Write a general formula to describe the variation: x varies jointly with the inverse of the sum of y and z

For this case we have that the equation of a line in the slope form intersection is given by:[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cut point with the y axis.

In the green graph we observe that[tex]b = 2[/tex], then its equation is [tex]y = 5x + 2[/tex]

We have the slope of the red line substituting two points:

[tex](0,2)\\(-1,0)[/tex]

[tex]m = \frac {0-2} {- 1-0} = 2[/tex]

Thus, the red line has equation[tex]y = 2x + 3[/tex]

Finally, the blue line is [tex]y = 3x + 3[/tex]

Answer:

Green line, y = 5x + 2

Red line, y = 2x + 3

Blue line, y = 3x + 3

Answer:

1 - green line: y = 5x + 2

2 - red line: y = 3x + 3

3 - blue line: y = 2x + 3

Step-by-step explanation:

1 - green line

The graph with the green line is the easiest to match with an equation.

If you look at the graph, you see that when x = 0, the y-value is 2.

There's only one of the given equations that y = 2 when x = 0, the first one.

y = 5x + 2

y = 5 (0) + 2 = 0 + 2 = 2

It's easy to spot, because in the format y = mx + b, the b is the value of Y when x = 0, as we just demonstrated.

2 - Red line

In this case, when x = 0, y = 3.  And there are 2 equations for which it's true... which is normal because the blue line (in next graph) also passes by this point.

Then to know which equation goes with the red line graph, we have two choices...

A. determine the slope (rate of change) of the red line and see if it matches one of the equations.

B. See what value of X yields a value of 0 for Y and see where it would land on the X-axis.

The second method is faster.  If you see on the graph, when y = 0, x = -1

If we take the 2nd equation (y = 3x + 3) and we set the value of y to 0, we have:

0 = 3x + 3

-3 = 3x

x = -1

Which is exactly what we wanted to find.

So, the red line is y = 3x + 3

3. blue line

Well, there's only one answer left (y = 2x + 3), so it's easy... but let's make sure by finding the slope (method A listed for the red line above), in case your teacher would be playing tricks on you.

The slope of a line is the variation of y-value (Δy) divided by the variation of x-value (Δx).

If we take the two points where the blue line crosses the axis, we have (-1.5, 0) and (0,3).

Now, let's calculate the slope:

S = (0 - 3) / (-1.5 - 0) = -3 / -1.5 = 2

And 2 is the slope of the equation y = 2x + 3

So, we're good.

Answer:

The volume of the pyramid is [tex]V=187\ ft^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the pyramid is equal to

[tex]V=\frac{1}{3}BH[/tex]

where

B is the area of the base of the pyramid

H is the height of the pyramid

we have

[tex]B=93.5\ ft^{2}[/tex]

[tex]H=6\ ft[/tex]

substitute

[tex]V=\frac{1}{3}(93.5)(6)=187\ ft^{3}[/tex]

Answer:The answer is 187 ft to the 3 power

Answer:

secΘ

Step-by-step explanation:

The reciprocal of cos x is

[tex]\frac{1}{cosx}[/tex] = sec x

reciprocal of cosΘ is secΘ

Answer:

The answer is secΘ

Answer:

f(x) = x² + 9x - 22

Step-by-step explanation:

Given that x = 2 and x = - 11 are zeros, then

(x - 2) and (x + 11) are factors

and f(x) equals the product of the factors

f(x) = (x - 2)(x + 11) ← expand factors

f(x) = x² + 9x - 22 ← is a possible function

The quadratic function [tex]\( f \)[/tex] with zeros at [tex]\( x = 2 \) and \( x = -11 \)[/tex] can be written in factored form as: [tex]\[ f(x) = x^2 + 9x - 22 \][/tex]

The standard form of a quadratic function is:

[tex]\[ f(x) = ax^2 + bx + c \][/tex]

To convert the factored form to standard form, we expand the factors:

[tex]\[ f(x) = a(x^2 + 11x - 2x - 22) \] \[ f(x) = a(x^2 + 9x - 22) \] \[ f(x) = ax^2 + 9ax - 22a \][/tex]

[tex]\[ b = 9a \] \[ c = -22a \][/tex]

So, the quadratic function with zeros at [tex]\( x = 2 \) and \( x = -11 \) is:[/tex]

[tex]\[ f(x) = ax^2 + 9ax - 22a \] \[ f(x) = x^2 + 9x - 22 \][/tex]

Answer:

x = 6

Step-by-step explanation:

5x - 10 = 2 - 2x + 10(x - 3)

Opening the brackets;

5x - 10 = 2 - 2x + 10x - 30

Putting the like terms together;

10x - 5x - 2x = 30 - 10 - 2

3x = 18

x = [tex]\frac{18}{3}[/tex] = 6

Final answer:

To find the value of x in the given equation, rearrange it to standard form, combine like terms, then isolate x to solve for its value.

