What is the rate of change of the linear equation 3.9x + y = 15.21?

A. -15.21
B. -3.9
C. 3.9
D.15.21​

Answer:

b = 4, b = 6

Step-by-step explanation:

consider the left side

x² + 10x + 24

consider the factors of the constant term (+ 24) which sum to give the coefficient of the x- term (+ 10)

the factors are + 4 and + 6

then

x² + 10x + 24 = (x + 4)(x + 6) = (x + 6)(x + 4)

then (x + b) = (x + 4) or (x + 6)

with b = 4 or b = 6

The speed of Car A when it travels 60 miles in 2 hours is 30 miles per hour. This is the rate. Therefore, that is true.

From the information, it should be noted that Car A travels 60 miles in 2 hours. It should be noted speed is calculated as:

Speed = Distance / Time

It should be noted that speed simply means the distance that's travelled with respect to time.

Speed = 60 / 2

Speed = 30 miles per hour

Note that an overview was given as enough information wasn't given about Car B.

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Answer: Square is a 17*17. Ok so its 121-25=96

Step-by-step explanation:

96

The system of inequalities fits in this scenario are x + y & lt; = 2815x + 10Y & lt;= 300.

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way.

The majority of the time, size comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations, including: The symbol a b indicates that an is smaller than b. When a & gt; b is used, it indicates that an is bigger than b. A is not equivalent to b in any scenario. Since an is strictly less than or strictly greater than b, these relationships are known as stringent inequalities. Equivalence is not considered. In the given questions the inequalities are x + y & lt;= 2815x + 10y & lt;= 300

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Answer:

Below

Step-by-step explanation:

To complete the square, the leading x^2 coefficient needs to be = 1 , so factor out a 3 to get

y = 3 ( x^2 + 5/3x )   +3                (I assumed it was a + sign between the terms)

 Then take 1/2 of the 5/3   ( 5/6 )  , square it  (25/36) , add it to the parentheses.... then subtract the amount you added (3 * 25/36) by doing this.....  to have this :

y = 3 ( x^2 + 5/3 x + 25/36)  -   3 * 25/36   +3      then simplify to

y = 3 ( x + 5/6)^2  + 11/12               Done.

Answer:

No, Jason's method is not a good one to follow, because u have to let x alone, and try to break down the constant.

Step-by-step explanation:

Jason should do 3x - 12 = 36

                            3x + 12 = + 12

                            3x = 48

                             x = 16

Answer:

It works and is a good one to follow if each term is divisible by the same number!

Step-by-step explanation:

Dividing each term by 3 will give us the equation x - 4 = 12 which leads to the correct answer of x = 16.

However, if there each term is not divisible by the same number, it is not a good method to follow (because it will not work).

The expressions 10x-7 and 7-10x represent the statement "seven less than ten times a number".

The verbal expression "seven less than ten times a number" can be written mathematically in different ways, depending on the intended meaning. One possible expression is:

10x - 7

In this expression, "10x" represents ten times a number, and "-7" represents seven less than that quantity. Thus, the entire expression represents the result of subtracting 7 from the product of 10 and the number x.

Another possible expression is 7 - 10x

In this expression, "10x" represents ten times a number, and "7 - 10x" represents seven less than that quantity. Thus, the entire expression represents the result of subtracting the product of 10 and the number x from 7.

If the focus is on finding the result of subtracting 7 from ten times a number, the first expression is more appropriate. If the focus is on finding the result of subtracting the product of 10 and a number from 7, the second expression is more appropriate.

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Answer: points lol

Step-by-step explanain

is ni_ E gr

Answer:

4

Step-by-step explanation:

note that \(\sqrt{x^2}\) = x , then

\(\sqrt{(2-\sqrt{5})^2 }\) + \(\sqrt{(2+\sqrt{5})^2 }\)

= 2 - \(\sqrt{5}\) + 2 + \(\sqrt{5}\) ← collect like terms

= 4

The probability of getting a not even number is 0.5.

The given outcomes are 3, 4, 5, 6.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes.

Total number of outcomes = 4

Number of favorable outcomes = 2

Now, P (not even) = 2/4

= 1/2

= 0.5

Therefore, the probability of getting a not even number is 0.5.

