the distance between the points (12,9) and (0,4) is A) 14 units B) 13 units C) 15 units D) 16 units

1. Domain: The set of natural numbers / Range: The set of natural numbers

2. Shown below

In this problem, we have that the number of frogs in a certain lake is inversely related to the number of snakes in the lake. Hence we are facing an Inverse Variation, so this means that if the number of snakes in the lake increases then the number of frogs in the lake decreases, because snakes eat frogs! The function that describes this is a rational function defined as:

[tex]y=\frac{100}{x}[/tex]

Where:

[tex]x: \ represents \ the \ number \ of \ snakes \ in \ the \ lake \\ \\ y: \ represents \ the \ number \ of \ frogs \ in \ the \ lake[/tex]

As you can see, [tex]x[/tex] is in the denominator, therefore [tex]x\neq 0[/tex]. Since we need to provide a reasonable domain, we say that  the domain is the set of natural numbers and this doesn't include the number 0. Why aren't negative values included in the domain as well? Well, although negative values are included in the function, they aren't reasonable because [tex]x[/tex] represents the number of snakes and you always get positive numbers when counting things.

To get the range, let's take the inverse of this function, so:

[tex]y=f(x)=\frac{100}{x} \\ \\ \\ Interchange \ x \ and \ y: \\ \\ x=\frac{100}{y} \\ \\ \\ Isolate \ y: \\ \\ y=\frac{100}{x} \\ \\ f^{-1}(x)=\frac{100}{x}[/tex]

So the domain of [tex]f^{-1}(x)[/tex] is the range of our given function [tex]y=f(x)[/tex]. As you can see the inverse function is the same as our given function, then the range is the set of natural numbers as well.

First of all, we can define the pattern of the rational function as:

[tex]y=g(x)=\frac{1}{x}[/tex]

So our function will be:

[tex]f(x)=100g(x)=100\frac{1}{x}=\frac{100}{x}[/tex]

So the graph of [tex]f(x)[/tex] will be the same graph of [tex]g(x)[/tex] but it's been stretched vertically by a constant of 100, that is, each y-value is multiplied by 100. Also, since [tex]x \neq 0[/tex] and [tex]y \neq 0[/tex] then at [tex]x=0[/tex] there is a vertical asymptote and at [tex]y=0[/tex] there is an horizontal asymptote. Finally, the graph is shown below for [tex]x>0 \ and \ y>0[/tex], but remember: Whenever [tex]x \ and \ y[/tex] are natural numbers.

Answer:

Both the number of snakes and the number of frogs will be positive, so positive values are reasonable for the domain and range.

Step-by-step explanation:

Answer:

Step 2: 4(2) + 4(3x)

Step-by-step explanation:

By definition, the area of a rectangle is given by:

Area = Length × Width

In this case, we know that:

Area = 8 + 12x

Width = 4

Therefore:

Step 1: 8 + 12x

Step 2: 4(2) + (4)(3x)

Step 3: 4(2 + 3x)

Therefore, the dimensions of the rectangle are 4 and 2 + 3x.

The mistake was made in STEP 2. Instead of 4(2) + 4(x2) it should be  4(2) + 4(3x). Which is the second option.

Answer: [tex]-\frac{8}{5}[/tex]

Remember: RISE/RUN (y/x). Lines that are increasing have a positive slope, and lines that are decreasing have a negative slope.

You can find the slope in two ways:

1. Useful if the line is graphed: count the units between 2 points on the line.

2. Useful if the line is not graphed: find the difference between the y-coordinate values divided by the difference of the x-coordinate values.

Answer:

[tex]m=-\frac{8}{5}[/tex]

Step-by-step explanation:

Let

[tex]A(-1,4),B(4,-4)[/tex]

we know that

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

substitute the values

[tex]m=\frac{-4-4}{4+1}[/tex]

[tex]m=\frac{-8}{5}[/tex]

[tex]m=-\frac{8}{5}[/tex]

Answer:

I believe it is the third one (C)

Step-by-step explanation:

Hello There!

Your answer would be the first one.

f(x) = \x/

F of x has to equal f of -x

Answer:

(-7, -3) (Answer A)

Step-by-step explanation:

We start with the point (-7, -3).  The x-coordinate does not change at all if we reflect this point across the x-axis.  Whereas the y-value of (-7, -3) is -3, we end up with +3 after this reflection.  The desired image is (-7, +3)  (Answer A)

The coordinates of the point (-7, - 3) reflected along the x-axis is

(- 7, 3).

Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.

Dilation: The preimage is scaled up or down to create the image.

Reflection: The picture is a preimage that has been reversed.

Rotation: Around a given point, the preimage is rotated to create the final image.

Translation: The image is translated and moved a fixed amount from the preimage.

We know reflection along the x-axis of a point (x, y) converts it into a

point (x, - y).

Given, A points (-7, - 3) is reflected along the x-axis.

Therefore, The new coordinates of the points (-7, - 3)  reflected along the x-axis is (- 7, 3).

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[tex] \frac{12 {a}^{2} {b}^{3} }{3ab } \\ = \frac{3 \times a \times b \times 4 \times a \times {b}^{2} }{3ab} \\ \\ cancelling \: common \: factors \\ \\ = 4a {b}^{2} [/tex]

Hence answer is 4ab²

Hope it helps...

Hope it helps...Regards;

Hope it helps...Regards;Leukonov/Olegion.

Answer:

5 miles apart

Step-by-step explanation:

(4,-6) is 5 units away from (9,-6)

Answer:

B: 4x − 2y = 2

B: 4x − 2y = 2  equation completes the system that is satisfied by the solution (1, 1).

A linear equation has one or two variables.

solving this we will get the valve of Y if x is given.

explanation:

line R = x + y = 2

putting the value of X=1 & y=1 as given (1,1)

x+y =2

1+1= 2

therefore, 4x - 2y = 2

4(1) - 2(1)= 2 answer

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Line graph because it shows differences

Answer:

* The monthly mortgage payment is $629.53 ⇒ answer C

Step-by-step explanation:

* Lets explain how to solve the problem

- Leila is considering buying her first home

- The house she is interested in buying is priced at $125,000

∴ She can put $20000 down  payment

* Lets find the balance to be paid off on mortgage

∴ The balance = 125000 - 20000 = 105000

- She qualifies for a 30-year mortgage at 6%

* Lets find the rule of the monthly payment

∵ [tex]pmt=\frac{\frac{r}{n}[P(1+\frac{r}{n})^{tn}]}{(1+\frac{r}{n})^{tn}-1}[/tex] , where  

- pmt is the monthly mortgage payment

- P = the initial amount  

- r = the annual interest rate (decimal)

- n = the number of times that interest is compounded per unit t

- t = the time the money is invested or borrowed for

∵ P = 105000

∵ r = 6/100 = 0.06

∵ n = 12

∵ t = 30

∴ [tex]pmt=\frac{\frac{0.06}{12}[105000(1+\frac{0.06}{12})^{30(12)}}{(1+\frac{0.06}{12})^{30(12)}-1}[/tex]

∴  [tex]pmt=\frac{0.005[105000(1.005)^{360}]}{(1.005)^{360}-1} =629.528[/tex]

* The monthly mortgage payment is $629.53

Answer:

4u= - 4i - 24j

u +w = -9i - 3j

Step-by-step explanation:

The question is on operation of vectors

Given u= -i -6j  and w= -8i+3j

Then 4u = 4{ -i-6j}

4u= - 4i - 24j

u+w= -i -6j + -8i+3j......................collect like terms

= -i -8i + -6j +3j

= -9i + -3j

= -9i - 3j

Answer:

Step-by-step explanation:

Mean, it is the average of all numbers and most accurately represents the data set.

The best measure of central tendency depends on the data set characteristics: the mean is suitable for outlier-free data, the median is better for skewed data or when outliers are present, and the mode indicates the most common value.

Choosing the Best Measure of Central Tendency

When analyzing a data set, selecting the appropriate measure of central tendency is crucial. The three main measures are the mean, median, and mode. The mean is the arithmetic average and is best used when the data set does not contain outliers that can skew the results. The median is the middle value when the data is ordered and offers a better representation when outliers are present. The mode is the most frequently occurring value and provides insight into the most common data point.

In a symmetrical data set where the data are evenly distributed, all three measures of central tendency—the mean, median, and mode—will be equal or close to each other. In a skewed distribution or when the data contains outliers, the median is generally the most reliable measure of the center, as it is unaffected by extreme values.

Answer: A The first Answer to the left

Step-by-step explanation:

The diagram could be used to prove that ABC-EDC  using similarity transformations is option A.

The first Answer to the left

We have given that,

The diagram could be used to prove ABC - EDC using similarity transformations.

A similarity transformation is one or more rigid transformations (reflection, rotation, translation) followed by a dilation.

We have to determine which diagram could be used to prove ABC-EDC.

