What is the equation of the line containing the points (5, 2), (10, 4), and (15, 6)?

A. y = 2/5x
B. y = x - 3
C. y = 1/5x + 1

c = 2.97r is the equation that describes the proportional relationship between r, the number of reams purchased and c, the total cost

Two variables have a proportional relationship if all the ratios of the variables are equivalent

In order to write an equation that describes the proportional relationship r, the number of reams purchased and c, the total cost, we need to write a proportional equation using the variables:

c α r                  (Note: α is the proportion symbol)

c = kr

k = c/r

Where k is the constant of proportionality

As shown in the image, you can see that 4 reams cost $11.88 and 6 reams cost $17.82

k = c/r

k = 11.88/4 = 2.97 or 17.82/6 = 2.97

c = kr

c = 2.97r

Therefore, the equation that describes the proportional relationship between r, the number of reams purchased and c, the total cost is c = 2.97r. Enter c = 2.97r in the box

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Answer:

solve for u= 6v/7

solve for v= 7u/6

Step-by-step explanation:

The equations that are  quadratic in form are:

x4 – 6x2 – 27 = 0

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

6x4 = -x2 + 5

The concept that is been used here is quadratic functions which can be written in three ways  :

Where  vertical line x = h and a not equal to zero, Hence we can see that the three selected options above followed the concept that is decribed as the quadratic function.

Therefore, the first, fourth and fifth options are correct.

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Answer:

A, D, E

Step-by-step explanation:

Naoki shifted the base of ladder by 14 feet as the updated distance is 39 feet and old distance was 25 feet.

Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six common trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and abbreviations (csc). Finding the elements of vectors, modeling the mechanics of waves (both electromagnetic and physical), summarizing the strength of fields, and using dot and cross products are all physics applications of trigonometry. You can use trigonometry quite a bit in projectile motion.

Here,

The length of ladder= 65 foot

It rest at a wall at height of 60 foot.

So distance of foot of ladder from wall,

=√(65²-60²)

=√625

=25 foot

Now, as the ladder is shifted, it rest on the wall at height of 52 foot.

=√(65²-52²)

=√1521

=39 foot

Shift in the base of ladder,

=39-25

=14 foot

As the updated distance is 39 feet and the previous distance was 25 feet, Naoki moved the base of the ladder up by 14 feet.

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The new mirror must have at least 81 cm² of the area.

The area of the square is defined as the product of the length and width.

As per the given question, we have

Dominic requires a new bicycle mirror. His old mirror was a square with a 9-cm side length.

He wants the replacement mirror to have an area that is as near to his previous bike mirror as feasible.

We have to determine the area of the previous bike mirror.

The area of the previous bike mirror = (side length)²

The area of the previous bike mirror = (9)² = 9 x 9

The area of the previous bike mirror = 81 cm²

So the new mirror must have greater than 81 cm² of area.

Thus, the new mirror must have at least 81 cm² of the area.

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Answer:

5 cm

Step-by-step explanation:

hope this helps

The amount of weight of bag increase is 4 pounds. The percent of increase is 13,33 %. The result is obtained by calculating the change of two numbers.

A number can increase or decrease to another number. This change can be counted by subtracting the first number from the second number. If the result is positive, it is an increase. If the result is negative, it is a decrease.

The percent of change would be the ratio of the amount of change to first number times 100.

Given the first figure of bag is 26 pounds and the last figure is 30 pounds.

The amount of increase is subtracting 26 from 30.

30 - 26 = 4 pounds.

The percent of increase is

[tex]= \frac{4}{30} \times 100[/tex] %

[tex]= 0.1333 \times 100[/tex] %

[tex]= 13.33[/tex] %

Hence, the amount of weight of bag increase is 4 pounds. The percent of increase is 13,33 %.

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Triangle ADC and ΔBDC are congruent.     then DE ≅ CE

What do you mean by congruent?

Given,

        AD ≅ BC

      ∠BCD ≅ ∠ADC

In triangle ADC and ΔBDC

                    AD ≅ BC    ( GIVEN )

      ∠BCD ≅ ∠ADC          ( GIVEN )

             DC = DC             ( Common line)

so  triangle ADC and ΔBDC are congruent.

             then DE ≅ CE

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"We are 95% confident that the mean sodium content for all beef hot dogs is between 353.2 and 449.1 mg." is the correct statement.

The true parameter must be properly and contextually stated.

We are researching confidence intervals for population means rather than for particular observations. The parameter is, to put it in plain English, the average sodium content of all beef hot dogs. The phrase "We are 95% confident" would be a better translation.

