A. 8pi

B. pi

C. 2pi

D. 4pi

Answer:

The equivalent ratio of (3m⁻²n)⁻³/6mn⁻² = m⁵/2n

Step-by-step explanation:

Points to remember

Identities

xᵃ * xᵇ = x⁽ᵃ ⁺ ᵇ⁾

xᵃ/xᵇ = x⁽ᵃ ⁻ ᵇ⁾

(xᵃ)ᵇ = xᵃᵇ

x⁻ᵃ = 1/xᵃ

To find the equivalent ratio of (3m⁻²n)⁻³/6mn⁻²

By using identities,

(3m⁻²n)⁻³ = 3m⁶n⁻³

(3m⁻²n)⁻³/6mn⁻² = 3m⁶n⁻³/6mn⁻²

 =  3m⁽⁶⁻¹⁾n⁽⁻³ ⁻ ⁻²⁾/6

 = m⁵n⁻¹/2

 = m⁵/2n

Therefore the equivalent ratio of (3m⁻²n)⁻³/6mn⁻² = m⁵/2n

ANSWER

Option C is correct.

EXPLANATION

The given function is

[tex]y = \sqrt[3]{x - 1} + 3[/tex]

The base function is

[tex]y = \sqrt[3]{x} [/tex]

The given function has the same domain as its base function which is all real numbers.

Any real number you plug into this function is defined.

Since the function has no restriction, the domain is all real numbers.

[tex]x | x \: is \: real \: number[/tex]

Answer: C. 30 degrees

Step-by-step explanation:

By definition, an hexagon is a polygon with six sides.

The sum of the interior angles of an hexagon is 720 degrees.

Based on this, the measure of eac interior angle is:

[tex]interior\ angle=\frac{720\°}{6}=120\°[/tex]

Therefore, the measure of ∠1 is:

 [tex]\angle 1=\frac{120\°}{2}\\\\ \angle 1=60\°[/tex]

So, to find the angle ∠2, you can divide ∠1 by 2:

[tex]\angle 2=\frac{60\°}{2}\\\\ \angle 2=30\°[/tex]

Since the numbers are not consecutive natural numbers, how about if I let the 4 numbers be a, b, c, and d?

The sum is given to be 1320.

a + b + c + d =1320...I will call this the first equation.

Can I then say that the second equation is b + c + d = 0.4a + a? Yes, I can do this.

Simplifying my second equation,

I get b + c + d = 1.4a.

Plugging this into my first equation, I get

a +1.4a =1320

2.4a =1320

So, a =1320/(2.4) =550.

Answer: 550

Answer:

550

Step-by-step explanation:

We aren't given that they are consecutive so lets just pretend the numbers are x, y, z , and r.

We are given x+y+z+r=1320

We are also given that y+z+r=.4x+x

Simplifying my second equation gives us y+z+r=1.4x. I'm going to plug this into first equation giving me

x+1.4x=1320

2.4x=1320

So x=1320/2.4=550

Answer: 2:1

Step-by-step explanation:

Volume of a pyramid (V) = [tex]\dfrac{1}{3}\times l\times w\times h\bigg[/tex]

For simplicity, let's assume that l = w = h, then [tex]V = \dfrac{1}{3}s^3[/tex]

Pyramid 1 has a volume of 64:

[tex]64=\dfrac{1}{3}s^3\\\\3\times 64=s^3\\\\\sqrt[3]{3\times 64}=\sqrt[3]{s^3}  \\\\4\sqrt[3]{3} =s[/tex]

Pyramid 2 has a volume of 8:

[tex]8=\dfrac{1}{3}s^3\\\\3\times 8=s^3\\\\\sqrt[3]{3\times 8}=\sqrt[3]{s^3}  \\\\2\sqrt[3]{3} =s[/tex]

Comparing the sides of Pyramid 1 to the sides of Pyramid 2:

[tex]\dfrac{4\sqrt[3]{3}}{2\sqrt[3]{3}}=\dfrac{2}{1}\implies \text{scale factor of }2:1[/tex]

The scale factor of two similar pyramids with volumes of 64 cubic feet and 8 cubic feet is 2.

Understanding the Scale Factor of Similar Pyramids

To find the scale factor between two similar pyramids, we need to understand the relationship between their volumes and their corresponding dimensions. The volumes of the two pyramids given are 64 cubic feet and 8 cubic feet.

The formula for the volume of similar shapes indicates that the volume varies as the cube of the scale factor. This can be mathematically expressed as:

If V1 and V2 are the volumes of two similar figures with a scale factor of k, then: V1 / V2 = k3

For this problem:

64 ÷ 8 = k3

Simplifying:

8 = k3

Taking the cube root of both sides:

k = 2

So, the scale factor of the two similar pyramids is 2.

