X 1 3 5 7
у -9 -17 -25 -33
find the equation of the linear function represented by the table in slope intercept form
​

The equation for hyperbola with given foci is [tex]\frac{(x+3)^{2}}{49}-\frac{(y-6)^{2}}{32}=1[/tex]

What is hyperbola?

In analytical geometry, a hyperbola is a conic section that results from the intersection of a plane with a double right circular cone at an angle that touches both of the cone's halves. The two distinct unbounded curves that result from the intersection of the plane and cone are known as hyperbolas.

The standard equation of a horizontal hyperbola with center (h,k) is

[tex]\frac{(x-h)^{2}}{a^{2} } -\frac{(y-k)^{2}}{b^{2} }=1[/tex]

The given hyperbola has vertices at (–10, 6) and (4, 6).

The length of its major axis is 2a= 4-(-10)

2a=14

a=7

The center is the midpoint of the vertices (–10, 6) and (4, 6).

The center is [tex](\frac{-10+4}{2} , \frac{6+6}{2} )= (-3,6)[/tex]

Now, we need to use the relation a^2+b^2=c^2 in order to find b^2.

The c-value is the distance from the center (-3,6) to one of the foci (6,6)

c= 6-(-3)=9

So, 7^2+b^2=9^2

b^2= 9^2-7^2

b^2= 81-49

b^2= 32

Hence, on substituting the obtained values in the standard equation of hyperbola, we get

[tex]\frac{(x-(-3))^{2} }{7^{2}}-\frac{(y-6)^{2} }{32} =1[/tex]

[tex]\frac{(x+3)^{2} }{49}-\frac{(y-6)^{2} }{32} =1[/tex]

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answer: -3 lmk if you want an explanation!

If a company has issued 8% debentures of INR 10 each at a 10% discount repayable after 10 years. then the cost of capital or pretax cost of debt is 8%.

A bond or other sort of financial instrument that is secured by collateral is referred to as a debenture. Debentures must rely on the issuer's trustworthiness and reputation for support because they lack a collateral backstop. Debentures are commonly issued by both businesses and governments to raise cash or money. The interest paid on these security can be termed as cost of Debt or pretax cost of Debt.

The pretax cost of debt is interest paid on debenture security without giving effect of corporate tax on the rate of interest to be yearly or as per terms and conditions attached to it.

When debt security issued on discount then the loss on issue of these debenture instrument shall also be form part of cost of security or cost of capital.

Thus the year one pretax cost of  Debt capital will be Rs. 1 per debenture and 8% cost of debt.  

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Answer:

Since the term "3" contains no variables, "3" IS a constant term. In the expression 2x - 5 the constant term is -5.

On solving the provided question, we can say that - As a result, Orthocenter triangle is the answer to the given triangle issue (0, - 5 ).

Three sides and three vertices make up a triangle, which is a polygon. It is among the fundamental forms in geometry. Triangle ABC is the name given to a triangle with vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are found. A triangle is a polygon that has three sides and three corners. The spots where the three sides join end to end make up the triangle's corners. Three triangle angles added together equal 180 degrees.

determine LN's slope.

[tex]m = (y2 - y1)/ (x2- x1) = 1-5/8-0 = 2[/tex]

formula for altitude

[tex]y - 1 = 2(x - 3) (x - 3)\\y - 1 = 2x - 6\\[/tex]

y = 2x - 5

Altitude of N and LM

[tex]m = (y2 - y1)/ (x2- x1) = 1-5/3-0 ⇒ -3/4\\y - 1 = (x - 8) (x - 8)\\y - 1 = x - 6\\[/tex]

y = x - 5

[tex]8x - 20 = 3x - 20\\5x - 20 = - 20 \\5x = 0 = > x = 0\\[/tex]

y =0 - 5 = - 5

It is the orthocenter (0, - 5 )

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Answer:

Part A: The equation of the planet's orbit is simply the equation of a circle with radius 70 (half the diameter) and center at the origin. The standard form equation of a circle with radius r and center at (h,k) is (x-h)^2 + (y-k)^2 = r^2. In this case, h and k are both 0, so the equation of the planet's orbit is simply x^2 + y^2 = 70^2.

