What is an equation of a line that passes through the points (1, 4) and (2, 9) in
5)
point-slope form? Analyze the steps and fill in the blanks. (4pts)
First, use the two given points to find the slope.
m=
Уг-У1

Use the slope and one point to write an equation of the line in
point-slope form.
Point-slope form of a linear equation.
Substitute

Answer:

81

Step-by-step explanation:

y = -9

y² = (-9)² = 81

The solution to the equation f(x)=g(x) are x=-2 and x=1.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

The given functions are f(x)=-x+6 and g(x)=-x²-2x+8.

Now, f(x)=g(x)

-x+6=-x²-2x+8

⇒ x²+x-2=0

⇒ x²+2x-x-2=0 (Splitting middle term method)

⇒ x(x+2)-1(x+2)=0

⇒ (x+2)(x-1)=0

⇒ x+2=0 and x-1=0

⇒ x=-2 and x=1

Therefore, the solution for the obtained equation are x=-2 and x=1.

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The value of x and z are x° = 6.71°, z° = 75.26° simulataneously,

What is the linear pair angles?

Linear pair of angles are formed when two lines intersect each other at a single point. The angles are said to be linear if they are adjacent to each other after the intersection of the two lines. The sum of angles of a linear pair is always equal to 180°.

We have,

Angles:

6x° + 35°

z°

8x° + 51°

To find the values of x and z

from the given figure

Linear pair angles:

6x° + 35° + 8x° + 51° = 180

14x° + 86° = 180

14x° = 180° - 86°

14x° = 94°

x° = 94°/14°

x° = 6.71°

Vertically opposites angles are equal

6x° + 35° = z°

z° =  6( 6.71°)° + 35

z° = 40.26 + 35

z° = 75.26°

Hence, the value of x and z are x° = 6.71°, z° = 75.26° simulataneously.

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The value of the x would be 9.

Option (A) is correct.

What is a complementary angle?

A complementary angle is an angle that, when added to another angle, forms a right angle (90 degrees). Complementary angles are pairs of angles that add up to 90 degrees.

Angle JKM and angle MKN are complementary angles

so

   (3x + 2) + (6x + 7) = 90

  9x + 9 = 90

  9(x + 1) = 90

     x + 1 = 10

    x = 9

Hence, the value of the x would be 9.

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After solving the equation the value of the x would be 9. Therefore, the correct option is A.

What is a complementary angle?

A complementary angle is a pair of angles that add up to 90 degrees. Complementary angles can be adjacent angles, or angles that share a common vertex and side, or they can be nonadjacent angles that have no common points or sides. Complementary angles are usually referred to by their sum, such as "90-degree angles" or "angles that add up to 90 degrees." Complementary angles can also be called supplementary angles when they add up to 180 degrees.

Angle JKM and angle MKN are complementary angles

so   (3x + 2) + (6x + 7) = 90

 9x + 9 = 90

 9(x + 1) = 90

    x + 1 = 10

   x = 9

Hence, the value of the x would be 9.

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Step-by-step explanation:

please refer to the attached sketch for the answer.

Answer:

 (a) A  and B are similar but not congruent

Step-by-step explanation:

All of the rectangles have sides in the ratio of 2:1, so are all similar. Only the rectangles that are the same size are congruent: A and C.

Answer:

me either

Step-by-step explanation:

The needed 3rd-degree polynomial function with real coefficients matching the specified constraints will be y=-5x³+10x²-45x+90.

A polynomial is a mathematical statement made up of indeterminates and coefficients that solely includes the operations of addition, subtraction, multiplication, and positive-integer powers of variables. x2 4x + 7 is an example of a polynomial with a single indeterminate x. Polynomials are sums of k-x^n terms, where k can be any number and n can be any positive integer. 3x+2x-5, for example, is a polynomial. Polynomials are introduced. This video defines words such as degree, standard form, monomial, binomial, and trinomial.

