Find the area of the rhombus.
9 m
9 m
9 m
9 m

The expression is simplified to x

g(x) = (x ^ 3 - 9x)/(x ^ 2 - 6x + 9)

First, we simplify the numerator

= [tex]\frac{x (x^2 - 3^2)}{x^2 - 6x + 9}[/tex]

Now, let's solve the quadratic equation in the denominator

= [tex]\frac{x(x^2 - 3^2)}{x^2 - 3x - 3x + 9}[/tex]

= [tex]\frac{x(x^2 - 3^2)}{x(x-3) - 3(x - 3)}[/tex]

= [tex]\frac{x(x - 3) (x -3)}{(x -3) ( x-3)}[/tex]

Divide the like factors

= x

The answer is x

Thus, the expression is simplified to x

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If  function 'f' is defined by f(x)=2-x and 2f(p)=8 then the value of f(2p) is 6.

Given, f(x) = 2-x

Solve this problem by making a series of substitutions.

First, find the value of p.

Then use the definition of the function f to find the value of f(2p).

We are given

f(x) = 2 - x

Multiply both sides by 2, and simplify.

2f(x) = 2(-x +2)

2f(x) = -2x + 4

Let x = p.

2f(p) = -2(p) + 4

We are given that 2f(p) = 8.

Substitute 20 for 2f(p).

8 = -2p + 4

2p = -4

p = -2

Now we know that p = -2, so we can find f(2p).

f(x) = -x + 2

f(2p) = -2p + 2

Substitute -2 for p.

f(2p) = -2(-2) + 2

f(2p) = 4 +2

f(2p) = 6

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The true statement of the parabola is (a) directrix will cross through the positive part of the y-axis.

Parabolas are examples of a conic section such that it is formed by the intersection of a cone with a plane parallel to its side.

From the question, the given parameters are:

Vertex = (0,0)

Focus = Negative side of the y-axis

A parabola has quite a number of forms, one of these forms is the general form.

The general form is represented as:

(x - h)^2 = 4p(y - k)

The vertex of the parabola is

(h, k) = (0, 0).

So, we have:

(x - 0)^2 = 4p(y - 0)

Evaluate the difference

x^2 = 4py

Since the focus is on the negative side, the value of p will be negative.

Also, because the vertex is at the origin, the directrix of the parabola will cross through the positive part of the y-axis.

This means that the true statement of the parabola is (a) directrix will cross through the positive part of the y-axis.

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Complete question

A parabola, with its vertex at (0,0), has a focus on the negative part of the y-axis. Which statements about the parabola are true?

Check all that apply.

The directrix will cross through the positive part of the y-axis.

The equation of the parabola will be in the form y2 = 4px where the value of p is negative.

The equation of the parabola will be in the form x2 = 4py where the value of p is positive.

The equation of the parabola could be y2 = 4x.

The equation of the parabola could be x2 = y.

The length of the segment [tex]pt[/tex]is [tex]10[/tex] if the coordinates of [tex]p[/tex] and [tex]t[/tex] is [tex](-6 )and( 4)[/tex]

How can find the length of the segment ?

The coordinate of [tex]p=-6[/tex]

The coordinate of [tex]t=4[/tex]

We can assume only [tex]x[/tex] coordinates given and [tex]y[/tex] coordinates is [tex]0[/tex]

so coordinate of [tex]p=(-6,0)\\[/tex]

And coordinate of [tex]t=(4,0)[/tex]

So the length of the segment

[tex]pt=x_{2} -x_{1} \\pt=4-(-6)\\pt=4+6\\pt=10[/tex]

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The probability of rolling an even number first and an odd number second is; One Fourth

As two cubes are 6 sided, the total number of possibilities as seen in the attached table are;

6 * 6 = 36 possible numbers

Now in those possibilities, the first number will be even and the second number will be odd.  From the the table, such possible pairs are,  

(2,1), (2,3), (2,5), (4,1), (4,3), (4,5), (6,1), (6,3), (6,5)

Therefore, we can see we have a total of 9 sets with the combination of first number even and second number odd.  So, the probability of rolling with this combination will be; 9/36 = 1/4

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The possible outcomes are WH, BH, BH, BH, RH, RH, WL, BL, BL, BL, RL, RL

The given parameters are:

Coin = Head (H) and Tail (T)

Marble = W, B, B, B, R, R

See attachment for the tree diagram

From the tree diagram, we have the following possible outcomes

WH, BH, BH, BH, RH, RH, WL, BL, BL, BL, RL, RL

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The expression for g in terms of other variables is g = Fd^2/m1m2

