Suppose f is a function. If f(6) = -9, give an ordered pair of numbers that is a solution of the function.

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: 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

Therefore , As a result 5, 10, and 15 make up the reasonable domain for the function 2 (l + w) = 64..

A connection between a group of sources and one output for each input is referred to as a function. A function is, to put it simply, a collection of equation  connected to a single, unique output. In mathematics, a function is a statement, rule, or law that describes the connection between two variables (the dependent variable). One input leads to one output when a rule of this type is used. by Alex Federspiel, the photographer. This statement gives an example of y=x2. There is just one output for y from any input for x. According to our definition, y is a function of x since x is the input value.

Here,

We have the following for the rectangle's perimeter:

2 ( l + w ) = 64

Here,

W = width, and L = length.

We must determine the length and breadth values necessary to make the rectangle's perimeter 64.

Now,

2 ( l + w ) = 64

l + w = 32

Thus, the sum of the length and breadth measurements must equal 32.

The possible widths are 5, 10, 15, 20, and 25.

Now,

l + 5 = 32

l = 27

l + 10 = 32

l = 22

l + 15 = 32

l = 17

l + 20 = 32

l = 12

l + 25 = 32

l = 7

We think about

The domain has widths of 5, 10, 15, 20, and 25.

The range for length is: 27, 22, 17, 12, and 7.

Values for width and length are used as the x- and y-axes, respectively.

Below is a graph of the data.

The following is the reasonable domain for the aforementioned situation:

5, 10, 15, 20, and 25

Below is a graph of the function 2 (l + w) = 64.

Therefore , As a result, 5, 10, and 15 make up the reasonable domain for the function 2 (l + w) = 64.

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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:

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.

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!

If Goran invested his savings in two investment funds. The amount that Goran invest in Fund B, if the total profit from the two funds together was 500?

Amount Invested in Fund  A = x

Amount invested in Fund  B = x+7000

Profit from fund A = 0.04x

Profit from fund B = 0.02(x+7000)

0.04x +0.02(x+7000) = 500

0.04 +0.02x + 140 =500

Combine like terms

0.06 x =360

Divide both side by 0.06x

x = 360 /0.06

x = 6,000

Amount Invested in Fund A = x =6,000

Amount invested in Fund B = x+7000

Amount invested in Fund B = 6,000 + 7,000

Amount invested in Fund B = 13,000

Therefore the amount invested in Fund A 6,000 and the Fund B is 13,000.

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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)

The perimeter of the isosceles triangle with altitude 30 inches and base 10 inches is calculated to be 70.82 inches

Perimeter of a triangle refers to the surface dimensions, this is calculated by the formula

Perimeter, P = a + b + c

where

a, b, c are sides of the triangle

The third side of the triangle will be calculated using Pythagoras theorem given by the  the formula

hypotenuse² = opposite² + adjacent²

The right triangle consist 1/2 the isosceles triangle base = 5 inches and the altitude = 30 inches

plugging the values as in the problem

let x be the required distance

x² = 30² + 5²

x² = 900 + 25

x² =  925

x = √925

x = 30.41 inches

Perimeter of the isosceles triangle

= 30.41 + 30.41 + 10

= 70.82 inches

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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.

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:

  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]

A line with a slope of three and the point three on the line have the equation y=3 z+1. The equation of a straight line can be found using the formula y = mx + b.

If a line has a slope of 3 and a y intercept of 1, you need to determine its equation. Remember the line's equation by first going back: when y=mz+b , M is the slope, and Y-intercept b is the value.

In order to solve for y in the equation y=m z+b, all you need to do is swap out m for 3, the slope you provided, and b for 1, the y-intercept. The line's equation is given by y=3 z+1, where z represents the line's y-intercept and slope. If you are aware of the slope of the line being studied and the provided point is also the y intercept, you can utilise the slope intercept formula, y=mx+b (0,b).

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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

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

Answer: y= -3/4x+8

Step-by-step explanation:

Answer:

Step-by-step explanation:

6

Step-by-step explanation:

hope this is right hehe.....

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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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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The nth term of the following sequence is: 5n²

Arithmetic sequence is a sequence where each consequtive term has a common constant difference.

An arithmetic sequence, therefore, is defined by two parameters, viz. the starting term and the common difference.

We are given the sequence are;

5, 20, 45, 80, 125

The quadratic sequence formula : an²+bn+c

2nd difference 2a = 10

a = 5

1st difference 3a+b = 15

Then substitute 5

3(5)+b = 15

b = 0

The nth term rule : a + b + c = 5

Now substitute a and b values into equation

5 + 0 + c = 5

c = 0

The nth term is: 5n²

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Answer:

y=-3.5

Step-by-step explanation:

substitute -4 for x

add 4 on both sides to get rid of the -4

divide -2 on both sides to isolate y

and you get 3.5 for y

The value of y that will satisfy the equation given is -3.5.

Mathematically, an equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”.

Given that, the missing coordinate in the ordered pair (−4, ?), we need to find the missing value that will satisfy the equation x-2y = 3,

To find the same, just replace the value of x by -4,

-4-2y = 3

-2y = 7

y = -3.5

Hence, the value of y that will satisfy the equation given is -3.5.

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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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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:

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

Therefore, the number of stickers David has in terms of d is d+10 and the number of stickers Matt has in terms of d is 2d-10.

A term is a phrase or statement that is used to convey a certain meaning. Rap, punk, grunge, and heavy metal are examples of words used to characterize certain musical genres. To the majority of people, at least, "sweetie" is a word of affection.

A phrase is a collection of words with significance but which is not usually a complete sentence. A set of words that form a sentence must have a topic.

We know that Matt has twice as many stickers as David, so if David has d stickers, then Matt has 2d stickers.

When Matt gives David 10 stickers, David has d+10 stickers and Matt has 2d-10 stickers.

So the number of stickers David has in terms of d is d+10 and the number of stickers Matt has in terms of d is 2d-10.

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Answer:

-50

Step-by-step explanation:

Answer:

Step-by-step explanation:

if she had $150 in he bank account and buys a bike that costs 200 she possibly can't afford it since she is $50 dollars short so even if she borrows $50 dollars she has to repay the person 50 dollars before she starts earning another money so i think it is -50. if it doesn't help am sorry I hope you got this answer correct. goodluck

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 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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