Thus the correct statement is as mentioned above.

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Answer:99

Step-by-step explanation:

1/2 x18x11

99

Answer:

the answer is 1.4N/kg

Each of Aaron's pals receives nine (9) rocks in total.

The question states that,

Aaron collects a total of 54 rocks at the beach.

He wants to give an equal number of rocks to six (6) of his friends.

It is given that let 'r' be the number of rocks each of his friends gets.

The required equation is;

Rock's Aaron's friends get,

→ 6*r = 54

   r = 54/6

   r = 9

The total number of rocks each of Aaron's friends get is 9.

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The domain of the function f(x) = 3x is (b) All positive integers less than or equal to 4

From the question, we have the following equation of the function that can be used in our computation:

f(x) = 3x

In this case, the notations are given as

x = Number of splits

f(x) = number of new roots in each split

From the question, we have

Splits = 4

This means that the maximum value of x is 4

The other values of x would be

x = 1, 2, 3, 4

This can be represented as

0 ≤ x ≤ 4

The interpretation of the above notation is all positive values less than or equal to 4

Hence, the domain value is option (b)

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Answer:

1.) 150/512 in.  

2.) 64/125 in.

Step-by-step explanation:

1.) V = l x w x h                That's the formula to find the volume of a rectangle

V = 6/8 x 5/8 x 5/8 in.    Plug in the numbers

V = 150/512 in.                Multiply

V = 75/256 in.                 Simplify

Since you're asked to not reduce don't write this answer. I only put it to show that it can be simplified.

2.) V = l^3                       This is the formula to find the volume of a cube

V = (4/5)^3 in.                 Plug in the numbers

V = 64/125 in.                 Miltuply

[tex]\fbox{90}[/tex]

In order to find 36 is 40% of what number, we will need to use the following formula:

[tex]number\times100/Percent[/tex]

[tex]\frac{36\times100}{40}[/tex]

[tex]36\times100=3,600[/tex]

[tex]3,600\div40[/tex]

[tex]=90[/tex]

The solution of the number in the expression ''40% of a number is 36'' is 90.

Given that,

To find the solution for 40% of that number is 36.

Used the concpet of percentage which stated that,

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating the hundredth part of any quantity is called a percentage.

Let us assume that the solution of the given condition is x.

So, it can be written as,

[tex]40\% \times x = 36[/tex]

[tex]\dfrac{40}{100} \times x = 36[/tex]

Multiply both sides by 100,

[tex]40x = 36 \times 100[/tex]

[tex]40x = 3600[/tex]

Divide both sides by 40,

[tex]x = \dfrac{3600}{40}[/tex]

[tex]x = 90[/tex]

So, the solution for the number is 90.

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Yes the miles driven and the amount of gasoline used can be said to have a causation as well as a correlation.

The strength and direction of a relationship between two or more variables are described by the statistical measure of correlation, which is given as a number. However, a correlation between two variables does not necessarily imply that a change in one variable is the reason for a change in the values of the other.

There is a causal relationship between the two occurrences, which means that causation shows that one event is the outcome of the occurrence of the other event. This concept is also known as cause and effect.

When the amount of gasoline is small, it would cause the miles covered to be just a few miles. Or if there is no gas, then no mile would be covered.

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The solution for r in equation 5 + r = 6 - r,   r =1/2

The solution for z in equation  z - 16 = - 16,  z= 0

The solution for n in equation 7n - 7 = 0 ,    n= 1

(8) 5 + r = 6 - r

Step 1: Rearrange the equation by collecting the like terms

r +r=6-5

Step 2: Simplify r +r=6-5

2r = 1

Step 3: Divide both sides by 2

2r/ 2 =1/2

r =1/2

9) z - 16 = - 16

Step 1; Add 16 to both sides

z-16 +16 = -16 +16

z= 0

10) 7n - 7 = 0

To solve for n

Step 1: Add 7 to both sides

7n - 7 +7 = 0+7

7n =7

Step 2: Divide both side by 7

7n/7 =7/7

n= 1

Therefore, the solution for r in equation 5 + r = 6 - r, r =1/2

The solution for z in equation  z - 16 = - 16,    z= 0

The solution for n in equation 7n - 7 = 0,   n= 1

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The proportional relationship between the cost and weight is given as y = 0.89x.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The absolute expense for clothing administration, in dollars, relies upon the heaviness of the clothing, in pounds. This relationship is corresponding, as it costs $22.25 for 25 pounds of clothing and $36.49 for 41 pounds of clothing.