Answer:

bru thats not the answer^

Step-by-step explanation:

Answer:

Marcus practiced for 4 hours and Donnell practiced for 7 hours

Step-by-step explanation:

We can set up this problem as a system of linear functions

We'll use d to represent Donnell and m to represent Marcus

Since Donnell practiced 3 hours more than Marcus, we can represent this as an equation:

d=m+3

And since they both practiced for a combined total of 11 hours, we can represent this an an equation:

d+m=11

We can substitute d=m+3 into d+m=11 and we get:

m+3+m=11

2m+3=11

2m=8

m=4

Now we can substitute m=4 into d+m=11

d+4=11

d=7

Therefore, Donnell practiced for 7 hours and Marcus practiced for 4 hours

Answer: 64 °

64-1=63.

The parallel lines make the angles equal so they have the same measurement.

Use two pints on the graph to find the slope:

(0,0) and (5,1)

Slope = Change in Y over the change in x.

Slope = (1-0) / (5-0) = 1/5 = 0.20

The slope of the given equation is 0.25 which is greater than 0.20.

The unit rate is greater in the equation.

Answer:

a

Step-by-step explanation:

thanks

Answer:

B: Permutation;  Number of ways are 60

Step-by-step explanation:

At a competition with 5 runners, medals are awarded for first, second, and third places.

Each of the 3 medals is different.

This is a case of Permutation and the Number of ways are 60.

We have to award 3 medals among 5 runners.

This can be done in 5P3 ways.

= [tex]\frac{5!}{(5-3)!}[/tex]

= [tex]\frac{5\times4\times3\times2\times1}{2\times1}[/tex]

= [tex]5\times4\times3=60[/tex]

Therefore, the answer is option A.

Answer:

Step-by-step explanation:

y=-x+3

x+y=-1

y=-x+3

y=-x-1

-x+3=-x-1

add x to both sides

3=-1

no solutions

Answer:

Step-by-step explanation:

[tex]\text{If}\ A(n)\ \text{represents a geometric sequence, then}\ \dfrac{A(n)}{A(n-1)}=\bold{constant}.\\\\A.\\\\A(n)=P(1+i)^{n-1}\\\\A(n-1)=P(1+i)^{n-1-1}=P(1+i)^{n-2}\\\\\dfrac{A(n)}{A(n-1)}=\dfrac{P(1+i)^{n-1}}{P(1+i)^{n-2}}\\\\=(1+i)^{(n-1)-(n-2)}=(1+i)^{n-1-n+2}=(1+i)^1=1+i=\bold{constant}[/tex]

[tex]B.\\\\A(n)=(n-1)(P+i)^n\\\\A(n-1)=(n-1-1)(P+i)^{n-1}=(n-2)(P+i)^{n-1}\\\\\dfrac{A(n)}{A(n-1)}=\dfrac{(n-1)(P+i)^n}{(n-2)(P+i)^{n-1}}=\left(\dfrac{n-1}{n-2}\right)(P+i)^{n-(n-1)}\\\\=\left(\dfrac{n-1}{n-2}\right)(P+i)^{n-n+1}=\left(\dfrac{n-1}{n-2}\right)(P+i)^1\neq\bold{constant}[/tex]

others the same

A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a constant. This is different from a quadratic function which does not represent a geometric sequence.

In mathematics, a function represents a geometric sequence when each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. The general form of a geometric sequence can be written as a, ar, ar^2, ar^3, ... where 'a' is the first term, and 'r' is the common ratio.

The important factor in a geometric sequence is the multiplication by a constant. For example, let's say we have a sequence 2, 4, 8, 16. This is a geometric sequence because each term is multiplied by 2 to get the next term.

In contrast, a quadratic function, for instance, does not represent a geometric sequence as it's formed by the equation ax^2 + bx + c where a, b, and c are constants.

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[tex](f-g)(x)=3x+10-(2x-4)=3x+10-2x+4=x+14[/tex]

Answer:

d = 6

Step-by-step explanation:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2 )

Givens

x2 = -12

x1   = -6

y2 = 4

y1 = 4

Solution

d = sqrt (-12 - - 6)^2 + (4 - 4)^2 )

d = sqrt ( ( - 6)^2 + 0)

d = sqrt(36)

d = 6

Answer:

6

Step-by-step explanation:

Calculate the distance (d) using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 6, 4) and (x₂, y₂ ) = (- 12, 4)

d = [tex]\sqrt{(-12+6)^2+(4-4)^2}[/tex]

  = [tex]\sqrt{(-6)^2+0^2}[/tex] = [tex]\sqrt{36}[/tex] = 6

Answer:

[tex]\text{The slope:}\ m=-\dfrac{7}{8}\\\\\text{The point-slope form:}\ y+4=-\dfrac{7}{8}(x-7)\\\\\text{The slope-intercept form:}\ y=-\dfrac{7}{8}x+\dfrac{17}{8}[/tex]

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have two points (7, -4) amd (-1, 3).

