In 1995, an earthquake in Mexico registered 8.0 on the Richter scale. In 2001 , an earthquake of magnitude 6.8 shook Washington state. How many times more intense was the 1995 earthquake than the 2001 earthquake?

√19 + √3 is greater than √5 +√13.

We first relate the two numbers √19 + √3 and √5 +√13 through an inequality and check if it is true.

First suppose that √19 + √3 > √5 +√13

On squaring both sides and using the identity [tex](a+b)^2=a^2+b^2+2ab[/tex],

⇒ [tex](\sqrt{19}+\sqrt{3})^2 > (\sqrt{5}+\sqrt{13})^2\\22+2\sqrt{57} > 18+2\sqrt{65} \\[/tex]

Dividing by 2 on both sides,

⇒ [tex]11+\sqrt{57} > 9+\sqrt{65}[/tex]

Subtracting 9 from both sides,

⇒ [tex]2+\sqrt{57} > \sqrt{65}[/tex]

Squaring again, we get,

⇒ [tex]61 +4\sqrt{57} > 65[/tex]

Subtract 61 on both sides,

⇒ [tex]4\sqrt{57} > 4[/tex]

Dividing by 4 on both sides,

⇒ [tex]\sqrt{57} > 1[/tex]

Finally squaring once more,

⇒ 57 > 1, which is true.

So our assumption that √19 + √3 > √5 +√13 is right.

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The number of books that Mrs. Johnson bought is 8 books.

How many magazines did she buy:

Let x represent the number of books she bought

The first step is to formulate an equation

12x + 16 = 112 dollars

The second step is to transpose

12x=112-16  

12x = 96

The third step is to divide both sides by 12

x=96/12  

x = 8

In conclusion, the number of books that Mrs. Johnson bought is eight books.

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Answer:

y = 12x

Step-by-step explanation:

For an equation to be parallel the slopes must be the same.  The slope from the equation is 12.

y = mx + b  is the slope-intercept form of a line'

y = 12x + 3.  The m is the slope and that is 12 ion this equation.

We will use the slope (12), the x (0) and the y (0) to write the new equation.  We need to find the y intercept.  We can see from the ordered pair given that the y - intercept would be zero, but here is another way to check.

y = mx + b

0 = 12(0) + b

0 = 0 + b

0 = b

y = 12x + 0

or

y = 12x

Answer:

if i am looking at this correct then number 4 is 6 faces number 5 is 5 and number 6 is 5

The value of the function f(-8) is -512

A function is defined as an expression, rule or law that shows the relationship between two variables;

Given the function:

f(x)= x × x²

To determine the function f(-8), we substitute the value of x  as -8 in the function

With this, we have;

f(-8) = (-8) × (-8)²

expand the bracket

f(-8) = -8 × 64

Multiply through

f(-8) = - 512

The value of the function is -512

Thus, the value of the function f(-8) is -512

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The equation of the line in fully simplified slope-intercept form is y = -x + 3

From the question, we are to write the equation of the line in fully simplified slope-intercept form

The slope-intercept form of the equation of a straight line is given as

y = mx + b

Where m is the slope of the line

and b is the y-intercept

From the graph,

The y-intercept is 3

∴ b = 3

Now, we will determine the slope, m, of the line

Given any two points (x₁, y₁) and (x₂, y₂) on a line, the slope, m, of the line is

m = (y₂ - y₁)/(x₂ - x₁)

Picking the points, (0, 3) and (2, 1)

m = (1 - 3)/(2 - 0)

m = -2/2

m = -1

Putting in the slope, m, and the y-intercept, b into the equation of a line

y = mx + b

We get

y = -1(x) + 3

Simplify

y = -x + 3

Hence, the equation of the line in fully simplified slope-intercept form is y = -x + 3

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the slope of that equation is -3/5

Answer:

53°

Step-by-step explanation:

Corresponding angles are congruent

Answer:

12-6 is the right answer

Step-by-step explanation:

Multiple 3 to 4 which is 12 and then then multiple it with two which is 6 so the answer is 12-6

The range of possible values of x from the given equation is 37.

