Find the value of the variables in each figure. Explain your reasoning.

The length of the line segment from negative 5 comma 5 to 3 comma negative 1 is 10 Units.

How to find the length of a line segment?

A line segment is defined as a line bounded by two  points on a line.

The line segment from negative 5 comma 5 to 3 comma negative 1

is found by using the formula

square root of (x2-x1)² +(y2-y1)²

[tex]\sqrt{(3+5)^{2} +(-1-5)^{2} }^[/tex]

[tex]\sqrt{8^{2}+6^{2} }[/tex]

[tex]\sqrt{100}[/tex]

=10 units

therefore the length of the line segment is 10 units

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The chief of police use sample statistical study  to estimate the number of people above the age of 18 who are using illegal substances in town.

In the given question,

The chief of police in statville wanted to estimate the number of people above the age of 18 who are using illegal substances in town.

He obtained 200 random names of statville residents from a computer database and sent his officers to survey these people about substance abuse.

Once the results came in, he calculated the margin of error and got an estimate of the percentage of residents who use illegal substances.

We have to explain what type of statistical study the chief of police use.

In the given question chief of police wants to check number of people who using illegal substances in town above the age of 18. So he take  200 random names from a computer database. That means he take the sample of 200 random people.

As we know that a sample is a selection from a larger population of individuals, things, or things that are used for measurement. To enable us to extrapolate the research sample's findings to the entire population, the sample must be representative of the population.

So we can say that the chief of police use sample statistical study  to estimate the number of people above the age of 18 who are using illegal substances in town.

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Answer: Sample Study

No because there’s a great risk of obtaining biased answers.

The slope of the line from the given points will be equal to 3/2 in the simplest form.

It is possible to determine a line's direction and steepness by looking at its slope. Finding the slope between lines inside a coordinate plane can aid in anticipating if the lines are perpendicular, parallel, or none at all without physically using a compass.

As per the given points in the question,

(1, -9) and (4, -7).

x1 = 1 and x2 = 4

y1 = -9 and y2= -7

Slope  = (x2- x1)/(y2- y1)

= (4 - 1)/(-7 - (-9))

Slope = 3/2

Therefore, the slope of the line will be 3/2.

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The slope and the intercepts of the graph are determined.

Given:

the equation is :

2x+3y=6

we first find the slope of the equation:

m = -a/b

m = -2/3

now solve the intercepts:

to find x intercept, substitute in 0 for y and solve for x.

⇒ 2x+3y=6

⇒ 2x+3(0)=6

⇒ 2x+0=6

⇒ 2x=6

⇒ x=6/2

⇒ x=3

hence we get (3,0)

now, to find y intercept, substitute in 0 for x and solve for y.

⇒ 2x+3y=6

⇒ 2(0)+3y=6

⇒ 0+3y=6

⇒ 3y=6

⇒ y=6/3

⇒ y=2

hence we get (0,2) as the intercepts.

Therefore we plot the required graph.

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The required values are x=0 and x=2/3.

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

f(x) = -3x² + 2x - 1

Substitute f(x) = -1

-1 = -3x² + 2x - 1

-3x² + 2x - 1+1=0

-3x² + 2x = 0

x( -3x+2)=0

=> x=0,

 -3x+2 = 0

-3x=-2

x=2/3

The required values are x=0 and x=2/3.

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angle bcd is 140. see explanation in image

The number that should be on the bottom left stamp is 1. It was gotten by dividing 2 by 2.

From the first picture, we have 82 and the number below it is 4. This was gotten as:

= 8 ÷ 2

= 4

The second picture has 93 and the number below it is 3. This was calculated as:

= 9 ÷ 3

= 3

The third picture has 61 and the number below it is 6. This was calculated as:

= 6 ÷ 1

= 6

The fourth picture will be:

= 2 ÷ 2

= 1

Therefore the value is 1.

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The approximate percentage of sales tax is 1%

A gymnastics mat priced at $53.

A cost of mat after adding sales tax = $53.53

So, the tax amount would be,

53.53 - 53 = 0.53

We need to find the sales tax percentage.

Let x be the percentage of sales tax.

x = (0.53)/(53.53)  * 100

x = 0.0099 * 100

x = 0.99%

x ≈ 1%

Therefore, the approximate percentage of sales tax is 1%

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Length of the line AB is 1.414 units and midpoint of AB is (3.5,5.5).

