Find the distance between the point (6.3) and the line 3x + 5y +1=0.

Answer:

None of the above.

No assumptions can be made because we do not know if the function is continuous or differentiable on those intervals.

Answer:

70

Step-by-step explanation:

Because 2100 divided by 30 is 70 I  hope this is the answer :)

Answer:

x = -4, 7

Step-by-step explanation:

We are given the graph of the function f(x), and we want to find the values that make the statement f(x) = 0.

f(x) = 0 means that there are certain values that make the value of f(x) (which can be considered as y) equal to 0.

We can look to the graph to help us - we should look at where y is equal to 0, which is the x-axis.

On the x-axis, we can see that the function passes through both -4 and 7 (the graph goes up by 1) on that line.

This means that when either -4 or 7 are substituted into the function (i.e. when they are equal to x), they will make the function equal 0.

So,  it means that x = -4, 7.

Answer:

The temperature is -5F

Step-by-step explanation:

You start at -3 then add 5 to get 2 degrees Fahrenheit then you subtract 7 to get -5 degrees Fahrenheit

Answer:

4 and 1/2

Step-by-step explanation:

7x + 2 +x = 8x + 2

8x + 2 = 4(2x + 1/2)

Answer:

Median: 5

Mean: 6

Step-by-step explanation:

4,4,4,5,7,9,9

(4x3)+5+7+(9x2)

12+5+7+18

17+25=42

42÷7=6

Answer:The volume of the soup pot is of 226.19 cubic inches.

Step-by-step explanation:

Format of a soup pot:

A soup pot has a cylindrical format.

Cylinder volume:

The volume of a cylinder, with radius r and height g is given by:

The soup pot is 8 inches tall with a radius of 3 inches.

This means that

What is the volume of the soup pot?

The volume of the soup pot is of 226.19 cubic inches.

The weight on the inflation gap has increased from 0.5 to 0.75. The real interest rate is 16.86% and Nominal interest rate is 20%

a. In the base scenario, the real interest rate will be 20%, and the nominal interest rate will be 20%.

b. In scenario B, inflation rate will be higher (4%) compared to the base scenario (3.14%).

Output gap is 0% in both the scenarios, however, in the base scenario inflation gap is 0% (3.14 - 3.14) and in scenario B, inflation gap is 0.86% (4 - 3.14).

Now, let's calculate the real interest rate.

Real interest rate in base scenario = 20% - 3.14%

= 16.86%.

Real interest rate in scenario B = 20% - 3.14% + 1.5 + 0.5 (4-3.14) + 0.5 (0-0/0)

= 19.22%.

The real interest rate has moved in the direction to move inflation rate towards its target.

c. In scenario C, the output gap will be 20% compared to 0% in the base scenario.

Inflation gap is 0% in both the scenarios

Inflation rate is 3.14% and in scenario C, inflation rate is 2%.

Let's calculate the real interest rate. Real interest rate in the base scenario = 20% - 3.14%

= 16.86%.

Real interest rate in scenario C = 20% - 2% + 1.5 + 0.5 (3.14 - 3.14) + 0.5 (20-0/20)

= 20.15%.

Real interest rate in scenario C = 20% - 2% + 1.5 + 0.75 (3.14-3.14) + 0.25 (20-0/20) = 18.78%.

The new policy rule has changed the weight of the output gap in the Taylor Rule from 0.5 to 0.25.

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ANSWER :

C. $210

EXPLANATION :

The shopkeeper marks his goods at 40% above the cost.

If the jacket costs $200, he will mark it as :

Then he offers a 25% discount.

