Which expression is equivalent to (4mn/m^-2n^6)^-2

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.

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]

For the system of equations, we need to plot a straight line passing through the intercepts.

Inequalities are equations separated by an equal sign. Given the following system of inequality

3y >2x + 12

2x + y ≤ -5

For the system of equations, we need to plot a straight line passing through the intercepts.

For the inequality 3y >2x + 12, the upper part of the graph will be shaded and the line dashed.

For the inequality 3y >2x + 12, the lower part of the graph will be shaded and the line solid.

The graph of the system of equations is graphed below

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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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The correct statement about the function represented by the table will be option (D) It is linear function because the y-value increases by an equal difference over equal interval of x-values

The terms "linear function" in mathematics apply to two different but related ideas: A polynomial function of degree zero or one that has a straight line as its graph is referred to as a linear function in calculus and related fields.

Given a table on which there are two column in which one column represents x values while other column represent the y values

We have to find whether the relationship between x value and y value is linear or exponential

From given table let,

y₁ = 34; y₂ = 41; y₃ = 48; y₄ = 55

x₁ = 1; x₂ = 2; x₃ = 3; x₄ = 4

If the relationship between the x value and y value is linear then the difference between two consecutive value of x value and y value would be equal

So y₂-y₁ = y₄-y₃ and x₂-x₁ = x₄-x₃

Putting the value we get difference of y value 7 and x value as 1 since it is same we can say that the relation ship between x value and y value is linear

Hence the correct statement about the function represented by the table will be option (D) It is linear function because the y-value increases by an equal difference over equal interval of x-values

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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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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 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:

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:

both the slopes and the y intercepts are the same for both of these functions because if you look at the graph you will notice that the y intercept is positive 3 just the function and to get its slope just use the formula y2-y1/x2-x1 to get the slope of also a -2 so answer is b

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

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

Answer:

Its option C

As,

x+8=3x

8= 3x-x

8=2x

8/2=x

4=x

#x=4

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]

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 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:

[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

Answer:-96

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

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

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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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:

-0.5

Step-by-step explanation:

Total distance around a shape

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.

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:

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

Answer:

453.592 grams or 454 grams if you round up

Answer:

1 pound = 454 grams

Step-by-step explanation:

Multiply 454 into the value.