Given the expression below as shown

F=gm1*m2/d2

We are to make g the subject of the formula

F=gm1*m2/d2

Cross multiply

Fd2 = gm1m2

Divide both sides by m1m2

Fd^2/m1m2 = g

g = Fd^2/m1m2

Hence the expression for g in terms of other variables is g = Fd^2/m1m2

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Answer:

[tex] \frac{6}{20} = \frac{3}{10?} [/tex]

Step-by-step explanation:

total amount of acts = 4+10+6 = 20

amount of dancers = 6

probability of picking a dancer = number of dancers / total number of talents = 6/20 = 3/10

The probability that a dancer performs first is 3/10.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

Given:

The acts in a talent competition consist of 4 instrumentalists, 10 singers, and 6 dancers.

Total participants = 4+ 10 +6 = 20

So, the probability that a dancer performs first

= 6 /20

= 3/10

Hence, the probability that a dancer performs first is 3/10.

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Answer:

see explanation

Step-by-step explanation:

[tex]\frac{3\pi }{4}[/tex] is an angle in the second quadrant where sin > 0 and cos < 0

cos([tex]\frac{3\pi }{4}[/tex] )

= cos (π - [tex]\frac{3\pi }{4}[/tex] )

= - cos ([tex]\frac{\pi }{4}[/tex] )

= - [tex]\frac{\sqrt{2} }{2}[/tex]

and similarly

sin ([tex]\frac{3\pi }{4}[/tex] )

= sin ([tex]\frac{\pi }{4}[/tex] )

= [tex]\frac{\sqrt{2} }{2}[/tex]

Based on the mean, standard deviation, and the graph, the indicated IQ score would be 115.

First, find the z value:

P(Z<z) = 1 - tail value

= 1 - 0.1587

= 0.8413

According to the z-value, this gives a value of:

z = 1

The indicated IQ score is:

= mean + z value z standard deviation

= 100 + 1 x 15

= 115

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Answer:

x = 103.8

Step-by-step explanation:

Calc: [2nd] [VARS] [invNorm]

area: 0.6

z = .2533471011

x = u + (z × o)

x = 103.8

Answer:

okay he's saying that each student gets 25 points to start with and then they get five more like 25 / 25 * 5 or like 25 + 5 or 25 - 5 like represent those numbers and like get the number or something like that

Answer: 39 units

Step-by-step explanation:

Using the distance formula, we get that:

[tex]PT=\sqrt{10^2 + 4^2}=\sqrt{116}\\\\TS=\sqrt{7^2 + 0^2}=7\\\\SR=\sqrt{7^2 + 1^2}=\sqrt{50}\\\\RQ=\sqrt{6^2 + 5^2}=\sqrt{61}\\\\PQ=\sqrt{2^2 + 6^2}=\sqrt{40}[/tex]

So, the perimeter is

[tex]\sqrt{116}+7+\sqrt{50}+\sqrt{61}+\sqrt{40} \approx 39[/tex]

To know the angle measure between the vertices, you divide 360° by 3. Option C

Formula for interior angles of polygon is given as;

= ( n -2 ) × 180 degrees

Hexagon has 6 sides, n = 6

= ( 6 - 2 ) × 180° = 4 × 180° = 720°

Each interior angle = 720/ 6 = 120

To get 120 from 360

= [tex]\frac{360}{120}[/tex]

= [tex]3[/tex]

Thus, to know the angle measure between the vertices, you divide 360° by 3. Option C

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Answer:

6

Step-by-step explanation:

In a regular polygon, all of the angles are congruent.

Answer:

D.) x = 2y²

Step-by-step explanation:

You can find the inverse of an equation by swapping the positions of the "x" and "y" variables. Then, you would need to rearrange the equation to re-isolate the "y" variable.

As such, D.) is the correct option because it is identical to the original equation except that the variables are swapped.

as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solving for "y", let's do so.

[tex]y = 2x^2\hspace{5em}\stackrel{\textit{quick switcheroo}}{\boxed{x = 2y^2}}\implies \cfrac{x}{2}=y^2\implies \sqrt{\cfrac{x}{2}}=\stackrel{f^{-1}(x)}{y}[/tex]

Answer:

look the answer is in the picture and don't forget to like and brainlest

The size of the monitor as measured by the diagonal to the nearest whole inch, 17 inch.

A number's square root is a quantity that, when multiplied by itself, yields the original quantity. There are two ways to calculate the square root of a number: method of prime factorization and division strategy.

