AND a card greater than 6 (assume the ace is equal to 1) from the deck?
Answers
The probability is P = 0.135
How to find the probability?
First, we need to find the individual probabilities, that are given by the quotient between the number of outcomes that meet the condition and the total number of outcomes.
P(head) = 1/2P(odd number) = 3/6 (there are 3 odd numbers on the dice)P(card greater than 6) = 28/52 (28 cards with numbers larger than 6).The joint probability is given by the product between the individual probabilities, so we get:
P = (1/2)*(3/6)*(28/52) = 0.135
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Use the scenario to choose the correct answers. Complete Steps 1-2 in order.
A company records its sales for each year.
9. Step 1: Find the equation of the line of regression
y=ax+b
y=3.7 x+8.5
y=8.5 x+3.7
y=-8.5 x+3.7
y=-3.7 x+8.5
10. Step 2: Use the regression line as a model to estimate the sales of the company in 2022.
71.7 million dollars
64.3 million dollars
85 million dollars
38.1 million dollars
Answers
9. The regression line is given as follows: y = 8.5x + 3.7.
10. The estimate for 2022 is given as follows: 71.7 million dollars.
How to obtain the regression line?The regression line is obtained inserting the points of the table into a linear regression calculator.
From the table, the points are given as follows:
(1, 13), (2, 19), (3, 31), (4, 36), (5, 47).
(considering x as the number of years since 2014).
Inserting these points into a calculator, the equation is given as follows:
y = 8.5x + 3.7.
2022 is 8 years after 2014, hence the estimate is given as follows:
y = 8.5(8) + 3.7 = 71.7 million dollars.
(numeric value at x = 8, replace the lone instance of x by 8).
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solve for x if,
3^2x+1 - 4 (3^x) = -1
Answers
Answer:
x=1.11772568, -0.48679593
I think this is right, hope it helps!
Answer:
\(x= 1.117725689 , -0.486795935...\)
Step-by-step explanation:
\(3^{2x}+1-4(3^{x})=-1\\\)
Let y=3^x
Rewrite in:
\(y^2+1-4y=-1\\y^2-4y=-2\\(y-2)^2=2\\y=2+\sqrt{2}, 2-\sqrt{2} \\y=3^{x}\\x=log(y)/log(3)\\x=\frac{log(2+\sqrt{2} )}{log(3)} , \frac{log(2-\sqrt{2}) }{log(3)} \\\\x= 1.117725689 , -0.486795935...\)
Which image below shows the result of an image that has been rotated 180 by the origin O?
Answers
Simplify the expression:
4x - (x + 3) + 5(2x - 8)
Answers
Answer:
Step-by-step explanation:
4x - (x + 3) +5(2x - 8) = 4x + x*(-1) + 3*(-1) + 2x * 5 + (-8) * 5
= 4x - x - 3 + 10x - 40 {combine like terms}
= 4x - x + 10x - 3 - 40
= 13x - 43
Answer:
13x-43
Step-by-step explanation:
have a spectacular day! <3
John charges $90 per hour for a landscaping job that takes 12 hours to complete. A helper is paid 14 of the total amount that John charges. Which THREE statements are true for this situation?
Answers
Answer:
A
Step-by-step explanation:
Which of the following statements is true about an approximation for V73 select all that apply
Answers
Answer:
It should be to the left of 9 on a number line.
Step-by-step explanation:
Please help me with this
Answers
Answer:
z = 99
Step-by-step explanation:
\(\frac{z}{9}\) + 4 = 15 ( subtract 4 from both sides )
\(\frac{z}{9}\) = 11 ( multiply both sides by 9 to clear the fraction )
z = 99
Put this numbers from least to greatest.
A: 3.2, 0.67, 9, 1.78
B: 1/2, 1/4, 6, 3/4, 7/8
please please please please help me please please please please please please please please please please.
Answers
Answer:
1/4, 1/2, .67, 3/4, 7/8, 1.78, 3.2, 6, 9
Answer:
A: 9, 3.2, 1.78, 0.67
B: 6, 7/8, 3/4, 1/2, 1/4
all together 9, 6, 3.2, 1.78, 7/8, 3/4, 0.67, 1/2, 1/4
Step-by-step explanation:
When is a repeating decimal acceptable to use during calculations? When should you convert a repeating decimal to a fraction for calculations?
Answers
A repeating decimal is acceptable to use during calculations when you require a certain level of precision
When is a repeating decimal acceptable to use during calculations?A repeating decimal is acceptable to use during calculations when you require a certain level of precision, but it's important to keep in mind that the result will be an approximation rather than an exact value.
It is commonly used in situations where a rounded value is sufficient and the level of precision doesn't significantly impact the final result.
On the other hand, you should convert a repeating decimal to a fraction for calculations when you need an exact value or when further mathematical operations or comparisons are required.
Converting a repeating decimal to a fraction allows for precise calculations and eliminates any potential rounding errors associated with working with decimal approximations.
Converting a repeating decimal to a fraction involves identifying the repeating pattern and expressing it as a fraction. This allows for exact calculations and maintains the mathematical properties of fractions.
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find the area of the triangular prism
Answers
The total surface area of the triangular prism using the net is 96 square units
Calculating the total surface area using the net.From the question, we have the following parameters that can be used in our computation:
The net of a triangular prism
The surface area of the triangular prism from the net is calculated as
Surface area = sum of areas of individual shapes that make up the net of the triangular prism
Using the above as a guide, we have the following:
Area = 2 * 3 * 7 + 6 * 7+ 2 * 1/2 * 2 * 6
Evaluate
Area = 96
Hence, the surface area is 96 square units
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Are these equivalent the the expression on the top right
Answers
Answer:
No
Yes
No
Yes
(choice 3 is a no)