Which of the following statements is true about the triangles below?
a. ΔABC = ΔDEF by SSA
b. ΔABC = ΔDEF by AAS
c. ΔABC = ΔDEF by SAS
d. ΔABC = ΔDEF by ASA
Answers
Answer:
The correct option is c.
Step-by-step explanation:
From the given diagram we have two triangles.
In triangle ABC and DEF,
[tex]AB=DE[/tex] (Given)
[tex]\angle A=\angle D[/tex] (Given)
[tex]AC=DF[/tex] (Given)
According to the SAS property of congruent triangles, two triangles are congruent if two sides and included angle is same.
By SAS property of congruent triangles, we get
[tex]\triangle ABC\cong \triangle DE F[/tex]
[tex]\triangle ABC= \triangle DE F[/tex]
Therefore the correct option is c.
To answer the student's question correctly, a visual representation of the triangles is required. SSA is not a valid congruence criterion, while AAS, SAS, and ASA are. One of the latter three must be matched to the triangles' sides and angles to determine congruency.
Explanation:The student's question involves determining which congruency criterion applies to the given triangles. Without a visual representation of the triangles, however, a concrete answer cannot be provided. The four congruence criteria mentioned are: SSA (Side-Side-Angle), AAS (Angle-Angle-Side), SAS (Side-Angle-Side), and ASA (Angle-Side-Angle). SSA is not a valid congruence criterion because it does not guarantee that two triangles are congruent. AAS, SAS, and ASA are valid criteria that, if satisfied, confirm that two triangles are congruent. A proper comparison of the triangles' sides and angles against these criteria is needed to establish which one is correct.
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Related Questions
Cassandra is trying to think of a good way to keep her financial records. She makes a lot of purchases, using cash, debit cards, and credit cards about equally. When she gets home every day, she tends to be very tired and doesn’t like to do a lot of organized thinking. She tends to lose individual pieces of paper if she doesn’t file them immediately. What might be a good method for Cassandra to use?
Answers
She would have easy access to everything she had done for years and she could also make a backup so as to never lose anything.
In the inequality n/7 - 8 < -11, you will need to flip the inequality sign to solve for n.
True
False
Answers
n/7-8+8 < -11+8
n/7 < -3
n < -21
Answer: False
Step-by-step explanation:
n/7 - 8 < -11
add 8 to each side
n/7 < -3
multiply by 7
n< -21
False
The only time we flip the inequality symbol is when we multiply or divide by a negative.
Hope this helps!
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What fraction is £1 of 13p?
Answers
Which of the following statements describes the absolute value of a number "a"?
A) The opposite value of a number "a" can be represented by the absolute value of a number "a."
B) Given |a|, "a" is always positive
C) The distance from the number "a" to 0 on a number line can be represented by the absolute value of a number "a."
D) The positive value of a negative number "a" can be represented by the absolute value of a number "a."
Answers
What is the explicit rule for this geometric sequence? 2, 6, 18, 54, …
Answers
Answer:
A term at position n can be expressed as \[2*3^{n-1}\]
Step-by-step explanation:
The given geometric sequence is 2, 6, 18, 54, …
Starting term = 2
Second term = 6
So second term is 3 times the first term.
Similarly, Third term = 18
This is 3 times the second term, that is , 3 * 6
Fourth term is is 54.
This is 3 times the third term, that is , 3 * 18
Generalizing, a term in the sequence can be expressed as \[2*3^{n-1}\]
where n represents the position of the term in the sequence.
24 plus something =120÷3
Answers
x = 40 - 24
x = 16
The function h(x) is quadratic and h(3) = h(–10) = 0. Which could represent h(x)?
h(x) = x2 – 13x – 30
h(x) = x2 – 7x – 30
h(x) = 2x2 + 26x – 60
h(x) = 2x2 + 14x – 60
Answers
Answer:
h(x) = 2x2 + 14x – 60 (D)
Step-by-step explanation:
The quadratic function that represents h(x) with roots at 3 and -10 is h(x) = x^2 - 7x - 30 since it correctly reflects the sum and product of its roots.