Part B: The equation of the comet's path is a parabola with directrix x=100 and vertex at (85, 0). The standard form equation of a parabola with directrix x=p, vertex at (h,k), and focus at (h,k+f) is y = (4f/p^2)(x-h)^2 + k. In this case, p=100, h=85, k=0, and f is the distance from the vertex to the focus. We can find f by using the equation f = sqrt(p^2+4ah), where a is the distance from the vertex to the directrix. In this case, a=50, so f = sqrt(100^2+45085) = 50. Plugging this value into the equation for the parabola, we get y = (4*50/100^2)(x-85)^2 + 0. Simplifying this gives us y = (2/25)(x-85)^2.

Part C: To find the points where the planet's orbit intersects the path of the comet, we need to find the points where the x and y coordinates of the two equations are equal. Setting the two equations equal to each other gives us (2/25)(x-85)^2 = x^2 + y^2 - 70^2. Expanding the left side and rearranging the terms gives us x^2 - 170x + 15129 = 0. We can use the quadratic formula to find the solutions for x: x = (170 +/- sqrt(170^2 - 4115129))/2. This simplifies to x = 85 +/- sqrt(40900). Therefore, the points of intersection are (85 + sqrt(40900), 0) and (85 - sqrt(40900), 0). Rounding these values to the hundredths place gives us (92.84, 0) and (77.16, 0).

The formula needed to transform a quadratic polynomial or equation into a perfect square with an additional constant is known as the square formula. It is expressed as, [tex]ax^2 + bx + c = a(x + m)^2 + n[/tex], where, m and n are real numbers.

When a square is complete, a quadratic is written in the shape of a squared bracket, and if necessary, a constant is added. A good example is [tex]x^2 + 6x + 7[/tex] . First, let's note that [tex](x + 3)^2 = (x + 3)(x + 3) = x^2 + 6x + 9. x[/tex]  because this is two more than our expression.

The polynomial equations of degree two in one variable of type[tex]f(x) = ax^2 + bx + c = 0[/tex] and with a, b, c, and R R and a 0 are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" for the absolute term of f(x).

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The second step of calculating the present value of an ordinary annuity by the table lookup is to look up the periods and rates in the PV annuity table.

The present value of an ordinary annuity is the current value based on future cash inflows of the annuity, given a specified discount rate.

The present value is higher when the discount rate is lower, and vice versa.

The present value of an ordinary annuity, which discounts the annuity to the current time, is computed as Annuity Payment x Present value of the ordinary annuity table.

In conclusion, an annuity simply means a series of periodic payments and may involve payment at the beginning (annuity due) or at the end of the period (ordinary annuity).

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Answer:

  See attached

Step-by-step explanation:

You want various combinations of the functions g(a) = -3a+1 and h(a) = 3a³ +4a.

The functions have no common factors, so their ratio leaves the function expressions unchanged:

  [tex]\dfrac{g(a)}{h(a)}=\boxed{\dfrac{-3a+1}{3a^3+4a}}[/tex]

The like terms are combined when the functions are added.

  [tex]h(a)+g(a)=(3a^3+4a)+(-3a+1)=3a^3+(4-3)a+1\\\\=\boxed{3a^3+a+1}[/tex]

Similarly, the like terms are combined when the functions are subtracted.

  [tex]g(a)-h(a)=(-3a+1)-(3a^3+4a)=-3a^3+(-3-4)a+1\\\\=\boxed{-3a^3-7a+1}[/tex]

The product is found the way products are usually found. Each term of one of the factors is multiplied by each term of the other factor, and these products are summed. You can think of it as repeated application of the distributive property.