The given equation is (x+20)=57.

The domain and range of a function are the components of a function. The domain is the set of all the input values of a function and the range is the possible output given by the function. Domain→ Function →Range.

The domain and range are defined for a relationship and they are the sets of all the x-coordinates and all the y-coordinates of ordered pairs respectively.

Now,

Domain = the set of all x-coordinates

Range = the set of all y-coordinates

Here, x+20=57

⇒x=37

Verification:

Put x=37 in x+20=57 and verify.

37+20=57

⇒57=57

LHS=RHS

Therefore, the range of possible values of x from the given equation is 37.

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From the graph of a function over the interval [-4,4]. the following are found for each function

The domain of a function refers to the input variables, often times the domain comprises of the x axis. for the given graph the domain is -4 ≤ x ≤ 4.

This would be through the points in the function. We are given  [-4,4]

-4 is the negative side while 4 is the positive. We have to write this out as

-4 ≤ x ≤ 4.

The positive part part of the function is at 4. This is because we can assume a +4 sign.

The negative part is the point -4.

Hence we can say that the domain is -4 ≤ x ≤ 4 with the positive and negative at 4 and -4 respectively

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The growth factor for the annual rate of change +100% is 2.

A quantity must vary by a specific percentage each time period in order for growth or decay to be exponential.

With the function displayed to the right, you may represent exponential growth or decay.

A(x) = a( 1 + r)ˣ

Where A is the amount after x time periods, a is the initial amount, x is the number of time periods, and r is the rate of change.

Now, we have the annual rate of change as:

r = + 100% = + 1

From the function A(x) = a( 1 + r)ˣ , the corresponding factor is 1 + r.

So, let B = 1 + r

B = 1 + r

B = 1 + (+1)

B = 2

Now, the value of B is greater than 1 therefore, the corresponding growth factor is 2.

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The solutions to the equation (3x - 5)²= 19 are: - [tex]\frac{\sqrt{19} + 5}{3}[/tex] and [tex]\frac{\sqrt{19} + 5}{3}[/tex] .

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.

In this question we have been given an equation that is (3x - 5)²= 19

Now taking square root both sides

(3x - 5)² = 19

3x - 5 = ± [tex]\sqrt{19}[/tex]

Add 5 to both sides to make equation simpler

3x = ± [tex]\sqrt{19}[/tex]+ 5

Divide both sides by 3

x = ±[tex]\frac{\sqrt{19} + 5}{3}[/tex]

Now separating the solutions we get

x = [tex]\frac{\sqrt{19} + 5}{3}[/tex] .

x = - [tex]\frac{\sqrt{19} + 5}{3}[/tex] .

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The components of -5RS are {-20; 65}.

The components of a vector in a two-dimensional coordinate system are usually thought of as the x and y components. This can be expressed as V = (vx, vy). where V is a vector. These are part of the vectors generated along the axis.

Suppose an angle θ is formed between the vector V and the x component of the vector. A vector V and its x component (vx) form a right triangle if you draw a line parallel to the y component (vy).

Due to the trigonometric relationship

cos θ = adjacent side/hypotenuse = vx/V

sin θ = opposite side/hypotenuse = vy/V

where V is the magnitude of vector V.

So, the Component of -5RS is Given by:

-5RS = -5* {Sx - Rx; Sy - Ry} = {2 - (-2); -8 - 5} = -5*{4; -13}

-5RS = {-20; 65}

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Considering the definition of an inequality, all possible values for the length of the sides of the square picture are greater than 3 inches but less than 8.75 inches.

An inequality is the existing inequality between two algebraic expressions, connected through the signs:

An inequality contains one or more unknown values ​​called unknowns, in addition to certain known data.

Solving an inequality consists of finding all the values ​​of the unknown for which the inequality relation holds.

The perimeter of a two-dimensional figure is the distance around the figure. That is, the perimeter of a flat geometric figure is called the length of its contour.

