Find the equation of the linear function represented by the table below in slope intercept form

The point of intersection for the two lines  [tex]y = -x + 2[/tex]  and  [tex]y = 3x + 6[/tex]   is [tex](2,4).[/tex]

To find the point of intersection, you can set the two equations equal to each other and solve for x and y.

[tex]y = -x + 2[/tex]

[tex]y = 3x + 6[/tex]

[tex]-x + 2 = 3x + 6[/tex]

[tex]-4x = 4[/tex]

[tex]x = -1[/tex]

then substitute [tex]x = -1[/tex] in any of the equation

[tex]y = -x + 2[/tex]

[tex]y = -(-1) + 2[/tex]

[tex]y = 1 + 2[/tex]

[tex]y = 3[/tex]

So the point of intersection is  [tex](-1,3)[/tex].

It is possible that there may be more than one point of intersection, but in this case, there is only one point of intersection.

To be sure that there is only one point of intersection, you could graph the two lines and visually check if they intersect at only one point.

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Julio needs to prove that two sides of the two triangles are congruent, in addition to the hypotenuse and one set of legs that are already congruent, to use the SAS Triangle Congruence Theorem.

Congruence, in mathematics, a term employed in several senses, each connoting harmonious relation, agreement, or correspondence .Two geometric figures are said to be congruent, or to be in the relation of congruence, if it is possible to superpose one of them on the other so that they coincide throughout. Thus two triangles are congruent if two sides and their included angle in the one are equal to two sides and their included angle in the other.

This idea of congruence seems to be founded on that of a "rigid body," which may be moved from place to place without change in the internal relations of its parts. The position of a straight line (of infinite extent) in space may be specified by assigning four suitably chosen coordinates. A congruence of lines in space is the set of lines obtained when the four coordinates of each line satisfy two given conditions. For example, all the lines cutting each of two given curves form a congruence.

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The given number lies between 64 and 81

A value that, when multiplied by itself, equals the original number is said to be the square root of a number. The character "√" stands for it. For instance, since 4 × 4 is 16, the square root of 16 is 4. Although a number's square root can be positive or negative, the positive value is more frequently utilized. To determine a distance or length, it is also used in mathematics.

given that square root is approximately 8.1066

let the value of the number be x

so √x>8 and √x<9

=>     8 < √x < 9

squaring on the both side we get

64 < x < 81

so the number lies between 64 and 81

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The results of this question are listed below:

Herein we find a quadratic function that relates doll production and production cost, of which we must determine what quantity minimizes production costs. This can be done by transforming the equation into vertex form.  First, write the equation in standard form:

PC = 0.2 · t² - 8 · t + 500

Second, use algebra properties until vertex form is obtained:

PC = 0.2 · (t² - 40 · t + 2500)

PC = 0.2 · (t² - 40 · t + 400) + 0.2 · 2100

PC - 420 = 0.2 · (t - 20)²

Third, determine the critical point:

(t, PC) = (20, 420)

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Answer: y = −1/2x + 2 is the answer to the slope-intercept form of the graph.

Step-by-step explanation:

I hope this helps!!

A product of mixed numbers is a fraction or a natural number.

We know that a mixed number is a number consisting of a natural number and a proper fraction.

It is a combination of a natural number and fraction

We can say that a mixed number can be written as [tex]a\frac{b}{c}[/tex]

where a, b and c are non-zero real numbers with c > b

When we need to multiply two mixed numbers, first we change each mixed number to an improper fraction. Then multiply the numerators.

Then we multiply the denominators. And simplfy the resultant fraction if needed.

Consider two mixed numbers [tex]2\frac{1}{4} , 3\frac{2}{5}[/tex]

After converting given mixed numbers into an improper fractions we get,

[tex]2\frac{1}{4} =\frac{9}{4} , 3\frac{2}{5}=\frac{17}{5}[/tex]

So the product of given mixed numbers would be,

[tex]2\frac{1}{4} \times 3\frac{2}{5}[/tex]

[tex]=\frac{9}{4} \times \frac{17}{5} \\\\=\frac{153}{20}[/tex]

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The (arithmetic operation)division equation at B (6/(2/3)=9) represent the situation.

What are arithmetic operations?

Arithmetic operations is a branch of mathematics, that involves the study of numbers, operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication and Division.

These basic mathematical operations (+, -, ×, and ÷) we use in our everyday life. Whether we need to calculate the annual budget or distribute something equally to a number of people, for every such aspect of our life, we use arithmetic operations.