  [tex]g(a)\cdot h(a)=(-3a+1)(3a^3+4a)=-3a(3a^3+4a)+1(3a^3+4a)\\\\=-9a^4-12a^2+3a^3+4a\\\\=\boxed{-9a^4+3a^3-12a^2+4a}[/tex]

We add  (x +7 ) (x - 10) up to -3 and multiply to -70.

What is a quadratic equation?

Any equation in algebra that can be written in the standard form where x denotes an unknown value and a, b, and c denote known numbers, where a 0 is a quadratic equation.

Here,

We illustrate and prove that -9 and 10 multiply to -90 and add up to 1:

7 × -10 = -70

-10 + 7 = -3

We are trying to determine how to factor the following quadratic equation.

x²  -3 x - 70 = 0

If so, the solution to factor the quadratic equation above is:

(x +7 ) (x - 10)

To summarize, -10 and 7 multiplied by -70 and add up to -3, you know that the following is true:

x² -3x - 70

= (x +7 ) (x - 10)

Hence, we add  (x +7 ) (x - 10) up to -3 and multiply by -70.

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Answer:

it's B

[tex] - \frac{9}{4} + 2i = - \frac{9}{4} - 4i[/tex]

Answer:

C

Step-by-step explanation:

please refer to the sketch

Answer:

x=4, y =5

Step-by-step explanation:

there's no factorization involved, just elimination and substitution. First subtract equation 1 and 2. The x's cancel out and you get y by itself and can solve for it. Then plug the value of y into equation 2 and solve for x and you get it. (In my picture I put value of y in equation 1 but your question asks for putting it in equation 2 so do that instead)

As a result, the necessary linear equations for the rectangle's area and perimeter are y = 18[x - 1] and z = 6[x + 1], respectively.

An object's surface area is a measurement of the total volume of space that it occupies. The entire region surrounding a three-dimensional shape is referred to as its surface area. Its surface area is the total area of a three-dimensional shape. By adding the surfaces of each of a cuboid's six rectangular sides, one may determine the cuboid's surface area. The box's dimensions could also be named using the following formula: Surface (SA) = 2lw + 2lh + 2hw. A three-dimensional shape's surface area is a measurement of the total area it occupies (a three-dimensional shape is a shape that has height, width, and depth).

given

here,

Length  = 3x + 3

Width = 6

Area of the rectangle = y, = length × width

y = [3x - 3 ] × [6]

y = 18x - 18 = 18[x -1]

Perimeter of the rectangle = 2[length + width]

z = 2 [3x + 3]

z = 6[x + 1]

As a result, the necessary linear equations for the rectangle's area and perimeter are y = 18[x - 1] and z = 6[x + 1], respectively.

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The correct question is :- Write a linear equation that represents the area and a linear equation that represents the perimeter of the rectangle (3x-3) cm and 6 cm .

The amount of change that Tina got back would be = $10

The amount of hours Tina spent in canoeing = 6 hours

The amount paid per hour for canoeing = $4

Therefore the total amount spent on canoeing = 6×4 = $24

The cost of the life jacket = $6

Therefore the total amount Tina spent = total amount spent on canoeing + cost of the life jacket.

That is; 24+6 = $30

The change Tina will receive from the two twenty dollars bills = (2×20) - 30

= 40-30 = $10

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Answer:hope this helps!

1. Step-by-step explanation:

there is a blanket costing 112

and a chair costing 113

after going to the register you find that the total is

225

2. Step-by-step explanation:

there is a printer costing 112

and a laptop costing 113

after going to the register you find that the total is

225

3. Step-by-step explanation:

there is a pillow costing 112

and some makeup  costing 113

after going to the register you find that the total is

225

hope this helps i was in a rush so sorry if it was bad

Answer:

Side BC: y = -2x + 10

Side AC: y = 2x + 4

Yes, these three points could form a right triangle. This is because the slopes of the two lines, Side BC and Side AC, are opposite reciprocals of each other. This means that when the two lines intersect, they will form a right angle.

Each of the questions should be correctly classified as statistical or not statistical as follows:

In Mathematics, a statistical question can be defined as a type of question in which the resulting answer is in the form of an average, percentage, or a range such as "How many TV shows did each student in my class watch yesterday?"