The perimeter is the measurement obtained as a result of the sum of the sides of a flat geometric figure.

A square is a flat geometric figure that has four equal sides, so the expression to calculate the perimeter of a square is:

Perimeter= 4× length of the sides

In this case, you know that the perimeter of a square picture frame is to be at most 35 inches but no less than 12 inches.

Being "S" the length of the sides of the square picture, the inequality that expresses the previous relationship is

12 inches< 4×S ≤35 inches

Solving:

12 inches ÷4< S ≤35 inches ÷4

3 inches <S≤ 8.75 inches

Finally, all possible values for the length of the sides of the square picture are greater than 3 inches but less than 8.75 inches.

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By  -236 dB approximately the noise is reduced on imparting sound barrier.

Given that, the foreman of a construction team puts up a sound barrier that reduces the intensity of the noise by 50%. Let the intensity of the sound is I and it is reduced 50% then, new intensity of sound will be

new intensity after reduction = I-50% of I = I/2

Now, the Loudness is calculated by using the formula,

L = 10 log I/I₀

now, I = I/2 and I₀ = 10⁻¹² W/m²

So, we have to find out by how many decibels(dB) the noise is reduced after putting a sound barrier.

This will simply be calculated by subtracting the two noise before and after the sound barrier indulgence. Let's proceed to solve accordingly.

L = 10 log I/I₀ - 10 log I/2I₀

= 10(log I/I₀ - log I/2I₀)

By using the logarithmic property, log(a/b) = log a - log b

= 10(log I-log I₀-log I-log2I₀)

= 10(-log I₀ - log2I₀)

= -10(log I₀ + log2I₀)

Now, we know that, I₀ = 10⁻¹² W/m²

Put the value of I₀ and solve accordingly, we get

L = -236 dB approximately

Therefore, L = -236 dB approximately is the required answer.

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The linear function slope, f(2)=-4, and f(3)=2 the equation for f(x) is y = 6x +6

This is the same as finding the line that goes through the two points (3,2) and (2,-4)

It has slope[tex]\frac{-6}{-1}[/tex] = 6 = [tex]\frac{(-4-2)}{(2-3)}[/tex] = m=6.  slope = rise/run.  or change in y coordinates/change in x coordinates

The y-intercept is given by(2,-4) as 6, b= 6. so plug that into the slope-intercept equation

y= MX + b

y = 6x +6

It's just a coincidence they both happened to = 6. m=b=6

In Mathematics, a slope of a line is the change in y coordinate with respect to the change in x coordinate.  the web change in the y-coordinate is represented by Δy and the net change in the x-coordinate is represented by Δx. Where “m”  is the slope of a line. So, tan θ to be the slope of a line.

Pick two points on the road and determine their coordinates. Determine the difference in y-coordinates of those two points (rise). Determine the difference in x-coordinates for these two points (run). Divide the difference in y-coordinates by the difference in x-coordinates (rise/run or slope).

Whenever the equation of a line is written within the form y = MX + b,  it's called the slope-intercept form of the equation. The m  is the slope of the line. And b  is that the b in the point that is the y-intercept (0, b).  for instance, for the equation y = 3x – 7, the slope is 3,  and therefore the y-intercept is (0, −7).

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The value of function  f(x) = x+4 when x=3 is 7.

By considering given function

f(x) = x+4

f(3)= 3+4

f(3)=7

A mathematical expression, rule, or law that establishes the relationship between an independent variable and a dependent variable (the dependent variable). In mathematics and the sciences, functions are fundamental for constructing physical relationships.

Four broad categories can be used to classify different types of functions. One to one function, many to one function, onto function, one to one and into function—all based on the element.

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The value of function f(x) = x+4 by evaluating it when x = 3 will be 7.

A function is defined as anything from a set X to a set Y assigns to each element of X exactly one element of Y.

We are given a function:

f(x) = x + 4

We need to evaluate for x = 3.

We will do this by putting x = 3 in the function given to us.