Calculate the slope:

[tex]m=\dfrac{3-(-4)}{-1-7}=\dfrac{7}{-8}=-\dfrac{7}{8}[/tex]

The point-slope form of an equation of a line:

[tex]y-(-4)=-\dfrac{7}{8}(x-7)\\\\y+4=-\dfrac{7}{8}(x-7)[/tex]

Convert to the slope-intercept form:

[tex]y+4=-\dfrac{7}{8}(x-7)[/tex]        use the distributive property

[tex]y+4=-\dfrac{7}{8}x+\dfrac{49}{8}[/tex]     subtract 4 = 32/8 from both sides

[tex]y=-\dfrac{7}{8}x+\dfrac{17}{8}[/tex]

The equation of the line passing through (7,-4) and (-1,3) has a slope of -7/8, the point-slope form is y + 4 = -7/8(x - 7), and the slope-intercept form is y = -7/8x + 17/8.

To write the equation of the line that passes through the points (7,-4) and (-1,3), we first need to calculate the slope of the line using the formula m = (y2 - y1) / (x2 - x1).

Applying this to our points, we get m = (3 - (-4)) / (-1 - 7), which simplifies to m = 7 / -8 = -7/8. Now, using the point-slope form y - y1 = m(x - x1), and the point (7, -4), we can write the equation as y - (-4) = -7/8(x - 7).

Next, to convert this to slope-intercept form, we simplify the point-slope equation to solve for y: y + 4 = -7/8x + 49/8, and then subtract 4 (or 32/8) from both sides to get y = -7/8x + 17/8. This is our slope-intercept form, where -7/8 is the slope, and 17/8 is the y-intercept.

Answer:

Remote Interior Angle

Step-by-step explanation:

The name of an interior angle of a triangle that is not adjacent to a given exterior angle of the triangle is Remote Interior Angle.

If you take a look at the picture attached, you will find three angles: ∠A, ∠C and ∠D. In this case, we have that ∠A comes to be the exterior angle while ∠C and ∠D are the remote interior angle given that they are not adjacent to ∠A

Answer:

The statement is true.

Step-by-step explanation:

The statement is true.

This is true. Since they could be considered similar even when they are congruent, since in similar triangles, the measurements are proportional. In congruent triangles, this proportion is just one. or 1/1

Hope this helps!

The solution of the system of equations is a = 4 and b = 5.

A system of equations is a set of two or more equations that you deal with at one time.

The given system of equations are;

8a + 12b = 92

6a – 4b = 4

From equation 1

[tex]\rm 8a + 12b = 92\\\\ 8a=92-12b\\\\a=\dfrac{92-12b}{8}[/tex]

Substitute the value of a in the equation 2

[tex]\rm 6a-4b=4\\\\6\times \dfrac{92-12b}{8}-4b=4\\\\3\times \dfrac{92-12b}{4}-4b=4\\\\ 276-36b-16b=16\\\\-52b=16-276\\\\-52b=-260\\\\b=\dfrac{-260}{-52}\\\\b=5[/tex]

Substitute the value of b in the equation 2

[tex]\rm 6a – 4b = 4\\\\6a-4\times 5=4\\\\6a-20=4\\\\6a=4+20\\\\6a=24\\\\a=\dfrac{24}{6}\\\\a=4[/tex]

Hence, the solution of the system of equations is a = 4 and b = 5.

Learn more about system of equation here;

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Answer:

[tex]17x[/tex]

Step-by-step explanation:

[tex]8x + 9x = 17x[/tex]

To simplify the expression 8x + 9x, you combine the like terms by adding the coefficients. The result is 17x.

The process involved in simplifying an equation like this is known as combining like terms. In this example, the terms are 8x and 9x. Because they both contain the same variable, x, you can combine them.

To perform this operation, you add the coefficients (the numbers in front of the variable). In this case, the coefficients are 8 and 9. So, 8x + 9x simplifies to 17x.

Therefore, the simplified form of the equation 8x + 9x is 17x.

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Answer:2

Step-by-step explanation:

the bars make the integers absolute value so it would be 10-8 when you drop the bars making the answer 2

Answer:

5

Step-by-step explanation:

By trial and error, we see that we can multiply by 3/2 every time to continue the sequence! So multiplying 10/3 by 3/2, we get 5. So 5 is the next term of the geometric sequence.

Answer:

0

Step-by-step explanation:

Final answer:

To find the output y for an input x of 6, assuming a linear relationship based on a derivative example provided, we use the equation y = 3x + 6. Substituting x with 6 gives us y = 24.