Therefore the answer is the first diagram.

The diagram could be used to prove that ABC-EDC  using similarity transformations is option A.

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Hey there! :)

We're given the equation : y = 1/3x - 2 & coordinates : (-3, 5)

If we're looking for an equation for a perpendicular line, then we know that the slope of our new equation MUST be the negative reciprocal of the original slope. This means that you flip the slope and add or remove a negative. Example : slope = -2 ⇒ negative reciprocal slope = 1/2

Before using this information, we must first find the slope of our original equation.

Using slope-intercept form, which is : y=mx+b ; where m=slope, b=y-intercept

Ask yourself : which value is in the "m" spot and which value is in the "b" spot?

Using this, we now know that 1/3 is our slope, and -2 is our y-intervept.

So, our negative reciprocal is -3.

Use point-slope form to find the y-intercept, and coordinates (-3, 5)

Point-slope = y - y1 = m(x - x1)

y - 5 = -3(x - (-3))

Simplify.

y - 5 = -3(x + 3)

Simplify.

y - 5 = -3x - 9

Add 5 to both sides.

y = -3x + 4 ⇒ slope-intercept form

~Hope I helped! :)

Answer:

  4. Your working and answers are correct: x = 44, y = 43.

  5. GH = 60°

Step-by-step explanation:

5. Arc GH is double the inscribed angle GFH, so we have ...

  2(4x+2) = 9x-3

  8x +4 = 9x -3 . . . . . simplify

  7 = x . . . . . . . . . . . . add 3-8x

Then the arc's measure is ...

  (9·7 -3)° = (63 -3)° = 60°

Answer:

Step-by-step explanation:

Your working and answers are correct: x = 44, y = 43.

5. GH = 60°

Answer:

Point B is (10 , -4)

Point D is (10/9 , 1)

Step-by-step explanation:

* Lets revise the rule of the point which divides of a line segment in

 a ratio

- If point (x , y) divides the line segment AB, where A is (x1 , y1) and

 B is (x2 , y2) in the ratio m1 : m2

∴ x = [m2(x1) + m1(x2)]/(m1 + m2)

∴ y = [m2(y1) + m1(y2)]/(m1 + m2)

* Now lets solve the problem

- Point C (3.6 , -0.4) divides AB in the ratio 3 : 2, where A is (-6 , 5)

# x = 3.6 , y = -0.4

# A is (x1 , y1) , B is (x2 , y2)

∴ x1 = -6 , y1 = 5

∵ m1 : m2 = 3 : 2

- Substitute these values in the rule

∵ x = [m2(x1) + m1(x2)]/(m1 + m2)

∴ 3.6 = [2(-6) + 3(x2)]/(3 + 2)

∴ 3.6  = [-12 + 3x2]/5 ⇒ multiply both sides by 5

∴ 18 = -12 + 3x2 ⇒ add 12 to both sides

∴ 30 = 3x2 ⇒ divide both sides by 3

∴ 10 = x2

* The x-coordinate of B is 10

∵ y = [m2(y1) + m1(y2)]/(m1 + m2)

∴ -0.4 = [2(5) + 3(y2)]/(3 + 2)

∴ -0.4 = [10 + 3y]/5 ⇒ multiply both sides by 5

∴ -2 = 10 + 3y2 ⇒ subtract 10 from both sides

∴ -12 = 3x2 ⇒ divide both sides by 3

∴ -4 = y2

* The y-coordinate of B is -4

∴ Point B is (10 , -4)

- Point D divides AB in the ratio 4 : 5 where A (-6 , 5) and B (10 , -4)

- To find the coordinates of point D use the same rule above

# D is (x , y)

# A is (x1 , y1) and B is (x2 , y2)

# m1 : m2 is 4 : 5

∵ x1 = -6 and y1 = 5

∵ x2 = 10 and y2 = -4

∵ m1 = 4 and m2 = 5

- Substitute these values in the rule

∵ x = [m2(x1) + m1(x2)]/(m1 + m2)

∴ x = [5(-6) + 4(10)]/(4 + 5) ⇒ multiply the numbers

∴ x = [-30 + 40]/9 ⇒ add

∴ x = [10]/9 ⇒ Divide

∴ x = 10/9

* The x-coordinate of D is 10/9

∵ y = [m2(y1) + m1(y2)]/(m1 + m2)

∴ y = [5(5) + 4(-4)]/(5 + 4) ⇒ multiply the numbers

∴ y = [25 + -16]/9 ⇒ add

∴ y = [9]/9 ⇒ Divide

∴ y = 1

* The y-coordinate of point D is 1

∴ Point D is (10/9 , 1)

Final answer:

To evaluate the expression (-5+7x1)-9x5, follow the order of operations: calculate inside the parentheses, multiply, and then subtract, resulting in a final answer of 47.

