Based on the figure, which pair of triangles is congruent by the Side Angle Side Postulate?
Answer
Triangle ABD and Triangle ECD
Triangle ABD and Triangle ADC
Triangle ADC and Triangle ABC
Triangle ABC and Triangle ECD
Answer: Triangle ABC and Triangle ECD
Step-by-step explanation:
In Triangle ABC and Triangle ECD
BD=CD and AD=ED [given in the figure]
∠BDA=∠EDC [Vertically opposite angles are equal]
⇒ΔABC ≅ ΔECD [By SAS postulate]
SAS postulate or Side Angle Side postulate tells that if two sides and their included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
Solve for n.
-7/2n = 49
n =
What is 0.43 as a fraction in simplest form?
Angela and Neil are going to the movies. They each bought a medium popcorn, and Neil got a small soft drink. Angela had a $5 gift certificate to put toward the cost, and Neil paid the rest, which came to $27.90. A movie ticket costs $10.00, and a medium popcorn costs $5.50. How much does a soft drink cost at the theater?
$1.90
$7.40
$2.90
$17.40
Answer:
$1.90
Step-by-step explanation:
Which description can be written as the expression 6b+5?
a) the difference of six times a number and five
b) the sum of six times a number and five
c) quotient of six times a number and five
d) the product of six times a number and five
Answer: b) the sum of six times a number and five
Step-by-step explanation:
The given expression is [tex]6b+5[/tex], where b represents any number.
The above expression has two terms combined by addition operation.
In the first term there is one variable b and 6 as coefficient of b and the second term is a constant term of 5.
Therefore, the correct description of the given expression [tex]6b+5[/tex] is " the sum of six times a number and five".
Option: b is the correct answer.
b) the sum of six times a number and five.
Step-by-step explanation:We are given an algebraic expression in term of a variable 'b' as:
6b+5
As we could see that here there are two terms in an expression one is: 6b and the other is 5 which is separated by a summation sign.
Hence, when 6 times of a number 'b' is added to 5 we get the given expression(i.e. 6b+5)
Hence, the answer is: Option: b
is 3/4 equivalent to 12/15
What is the measure of angle TRV?
Measure of angle TRV is [tex]130^{0}[/tex].
What is an angle?An angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle.
According to the question
< TRS + < TRV = [tex]180^{0}[/tex]
(x - 10) + (2x + 10) = [tex]180^{0}[/tex]
3x = [tex]180^{0}[/tex]
x = [tex]\frac{180}{3}[/tex]
x = [tex]60^{0}[/tex]
< TRV = 2x + 10
= 2([tex]60^{0}[/tex])+10
= 120 + 10
= [tex]130^{0}[/tex]
Hence, measure of angle TRV is [tex]130^{0}[/tex].
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A code is formed using four of these letters: A, B, I, K, N, O, and T. (Note that the order of the letters in the code matters; for example, ABIK is a different code from BAIK.) The size of the sample space is___ . The probability that the first three letters of the four-letter code are vowels is___ .
Answer:
[tex]7^4[/tex][tex]\dfrac{27}{343}[/tex]Step-by-step explanation:
we are given 7 alphabets out of which we need to choose 4 alphabets in order to make a code of 4 letters.Hence the size of the sample space is: [tex]7^4[/tex]
since we have to fill in 4 places with the help of these 7 letters.
so in first place we can select one out of any 7 letters, similarly for the second place as it is not mentioned that repetition is not allowed and the same can be done for third and fourth place.
