Given: triangle ABC is congruent to triangle ADC
Prove: AC bisects angle BAD and AC bisects angle BCD

Please help and thanks if you do

The size of the angle to the nearest degree of tan v = 0.9657 will be 44°.

The fundamental 6 functions of trigonometry have a range of numbers as their result and a domain input value that is the angle of a right triangle.

The trigonometric function is very good and useful in real-life problems related to the right-angle triangle.

As per the given,

tan v = 0.9657

Take inverse tan on both sides of the above expression,

v = [tex]tan^{-1} 0.9657[/tex]

v = 44°

Hence "The angle at tan v = 0.9657 will be 44° to the closest degree.".

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Amount paid by Ethan to buy a video game on sale of 20% with usual cost of $39.99 is equal to $32 ( nearest cent ).

As given in the question,

Usual cost of Video game bought by Ethan = $39.99

Sale discount received by Ethan on video game = 20%

Let 'x' be the amount paid by Ethan for video game.

Discount amount = 20% of $39.99

                             = ( 20 / 100 ) × 39.99

                             = 799.8/100

                             = $ 7.998

                             = $7.99

Amount to be paid by Ethan 'x' = $39.99 - $7.99

                                                   = $32 ( nearest cent)

Therefore, the amount paid by Ethan to purchase a video game on sale discount of 20% is given by $32.

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Answer:

Step-by-step explanation:

A......

The equations that represent the pattern are:

P = 3n

P = 2n + 1

Options A and C are the correct answer.

An equation is a mathematical statement of two expressions connected by an equal sign.

Example:

2x = 5 is an equation.

We have,

P = 3 when n = 1.

a) P = 3n

P = 3 x 1 = 3

b) P = n + 3

P = 1 + 3 = 4

c) P = 2n + 1

P = 2x 1 + 1 = 2 + 1 = 3

d) P = 3 - n

P = 3 - 1 = 2

We see that,

P = 3n and P = 2n + 1 gives P = 3 when n = 1.

Thus,

P = 3n and P = 2n + 1 gives P = 3 when n = 1.

Options A and C are the correct answer.

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Answer:

13.8

Step-by-step explanation:

2b+3a

2(3)+3(2.6)

6+3(2.6)

6+7.8

13.8

Answer: x ≤ -1

Step-by-step explanation:

8 ≤ -4x+4

4x+8 ≤4

4x ≤-4

x ≤ -1

Answer:

Step-by-step explanation:

first open the bracket by multiplying -4 through

8 ≤ -4x + 4

then group like terms and unlike terms  

therefore; 8 - 1 ≤ -4x or -4x ≤ 8-4

-4x ≤ 7 then divide both side by -4

so, ⇒ x ≤ -4/4

x≤-1

Thus , the probability of that  a) a flush (5 cards of the same suit) is  .198% and probability of a 3 card of same rank and2 from single other rank is  0.07612 %

The field of mathematics known as probability studies numerical representations of the likelihood that an event will occur or that a statement is true. The probability of an event is a number between 0 and 1, with 0 generally signifying the event's impossibility and 1 generally signifying its certainty.

Here,

a) It doesn't matter what suit the first card is. Any of the suits may be drawn first, provided that the following four cards are taken from the same deck and have the same suit.

The deck contains 13 of each suit, so after the first card is pulled, there are only 12 of that suit remaining. There are then 11 remaining for the third card, 10 remaining for the fourth card, and 9 remaining for the fifth and final card. The deck will also contain one fewer card overall each time.

(ℎ) = (2   ) ∙ (3   ) ∙ (4ℎ   )\s∙ (5ℎ   )

(ℎ) = [tex]\frac{12}{51} *\frac{11}{50} *\frac{10}{49} *\frac{9}{48}[/tex]

(ℎ) =11880 / 5997600

(ℎ)= 33/16660 = .00198  .198%

c) The probability of a 3 card of same rank and2 from single other rank

Since there are 13  ranks in the cards

So, P =  [tex]\frac{13}{52} * \frac{12}{51} *\frac{11}{50} *\frac{13}{52} *\frac{12}{51}[/tex]

P = 267696/351655200

P=0 .0007612 or 0.07612 %

Thus , the probability of that  a) a flush (5 cards of the same suit) is  .198% and probability of a 3 card of same rank and2 from single other rank is  0.07612 %

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By using Gram Schmidt process of orthogonalization, it can be calculated that-

Distance from a vector (2; 3; 1)t to the subspace spanned by the vectors [tex](1; 2; 3)^T , (1; 3; 1)^T[/tex] IS 2.51 units

What is Gram Schmidt process of orthogonalization?

In an inner product space, the set of mathematical operations which converts a set of linearly independent vectors into an orthonormal vector that spans the same set as spanned by the original vectors is called Gram Schmidt process of orthogonalization.