Explanation:

To evaluate the expression (-5+7×1)-9×5, we need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction). Let's break down the expression step by step:

Inside the parentheses: -5 + (7 × 1) = -5 + 7 = 2.

Multiply: -9 × 5 = -45.

Subtract the value obtained from step 2 from the result of step 1: 2 - (-45).

Change the subtraction of a negative value to addition: 2 + 45 = 47.

Thus, the expression (-5+7×1)-9×5 evaluates to 47.

250

100 + 200 + 300 + 400 = 1000

1000/4 = 250

Answer:

250

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

Given the 2 equations

x² + y² = 5 → (1)

2x + y = 4 → (2)

Rearrange (2) expressing y in terms of x by subtracting 2x from both sides

y = 4 - 2x → (3)

Substitute y = 4 - 2x in (1)

x² + (4 - 2x)² = 5 ← expand factor on left side

x² + 16 - 16x + 4x² = 5

5x² - 16x + 16 = 5 ( subtract 5 from both sides )

5x² - 16x + 11 = 0 ← in standard form

(5x - 11)(x - 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 1 = 0 ⇒ x = 1

5x - 11 = 0 ⇒ 5x = 11 ⇒ x = [tex]\frac{11}{5}[/tex]

Substitute each of these values into (3) for corresponding values of y

x = 1 : y = 4 - 2 = 2 ⇒ P(1, 2)

x = [tex]\frac{11}{5}[/tex] : y = 4 - [tex]\frac{22}{5}[/tex] = - [tex]\frac{2}{5}[/tex]

Hence Q( [tex]\frac{11}{5}[/tex], -[tex]\frac{2}{5}[/tex] )

Answer:

the other zero is represented by the ordered pair (4, 0)

Step-by-step explanation:

We have the factored expression

[tex]x (x-4)[/tex]

We must find out for what values of x this function is equal to zero.

Then we equal the function to zero and solve for the variable x

[tex]x (x-4)=0[/tex]

The function is equal to zero when one of the two terms of the product is equal to zero.

So

[tex]x =0[/tex]   We already know that this is a solution

or

[tex]x-4=0\\x =4[/tex]

Then the other zero is represented by the ordered pair (4, 0)

Answer:

64

Step-by-step explanation:

To complete the square

add ( half the coefficient of the b- term )² to b² + 16b

b² + 2(8)b + 8²

= b² + 16b + 64 = (b + 8)²

Answer:

Step-by-step explanation:

If you use pemdas, you would do 3÷1/3 which equals 9. Then do 9-9, which equals 0. Then, do 0+1, which equals 1. Hope this helps! <3

[tex]9 - 3 \div \frac{1}{3} + 1 = [/tex]

Divisions go first, to do it we have to reverse the fraction and turn ÷ into ×

[tex] = 9 - 3 \times 3 + 1 = [/tex]

Now the multiplication

[tex] = 9 - 9 + 1 = [/tex]

[tex] = 1[/tex]

Answer:

the answer is d

Step-by-step explanation:

A line segment is best described as a path between two points.

A line segment is a line that is definite from one point to another. The length of a line segment can be measured and it is not infinite.

Four options are given.

We have to find the geometric term that is best described as a straight path between two points.

From the given options, the only term that satisfies these conditions is a line segment.

A line segment is a line that is definite from one point to another. The length of a line segment can be measured and it is not infinite.

Therefore, we have found that a line segment is best described as a path between two points. The correct answer is option D.

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Answer:

d

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

I just finished the quiz, and this was my only incorrect one. The correct answer is A. Also, think logically. If the sun is spread out over more area, then it must be at a smaller angle. This leads to cooler temperatures, of course.

each gallon has 8 pints

4 [tex]\frac{1}{2}[/tex] * 8  = 36

so there would be 36 servings

ANSWER

D. 1.25,1¼,125%

EXPLANATION

The number 1.25 can be rewritten as a fraction to obtain:

[tex]1 \frac{1}{4} [/tex]

We can covert 1.25 into percentage by multiplying by 100%

This implies that,

[tex]1.25 = 1.25 \times 100\% = 125\%[/tex]

Therefore the equivalent numbers are:

