Here is a list of ages (years) of children in a room:

8
,


8
,


9
,


5
,


10
,


4
,


9


State the median.

The value of x in the equation [tex]\frac{4x}{x - 1} - \frac{5x}{x -2} = \frac{2}{x^2 - 3x + 2}[/tex] is x = -1 or x = -2

The equation is given as:

[tex]\frac{4x}{x - 1} - \frac{5x}{x -2} = \frac{2}{x^2 - 3x + 2}[/tex]

Start by taking the LCM

[tex]\frac{4x(x - 2) - 5x(x - 1)}{(x - 1)(x -2)} = \frac{2}{x^2 - 3x + 2}[/tex]

Expand the denominator

[tex]\frac{4x(x - 2) - 5x(x - 1)}{x^2 -3x +2} = \frac{2}{x^2 - 3x + 2}[/tex]

Cancel out the common factor

4x(x - 2) - 5x(x - 1)= 2

Expand

[tex]4x^2 - 8x - 5x^2 + 5x = 2[/tex]

Evaluate the like terms

[tex]-x^2 - 3x = 2[/tex]

Rewrite as:

[tex]x^2 + 3x + 2 = 0\\[/tex]

Expand

[tex]x^2 + 2x + x + 2 = 0[/tex]

Factorize

x(x + 2) + 1(x + 2) = 0

Factor out x + 2

(x + 1)(x + 2) = 0

Solve for x

x = -1 or x = -2

Hence, the value of x in the equation [tex]\frac{4x}{x - 1} - \frac{5x}{x -2} = \frac{2}{x^2 - 3x + 2}[/tex] is x = -1 or x = -2

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Using the graph of the function concept, the numeric value at x = 2 is f(-2) = 0.

To find the numeric value of a function at x = a, we look at the value of y(vertical axis) where x = a has a closed interval.

Researching the problem on the internet, looking at it's graph, it is found that when x = -2, there is a closed interval at y = 0, hence f(-2) = 0.

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Answer:

Step-by-step explanation:

(√3 + √11)² + (√3 - √11)²

Now ,

(√3 + √11)² + (√3 - √11)²

(3 + 11 + 2√3√11)+ (3 +11 - 2√3√11)

14 + 2√33+ 14 - 2√33

14 + 14 = 28

Hence , The value of (√3 + √11)² + (√3 - √11)² is 28 .

Answer:

28

Step-by-step explanation:

(a + b)² + (a - b)² = 2a² + 2b²

(√3 + √11)² + (√3 - √11)²

= 2√3² + 2√11²

= 28

Answer:

Which one does not belong to the group

Answer:

12x

Step-by-step explanation:

It has no exponent so it is not a polynomial

Answer:

5.25

Step-by-step explanation:

Answer:

Step-by-step explanation:

type 63 : 12 in your calculator

see the example in the attachment.

Answer:

y=8+10x that then answer I guess

The graph of the greatest integer function is graph A.

A graph is a diagram or a pictorial representation of data or values that show the relationship between quantities or objects.

Given are graphs we need to find the graph of the greatest integer function,

The graph of the greatest integer function is graph A because since it is a greatest integer function, it includes the highest integer, but excludes the lowest since it is the highest integer when x is less than or equal to an integer but greater than x-1.

Hence the graph of the greatest integer function is graph A.

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Answer:

x = 136

Step-by-step explanation:

x = 180 - 22 - 22

  = 136

    Sin and cos are trigonometry functions used to find measurements in a right triangle.

         [tex]\displaystyle sin=\frac{\text{opposite side}}{hypotenuse}[/tex]

         [tex]\displaystyle cos=\frac{\text{adjacent side}}{hypotenuse}[/tex]

Step-by-step explanation:

the perimeter of a rectangle is

2×length + 2×width

so, here

2×95 + 2×72 = 190 + 144 = 334 m

so, yes, the answer 2. 334 is correct.

The solution is Option B.

The total number of posts is the total perimeter of the rectangular field and the value of N = 334 posts

What is the Perimeter of a Rectangle?

The perimeter P of a rectangle is given by the formula, P=2 ( L + W) , where L is the length and W is the width of the rectangle.

Perimeter P = 2 ( Length + Width )

Given data ,

Let the number of posts be = N

Fencing posts have to be fixed at 1-metre intervals

The perimeter of the rectangular field = number of posts

Now , the equation will be

The length of the rectangular field = 95 m

The width of the rectangular field = 72 m

Perimeter P of the rectangle = 2 ( Length + Width )

Substituting the values in the equation , we get

Perimeter of the rectangle P = 2 ( 95 + 72 )

On simplifying the equation , we get

Perimeter of the rectangle P = 2 ( 167 )

Perimeter of the rectangle P = 334 m

Now , the number of posts = perimeter of the rectangular

So , the number of posts N = 334 posts

Therefore , the value of N is 334

Hence , the number of posts is 334 posts

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Answer:

D

Step-by-step explanation:

Trust me

An equation is formed of two equal expressions. The correct option is A, the sum will be equal to 5x = 10.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Given the two systems of equations Equation1: 2x+y=4 and Equation 2: 3x-y=6. Now if the two of the given equations are added the result will be,

2x + y + 3x - y = 4 + 6

5x  = 10

Hence, the correct option is A, the sum will be equal to 5x = 10.

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Answer:

$390

Step-by-step explanation:

The wage rate for Kailyn is ($146.25/15 hours) = $9.75/hour

40 hours would result in:

(40 hours)*($9.75/hour) = $390

Answer:

∠1 and ∠2, ∠7 and ∠8

Answer:

∠1 and ∠7, ∠2 and ∠8

Step-by-step explanation:

just took the quiz

Based on the calculations on the bisector of ST, the value of ST are equal to 38 and 30 respectively.

In order to determine the bisector of a line segment with two (2) endpoints, we would add each point together and divide by two (2).

For exercise 1, we have:

ST = SM + MT

ST = 19 + 19

ST = 38.

For exercise 2, we have:

First of all, we would determine the value of x as follows;

3x - 6 = x + 8

3x - x = 8 + 6

2x = 14

x = 14/2

x = 7.

ST = SM + MT

ST = 3x - 6 + x + 8

ST = 3(7) - 6 + 7 + 8

ST = 30.

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Answer:

r = - 3.25, p = -1.5

Step-by-step explanation:

→ Rearrange p - 2r = 5

p = 5 + 2r

→ Substitute into 6p - 4r = 4

6 ( 5 + 2r ) - 4r = 4

→ Expand

30 + 12r - 4r = 4

→ Simplify and solve

r = - 3.25

→ Substitute into p - 2r = 5

p + 6.5 = 5

→ Minus 6.5 from both sides

p = -1.5

Answer:

[tex]\textsf{B.} \quad (f \cdot g)(x)=10x[/tex]

Step-by-step explanation:

Given:

[tex]\begin{cases}f(x)=\sqrt{50x}\\g(x)=\sqrt{2x}\end{cases}[/tex]

[tex]\begin{aligned}\textsf{As }(f \cdot g)(x) & = f(x) \cdot g(x)\\\implies (f \cdot g)(x)& = \sqrt{50x} \cdot \sqrt{2x}\end{aligned}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{a}\sqrt{b}=\sqrt{ab}:[/tex]

[tex]\begin{aligned}\implies (f \cdot g)(x) &= \sqrt{50x2x}\\& = \sqrt{100x^2}\end{aligned}[/tex]

Rewrite 100 as 10²:

[tex]\implies (f \cdot g)(x)=\sqrt{10^2x^2}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^bc^b=(ac)^b:[/tex]

[tex]\implies (f \cdot g)(x)= \sqrt{(10x)^2}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{a^2}=a, \quad a \geq 0:[/tex]

[tex]\implies (f \cdot g)(x)=10x[/tex]

Solution:

[tex]\dfrac{\left[\left(\sin ^{2} A+2 \times \sin A \times (1-\cos A)+(1-\cos A)^{2}\right]\right.}{\left[\left(1-\cos ^{2} A\right)-(1-\cos A)^{2}\right]}[/tex]

[tex]\dfrac{\left[\left(1-\cos ^{2} A\right)+2 \times \sin A \times (1-\cos A)+(1-\cos A)^{2}\right]}{\left[(1-\cos A)(1+\cos A)-(1-\cos A)^{2}\right]} [/tex]

[tex]\dfrac{(1-\cos A)[1+\cos A+2 \sin A+1-\cos A]}{[1-\cos A][1+\cos A-1+\cos A]} [/tex]

[tex]\dfrac{[2+2 \sin A]}{[2 \times \cos A]}[/tex]

[tex]\dfrac{2(1+\sin A)}{2 \times \cos A}[/tex]

[tex]\dfrac{1+\cos A}{\sin A} [/tex]

Hence Proved.

First find the Slope-intercept form of the graph:

b=1

Given the points: (0,1)&(3,0)

slope= [tex]\frac{y1-y2}{x1-x2} =\frac{1-0}{0-3} =\frac{-1}{3}[/tex]

The line is not a dashed line, so that means the values on the slope (blue) are also counted

All the y values below the slope are counted, the inequality is:

y[tex]\leq \frac{-1}{3}x +1[/tex]

Hope it helps!

The cost to buy 18 notebooks and 12 desktop computers will be $8100.

The cost to buy n notebooks and d desktop computers will be 300n + 225d

The cost of a given material is the amount attached and to be paid for getting that material.

From the given information:

The cost to buy 18 notebooks and 12 desktop computers will be:

= 300(18) + 225(12)

= 5400 + 2700

= $8100

The cost to buy n notebooks and d desktop computers will be:

= 300(n) + 225(d)

= 300n + 225d

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Answer:

A

Step-by-step explanation:

Since x has a negative coefficient, the graph opens downwards meaning that it has a maximum.

The vertex formula is y = a(x - h)^2 + k so the coordinate must be (-6, 6).

Using limits, it is found that the true statement regarding the end behavior of the function is given by:

B. As the value of x increases, f is the only function to approach 0.

The end behavior of a function is given by the limit of the function as x goes to infinity.

In this problem, we have that:

Hence statement B is correct.

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Answer:

5377

Step-by-step explanation:

this is a vector question where how far is the Resultant. that is, it is determined by the magnitude of the Hypotenuse.

using Pythagoras theorem

Hypotenuse ²= Opposite ²+Adjacent²

Hypotenuse ²= 2865²+4550²

Hypotenuse ²= 8208225+20702500

Hypotenuse ²=28910725

Hypotenuse=√28910725

Hypotenuse=5376.86944234282

Hypotenuse= 5377 approximated

Answer

c 

I'm not sure how to explain my bad

Answer:

1.19

Step-by-step explanation:

1) Shift the decimals of both 0.8449 and 0.71 to the right by 2 decimal places. (This is needed to convert 0.71 to 71, since long division must divide by a whole number.)

84.49 ÷ 71

2)  Use the algorithm method.

1 . 1 9

7 1 | 8 4 . 4 9

7     1 .  

1 3 . 4

7 . 1

6 . 3 9

6 . 3 9

3) Therefore,  0.8449 ÷ 0.71 = 1.19.

1.19

Answer:

[tex]x=-8, -1[/tex]

Step-by-step explanation:

Given the equation [tex]x^{2} +9x+8=0\\[/tex],

By the quadratic formula,

[tex]x=\frac{-b+-\sqrt{b^{2}-4ac } }{2a}[/tex],

[tex]x=\frac{-(9)+-\sqrt{(9)^{2}-4(1)(8) } }{2(1)}=\frac{-9+-\sqrt{49 } }{2}=\frac{-9+-7 }{2}[/tex]

We have two different solutions for x where [tex]x=\frac{-9-7 }{2}[/tex] and [tex]x=\frac{-9+7 }{2}[/tex]

So, x = [tex]-16/2=-8[/tex] and [tex]x=-2/2=-1[/tex]

Therefore, the solutions to this quadratic equation is x = -8, -1, by the quadratic formula.

The substance's half-life is 4.7 days if the 11-gram sample of a substance that’s used to treat thyroid disorders has a k- the value of 0.15

During exponential decay, a quantity falls slowly at first before rapidly decreasing. The exponential decay formula is used to calculate population decline and can also be used to calculate half-life.

We have an exponential function:

[tex]\rm N = N_oe^{-kt}[/tex]

Plug N = N⁰/2

[tex]\rm N_o/2 = N_oe^{-kt}[/tex]

[tex]\rm \dfrac{1}{2} = e^{-0.15t}[/tex]

Solving for t:

t = 4.62≈ 4.7 days

Thus, the substance's half-life is 4.7 days if the 11-gram sample of a substance that’s used to treat thyroid disorders has a k- the value of 0.15

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