Sketch the graph using partial factoring.
y = 2x^2 - 6x + 5
(You don't need to draw it if you answer. Just show how to find the vertex and zeros.)

Each line in every set of lines of the same color intersects with each line in two other sets. Because of that fact, there's a segment formed on each line in every set. Therefore, by tracing any segment from every set, we get a closed shape, which is a pentagon, as a result. Since there are 3 segments in each set and a pentagon has 5 sides, the number of pentagons we can trace is \(3\cdot3\cdot3\cdot3\cdot3=3^5=243\).

(a) The intercepts of the sine graph occur when the value of the function is equal to zero. The graph intersects the x-axis at the points (0, 0), (π, 0), and (2π, 0). Therefore, the sine graph has three x-intercepts.

What is Graph ?

A graph is a visual representation of data or mathematical relationships, often displayed as a diagram showing the relationship between two or more variables. Graphs are commonly used in various fields, such as mathematics, science, engineering, economics, and social sciences, to display data and to help analyze and interpret relationships and trends.

There are many different types of graphs, such as line graphs, bar graphs, scatter plots, pie charts, and histograms, each designed to represent data in a different way. Graphs can be created by hand or using computer software, and are often used to illustrate complex data or relationships that are difficult to understand from raw data alone.

(b) The domain of the sine function is all real numbers, as the function is defined for every value of x. The range of the sine function is between -1 and 1, as the values of the function oscillate between these two values.

(c) The sine function is increasing on the interval (0, π/2) and (3π/2, 2π), as the function values increase as x increases within these intervals. The sine function is decreasing on the interval (π/2, 3π/2), as the function values decrease as x increases within this interval. The function is constant at the x-intercepts (0, 0), (π, 0), and (2π, 0).

(d) The sine function is an odd function, as f(-x) = -f(x) for all x. This can be seen by observing that the graph of the sine function is symmetric about the origin, and that the function values alternate in sign as x is negated.

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The theorem is shown in a pythagoras theorem is c² = a² + b²

The theorem shown in the Pythagorean theorem is "a² + b² = c²". This theorem is named after the ancient Greek mathematician Pythagoras, who is credited with discovering it.

The Pythagorean theorem applies to right-angled triangles and states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Mathematically, we can express this as:

c² = a² + b²

Where c is the length of the hypotenuse, and a and b are the lengths of the other two sides (called the legs) of the right-angled triangle.

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Let's translate the argument into symbolic form using the following symbols:

B: Brazil has a huge foreign debt.

A: Argentina has a huge foreign debt.

The argument can be represented as follows:

B → (B ∨ A)

To determine the validity of the argument, we can construct a truth table for the expression (B → (B ∨ A)). The truth table will include all possible combinations of truth values for B and A, and we will evaluate the truth value of the entire expression for each combination.

The truth table for the argument is as follows:

B A B ∨ A B → (B ∨ A)

T T T T

T F T T

F T T T

F F F T

As we can see from the truth table, regardless of the truth values of B and A, the expression B → (B ∨ A) always evaluates to true. Therefore, the argument is valid because the conclusion is always true when the premise is true.

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Answer:

In plane Euclidean geometry, a rhombus is a quadrilateral whose four sides all have the same length. Another name is equilateral quadrilateral, since equilateral means that all of its sides are equal

Step-by-step explanation:

Answer:

create a problem that can be repersented by the equation

Step-by-step explanation:

Answer:

The rate change between these points is 3.

Step-by-step explanation:

Answer:

Rate of Change is 3

Step-by-step explanation:

The rate of change between two points is called the 'slope'.

x1-x2         -6-8          -14

____  =      ____  =   ___  = Divide  = 3

y1-y2      -20 - 22      -42

Each time X increases, there is a perfectly predictable increase in Y  is indicated by a Pearson correlation of r= +1.00 between X and Y

A Pearson correlation coefficient of +1.00 indicates a perfect positive linear relationship between the variables X and Y. It means that as X increases, Y increases in a perfectly predictable manner. The correlation coefficient of +1.00 indicates a strong and direct relationship between the two variables, where the values of Y can be precisely determined based on the values of X.