The question asks us to find which function could represent h(x), given that h(3) = h(–10) = 0. This means the quadratic function has roots at x = 3 and x = -10. A quadratic function with these roots can be written as h(x) = a(x - 3)(x + 10), where a is a non-zero coefficient.
By expanding this expression, we would get h(x) = a(x^2 + 7x - 30). We can then see if any of the given options matches this form upon factoring out the leading coefficient.
Comparing the given options:
h(x) = x^2 - 13x - 30 does not match because the sum of the roots should be -7 based on the roots 3 and -10.h(x) = x^2 - 7x - 30 matches the expected roots since the sum of the roots (-7) and the product of the roots (-30) align with the roots 3 and -10.h(x) = 2x^2 + 26x - 60 does not match because the coefficient of x is positive, while the sum of the roots derived from the roots of the function is negative.h(x) = 2x^2 + 14x - 60 does not match for similar reasons to the previous one and also the coefficients do not align.Therefore, the correct function that could represent h(x) is h(x) = x^2 - 7x - 30.
what is 7x10^-5 in decimals
Answers
hope this helps
7x10^-5 as a decimal is 0.00007, achieved by multiplying 7 by 0.00001, which represents 10^-5.
To convert 7x10^-5 into decimal form, you can use the concept that a negative exponent indicates the inverse. This means that 10^-5 is the same as 1/10^5 or 1 divided by 100,000. Thus, to find 7x10^-5 in decimal form, you multiply 7 by 0.00001.
Here's the calculation:
7 x 0.00001 = 0.00007
Therefore, 7x10^-5 in decimal form is 0.00007.
If BC bisects the angle ACD, then B is the midpoint of AD.
A. True
B. False
Answers
Answer:
It’s true
Step-by-step explanation: just took the test
PLEASE HELP ASAP!!!!!!!!!!
Use the table below to answer this question:
x y
0
2
1
−1
2
−6
Find the average rate of change for the given function from x = 0 to x = 2.
2
4
−4
1
Answers
If ΔABC and ΔGEF are congruent by the ASA criterion, which pair of angles must be congruent?
Answers
Answer:
it should be CAB and GEF
Step-by-step explanation
Marty has saved $72. He spent $8 on a video rental. Write a ratio as a fraction in simplest form to represent what portion of his savings he has left.
Answers
The savings left is just $72 - $8 = $64.
Therefore, the ratio is $64 : $72 = 8 : 9.
I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
Answer: [tex]\dfrac{8}{9}[/tex]
Step-by-step explanation:
Given : Marty has saved $72. He spent $8 on a video rental.
i.e. The amount of money he saved = $72
The amount of money he spent on video rental = $8
Now, the amount of money he had left = [tex]\$72-\$8=\$64[/tex]
Thus , the ratio that represent what portion of his savings he has left :-
[tex]\dfrac{64}{72}=\dfrac{8}{9}[/tex]
Hence, the ratio that represent what portion of his savings he has left :-
[tex]=\dfrac{8}{9}[/tex]
Oscar needs to ship 14 rock cds, 12 classical cds, and 8 pop cds. he can only pack only one type of cd in each box and he must pack the same number of cds in each box. what is the greatest number of cds oscar can pack in each box?
Answers
Answer:
2
Step-by-step explanation:
Oscar needs to pack only one type of cd in each box and he must pack the same number of cd's in each box.
To solve this problem we would need to find the greatest common factor of the numbers given; the numbers that we have are 14, 12, 8.
First we are going to find the factors of all these three numbers:
14 = 1 x 2 x 7
12 = 1 x 2 x 2 x 3
8 = 1 x 2 x 2 x 2
The common factors of these three numbers are bolded:
14 = 1 x 2 x 7
12 = 1 x 2 x 2 x 3
8 = 1 x 2 x 2 x 2
We can see that the common factors are 1 and 2. The biggest of them is 2.