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Answer:

30 + 15d = 105, I think

Step-by-step explanation:

Using the given natural abundances of titanium-46, titanium-47, and titanium-48, we find that the average atomic mass of titanium on this planet is approximately 46.4 amu.

To calculate the average atomic mass of titanium on another planet, we need to consider the natural abundances of its isotopes. The average atomic mass is calculated by multiplying the mass of each isotope by its relative abundance and summing up these values.

Let's assume that the three isotopes of titanium on this planet are denoted as titanium-46, titanium-47, and titanium-48. The natural abundances of these isotopes are given as follows:

Isotope Natural Abundance

Titanium-46 70%

Titanium-47 20%

Titanium-48 10%

To calculate the average atomic mass, we multiply the mass of each isotope by its relative abundance and sum up these values. The atomic masses of titanium-46, titanium-47, and titanium-48 are approximately 46.0 amu, 47.0 amu, and 48.0 amu, respectively.

Average Atomic Mass of Titanium:

(46.0amu×70%)+(47.0amu×20%)+(48.0amu×10%)

=(32.2amu)+(9.4amu)+(4.8amu)

=46.4amu

Therefore, the average atomic mass of titanium on this planet is approximately 46.4 atomic mass units (amu).

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The equation given as -y = 3x is a direct variation. The constant of variation is - 1/3

It shows the relationship between two variables that can be described mathematically by an equation where one variable equals a constant multiplied by the other.

A straightforward correlation between two variables is referred to as direct variation. In this case, the constant of variation will be k.

This will be Illustrated as:

y = kx

-1 = 3k

Divide

k = -1/3

The constant is - 1/3.

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Answer:

y = 3/2x+5

Step-by-step explanation:

Andrew gets on a scale and reads his weight as 66 lb. If 1 kg ≈ 2. 2 lb, what is his mass in kilograms? His mass is 29.93 kilograms.

A pound( symbol lb) is a unit of mass used in the customary systems of dimension. The transnational avoirdupois pound( the common pound used moment) is defined as exactly 0.45359237 kilograms. The avoirdupois pound is original to 16 avoirdupois ounces.

A kilogram( symbol kg) is the base unit of mass in the International System of Units( SI). It's presently defined grounded on the fixed numerical value of the Planck constant, h, which is equal to 6.62607015 × 10- 34 in the units of J · s, or kg · m2 · s- 1. The cadence and the second are defined in terms of c, the speed of light.

The unitary method is used to find the value of a single unit from a given multiple, 1 pound = 0.45359237 kilograms ≈ 0.454 kilograms

66 pounds = 66 X 0.454 kilograms ≈ 29.93 pounds.

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Answer:

m=-38

Step-by-step explanation:

-(6m+8)=4(17-m)

We move all terms to the left:

-(6m+8)-(4(17-m))=0

We add all the numbers together, and all the variables

-(6m+8)-(4(-1m+17))=0

We get rid of parentheses

-6m-(4(-1m+17))-8=0

We calculate terms in parentheses: -(4(-1m+17)), so:

4(-1m+17)

We multiply parentheses

-4m+68

Back to the equation:

-(-4m+68)

We get rid of parentheses

-6m+4m-68-8=0

We add all the numbers together, and all the variables

-2m-76=0

We move all terms containing m to the left, all other terms to the right

-2m=76

m=76/-2

m=-38

The solution to the given equation is \(-38\)

\(-6m - 8 = 68 - 4m\)

\(-6m + 4m = 68+8\)

\(-2m = 76\)

\(m= \frac{-76}{2}\)

\(= -38\)

Therefore, the value of m is\(-38\)

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The Task objective chosen is: A Measuring Task

The Objective is: To investigate the fairness of a local athlete's track for runners starting on different lines.

To carry about the investigation, follow the steps given below.

Lastly, make a crossword puzzle that includes mathematical vocabulary in a clever manner.

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```Class IX```

*Mathematics Project work*

*Do any one*

1. *A Measuring Task*

To investigate your local athletes track to see whether it is worked fairly for runners who start on different lines.