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Answer:

Step-by-step explanation:

slope formula: \(\frac{y_{2} -y_{1} }{x_{2}-x_{1} }\)

Points (–3, 3) and (18, 26)

\(\frac{26-3}{18-(-3)}\)  = \(\frac{23}{21}\)

I got it right on the test (ed)

Answer:

(x=1) - Below

0-6 = 6

1

(-6x) = -6

(0 - (6x))+6 = 12

Step-by-step explanation:

Step 1: Subtract 6 from both sides.

−6x+6−6=0−6

−6x=−6

Step 2: Divide both sides by -6.

−6x/−6 =− 6/−6

Step 3: x = 1

Answer:

616

Step-by-step explanation:

22 * 28 = (25 - 3)(25 + 3) = 25^2 - 3^2 = 625 - 9 = 616

Answer:

3 1/2 pounds

Step-by-step explanation:

enVision math pdf

Answer:

v=v

Step-by-step explanation:

6v+8=8+6v

    -8

6v=6v

/6

v=v

STEP

1

:

           2v - 6

Simplify   ——————

           v + 2

STEP

2

:

Pulling out like terms

2.1     Pull out like factors :

  2v - 6  =   2 • (v - 3)

Equation at the end of step

2

:

 (((v2)+v)-12)   2•(v-3)

 ————————————— ÷ ———————

 (((v2)+6v)+8)     v+2  

STEP

3

:

           v2 + v - 12

Simplify   ———————————

           v2 + 6v + 8

Trying to factor by splitting the middle term

3.1     Factoring  v2 + v - 12

The first term is,  v2  its coefficient is  1 .

The middle term is,  +v  its coefficient is  1 .

The last term, "the constant", is  -12

Step-1 : Multiply the coefficient of the first term by the constant   1 • -12 = -12

Step-2 : Find two factors of  -12  whose sum equals the coefficient of the middle term, which is   1 .

     -12    +    1    =    -11

     -6    +    2    =    -4

     -4    +    3    =    -1

     -3    +    4    =    1    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -3  and  4

                    v2 - 3v + 4v - 12

Step-4 : Add up the first 2 terms, pulling out like factors :

                   v • (v-3)

             Add up the last 2 terms, pulling out common factors :

                   4 • (v-3)

Step-5 : Add up the four terms of step 4 :

                   (v+4)  •  (v-3)

            Which is the desired factorization

Trying to factor by splitting the middle term

3.2     Factoring  v2+6v+8

The first term is,  v2  its coefficient is  1 .

The middle term is,  +6v  its coefficient is  6 .

The last term, "the constant", is  +8

Step-1 : Multiply the coefficient of the first term by the constant   1 • 8 = 8

Step-2 : Find two factors of  8  whose sum equals the coefficient of the middle term, which is   6 .

     -8    +    -1    =    -9

     -4    +    -2    =    -6

     -2    +    -4    =    -6

     -1    +    -8    =    -9

     1    +    8    =    9

     2    +    4    =    6    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  2  and  4

                    v2 + 2v + 4v + 8

Step-4 : Add up the first 2 terms, pulling out like factors :

                   v • (v+2)

             Add up the last 2 terms, pulling out common factors :

                   4 • (v+2)

Step-5 : Add up the four terms of step 4 :

                   (v+4)  •  (v+2)

            Which is the desired factorization

Canceling Out :

3.3    Cancel out  (v+4)  which appears on both sides of the fraction line.

Equation at the end of step

3

:

 (v - 3)   2 • (v - 3)

 ——————— ÷ ———————————

  v + 2       v + 2  

STEP

4

:

         v-3       2•(v-3)