Distance from [tex]b=(2,3,1)^T[/tex] to   W= [tex]Span\left \{u_1= (1,2,3)^T,u_2=(1,3,1)^T \right \}[/tex]

Here, Gram Schmidt process of orthogonalization is used

[tex]v_1=u_1=(1,2,3)^T\\ v_2=u_2-\frac{ < u_2,v_1 > }{||v_1||^2}v_1[/tex]

     [tex]=(1,3,1)^T-\frac{(1,2,3)^T.(1,3,1)^T}{(1,2,3)^T.(1,2,3)^T}(1,2,3)^T\\ =(1,3,1)^T-\frac{1+6+3}{1+4+9}(1,2,3)^T\\ =(2/7,11/7,-16/14)^T[/tex]

[tex]v_2 =(2/7,11/7,-8/7) ^T[/tex]

[tex]proj_bW=\frac{(2,3,1)(1,2,3)}{(1,2,3)(1,2,3)}(1,2,3)+\frac{(2,3,1)(2/7,11/7,-8/7)}{(2/7,11/7,-8/7)(2/7,11/7,-8/7)}(2/7,11/7,-8/7)[/tex]

             =(1.42, 5.11,  -0.22)

[tex]b-proj_bW[/tex]=(2,3,1)-(1.42,5.11, -0.22)=(0.58,-2.11,1.22)

Required distance from b onto W=

[tex]||b-pro_bW||=||(0.58,-2.11,1.22)||=\sqrt{(0.58)^2+(-2.11)^2+(1.22)^2}[/tex] = 2.51 units

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The volume flow rate of the water passing through the pipe increases by a factor of 6.

Assuming that the initial cross sectional area of the pipe is A m² and the initial velocity of the water is V m/s, the water flow rate is:

= initial flow rate = area × velocity = AV m³/s

As the water speed doubles (2V m/s) and the pipe cross-sectional area triples (3A m²), the volume flow rate becomes:

Final flow rate = 2V × 3A = 6AV m³/s

As a result, the volume flow rate of the water moving through it multiplies by a ratio of six.

The basic equation for cases like these is

Q=AV,

where Q is the volume flow rate, A is the cross-sectional area occupied by the flowing material, and V is the average velocity of flow.

V is considered an average since not every component of a flowing fluid flows at the same rate. If you monitor the waters of a river moving slowly downstream at a consistent rate of gallons per second, you will see that the surface has slower currents here and faster currents there.

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Answer:Yes

Step-by-step explanation: It came because your asking questions that you have to gather data for.

The required proportional ratio is y = 0.08 x. gives Halona 23 minutes to move her 1.93 kilometers to her neighbor's house. As long as you move at a steady pace.

How many kilometers Halona can run in x minutes y expressed as a ratio. Then find y in percentage. The relationship between two or more proportional or inversely proportional sets of values, whether they are directly related or not, is called proportionality.

Here we have

Substitute k into the proportional equation.

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Answer:

5

Step-by-step explanation:

3 × 5= 15

15 + 5= 20

Answer: 5

Step-by-step explanation: 20-5 is 15 and then 3 * x must be 5 since 3x5=15.

Answer: No

Step-by-step explanation:

By using the concept of intercept, it can be calculated that-

y-coordinate of the y-intercept is -5

What is intercept?

The distance from the origin to the point where the curve cuts the x axis is the x intercept of the curve.

The distance from the origin to the point where the curve cuts the y axis is the y intercept of the curve

The polynomial function is

f(x) = [tex]7x^2-5x+9x^3-5+2x^4[/tex]

For  y-coordinate of y- intercept, we put x = 0

[tex]f(0) = 7(0)^2-5(0)+9(0)^3-5 + 2(0)^4[/tex]

       = -5

y-coordinate of the y-intercept is -5

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Answer: -7/4

Step-by-step explanation: see attached

8(−5x−8)=-3x-4−3x−4

-40x-64=-3x-4-3x-4

-40x-64=-6x-8

-36x=-56

[tex]x=\frac{56}{36}[/tex]

[tex]x=\frac{14}{9}[/tex]

The transformation equivalent to the reflection across the line q = -1, followed by the reflection across the line p = 2, [tex]r_p \circ r_q[/tex] is a translation of 6 units to the right.

A reflection transformation is one in which the points of the image are mirrored across the line of reflection.

