Writing equations in standard form:

Hi I need help with writing equations in standard form using points. The points are (4,5) and (-3,-1) I already found the slope which is 6/7 but I don’t know how to do the point slope form. This is the slope form if you don’t know:
Y-y1=m(x-x1)

Answer:

The length of the longer piece is 180.

Step-by-step explanation:

If one piece is 3 times the other piece than their are 4 pieces. So, divide 240 by 4 to get 60. Since it is 3 times you multiply the 60 by 3 to get 180. Thus, the small piece is 60 and the large piece is 180. 180 is 3 times as long as 60 and 60 + 180 = 240.

Answer:

U did not add a picture but if u do I will help.

Step-by-step explanation:

It should be 8 to the right and 12 to the left which should end at -4

Answer:

The answer is 4?? tell me if it's wrong or not.

Answer:

\(7,500\)

Step-by-step explanation:

Let's solve this problem step-by-step. The library had 1,500 books in 2011. The ratio of books in 2011 and in 2012 is 1:2. Therefore, let the number of books in 2012 be \(x\).

We have the following proportion:

\(\frac{1}{1,500}=\frac{2}{x},\\x=2\cdot 1,500=3,000\)

Therefore, there were 3,000 books in 2012. The ratio of books in 2012 and in 2013 is 2:5. Let the number of books in 2013 be \(y\).

We have:

\(\frac{2}{3,000}=\frac{5}{y},\\2y=5\cdot 3,000,\\2y=15,000\\y=\boxed{7,500}\)

Therefore, there were 7,500 books in 2013.

Answer:

7,500 books

Step-by-step explanation:

Answer:

1/50,

2/10,

10/50,

20/100,

40/200,

80/400

160/800

Multiply the common denominator and numerator by a number.

Answer:

10/50, 5/25, 1/5

40/200, 60/300, 80/400, 100/1000

Step-by-step explanation:

There's more that are equivalent but I wasn't really sure what you meant so....There you go.

Hope this helps. Have a nice day. May it be filled with joy and happiness. Please, stay safe and wash your hands. Happy Holidays.

Answer:

as shown in underline ^^

Step-by-step explanation:

Fill in the missing words:

When a solid mixes with a liquid and becomes part of the liquid it dissolves.

A solid that dissolves in a liquid is soluble.

A solid that does not dissolve in a liquid is insoluble.

(A) The derivative of f(x) = 2x^4 - 4x^2 + 1 is f'(x) = 8x^3 - 8x.

(B) The slope of the graph of f at x = 2 is 40.

(C) The equation of the tangent line at x = 2 is y = 36x - 63.

(D) The value(s) of x where f'(x) = 0 are x = 0 and x = 1.

(A) To find the derivative of f(x) = 2x^4 - 4x^2 + 1, we differentiate each term using the power rule. The derivative of 2x^4 is 8x^3, the derivative of -4x^2 is -8x, and the derivative of the constant term 1 is 0. Therefore, f'(x) = 8x^3 - 8x.

(B) The slope of the graph of f at a specific value of x can be found by evaluating f'(x) at that point. Substituting x = 2 into f'(x) gives f'(2) = 8(2)^3 - 8(2) = 40. Hence, the slope of the graph of f at x = 2 is 40.

(C) To find the equation of the tangent line at x = 2, we use the point-slope form of a line. Using the point (2, f(2)), we substitute x = 2 and evaluate f(2) = 2(2)^4 - 4(2)^2 + 1 = 33. Therefore, the equation of the tangent line is y - 33 = 40(x - 2), which simplifies to y = 40x - 63.

(D) To find the value(s) of x where f'(x) = 0, we set f'(x) equal to zero and solve the equation 8x^3 - 8x = 0. Factoring out 8x gives 8x(x^2 - 1) = 0. Thus, the values of x that satisfy f'(x) = 0 are x = 0 and x = ±1.

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Answer:

mm

Step-by-step explanation:

Answer:

a = 55

b = 13

c = 8

Step-by-step explanation:

2a - 5 = 105° (alternate exterior angles are congruent)

Add 5 to both sides

2a - 5 + 5 = 105 + 5

2a = 110

Divide both sides by 2

2a/2 = 110/2

a = 55

(2a - 5) + (5b + 10) = 180° (consecutive interior angles/same side interior are supplementary)

Plug in the value of a

2(55) - 5 + 5b + 10 = 180

110 - 5 + 5b + 10 = 180

Add like terms

115 + 5b = 180

Subtract 115 from each side

115 + 5b - 115 = 180 - 115

5b = 65

Divide both sides by

5b/5 = 65/5

b = 13

10c - 5 = 5b + 10 (corresponding angles are congruent)

Plug in the value of b

10c - 5 = 5(13) + 10

10c - 5 = 65 + 10

10c - 5 = 75

Add 5 to both sides

10c - 5 + 5 = 75 + 5

10c = 80

Divide both sides by 10

10c/10 = 80/10

c = 8

Answer:

False

Step-by-step explanation:

If the square root can be simplified to a rational number the solution will not be irrational.