So, we get that:

f ( 3 ) = 3 + 4

Adding the terms, we get that:

f ( 3 ) = 7

Therefore, value of function f(x) = x+4 by evaluating it when x = 3 will be 7.

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The slope is positive for the points (12,3),(-2,-5),(1,15)

The slope of a line is that the quantitative relation of quantity|the quantity|the number} that y will increaseas x will increase some amount.

Slope tells you ways steep a line is, or what quantity y will increaseas x will increase. The slope is constant (the same) anyplace on the road.

One way to think about the slope of a line is by imagining a roof or a side. each roofs and ski slopes may be terribly steep or quite flat. In fact, each ski slopes and roofs, like lines, may be utterly flat (horizontal). you'd ne'er realize a side or a roof that was utterly vertical, however a line may be.

formula of slope for 2 point line =y2-y1/x2-x1

for point (12,3). m=3+1/12 =4/12 =1/3 which is correct.

for point (-2,-5)m=-4/-2=2 which is correct

for point (-3,1) m=2/-3 which is not correct

for point (1,15)m=16/1 which is correct

for point (5,-2)m=-1/5 which is not correct.

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Answer:

Step-by-step explanation:

A=(1/2) x b xh

h=6

A = (1/2) x b x 6

24=3b

b=24/3

b=8

By basic algebra, we can say that: the satellite to run for about 130 days if it requires 15W of power.

Given:

To find: t when P = 15.

Finding:

On substituting the given values in the given formula, by basic algebra, we get:

15 = 50 [tex]e^{\frac{-t}{250}}[/tex]

=> [tex]\frac{15}{50}=\frac{3}{10}[/tex] = [tex]e^{\frac{-t}{250}}[/tex]

=> log [tex]\frac{3}{10}[/tex] = [tex]\frac{-t}{250}[/tex]

=> - 0.522 = [tex]\frac{-t}{250}[/tex]

=> 130.5 = t

Hence, the satellite to run for about 130 days if it requires 15W of power, as solved by basic algebra.

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If (x+1) is a factor p(x)= x² + x + 2 then the value of x is -1.

An expression of one or more algebraic terms each of which consists of a constant multiplied by one or more variables raised to a nonnegative integral power

We have,

(x + 1) is a factor of p(x) = x² + x + 2

We need to find x.

Since (x + 1) is a factor of p(x) it should satisfy p(x).

x + 1 = 0

x = -1

Thus if (x+1) is a factor p(x)= x² + x + 2 then the value of x is -1.

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$600.

Given that

Profit per kg =  $4.

we find out the overall profit for 150 kg of rice.

Profit is a term that often describes the financial gain a business receives when revenue surpasses costs and expenses.

Total Revenue - Total Expenses = Profit.

for 1 kg profit is $4

then for 150 kg profit is =  (profit of 1 kg × total rice)

                                     = 4×150$

                                      = $600

Hence the overall profit on 150 kg of rice is $600 .

Profit and Loss formula is used in mathematics to determine the price of a commodity in the market and understand how profitable a business is. Every product has a cost price and a selling price. Based on the values of these prices, we can calculate the profit gained or the loss incurred for a particular product.

Profit(P) - The amount gained by selling a product with more than its cost price.

Profit or Gain = Selling price – Cost Price

Profit percentage (P%) = (Profit /Cost Price) x 100

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The value of x for the equation log₄64=x is 3.

Due of their connection to exponential functions, logarithmic functions are crucial. Exponential equations and the characteristics of exponential functions may both be investigated using logarithms. Additionally, they will be of great service in calculus, where they will be used to determine the slope of specific functions and the region enclosed by particular curves. They also have useful uses in economics.

Given,

log₄64=x

It can be expressed as -

64 = 4ˣ

4³ = 4ˣ

As base is same,

x = 3

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24units² is the area of the given triangle.

The formula of the area of a triangle using coordinates:

Now, substitute the values in the formula as follows:

Therefore, the area of the given triangle is 24units².

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Answer: anwser is negative 6

Step-by-step explanation:

i hope you get i had it too and got it right if its not they are giving diffrent anwser then