The four basic arithmetic operations in Maths, for all real numbers, are:

Addition (Finding the Sum; ‘+’)

Subtraction (Finding the difference;  ‘-’)

Multiplication (Finding the product; ‘×’ )

Division (Finding the quotient; ‘÷’)

As

Model having length 6 feet is divided into 9 pieces.

Therefore,

                 6/9=2/3

hence,

6/(2/3)=9

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[tex] - 12 + 3m = m - 2[/tex]

[tex]3m - m = - 2 + 12[/tex]

[tex]2m = 10[/tex]

[tex]m = \frac{10}{2} \\ [/tex]

answer: [tex]m = 5[/tex]

Answer:

Part 1

The triangle is an isosceles triangle because it has no equal sides. The measurement of B will equal 95°.

Step-by-step explanation:

1.It has no equal sides

2.180° in a triangle, added the other degrees given, then subtracted 180 by the added degree sum.

you figure out the shortest to longest side by looking at the degrees.

Where 30° is, the opposite line from it is the seat tube . Meaning its the shortest. use the same tactic for the others. Opposite of 55° is top tube. Finally Opposite of 95° is the down tube.

Hope this helps! Good Luck!

I tried to simplify the answers as well as explaining it at the same time. I know when I have graded assignments they check them all for plagiarism. If you still a little confused I can help and be a little more in depth.

Answer: The graph that could be the graph of f(x) is a parabola that opens upwards, with a vertex at (2,-4) and x-intercepts at x = -1 and x = 4. Since the degree of the polynomial function f(x) is 3 and the roots are -1, 0, and 4, the polynomial function is a cubic function and its graph is a parabola.

The roots of a polynomial function are the x-coordinates of the x-intercepts of the graph of the function. Therefore, since the roots of the equation f(x) = 0 are -1, 0, and 4, the graph of f(x) will have x-intercepts at x = -1 and x = 4.

The fact that the vertex is at (2, -4) mean that the parabola will open upwards and pass through the point (2, -4)

It's important to note that, if the polynomial function has a degree greater than 3, there may be multiple graphs that could represent the polynomial function, as long as they have the same roots.

Step-by-step explanation:

The total number of ceiling tiles required is 78

Measurement in the ceiling =  24 feet by 26 feet.

Measurement of the tiles =  2 feet by 4 feet

Mathematicians use units of measurement, rules, and formulas to calculate various measurement parameters, including area, volume, length, perimeter, surface area, time, etc. The process of comparing a physical quantity with a recognised standard quantity of the same kind is called comparison.

Calculating the total number of tiles required -

= Measurement in the ceiling / Measurement of the tiles

= 24 x 26 / 2 x 4

= 624 / 8

= 78

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Answer:

  75.5°

Step-by-step explanation:

You want the angle between a 50 pound force and a 75 pound force given that their resultant is a 100 pound force. Force 1 is aligned with the +x axis, and Force 2 is in the first quadrant.

The forces and their resultant form a triangle such that the angle opposite the resultant is the supplement of the angle between the forces. We can find the angle opposite the resultant using the law of cosines:

  c² = a² +b² -2ab·cos(C)

  cos(C) = (a² +b² -c²)/(2ab)

  C = arccos(a² +b² -c²)/(2ab) = arccos((50² +75² -100²)/(2·50·75))

  C = arccos(-1875/7500) = arccos(-1/4) ≈ 104.48°

The angle between the vectors is the supplement of this:

  angle12 = 180° -104.48° = 75.52° ≈ 75.5°

The angle between the forces is about 75.5°.

the answer is number 4, you are basically multiplying everything together. 3×-2=-6 and for the letters (i forgot the term to call them) you just add them together which gives the answer on number 4.

The height of the actual glass is equal to 10 cm.

In Geometry, a scale factor is the ratio of two corresponding side lengths or diameter in two similar geometric figures such as drinking glasses, which can be used to either horizontally or vertically enlarge (increase) or reduce (decrease or compress) a function that represents their size.

Mathematically, the scale factor of a geometric figure can be calculated by dividing the dimension of the image by the dimension of the pre-image (original figure):

Scale factor = Dimension of image (new figure)/Dimension of pre-image(original figure)

Scale factor = 2/2.5

For the height of the actual glass, we have:

2/2.5 = 8/x

x = (2.5 × 8)/2

x = 20/2

x = 10 cm.

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Let P and Q represent the intersections of two triangle sides. Consequently, the third side's length is divided in half by the length of the section that connects P and Q.

Vega is attempting to prove that the segment joining the midpoints of two sides of a triangle is equal to half the length of the third side. To do this, she must first identify the two midpoints of any given triangle. Let P and Q be the midpoints of two sides of the triangle. She must then demonstrate that the segment connecting P and Q is equal to half the length of the third side. To do this, Vega must calculate the distance between P and Q and then compare it to the length of the third side. If the two measurements are equal, then Vega will have proven her point. This statement can be rephrased as "the length of the segment connecting P and Q is equal to half the length of the third side."