Divide  —————  by  ———————

        (v+2)       (v+2)

4.1    Dividing fractions

To divide fractions, write the divison as multiplication by the reciprocal of the divisor :

v - 3      2 • (v - 3)        v - 3         v + 2  

———————  ÷  ———————————   =   ———————  •  ———————————

(v + 2)       (v + 2)         (v + 2)     2 • (v - 3)

Canceling Out :

4.2    Cancel out  (v - 3)  which appears on both sides of the fraction line.

Canceling Out :

4.3    Cancel out  (v + 2)  which appears on both sides of the fraction line.

Final result :

 1          

 — = 0.50000

 2          

The truth value of the ~[P v (Q v R)] >~ (S v P) is true.

Truth-value, in logic, is the degree to which a particular proposition or assertion is true (T or 1) or false (F or 0). Because the truth-value of a compound proposition is a function of, or a quantity depending upon, the truth-values of its component components, logical connectives like disjunction and negation can be conceived of as truth-functions.

Given, ~[P v (Q v R)] >~ (S v P) since P v (Q v R) is true, thus ~ [ P v ( Q v R ) ] is false, therefore the implication is true.

⇒~[T v (F v T)] >~ (F v T)

⇒[F v (F v T)]>(T v T)

⇒[F v (F v T)]>(T v T)

⇒F v T

⇒T

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To determine whether the sequence converges or diverges, we can use the Squeeze Theorem.

We can see that

\(4/(n + 5n^2) < = An < = (4 + 3n^2)/(n + 5n^2)\)

As n tends to infinity, \(4/(n + 5n^2)\)  tends to 0 and\((4 + 3n^2)/(n + 5n^2)\)  tends to\(4/(5n^2)\)  which also tends to 0.

So by the Squeeze Theorem, we can say that An tends to 0 as n tends to infinity. Hence the limit of the sequence is Lim n-> An = 0

We can also see that the numerator of An is a constant and the denominator is a polynomial with degree 2. Since the denominator's degree is greater than the numerator, the limit will be zero as n -> infinity.

Therefore, the sequence converges to 0.

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Interpreting a correlation requires careful consideration of factors such as causation, confounding variables, nonlinearity, outliers, and sample characteristics.

Interpreting a correlation between two variables can be difficult for several reasons:

Causation vs. correlation: Correlation measures the strength and direction of the relationship between two variables but does not imply causation. Just because two variables are correlated does not mean that one variable causes the other. It is essential to avoid making causal claims based solely on correlation.

Confounding variables: Correlations can be influenced by the presence of confounding variables that affect both variables being studied. Without accounting for these confounding factors, it can be challenging to determine the true nature of the relationship between the variables of interest.

Nonlinear relationships: Correlation coefficients, such as Pearson's correlation coefficient, measure linear relationships between variables. If the relationship is nonlinear, the correlation may not accurately capture the association. It is crucial to consider other types of analysis or transformations to capture more complex relationships.

Outliers and influential observations: Extreme values or outliers in the data can have a significant impact on correlation coefficients. These outliers may distort the correlation and lead to incorrect interpretations. It is important to examine the data for influential observations that may unduly influence the correlation results.

Sample size and representativeness: The size and representativeness of the sample can affect the reliability and generalizability of correlation results. Small or biased samples may not provide a representative picture of the population, leading to misleading interpretations.

Overall, it is important to use correlations as part of a broader analysis and consider additional evidence before drawing definitive conclusions about the relationship between variables.

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Answer:

Step-by-step explanation:

interval in mathematics stands for a set of real numbers,

denoted by [a,b] where a and b are the starting and ending real numbers both inclusive respectively.

thus, interval [a,b] is the set of real numbers starting from a to b both are real numbers and are included.

His/her lowered score was most likely due to statistical regression.

The missing options in the question are:

A. compensation rivalry  B. Demoralization C.  Differential selection

D.  Testing E.  Statistical regression

From the question, we have:

A change (whether higher or lower) in the score is caused by statistical regression.