For example, both 3 and –3 are square roots of 9

The length of the diagonal of his laptop monitor is squared root of 290

Let 'D' be the diagonal of the monitor.

The,

Diagonal = √290

Use long division method to solve the value,(attached in the file)

√290 = 17.029

          = 17.03

Therefore, the value of √290 rounds to the nearest whole inch is 17 inch.

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The correct question is -

Carlos found that the length of the diagonal of his laptop monitor is squared root of 290. If the manufacturer rounds to the nearest whole inch, what size is the monitor as measured by the diagonal? 12 17 97 245

As currently written, solving for [tex]x[/tex], we have

[tex]\sqrt{15} - x + \sqrt3 - x = 6[/tex]

[tex]2x = \sqrt{15} + \sqrt3 - 6[/tex]

[tex]x = \dfrac{\sqrt{15} +\sqrt3 - 6}2[/tex]

I suspect you meant to write

[tex]\sqrt{15 - x} + \sqrt{3 - x} = 6[/tex]

Move one of the roots to the other side, then take squares on both sides.

[tex]\sqrt{15 - x} = 6 - \sqrt{3 - x}[/tex]

[tex]\left(\sqrt{15 - x}\right)^2 = \left(6 - \sqrt{3 - x}\right)^2[/tex]

[tex]15 - x = 36 - 12 \sqrt{3 - x} + (3 - x)[/tex]

[tex]12 \sqrt{3 - x} = 24[/tex]

Take squares again

[tex]\left(12\sqrt{3-x}\right)^2 = 24^2[/tex]

[tex]144 (3 - x) = 576[/tex]

[tex]432 - 144x = 576[/tex]

[tex]144x = -144[/tex]

[tex]\boxed{x = -1}[/tex]

The distance of the car to the base of the building is 23 metres.

The situation will form a right angle triangle.

Therefore, the distance of the car to the base of the building is the adjacent side of the right angle triangle formed.

Therefore,

tan 35 = opposite / adjacent

tan 35 = 16 / x

x tan 35 = 16

x = 16 / tan 35

Therefore,

x = 16 / 0.70020753821

x = 22.8506141103

x = 23 meters

Therefore, the distance of the car to the base of the building is 23 metres.

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Answer:

20.8

Step-by-step explanation:

Just use the The Pythagorean Theorem

which is a^2+b^2=c^2

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The equation of the line of best fit is y = 1.7x  - 58

We start by drawing the line of best fit (see attachment)

From the attached graph, we have the following points

(x, y) = (70, 75) and (61, 60)

The slope (m) is:

m = (y2 - y1)/(x2 - x1)

This gives

m = (60 - 75)/(61 - 70)

Evaluate

m = 1.7

The line of best fit is then calculated as:

y = m(x - x1) + y1

This gives

y = 1.7(x - 70) + 61

This gives

y = 1.7x - 119 + 61

Evaluate

y = 1.7x  - 58

Hence, the equation of the line of best fit is y = 1.7x  - 58

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The correct options about parabola are:

The focus is located at (0,–3).

The parabola can be represented by the equation x^2 = –12y.

According to the statement

we have given that the vertex is at the origin and directrix at y = 3.

and from these given information and we have to find the all abot the parabola like its focus point etc.

So,

We know that the equation of parabola is

(x-h)^2 = 4p(y-k)

Here The vertex is (h,k). and the focus is at (h,k+p). and the directrix is   y(k - p.)

So, From the given information

Vertex at the origin means that h=0 and k=0

Directrix at y = 3 means that p=-3

Directrix at the y-axis means the parabola opens upwards.

Thus, the focus is: (0,-3)

And The p-value becomes

: 4(-3) = -12.

And from all these the equation of the parabola is becomes

(x)^2 = -12y

So, The correct options about parabola are:

The focus is located at (0,–3).

The parabola can be represented by the equation x^2 = –12y.

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Disclaimer: The question was incomplete. Please find the full content Below.

Question:

A parabola, with its vertex at the origin, has a directrix at y = 3. Which statements about the parabola are true? Select two options.

The focus is located at (0,–3).

The parabola opens to the left.

The p value can be determined by computing 4(3).

The parabola can be represented by the equation x2 = –12y.

The parabola can be represented by the equation y2 = 12x.

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To calculate accurate vital statistics rates to represent the entire United States, the quotient is multiplied by an appropriate factor such as 1,000 or 100,000 to represent the larger population.

As it is given in the description itself, to compute accurate vital statistics rates for the full United States, multiply the quotient by a suitable factor, such as 1,000 or 100,000 to represent the greater population.