Hence size of sample space is: [tex]7\times7\times7\times7=7^4[/tex]
Now the probability of an event is given by:Probability=(Number of favourable outcomes)/(Total number of outcomes)
Hence here the total number of outcomes=[tex]7^4[/tex]
Total number of favourable outcomes=outcomes that the first three letters are vowels=[tex]3\times3\times3\times7[/tex] (since in the first place we have three choices for a vowel{A,I,0} similarly for second and third place and in the fourth place any one of the 7 letters could come)
Hence the probability(P) that the first three letters of the four-letter code are vowels is given by:
[tex]P=\dfrac{3\times3\times3\times7}{7\times7\times7\times7}=\dfrac{3\times3\times3}{7\times7\times7}=\dfrac{27}{343}[/tex]
Hence, the Probability is: [tex]\dfrac{27}{343}[/tex]
One fifth of todays college students began using computers between the ages 5 and 8. if a college has 3,500 students, how many of the students began using computers between the ages 5 and 8?
How do you prove vertical angles are congruent?
Answer:
(<2 and <4 are vert angles) reason:given
(lines m and n intersect at p) reason: def of vertical angles
(<2 and <3 are a linear pair) reason: def of a linear pair
(<2 and <3 are a linear pair) reason: def of a linear pair
(m<2+m<3=180) reason:angle addition postulate
(m<3+m<4=180) reason:angle addition postulate
(m<2+m<3=m<3+m<4 reason:substitution property
(m<2 = m<4) reason:subtraction property
<2 ~<4 reason:definition of ~ angles
Step-by-step explanation:
edgenuity 2020
in uniform circular motion, the speed v of point on the edge of a spinning disk is v=2π/T times r. where r is the radius of the disk and T is the time it takes the point to travel once around the circle. Solve the formula for r.
Ryan bought a calculator for $200 he resold it and made a profit of 25% how much did he sell the calculator for?
How many feet are in 120 inches?
__ ft
Rectangle ABCD is reflected over the x-axis, followed by a reflection over the y-axis, and then rotated 180 degrees about the origin. What is the location of point A after the transformations are complete?
Rectangle ABCD is shown. A is at negative 5, 1. B is at negative 5, 3. C is at negative 1, 3. D is at negative 1, 1.
(−5, 1)
(5, −1)
(−5, −1)
(5, 1)
Answer:
First option is correct. The location of point A after the transformations is (-5,1).
Step-by-step explanation:
It is given that the coordinates of point A are (-5,1).
Rectangle ABCD is reflected over the x-axis. then x-coordinate remains the same but the sign of y-coordinate is changed.
[tex](x,y)\rightarrow (x,-y)[/tex]
Coordinates of point A are
[tex](-5,1)\rightarrow (-5,-1)[/tex]
After that ABCD is reflected over the y-axis, then y-coordinate remains the same but the sign of x-coordinate is changed.
[tex](x,y)\rightarrow (-x,y)[/tex]
Coordinates of point A are
[tex](-5,-1)\rightarrow (5,-1)[/tex]
After that ABCD rotated 180 degrees about the origin, then the sign of both coordinates are changed.
[tex](x,y)\rightarrow (-x,-y)[/tex]
[tex](5,-1)\rightarrow (-5,1)[/tex]
Therefore option 1 is correct.
How do i write 7.6% as a fraction in simplest form and as a decimal?
Mia is three years older than twice her sister Brooke's age. The sum of their ages is less than 30. What is the greatest age Brooke could be?
a.)7
b.)8
c.) 9
d.)10 ...?
The correct answer is b. 8. 8 is the greatest age Brooke could be.
Let's denote Brooke's age as B and Mia's age as M. According to the information given:
M = 2B + 3 (since Mia is three years older than twice Brooke's age).
We also know that the sum of their ages is less than 30:
M + B < 30.
Substituting the expression for M into the inequality, we get:
2B + 3 + B < 30,
3B + 3 < 30,
3B < 27,
B < 9.
Since Brooke's age must be a whole number, the greatest integer less than 9 is 8. Therefore, the greatest age Brooke could be is 8 years old.
About 11% of the population is math phobic. If two people are randomly selected, what is the probability that both are math phobic? What is the probability that at least one is math phobic? ...?