Given in the graph,

A(4,6)  and B(3,5)

Distance formula = [tex]\sqrt{(x1-x2)^{2} +(y1-y2)^{2} }[/tex]

                      AB =  [tex]\sqrt{(4-3)^{2} +(6-5)^{2} }[/tex]

                            = [tex]\sqrt{1^{2} +1^{2} }[/tex]

                            = [tex]\sqrt{2}[/tex]

                            = 1.414 units

Midpoint = [tex](\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]

Let midpoint of AB be C(x,y)

C = (x,y) = [tex](\frac{4+3}{2},\frac{6+5}{2})[/tex]

             = [tex](\frac{7}{2},\frac{11}{2})[/tex]

             = (3.5,5.5)

Hence, length is 1.414 units and midpoint is (3.5,5.5).

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Answer:

Im gonna assume its counter clockwise (excuse the bad drawing)

Step-by-step explanation:

The vertices of triangle F'G'H' after a rotation of 180° about (-3, -6) are F'(0, 10), G'(5, 6) and H'(2, 4).

Rotations are transformations that turn a shape around a fixed point. To rotate a shape we need: a centre of rotation. an angle of rotation (given in degrees) a direction of rotation – either clockwise or anti-clockwise.

Given that, triangle FGH has vertices F(-3, 4), G(2, 0), and H(-1, -2).

180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y).

So, (x, y) → (x+3, y+6)

F(-3, 4) → (-3+3, 4+6) → F'(0, 10)

G(2, 0) → (2+3, 0+6) → G'(5, 6)

H(-1, -2) → (-1+3, -2+6) → H'(2, 4)

Therefore, the vertices of triangle F'G'H' after a rotation of 180° about (-3, -6) are F'(0, 10), G'(5, 6) and H'(2, 4).

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The sales tax of his purchase if he lives in Florida where the sales tax rate is 6 percent is $67.92

The word "percent" comes from the Latin per centum, which means "hundred" or "by the hundredth." The symbol for "percent" emerged gradually from the Italian expression per cento, which means "for a hundred." The "per" was frequently shortened as "p." and eventually vanished. The "cento" symbol was simplified to two circles divided by a horizontal line, from which the contemporary "%" symbol was formed.

The abbreviation "pct.", "pct," and sometimes "pc" are also used. A % is a dimensionless (pure) number with no unit of measurement.

Given,

Total purchase=$878

For two tables,

2×127=254

Total=878+254

=1132

6% of 1132 is,

(6/100)×1132

=$67.92

The sales tax of his purchase if he lives in Florida where the sales tax rate is 6 percent is $67.92

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The simple interest is given as PRT/100, thus the simple percent interest per year is 1%.

Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time.

Unlike compound interest, which adds the interest from the principal of prior years to determine the interest of the following year.

As per the given,

Investment = $70

Investment after one year is $70.70

Interset = 70.70 - 70 = $0.70

The interest is given as = PRT/100

0.70 = PR(1)/100

R = (0.70×100)/70

R = 1%

Hence, "The simple interest is given as PRT/100, thus the simple percent interest per year is 1%".

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The total number of skittles in the bag will be 65.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that In a pack of Skittles, 20% are red. If 13 are red. The total number of skittles will be calculated as,

N = ( 13 / 20 ) x 100

N = 130 / 2

N = 65

Therefore, the total number of skittles in the bag will be 65.

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Answer:

f(- 5) = 7

Step-by-step explanation:

f(- 5) means what is the value of y when x = - 5

locate x = - 5 on the x- axis, go vertically up to meet the graph at (- 5, 7 ), then

f(- 5) = 7

The value of g(-2) is -2, f(4) is -15.5, f(1/4) is 3.25, g(2.5) is 1.375, the value of x when f(x) = 2 is 0.5 and the value of x when g(x) = 16 is (plus minus)4.

According to the question,

We have the following expressions:

f(x) = -5x+9/2

Now, we will find the all the values of f(x) by replacing x with the given digits:

f(4) = -5*4+4.5

f(4) = -20+4.5

f(4) = -15.5

The value of f(1/4):

f(1/4) = -5/4+4.5

f(1/4) = -1.25+4.5

f(1/4) = 1.375

The value of x when f(x) = 2:

-5x+4.5 = 2

-5x = 2-4.5

-5x = -2.5

x = 2.5/5

x = 0.5

g(x) = 1.5[tex]x^{2}[/tex]-8

Now, we will find all the values of g(x) by replacing x with the given digits.

