How do you factorise α²-b²

The value 'k' for which '4x^2 + 8xy + ky^2 = 9' is the second degree equation of a pair of straight lines is 4.

Therefore the answer is 4.

A general second-degree equation of a pair of straight lines is given by:

ax² + 2hxy + by² + 2gx + 2fy + c = 0

Where a, b, c, d, e, and f are constants, x and y are variables.

For the equation to represent a pair of straight lines, the following conditions must be met :

abc + 2fgh - af² - bg² - ch² = 0

In the equation 4x^2 + 8xy + ky^2 = 9, a = 4, h = 4, b = k, g = f = 0 and c = -9.

That is 4×k×(-9) + 2×0×0×4 - 4×0² - k×0² + 9×4² = 0

4×k×9 = 9×4²

k = 4

--The question is incomplete, complete question is given below--

"For what value of k is 4x^2 + 8xy + ky^2 = 9 the equation of a pair of straight lines?"

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let's reword this a bit differently, since it looks jumbled

let's find the equation of a line that is perpendicular to y = -5x + 5, and it also passes through (10 , 7), well, keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]y=\stackrel{\stackrel{m}{\downarrow }}{-5}x+5\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ -5 \implies \cfrac{-5}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{-5}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{-5} \implies \cfrac{1}{ 5 }}}[/tex]

so we're really looking for the equation of a line with a slope of 1/5 and that it passes through (10 , 7)

[tex](\stackrel{x_1}{10}~,~\stackrel{y_1}{7})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{7}=\stackrel{m}{ \cfrac{1}{5}}(x-\stackrel{x_1}{10}) \\\\\\ y-7=\cfrac{1}{5}x-2\implies {\Large \begin{array}{llll} y=\cfrac{1}{5}x+5 \end{array}}[/tex]

The compound inequality that shows the possible heights of the third tree is 8 ≤ x ≤ 18

An equation shows how two or more numbers and variables are related to each other.

The height of two of the trees are 8 feet and 16 feet. If the height of the third tree is x feet, hence:

Sum of three palm tree heights = x + 8 + 16 = x + 24

The sum of three palm tree heights range from 32 to 42 feet. Hence:

32 ≤ x + 24 ≤ 42

32 - 24 ≤ x ≤ 42 - 24

8 ≤ x ≤ 18

The solution to the compound inequality is 8 ≤ x ≤ 18

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The true statement about the function in the list of options is (d) none of these

From the question, we have the following parameters that can be used in our computation:

p c

0.25 1.69

0.45 3.04

0.75 5.06

1.25 11.81

Where

The values in the p column represent the domain

In this case, the domain is

Domain = [0.25, 1.25]

The values in the c column represent the range

In this case, the range is

Range = [1.69, 11.81]

This means that the options (a), (b) and (e) are false

For option (c), we have

c = 6.75p

This means that

c = 6.75 * 0.25 = 1.69

c = 6.75 * 0.45 = 3.04

c = 6.75 * 0.75 = 5.06

c = 6.75 * 1.25 = 8.43 -- false

This means that the option (d) is false

Hence, none of the options is true

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Answer:

-----------------------------

15 inches of wire costs 90 cents, then 1 inch of wire costs:

The length of wire for 72 cents:

The difference between logarithmic and exponential functions can be determined by looking at the form of the equation and by performing a calculation.

A logarithmic equation is written as log_b(x) = y, where b is the base and x and y are variables. An exponential equation is written as b^x = y, where b is the base and x and y are variables.

To determine if an equation is logarithmic or exponential, begin by comparing the form of the equation to the two equations above. If the equation is written in the form of log_b(x) = y, then it is a logarithmic equation. If the equation is written in the form of b^x = y, then it is exponential.

To perform a calculation, plug in a known value for x and then solve for y. For example, if the equation is log_2(x) = 4, then plug in x = 8. The calculation would then be:

log_2(8) = 4

This is a logarithmic equation, as the form of the equation matches log_b(x) = y.