Therefore, to calculate accurate vital statistics rates to represent the entire United States, the quotient is multiplied by an appropriate factor such as 1,000 or 100,000 to represent the larger population.

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Answer: [tex]y+4=\frac{7}{3}(x+8)[/tex]

Step-by-step explanation:

See attached image.

The probability that the number chosen is divisible by 5 is; 1/5.

It follows from the task content that the number of possible outcomes in the probability event is; 100. Additionally, the number of required outcomes is 20 as only 20 numbers are divisible by 5.

Ultimately, the required probability is; 20/100 = 1/5.

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Answer:  C) Sometimes positive; sometimes negative

============================================================

Explanation:

Pick a value between x = -1 and x = 0. Let's say we go for x = -0.5

Plug this into f(x)

f(x) = x(x+3)(x+1)(x-4)

f(-0.5) = -0.5(-0.5+3)(-0.5+1)(-0.5-4)

f(-0.5) = -0.5(2.5)(0.5)(-4.5)

f(-0.5) = 2.8125

We get a positive value.

This shows that f(x) is positive on the region of -1 < x < 0

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

Now pick a value between x = 0 and x = 4. I'll use x = 1

f(x) = x(x+3)(x+1)(x-4)

f(1) = 1(1+3)(1+1)(1-4)

f(1) = 1(4)(2)(-3)

f(1) = -24

Therefore, f(x) is negative on the interval 0 < x < 4

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

In short, f(x) is both positive and negative on the interval -1 < x < 4

It's positive when -1 < x < 0

And it's negative when 0 < x < 4

Answer:

sometimes positive sometimes negative

Step-by-step explanation:

I did it on Khan Academy

There are 5005 different groups

The given parameters are:

Players, n = 15

Selected, r = 6

The number of groups is then calculated as:

[tex]Group = ^{n}C_r[/tex]

This gives

[tex]Group = ^{15}C_6[/tex]

Apply the combination formula

[tex]Group = \frac{15!}{9!6!}[/tex]

Evaluate the expression

Group = 5005

Hence, there are 5005 different groups

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The function f(x) = -(1/1500)(x³ + 10x² - 275x - 1500) the zeros are at (-20, 0), (-15, 0) and (15, 0). Hence the factors of the function are x + 20, x + 15 and x - 15.

An equation is an expression that shows the relationship between two or more numbers and variables.

From the graph of the function f(x) = -(1/1500)(x³ + 10x² - 275x - 1500) the zeros are at (-20, 0), (-15, 0) and (15, 0). Hence the factors of the function are x + 20, x + 15 and x - 15.

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If this is the one you are talking about then:

horizontal translation of 3 units is:     y= f(x-3)

vertical stretch by a scale factor of 3 is:     y= 3f(x)

reflection over the x-axis is:     y= -f(x)

vertical translation of 3 units is:     y= f(x)+3

Step-by-step explanation:

Adding a value to f(x) translates the graph of f vertically. So, the equation that shows a vertical translation of 3 units is y = f(x) + 3.

Adding a value to the input, x, of f(x) translates the graph of f horizontally. So, the equation that shows a horizontal translation of 3 units is y = f(x − 3).

Multiplying f(x) by a negative value reflects the graph of f over the x-axis. So, the equation that shows a reflection over the x-axis is y = -f(x).

Multiplying f(x) by a constant, k, vertically stretches the graph of f by a scale factor of k. So, the equation that shows a vertical stretch by a scale factor of 3 is y = 3f(x).

The solution for the system of linear inequalities 7x+2y > 3 and x-2y < 2 are x = 5/8 and y = -11/16

Linear inequalities are inequalities that have constant average rates of change, slope or gradient

A system of linear inequalities is a collection of at least two linear inequalities.

In this case, the system of linear inequalities is given as

7x+2y > 3

x-2y < 2

Rewrite the inequalities as equations

7x+2y = 3

x-2y = 2

Make x the subject in the second equation, by adding 2y to both sides of the equation

x - 2y +2y = 2 + 2y

This gives

x = 2 + 2y

Substitute x = 2 + 2y in 7x+2y = 3

7(2 + 2y) +2y = 3

Expand the brackets

14 + 14y + 2y = 3

Evaluate the like terms

16y = -11

Divide both sides by 16

y = -11/16

Substitute y = -11/16 in x = 2 + 2y

x = 2 - 2 * 11/16

Evaluate the product

x = 2 - 11/8

Evaluate the difference

x = 5/8

Hence, the solution for the system of linear inequalities 7x+2y > 3 and x-2y < 2 are x = 5/8 and y = -11/16

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