To prove <ABC is congruent to <ABD
What is the meaning of incongruent?congruent figures are those that match in terms of size and shape or are the same size and shape. The geometry of congruent angles
What does congruent mean Example?Congruent refers to something that is "exactly equal" in terms of size and shape. The shapes hold true regardless of how we rotate, flip, or turn them. Draw two circles with the same radius, for instance, cut them out, and stack them on top of one another.
According to the question
Both the triangles are right-angled
From RHS criterion
∠ABC ≅ ∠ABD
Definition of angle bisector segment addition property
The line or line segment that splits an angle into two equal pieces is known as the internal angle bisector (internal angle bisector)
definition of congruent angle transitive property
According to the transitive property of congruence, all shapes are congruent to one another if two shapes are congruent to a third shape.
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Simplify the following monomials. Express final answers using only positive exponents.
[tex]\frac{8}{8^{3} }[/tex]
[tex]\frac{(-3)^{4} }{(-3)^{3} }[/tex]
The simplified monomial for the first scenario will be 1/8². The simplified monomial for the second situation will be (-3)¹.
What is exponent?Exponent, then, is the number of times a number has been multiplied by itself. For instance, the number 6 is multiplied by itself four times, yielding 6*6*6*6. You can write this as 6^4. In this case, the exponent is 4 and the base is 6. This can be understood as 4 increased to the power of 6. A number or letter written above and to the right of a mathematical expression known as the base is termed an exponent. It denotes that the base is to be increased in strength. The base is x, while the exponent or power is n.
Here,
The law of exponents say that,
aⁿ/aˣ=aⁿ⁻ˣ
1. 8/8³
=8¹-³
=8⁻²
=1/8²
2. (-3)⁴/(-3)³
=(-3)⁴⁻³
=-3¹
For first case, the monomial resulted after simplifying will be 1/8². For second case, the monomial resulted after simplifying will be (-3)¹.
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A person saves 12.5% of his income how much does he spend in a month if his monthly income is Rs 10,000. Give full explanation 
If person saves 12.5% of his income how much does he spend in a month if his monthly income is Rs 10,000 then he spends 8750 of his monthly income.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that a person saves 12.5% of his income.
The monthly income of the person is 10000.
We need to find how much he spend in a month.
Convert 12.5 % to the decimal value by dividing 12.5 by 100.
12.5/100=0.125
Now multiply 0.125 with 10000
0.125×10000
1250
Subtract 1250 from 10000
10000-1250
8750
Hence, person spends 8750 of his monthly income.
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How many ounces of iodine worth 30 cents an ounce must be mixed with 50 ounces of iodine worth 18 cents an ounce so that the mixture can be sold for 20 cents an ounce?
Find BR if D is the circumcenter of △ABC, CD=11.1 and RD=5.2. Round to the nearest tenth
Answer:
BR=9.8
Step-by-step explanation:
a²+b²=c²
5.2²+b²=11.1²
27.04+b²=123.21
b²=96.17
b=[tex]\sqrt{ 96.17}[/tex]
b=9.8
An Imaginary Poll in June 2021 asked KHS students to list their favorite Marvel comic
character. The responses are shown below.
Spiderman - 45
Hulk - 30
Black panther - 28
Black widow - 17
Rocket raccoon - 5
Total = 125
If we randomly select two different people from this sample, what is the probability that both
chose Black Panther as their favorite character?
a. 2/125
b. 1/250
c. 189/3875
d. 1/15500
e. 756/15625
The probability that both choose Black Panther as their favourite character is 189/3875.
How is the probability calculated?KHS students' list of their favourite Marvel comic character:
Spiderman - 45
Hulk - 30
Black panther - 28
Black widow - 17
Rocket raccoon - 5
Total = 125
The chances that two people can be drawn from a sample of 125 playing cards in 125[tex]C_{2}[/tex] ways.