Explanation:

The question requires us to find the output y when the input x is 6. The equation provided in the excerpts can be interpreted in many ways due to lack of clarity in the given information. However, a linear function example is given by dy/dx = 6+3x, where the derivative suggests an initial value of 6 increasing by 3 with each unit increase in x. If we assume a linear relationship y = mx + b, we can use the pattern in the derivative example and set the slope m as 3 and the y-intercept b as 6. This yields the equation y = 3x + 6. When x is 6, the output y is calculated as y = 3(6) + 6 = 18 + 6 = 24.

Remember, the equation provided in the tutorial only applies if we assume a linear relationship based on the derivative example mentioned. It is important to have the exact equation or context to provide the precise output y.

Answer:

[tex]\large\boxed{(3a+2)(4a^2-2a+9)=12a^3+2a^2+23a+18}[/tex]

Step-by-step explanation:

[tex](3a+2)(4a^2-2a+9)\qquad\text{use FOIL:}\ (a+b)(c+d)=ac+ad+bc+bd\\\\=(3a)(4a^2)+(3a)(-2a)+(3a)(9)+(2)(4a^2)+(2)(-2a)+(2)(9)\\\\=12a^3-6a^2+27a+8a^2-4a+18\qquad\text{combine like terms}\\\\=12a^3+(-6a^2+8a^2)+(27a-4a)+18\\\\=12a^3+2a^2+23a+18[/tex]

Answer:

y=4x+48

Step-by-step explanation:

Answer:

a=1, b=-6, c=2, d=1

Step-by-step explanation:

You are given the function

[tex]y=x^4+ax^3+bx^2+cx+d[/tex]

Find the derivative:

[tex]y'=4x^3+3ax^2+2bx+c[/tex]

The curve has a tangent line when x = 0 with equation y = 2x + 1, so

[tex]y'(0)=2\\ \\y(0)=1[/tex]

Hence,

[tex]y'(0)=4\cdot 0^3+3a\cdot 0^2+2b\cdot 0+c=2\Rightarrow c=2\\ \\y(0)=0^4+a\cdot 0^3+b\cdot 0^2+2\cdot 0+d=1\Rightarrow d=1[/tex]

The curve has a tangent line when x = 1 with equation y = -3x + 2, so

[tex]y'(1)=-3\\ \\y(1)=-3+2=-1[/tex]

So,

[tex]y'(1)=4\cdot 1^3+3a\cdot 1^2+2b\cdot 1+c=4+3a+2b+2=-3\Rightarrow 3a+2b=-9\\ \\y(1)=1^4+a\cdot 1^3+b\cdot 1^2+2\cdot 1+d=1+a+b+2+1=-1\Rightarrow a+b=-5[/tex]

From the second equation, a=-5-b, substitute it into the first one:

[tex]3(-5-b)+2b=-9\\ \\-15-3b+2b=-9\\ \\-b=-9+15\\ \\-b=6\\ \\b=-6\\ \\a=-5-b=-5-(-6)=-5+6=1[/tex]

Answer:

The angular velocity of Earth is π/12 radians per hour.

The angular velocity of Earth is 2π radians per day.

Step-by-step explanation:

A full circumference of a circle (as the Equator line on Earth) is 2π radians.

Since the planet does a full revolution in 24 hours... that means it makes a full turn in a day.

So, we can see that in a day, the planet rotates 360 degrees... or 2π radians per day!

Now, if you want to find the angular velocity per HOUR... you divide that by 24... so  2π/24 = π/12 radians

So, we can also say it does π/12 radians per hour.

Answer:

a and d on ed

Step-by-step explanation:

Answer:

X = 14

Step-by-step explanation:

The given figure is a quadrilateral  .In a Quadrilateral sum of angles is 360 degrees.

The given four angles in the quadrilateral are 70°,110°,110° and 5x °.

Applying angle sum property of quadrilateral:

70+110+110+5x=360°

Adding ,

290+5x=360

Subtracting both sides by 290 so that  x term can be isolated,

290-290+5x=360-290.

5x=70

Dividing both sides by 5

x=14.

Value of x is 1

Answer:

x=14

Step-by-step explanation:

Answer:

8 inches

Step-by-step explanation:

The problem gives us a basic formula, the volume formula for a rectangular prism. All we have to do is use this formula, plug in all the values that are given, and solve for the unknown value.

[tex]V = lwh[/tex]

[tex]192 = l(12)(2)[/tex]

[tex]192 = 24l[/tex]

From here, all we need to do is divide 24 from both sides of the equation, since what you do to one side of the equation you must do to the other!

[tex]8 = l[/tex]

The length of the box will thus be 8 inches.

it is going to be 8 inches                                                                                                    Hope it helps !!!!!