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The inverse of a square root function looks like a half parabola when we plot it on the graph.

Curved graphs of square root functions are typical. In actuality, the curve above is a parabola's half that is lying on its side. On a graph of the equation y² = x, it represents one half of the parabola.

A quadratic function is defined as f(x) = ax² + bx + c, where a, b, and c are all integers and an is not equal to zero. The graph of a quadratic function has the form of a parabola.

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An inequality in math is a statement that compares two values using an inequality sign. Inequalities can be used to describe a range of values, such as greater than, less than, greater than or equal to, and less than or equal to.

For example, the inequality 7 > 5 states that the value 7 is greater than the value 5. This type of inequality is known as a strict inequality, meaning that the values must be greater or less than one another in order for the statement to be true.

Another type of inequality is a non-strict inequality, which uses the symbols “≥” and “≤”. Here, "greater than or equal to" and "less than or equal to" are the appropriate definitions. For example, the inequality 5 ≤ 7 states that the value 5 is less than or equal to the value 7. This type of inequality allows the values to be equal to each other, rather than just strictly less or greater than one another.

Inequalities are used in a variety of mathematical equations, including linear equations, quadratic equations, and polynomial equations. They can also be used to solve for unknown values, such as the solution to an equation. Inequalities are also used to describe ranges of values, such as the range of numbers on a number line.

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Circle M has a center (h+d, k+e) and the radius is rs. Therefore, option C is the correct answer.

A translation in math moves a shape left or right and/or up or down. The translated shapes look exactly the same size as the original shape, and hence the shapes are congruent to each other. They just have been shifted in one or more directions.

Given that, circle B has a center (h, k) and a raius of r. Circle B is translated d units to the right and e units up. Then it is dilated about its new center by a scale factor s resulting in a new circle

Translation rules:

When the shape is moved towards the right by k units, then replace x with x + k.

When the shape is moved up by k units, then replace y with y + k.

Now, (h, k)→(h+d, k+e) and the radius is rs.

Therefore, option C is the correct answer.

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Answer: 1.5

Step-by-step explanation: 12/8=1.5

Answer:

One pound of peanuts costs 1 dollar and 50 cents.
Ten pound of peanuts costs 15 dollars.

Step-by-step explanation:

1. If 8 pounds of peanuts cost $12 how much does 1 pound of peanuts cost?
One pound of peanuts costs 8 times less:

$12 : 8 = $1.5 = 1 dollar and 50 cents

2. Use the answer to find how much 10 pounds cost:
Ten pounds of peanuts will cost 10 times more than one pound:

$1.5 x 10 = $15

Answer:

the correct answer would be "the team that installs the new pools" and "the employees who clean and maintain pools" are services provided by this business to its customers, as they are actively performing tasks for the customer related to swimming pools.

O pool cleaning is a service that is provided by this business to its customers.

The correct option is C. The team that installs the new pools.

Business-to-consumer (B2C) refers to the process of selling goods and services directly between an organization and the customers who will ultimately use them. The majority of businesses that sell directly to customers are referred to as B2C businesses.

The correct answer would be "the team that installs the new pools" and "the employees who clean and maintain pools" are services provided by this business to its customers, as they are actively performing tasks for the customer related to swimming pools. Pool cleaning is a service that is provided by this business to its customers.

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hope it helps you

Step-by-step explanation:

hope it helped you

4(6x³ -2x² + 1) is the  polynomial expression  with GCF 4.

Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables

The polynomial expression is 24x³ - 8x² + 4

We have to write this polynomial expression in the factored from by taking GCF.

Rewrite 24 as 4×6

8 as 4×2

24x³ - 8x² + 4

4(6x³ -2x² + 1)

Hence, 4(6x³ -2x² + 1) is the  polynomial expression  with GCF 4.

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The total salary of Saul is given by the equation A = $ 1,740

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total salary of Saul be represented as A

Now , the equation will be

The basic monthly salary of Saul = $ 1,500

The total commission percentage of Saul = 4 %

The minimum amount of items to sell = $ 20,000

The amount of items worth sold = $ 26,000

So , the extra amount of items sold by Saul = 26,000 - 20,000 = $ 6,000

Now ,

The total salary of Saul A = basic monthly salary of Saul + ( commission percentage x extra amount of items sold by Saul )

Substituting the values in the equation , we get

The total salary of Saul A = 1,500 + ( 4 % x 6,000 )

On simplifying the equation , we get

The total salary of Saul A = 1500 + ( 4/100 ) x 6,000

The total salary of Saul A = 1500 + 240

The total salary of Saul A = 1,740

Hence , the total salary including the commission is $ 1,740

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Answer: Circle 3

Step-by-step explanation:

There are p plates, and 4 are unable to be used, so the expression is p - 4 = Circle 3

Answer:

c

Step-by-step explanation:

Because the number of plates on the table minus 4 saved for dessert mean p-4

The slope of line 3x-7y=9 is 3/7.