Explanation:

Solving the equation: 5x-10=2-2x+10(x-3)

1. Rearrange the equation to standard quadratic form: 5x - 10 = 2 - 2x + 10x - 30

2. Simplify and combine like terms: 5x - 10 = -28 + 8x

3. Bring all terms to one side to get: 3x = 18

4. Solve for x: x = 18/3 = 6

To find the cost of the magazine, represent the cost of each book as 'x'. Use the given information to set up an equation and solve for 'x'.

To find the cost of the magazine, let's represent the cost of each book as 'x'. Since the magazine costs twice as much as each book, we can represent the cost of the magazine as '2x'.

According to the problem, Ryan bought 3 books and a magazine and paid $30. We can write this information as an equation:

3x + 2x = 30

Combining like terms, we get:

5x = 30

To isolate the variable 'x', we divide both sides of the equation by 5:

x = 6

Therefore, each book costs $6 and the magazine costs twice as much, which is $12.

The cost of the magazine is $10.

Let's denote the cost of each book as B and the cost of the magazine as M. According to the given information:

Now, we also know that the magazine costs twice as much as each book, so M = 2B. Substitute M with 2B in the equations:

Now that we know the cost of each book (B = 6), we can find the cost of the magazine (M) using M = 2B:

M = 2 times 5 = 10

So, the cost of the magazine is $10.

Answer:

( 19/3 , 2 )

Step-by-step explanation:

Given in the question,

point D(7,1)

x1 = 7

y1 = 1

point F(5,4)

x2 = 5

y2 = 4

Location of point E which is 1/3 of the way from D to F

which means ratio of point E from D to F is 1 : 2

1 : 2

xk = [tex]x1 + \frac{a}{a+b}(x2-x1)[/tex]

yk = [tex]y1 + \frac{a}{a+b}(y2-y1)[/tex]

Plug values in the equation

xk = 7 + (1)/(1+2) (5-7)

xk = 19/3

yk = 1 + (1)/(1+2)(4-1)

yk = 2

Answer:

Area of 81 sq in: 40.2

Perimeter of 36 in : 9

Step-by-step explanation:

Hope I'm right! :)

Answer:

9 inches

Step-by-step explanation:

A square has an area of 81 in^2

A = s^2

81 = s^2

Take the square root of each side

sqrt(81) = sqrt(s^2)

9 = s

The side length is 9 inches

A square has a perimeter of 36 in

P = 4s

36 = 4s

Divide each side by 4

36/4 = 4s/4

9 = s

Each side is 9 inches

27/8

try the internet, it helps

The required, 3.375 can be written as the fraction 27/8 in simplest form.

To write 3.375 as a fraction in simplest form, we can follow these steps:

Therefore, 3.375 can be written as the fraction 27/8 in simplest form.

Learn more about fractions here:

https://brainly.com/question/11709591

#SPJ6

d, 'y-axis, x-axis, y-axis, x-axis'

its the correct answer on the test :)) Goodluck !

The correct set of reflections that would carry triangle ABC onto itself is:

d. y-axis, x-axis, y-axis, x-axis

As per the shown graph, the coordinates of the vertices:

A(0,2)

B(2,4)

C(3,0)

We observe that the y-axis is the vertical line passing through x = 0, and the x-axis is the horizontal line passing through y = 0.

By analyzing the positions of the vertices, we can see that the triangle has rotational symmetry of 180 degrees around points (1, 2) and reflectional symmetry across both the x-axis and the y-axis.

Therefore, the correct set of reflections that would carry triangle ABC onto itself is:

d. y-axis, x-axis, y-axis, x-axis

To learn more about the reflections click here:

https://brainly.com/question/15487308

#SPJ2

Answer:

The gcf of 42 and 84 is 42. The lcm of 4 and 10 is 20.

Step-by-step explanation:

We will now calculate the prime factors of 42 and 84, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 42 and 84.We found the factors and prime factorization of 42 and 84. The biggest common factor number is the GCF number.

So the greatest common factor 42 and 84 is 42.

The Least Common Multiple (LCM) of the numbers

4, 10

is

20

because 20 is the smallest number that all of the numbers divide into evenly.