The value of g(-2):

g(-2) = 1.5(-2)(-2)-8

g(-2) = 6-8

g(-2) = -2

The value of g(2.5):

g(2.5) = 1.5*2.5*2.5-8

g(2.5) = 9.375-8

g(2.5) = 1.375

The value of x when g(x) = 16:

1.5[tex]x^{2}[/tex]-8 = 16

1.5[tex]x^{2}[/tex] = 16+8

1.5[tex]x^{2}[/tex] = 24

[tex]x^{2}[/tex] = 24/1.5

[tex]x^{2}[/tex] = 16

x = +4 and -4

Hence, the value of g(-2) is -2, f(4) is -15.5, f(1/4) is 3.25, g(2.5) is 1.375, the value of x when f(x) = 2 is 0.5 and the value of x when g(x) = 16 is (plus minus)4.

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Answer:

The Answer is B

Step-by-step explanation:

Since 1.8 times 10 is bigger than 18% meaning its the only one that would be in correct descending order.

Answer:

Pretty sure it’s A

Step-by-step explanation:

18% is 18/100 which is then .18

1/8 is .125

1.8x10 is 18

And .188 is just .188

For 0 < a < b <  1,  a^x < b^x, for x < 0.

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

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given,  0 < a < b < 1.

Assuming a = 0.25 and b = 0.5.

∴ (0.25)^x < (0.5)^x for x > 0, again assuming x to be 2.

∴ (0.25)^2 = 0.625 and (0.5)^2 = 0.25.

Now, 0.625 > 0.25 which is not satisfying a^x < b^x, for x > 0.

Therefore, if 0 < a < b <  1, then a^x < b^x, for x < 0.

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The parent function is y = x ; shift 2 units downwards.

Given,

In the question:

The function is :

g(x) = x - 2

Now, According to the question ;

Let's know

What is the Parent function and transformation?

The transformation of the parent function is shown in blue. It is a shift down (or vertical translation down) of 1 unit. Reflection. A reflection on the x-axis is made on a function by multiplying the parent function by a negative. Multiplying by a negative “flips” the graph of the function over the x-axis.

According to the above statement is;

g(x) = x -2

Hence, The parent function is y = x ; shift 2 units downwards.

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Since the physics books must be together and the mathematics books must be together, There are 1728 ways to arrange the books.

The basic counting principle is a method for keeping track of all the potential outcomes in a situation. According to this statement, there are n m n times m n ways to carry out both of these actions if there are n ways to perform one action and m ways to perform another action after that. How selection is made based on options is determined by the Fundamental Principle of Counting. The approach of selection, taking into account all of the potential options and their combinations for calculating the probability, is made simpler by the Fundamental Principle of Counting.

Here,

There are 3 book,

3!=6

3 different mathematics books,

3!=6

4 different physics books,

4!=24

2 psychology books

2!=2

by fundamental counting principle,

6*6*24*2=1728

There are 1728 different ways to arrange the books because the mathematics and physics books must be together.

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Answer:

41.2

Step-by-step explanation:

1 is in the tenths place.  Because the number the next number is a five, we must round up and 0.20 is the nearest tenth to 0.153.

(4, 1) is the solution for the given inequalities

Given,

The system of inequalities;

3x + y ≤ 14

3x + 5y < 19

We have to find that (4, 1) is a solution to the given system of inequalities;

So,

(x, y) = (4, 1)

Then,

Substitute the values of x and y in the equation;

3x + y ≤ 14

3 x 4 + 1 ≤ 14

12 + 1 ≤ 14

13 ≤ 14

Next,

3x + 5y < 19

3 x 4 + 5 x 1 < 19

12 + 5 < 19

17 < 19

Here,

(4, 1) is the solution for the given inequalities

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The value of y which the slope formula  is 34.

Slope can be defined as the rate of change of a body.

To calculate the value of y, we use the formula below.

Formula:

Where:

From the question,

Substitute these values into equation 1 and solve for y

Hence, the value of y is 34.