Here,

y=-5(x-2)(x-3i)(x+3i)

y=-5(x-2)(x²+9)

y=-5(x³-2x²+9x-18)

y=-5x³+10x²-45x+90

The required 3rd-degree polynomial function with real coefficients satisfying the given conditions will be y=-5x³+10x²-45x+90.

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Sample is biased. Based on her findings, Arianna revealed the percentage in her state after polling 600 residents of her city. Thus, the sample fails to accurately reflect the population. Option (4) is correct.

When some members of a population are systematically more likely to be chosen in a sample than others, this is known as sampling bias. What makes sampling bias significant? Sampling bias poses a risk to external validity since it restricts the applicability of your findings to a larger population. When some population members have a higher or lower sampling probability than others, the sample is biased.

This includes choosing or sampling people according to their hobbies, gender, or age. Therefore, a fair or impartial sample must be representative of the entire population under investigation. When a research study design fails to gather a representative sample of a target population, the phenomenon known as sampling bias takes place. This usually happens as a result of the respondents' selection criteria not capturing a broad enough sampling frame to include all points of view.

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Correct Question:

Arianna collected data from a random sample of 600 people in her city asking whether or not they bike to work. Based on the results, she reports that 44% of the people in her state bike to work. Why is this statistic misleading?

Select the correct answer below:

1. The statistic contains a calculation error.

2. The sample is self-selected.

3. The data contains an outlier.

4. The sample is biased.

Answer:

A,D,E

Step-by-step explanation:

A:

14/4 = 3.5

D:

7/2 = 3.5

E: 14/4 = 3.5

The constant of proportionality for the table is 3.5. Any other table that satisfies the equations x/y = 3.5 will have the same constant of proportionality.

To find the constant of proportionality, we can divide the y-values by the corresponding x-values and see if they are the same for all given points. In this case, if we divide 24.5 by 7, we get approximately 3.5. If we divide 31.5 by 9, we also get approximately 3.5. Therefore, the constant of proportionality is 3.5 for this table.

Now, we need to find the relationships that have the same constant of proportionality.

For example, if we have a table with the following values:

x1 y1

x2 y2

x3 y3

and the constant of proportionality is k, then we have the following equations:

x1/ y1 = k

x2/ y2 = k

x3/ y3 = k

So, any other table that satisfies these equations will have the same constant of proportionality as the given table.

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The domain of the function is { (x, y) ∈ R² | x² + y² ≥ 1 }

What is Domain of function?

A function's domain is the collection of all potential inputs. For instance, all real numbers are in the domain of f(x)=x², and all real numbers are in the domain of g(x)=1/x, with the exception of x=0. Special functions with more constrained domains can also be defined.

According to question

⇒ [tex]z = e^{\sqrt{x^{2}+ y^{2} -1 } }[/tex]

⇒ x² + y² - 1 ≥ 0

 ⇒ x² + y² ≥ 1

Hence, the Domain of f(x, y) is  { (x, y) ∈ R² | x² + y² ≥ 1 }

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The value of baseball card has increased by 160(%) percentage.

What is the percentage?

A number or ratio that may be stated as a fraction of 100 is a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the word per cent means. The letter "%" stands for it.

Increase = New Number - Original Number

Then: we divide the increased number by the original number and multiply by 100.

Therefore, % increase = (Increase ÷ Original Number)× 100.

Given, the new price of a baseball card = $13

The original price of a baseball card = $5

Then from the above definition,

Increase = 13-5 = 8

% increase = (8/5)*100 = 160%

Hence, its value has increased by 160 percentage.

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The point of the compass located in order to make the arcs is points X and Y.

An "arc" in mathematics is a straight line that connects two endpoints. An arc is typically one of a circle's parts. In essence, it is a portion of a circle's circumference. A curve contains an arc. A circle contains an arc. For instance, a quarter-circle and a semicircle are both examples of arcs. A minor arc is one that is smaller than half of the circle it is a part of, or less than a semicircle, whereas a major arc is one that is more than half of its circle.

Given

The following figure was drawn using a straightedge and a compass.

The point of the compass located in order to make the arcs:

1. points X and Y

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the area of the generic rectangle will be x²-2x-15.