The equations are given below.

22.25 = 25m + c          ...1

36.49 = 41m + c           ...2

From equations 1 and 2, then we have

41m - 25m = 36.49 - 22.25

16m = 14.24

m = 0.89

Then the value of c will be given as,

22.25 = 25 (0.89) + c

c = 0

The proportional relationship between the cost and weight is given as y = 0.89x.

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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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If the two events described in the questions are independent events, the probability of both happening next year is 28.67%.

Independent events refer to events whose occurrence is not interdependent. In other words, if the probability of occurrence of event A is not influenced by the probability of occurrence of event B, then A and B are independent events. Mathematically, independent events are represented as P(A│B) and is calculated by multiplying the individual probabilities of the two events. The formula of probability of two independent events is:

P(A│B) = P(A)*P(B)

Hence,

P(A│B) = 0.47*0.61

P(A│B) = 0.47*0.61

P(A│B) = 0.2867

The probability of two events happening next year is 28.67%.

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Answer:

5 feet.

Step-by-step explanation:

if we see that 3 feet is the model and 15 feet is the actual, we find the ratio is 3:15 or 1:5. since the width is 1 foot, then we see the actual is 5 feet long.

Answer:

  f^-1(x) = √((y +9)/3)

Step-by-step explanation:

You want the inverse function of y = 3x² -9.

The given relation will only have an inverse function if its domain is restricted to values x ≥ 0.

We can find that inverse function by interchanging the variables x and y, then solving for y:

  x = 3y² -9

  x +9 = 3y² . . . . . . . add 9

  (x +9)/3 = y² . . . . . . divide by 3

  y = √((x+9)/3) . . . . . take the square root

The inverse function is f^-1(x) = √((x +9)/3).

The length of the table is 1.51 meters.

Allan is measuring his dining room table to make a tablecloth. The table is 0.45 meter longer than it is wide. The width of the table is 1.06 meter. We need to find out the length of the table.

Let the length of the table be represented by the variable "L". In the context of a mathematical problem or experiment, a variable is a quantity that may vary. The length of the table is the sum of the width of the table and the difference between the two quantities.

L = 1.06 + 0.45

L = 1.51

Hence, the length of the table is 1.51 meters.

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Only function (a) is one-to-one.

acc to our question-

If every element of the range of the function corresponds to exactly one element of the domain, then the function is called one-to-one.

The elements of a function are

A = {a,b,c,d}

Therefore, this function is one-to-one.

(b).f (a) = b, f (b) = b, f (c) = d, f (d) = c.

Here, the value of function is b for x=a and x=b. For two domains the functions has same range.

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(7) 55 is 181.81% of 100

(8) 22% of 110 is 24.2

(9) 19 is 50% of 38

(10) 25 is 32% of 78.125

(11)  40% of 70 is 28.

(12) 30 is 200% of 60.

What is percent?

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.", "pct.", and occasionally "pc" are also used to indicate it, while the percent symbol, "%," is most frequently employed. A % has no dimensions and no standard measurement.

(7) Suppose 55 is x%  of 100.

So,

55x/100 = 100

x/100 = 100/55

x = 1.8181 x 100

x = 181.81%

Therefore, 55 is 181.81% of 100.

(8) Suppose 22% of x is 24.2

So,

x(22)/100 = 24.2

x = 24.2 x 100/22

x = 110

Therefore, 22% of 110 is 24.2

(9) Suppose 19 is 50% of x.

So,

19 = 50(x)/100

x = 19 x 100/50

x = 38

Therefore, 19 is 50% of 38.

(10) Suppose 25 is 32% of x.

So,

25 = 32(x)/100

x = 25 x 100/32

x = 78.125

Therefore, 25 is 32% of 78.125

(11) Suppose 40% of x is 28

So,

40(x)/100 = 28

x = 28 x 100/40

x = 70

Therefore, 40% of 70 is 28.

(12) Suppose 30 is x% of 60

So,

30(x)/100 = 60

x = 60 x 100/30

x = 200

Therefore, 30 is 200% of 60.

