What is the equation of a line that passes through the point (- 1/4 and is parallel to the y axis?

The coefficient of the variable term of the equation A = 4x - 20 is 4

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is given as

A = 4x - 20

On simplifying the equation , we get

The value of A = 4x - 20

Taking 4 as the common factor of the equation , we get

The value of A = 4 ( x - 5 )

Therefore , the coefficient of the equation A is 4

Hence , The coefficient of the variable term of the equation A = 4x - 20 is 4

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Answer:

[tex]\textsf{a)} \quad y=-4x+19[/tex]

[tex]\textsf{b)} \quad y=\dfrac{1}{4}x+2[/tex]

Step-by-step explanation:

From inspection of the graph, two points on the line are:

Substitute these points in the slope formula to find the slope of the line:

[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{2-6}{2-1}=\dfrac{-4}{1}=-4[/tex]

Lines that are parallel have the same slope.

Therefore, a line parallel to the given line has a slope of -4.

To write an equation of the parallel line, substitute the found slope and point (4, 3) into the point-slope formula and rearrange:

[tex]\implies y-y_1=m(x-x_1)[/tex]

[tex]\implies y-3=-4(x-4)[/tex]

[tex]\implies y-3=-4x+16[/tex]

[tex]\implies y=-4x+19[/tex]

If two lines are perpendicular to each other, their slopes are negative reciprocals.

Therefore, a line perpendicular to the given line has a slope of ¹/₄.

To write an equation of the parallel line, substitute the found slope and point (4, 3) into the point-slope formula and rearrange:

[tex]\implies y-y_1=m(x-x_1)[/tex]

[tex]\implies y-3=\dfrac{1}{4}(x-4)[/tex]

[tex]\implies y-3=\dfrac{1}{4}x-1[/tex]

[tex]\implies y=\dfrac{1}{4}x+2[/tex]

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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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 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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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]

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:-2/3

Step-by-step explanation: the rise is 2 and the run is 3

Answer:

c=8b

Step-by-step explanation:

The number of crayons is equal to 8 times the number of boxes.

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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If winners are chosen randomly from the 300 people who bought this lottery, the expected profit of a random person is $0.766..

The expected profit under a probability demand distribution is calculated by multiplying the profit amount by the probability of achieving that profit.

It is denoted as E(X) . We have given that,

A $1 lottery ticket has a number of prizes.

Probability of winning first prize , $10 = p₁ = 3/300 = 1/100

probability of winning a 2nd prize, $50

= p₂= 2/300= 1/150

probability of winning a 3rd prize, $100

= p₃ = 1/300 = 1/300

E = expectation value = ∑ Vᵢpᵢ where Vᵢ = value of prize, pᵢ = probability of winning prize,

E = $10 ×1/100 + $50×1/150 + $100×1/300

=> E = $10/100 + $50/150 + $100/300

Taking LCM as 300 on right hand side,

=> E =( $30+ $100+$100)/300

=> E = $(230/300) = $0.766

So, expected winnings for a person buying one ticket is $0.766..

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Article IV Clause 2 of the US Constitution is referred to as the Supremacy Clause. It proves that all other laws and international treaties are subordinate to US federal law.

The United States Constitution's Supremacy Clause declares that the Constitution, federal laws adopted in accordance with it, and treaties signed in accordance with its authority are the "supreme Law of the Land" and supersede any conflicting state laws. According to its provisions, state constitutions are subservient to the supreme law and state courts are obligated by it.

Moreover, federal statutes and treaties must be within the bounds of the Constitution, i.e., they must be in accordance with the enumerated powers of the federal government and must not violate other constitutional restraints on federal power that specify that the federal government only has the authority granted to it by the Constitution.

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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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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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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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Answer:

[tex]\frac{1}{6}[/tex]

Step-by-step explanation:

[tex]\frac{1}{2}[/tex]  of  [tex]\frac{1}{3}[/tex]

[tex]\frac{1}{2}[/tex]  ×  [tex]\frac{1}{3}[/tex]  =  [tex]\frac{1}{6}[/tex]

Hope this helps! :)

Answer:

= 1/6

Step-by-step explanation:

1/2 0f 1/3

is:

(1/2) (1/3) = (1*1) / (2*3)

= 1/6

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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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:

  P(x) = (x +1)(x -2)(x -4)

  see the 2nd attachment for a graph

Step-by-step explanation:

You want the factors of P(x) = x³ - 5x² + 2x + 8, given that (x+1) is one of the factors. You also want a graph of it.

The quotient from dividing P(x) by the given factor will be a quadratic we can factor to find the other two binomial factors. The first attachment shows that quotient is (x² -6x +8).

To factor this quadratic, we look for factors of 8 that have a sum of -6. They are -2 and -4. Hence the remaining binomial factors are (x -2)(x -4).

The desired product is ...

  P(x) = (x +1)(x -2)(x -4)

The second attachment shows a graph of P(x). The y-intercept is the constant in the equation, 8. The x-intercepts are the values of x that make the factors zero.

Answer:Yes

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

The measure of angle 2 is 61 degrees.

The measure of angle 4 is 119 degrees.

What is triangle?

A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.

In the given triangle the measure of two triangles is given which is 61° and 58°.

We have to solve for the measure of angle 2.

Since, the sum of three angles of triangle's is 180 degrees.

⇒ 61° + 58° + ∠2 = 180°

          119 ° + ∠2 = 180°

                     ∠2 = 180° - 119°

                     ∠2 = 61°

Hence, the measure of angle 2 is 61 degrees.

Now to find measure of angle 4.

Here ∠2 and ∠4 are planer angles and their addition is 180°.

⇒ ∠2 + ∠4 = 180°

61° + ∠4 = 180°

∠4 = 180° - 61°

∠4 = 119°

Hence, the measure of angle 4 is 119°.

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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 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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10 choose 3 with replacement gives you a mere 220 combinations. A “combination” lock uses permutations, so there would be 1000 possibilities.

What is Combination?

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant.

Mathematically, a combination is a selection of things without regard for order.

The formula for “combination with replacement” is:

   [tex]C^{R} (n,r)=\frac{(n+r-1)!}{r! (n-r)!}[/tex]

10 choose 3 with replacement gives you a mere 220 combinations.

The toss of three identical 10-sided dice would have 220 possible outcomes.

Hence, A “combination” lock uses permutations, so there would be 1000 possibilities.

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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.

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=

Answer: 9,585

Step-by-step explanation:

Answer:

$9,585.00

6.5x9000 over 100

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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The weight of a randomly selected pack of gum that has a z-score of 3.11 is 54.6 grams

Z-score aids in determining how much the data deviates from the mean. It represents the frequency with which the data is above or below the mean.

Z-scores are calculated using the formula z = (x-)/, where x represents the raw score, the population mean, and the population standard deviation. The z-score is just the raw scoreless population mean, divided by the population standard deviation, as the calculation demonstrates.

According to the formula,

Z = ( X - μ ) / σ

Z being the Z-score,

The data point is X,

The standard variable is, and the mean is.

The z-score of the weight of a randomly chosen pack of gum is 3.11. As a result, this pack of gum weighs 3.11 standard deviations more than the average.

Z = ( X - μ ) / σ

3.11 X 2.4 = X - 47.1

X = 54.6 g

Therefore, choice B is the right one.

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