A non-statistical question simply refers to a question that is not non-statistical and it can be defined as a type of question which has an exact or fixed answer such as "How many students in my class can swim?"

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Answer:

Rate of change= 1/3

Initial value = -4

Step-by-step explanation:

The rate of change is rise/run = 1/3.

the initial value is the y-intercept which is -4.

the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

to get the slope of any straight line, we simply need two points off of it, let's use those two in the picture below

[tex](\stackrel{x_1}{-6}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-3}-\stackrel{y1}{(-6)}}}{\underset{\textit{\large run}} {\underset{x_2}{3}-\underset{x_1}{(-6)}}} \implies \cfrac{-3 +6}{3 +6} \implies \cfrac{ 3 }{ 9 } \implies \cfrac{1 }{ 3 }[/tex]

now as far as the "initial value", dunno what that means.

The start of the line? well, the line by definition goes to infinity both ways.

the y-intercept? well, just look at the graph, the graph intercepts the y-axis when x = 0 and y = -4, so at (0 , -4).

Answer:

How are algebraic expressions used to represent and solve problems?

The purpose of solving an algebraic expression in an equation is to find the unknown variable. When two expressions are equated, they form an equation, and therefore, it becomes easier to solve for the unknown terms. To solve an equation, place the variables on one side and the constants on the other side.

Step-by-step explanation:

How can you use algebraic expressions to solve problems?

To solve an algebraic word problem:

1. Define a variable.

2.Write an equation using the variable.

3.Solve the equation.

4.If the variable is not the answer to the word problem, use the variable  

   to calculate the answer.

How are algebraic expressions applied in real life situations?

utilizing linear algebra, and this uniqueness starts to expose a lot of applications. Other real-world applications of linear algebra include ranking in search engines, decision tree induction, testing software code in software engineering, graphics, facial recognition, prediction and so on.

What is algebraic expression why it is used in mathematics?

In mathematics, an algebraic expression is an expression built up from integer constants, variables, and the algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number). For example, 3×2 − 2xy + c is an algebraic expression.

The simple interest for principal of 640 and rate of 3% and time of 2 years is $3.84

The Simple interest the end of 2 years is calculated using the simple interest formula

The formula is stated as

Simple interest = Principal *  time *  rate / 100

In the problem the give data include

principal = $640

rate= 3%

time = 2 years

plugging in the values

Simple interest = Principal *  time *  rate / 100

Simple interest = 640 * 2 * 3 /100

Simple interest = 3840 / 100

Simple interest = $3.84

The simple interest  is $3.84

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The polynomial 4 · x³ is a monomial of degree 3.

In algebra there are two types of numbers: constants and variables. Constants are constant real numbers, while variables are real numbers that may represent more than a real number.

Polynomials are the result of combination of constants, variables and fundamental operators (addition, multiplication) and can be classified according to the number of terms:

Monomial - Polynomial with one term.

Binomial - Polynomial with two terms.

Trinomial - Polynomial with three terms.

Polynomial - Polynomial with four or more terms.

The grade of the polynomial is the maximum power that accompany a term in a polynomial in standard form. Then, we can bring an example of polynomial with a degree 3 below:

p(x) = 4 · x³

This is a monomial (polynomial with one term) with degree 3.

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Answer:

53/75

Step-by-step explanation:

15 = 3 × 5

25 = 5²

PPCM = 3 × 5² = 75

75/15 = 5

75/25 = 3

7/15 + 6/25 =

= (7 × 5)/(15 × 5) + (6 × 3)/(5 × 3)

= 35/75 + 18/75

= 53/75

The model lies between 0 and 1 on the number line.We can find by dividing number and then add both of number.

The real number line is a horizontal line with arrows on both sides. It consists of the origin “0”. All the positive numbers are represented on the right side of the origin and all the negative numbers are represented on the left side of the origin, with a definite scale.

