disjointed and overlapping events

We are given the following system of equations:

3 x + 5 y = 8

y = x + 8

So we can use the "substitution method" to solve it, since the second equation is already giving us a possible substitution to make:

Replace y with x + 8 in the other equation.

We proceed as shown below:

3 x + 5 y = 8

3 x + 5 (x + 8) = 8

Use distributivr property to remove the parenthesis:

3 x + 5 x + 40 = 8

8 x + 40 = 8

subtract 40 from both sides to isolate the term in "x"

8 x = 8 - 40

8 x = - 32

divide both sides by 8 to isolate "x"

x = - 32 / 8

x = - 4

We found the requested x value

We are also asked to find y , so we use the value for x in the substitution equation:

y = x + 8

y = -4 + 8 = 4

Then y = 4

The pair that satisfies this system is x = -4 and y = 4 or in pair form: (-4, 4)

7.2

1) Examining the picture, we can assume this is a Right Triangle, and then use the Pythagorean Theorem

a²=b² +c²

14² = 12² +c² The hypotenuse is the larger side a

196=144 +c²

196-144 = c²

52 =c²

√52 =√c²

c= √52

2) Rounding off to the nearest tenth we can write

c= √52 is approximately 7.2

Data:

• Point ,A( 0, 3 )

• Point ,B( 1, -2 )

• Equation in slope-intercept form:

Procedure:

0. Finding the slope ( ,m ,):

2. Finding the intersection with y-axis ( b ) using point A:

Answer:

Summary:

0. We found the slope of the equation ( ,m ,)

1. We found the intersection with the ,y-axis ,( ,b ,)

2. We displayed the values in the correct position of the equation.

Given:

Required:

To find the accumulated value.

Explanation:

Consider

Here

Final Answer:

The accumulated value is $27,695.7

Tangent theorem states that when two tangents intersect out a circle they are said to be equal

Therefore,

Tangent 2x+13 is equal to tangent 4x-8

Hence,

The value of x =10.5

The slope of the function is m = -3.5, which indicates that the temperature decreases by 3.5 degrees for each 1000 feet increase in elevation.

The temperature at Sea level is 87 °F

The slope of a straight line function is the ratio of the rise to the run of the function.

Parts of the question that appear missing includes; The slope and the temperature at Sea level is required.

A point on the table of the graph is that at 4 feet, the temperature is 73 °F

The rate at which the the temperature changes = -3.5 °F  per 1,000 feet

The slope of the equation is therefore;

y - 73 = -3.5·(x - 4)

y = -3.5·x + 14 + 73 = -3.5·x + 87

y = -3.5·x + 87

The equation of the the line of the temperature above Sea level is an equation of a straight line, which is of the form; y = m·x + c

Where;

m = The slope of the function

By comparison, the slope of the equation of the line the function is; m = -3.5

The temperature at Sea level, which is the y-intercept is found at the point where x = 0, which gives;

y = -3.5 × 0 + 87 = 87

The temperature at Sea level is 87 °F

The slope of line of the graph of the function, m = -3.5

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Answer:

xy - 3x = 8

when x = 4 and y = 5

Explanation:

Given the expression

xy - 3x

When x = 4 and y = 5, the equation becomes

(4)(5) - 3(4)

= 20 - 12

= 8

Solution:

Given:

The domain of the function is;

Therefore, OPTION A is correct.

Answer:

The equation that represents the perpendicular line is;

Explanation:

We want to find the equation of a line perpendicular to the line;

Recall that for two lines to be perpendicular to each other, their slope must be a negative reciprocal of one another.

so;

For the given equation, the slope of the given line is;

To get the slope of the perpendicular line, let us substitute m1 to the equation above;

So, the equation of the perpendicular line would be of the form;

The equation of the perpendicular line will be of the form;

Where c is a constant;

From the options, the only equation that is similar to the derived equation is;

Therefore, the equation of the perpendicular line is;

We have 4 rational numbers which we are asked to express in decimal numbers.

To do this, we divide the numerator of each rational number by its denominator, when we do that, we get the following results:

If two fractions are in proportion, their inverse ratio are also in proportion.

Proportion:

Proportion means an equation in which two ratios are set equal to each other.

Given,

a/b = c/d is equivalent to b/a = d/c. in other words, if two fractions are in proportion, their _____ are also in proportion.

Here we need to fill the blank with the correct answer.

According to  Invertendo Property,

For the four numbers a, b, c, d,

Consider if a : b = c : d, then b : a = d : c; which means

if two ratios are equal, then their inverse ratios are also equal.

It can be written as,

If a : b :: c : d then b : a :: d : c.

Then it can be written as,

=> a : b :: c : d

⟹ a/b= c/d

When take the inverse, then we get,

⟹ b/a= d/c

Which implies the following,

⟹ b : a :: d : c

Therefore, the answer is inverse ratio.

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Answer:

An exponential function is a mathematical function, which is used in many real-world situations. It is mainly used to find the exponential decay or exponential growth or to compute investments, model populations, and so on. In this article, you will learn about exponential function formulas, rules, properties, graphs, derivatives, exponential series, and examples.