[tex]125C_{2}=\frac{125*124}{1*2} \\\\125C_{2}=\frac{15500}{2}\\\\125C_{2}= 7750[/tex]
The event of choosing 2 Black Panthers from 28 can happen in 28 [tex]C_{2}[/tex] ways.[tex]28C_{2}=\frac{28* 27}{1*2} \\\\28C_{2}=\frac{756}{2}\\\\28C_{2}= 378[/tex]
The probability that both choose Black Panther as their favourite character is:[tex]P(BP) = \frac{28 C _{2}}{125C_{2}} \\\\P(BP) = \frac{378}{7750} \\\\P(BP) = \frac{189}{3875}[/tex] or 0.04877
So, option c is correct.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty. The likelihood that an event will occur increases with its probability. Probability informs us of the likelihood that an event will occur given enough trials.Probabilities can be expressed numerically by the number of desired outcomes, divided by the total number of outcomes, when dealing with experiments that are random and well-defined in a purely theoretical context (like flipping a coin).To learn more about probability, refer:
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Identify the vertex, axis of symmetry, and the direction of opening of the graph of g(x) = |x| - 8.
A. (0, -8); y = -8; opens up
B. (0, -8); x = 0; opens up
C. (8, 0); x = 0; opens down
D. (-8, 0); x = -8; opens down
A. (0, -8); y = -8; opens up will be the correct solution for the graph of given modulus function g(x) = |x| - 8.
What is modulus function?
Regardless of whether a number is positive or negative, the modulus function, also known as the absolute value function, determines its magnitude. No matter what the number or variable, it always returns a non-negative value. The expression y = |x| or f(x) = |x|, where f: R (0,) and x R, denotes a modulus function.
When x is a real number, then |x| is its modulus. f(x) will have the same value as x if x is not negative. If x is negative, then f(x) will have the magnitude of x; if x is negative, then f(x) = -x. Here is a summary of the modulus function formula.
As we can see in the graph attached that the f(x) is zero at y=-8 and it is a modulus function so the graph will open upwards
but the graph is little shifted to y=-8 because the equation given to us is |x|-8 =g(x) so it will shift down according to the rule
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help please!! involves range
Answer: D
Step-by-step explanation:
Please Help
The product of two consecutive, negative integers is 182.
What equation represents the situation?
Thanks to whoever can solve it
The equation that represent the product of to consecutive numbers being 182 is x^2 + x -182 = 0
What is a quadratic equation?Quadratic equations are second-degree algebraic expressions and are of the form ax^2+ bx + c = 0. The word "Quadratic" is derived from the word "Quad" which means square. In other words, a quadratic equation is an “equation of degree 2.”
let the two consecutive negative numbers be -x and -x-1
their product - x( -x-1) = 182
multiply out you have
x^2 + x = 182
which is finally reduced to
x^2 + x - 182 = 0
In conclusion the equation that represent the above question is x^2 + x - 182 = 0
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Martin and three of his friends take turns driving on a trip. The gas mileage for their car ranges from 28.94 to 24.68 miles per gallon. Each friend drives between 63 and 69 miles, so Martin estimates they will need about 7 gallons of fuel for their trip. Is this a reasonable estimate?
A.
Yes, the estimate given is reasonable.
B.
No, the estimate should be higher.
C.
No, the estimate should be lower.
No, the estimate should be higher
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
As, Maximum miles driven=highest consumption per gallon × Maximum
gallons
where;
Maximum miles driven per person=64 mile
Maximum miles driven = 64×4
=256 miles
So, highest consumption =24.56 miles per gallon
let the Maximum gallons needed be x
256=24.56 x
24.56 x=256
x ≥ 256/24.56
x ≥10.42 gallons
Hence, No, the estimate should be higher
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Find the 96th term of the arithmetic sequence 3, -14, -25,
the 96th term of the arithmetic sequence 3, -14, -25 is -1048.
What is an arithmetic sequence?An arithmetic sequence is an ordered set of numbers that have a common difference between each consecutive term.