Answer:

False

Step-by-step explanation:

Consider reducible quadratic equations. They have rational solutions.

Answer:

1 gallon and 1 pint

Step-by-step explanation:

I guess that the actual amount of water needed per player is 1/8 of gallon and not 18 gallons.

You will need to bring 9 x 1/8 = 9/8 = 1 ¹/₈ gallons or 1 gallon and 1 pint

1 gallon = 4 quarts = 8 pints = 16 cups = 128 ounces

or

1 gallon = 3.785 liters

The US is one of the few countries (along with Liberia, and Myanmar) that still uses the imperial system to measure things, e.g. inches, feet, yards, pounds, miles, pints, gallons, etc. The rest of the world uses the metric system, e.g. meters, liters, kilograms, etc.

Answer:

1 1/8

Step-by-step explanation:

i did it on edge

Answer:10,559.7000

Step-by-step explanation:

Triangle PUB is divided into 2 triangles that is ΔPUM and ΔPMB. We have angles ∠B=35°,∠U=62°,∠P=21°. The angles are ∠1=56° and ∠2=62°.

Given that,

In picture there is a triangle with the intersection line in between the triangles.

Triangle PUB is divided into 2 triangles that is ΔPUM and ΔPMB.

We have angles

∠B=35°,∠U=62°,∠P=21°

We have to find the angle of angle 1 and 2.

We know,

In triangle sum of the 3 angles is 180°.

Now, we take ΔPMB

We find the other angle of M.

21°+35°+M=180°

M=180°-21°-35°

M=180°-56°

M=124°

So, now we can find the angle 1.

the straight line has a angles of 180°.

124°+∠1=180°

∠1=180°-124°

∠1=56°

Now, we find angle 2.

Take ΔPUM

62°+∠1+∠2=180°

62°+56°+∠2=180°

∠2=180°-62°-56°

∠2=180°-118°

∠2=62°

Therefore, the angles are ∠1=56° and ∠2=62°.

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The value of C₂, we can rewrite the expression for f(x) as:

\(f(x) = 1 + 5x - x^3 + 2x^2 - 31x + 28\)

To find the value of C₂, we need to substitute x = 1 into the expression for f(x) and equate it to the given value of f(1) = 4.

Let's substitute x = 1 into the expression for f(x):

\(f(x) = 1 + 5x - x^3 + 2x^2 - 31x + C₂f(1) = 1 + 5(1) - (1)^3 + 2(1)^2 - 31(1) + C₂ = 1 + 5 - 1 + 2 - 31 + C₂ = -24 + C₂\)

We know that f(1) = 4, so we can equate it to -24 + C₂ and solve for C₂:

-24 + C₂ = 4

C₂ = 4 + 24

C₂ = 28

Now that we have the value of C₂, we can rewrite the expression for f(x) as:

\(f(x) = 1 + 5x - x^3 + 2x^2 - 31x + 28\)

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The statement "P implies Q" is false under the following conditions: a) P is true and Q is false, and d) P is false and Q is true.

The statement "P implies Q" can be expressed as "if P, then Q." It is a conditional statement where P is the antecedent (the condition) and Q is the consequent (the result).

To determine when the statement is false, we need to identify cases where P is true but Q is false, or when P is false but Q is true.

Option a) states that both P and Q are true. In this case, the statement "P implies Q" holds true because if P is true, then Q is true.

Option b) states that both P and Q are false. In this case, the statement "P implies Q" is considered true because the antecedent (P) is false.

Option c) states that P is true and Q is false. Under this condition, the statement "P implies Q" is false because when P is true, but Q is false, the implication does not hold.

Option d) states that P is false and Q is true. In this case, the statement "P implies Q" is true because the antecedent (P) is false.

Therefore, the conditions under which the statement "P implies Q" is false are a) P is true and Q is false, and d) P is false and Q is true.

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Answer:

11m

I did it by Geometry and used the scale : 1cm represents 5m

Please find attached the completed table of the percentage changes on the amounts drawn with MS Word.

The percentage change on an amount is found by finding ratio of the change in the amount to the original amount then multiplying the obtained ratio by 100.