The greatest common factor of 42 and 84 is 42

The least common multiple of 4 and 10 is 20

A factor refers to a number or an algebraic expression that divides another number or expression evenly, that is, with no remainder.

42 = 1, 2, 3, 6, 7, 14, 21 and 42.

84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and 84.

The greatest common factor of 42 and 84 is 42

least common multiple of 4 and 10

Find the multiples of 4 and 10

4 = 4, 8, 12, 16, 20, 24

10 = 10, 20, 30

The least common multiple of 4 and 10 is 20

Read more on greatest common factor:

https://brainly.com/question/219464

#SPJ6

john because 1 yard is equal to 3 ft, 4x3=12 ft

Final answer:

Jane has more fabric than John with a difference of 24 inches.

Explanation:

To compare the amount of fabric John and Jane have, we need to convert their measurements into the same unit. Since John has 4 yards of fabric and Jane has 120 inches, we need to convert yards to inches or inches to yards.
To convert yards to inches, we know that 1 yard is equal to 36 inches. So, multiplying 4 yards by 36 inches per yard, we get 144 inches of fabric for John.
Comparing the two measurements, we can see that Jane has more fabric with 120 inches compared to John's 144 inches. The difference is 144 inches - 120 inches = 24 inches. Therefore, Jane has 24 inches more fabric than John.

Answer:

11.066666666667 or simplified 12

Step-by-step explanation:

Answer:  11.0667

Step-by-step explanation:

= Mean just incase you need is :

83

And population size just incase you need as well is :

15

* Hopefully this helps:) Mark me the brainliest:)!!

~234483279c20~

Answer:

This is a Pythagorean triple.

Step-by-step explanation:

In order to find this, use the Pythagorean Theorem to and see if it gives a true statement.

a^2 + b^2 = c^2

15^2 + 20^2 = 25^2

225 + 400 = 625

625 = 625

Since this is a true statement, we know that this is a Pythagorean Triple.

Answer:

Yes, she has enough strong to make necklaces for five friends

Step-by-step explanation:

10 ft= 120 inches

120/20 9=in per necklace= 6

she has enough to make 6 necklaces and she only has to make five so yes

Answer:

25%

Step-by-step explanation:

25% between min and Q1

25% between Q1 and median

25% between median and Q3

25% between Q3 and max

25% but its the beginning

Answer:

 y = 3/7 x

Step-by-step explanation:

Slope intercept form y = mx + b

In this case 3x - 7y = 0​

7y = 3x  

 y = 3/7 x (b = 0)

Answer:

y= 0- 3x over -7

Step-by-step explanation: Slope intercept form is Y= mx+ b

Hope this helps

Answer:

[tex]\boxed{\text{22.5 ft}^{2}}[/tex]

Step-by-step explanation:

Existing walkway

 l = 10 ft

w = 4 ft

A₁ = lw = 10 ft × 4 ft = 40 ft²

New walkway

Expanding a measurement by 25 % means that you multiply it by a factor of 1.25.

New length = 10 × 1.25 = 12.5 ft

New width =    4 × 1.25 =   5    ft

A₂ = lw = 12.5 ft × 5 ft = 62.5 ft²

Increase in area

A₂ - A₁ = 62.5 – 40 = 22.5 ft²

The increase in area is [tex]\boxed{\textbf{22.5 ft}^{2}}[/tex]

Answer:

D

Step-by-step explanation:

The dependent variable in the experiment will be the number of plants.

The dependent variable is the variable that is being measured or tested in an experiment. it is the variable whose value depends upon the other variables if we change that independent variable the value of the dependent variable changes.

here in the question dependent variable in the experiment will be the number of plants.

To know more about dependent variable follow

https://brainly.com/question/25223322

#SPJ2

Answer:

Yes, because he could divide by 3.14 to find the diameter and then divide that result by 2 to find the radius. Once he has the radius, he can use the formula.

Answer:

the answer is A

Step-by-step explanation:

Answer:

Part A:

Since the slopes of the lines are not equal, the pair of equations for lines A and B will have one solution.

Part B:

(3 ,5 ) is the solution to the equations of lines A and B.

Step-by-step explanation:

Part A:

We are required to determine the number of solutions that the pair of equations for lines A and B have. To do this, we shall determine the slope of each line;

A straight line labeled A joins the ordered pair 2, 6 with the ordered pair 6, 2. The slope is defined as;

(change in y) / (change in x)

The slope of line A is thus;

(2 - 6)/(6 - 2) = -1

A straight line B joins the ordered pair 0, 3 with the ordered pair 4.5, 6.