The general form of an arithmetic sequence is
aₙ = a₁ + d(n-1)
where aₙ is the nth term, a₁ is the initial term, and d is the common difference.
Given that n =96, a₁=-3, and d = -11
Substituting these value in the above equation
a₉₆ = -3 - 11(96-1) = -3 - (11*95) = -3-1045 = -1048
Hence, -1048 is the 96th term of the given arithmetic sequence.
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how can I solve this
Answer: S=$2 and L=$8
Step-by-step explanation:
This question is a simultaneous equation.
(1) 4L+3S=$34
(2) 2L+S=$16 (*2)
(3) 4L+2S=$32
(1)-(3)
4L+3S=$34
-4L+2S=$32
S=$2
Substitute s=2 into (2)
2L+S(2)=$16
2L+2=$16 (-2)
2L=$16 (/2)
L=$8
Consider 3x=y. a. Complete the table for the equation. x: 0 1 2
The values of y when x is 0 1 2 is 0,3,6
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7.
To get the values of y, we substitute for the values of x in the equation 3x=y
When x = 0
3(0)=y; y = 0
When x = 1
3(1)=y; y = 3
When x = 2
3(2)=y; y = 6
x | 3x | y | (x, y)
----------------------------------------
0 | 3(0) | 0 | (0, 0)
----------------------------------------
1 | 3(1) | 3 | (1, 3)
----------------------------------------
2 | 3(2) | 6 | (2, 6)
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How many solutions does the equation -2 (4x − 1) = −8x – 1 have?
Answer:
No Solution
Step-by-step explanation:
[tex]\tt -2\left(4x-1\right)=-8x-1[/tex]
Expand:-
[tex]\tt -8x+2=-8x-1[/tex]
Add 8x to both sides:-
[tex]\tt -8x+2+8x=-8x-1+8x[/tex]
Simplify:-
[tex]\tt 2=-1[/tex]
The sides are not equal, therefore there is No Solution.
_____________________
Hope this helps!
Have a nice day!
Which system of inequalities is shown in the graph?
y<3 and y>2/3x+1
y<3 and y<2/3x+1
y>3 and y>2/3x+1
y>3 and y<2/3x+1
Answer: A y<3 and y>2/3x+1
Step-by-step explanation: y<3 shades everything under the line because 3 is greater than all the possible values.
y>2/3x+1 shades everything over the line because 2/3x+1 is less than all the possible values.
solve
2(2.1z+4.5)<21.6
Answer:
Z< 3
Step-by-step explanation:
Hope this helps :)
Given the matrices A and B shown below, find A + B.
A = 1 -1 1] B = [-4 -4 0]
.
In Alaska, the temperature is currently -14°F, and in Mt. Olive it is currently 67°F.
What is the difference in temperature between Alaska and Mt. Olive?
And please explain
Answer:
81
Step-by-step explanation:
it is asking only for the difference nothing else so do
14+67 because the value is in the - we use addition for this scenario if it's for example
difference between 10f and 50f you minus it
10-50 = 40
what is the distance between P(9,-5) and Q(-2,3) round to nearest tenth if necessary
Answer:
3.6
Step-by-step explanation:
CC wants to buy online tickets for a concert. two options are given here. option 1: $85 for each ticket plus a shipping fee of $15 option 2: $95 for each ticket and free shipping. select the equation for option 2.
a. y=85x+15
b. y=-95x
c. y=15x+85
d. y=95x
Answer:
Step-by-step explanation:
i want to know too:((
The equation for the second plan is y = 95x, therefore, option (d) is correct.
What is an equation?Two or more expressions with an equal sign are defined as an equation.
Given that, the second plan costs $95 for each ticket and free shipping.
The total cost, y, for x tickets are:
y = 95x.
Hence. the equation for the second plan is y = 95x, therefore, option (d) is correct.