What is a rectangle?

Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A quadrilateral with equal angles and parallel opposite sides is referred to as a rectangle. Around us, there are a lot of rectangle items. The length and width of any rectangle form serve as its two distinguishing attributes. The width and length of a rectangle, respectively, are its longer and shorter sides.

Area of rectangle is A = a*b

(x + 3)(x - 5) in a generic rectangle

The product will give the area

x²-2x-15

hence the area of the generic rectangle will be x²-2x-15.

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In the given relation, 1 is not a domain.

The domain of a function is the set of all possible inputs for the function. or we can that in an ordered pair, all the values of x are called domain.

All the values that go into a function. The output values are called the range.

The domain of a function is the set of all possible inputs for the function.

If a function f provides a way to successfully produce a single value y using for that purpose a value for x than that chosen x-value is said to belong to the domain of f.

Given that, a function,

{(5, 1), (4, -3), (3, -1)}

We know, a domain is the set of all "x" values.

Therefore, domain of the function are, 5, 4 and 3

But, if we see, 1 is one of the values of y.

Hence, 1 is not a domain.

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The depth of the submarine after 8 minutes is -123.6 feet below sea level.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Depth of the submarine after y minutes.

= -270 + 18.3y

The depth of the submarine after 8 minutes.

= -270 + 18.3 x 8

= -270 + 146.4

= -123.6

Thus,

The submarine is at -123.6 feet below sea level.

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If BD bisects ∠ABC and ∠ADC, then AD is congruent to CD.

What is bisector of an angle?

In geometry, anything is said to have been bisected when it is split into two identical or similar parts, typically by a line. In that case, the line is known as the bisector. The types of bisectors that are most usually taken into account are segment bisectors and angle bisectors..

Since BD bisects ∠ABC, thus ∠ABD = ∠DBC.

Since BD bisects ∠ADC, thus ∠ADB = ∠BDC.

AA theorem: According to the AA similarity theorem, two triangles are similar if two of their triangles are congruent with two of their respective triangles' angles.

Consider △ABD and △DBC:

∠ABD = ∠DBC

∠ADB = ∠BDC

Therefore, △ABD ≅ △DBC

According to CPCT, AD ≅ CD.

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Answer:

see below.

Step-by-step explanation:

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]

[tex]8^{2}[/tex] + [tex]15^{2}[/tex] = [tex]c^{2}[/tex]

64 + 225 = [tex]c^{2}[/tex]

289 = [tex]c^{2}[/tex]

[tex]\sqrt{289}[/tex] = [tex]\sqrt{c^{2} }[/tex]

17 = c

Using the rules of cryptarithmetics problems and with the provided words and condition for a word, The answer is 9738+2558+1378==13674.

Mathematical puzzles known as cryptarithmetic problems use letters from the alphabet in place of the digits.

A rare version in which a formula is written and the matching cryptarithm's solution is the supplied formula is used to find the solution.

since the digits used are 0 to 9.

first letter can't be zero.

and we can't repeat the same digit for same different alphabets.

Using these rules with the condition that food is multiple of 1279.

The answer is : 9738+2558+1378==13674

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Using the rules of cryptarithmetics problems and with the provided words and condition for a word, The answer is 9738+2558+1378 =13674.

What is a cryptarithmetic problem?

Mathematical puzzles known as cryptarithmetic problems use letters from the alphabet in place of the digits.

What is reverse cryptarithm?

A rare version in which a formula is written and the matching cryptarithm's solution is the supplied formula is used to find the solution.

since the digits used are 0 to 9.

first letter can't be zero.

and we can't repeat the same digit for same different alphabets.

Using these rules with the condition that food is multiple of 1279.

The answer is : 9738+2558+1378 = 13674

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Answer:

80 kg

Step-by-step explanation:

To find the mass of the skater, you can use the formula for centripetal force:

F_centripetal = m * v^2 / r

Where F is the centripetal force, m is the mass of the object, v is the velocity of the object, and r is the radius of the circular path.