The equation for the slope of a line and the points also called a point-slope form of the equation of a straight line is given by:

y − y₁ = m(x − x₁)

If P(x₁,y₁) and Q(x₂,y₂) are the two points on a straight line, then the slope formula is given by:

Slope,m = Change in y-coordinates/Change in x-coordinates

m=(y₂–y₁)/(x₂– x₁)

First, rewrite this to isolate y.

7y = 3x - 9

y = (3/7)x - (9/7)

In this form, the slope is given by the number multiplying the x, so the slope is 3/7

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Answer:

  (x, y) = (2, 4)

Step-by-step explanation:

You want to solve the system of equations ...

There are numerous ways to solve this system of equations. One of the simplest is to use a graphing calculator. (See the attachment)

  (x, y) = (2, 4)

The second equation gives an expression for x that can be substituted into the first equation:

  y = -2(y -2) +8

  3y = 12 . . . . . . . . add 2y and simplify

  y = 4

  4-2 = x = 2

The solution is (x, y) = (2, 4).

The y-variable has a coefficient of 1 on the left side of the equal sign, so we can eliminate the y-variable by subtracting the second equation from the first.

  (y) -(y -2) = (-2x+8) -(x)

  2 = -3x +8 . . . . . . . . . . . simplify

  3x = 6 . . . . . . . . . . add 3x-2

  x = 2 . . . . . . . . divide by 3

  y = -2(2) +8 = 4 . . . . . substitute for x in the first equation

The solution is (x, y) = (2, 4).

Sublimation is the straight transition from a solid state of materials to a vapor state upon heating (without becoming liquid).

When a substance changes from one state to another, as as from a solid to a gas, this transition, transformation, or conversion is referred to as sublimation.

Sublimation is the procedure through which a material is converted from its solid to gaseous phase without moving to its liquid form. At a temperature and pressure below the substance's triple point, this process, an endothermic phase transition, takes place. The opposite of this process, in which a gas is transformed straight into a solid state, is desublimation or deposition.

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An isosceles right triangle has a right angle (90 degrees) and two congruent acute angles(45 degrees).

A triangle's isosceles quality is characterised by its two equal-length sides. The third side which is not equally long as the first two is referred to as the base. The legs are the two equal sides. The vertex opposite the base has an obtuse, acute, or straight angle, and the angles at that vertex are congruent.

A right angle of 90 degrees and two congruent acute angles make up an isosceles right triangle (45 degrees). A right triangle has three angles, two of which are acute and one of which is always a right angle (90 degrees). Because the two legs of an isosceles right triangle are congruent, the two acute angles are likewise congruent. An isosceles right triangle, therefore, has angles of 90 degrees, 45 degrees, and 45 degrees.

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Yes, it is possible to order a list of numbers by their number of words. To do this, you will need to count the number of words in each number, then order them in ascending or descending order based on this number.

Here is an example of how to do this:

1. Count the number of words in each number. For example, the number “twenty-nine” has two words (“twenty” and “nine”).

2. Order the numbers from least to greatest or greatest to least based on the number of words. For example, “nine” has one word, so it would come before “twenty-nine” which has two words.

3. Place the numbers in order from least to greatest or greatest to least.

This method can also be used to order numbers that are written in words or numbers that are written in numerals. However, if the numbers are written in numerals, you will need to convert them to words before you can count the number of words.

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[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{f(x) = 8x + 3}\\\mathsf{f(x) = 8x + 3}\\\mathsf{f(x) = 8(3) + 3}\\\mathsf{f(x) = 24 + 3}\\\mathsf{f(x) = 27}\\\\\huge\text{Therefore, your answer could possibly be: }\\\huge\boxed{\mathsf{f(x) = 27}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

[tex] \sf \: f(3) = 27[/tex]

Step-by-step explanation:

Given function,

→ f(x) = 8x + 3

Now the value of f(3) will be,

→ f(x) = 8x + 3

→ f(3) = 8(3) + 3

→ f(3) = 24 + 3

→ [ f(3) = 27 ]

Hence, the value of f(3) is 27.