The coordinate of a point (x, y) following a reflection about the y-axis is the point (-x, y)

The line x = -1 is parallel to the y-axis, therefore, only the x-coordinate of the preimage point (x, y) will change following the reflection across the line, q, [tex]r_q[/tex], x = -1

The relative x-coordinate of a point (x, y) to the line x = -1 is x + 1

Therefore, the image of the point (x, y) following the reflection across the line x = -1 and relative to the line is the point (-(x + 1), y) = ((-x - 1), y)

Relative to the x-axis, the point ((-1 - x), y) is (-1 + (-1 - x), y) = (-2 - x, y)

The coordinate of a point (x, y) relative to the line x = 2 is (x - 2, y)

Therefore, the coordinate of the point ((-2 - x), y) relative to the line x = 2 is ((-2 - x) - 2, y) = ((-4 - x), y)

The image of the point ((-4 - x), y) following a reflection across the line x = 2, [tex]r_p[/tex], is (-(-4 - x), y) = ((4 + x), y)

Relative to the y-axis, the coordinate of the image point ((4 + x), y) is ((2 + (4 + x)), y)

((2 + (4 + x)), y) = ((6 + x), y)

The translation equivalent to the transformation, [tex]r_p \circ r_q[/tex] is a translation of 6 units to the right

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The height of a Wolsey Hall student is an example of continuous data. Option 1. is the answer

Continuous data is data that can take any value. An easy way of identifying continuous data is that they are measured and not counted.

For example, height, weight, temperature and length are all examples of continuous data. Over time, some continuous data can change.

Thus, the height of a Wolsey Hall student is an example of continuous data because it is measured and not counted

Note: Other options are NOT continuous data because they include only data that can only be counted in whole numbers or integers, which implies that the data can not be split into fractions or decimals.

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The administrative costs is approximately 10% of sponsorship revenue expressed as percentage.

Total amount of money received for equipment = $258,000

Total administrative cost = $27000

Percentage representation of the administrative costs =

= 27000 / 258000 × 100%

= 0.10465 × 100%

= 10.46...%

≈ 10 %

therefore the administrative cost is about 10 % of the whole  sponsorship.

Long before the decimal system, calculations in Ancient Rome were regularly conducted in fractional multiples.

Augustus, for example, levied a centesima rerum venalium tax of one cent on commodities sold at auction. With these fractions, it was similar to computing percentages.

As money denominations grew in the Middle Ages, computations with a denominator of 100 became more widespread, becoming typical in mathematical literature from the late 15th through the early 16th centuries.

Several of these works used similar methodologies to investigate profit and loss, interest rates, and the Rule of Three. By the 17th century, interest rates were expressed in hundredths.

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The measure of x = 93 degree and y = 36 degree.

According to the triangle's "angle sum property," a triangle's angles add up to 180 degrees.

The total of a triangle's three internal angles is 180 degrees, as stated by the angle sum feature of a triangle.

Given:

As, <QRP= 51

So, <QRP = <QPR= 51 {Angles opposite to equal sides are also Equal}.

In ΔPQR

<P+ <Q+ <R= 180

51 + 51 + <Q= 180

<Q= 180- 102

<Q= 78 degree.

So, <y = 1/2 <Q= 78/20 = 36 degree.

and, In small left Triangle

36 + 51+ x= 180

x = 180 - 87

x= 93 degree.

Hence, the measure of x = 93 degree and y = 36 degree.

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Answer:

$9.01

Step-by-step explanation:

10 percent off of 15 is 8.5 and since sales tax is 6%, that means it adds 0.51 cents to the total, bringing the total to $9.01

Answer:

17.49

Step-by-step explanation:

15x0.10= 1.5
15+1.5= 16.5
16.5x0.06=0.99
16.5+0.99=

Yes lower production cost increase profit.

Production costs are expenses, such as labor and materials that your company incurs within the course of producing the product that you simply offer to consumers. In common, the lower your generation cost, the higher your benefit, or the sum you've got remaining after you subtract your costs from your sales revenue. lower production costs generally lead to higher profits. When production costs are lower, companies can charge lower prices and still make a profit, or they can keep prices the same and earn higher profits. Lower production costs also reduce the amount of money spent on materials, labor, and other expenses, leaving more of the revenue as profit.

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Answer: -1

Step-by-step explanation: If you plug in 0 as x, the equation will become f(0)=-0-1. If you solve this, then f(0)=-1

Answer:

Below

Step-by-step explanation:

x = amount of 80% to use

amount of alcohol in ingredients = amount of alcohol in final product

  .8 x   =  .7 (560)

   x = 490 ml

The inverse functions required from the given table of values are;

f⁻¹(1) = 1/3

f⁻¹(12) = 1/13

f⁻¹(7) = 1/9

An inverse function also called an anti function is defined as a function, that can reverse into another function. This simply means that, if any function “f” takes x to y then, the we can say that the inverse of the function “f” will take y to x. If the function is denoted by 'f' it means that the inverse function is denoted by f⁻¹(x)

For example, we have the function;

y = 2x + 3, the inverse would be;

f⁻¹(y) = (x - 3)/2

Thus, from the given table;

f⁻¹(1) = 1/3

f⁻¹(12) = 1/13

f⁻¹(7) = 1/9

Thus, we conclude that the inverse functions of f⁻¹(1), f⁻¹(12) and f⁻¹(7) are respectively 1/3, 1/13 and 1/9.