1.25,1¼,125%

The correct answer is D

Answer:

Step-by-step explanation:

For angle A we have

opposite = 8

adjacent = 6

hypotenuse = 10

sin A = opposite/hypotenuse

cos A = adjacent/hypotenuse

tan A = opposite/adjacent

cot A = adjacent/opposite

6/10 = adjacent/hypotenuse = cos A

The trigonometric function of the triangle is given by cos A = 6/10

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

Let the triangle be represented as ΔABC

where the measure of ∠ABC = 90°

Now , from the trigonometric relations ,

cos θ = adjacent / hypotenuse

So , on simplifying , we get

The measure of BC = 6 units

The measure of AB = 8 units

The measure of AC = 10 units

cos A = 6 / 10

Hence , the measure of cos A of triangle is cos A = 6 / 10

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Answer:

The expression which is equivalent to (k ° h)(x) is [tex]\frac{1}{(5 + x)}[/tex] ⇒ 2nd answer

Step-by-step explanation:

* Lets explain the meaning of the composition of functions

- Composition of functions is when one function is inside of an another

 function

# If g(x) and h(x) are two functions, then (g ° h)(x) means h(x) is inside

  g(x) and (h ° g)(x) means g(x) is inside h(x)

* Now lets solve the problem

∵ h(x) = 5 + x

∵ k(x) = 1/x

- We need to find (k ° h)(x), that means put h(x) inside k(x)

* Lets replace the x of k by the h(x)

∵ k(x) = [tex]\frac{1}{x}[/tex]

∵ h(x) = 5 + x

- Replace the x of k by 5 + x

∴ k(5 + x) = [tex]\frac{1}{5 + x}[/tex]

∴ The expression which is equivalent to (k ° h)(x) is [tex]\frac{1}{5+x}[/tex]

Answer:

Dealership A is cheaper. Hope it helps.

Answer:

By comparing both the payments we can say that Dealer A is cheaper by $4.50.

Step-by-step explanation:

Dealership A: The car costs $30,000, and the loan has an annual interest rate of 4.8% for 5 years.

The EMI formula is :

[tex]\frac{p\times r\times(1+r)^{n} }{(1+r)^{n}-1 }[/tex]

Now, p = 30000

r = [tex]4.8/12/100=0.004[/tex]

n = [tex]5\times12=60[/tex]

Putting values in formula we get;

[tex]\frac{30000\times0.004\times(1+0.004)^{60} }{(1+0.004)^{60}-1 }[/tex]

=> [tex]\frac{30000\times0.004\times(1.004)^{60} }{(1.004)^{60}-1 }[/tex]

EMI is = $563.34

Dealership B: The car costs $29,800, and the loan has an annual interest rate of 5.4% for 5 years.

p = 29800

r = [tex]5.4/12/100=0.0045[/tex]

n = [tex]5\times12=60[/tex]

Putting values in formula we get;

[tex]\frac{29800\times0.0045\times(1+0.0045)^{60} }{(1+0.0045)^{60}-1 }[/tex]

=> [tex]\frac{29800\times0.0045\times(1.0045)^{60} }{(1.0045)^{60}-1 }[/tex]

EMI = $567.84

By comparing both the payments we can say that Dealer A is cheaper by $4.50.

Answer: [tex]x=-\frac{17}{3}[/tex]

Step-by-step explanation:

Given the equation [tex]\frac{(x+5)}{(x+8)}=1+\frac{6}{(x+1)}[/tex], you need to make the addtition indicated on the right side of the equation:

[tex]\frac{(x+5)}{(x+8)}=\frac{(x+1)+6}{(x+1)}\\\\\frac{(x+5)}{(x+8)}=\frac{(x+7)}{(x+1)}[/tex]

Now, multiply both sides of the equation by (x+8) and (x+1):

[tex](x+1)(x+8)\frac{(x+5)}{(x+8)}=\frac{(x+7)}{(x+1)}(x+1)(x+8)\\\\(x+1)(x+5)=(x+7)(x+8)[/tex]

Now, apply Distributive property:

[tex]x^2+5x+x+5=x^2+8x+7x+56[/tex]

Simplifying, you get:

[tex]6x+5=15x+56[/tex]

Subtract 5 and 15x from both sides:

[tex]6x+5-15x-5=15x+56-15x-5\\\\-9x=51[/tex]

Finally, divide both sidesby -9:

[tex]\frac{-9x}{-9}=\frac{51}{-9}\\\\x=-\frac{17}{3}[/tex]