Answer:
P(at least one phobic)
= 1 - P(none phobic)
= 1 - 0.89^2
= 1-0.7921
= 0.2079
Step-by-step explanation:
Holly records the temperature, in degrees fahrenheit, for two different cities. ln one of the cities, the temperature is 15 degrees above zero. holly records this as 15. ln the other city, the temperature is 15 degrees below zero.
What is the next term of the following sequence? 20, 10, 5, 2 1/2, ... 1 1/2 1 1/4 3/4
At a candy store, Jenny bought 1 pound of jelly beans and 5 pounds of gummy worms for $41. Meanwhile, Ozzie bought 6 pounds of jelly beans and 2 pounds of gummy worms for $50. How much does the candy cost?
Which set of side lengths represents a triangle with 3 lines of reflectional symmetry?
Answer:
The answer is 5,5,5.
Step-by-step explanation:
Reflection mean same like a mirror, it says reflectional symmetry. So the sides are the same.
Simplify (6 +i)(8 – 3i)
51 – 10i
48 – 32i
45 – 10i
48 – 10i – 3i^2 ...?
What is 4/3 divided by 6?
A fox, a coyote, and a wolf weigh a total of 120 pounds. The ratio of the weight of the fox to the weight of the coyote is 3:8. The weight of the coyote is 32 pounds. What is the weight of the wolf?
Answer:
the wolf is 76 lbs.
Step-by-step explanation:
first you have to divide 32 by 8, which is 4. Then you know that 4 is the divider to the simplified ratio, 3:8. So you multiply 3 and 4 which is 12. so you add 32 and 12 which is 44. then you subtract 44 by 120 which is 76. So The weight of the wolf is 76 lbs.
What is eight times four?
m plus 4 equals minus 12
Haley substituted the values of a, b, and c into the quadratic formula below.
What is the square root of 1.395?
Planning for the possibility that your home might get struck by lightning and catch on fire is part of a plan for
Answer:
Th answer is - protecting assets
Step-by-step explanation:
Planning for the possibility that your home might get struck by lightning and catch on fire is part of a plan for protecting assets.
The protection of assets is a module of financial planning where one is needed to protect his assets against anything like - natural disaster or creditor's claims etc.
If f(x) = {ln x for 0 < x less than or equal to 2
{x^2 ln2 for 2 < x less than or equal to 4, then the limit as x approaches 2 of f(x) is..
The function f(x) is a piecewise function. To find the limit as x approaches 2, you must consider it from the left and right. From the left, the limit is ln(2), from the right, it's 4ln(2). Since these are not equal, the limit does not exist.
Explanation:The function f(x) is a piecewise function where the first range covers 0 < x <= 2 and the second ranging from 2 < x <= 4. To find the limit of f(x) as x approaches 2, we need to find the limit from both directions, as x approaches 2 from the left (<) and the right (>).
For x approaches 2 from the left (<), f(x) boils down to ln(x), so the limit as x approaches 2 would be ln(2).
For x approaching 2 from the right (>), f(x) translates to x^2 * ln(2). Substituting x = 2 in this function gives us (2)^2 * ln(2) which is 4ln(2)
The limit does not exist since ln(2) not equal to 4ln(2).
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The limit of the function f(x) as x approaches 2 does not exist, because the values obtained when approaching from the left (ln2) and from the right (4ln2) do not match.
Explanation:The question is asking us to find the limit of the function f(x) as x approaches 2. This is a well-known concept in calculus, called the limit of a function. It is easy to solve using the rule that if f(x) and g(x) are two functions that agree at every point of a certain interval, except perhaps at one single point 'a', then their limits as x approaches 'a' are the same.
So let's find the limit as x approaches 2 by looking at each side independently. For x less than or equal to 2, the function is defined as ln(x). So when x approaches 2 from the left, we get ln(2). For x greater than or equal to 2, the function is defined as x^2ln(2). So when x approaches 2 from the right, we get 4ln(2).
Since the values obtained when approaching 2 from the left (ln2) and from the right (4ln2) do not match, we can conclude that the limit of f(x) as x approaches 2 does not exist.
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