If the equation is b^x = 16, then plug in x = 4. The calculation would then be:

2^4 = 16

This is an exponential equation, as the form of the equation matches b^x = y.

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The length of each diagonal is √(196x^2 + 816x + 324) units.

The diagonal of a rectangle can be estimated using the hypotenuse formula, such as using the Pythagorean theorem calculator.

WX^2 = WY^2 + XZ^2

Given that WY = 14x + 10 and XZ = 11x + 22, we can substitute those values in the equation:

WX^2 = (14x + 10)^2 + (11x + 22)^2

WX^2 = 196x^2 + 816x + 324

WX = √(196x^2 + 816x + 324)

The same goes for the other diagonal, WZ.

WZ = √(196x^2 + 816x + 324)

So, the length of each diagonal is √(196x^2 + 816x + 324) units.

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CPCTC

This acronym stands for "corresponding parts of congruent triangles are congruent". The triangles being congruent leads to their corresponding pieces being the same length. It's like saying if two houses are identical, then the front doors must be identical as well. Notice how this builds off the fact the triangles are proven congruent in line 5.

[tex](\stackrel{x_1}{-7}~,~\stackrel{y_1}{-8})\qquad (\stackrel{x_2}{-5}~,~\stackrel{y_2}{6}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{6}-\stackrel{y1}{(-8)}}}{\underset{\textit{\large run}} {\underset{x_2}{-5}-\underset{x_1}{(-7)}}} \implies \cfrac{6 +8}{-5 +7} \implies \cfrac{ 14 }{ 2 } \implies \text{\LARGE 7}[/tex]

The required volume of the given solid is (√16 - r²) -(-√16 - r²).

The measurement of three-dimensional space is volume. It is frequently expressed quantitatively using SI-derived units, as well as several imperial or US-standard units.

Volume and the notion of length are connected.

Volume, which is measured in cubic units, is the 3-dimensional space occupied by matter or encircled by a surface.

The cubic meter (m3), a derived unit, is the SI unit of volume.

So, the integrand often takes the form z upper z lower, where z stands for the solid's lower and upper borders.

We are treating the sphere as a hemisphere as of right now, with the XY-plane serving as its lower boundary. Consequently, you must multiply by 2.

The solid's volume is (√16 - r²) -(-√16 - r²).

Therefore, the required volume of the given solid is (√16 - r²) -(-√16 - r²).

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Correct question:

Use polar coordinates to find the volume of the given solid: Inside the sphere x^2 + y^2 + z^2 = 16 and outside the cylinder x^2 + y^2 = 4.

Answer:

g>5

Step-by-step explanation:

Simply add 6 to both sides to get g>5

Answer:

F = 24

Step-by-step explanation:

simplify 1/8

(1/8 x F) - 3 = 0

3 = 3/1 = 3 x 8/ 8

F x (3 x 8) / 8 F - 24/ 8

F - 24/ 8 = 0

F - 24/ 8 = 0 x 8

Answer:

  24

Step-by-step explanation:

You want to know f for 1/8f = 3.

Multiply the given equation by 8 to undo the multiplication by 1/8:

  8(1/8f) = 8(3)

  f = 24 . . . . . . . . simplify

The value of f is 24.

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The ratio of spice A to spice B is : 49/87

Here, 2 1/3 grams of spice A was mixed with 4 1/7 grams of spice B.

First we convert the improper fraction into a proper fraction.

For improper fraction2 1/3,

2 1/3

= (2 × 3)/3 + 1/3

= 6/3 + 1/3

= (6 + 1)/3

= 7/3 which is a proper fraction.

and for 4 1/7

= (4 × 7)/7 + 1/7

= 28/7 + 1/7

= (28 + 1)/7

= 29/7

The ratio of spice A to spice B would be,

(2 1/3) / (4 1/7 )

= (7/3) / (29/7)

= (7/3) × (7/29)

= (7 × 7)/(3 × 29)

= 49/87

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The two lines are neither parallel nor perpendicular to each other.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given that the two equations of the lines are y= -1/3x+2 and 5y+15x=-40.

y= -1/3x+2

5y+15x=-40.