That will be :

To determine the distance between two points on the coordinate system you can use the following formula, which is derived from the Pythagorean theorem:

Where

(x₁,y₁) are the coordinates of one of the endpoints of the line

(x₂,y₂) are the coordinates of the second endpoint of the line

Using C(8,-3) as (x₂,y₂) and D(-9,-6) as (x₁,y₁), you can calculate the length of CD as follows:

The length of CD rounded to the nearest tenth is 17.3 units

The function graphed on the axis above should be expressed as a piecewise function as follows;

f(x) = x + 1       {x < -5}

     = 5x - 10   {x > 1}

In order to determine the piecewise function, we would determine an equation that represent each of line shown on the graph. Therefore, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (-7 + 4)/(-8 + 5)

Slope (m) = -3/-3

Slope (m) = 1.

At data point (-5, -4) and a slope of 1, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y + 4 = 1(x + 5)  

y = x + 1

1, -5 2 0

For the second line, we have:

Slope (m) = (0 + 5)/(2 - 1)

Slope (m) = 5/1

Slope (m) = 5.

At data point (2, 0) and a slope of 5, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 0 = 5(x - 2)  

y = 5x - 10

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Answer:

2 sides 16 cm , 2 sides 12 cm

Step-by-step explanation:

the opposite sides of a parallelogram are congruent.

given ratio of sides = 4 : 3 = 4x : 3x ( x is a multiplier )

perimeter is the sum of the 4 sides

given perimeter = 56 cm , then

2(4x) + 2(3x) = 56

8x + 6x = 56

14x = 56 ( divide both sides by 14 )

x = 4

then

4x = 4 × 4 = 16

3x = 3 × 4 = 12

2 congruent sides of length 16 cm and 2 congruent sides of 12 cm

Answer:

slope = 15

Step-by-step explanation:

calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (1, 6) and (x₂, y₂ ) = (2, 21) ← 2 ordered pairs from the table

m = \(\frac{21-6}{2-1}\) = \(\frac{15}{1}\) = 15

the linear relationship is then of the form

y = mx + c ( m is the slope and c the y- intercept )

from the table the point (0, - 9 ) crosses the y- axis at - 9 ⇒ c = - 9

y = 15x - 9 ← linear relationship

Answer:

Step-by-step explanation:

Figure J is rotated 90° clockwise and then translated by 3 units toward the right.

A point, line, or mathematical figure can be converted in one of four ways, and each has an effect on the object's structure and/or position.

Rotation does not change the shape and size of the geometry. But changes the orientation of the geometry.

The translation does not change the shape and size of the geometry. But changes the location.

Figure J is rotated 90° clockwise and then translated by 3 units toward the right.

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Answer:

28.86

Step-by-step explanation:

It's the Pythagorean theorem just relearn it and you should be fine

Step-by-step explanation:

5.|12 - r| > 15

|12 - r| > 15/5

|12 - r| > 3

12 - r < -3 or 12 - r > 3

-r < -3 - 12 or -r > 3 - 12

-r < -15 or -r > -9

r > 15 or r < 9

Answer:

0.2159 = 21.59% probability this student’s score will be at least 1500.

Step-by-step explanation:

To solve this question, we need to understand the normal distribution and conditional probability.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Conditional Probability

We use the conditional probability formula to solve this question. It is

\(P(B|A) = \frac{P(A \cap B)}{P(A)}\)

In which

P(B|A) is the probability of event B happening, given that A happened.

\(P(A \cap B)\) is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Recognized student(scored more than 1350)

Event B: Score of at least 1500.

SAT scores (out of 1600) are distributed normally with a mean of 1100 and a standard deviation of 200

This means that \(\mu = 1100, \sigma = 200\)

Probability of being recognized.

1 subtracted by the pvalue of Z when X = 1350. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{1350 - 1100}{200}\)

\(Z = 1.25\)

\(Z = 1.25\) has a pvalue of 0.8944.

1 - 0.8944 = 0.1056

So \(P(A) = 0.1056\)

Probabibility of being recognized and scoring at least 1500.

Intersection between more than 1350 and more than 1500 is more than 1500. So this probability is 1 subtracted by the pvalue of Z when X = 1500.