This is so because several variables could attribute to the change in the score.

The relationship between these variables is referred to as statistical regression

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Answer:

it 4.262295082

Step-by-step explanation:

you have to divid the ounces by the cost

Answer:

What is your question?

Step-by-step explanation:

Answer:

well, what is your question?

Step-by-step explanation:

Answer: 120

Step-by-step explanation: divide 24 by 5 to get 4.8 so its 4.8 minutes for one question

25 x 4.8 = 120

Answer:

Step-by-step explanation:

First look at the tangent function f(x) = tan x.  Its domain is restricted:  (-pi/2, pi/2).  There are no restrictions on the function value, so the range is (-infinity, +infinity).  The primary interval on which tan x is defined is (-pi/2, +pi/2, which has length pi.

In comparison, the domain of f(x) = tan 2x is only half as long as that of f(x) = tan x:  (-pi/4, +pi/4), with length pi/2.

Now, focusing on f(x) = 3cot(2x):  the range is the same:  (-infinity, +infinity).  The period is half that of tan x:  pi/2 instead of pi.  Remember that the cotangent function repeats itself every pi/2 radians.

Domain:  (-pi/4, +pi/4) (centered on the origin), (-3pi/4. 3pi/4), and so on, continuing to both the left and the right.

Range:  (-infinity, infinity)

Step-by-step explanation:

the correct answer is option a 6a-7

The linear equation is f(x) = 2^2 + x, while the other two functions are nonlinear functions

From the question, we have the following parameters that can be used in our computation:

The three equations

A linear equation is any equation that has a degree of 1

From the three equations, we can see that

Degree = 1

Degree = 2

Degree = 3

Hence, the linear function is f(x) = 2^2 + x

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Home owners loan corporation(HOLC) aims and objectives is to assist home owners who are unable to pay their mortgage loan.

Home owners loan corporation(HOLC) can be defined as the corporation whose sole aims and objectives is to help or assist home owners who are unable to pay their mortgage loan.

This corporation play an important role as they help to prevent mortgage home owner who have the tendency of losing their homes  or at risk of losing their home from losing their homes and they as well give out long-term mortgage loans to homeowners who are at risk of losing  of their property.

Therefore Home owners loan corporation(HOLC) aims and objectives is to assist home owners who are unable to pay their mortgage loan.

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Answer:

Step-by-step explanation:

The area of a circle is given by the formula:

A = πr^2

where A is the area and r is the radius.

Substituting the given values, we get:

A = π(2.1 m)^2 = 13.85 m^2

So the total cost of the glass with a price of $7.10 per square meter is:

Cost = Price per square meter x Total area

Cost = $7.10/m^2 x 13.85 m^2 = $98.24

Therefore, the cost of the glass is $98.24.

As the standard error decreases, a width of the confidence intervals narrows with sample size becomes larger.

A degree of uncertainty as well as surety in a sampling method is measured by confidence intervals.

Some key features regarding the confidence interval are-

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Answer: \(x \leq 12\)

Step-by-step explanation:

\(3(x-3) \leq 27\\\\x-3 \leq 9\\\\x \leq 12\)

Step-by-step explanation:

To solve the inequality 3(x - 3) ≤ 27, we can use the following steps:

Distribute the 3 on the left side of the inequality: 3x - 9 ≤ 27

Add 9 to both sides of the inequality: 3x ≤ 36

Divide both sides of the inequality by 3: x ≤ 12

Therefore, the solution to the inequality is x ≤ 12.

This solution is valid for any value of x less than or equal to 12, including 12.

Examples of values that satisfy this inequality are:

x = -6, -4, -2, 0, 2, 4, 6, 8, 10, 11, 12

x = -1, -0.5, 0.1, 4.5, 8.9, 12

Note that the solution set is a set of real numbers, that includes all x that are less or equal than 12.