The percentage change formula is presented as follows;

Where;

Making each of the variables the subject, indicates;

The new amount, \(x_2 = \dfrac{\%C \times x_1}{100} + x_1\)

\(\%C \times x_1+100\cdot x_1 = 100\cdot x_2\)

\(x_1\cdot (\%C+100) = 100\cdot x_2\)

The original amount, \(x_1 = \dfrac{100\cdot x_2}{(\%C+100)}\)

The percentage change, \(\%C = \dfrac{c}{x_1} \times 100\)

The original amount, \(x_1 = \dfrac{c}{\%C} \times 100\)

Using the above formulas, the completed table is created with MS Excel and is presented as follows;

Original amount  Change  Percent Change   New Amount

68 \({}\)                        15            22.1                        83

590 \({}\)                    -40          -6.8                         550

115 \({}\)                       20           17.4                         135

120\({}\)                      -33           -27.5                       87

125\({}\)                     -39           -31.2                        86

163   \({}\)                   47             28.8                       210

274\({}\)                     145.22       17.4                        419.22

70 \({}\)                      -15.4         -27.5                       54.6

1400\({}\)                  -1050         22.1                        350

1250\({}\)                  -25            -2.0                         1225

0.24\({}\)                    0.3            125.0                      0.54

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False. Each triangle in the STL file is defined by the vertices, but not necessarily by the inward pointing surface normal vector. The surface normal vector is often calculated based on the vertex positions.

False. The STL file is a mesh representation of the CAD model, and it does not contain all the information needed to fully reconstruct the original CAD model. It lacks information such as parametric features, assembly relationships, and design intent, making it difficult to recreate the exact original model.

The option "Increasing the heat exchange area for a heat exchanger" is NOT an advantage of using a lattice structure. Lattice structures are known for their lightweight properties, material-saving benefits, and simplified design and manufacturing processes.

However, increasing the heat exchange area for a heat exchanger is not typically associated with lattice structures. Heat exchangers usually rely on other design considerations, such as fin arrays or extended surfaces, to enhance heat transfer efficiency, rather than lattice structures.

Therefore, increasing heat exchange area is not a direct advantage of lattice structures.

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Hey there! :)

Answer:

f(n) = n²

Step-by-step explanation:

Let n be the term number of this pattern and f(n) the number of shapes: Examine the pattern shown:

When n = 1, f(n) = 1.

When n = 2, f(n) = 4.

When n = 3, f(n) = 9.

The pattern of this sequence is:

f(n) = n².

This means that the # of shapes shown is the square of the term number.

In probability theories, events which can never occur together are classified as "mutually exclusive events" that is option A.

Two events are mutually exclusive or disjoint in logic and probability theory if they cannot both occur at the same time. The results of a single coin toss, which can result in either heads or tails but not both, serve as an obvious illustration. Events that do not take place at the same time are said to be mutually exclusive. For instance, if a coin is tossed, the outcome will either be head or tail; we cannot get both outcomes. Since they do not occur at the same time, such events are also known as disjoint events.

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Step-by-step explanation:

\( \underline{ \underline{ \text{Given}}} : \)

\( \underline{ \underline{ \text{To \: find \: }}} : \)

\( \underline{ \underline{ \text{Solution}}} : \)

\( \tt{8 {(a - b)}^{2} + 3b}\)

~Plug the values and then simplify !

⇢ \( \tt{8 {(6 - 3)}^{2} + 3 \times 3}\)

⇢ \( \tt{8 {(3)}^{2} + 9}\)

⇢ \( \tt{8 \times 9 + 9}\)

⇢ \( \tt{72 + 9}\)

⇢ \( \tt{81}\)

\( \red{ \boxed {\boxed{ \text{Our \: final \: answer : \boxed{\tt{81}}}}}}\)

Hope I helped ! ♡

Have a wonderful day / night ! ツ

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Answer:

1: pi, right

2: pi, left

3: coincides with

Step-by-step explanation:

When h = π, the orange graph shifts pi units to the right. When h = −π, the orange graph shifts pi units to the left.

In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between multiple things are frequently represented by the points on a graph. Here, for example, we can plot a graph showing the type and quantity of school supplies in use by pupils in a class based on the data provided below.

A bar graph can also be used to display the data. Bar graphs show how many of each supply there are. The more supplies or goods are used, the higher the bar's height. When h = π, the orange graph shifts pi units to the right. When h = −π, the orange graph shifts pi units to the left.

Therefore, when h = π, the orange graph shifts pi units to the right. When h = −π, the orange graph shifts pi units to the left.

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Answer:

V=  480.7 m cubed

The volume of the cylinder nearest to tenths place is 480 m^3.

A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface.

For the given situation,

The formula for volume of the cylinder is \(V=\pi r^{2} h\)

Radius of the cylinder,r = 3 m

Height of the cylinder, h = 17 m

The value of π = 3.14

On substituting the above values,

\(V=(3.14) (3^{2})(17)\)

⇒ \(V=480.42\) ≈ 480

Hence we can conclude that the volume of the cylinder is 480 m^3.