A number line model is a representation of numbers plotted on an infinite line that extends at both ends.It is a visual representation of numbers on a straight line. This line is used to compare numbers that are placed at equal intervals on an infinite line that extends on both sides horizontally or vertically.

Now we find

-2/4 =-0.5

3/4= 0.75

0.75- 0.5=0.25

which is lies between 0 and 1 on the number line.

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Answer:

[tex]\boxed{\boxed{\sf x=1}}[/tex]

Step-by-step explanation:

[tex]\sf 25x^2=-25+50x[/tex]

Simplify both sides of the equation:-

[tex]\sf 25x^2-50x=-25[/tex]

Subtract 50x-25 from both sides:-

[tex]\sf 25x^2-(50x-25)=50x-25-(50x-25)[/tex]

[tex]\sf 25x^2-50x+25=0[/tex]

Factor left side of equation:-

[tex]\sf 25(x-1)(x-1)=0[/tex]

Set factors equal to 0:-

[tex]\sf x-1=0\: or\: x-1=0[/tex]

[tex]\sf x=1[/tex]

___________________

Hope this helps!

Have a great day!

The data provided in the table implies that Alonzo's Cycling should produce five or six bikes if it wants to maximize its profits.

Profit maximization is a process that businesses go through to make sure the best levels of output and prices are realized in order to maximize their returns. The company modifies important variables like sale price, production costs, and output levels in order to achieve its profit objectives.

This is because the sixth bike is the point at which the marginal revenue matches the marginal cost. The company will make $90 in profit with the sale of its fifth or sixth bike each day. After that, the profit begins to fall with each sale.

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Answer: y= -3/4x+8

Step-by-step explanation:

Answer: 2.) Blue and red

Step-by-step explanation:

The slope of the red and blue ones is - 3 while the green one's slope is -4

False

The parent function is the simplest function within a family of functions that defines the general form of that family.

Parent Functions

Parent functions are given in terms of y and x, where y is the output and x is the input. In linear functions, b represents a constant, specifically the y-intercept. Since the form y=b does not have an input it cannot be the parent function of linear lines. The graph of y=b would be a horizontal line with no slope. This does not define the general form of most linear functions. Additionally, since the slope has been changed to zero, it is not considered the simplest form of linear functions.

Linear Parent Function

The true parent function of linear functions is y=x. This function is the simplest linear function and has no transformations. Additionally, when graphed it is a diagonal line that defines the general shape of lines.

To create new linear functions the parent function, y=x, can be transformed by changing the coefficient of x to change the slope or by adding a constant to shift the graph vertically.

The total number of muffins in 4 boxes by the arithmetic equation is (4 × 10) + (4 x 3) = 52.

The series where the common difference between any two next words stays constant is known as an arithmetic sequence. Let's review what a sequence is. A collection of numbers that follow a pattern is called a sequence.

Every term in an arithmetic sequence is created by adding a specified number (either positive, negative, or zero) to the term before it.

the number of boxes of muffins is 4

The muffins in each box is 13

so the total number of muffins in 4 boxes is 4 x 13

⇒ 4 x (10 + 3)

⇒ (4 x 10) + (4 x 3) = 52

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Radicals

Let's organize what the problem gives us.

We are given an expression to simplify:  [tex]\displaystyle (\sqrt{22})(5 \sqrt{2})[/tex]

Recall the specific rules to simplify radicals. We will apply those rules here to help us answer the question:

[tex]\displaystyle\begin{aligned}(\sqrt{22})(5 \sqrt{2}) & = 5 \sqrt{44} \\& = 5 \sqrt{4 \cdot 11} \\& = (5 \sqrt{4})(\sqrt{11}) \\& = (5 \cdot 2)(\sqrt{11}) \\& = \boxed{ 10 \sqrt{11} }\end{aligned}[/tex]

∴ the expression (√22)(5√2) simplifies down to 10√11.

∴ the expression in simplified form is equal to A. 10√11.

___

Topic: Pre-Algebra

Unit: Radicals