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Please help! Pleaseeeee
Answer: (C) or (44in^2 )
Step-by-step explanation:
Answer:
A = 40 in²
Step-by-step explanation:
the figure is composed of a rectangle and a triangle.
then area (A) is calculated as
A = area of rectangle + area of triangle
= (16 × 2) + ( [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
here b = 6 - 2 = 4 and h = 20 - 16 = 4 , then
A = 32 + ( [tex]\frac{1}{2}[/tex] × 4 × 4)
= 32 + 8
= 40 in²
Let y = (5 +b)x-c be perpendicular to 8x + 12y = 40. What is the value of b?
The value of b is -11/2.
What is the slope of the equation?
The slope of a line is a measure of its steepness. Mathematically, the slope is calculated as "rise over run" (change in y divided by change in x).
To find the value of b, we need to find the slope of the given line and the line that is perpendicular to it.
The slope of the line 8x + 12y = 40 is -8/12 = -2/3.
The slope of a line that is perpendicular to this line is the negative reciprocal of -2/3, which is 3/-2 = -3/2.
The slope of the line y = (5 + b)x - c is 5 + b. Therefore, to find the value of b, we need to set 5 + b equal to -3/2:
5 + b = -3/2
b = -3/2 - 5
b = -11/2
Therefore, the value of b is -11/2.
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Which value best estimates the value for the correlation coefficient of the scatter plot below: 1, -0.8, -0.2, 0.2, 0.8, or 1?
A rocket is fired with an initial vertical velocity of 40 m/s from a launch pad 45 m high. Its height is given by the formula , where h is in meters and t is in seconds. How high does the rocket go? How much time is the rocket in flight?
The maximum height which the rocket attains is 80 m and the time taken by the rocket is 8 sec.
Given,
the following formula yields the height h,
h= -5t² + 40t +45
45m is the height of the launch pad.
We take the first derivative of the function h and then set it to zero to determine the height the rocket reaches.
h' = 0
-10t + 40 =0
-10t = -40
t = 4
Therefore, height reached by the rocket in time t = 4 is,
h= -5t² + 40t +45
= -5(4)² + 40(4) + 45
=125 m
As a result, the rocket can reach:
125- 45
= 80 m
(To determine the real height the rocket travels, we have subtracted the height of the launch pad.)
The rocket takes twice as long to launch as it does to reach the peak.
t = 2*4 = 8 sec
Therefore,
the rocket goes 80 meters in height
the rocket's flight time is 8 seconds.
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PLEASE HELP I BEG I NEED JUST THIS ONE PROBLEM:
In the trapezoid ABCD ( AB ∥ CD ) point M∈ AD , so that AM:MD=3:5. Line l ∥ AB and going trough point M intersects diagonal AC and leg BC at points P and N respectively. Find: BC:BN.
Please give Statement/Reasoning proof as well. THANK YOU PLEASEE
For the given Trapezoid ABCD the value of BC:BN is BC:BN=8:3.
What is Trapezoid?
A trapezoid is a quadrilateral in American and Canadian English that has at least one pair of parallel sides. A trapezium is the term used in British and other varieties of English. In Euclidean geometry, a trapezoid is invariably a convex quadrilateral. The trapezoid's parallel sides are referred to as its bases.
Given:
In the trapezoid ABCD ( AB ∥ CD ) point M∈ AD , so that AM:MD=3:5.
Line l ∥ AB and going trough point M intersects diagonal AC and leg BC at points P and N respectively.
We have to find BC:BN
ABCD is a trapezoid and there is a point m which belongs to AD such that AM:MD=3:5.Line "l" parallel to AB intersects the diagonal AC at p and BD at N.
Now, we know that the parallel lines divide the transversal into the segments with equal ratio, therefore, BN:NC=AM:MD
But, BC= BN+NC
Therefore, BC:BN = (BN + NC): BN
⇒ BC:BN = (3 + 5): 3
⇒ BC:BN = 8:3
Hence, for the given Trapezoid ABCD the value of BC:BN is BC:BN=8:3.