5y = -15x - 40

y =-3x - 40/3

Here the slopes of the lines are,

m₁= -1 / 3

m₂ = -3

For the lines to be parallel the slopes should be equal and for the lines to be perpendicular the slopes should be inverse and reciprocal.

Here the slopes are neither equal nor have the inverse reciprocal.

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The functions are p(x) = b² - 16b +32 and q(x) = -32b-32 the x value when the functions are equivalent to each other is 8.

Given that,

The functions are p(x) = b² - 16b +32 and q(x) = -32b-32

We have to find the x value when the functions are equivalent to each other.

We know that,

Take the functions

p(x) = b² - 16b +32 and q(x) = -32b-32

When the function are equivalent

p(x) = q(x)

b² - 16b +32 = -32b-32

b² - 16b +32 +32b+32=0

b² + 16b +64 = 0

Now find the factors for 64

64 =  8×8

b² + 8b + 8b +64 = 0

Taking common terms

b(b + 8) + 8(b + 8)=0

(b + 8)(b + 8)=0

b=8

Therefore, The functions are p(x) = b² - 16b +32 and q(x) = -32b-32 the x value when the functions are equivalent to each other is 8.

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The x-intercept will be  -2.

Now, According to the question:

How do you find the x-intercept?

To find the x-intercept we set y = 0 and solve the equation for x. This is because when y=0 the line crosses the x-axis. When an equation is not in y = mx + b form, we can solve for the intercepts by plugging in 0 as needed and solving for the remaining variable. To find y-intercept: set x = 0 and solve for y.

Here the equation is 2x-y = -4.

For finding the x-intercept

let us put the value of y as 0 we get,

2x−0=−4

⇒2x=−4 .

Dividing both sides by 2 we get,

2x2=−4/2⇒x=−2 .

Therefore, the x-intercept is -2.

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A linear graph is one whose equation is in the form y = mx + b, where m and b are constants. A quadratic graph is one whose equation is in the form y = ax^2 + bx + c, where a, b, and c are constants.

To determine if a given graph is linear, calculate the equation of the line by finding two points on the graph and plugging them into the equation y = mx + b.

For example, if the two points on the graph are (2, 3) and (5, 7), then plugging these values into the equation gives us:

y = mx + b

3 = m*2 + b

7 = m*5 + b

Solving this system of equations gives m = 2 and b = -1, so the equation of the line is y = 2x - 1.

A quadratic graph is one whose equation is in the form y = ax^2 + bx + c, where a, b, and c are constants. To determine if a given graph is quadratic, calculate the equation of the parabola by finding three points on the graph and plugging them into the equation y = ax^2 + bx + c.

For example, if the points on the graph are (1, 6), (2, 13), and (3, 24), then plugging these values into the equation gives us:

y = ax^2 + bx + c

6 = a*1^2 + b*1 + c

13 = a*2^2 + b*2 + c

24 = a*3^2 + b*3 + c

Solving this system of equations gives a = 4, b = -5, and c = 6, so the equation of the parabola is y = 4x^2 - 5x + 6.

An exponential graph is one whose equation is in the form y = a*b^x, where a and b are constants. To determine if a given graph is exponential, calculate the equation of the line by finding two points on the graph and plugging them into the equation y = a*b^x.

For example, if the two points on the graph are (2, 16) and (3, 24), then plugging these values into the equation gives us:

y = a*b^x

16 = a*b^2

24 = a*b^3

Solving this system of equations gives a = 2 and b = 2, so the equation of the line is y = 2*2^x.

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per year unit rate becomes 6 inches. This can be solved using the concept of unit rate.

