Work out the value of a in the equation below.

x²-18x +81 = (x − a)²

the probability that the card you select is a diamond or 7 is 4/13

Mathematical representations of the likelihood of an event occurring or of a proposition being true are dealt with in the area of probability. A number between 0 and 1 represents the likelihood of an event, with 0 roughly denoting impossibility and 1 representing certainty.

Lets take diamond first total diamonds are 13 and total cards are 52 So prob is 13/52 which is 1/4

Lets take 7s

total 10s in the deck is 4 (one in each suite) (one in each suite)

Prob of 7s is 4/52 which is 1/13

Final answer =1/13+1/4=17/52 Total prob is addition of above two as it is "or."

Because the prob of the 7th diamond has been inserted twice, edit it as follows: 17/52-1/52=16/52=4/13

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The solutions of the equation x³ + 5x² = - x² + 5x + 3 when solved graphically is x = - 0.41, 1.09.

Draw a graph for each side, or component, of the equation and check to see where the curves intersect or are equal, to solve an equation graphically. The answers to the equation are the x values of these places.

Consider the equation,

x³ + 5x² = - x² + 5x + 3

Solving Equations Graphically:

The solution(s) of the equation f(x) = g(x) are the values of x where the graphs of f and g intersect.

Therefore,

f(x) = x³ + 5x² and g(x) = - x² + 5x + 3

By graphing the function we find the intersection of the two functions.

Hence, the graphs intersect each other at ( - 0.411, 0.776) and ( 1.092, 7.268).

Therefor,e the solution of the equation x³ + 5x² = - x² + 5x + 3 is x = - 0.41 and x = 1.09.

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The value for the height of the rectangular prism is found as; h = 7.

The formula for the surface area of rectangular prism is;

S = 2(ab+bh+ah)

Where,

a=6, b=5 and s=214

Substitute the values in the formula.

214 = 2(6×5 + 5h + 6h)

Simplifying;

30 + 11h = 107

11h = 107 - 30

11h = 77

h = 7

Thus, the value for the height of the prism is found as; h = 7.

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For given equation y = -2x + 8, the x-intercept is (4, 0) and the y-intercept is (0, 8)

In this question, we have been given an equation y = -2x + 8

We need to find the x-intercept and y-intercept. Also, we need to write it as a coordinate (a, b)

To find the x-intercept we need to substitute y = 0 in the above equation.

0 = -2x + 8

2x = 8

x = 4

So, the x-intercept is (4, 0)

To find the y-intercept we need to substitute x = 0 in the above equation.

y = -2(0) + 8

y = 0 + 8

y = 8

So, the y-intercept is (0, 8)

Therefore, for given equation y = -2x + 8, the x-intercept is (4, 0) and the y-intercept is (0, 8)

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Answer:

h(1) = 6

Step-by-step explanation:

h(1) will be

h(x) = 2x² + 4

h(1) = 2(1)² + 4 = 2 + 4

h(1) = 6

Subtract 6 from both sides.

Subtract 6 from 12 to get 6.

Divide both sides by −6. Since −6 is <0, the inequality direction is changed.

Divide 6 by −6 to get −1.

A tangent and a radius of a circle meet to form a 90 angle is a true statement about a tangent and a radius.

The straight line that "just touches" the curve at a particular location is known as the tangent line (or simply tangent) to a plane curve in geometry. A circle or sphere's radius is any line segment that connects the object's center to its perimeter in classical geometry; in more contemporary use, it also refers to the length of such line segments.

A tangent is a line that very slightly touches the circumference of a circle. The angle between a radius and a tangent is always exactly 90 degrees if the radius and circumference are drawn at the same location.

Hence the correct option is B

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Answer:

He still owes Nikki $5.

Step-by-step explanation:

7 - 2 = 5

Answer:

5

Step-by-step explanation:

7-2=5

Step 1

Given; Austin has a granola recipe that requires 5/6 pounds of oats to make one batch of granola. if Austin uses 2 1/2 pounds of oats while making granola, how many batches has he made?

Step 2

Using ratio

Answer;

Answer:3

Step-by-step explanation:if austin has to make 1 granola with 5/6pounds but he is using only 5/2 pounds to make 1 granola so that he can make 3 granulas with 5/6

According to the graph we have:

Domain are the values of x. We can see that the graph extends horizontally from -5 to 3, but -5 and 3 are not included. Then, the domain is

Range are the values of y. Therefore, we see that the graph extends vertically from 4 to -3, so the range is:

Answer:

a. domain = (-5, 3)

b. range = (-3, 4)

Answer: first six cannot go into three because three is too small so six is going to go into 31 Six can go into 31 five times because 6×5 = 30 then since you’re subtracting 31 and 30 you would be left with one you would have to bring the 1 from the 12 down and then it would be 11.  11 can go into six once so 6-11 =5 so then you have to bring the two from the 12 down so then that would equal 6-2=4 and your done! It was a little confusing so if it didn’t make sense I’m sorry

ANSWER:

m = -3/4

b = -3

STEP-BY-STEP EXPLANATION:

We have that the equation in its slope-intercept form is the following:

We calculate the slope as follows:

To calculate the slope we use the intercepts that are (-4, 0) and (0, -3), we replace:

Now, the value of b would be -3, since the y-intercept is (0,-3), therefore, the equation would be:

I adore BTS (the Korean boy band) because they encourage self-love. Their songs are artistically and romantically rich. They're well-known throughout the world and at the moment's top boy band in the US.