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Answer:

[tex]x=\dfrac{\pi }{3}+2\pi n, \quad x=\dfrac{5\pi }{3}+2\pi n,\quad x=2\pi n,\quad x=\pi+2\pi n[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6.5 cm}\underline{Trigonometric Double Angle Identities}\\\\$\sin (A \pm B)=\sin A \cos B \pm \cos A \sin B$\\\\$\cos (A \pm B)=\cos A \cos B \mp \sin A \sin B$\\\\$\tan (A \pm B)=\dfrac{\tan A \pm \tan B}{1 \mp \tan A \tan B}$\\\end{minipage}}[/tex]

Given equation:

[tex]\tan (x + \pi) + \sin(x + \pi) + \sin(x - \pi)=0[/tex]

Simplify using the double angle identities:

[tex]\implies \dfrac{\tan x + \tan \pi}{1 -\tan x \tan \pi} + \sin x \cos \pi+\cos x \sin \pi + \sin x \cos \pi -\cos x \sin \pi=0[/tex]

[tex]\implies \dfrac{\tan x + 0}{1 -\tan x(0)} + \sin x (-1)+\cos x (0) + \sin x(-1) -\cos x (0)=0[/tex]

[tex]\implies \dfrac{\tan x}{1} -\sin x - \sin x=0[/tex]

[tex]\implies \tan x-2\sin x =0[/tex]

Use the tan identity to rewrite tan(x) in terms of sin(x) and cos(x):

[tex]\implies \dfrac{\sin x}{ \cos x}-2\sin x=0[/tex]

Multiply both sides by cos(x):

[tex]\implies \dfrac{\sin x\cos x}{ \cos x}-2\sin x\cos x=0(\cos x)[/tex]

[tex]\implies \sin x-2\sin x \cos x=0[/tex]

Factor out sin(x) from the left side of the equation:

[tex]\implies \sin x(1-2 \cos x)=0[/tex]

Apply the zero-product property.

Case 1

[tex]\implies \sin x=0[/tex]

[tex]\implies x=\sin^{-1}(0)[/tex]

[tex]\implies x=2\pi n, \; \pi+2\pi n[/tex]

Case 2

[tex]\implies 1-2 \cos x=0[/tex]

[tex]\implies 1=2 \cos x[/tex]

[tex]\implies \cos x=\dfrac{1}{2}[/tex]

[tex]\implies x= \cos ^{-1} \left(\dfrac{1}{2}\right)[/tex]

[tex]\implies x=\dfrac{\pi }{3}+2\pi n, \;\dfrac{5\pi }{3}+2\pi n[/tex]

Solution

[tex]x=\dfrac{\pi }{3}+2\pi n, \quad x=\dfrac{5\pi }{3}+2\pi n,\quad x=2\pi n,\quad x=\pi+2\pi n[/tex]

The function g(X) will be of the form g(x) = |x/6| ,when stretched by a factor of 6.

The function is f(x)=|x| .

We know that for transformation of a function of the form horizontal stretch by a factor of 'a' is given by the g(x)= f(x/a)

So in this given function the horizontal stretch is by a factor of 6.

Therefore g(x) = f(x/6)

or, g(x) = |x/6|

In the graph attached the green represents the function f(x) while the red represents the function g(x).

A function transformation either "moves," "resizes," or "reflects" the graph of anything similar to the parent function. The following are the three main types of function transformations:

Dilation is the only one of these changes that modifies the size of the original shape; the other two just change its location.

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The height of utility poles is B. 12 meters.

The height of the utility pole will be calculated by the formula -

tan theta = perpendicular ÷ base, where theta is the angle of elevation, perpendicular is the height of utility pole and base is the distance from the base of pole to the wire.

Keep the values in formula to find the height of utility pole.

tan 59 = perpendicular ÷ 7

Perpendicular = tan 59 × 7

Perpendicular = 1.66 × 7

Performing multiplication on Right Hand Side of the equation

Perpendicular = 11.65 metres

On rounding off, we get 12 metres.

Thus, the height is B. 12 meters.

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Answer:

20 gallons

Step-by-step explanation:

2/5 = 4/10

3/10 = 6 gallons

1/10 = 6 : 3= 2 gallons

10/10 = 2 * 10 = 20 gallons

The equations represent functions where x is the input and y is the output are y = 2x and x+y = 2

The 1st equation is x =2

Since there is no component of y and the value of x is fixed. So this is not the desired option.

The 2nd equation is y = 2

Since there is no component of x, and the value of y is fixed. So this is not the desired option.

The 3rd equation is y = 2x

In this equation, x is the input and y is the output. For different values of x, we will have different values of y.

Thus, this is the desired option.

The 4th equation is x =2y

In this equation, y is the input and x is the output. For different values of y, we will have different values of x.

The 5th equation is x+y = 2

So, x + y = 2

y = 2 - x

In this equation, x is the input and y is the output. For different values of x, we will have different values of y.

Thus, this is the desired option.

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