Therefore, the greatest number of cd's Oscar can pack in each box is 2
Since 2 is common to them all, hence the greatest number of cds oscar can pack in each box is 2 CDs
Given the number of cars needed to ship 14 rock CDs, 12 classical CDs, and 8 pop CDs
In order to get the greatest number of cds oscar can pack in each box, we will have to calculate the GCF of each value as shown:
The prime factors of each value is as shown
14 = 2 * 7
12 = 3 * 2 * 2
8 = 2 * 2 * 2
From the factors, we can see that only 2 is common to them all, hence the greatest number of CDs oscar can pack in each box is 2 CDs
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Two numbers are in a ratio of 3:6 their sum is 63 find the bigger number
Answers
To find the bigger number in the given ratio of 3:6 with a sum of 63, simplify the ratio to 1:2, assign a variable to the smaller number, and solve for the larger one. The bigger number is found to be 42.
Explanation:To find the bigger number when two numbers are in a ratio of 3:6 and their sum is 63, first simplify the ratio to its lowest terms. The ratio 3:6 simplifies to 1:2, since both terms can be divided by 3. Let's assign the variable x to the smaller number, which corresponds to the '1' part of the ratio. Therefore, the bigger number is twice the smaller one, so it can be represented as 2x.
The sum of the two numbers is given by the equation x + 2x = 63. Combine like terms to get 3x = 63. Dividing both sides by 3 gives x = 21. Since 2x represents the bigger number, we have 2x = 2 imes 21 = 42.
Hence, the bigger number in this ratio is 42.
If you were to place $5,000 in a savings account that pays 6% interest compounded continuously, how much money will you have after 4 years? Assume you make no other deposits or withdrawals.
A. $6,356.25
B. $11,821.07
C. $5,024
D. $6,312.38
...?
Answers
Answer:
Option D - $6312.38
Step-by-step explanation:
Given : If you were to place $5,000 in a savings account that pays 6% interest compounded continuously.
To find : How much money will you have after 4 years?
Solution :
Using compound interest formula,
[tex]A=P(1+r)^t[/tex]
Where A is the amount,
P is the principle P=$5000
r is the rate r=6%=0.06
t is the time t= 4 years
Substitute the value,
[tex]A=P(1+r)^t[/tex]
[tex]A=(5000)(1+0.06)^4[/tex]
[tex]A=(5000)(1.06)^4[/tex]
[tex]A=5000\times 1.262[/tex]
[tex]A=6312.38[/tex]
The money he have after 4 years is $6312.38
Therefore, Option D is correct.
Answer:
A. $6,356.25
Step-by-step explanation:
To calculate the amount of money you will have after 4 years in a savings account with continuous compounding, we can use the formula:
A = P * e^(rt)
Where:
A = the amount of money accumulated after t years
P = the initial principal amount (in this case, $5,000)
e = the base of the natural logarithm (approximately 2.71828)
r = the annual interest rate (in decimal form, so 6% becomes 0.06)
t = the number of years (in this case, 4)
Plugging in the values, we get:
A = 5000 * e^(0.06 * 4)
Using a calculator, we can evaluate this expression:
A ≈ 5000 * 2.71828^(0.24)
A ≈ 5000 * 1.276281
A ≈ 6381.405
Rounding to the nearest cent, the amount of money you will have after 4 years is approximately $6,381.41.
Therefore, the closest answer option is A. $6,356.25.
A subtending arc on a circle with a radius of 4.5 centimeters has an arc length of 8π. What is the measure of the angle subtended by the arc?
Answers
What is 75% of 60? tell me the answer?
Answers
Did hamiltons plans favored the northern states? true or false
Answers
Answer:
true
Step-by-step explanation:
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9 is 35 percent of what number
Answers
Solve for x: -4 [x 5] = -16
Answers
x=4/5
...................
The solution to the equation -4[x + 5] = -16 is x = -1.