In this sense, understanding the worth and excellence of various musical genres is referred to as appreciation. The word "appreciation" has philosophical roots; in that discipline, it is defined in relation to music as "a type of formal counterpart of emotional experience."

Someone's mood can be improved by listening to their music, which can also thrill or calm the listener. Importantly, music also enables us to experience almost all of the emotions we go through in life. There are countless options. Dopamine release in the mesolimbic reward system can be triggered by listening to extremely pleasurable music.

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The height of balloon is 1.99 miles above the ground.

In the event when the line of sight is directed downhill from the horizontal line, an angle is created with it. Angle of depression is the angle produced between the horizontal line and the observer's line of sight when the object being observed is below the level of the observer.

Let's give the balloon's height above the earth and the distance it is from the first milepost horizontally a name.

We can state the following if the angle of this milepost's depression is 24 degrees:

Tan(24)=[tex]\frac{h}{b}[/tex]

b = [tex]\frac{h}{tan(24)}[/tex]

We can state the following for the following milepost as there will be (b+1)miles horizontal distance of and a 20 degree depression at that location.

tan(20)=[tex]\frac{h}{b+1}[/tex]

b +1  = [tex]\frac{h}{tan(20)}[/tex]

Therefore, substituting equation 1

[tex]\frac{h}{tan(24)}[/tex] = [tex]\frac{h}{tan(20)} -1[/tex]

1 =   [tex]\frac{h}{tan(20)}[/tex] - [tex]\frac{h}{tan(24)}[/tex]

1 = h× ( [tex]\frac{h}{tan(20)}[/tex] - [tex]\frac{h}{tan(24)}[/tex] )

h = 1.99 miles

Consequently, the height of balloon is 1.99 miles above the ground.

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Answer:

72

Step-by-step explanation:

8 = 2×2^2

18 = 2×3^2

32 = 2×4^2

50 = 2×5^2

72 = 2×6^2

Option A, Y- axis is the line of reflection used to map the preimage to its image.

The graph shows that if the graph is folded by a y-axis, Point G will cross Point G', which is two coordinates away from the y-axis.

Point F will cross point F', which is four coordinates away from the y-axis.

Points H will cross point H', which is in negative coordinates and 7 coordinates away from the y-axis.

Mirror images are symmetrical from any axis, which might be the x-axis or the y-axis. Flipping geometry refers to reflection. Mirror reflection is a type of reflection. When lines reflect an image, reflection lines form. A form is said to mirror another shape if each of its points is equidistant from each of the other shape's points.

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The firm should produce 12 oak chairs and 8 walnut chairs to maximize its profit to $8,800.

So,

(Refer to the graph attached below)

Then,

So, oak chair produced:

Therefore, the firm should produce 12 oak chairs and 8 walnut chairs to maximize its profit to $8,800.

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The correct question is given below:

Solve the linear programming problem: A small business produces oak chairs and walnut chairs. The business can make at most 20 chairs per week. Materials cost $100 per oak chair and $150 per walnut chair. The business has a budget of $2400 per week for materials. Each oak chair sells for $400 and each walnut chair sells for $500. How many each types of chairs should the business make each week to maximize income?

The equation y = - 1 / 6 x + 3 in standard form is x + 6y = 18.

The standard form for linear equations in two variables is Ax + By = C.

where

Therefore, let's represent the equation y = - 1 / 6 x + 3 in standard form .

y = - 1 / 6 x + 3

multiply the equation by 6 to eliminate the fraction

6y = 6(- 1 / 6 x) + 6(3)

Therefore,

6y = - x + 18

x + 6y = 18

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SOLUTION

Given the question in the question tab, the following are the solution steps to get the equation

Step 1: Represent the statement using mathematical notation

Base salary is $2500 (Base salary is constant since it does not change)

P represent his total pay (in dollars)

N represent the number of copies of English is Fun he sells

price made per copy of the product is $80

The equation relating P to N will be written as:

Part B: Using this equation in step 1 above to find his total pay if he sells 28 copies of English is Fun

Hence, his total pay if he sells 28 copies of English is Fun is $4740

An arc is, in general, any straight curve that connects two points. The term "arc length" refers to an arc's length. Make an arc by setting the compass's needle at A. Please indicate intersections B and C.