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If the value of the land fell to $100000 , then the amount of loss albert can claim in 2022 is $0   .

In the question ,

it is given that ,

the value of the tract land in 2019 that Albert purchased = $140000

and he heard that after the new highway project the property and  land would soon be worth of $200,000 .

after survey the value of the project will be = $180000 ,

after the abandoning of highway project , the value = $100000 .

but Albert cannot claim any loss because there was no transaction.

It is not given that Albert sold the land so neither did he gain or make a loss.

Therefore , the correct option is (e)None of these choices are correct .

The given question is incomplete , the complete question is

Albert purchased a tract of land for $140,000 in 2019 when he heard that a new highway was going to be constructed through the property and that the land would soon be worth $200,000. highway engineers surveyed the property and indicated that he would probably get $180,000. the highway project was abandoned in 2022 and the value of the land fell to $100,000. what is the amount of loss albert can claim in 2022 ?

(a) $100,000

(b) $60,000

(c) $40,000

(d) $80,000

(e) None of these choices are correct.

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The number of red bricks is 6, and there are 8gray bricks.

Here given,

A red brick weighs 9 kg and a gray brick weighs 8 kg. The total number of bricks is 14, with a weight of 120kg.

Let x be a red brick and y be a gray brick.

x + y = 14bricks,

=> x = 14 - y bricks

9x + 8y = 120kg

9(14 - y) + 8y = 120

126 - 9y + 8y = 120

-y = -6

y = 6

14 - 6 = 8

The number of red bricks is 6, and the number of gray bricks is 8.

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a) The amount of water in the tank will be 0 after 5 minutes.

b) As time increases, the amount of water decreases at a rate of -60 L/min.

Here we can see a graph of a linear function that relates the amount of water in an aquarium (vertical axis) with the time (horizontal axis).

The amount of water in the aquarium will reach the 0 liters mark when the line intercepts the x-axis.

We can see that happens for x =  5 minutes

b) We can see that as we move to the right (time flows to the right in that graph) the line goes downwards. This means that the amount of water on the tank decreases as the time increases.

We can see that in 5 minutes, the amount of water goes from 300 lites to 0 liters, so the rate at which the water comes out of the tank is:

R = 300L/5min = 60 liters per minute.

It should actually be written with a negative sign so we are 100% clear that it means that the water is coming out from the tank, so the rate is:

R = -60 L/min

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Using SAS, it can be shown that the two triangles formed are congruent. Then using SSS the length of the road from the intersection to the first turn can be found to be 200ft. Thus the total length of the tour is 1700ft.

What is congruent triangles?

If the three sides and the three angles of both angles are equal in any orientation, two triangles are said to be congruent.

The SAS formula states that if two sides and one angle of two triangle are the same then the triangles are congruent to each other.

Two lines AD, EC intersects each other at the point B . Therefore, ∠ABC = ∠DBE  .

The length of the sides AC = DE, BC = BE .

The triangles ΔABC, ΔBDE  are congruent to each other by the SAS formula.

The SSS formula states that two triangles are congurent to each other if the ratio of corresponding sides of two triangles are the same and vice-versa.

Use the SSS formula in the triangles ΔABC, ΔBDE and simplify to calculate the length of BD.

BD/200 = 300/300

BD/200 = 1

BD = 200  

Therefore, using SSS the length of the road from the intersection to the first turn can be found to be 200ft.

Add the lengths of AB, BD, DE, EB, BC, CA to calculate the total length of the tour.

200 + 200 + 300 + 350 + 350 + 300 = 1700

The total length of the tour is 1700ft.

Hence, using SAS, it can be shown that the two triangles formed are congruent. Then using SSS the length of the road from the intersection to the first turn can be found to be 200ft. Thus the total length of the tour is 1700ft.

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Answer and Step-by-step explanation:

Let the cost of each ticket for Jessica be $x. If she sold one of the tickets at a profit of 10%, she got $x + 0.1*x = $1.1x from selling it. Similarly, if she sold the other ticket at a loss of $18, she got $x - $18 from selling it.

Since the difference in the selling prices of the two tickets is $36, we have $1.1x - ($x - $18) = $36. Solving this equation for x, we get $x = $36 / 0.1 = $360. Therefore, the cost of each ticket for Jessica was $360.

To determine whether Jessica made an overall profit or loss, we need to compare the total amount she received from selling the two tickets to the total cost of the tickets. The total amount she received from selling the two tickets was $1.1x + ($x - $18) = $1.1x - $18 + $x = $1.1x = $396. The total cost of the tickets was 2 * $360 = $720. Since $396 < $720, Jessica made a loss of $720 - $396 = $324 overall.