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Engineers can be held most morally blameworthy for foreseeable harms resulting from technological innovations, engineers have a responsibility to anticipate the potential consequences of their work,

and to take steps to mitigate those consequences. If they fail to do so, and their work results in harm, they can be held morally blameworthy. When engineers develop new technologies, they have a responsibility to consider the potential consequences of their work.

They need to think about how their technology could be used, and whether it could be used to harm people or the environment.

They also need to consider how their technology could be misused, and what steps they can take to prevent misuse.

If engineers fail to consider the potential consequences of their work, and their work results in harm, they can be held morally blameworthy. This is because they have a duty to protect the public from harm, and they have failed to fulfill that duty.

For example, engineers who develop new weapons systems have a responsibility to consider the potential consequences of their work. They need to think about how their weapons could be used,

and whether they could be used to kill or injure innocent people. They also need to consider how their weapons could be misused, and what steps they can take to prevent misuse.

If engineers fail to consider the potential consequences of their work, and their weapons are used to kill or injure innocent people, they can be held morally blameworthy. This is because they have a duty to protect the public from harm, and they have failed to fulfill that duty.

It is important to note that engineers cannot be held morally blameworthy for unforeseeable harms. This is because they did not have the opportunity to anticipate the harm, and they could not have taken steps to prevent it.

For example, engineers who develop new medical treatments cannot be held morally blameworthy if the treatments have unforeseen side effects. This is because the engineers did not have the opportunity to anticipate the side effects, and they could not have taken steps to prevent them.

In conclusion, engineers can be held morally blameworthy for foreseeable harms resulting from technological innovations.

This is because they have a responsibility to anticipate the potential consequences of their work, and to take steps to mitigate those consequences.

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To express a product as a sum or difference containing only sines or cosines, we can use trigonometric identities such as the sum and difference identities. These identities allow us to rewrite products involving sines and cosines as sums or differences of sines or cosines.

Let's consider an example:

Suppose we have the product cos(x)sin(x). We can rewrite this product using the double angle identity for sine:

cos(x)sin(x) = (1/2)sin(2x)

In this case, we have expressed the product as a sum of sines.

Similarly, if we have the product sin(x)cos(x), we can use the double angle identity for cosine:

sin(x)cos(x) = (1/2)sin(2x)

In this case, we have also expressed the product as a sum of sines.

In summary, to express a product as a sum or difference containing only sines or cosines, we can use trigonometric identities like the double angle identity for sine or cosine. By applying these identities, we can rewrite the product in terms of sums or differences of sines or cosines.

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Answer:11486.34

Step-by-step explanation:

p is semiperimeter

p=(a+b+c)/2

p=(174+138+188)/2

For Heron equation,

S=\(\sqrt{p*(p-a)*(p-b)*p-c}\)

so, it is 11487.34

Answer:

  11,486.3 square units

Step-by-step explanation:

You want the area of the triangle with side lengths a=174, b=138, c=188.

The area of a triangle can be found from the lengths of the three sides using Heron's formula:

  A = √(s(s -a)(s -b)(s -c)) . . . . . . . where s = (a+b+c)/2, the "semiperimeter"

The calculation is shown in the second attachment.

  s = (174 +138 +188)/2 = 500/2 = 250

  A = √(250(250 -174)(250 -138)(250 -188)) = √(250(76)(112)(62))

  A = √131936000 ≈ 11486.3

The area of the triangle is about 11486.3 square units.

__

Additional comment

An effectively equivalent way to find the area is to use the Law of Cosines to find an angle, then use the trig formula for the area.

  C = arccos((a²+b²-c²)/(2ab)) = arccos(13976/48024) ≈ 73.080899°

  Area = 1/2(ab·sin(C)) = 1/2(24012·0.9567166) ≈ 11486.3

We say this is "effectively equivalent" not only because it gives the same area, but because using the relation between cos(C) and sin(C), you can demonstrate that this formula gives Heron's formula for the area.

Answer:

Profit % = 39%

Step-by-step explanation:

Cost price of the article = 9

Price for repairing = 4

Therefore, Total cost of the article = 9 + 4 = 13

Selling price  of the article = 18

Profit = 18 - 13 = 5

Hence,

          \(Profit \% = \frac{Profit}{Cost \ price} \times 100\\\\\)

                        \(= \frac{5}{13} \times 100\\\\=38.46 \%\\\\=38.5 \%\)

Profit percent (to the nearest %) = 39%

An inverse relationship can not direct.

We know that an inverse proportion represents inverse or indirect relation between two quantities.

In inverse relationship, one value increases while the other value decreases, and vice versa.

But in case of direct relationship, if one quantity increases , the other quantity also increases, and  if one quantity decreases , the other quantity also decreases.

When two quantities 'm' and 'n' are inversely proportional to each other, it means when the value of m increases while the value of quantity  'n' decreases, and vice versa.

Also, an inverse relationship always has a negative slope.

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Answer:

Step-by-step explanation:

1,2,4