An arc is, in general, any straight curve that connects two points. The term "arc length" refers to an arc's length. A graph arc is an ordered pair of adjacent vertices in a graph. An arc is specifically any section of a circle's circumference (other than the full curve).

An "arc" in mathematics is a straight line that connects two endpoints. An arc is typically one of a circle's parts. In essence, it is a portion of a circle's circumference. A curve contains an arc.

A circle's circumference forms an arc. An arc length is the length of the arc, whereas an arc measure is the measurement of the angle the arc makes at the center of a circle.

Therefore, the correct answer is option b) Step 2. Put the point of the compass at A and make an arc. Label the intersections B and C

The complete question is:

What is the next step in the construction?

a) Step 1: Select a point on line 1 and label it point A. Draw in PA.

b) Step 2. Put the point of the compass at A and make an arc. Label the intersections B and C

c) Step 3. Without changing the compass setting. put the compass at point P and make an identical arc. Label the intersection D

d) Step 4. Put the compass at point B and use it to measure the distance to C.

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The correct option regarding the continuity of f(x) at x = 2 is given by:

B. lim x -> 2 f(x) exists, but f(2) exist.

A function f(x) is continuous at x = a if it is defined at x = a, and the lateral limits are equal, that is, if these three conditions are respected:

[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]

For this problem, the denominator of the function is:

8cos(0.5πx) + 2x²

At x = 2, the denominator of the function is:

8cos(0.5π(2)) + 2(2)² = 8cos(π) + 8 = -8 + 8 = 0 (as cos(π) = -1).

Then the function does not exist at x = 2, as the denominator is of 2.

From the graph of the function given at the end of the answer, we have that the lateral limits are as follows:

Since the lateral limits are equal, the limit exists, hence option B is correct.

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Answer:

y = 3 - 2x

Step-by-step explanation:

Subtract 2x from both sides of the equation.

Answer:

y = x or 1x

Step-by-step explanation:

x as a variable can also be expressed as 1x.

so we can say that    2x + 1x

because x & y are two different type of variables. you think of y as a question mark ( ? ).

Now the new equation is

y = ?

so 1x + ? = 3

because x is the same thing as a 1x you can say that 2x + 1x = 3

To find the inverse of a function:

[tex]f(x)= 2x-\dfrac{9}{4}[/tex]

⇒ Replace f(x) with y:

[tex]y= 2x-\dfrac{9}{4}[/tex]

⇒ Switch around y and x:

[tex]x= 2y-\dfrac{9}{4}[/tex]

⇒ Isolate y:

[tex]x+\dfrac{9}{4}= 2y\\\\\dfrac{1}{2}(x+\dfrac{9}{4})= 2y(\dfrac{1}{2})\\\\\dfrac{1}{2}x+(\dfrac{1}{2}*\dfrac{9}{4})= y\\\\\dfrac{1}{2}x+\dfrac{9}{8}= y\\\\y=\dfrac{1}{2}x+\dfrac{9}{8}[/tex]

⇒ Replace y with f⁻¹(x):

[tex]f^{-1}(x)=\dfrac{1}{2}x+\dfrac{9}{8}[/tex]

[tex]f^{-1}(x)=\dfrac{1}{2}x+\dfrac{9}{8}[/tex]

The midpoint of two coordinates can be obtained using the formula:

x1 = -1

y1= 2

x2= -7

y2= -4

You can never achieve break even by selling any number of boxes of candy if it costs them an additional $3 to manufacture each box of candy.

In economics, business, and particularly cost accounting, the break-even point is the point at which total cost and total income are equal, or "even."

Although these opportunity costs have been paid and then capital has received the risk-adjusted, projected return, there is no net loss or gain, and one has "broken even."

Fixed cost (in manufacturing) = $500

Manufacturing cost of each candy = $3

and selling price of candy = $3

let x be a box of candy sold,

hence for no of box to be sold for a break even,

3x + 500 = 3x

but if you see above equation, that has no solution

Hence by providing each candy at $3 with $500 fixed cost and selling cost again at $3 you cannot achieve a break-even point.

hence there is no solution, and you will never be able to achieve break even.

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Answer: P=212*(1.240)n

Step-by-step explanation:

1) Find the % growth

263-212= 51

51/212 = 0.240566037735849

2) Add 1 to the decimal as the population isn't decreasing but increasing.

0.240566037735849 + 1 = 1.240

3) Fill in the equation

P=212*(1.240)n

Answer:

360 naira hope it will be helpful

Step-by-step explanation:

In this case, we have 6 places to fill from a pool of 22 candidates. There is no difference in the places: they are all commissioners, so if candidate A is selected, the order does not matter, but there is only one candidate, so there is no repetition.

Then, this is a combination (as the order does not matter) with no repetition of 22 elements in 6 places.

We can calculate this as:

Answer: there are 17,907,120 ways this can be done.