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If you spin a 3 circle spinner 120 times, about how many times would you expect it to land on B?
Around 80 times we should expect it to land on B.
What is time?Time is basically a measure of non-stop, consistent change in our own surroundings. Usually we can see through a specific point of view. Concept of time is self-evident and intuitive. Describing the fundamental nature of time is quite difficult.
As per the given condition-
Spin circle=3
Time = 120 sec
the total is 3
the red and orange equals to 2
2/3 times 120
240/3
=80 times
Thus, the correct answer is 80 times.
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0) The sum of the first and second of three
consecutive even integers is 126. Find the
three even integers.
Answer:
The three consecutive even integers are 40, 42 and 44.
Step-by-step explanation:
Let the consecutive even integers be
x, (x + 2) and (x + 4)The sum of the first and second of three consecutive even integers is 126.
So,
x + (x + 2) + (x + 4) = 126
Open the brackets
x + x + 2 + x + 4 = 126
Combine like terms we get,
3x + 6 = 126
Subtract 6 from both sides we get,
3x + 6 - 6 = 126 - 6
3x = 120
Divide 3 from both sides we get,
3x/3 = 120/3
x = 40
The value of x is 40 and the the consecutive even integers are
x = 40
x + 2 = 40 + 2 = 42
x + 4 = 40 + 4 = 44
Thus, The three consecutive even integers are 40, 42 and 44.
Evaluate the expression.
5+ [4•3(2 + 1)]
Answer:
41
Step-by-step explanation:
Hello please solve this with steps Factor
f(x)=x^3-12x^2+36x-32 completely given that (x-2) is a factor.
f(x)=x^3-12x^2+36x-32 completely given that (x-2) is a factor is [tex](x-2)^2(x-8)[/tex].
What is factor?
In mathematics, an integer m that can be multiplied by another integer to produce n is known as a divisor of an integer n, also known as a factor of n. One can also state that n is a multiple of m in this situation.
Knowing that (x−2) is a factor you can divide the polynomial:
2.....|.......1.........-12.........+36.........-32
........|...................2..........-20.........+32
........|.......1.........-10..........+16...........0
and find:
[tex]x^3-12 x^2+36 x-32=(x-2)\left(x^2-10 x+16\right)[/tex]
We could use the quadratic formula to find the factors of [tex]$q(x)=\left(x^2-10 x+16\right)$[/tex]
or go simply by inspection:
1) q(x) has two changes in sign, so it has two positive real roots.
2) The product of the roots is 16
3) the sum of the roots is 10
It's easy to see that x=2 and x=8 are such roots, and thus:
[tex]x^3-12 x^2+36 x-32=(x-2)^2(x-8)[/tex]
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Antonio is saving money to buy a CD player that costs
$120. He also wants to buy some CDs to play in it.
New CDs cost $15 and used CDs cost $5. Antonio
wants to buy the same number of new and used CDs.
Write and solve an equation to find the number of each
type of CD Antonio can buy if he spends all of the $200
he has saved.
Equation : 200 = 15x + 5y + 120
what is the probability of having the first head at the k-th trial? what is the name of this random variable?
The probability of having the first head at the k-th trial is 1/2.
The formula for the binomial distribution of probability is shown below. It can be used to determine the likelihood of getting K heads out of N coin tosses.
[nC k]* [pk]* [qn-k]
p= probability of receiving a head and
q= probability of having a tail.
Both p and q are 1/2.
As a result, the equation is [f12n! * f! r! * (n-r)!]
If you obtain exactly r successes, you also get (n - r) failures at the same time.
qn - rpr = P(getting r successes and n - r failures) (since the n trials are independent) Using the product theorem
There is no mention of the challenges from which the results were attained. There are nCr methods for selecting successful trials among r trials. The remaining (n - r) trials should be failures once the r trials that were picked for successes have been chosen. These nCr methods are incompatible. P(obtaining exactly r successes) in each of these nCr methods equals qn - rpr.
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