An example of an exponential formula is given below as

The following figure represents the graph of exponents of x. It can be seen that as the exponent increases, the curves get steeper and the rate of growth increases respectively. Thus, for x > 1, the value of y = fn(x) increases for increasing values of (n).

Are there restrictions on the domain why or why not?

For any exponential function, f(x) = ab^x, the domain is the set of all real numbers. For any exponential function, f(x) = ab^x, the range is the set of real numbers above or below the horizontal asymptote, y = d, but does not include d, the value of the asymptote.

Hence,

The domain of exponential functions is equal to all real numbers since we have no restrictions with the values that x can take.

Are exponential and logarithmic function inverse. why or why not?

Logarithmic functions are the inverses of exponential functions. The inverse of the exponential function y = a^x is x = a^y. The logarithmic function y = logx base a is defined to be equivalent to the exponential equation x = a^y

Hence,

Exponential functions and logarithmic functions are inverses of each other

By dilation with a scale factor of 1 / 3 centered at the origin, the image of the resulting point is (- 3, - 4).

In this problem we find the coordinates of a point set on Cartesian plane, whose image is the result of using a dilation centered at the origin, whose definition is introduced below:

P'(x, y) = O(x, y) + k · [P(x, y) - O(x, y)]

Where:

If we know that O(x, y) = (0, 0), k = 1 / 3 and P(x, y) = (- 9, - 12), then the image of the original point is:

P'(x, y) = (0, 0) + (1 / 3) · [(- 9, - 12) - (0, 0)]

P'(x, y) = (- 3, - 4)

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To find the area of a circle given the radius;

Given

Solution

Apply exponent rule

We have

Using the Pythagorean theorem, the length of the side x is √147.

So, the formula of the Pythagorean theorem:

Now, substitute the values and calculate as follows:

Therefore, using the Pythagorean theorem, the length of the side x is √147.

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In order to solve this equation for y, we just need to isolate the variable y in the equation.

So, we have that:

So we have that y = (T - 2x + z) / 3

Quadrant IV.

1) Let's Draw this to give us a better idea.

In a 270º CCW Rotation, the rule is every coordinate to be translated

(x.y) ---(y,-x)

2) Let's give to our quadrilateral

A(-2,3) ---- A'(3,2)

B(-4, 3) -----B'(3,4)

C(-6, 4) -----C' (4,6)

D( -8, 4) ---- D' (4, 8)

And so forth

So Quadrant IV is the answer.

To find the slope and the intercept of the line

y = -4x + 2

y = mx + b

so in this case the m = -4, because is the coefficient on x rigth over there

and b is going to be the constant term

b = 2

1) Evaluating

-3x -8= 4 Adding 8 to both sides

-3x -8 +8=4+8

-3x = 12 Dividing both sides by 3

x=-4

2) Examining the options then

C Add 8 to both sides then divide both sides by 3

When two numbers are exactly the same, we say that they're equal. Is denoted by the sign '='

Given:

A math teacher said that 18 out of 25 students passed the test.

So,

Total number of students = 25 student

Number of students who passed the test = 18

Number of students who did not pass the test = 25 - 18 = 7

So, the percent of the students who did NOT pass the test =

So, the answer will be 28%

ANSWER

Yes, it is.

EXPLANATION

A finite set is a set that contains a finite number of elements. That is, the number of elements in a finite set are countable.

The set given is:

A = {9000, 5, 8, 119}

There are 4 elements in this set and hence, it is countable.

According to the definition of a finite set, this set is a finite set.

Celeste, this is the solution to the exercise:

Let's recall that √-1 = i, therefore:

The first term of the sum is √-25 = √25 * -1 = 5i

The second term remains the same. + 10

Thus, the correct answer is D. 5i + 10

ANSWER

EXPLANATION

We have that the line EG = 71.

We are given that

EF = 8x - 17

and

FG = 5x - 3

We see from the diagram that:

EF + FG

The account balance this month is $4020

Let the account balance this month = x

From the question, we have

The account balance was $2,010 last month.

∴x* 50%= $2,010

⇒x* 50/100= $2,010

⇒x* 1/2= $2,010

⇒x = $4020

Multiplication:

Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.

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To see the equation we know that the general equation of a line is:

Where m is the slope. So you know that the slope is 1.2, then you have an equation like this:

Since b is just a number we can say that this is also equal to:

We'll write it this way so it's similar to the options.

Then you know that the line pases through point (5,0). To find the value of constant c we replace the value of x and y from this point (x = 5 and y=0):

And clear c from this expression

So the answer is:

The cost of sending mail is given as $0.51 for the first ounce and then every ounce after that costs $0.20.

For each letter, the cost would be expressed as;

Therefore, Stephanie's letter weighs 5 ounces.

The correct answer is option D

Given

Solution

Formula

where

Substitute the parameters into the Confident Interval formula

Then we calculate the Addition and subtraction

First the Addition

Then now for subtraction

The final answer