To solve the equation -4[x + 5] = -16 for x, we will follow these steps:
First, we need to isolate the term with the variable. We can start by dividing both sides of the equation by -4 to get rid of the coefficient:
-4[x + 5] / -4 = -16 / -4
Simplifying both sides, we get:
x + 5 = 4
Next, solve for x by subtracting 5 from both sides:
x + 5 - 5 = 4 - 5
Simplifying this, we find:
x = -1
which is a factor of 54xy+45x+18y+15?
a) x-5
b)6y+5
c)6y+1
d)3y+5 ...?
Answers
and the factor, which is b)6y+5.
One of the factors of 54xy + 45x + 18y + 15 is b) 6y + 5.
What are GCF and distributive property?The GCF of two or more than two numbers is the highest number that divides the given two numbers completely.
We also know that distributive property states a(b + c) = ab + ac.
Given,
54xy + 45x + 18y + 15.
= 54xy + 18y + 45x + 15.
= 18y(3x + 1) + 15(3x + 1).
= (3x + 1)(18y + 15).
= (3x + 1)(3)(6y + 5).
So, a factor of 54xy + 45x + 18y + 15 is (6y + 5).
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Please Help,
Given z = 8 and x = 6, what is the ratio of x to z in the simplest form? ...?
Answers
Which system of equations models the problem if x represents the number of parrotfish Jenna bought and y represents the number of triggerfish she bought?
Jenna bought 280 tropical fish for a museum display. She bought 4 times as many triggerfish as parrotfish. How many of each type of fish did she buy?
A. {x+y=280
{y=4x
B.{x−y=280
{y=4x
C.{x+y=4
{y=280x
D.{x+4y=280
{y=4x
Answers
Answer:
The system of equations is the option A
[tex]x+y=280[/tex]
[tex]y=4x[/tex]
Jenna bought [tex]56[/tex] parrot fish and [tex]224[/tex] trigger fish
Step-by-step explanation:
Let
x-----> the number of parrot fish
y-----> the number of trigger fish
we know that
[tex]x+y=280[/tex] -----> equation A
[tex]y=4x[/tex] ------> equation B
The answer Part 1) is the option A
Substitute equation B in equation A
[tex]x+4x=280[/tex]
Solve for x
[tex]5x=280[/tex]
[tex]x=56[/tex]
Find the value of y
[tex]y=4x[/tex]
[tex]y=4*56=224[/tex]
therefore
The answer part 2) is
Jenna bought [tex]56[/tex] parrot fish and [tex]224[/tex] trigger fish
Final answer:
The correct system of equations modeling Jenna's purchase of tropical fish, where x is the number of parrotfish and y is the number of triggerfish, is x + y = 280 and y = 4x, which is option A.
Explanation:
The problem given is about modeling a real-world situation with a system of equations where x represents the number of parrotfish Jenna bought and y represents the number of triggerfish she bought. Jenna bought 280 tropical fish for a museum display, and she bought 4 times as many triggerfish as parrotfish. The system of equations that models this situation is:
x + y = 280
y = 4x
This matches option A from the given choices. The first equation represents the total number of fish Jenna bought, while the second equation represents the relationship between the number of triggerfish and parrotfish, with the triggerfish being four times the number of parrotfish. To solve, substitute the second equation into the first to find the values of x and y.
What is the length of the conjugate axis?
(x-1)^2/25-(y+3)^2/9=1 ...?
Answers
Answer:
Length of the conjugate axis is 6 units.
Step-by-step explanation:
Given Equation is ,
[tex]\frac{(x-1)^2}{25}-\frac{(y+3)^2}{9}=1[/tex]
To find: Length of the conjugate axis.
We know that given equation is Equation of Hyperbola.
First Transverse Axis: Axis passing through the vertices is called the transverse axis. Length of the transverse axis is 2a.
Now, Conjugate Axis: Axis which is perpendicular to the transverse axis through the center is called the conjugate axis. Length of the Conjugate axis is 2b.
Equation in standard form is written as ,
[tex]\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1[/tex]
So, Comparing with Standard equation,
we get, a² = 25 ⇒ a = 5 and b² = 9 ⇒ b = 3
Thus, Length of the conjugate axis = 2 × 3 = 6 unit
Therefore, Length of the conjugate axis is 6 units.