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{1500 - 1100}{200}\)

\(Z = 2\)

\(Z = 2\) has a pvalue of 0.9772

1 - 0.9772 = 0.0228

So, \(P(A \cap B) = 0.0228\)

What is the probability this student’s score will be at least 1500?

\(P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.0228}{0.1056} = 0.2159\)

0.2159 = 21.59% probability this student’s score will be at least 1500.

Answer: 2x^3 - x^2 - 29x + 28

The value of x is -15

Functions are simply defined as expressions or rules showing the relationship between two variables.

These variables are listed as;

From the information given, we have that;

g(x) =x  -1, if g(x) = -16

Now, we have to equate the two functions, we get;

x - 1 = -16

collect the like terms, we get;

x =-16 + 1

add the values, we have;

x = -15

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The complete question:

Given g(x) =x  -1, if g(x) = -16, find x.

We can see here that the Pythagorean theorem can help one determine whether the roped off area is in the shape of a right triangle because the converse of Pythagorean Theorem is actually used to prove that a triangle is a right triangle.

Let's understand the definition and meaning of  Pythagorean Theorem.  Pythagorean Theorem is actually seen as the fundamental concept that is used to describe the relationship that exists  between all the sides of a right-angled triangle.

The theorem actually states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Mathematically, it can be expressed as a² + b² = c², where "a" and "b" are the lengths of the two shorter sides, and "c" is the length of the hypotenuse.

When we don't know that a triangle is a right-angle triangle, we use the converse to prove it.

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In the function, f(x) = a(b)ˣ the value of a and b is

The function defined by f(x) = a(b)ˣ is a exponential function

Where

a is the starting function

b is the base function

The starting function from (0,24)

24 = a(b)ˣ

a = 24

using (1, 18), we solve for the base

18 = 24(b)

b = 0.75

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Answer:

Step-by-step explanation:

Find the coordinates:

Correct choice is A

Enseñanza Básica is the term used to describe the first level of education in the Chilean education system, which includes the first to eighth grades. A teacher of Enseñanza Básica asked his students to choose three-digit mixed numbers that can be formed.

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The difference between the greatest and the least mixed numbers is 9.87 - 6.0789 ≈ 3.7911.

The three digits different from {1, 2, 3, 4, 5} can be chosen from {0, 6, 7, 8, 9}.

The greatest mixed number is formed by placing the largest digit as the whole number and the remaining two digits as the fraction in descending order, i.e., 9 87/100 or 9.87.

The smallest mixed number is formed by placing the smallest non-zero digit as the whole number and the remaining two digits as the fraction in ascending order, i.e., 6 07/90 or 6.0789.

The difference between the greatest and the least mixed numbers is 9.87 - 6.0789 ≈ 3.7911.

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The Question in English

A Basic Education teacher tells his students to choose three digits

different from the set {1, 2, 3, 4, 5} and form mixed numbers by placing the digits

in the locker It also reminds them that the fractional part has to be

less than 1, for example

2

3

5

. What is the difference between the greatest and the least of the

mixed numbers that can be formed?

On solving the provided question we can say that The following is the data table of the function.

The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.

here,

the provided functions that can be formed are

           x            -infinity < x < -10

f(x) =    2x + 10          -10 < x < 10

           4X - 10       10 < x < infinty

The following is the data table of the function.

x              y

-20          -20

-15          -15

-10          -10

-5             0

0              10

5               20

10              30

15              50

20              70

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An example of the piecewise defined function is: \(f(x)= \begin{cases}x & -\infty < x \leq-10 \\ 2 x+10 & -10 < x \leq 10 \\ 4 x-10 & 10 < x < \infty\end{cases}\)

The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output.

A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or range.

Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.

The following is the data table of the function.

x               y

-20          -20

-15           -15

-10           -10

-5              0

0              10

5              20

10              30

15              50

20             70

The provided functions that can be formed are

\(f(x)= \begin{cases}x & -\infty < x \leq-10 \\ 2 x+10 & -10 < x \leq 10 \\ 4 x-10 & 10 < x < \infty\end{cases}\)

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