2. *Design a crossword puzzle with mathematical terms*

To review mathematics vocabulary, to give the opportunity for creative expression in designing puzzles, to act as a means of motivating the study of a given unit and to given recreation .​

Answer:

y=29x+50; 30 months

Step-by-step explanation:

$920-50=870

870/29=30

Answer:

c=29m+50

30 months

Step-by-step explanation:

If you pay $29 per month, (using m as the variable), the equation would be 29m. Since there is a one-time fee of $50, we add that once. Your equation is c=29m+50. (Assuming the variable for months is m)

If you paid 920$ dollars, first we need to subtract your $50 one time fee. 920-50=870. Since you paid $29 per month, divide 870 by 29. The answer is 30. This means you were a member of the gym for 30 months.  

(a) The approximated root of f(x) = e^x + x^2 - x - 4 is x ≈ 2.151586.

(b) The approximated root of f(x) = x^3 - x^2 - 10x + 7 is x ≈ -0.662460.

(c) The approximated root of f(x) = 1.05 - 1.04x + ln(x) is x ≈ -1.240567.

(a) Purpose: f(x) = ex + x2 - x - 4 To apply Newton's method, we must determine the function's derivative as follows: f'(x) = e^x + 2x - 1.

Now, we can use the formula to iterate: Choose an initial guess, x(0) = 0, and carry out the iterations as follows: x(n+1) = x(n) - f(x(n))/f'(x(n)).

1. Iteration:

Iteration 2: x(1) = 0 - (e0 + 02 - 0 - 4) / (e0 + 2*0 - 1) = -4 / (-1) = 4.

2.229280 Iteration 3: x(2) = 4 - (e4 + 42 - 4 - 4) / (e4 + 2*4 - 1)

x(3)  2.151613 The Fourth Iteration:

x(4)  2.151586 The Fifth Iteration:

x(5)  2.151586 The equation f(x) = ex + x2 - x - 4 has an approximate root of x  2.151586.

(b) Capability: f(x) = x3 - x2 - 10x + 7 The function's derivative is as follows: f'(x) = 3x^2 - 2x - 10.

Let's apply Newton's method with an initial guess of x(0) = 0:

1. Iteration:

x(1) = 0 - (0,3 - 0,2 - 100 + 7), or 7 / (-10)  -0.7 in Iteration 2.

x(2)  -0.662500 The Third Iteration:

x(3)  -0.662460 The fourth iteration:

The approximate root of the equation f(x) = x3 - x2 - 10x + 7 is x  -0.662460, which is x(4)  -0.662460.

c) Purpose: f(x) = 1.05 - 1.04x + ln(x) The function's derivative is as follows: f'(x) = -1.04 + 1/x.

Let's use Newton's method to make an initial guess, x(0) = 1, and choose:

z

1. Iteration:

x(1) = 1 - (1.05 - 1.04*1 + ln(1))/(- 1.04 + 1/1)

= 0.05/(- 0.04)

≈ -1.25

Cycle 2:

x(2) less than -1.240560 Iteration 3:

x(3) less than -1.240567 Iteration 4:

x(4)  -1.240567 The equation f(x) = 1.05 - 1.04x + ln(x) has an approximate root of x  -1.240567.

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Answer:

A half is not a unit of measure for weight, so it is not possible to answer this question.

Answer:

y = 45, x = 25

Step-by-step explanation:

Since 120 and (2y + 30) are vertical angles, (2y + 30) will equal 120.

2y + 30 = 120, Subtract by 30 on both sides

2y = 90, Divide 90 by 2

y = 45

Since 120 and (2x + 10) equal a straight line, it's a supplementary angle. Supplementary angles are equal to 180. Then you do 180 - 120, which equals 60. That means (2x + 10) equals 60.

2x + 10 = 60, Subtract 10 by both sides

2x = 50, Divide 50 by 2

x = 25

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\(2 {y}^{2} - 9y - 2 + 4(y + 1) = \)

\(2 {y}^{2} - 9y - 2 + 4y + 4 = \)

\(2 {y}^{2} - 9y + 4y - 2 + 4 = \)

Collect like terms

\(2 {y}^{2} - 5y + 2 = \)

\((2y - 1 )(y - 2)\)

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Answer:

2y² - 5y + 2

Step-by-step explanation:

Original equation:

2y² - 9y - 2 + 4(y + 1) =​

Use distributive property

4 · y = 4y

4 · 1 = 4

Plug these values back into the equation:

2y² - 9y - 2 + 4y + 4 = ?