Plugging in the values you know, you get:

720 N = m * (15 m/s)^2 / 25 m

Solving for m, you find that the mass of the skater is:

m = 720 N * 25 m / (15 m/s)^2

= 720 N * 25 m / 225 m^2/s^2

= 80 kg

So the mass of the skater is approximately 80 kilograms.

The remainder of polynomial g(x) divides (x - 3) that is  g(x) / (x - 3) is 0.

What is polynomial?

A polynomial is a mathematical expression made up of variables, constants, and exponents that are combined using addition, subtraction, multiplication, and division operations.

Given: g(x) = 2x^3 + 5x^2 - 28x - 15

(x - 3) is a factor of g(x).

We have to find the remainder of g(x) / (x - 3).

Consider,

                 2x^2 + 11x + 5

         [tex]\sqrt[(x-3)]{2x^3+5x^2 -28x -15}[/tex]

          -    2x^3 -6x^2

____________________________

                      11x^2 - 28x

               -      11x^2 - 33x

____________________________

                               5x - 15

                          -    5x - 15

_______________________________

                                      0

Hence, the remainder of polynomial g(x) divides (x - 3) that is

g(x) / (x - 3) is 0.

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Hello,

I hope you and your family are doing well!

To solve this problem, we can use the formula:

total cost = set-up fee + (cost per copy * number of copies)

In this case, we know the total cost and the set-up fee, and we want to find the number of copies. We can substitute these values into the formula and solve for the number of copies:

$32.20 = $14.95 + ($0.03/copy * number of copies)

Subtracting the set-up fee from both sides of the equation gives:

$17.25 = $0.03/copy * number of copies

Dividing both sides of the equation by the cost per copy gives:

number of copies = $17.25 / $0.03/copy = 575 copies

So Emilio was charged $32.20 to print 575 copies of the brochures.

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Happy Holidays!

The Co-ordinates of the point C that divides the line in the ratio of 3:4 is (-20/7, -17/7)

What is Section Formula?

The Section formula is used in coordinate geometry to compute the ratio of a line segment split by a point, either internally or externally. It determines the centroid, incenter, and excenters of a triangle. It is used in physics to determine the centre of mass of systems, equilibrium locations, and so on.

Solution:

A(-8, 1) and B(4, -7)

Ratio is 3:4

Section Formula is (mx2 + nx1/ m + n), (my2 + ny1/ m + n)

m = 3 and n = 4

Co-ordinates of C are (3*4 + 4*(-8)/ 3+4), (3*(-7) + 4*1 / 3+4)

= (12 - 32 / 7), (-21 + 4 / 7)

= (-20/7, -17/7)

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The sum of the lengths of two sides is equal to the length of the third side is 45°.

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Answer:

D.  b + c = 68

    0.08b + 0.15c = 6.00

Step-by-step explanation:

The total cost is $6.00

The total amount of copies is 68

To find the total cost, we multiply the amount of copies by the individual price. So we get

0.08b + 0.15c = 6.00

We add the amount of copies bought to get a total of 68, so we get this equation:

b + 6 = 68

The required solution of the given inequality is given as x > 4, and the answer for the blanks is to Divide both sides by -8 and change the inequality sign.

Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

Here,
Given inequality,
-8x < 32
Divide both sides by -8
x > 4

The sign of the inequality change because multiplication with the negative value changes the inequality sign and the higher negative value is the least value.

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A car manufacturer wants to lean about the brand preferences, then the company should survey a sample of all electric car owners.

A survey is a set of questions used in human subject research with the goal of gathering specific information from a particular population. Surveys can be carried out via the phone, by mail, online, at street corners, and even in shopping centers. Surveys are employed to collect data or learn more in areas like demography and social research.

Survey research is frequently used to evaluate ideas, beliefs, and emotions. Surveys may have narrow, specialized objectives, or they may have more general, extensive objectives.

As the manufacturer wants to learn about the brand preferences of electric car owners that what type of things people like nowadays, or what kind of improvement he can do in his model or design or other things, he should prefer a sample of all electric car owners.

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