For the given equation of hyperbola:
[tex]\dfrac{(x-1)^2}{25}-\dfrac{(y+3)^2}{9}=1[/tex]
The length of the conjugate axis is 6 units.
In analytic geometry, a hyperbola is a conic section created when a plane meets a double right circular cone at an angle that overlaps both cone halves.
The standard equation of the hyperbola is,
[tex]\dfrac{(x-h)^2}{a^2}- \dfrac{(y-k)^2}{b^2} =1[/tex]
Where,
a is half of the transverse axis.
b is the half of the conjugate axis.
The given equation is,
[tex]\dfrac{(x-1)^2}{25}-\dfrac{(y+3)^2}{9}=1[/tex]
Comparing it with the above standard equation, we get:
a² = 25
⇒ a = ± 5
b² = 9
⇒ b = ± 3
Since, the length of the conjugate axis of hyperbola = 2b
Therefore,
The length of the conjugate axis:
= 2x3
= 6 units.
Hence,
The required length of the conjugate axis is 6 units.
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How many x-intercepts are there in y = –3x2 + 4x + 4
Answers
Educated guess: There may be about 2 x - intercepts in the equation.
–3x^2 + 4x + 4
–(3x^2 - 4x - 4)
–(3x + 2)(x - 2)
x=-2/3 or 2, which means that there are x intercepts, at -2/3 and 2.
how to find the hypotnuse
Answers
There are 3 sides of a right angled triangle, the opposite, the adjacent(base) and the hypotenuse (longest side). If you are given the measurements of 2 sides you can find the third. if you are given the opposite and the adjacent , the formula for finding the hypotenuse is a²+b²=c², where a is the opposite, b is the adjacent and c is the hypotenuse.
Final answer:
To find the hypotenuse of a right triangle, apply the Pythagorean theorem: a² + b² = c². After squaring the lengths of the two other sides and adding them together, take the square root of the sum to get the length of the hypotenuse, which is approximately 10.3 units in the example provided.
Explanation:
To find the hypotenuse of a right triangle, you can use the Pythagorean theorem, which states that the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). This can be written as the equation a² + b² = c². To solve for the hypotenuse, you would rearrange the equation to c = √(a² + b²).
For example, if the legs of a right triangle measure 9 and 5 units:
First, square both of the leg lengths: 9² = 81 and 5² = 25.Add these two values together: 81 + 25 = 106.Take the square root of the sum: √106 ≈ 10.3 units.Thus, the hypotenuse would measure approximately 10.3 units, where we use three significant figures for precision in measurement.
List the first three commen multiples of 2 3 9
Answers
How many points are used to define a plane?
A. zero
B. one
C. two
D. three
Answers
Answer:
it will be D
Step-by-step explanation:
Snooker is a kind of pool or billiards played on a 6-foot-by-12-foot table. the side pockets are halfway down the rails (longside)
|------|
| |12
| |
| |
|------|
6
Find the distance, to the nearest tenth of an inch, diagonally across from the corner pocket to side pocket ...?
Answers
Let length be 12 ft (l = 12 ft) and width be 6 ft (w = 6ft).
The side pocket will be on the half of its length (l). To calculate the distance, we will use the distance d as a hypotenuse of the right triangle with sides w and l/2.
According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of two other sides:
d² = w² + (l/2)²
We have:
d = ?
w = 6 ft
l = 12 ft
d² = 6² + (12/2)²
d² = 6² + 6²
d²= 2 * 6²
d² = 2 * 36
d² = 72
d = √72
d = 8.48 ft
Since 1 ft is 12 in, then 8.48 ft is 101.76 in:
8.48 * 12 in = 101.76 in
Compare and contrast simplifying the numeric expression 3 – (2 + 5) to the algebraic expression 3x – (2x + 5)
Answers
The numeric one simplifies to:
3 - (2 + 5) = 3 - 7 = -4
While the algebraic one simplifies to:
3x - (2x + 5) = 3x - 2x - 5 = x - 5