Given: ∠ABC i a right angle, ∠DBC i a traight angle
Prove: ∠ABC ≅ ∠ABD

A horizontal line ha point D, B, C. A line extend vertically from point B to point A. Angle A B C i a right angle. Definition of angle biector
egment addition property
definition of congruent angle
tranitive property

The simplified monomial for the first scenario will be 1/8². The simplified monomial for the second situation will be (-3)¹.

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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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

Around 80 times we should expect it to land on B.

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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Answer: D

Step-by-step explanation:

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

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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Answer:

Step-by-step explanation:

i want to know too:((

The equation for the second plan is y = 95x, therefore, option (d) is correct.

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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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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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

The probability that both choose Black Panther as their favourite character is 189/3875.

KHS students' list of their favourite Marvel comic character:

Spiderman - 45

Hulk - 30

Black panther - 28

Black widow - 17

Rocket raccoon - 5

Total = 125

             [tex]125C_{2}=\frac{125*124}{1*2} \\\\125C_{2}=\frac{15500}{2}\\\\125C_{2}= 7750[/tex]

              [tex]28C_{2}=\frac{28* 27}{1*2} \\\\28C_{2}=\frac{756}{2}\\\\28C_{2}= 378[/tex]

               [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.

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Equation : 200 = 15x + 5y + 120

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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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!

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.

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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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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The equation that represent the product of to consecutive numbers being 182 is x^2 + x -182 = 0

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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Answer:

Z< 3

Step-by-step explanation:

Hope this helps :)

The values of y when x is 0 1 2  is 0,3,6

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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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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Answer:

The three consecutive even integers are 40, 42 and 44.

Step-by-step explanation:

Let the consecutive even integers be

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.

Answer:

41

Step-by-step explanation:

No, the estimate should be higher

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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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

the 96th term of the arithmetic sequence 3, -14, -25 is -1048.

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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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.

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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Answer:

3.6

Step-by-step explanation: