help mee answer the question

[tex]\dfrac{7x^2+14}{(x^2+3)^2}=\dfrac{7x^2+21-7}{(x^2+3)^2}=\dfrac{7x^2+21}{(x^2+3)^2}-\dfrac{7}{(x^2+3)^2}=\dfrac{7(x^2+3)}{(x^2+3)^2}-\dfrac{7}{(x^2+3)^2}=\\=\dfrac{7}{x^2+3}-\dfrac{7}{(x^2+3)^2}[/tex]

Answer:

[tex]y = \frac{2}{3}x -6[/tex]

Step-by-step explanation:

I'm just gonna assume you want the equation of the line

Standard slope-intercept form is [tex]y=mx+b[/tex] with [tex]m[/tex] being the slope [tex]\frac{rise}{run}[/tex] (aka [tex]\frac{y_1 - y_2}{x_1 - x_2}[/tex]) and [tex]b[/tex] being the y-intercept (the point where the line crosses the y-axis)

First we will find the slope using the 2 points on the line.

[tex]\frac{-2 - (-4)}{6-3} = \frac{2}{3}[/tex]

This means our slope ([tex]m[/tex]) is [tex]\frac{2}{3}[/tex].

Next we can find our y-intercept. The line crosses the y-axis at [tex](0, -6)[/tex] meaning the y-intercept ([tex]b[/tex]) is -6.

Finally we can plug in our values and find the equation of the line.

[tex]y = \frac{2}{3}x -6[/tex]

That might be the answer (i don't know the question)

- Kan Academy Advance

mean is average, add all numbers and divide by quantity of numbers.

Median is the middle value, list the numbers from smallest to largest and find the middle number.

mode is the number that appears the most.

1. Mean = 6

Median = 5

Mode = 6

2. Mean = 86.1

Median = 86.5

Mode = 85

The correct solution to the limits of x in the tiles can be seen below.

The limits of x approaching a given number of a quadratic equation can be determined by knowing the value of x at that given number and substituting the value of x into the quadratic equation.

From the given diagram, we have:

1.

[tex]\mathbf{ \lim_{x \to 9^+} (\dfrac{|x-9|}{-x^2-34+387}) }[/tex]

So, x - 9 is positive when x → 9⁺. Therefore, |x -9) = x - 9

[tex]\mathbf{ \lim_{x \to 9^+} (\dfrac{x-9}{-x^2-34+387}) }[/tex]

Simplifying the quadratic equation, we have:

[tex]\mathbf{ \lim_{x \to 9^+} (-\dfrac{1}{x+43}) }[/tex]

Replacing the value of x = 9

[tex]\mathbf{ = (-\dfrac{1}{9+43}) }[/tex]

[tex]\mathbf{ = -\dfrac{1}{52} }[/tex]

2.

[tex]\mathbf{ \lim_{x \to 8^-} (\dfrac{8-x}{|-x^2-63x+568|}) }[/tex]

Thus |-x²-63x+568| = -x²-63x+568

[tex]\mathbf{ \lim_{x \to 8^-} (\dfrac{1}{x+71}) }[/tex]

[tex]\mathbf{=\dfrac{1}{8+71} }[/tex]

[tex]\mathbf{=\dfrac{1}{79} }[/tex]

3.

[tex]\mathbf{ \lim_{x \to 7^+} (\dfrac{|-x^2-17x+168| }{x-7}) }[/tex]

[tex]\mathbf{ \lim_{x \to 7^+} (\dfrac{-x^2-17x+168 }{x-7}) }[/tex]

[tex]\mathbf{ \lim_{x \to 7^+} (-x-24)}[/tex]

[tex]\mathbf{ \lim_{x \to 7^+} (-7-24)}[/tex]

= -31

4.

[tex]\mathbf{ \lim_{x \to 6^-} (\dfrac{|x-6| }{-x^2-86x+552}) }[/tex]

[tex]\mathbf{ \lim_{x \to 6^-} (\dfrac{-x+6 }{-x^2-86x+552}) }[/tex]

[tex]\mathbf{ \lim_{x \to 6^-} (\dfrac{1}{x+92}) }[/tex]

[tex]\mathbf{ \lim_{x \to 6^-} (\dfrac{1}{6+92}) }[/tex]

[tex]\mathbf{ =\dfrac{1}{98}}[/tex]

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The least integer value that satisfies the inequality   [tex]2^{x-7} - 3[/tex] ≥ y is 7.

Exponential function, as its name suggests, involves exponents. But note that, an exponential function has a constant as its base and a variable as its exponent but not the other way round.

Here, In the given function

            Least possible value of 2ˣ⁻⁷ is 1

                     2ˣ⁻⁷ = 2⁰

    On comparing both sides, we get

                 x-7 = 0

                  x = 7

Thus, The least integer value that satisfies the inequality   2ˣ⁻⁷-3≥ y is 7.

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Answer:

7

Step-by-step explanation:

edg 2022

Answer:

this answer is of 2nd question

Step-by-step explanation:

since it is an isosceles triangle

3y-1=y+11

3y-1=y+113y-y=11+1

2y=12

y=6

now putting the value of y in 3y-1,y+11,4y-9

we get,

3y-1=3*6-1=17

y+11=6+11=17

4y-9=4*6-9=15

Answer:-96

Step-by-step explanation:The answer is -96

Check the picture below.

The perimeter of the triangle with the given dimension of leg is 6+3√2.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem.

Using Pythagoras theorem

c² = a² + b²

where c is the hypotenuse.

Here, c² = 3² + 3²

c = 3√2

So, the perimeter of triangle is

= 3 + 3 + 3√2

= 6 + 3√2

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Answer:

The value of x is 30 degrees.

Step-by-step explanation:

We know that angle 1 is 60 degrees, and that angle two is a right angle (meaning 90 degrees.) 60+90 is equal to 150 degrees. 180 degrees - 150 degrees is equal to 30 degrees. I hope this helps! :)

[tex]~~~~~~\sin \theta = \dfrac{\text{Perpendicular}}{\text{Hypotenuse}}\\\\\\\implies \sin 60^{\circ} = \dfrac{x}{8}\\\\\\\implies x = 8 \sin 60^{\circ}\\\\\\\implies x = 8 \cdot \dfrac {\sqrt3}2\\\\\\\implies x = 4\sqrt 3[/tex]

Answer:

B

Step-by-step explanation:

(f + g)(x)

= f(x) + g(x)

= 2x + 1 + x² - 7 ← collect like terms

= x² + 2x - 6 ← in standard form

The value of (f + g)(x) is x² + 2x - 6.

Arithmetic operations are a set of four basic operations to be performed to add, subtract, multiply or divide two or more quantities. They include the study of numbers including order of operations which are useful in all the other parts of mathematics such as algebra, data handling, and geometry.

Given are two functions, f(x) = 2x+1 and g(x) = x²-7, we are asked to find

(f + g)(x),

So we know,

(f + g)(x) = f(x) + g(x)

Therefore,

(f + g)(x)

= f(x) + g(x)

= 2x + 1 + x² - 7

= x² + 2x - 6

Hence the value of (f + g)(x) is x² + 2x - 6.

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Answer:

a)  26 tickets

b)  £5

c)  chips, pastie and a soft drink

Step-by-step explanation:

Given:

Part (a)

Greatest number of tickets = total available to spend ÷ cost of one ticket

                                             = 200 ÷ 7.5

                                             = 26.66666...

                                             = 26 tickets

(We can't round up, as 27 tickets would cost £202.50)

Part (b)

Money left = Total available spend - cost of 26 tickets

                  = 200 - (26 × 7.50)

                  = 200 - 195

                  = £5

Part (c)

Cost of 3 items = £10 - change

                         = £10 - £4.70

                         = £5.30

One of the items can't be a burger, as £5.30 - £3.50 = £1.80
and £1.80 is not enough to buy 2 items.

If he buys chips, he has: £5.30 - £2.40 = £2.90 left to spend on the other 2 items.

Pastie + Soft Drink = £1.60 + £1.30 = £2.90

So he can buy: chips, pastie and a soft drink

By applying knowledge on complex analysis, the complex numbers that satisfy the three conditions defined in the statement are z₁ = 4 - i 3 and z₂ = 5 + i 12.

In this question we must derive two complex numbers such that the following conditions are fulfilled:

a² + b² = 5²     (1)

c² + d² = 13²     (2)

13 · (a + i b) - 5 · (c + i d) = 27 - i 99     (3)

If we assume that a, b, c, d are integers, then we can suppose that (a, b) = (4, -3) and (c, d) = (5, 12) and we check if these values satisfy (3):

13 · (4 - i 3) - 5 · (5 + i 12)

52 - i 39 - 25 - i 60

27 - i 99

By applying knowledge on complex analysis, the complex numbers that satisfy the three conditions defined in the statement are z₁ = 4 - i 3 and z₂ = 5 + i 12.

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Answer:

-0.5

Step-by-step explanation:

Answer:

112

Step-by-step explanation:

▪︎ Volume of pyramid = (1/3) * base area * height

▪︎ Base area = 8 * 7

▪︎ Height = 6

▪︎ Volume = 8 * 7 * 6 / 3 = 112

To better give a visual, I drew it out instead.

The attachment is the solution.

Answer:

(4, 5)

(4, 2)

(6, 2)

Step-by-step explanation:

add 3 in "x" and 1 in "y"

(1, 4) ⇒ (1+3, 4+1) = (4, 5)

(1 , 1) ⇒ (1+3 , 1+1) = (4, 2)

(3, 1) ⇒ (3+3, 1+1) = (6, 2 )

Hope this helps

The coordinates of point R of the given line segment are (-3.5, -7)

We are given the coordinates;

L (-8,-10) to M (4,-2)

We are told that they are partitioned in the ratio 3 to 5.

Thus;

The coordinates of R divide directed line segment from L (-8,-10) to M (4,-2) in ratio 3:5will be :

x = [3(4) + 5(-8)]/(3 + 5)

x = -3.5

y = [3(-2) + 5(-10)]/(3 + 5)

y = -7

Thus, the coordinates of point R are (-3.5, -7)

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The distance travelled from the starting point is 29 km , the bearing is 344 degree

The missing diagram is attached with the answer.

It is the horizontal angle between the object and another object.

It is given that the car starts from point travels for 30km on a bearing of 145, then 10 km on a bearing of 250

(a) the distance travelled from the starting point

It can be understood from the diagram that

To determine the distance , b is to determined4

By applying Cosine rule

b² = a² +c²-2ac cos[tex]\rm \theta[/tex]

b² = 10²  +30²  - 2* 30*10 cos75

b² = 100+900 -600* 0.2588

b² = 100-155.2914

b² = 844.7

b = 29 km

Therefore the distance travelled from the starting point is 29 km.

(b) the bearing of the starting point from the car.

To determine the bearing ,

angle C has to be determined

By sine rule

sin C / c = sin B / b

sin C = sin 75 * 30 / 29

sin C = 0.9970

C = sin⁻¹ 0.9970

C = 85.59 degree

angle C = α +70 degree

α  = 15.59 degree

Bearing = 70 + 20 + 9 0 + 90+74 = 244 degree

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Answer:

0.25m or 1/4m

Step-by-step explanation:

Given Height of Dorsal Fin = 1/6 of Length of whale Sculpture,

and given length of whale sculpture = 1.5m or [tex]1\frac{1}{2} m\\[/tex]

Height of Dorsal fin on scuplture = [tex](\frac{1}{6})(1\frac{1}{2} )\\[/tex]

= [tex](\frac{1}{6} )(\frac{3}{2}) \\= \frac{3}{12} \\= \frac{1}{4}m or 0.25m[/tex]

The measure of the radius of the cylinder to the nearest tenth is 1.7cm

The formula for calculating the surface area of a cylinder is expressed as:

S = 2πr(r+h)

Given the following

S=. 125cm²

h = 10cm

Substitute

125 = 2πr(r+10)

Expand

125 = 2(3.14)r² + 20(3.14)r
6.28r² + 62.8r - 125 = 0

Factorize

On factorizing, the measure of the radius of the cylinder will be 1.7cm

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Answer:

Negative; it describes a violent reaction based on rage.

Step-by-step explanation:

Answer:

A) z

Step-by-step explanation:

(8z - 10) ÷ (-2) + 5(z - 1)

1. Rewrite:

 [tex]\large \textsf{$\dfrac{(8x-10)}{-2}+5(z-1)$}[/tex]

2. Distribute 5

[tex]\large \textsf{$5(z-1)$}\\\\\large \textsf{$5(z)+5(-1)$}\\\\\large \textsf{$5z-5$}[/tex]

Now we have:

[tex]\large \textsf{$\dfrac{(8x-10)}{-2}+\large \textsf{$5z-5$}$}[/tex]

3. Reduce the fraction:

[tex]\large \textsf{$\dfrac{(8x-10)}{-2}+\large \textsf{$5z-5$}$}\\\\\large \textsf{$-4x+5+5z-5$}[/tex]

4. Combine like terms:

[tex]\large \textsf{$-4x+5+5z-5$}=\large \textsf{z}[/tex]

Final answer: z

Hope this helps!

Answer:

width is 30-22 = 8 feet

George would need 76 feet of fencing for the dog run

Step-by-step explanation:

30 x (30-x) = 240

30-x = 8

-x = -22

x = 22

Therefore width is 30-22 = 8 feet

8+8+30+30 = 76

Thus, George would need 76 feet of fencing for the dog run

The expression that signifies Katherine’s final cost F= P + T= $466

The number of pansies to be arranged around each tree = 15 pansies

The cost of pansies(P) = 15 × 8 × 2.50 = $300

The number of juniper trees available = 8

The cost of the trees available(T) = 8 × 20.75= $166

Therefore Katherine's final cost(F)= $300 + $166 = $466

The expression to find Katherine’s final cost = F= P + T

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The probability a randomly selected student eats breakfast is 0.58.

The probability a randomly selected student is a middle schooler is 0.60.

The probability a randomly selected student is either a high schooler OR eats breakfast is 0.98.

The probability a randomly selected student is a high schooler AND eats breakfast is 0.23.

The probability a randomly selected student is a high schooler, given that they eat breakfast is 0.33.

The probability a randomly selected student eats breakfast given the student is a high schooler is 0.23.

The probability a randomly selected student eats breakfast = number of students that eat breakfast / total number of students

52 / (52 + 38) =  0.58.

The probability a randomly selected student is a middle schooler = total number of middle schoolers / total number of students = (40 + 14) / 90 =  0.60.

The probability a randomly selected student is either a high schooler OR eats breakfast = (total number of high schoolers / total number of students) + (number of students that eat breakfast / total number of students) = 36 / 90 + 52 / 90 =  0.98.

The probability a randomly selected student is a high schooler AND eats breakfast = (total number of high schoolers / total number of students) x (number of students that eat breakfast / total number of students) = 36 / 90 x 52 / 90 =  0.23.

The probability a randomly selected student is a high schooler, given that they eat breakfast = high schooler that eats breakfast / total number of students that eat breakfast

12 / 52 =  0.33.

The probability a randomly selected student eats breakfast given the student is a high schooler = high schooler that eats breakfast / total number of high schoolers = 12 / 36 = 0.23.

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Answer:

15

Step-by-step explanation:

For this question you would need to do a squared + b squared so 9x9 is 91 + 12x12 which is 144. you add the two up then find the square root of that which should make your answer 15

The required total distance the ball travels, approximately, is 180 feet.

Let's denote the height of the first fall as a (initial height of 60 feet), and the distance covered during each rebound as r (two-thirds the distance of the previous fall).

The first fall distance (a) is 60 feet.

The first rebound distance (r) is (2/3) * 60 feet.

The total distance covered during the first fall and rebound cycle is:

60 + (2/3) * 60 = 60 + 40 = 100 feet.

Now, for the subsequent cycles, the ball will continue to fall and rebound in the same pattern:

Second fall distance = r * a
                                  = (2/3) * 60
                                  = 40 feet.

Second rebound distance = r*(2/3) * 60
                                            = (2/3) * 40
                                            = 80/3 feet.

The total distance covered during the second fall and rebound cycle is:

40 + (80/3) ≈ 66.67 feet.

The pattern will continue for the subsequent cycles.

To represent this as an infinite geometric series, we can write:

Total distance = [tex]a + (a * r) + (a * r^2) + (a * r^3) + ...[/tex]

Where:

a = 60 feet (height of the first fall)

r = 2/3 (rebound factor)

Using the formula for the sum of an infinite geometric series:

Total distance = a / (1 - r)

Total distance = 60 / (1 - 2/3)

Total distance = 60 / (1/3)

Total distance = 60 * 3

Total distance = 180 feet.

Therefore, the total distance the ball travels, approximately, is 180 feet.

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Answer:

y=-1/1x

Step-by-step explanation:

First, let's take the slope of a line equation:

y=mx+b

Now, all we have to do is find the slope(m) and the y-intercept(b).

The line intercepts the y axis at 0, so b=0.

Next, find the slope.

The equation to FIND slope is rise/run, so we can solve that:

1/1=1, but since the line goes down, it's negative.

The slope is 1, so m=1.

Now, put that into m.

y=-1x+0, but we don't need 0, so the answer is y=-1x.

Answer:

Yes! |-15| = 15

Step-by-step explanation:

Many people think of absolute value (the two bars symbol around the -15) as ALWAYS POSITIVE.

You can also think of absolute value as a distance. If you move 15 units, it doesn't matter in what direction you go. 15 units travelled is 15 units.

Lastly, absolute value has a V-shaped graph, that is because its always positive.