A unit rate is a price for one of anything. This is expressed as a proportion with such a base of one. For instance, you would cover 7 yards on average every second if you covered 70 yards in 10 seconds. The ratios of 70 yards in 10 seconds and 7 yards in 1 second are both rates, however, the latter is a unit rate.

A rate is the ratio of two different measurement units, whereas a unit rate seems to be the ratio of two different units of measurement for just a single object.

unit rate for 30 inches per 5 years:

= 30 inches / 5 years

= 6 inches / 1 year

Thus, per year unit rate becomes 6 inches.

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Log () helps to determine the single number to be multiplied.

Log stands for logarithm in algebra. The inverses of equations using exponents are called logarithms. Logs can be used to determine how many times one number needs to be multiplied to get another in its most basic form. For instance, to get 100 in the base-10 system, 10 must be multiplied by 10. In a base-10 system, the logarithm of 100 is therefore 2.

Log () expresses the power or exponent that a base number must be raised to or multiplied by in order to create another number in an ideal world. In situations where the user has data values that are significantly greater or lower than the other values, log scales are quite helpful. When displaying major percentage variations between data points, the user can also utilize a log scale.

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Answer:

cant answer sorry i didnt realize it was an equation

Step-by-step explanation:

Answer:

it 33 pts not 50

The system X² y² 25 and ay 10 has no real solutions.

To solve this system, we need to solve each equation for y.

For the first equation, X² y² 25, we can divide both sides by X² to get:

y² = 25/X²

Then, take the square root of both sides to get:

y = ± √(25/X²)

For the second equation, ay = 10, we can divide both sides by a to get:

y = 10/a

To find out if the system has real solutions, we need to compare the two equations. Since the two equations are not equal, the system has no real solutions.

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The total number of students on the honor roll increased by 20%.

Given that, 75 boys and 50 girls on the honor roll

=> boys increased by 24% =  75*24/100  = 18

So, the number of boys is increased by 18.

=> girls increased by 14% =  50*14/100  = 7

So, the number of girls is increased by 7.

After the increment, the number of boys and girls on the honor roll is 93 and 57, respectively.

Thus, the total number of students increased = 18+7 = 25

Therefore, the percentage increment in total = 25 / 125 * 100 = 20%

Hence, The total number of students on the honor roll increased by 20%.

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Answer:

that is the persons username I got it from

Step-by-step explanation:

3 and 7

6 and 14

9 and 21

12 and 28

15 and 35

Step-by-step explanation:

If the two numbers they give you are 9 and 21, then the cranberry's are 3 ounces and the apples are 7 fliud ounces, then you can divide and multiply them to your will.

[tex](\stackrel{x_1}{8}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{-4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-4}-\stackrel{y1}{(-4)}}}{\underset{\textit{\large run}} {\underset{x_2}{2}-\underset{x_1}{8}}} \implies \cfrac{-4 +4}{-6} \implies \cfrac{ 0 }{ -6 } \implies \text{\LARGE 0}[/tex]

Answer: -2/3x is the slope and the beginning amount is 5 so the equation would be -2/3x+5.

Step-by-step explanation:

Once you find the slope using the formula rise/run you will get 2/3 but since the slope is going downwards it would be -2/3 which gives you the mx. Now to find the beginning amount look where the line intersects the graph which will give you the equation.

Answer:

[tex]x = \frac{9}{5} [/tex]

Step-by-step explanation:

[tex] - 7( - 7 \times ( - x - 1)) = 6 (- \times ( - 2x - 3))[/tex]

[tex] - 7 + 7x + 7 = 6 + 2x + 3[/tex]

[tex]7x - 2x = 6 + 3 + 7 - 7[/tex]

[tex]5x = 9[/tex]

[tex] \frac{5x}{5} = \frac{9}{5} [/tex]

[tex]x = \frac{9}{5} [/tex]