Combine like terms

2y² - 5y - 2 + 4

Combine more like terms

2y² - 5y + 2

That is the most simplified version

Hope this helps :)

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Answer:

8 — 16 — 8n = 0 +> -8-8n=0 => -8(n+1)=0

=> = - 1

Step-by-step explanation:

Avani wrote the linear equation y = 5x + 4. Then, she wrote the equation of the line that is perpendicular to y = 5x+ 4 and that passes through (15,–2). If her new equation is in the form  \(y-\frac{1}{5}x+b\), what is the value of b?

\(\bf y=mx+b\)

The equation of a line that is perpendicular to another line always has the opposite reciprocal slope. In the original equation, the slope is 5. The opposite of 5, which refers to the sign, is -5. The reciprocal of -5 is -1/5. That means the slope of the new line is -1/5.

The perpendicular line:

To find the equation of a line that passes through a specific point, you need to use slope-intercept form.

\(\bf y-y_{1} =m(x-x_{1})\)

y₁ is -2, m is -1/5,  and x₁ is 15.

Substitute the known values into the equation:

\(y-(-2)=-\frac{1}{5}(x-15) \rightarrow y+2= -\frac{1}{5}(x-15)\)

Open the parentheses and distribute:

\(-\frac{1}{5}(x-15) \rightarrow -\frac{1}{5} \cdot x\ + -\frac{1}{5} \cdot -15 \rightarrow -\frac{1}{5}x +3\)

The new equation will be:

\(y+2=-\frac{1}{5}x+3\)

Lastly, you need to move the positive 2 to the other side to keep it in y = mx + b form.

\(y+2-2=-\frac{1}{5}x+3-2 \rightarrow y=-\frac{1}{5}x+1\)

The equation of the perpendicular line is:

\(\bf y=-\frac{1}{5}x+1\)

The value of b is 1.

The value of b is:

1

In-depth explanation:

Perpendicular lines' slopes are inverse reciprocals of one another.

The slope of y = 5x + 4 is 5; the inverse reciprocal of that is -1/5.

Now we use point slope

\(\rm{y-y_1=m(x-x_1)}\)

where m = slope and (x₁,y₁) is a point on the line.

Plug in the data:

\(\rm{y-(-2)=-1/5(x-15)}\)

Simplify each side

\(\rm{y+2=-\dfrac{1}{5}x+3}\)

Subtract 2 from the left

\(\rm{y=-\dfrac{1}{5}x+1}\)

Answer:

16

Step-by-step explanation:

Answer: 16 years old

Step-by-step explanation:

Answer:

10x^2 -623x +2

Step-by-step explanation:

the numbers were put in weird so im not sure if this is the answer you were looking for, but thats what i got

Answer:

every other term is negative, so it would be -64

Step-by-step explanation:

hope it helps!

Hi! So, the missing coordinate of a point p from which a line is passing is approximately P(16, 19.14).

To find the missing coordinate of point P(16, b) on a line that passes through the origin and forms an angle of 50 degrees with the x-axis, we can use the following steps:
Step 1: Understand that the line passing through the origin (0,0) and point P(16, b) creates a right triangle with angle theta (50 degrees) at the origin.

Step 2: Use the tangent function to relate the angle with the coordinates. The tangent of angle theta is equal to the ratio of the opposite side (the vertical side or y-coordinate, b) to the adjacent side (the horizontal side or x-coordinate, 16).
tan(theta) = b / 16

Step 3: Plug in the angle theta as 50 degrees and solve for the missing coordinate b.
tan(50) = b / 16

Step 4: Multiply both sides by 16 to isolate b.
16 * tan(50) = b

Step 5: Calculate the value of b.
16 * tan(50) ≈ 19.14
Therefore, The coordinates of the point p are (16, 19.14).

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