On the other hand, the slope of line B is;

(6 - 3) / (4.5 - 0) = 2/3

Since the slopes of the lines are not equal, the pair of equations for lines A and B will have one solution.

Part B:

What is the solution to the equations of lines A and B?

We first need to determine the equation of each line;

Line A, the slope was found to be -1 and the line passes through (2,6)

The equation of the line in slope intercept form is;

y = -x + c

6 = -2 + c

c = 8

y = -x + 8

On the other hand, the slope of line B was found to be 2/3 and the line passes through (0,3). Therefore, we have;

y = 2/3x + c

3 = 2/3 (0) + c

c= 3

y = (2/3)x + 3

The graph of these two lines is shown in the attachment below. The lines intersect at (3 ,5 ) which is the solution to the equations of lines A and B.

The graphical solution to a system of linear equations is given by the point of intersection of the two lines representing each equation.

Answer:

Other guy is correct :)

Step-by-step explanation:

Answer:Step-by-step explanation:

The sine of 35 degrees = x / 15

x = sine (35) * 15

x = 0.57358 * 15

x = 8.6037

Answer:

hello :  y = 3x² -24x +26 ......answer: C

Step-by-step explanation:

y = 3(x-4)² -22

by idetity : (x-4)² = x²- 8x+16

y = 3(x²- 8x+16 ) -22

y = 3x² - 24x +48 -22

y = 3x² -24x +26 ......answer: C

Answer:

Exact volume = 294π in³

Approximate volume = 923.6 in³

Explanation:

The volume of a cylinder can be calculated using the following rule:

volume = πr²h

where r is the radius and h is the height of the cylinder

In the given cylinder:

radius = r = 7 in

height = h = 6 in

Substitute with the givens in the formula to get the volume:

Volume of cylinder = πr²h = π(7)²(6) = 294π in³ ≈ 923.6 in³ to the nearest tenth

Hope this helps :)

Answer: its 48% i took the test

Step-by-step explanation:

Answer:

the actual answer is 43%

Step-by-step explanation:

Answer:

A.

Step-by-step explanation:

btw this is a biology question, but the reason it's A because think of external+ outside. all the other multiple choices are internal. Such as when you're hungry that's inside of your body same as being thirsty

Answer: a rabbit runs away from a fox that is chasing it

Step-by-step explanation: External stimuli is a reaction. So the rabbit running away from the fox would be a reaction

Answer:

0

Step-by-step explanation:

(27x)(2z)/(-3x)(2z)(4)

-9/4

When you divide 2z by 2z, there is an imaginary exponent 1 on the z's. The rule for dividing numbers with exponents is to subtract the exponents. So, 2z/2z = 1(z^1-1) = 1(z^0) = 1

Answer:

B = 53.13

Step-by-step explanation:

Since this is a right triangle, we can use the tan function

tan B = opposite side/ adjacent side

tan B = 4/3

Take the inverse tan of each side

tan ^-1 (tan B) = tan^-1 (4/3)

B = 53.13010235

To the nearest hundredth

B = 53.13

Using it's concept, it is found that there is a [tex]\frac{3}{4}[/tex] probability that the red die shows an even number or the green die shows an even number.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

A die has six sides, of which three are even and three are odd, hence:

The "or probability" is given by:

[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]

Hence:

[tex]P(A \cup B) = \frac{1}{2} + \frac{1}{2} - \frac{1}{4} = \frac{3}{4}[/tex]

More can be learned about probabilities at https://brainly.com/question/14398287

#SPJ1

Answer:

61

Step-by-step explanation:

The first thing that you want to do is distance formula

[tex]d=(x_{2}-x_{1} )^{2} + (y_{2}-y_{1} )^{2}[/tex]

I'm going to make the start of the line at (1,1) and that means that the end of the line is at (7,6). Now, you plug these numbers into the formula.

[tex]d=(7-1 )^{2} + (6-1 )^{2}[/tex]

Then you slove

[tex]d=(6 )^{2} + (5 )^{2[/tex]

[tex]d=36 + 25[/tex]

[tex]d=61[/tex]

Distance formula: d =√(x2-x1^2 +y2-y1^2)

Find the points of the line: (2,2) and (8, 7)

Length = √((8-2)^2 + (7-2)^2)

Length = √(6^2 + 5^2)

Length = √(36+25)

Length = √61 ( exact answer) or as a decimal: 7.81