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Answer:

70%

Step-by-step explanation:

The equation of the line is y = -3/4x + 10, the graph of the equation has been plotted

The slope of the line = -3/4

The slope of the line the change in y coordinate with respect to the change in x coordinate of the function

The line is passing through the point (0,10)

The point slope form is

[tex](y-y_1)=m(x-x_1)[/tex]

Substitute the values in the equation

y-10 = -3/4(x-0)

y - 10 = -3/4x

y = -3/4x + 10

The equation of the line in slope intercept form is

y = -3/4x + 10

Plot the graph using the slope intercept form

Hence, the equation of the line is y = -3/4x + 10, the graph of the equation has been plotted

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Answer:

13

Step-by-step explanation:

-3-10, or 10+3 is equal to 13

Answer:

13

Step-by-step explanation:

-3+13=10

Answer:

y=100t+1200, where t is years since 2013 and

Step-by-step explanation:

We only have two points from which to form an equation.  Since we are told that it is a linear equation, two points is all we need to find an equation in the form of y=mx+b, where m is the slope (the rate of change) and b is the y-intercept (the value of y when x=0).  Let's make the x axis the year and y the student population.

Let's put the data into an x,y format, but before we do, lets be sure to adopt the problem's fervent wish that we treat the x variable, t, as the years since 2013.  "t is the number of years after 2013."  (0,1200) becomes is the data point for 2013.  The school's population will be the y-axis.

(0,1200)   [primary school had 1200 students enrolled in 2013], and

(3,1500)   [1500 students in 2016]

---

First calculate m, the slope.  Slope is the Rise/Run between the two points (the change in y over the change in x)

Going from (2013,1200) to (2016,1500) we find that:

  Rise  (in y) = (1500 - 1200) = 300 students

  Run  (on x) = (2016 - 2013) =     3 years

The Rise/Run, or slope, m, is 300/3 or 100:  m = 100

Lets put that into our equation format:

y = 100x + b

X will be the time, in years.  The problem asks that we define x in terms of years after 2013, and that this be assigned the variable, t:

y = 100t +b, where t is years after 2013.

(The 100 tells us that the student population increases by 100 per year)

We now need b, the y-intercept.  One can either graph this and look for the value of y when x=0, of simply input either of the data points.  This looks easy enough to input a point and solve for b:

Remember that t is the (year - 2013)

y = 100t +b   Solve for (2013,1200)

 t = 2013 - 2013 = 0

1200 = 100*(0) + b

b = 1200

Actually, b was easy enough to find without either calculating or graphing, since one of our two points tells us the y-intercept (0,1200).

The equation becomes y = 100t + 1200

See the attached graph.

Answer: “y is a function of x.” The letter x represents the input value or independent variable. The letter y, or f(x), represents the output value, or dependent variable.

Step-by-step explanation:lol i have no idea

The zero of the function f(x) = 2x² - 8 is ± 2.

Zeros of the function

Zero of the function means the values of x when f(x) is equal to 0. Which  means that when f(x) = 0, x is a zero of the function.

Given,

Here we have the function f(x) = 2x² - 8.

Here we need to find the zero of the function.

As per the definition of the zeros of the function,

We have to apply the value of f(x) = 0, then we get,

2x² - 8 = 0

Now, we need the value of x only, so we have to move the other numbers to the other side , then we get,

2x² = 8

Now, move the number 2 to the right hand side then it will be dividing the number 8,

x² = 8/2

x² = 4

x = √4

Therefore, the value of x is ± 2.

So, the zeros of the function is either +2 or -2.

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There are two equations which are true. They are 1.5 - k/5 = 11.5 and K/10 -3 = -8.

Given,

The equations;

The value of k = -50

We have to solve the given equations using k as -50 and find the true ones;

Lets check;

1.5 - (-50/5) = 11.5

1.5 - (-10) = 11.5

1.5 + 10 = 11.5

11.5 = 11.5

This equation is true.

(-2 x -50) + 78 = -22

100 + 78 = -22

178 ≠ -22

This equation is false

(-4 x -50) + 80 = -120

200 + 80 = -120

280 ≠ -120

This equation is false

(6 x -50) - 150 = -150

-300 - 150 = -150

-450 ≠ -150

This equation is false

(-50/10) - 3 = -8

-5 - 3 = -8

-8 = -8

This equation is true.

That is,

There are two equations which are true. They are 1.5 - k/5 = 11.5 and K/10 -3 = -8.

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