calculate the length of the circumference of a circle with diameter of 9cm

The scale factor from the smaller figure to the larger figure is found by taking the cube root of the ratio of their volumes, which is the cube root of 216/343.

The student asked: Which of the following could represent the scale factor of the smaller figure to the larger figure? When comparing the volumes of two geometric figures, we can determine the scale factor of their linear dimensions by understanding the relationship between volume and linear scale factor.

Given that the smaller figure's volume is 216 cubic inches and the larger figure's volume is 343 cubic inches, we are looking for the cube root of the ratio of these volumes to find the linear scale factor.

To find the scale factor from the smaller figure to the larger figure, divide the volume of the smaller figure by the volume of the larger figure and then calculate the cube root: Scale factor = ∛(216/343). This calculation will give you the scale factor of the linear dimensions from the smaller figure to the larger figure.

Answer:

In first blank : y = - 2,

In second blank : ( 0, 1 )

Step-by-step explanation:

Given function is,

[tex]f(x)=3^{x+1}-2[/tex]

The horizontal asymptote of the function f(x),

[tex]y=lim_{x\rightarrow \infty} f(x)[/tex]

[tex]y=lim_{x\rightarrow \infty} 3^{x+1}-2[/tex]

[tex]y=3^{\infty+1}-2[/tex]

[tex]y=3^\infty - 2[/tex]

[tex]y=0-2[/tex]

⇒ y = -2

First option is correct.

Also, the function has no vertical asymptote,

2. For finding the y-intercept, x = 0,

[tex]f(0)=3^{0+1}-2=3-2=1[/tex]

Hence, the y-intercept = (0,1)

Third option is correct.

Final answer:

The function f(x) = 3x + 1 – 2 is a linear function and does not have an asymptote, contrary to the options provided. The y-intercept is found by setting x to 0, which results in the point (0, – 1).

Explanation:

The function in question is f(x) = 3x + 1 – 2. To determine its asymptote and y-intercept, we analyze its structure.

Since this is a linear function and not a rational function, it does not have an asymptote like those found with rational functions, whose denominators can become zero. Instead, the original function is a modification of the function f(x) = 3x, with vertical shifts up by 1 and down by 2, effectively canceling each other out. Therefore, the asymptote is essentially the x-axis, which can be represented by the equation y = 0. However, since none of the provided options include y = 0, and the function we are analyzing is, in fact, linear without any asymptotes, there must be an error in the question regarding this part.

To find the y-intercept, we set x equal to 0 and solve for f(0):

f(0) = 3(0) + 1 – 2 = 1 – 2 = – 1.

Therefore, the y-intercept of the function is the point (0, – 1).

I have the same problem but with 14 being 15 in and 9 being 7 in, can someone help?

The given arithmetic series is

[tex] \sum_{t=1}^{18} (3t-4) [/tex]

When t =1, we will get the first term,a, which is

[tex] 3(1)-4 =3-4=-1 [/tex]

When t =18, we will get the last term,l , which is

[tex] 3(18)-4 = 50 [/tex]

Now we use the formula of sum of n terms which is

[tex] S = \frac{t}{2} (a+l) [/tex]

Substituting the values of t,a and l, we will get

[tex] S = \frac{18}{2} (-1+50) = 9*49 =441 [/tex]

Consider the arithmetic series [tex] _{t=1}\Sigma^{t=18} (3t-4) [/tex]

Let t=1 in the given series, we get

first term = [tex] a_{1} [/tex] = 3-4 = -1.

Let t=2 in the given series, we get

second term = [tex] a_{2} [/tex] = [tex] (3 \times 2)-4 = 2 [/tex]

Let t=3 in the given series, we get

third term = [tex] a_{3} = (3 \times 3)-4=5 [/tex]

Now, let t=18 in the given series, we get

last term = l = [tex] l = (3 \times 18)-4 = 50 [/tex]

We get the series as

-1, 2, 5,..... 50

Sum = [tex] \frac{n}{2}(a+l) [/tex]

= [tex] \frac{18}{2}(-1+50) [/tex]

= [tex] = 9 \times 49 [/tex]

= 441

Therefore, the sum of the given arithmetic series is 441.

Answer:

d

Step-by-step explanation:

The correct combining of like term is

f(m, n) = [tex]n^{6}[/tex] + 7m[tex]n^{5}[/tex] + 14m²[tex]n^{4}[/tex] - 5m³n³ -6[tex]m^{6}[/tex] - 2[tex]m^{6}[/tex]

A polynomial equation is the equation in which the unknown variable is one and the highest power of the unknown variable is n.

Given:

8m[tex]n^{5}[/tex] - 2[tex]m^{6}[/tex] +5m²[tex]n^{4}[/tex] - m³n³ +  [tex]n^{6}[/tex] - 4[tex]m^{6}[/tex] + 9m²[tex]n^{4}[/tex] - m[tex]n^{5}[/tex] - 4m³n³

Now, Combining the like terms

(8m[tex]n^{5}[/tex] - m[tex]n^{5}[/tex]) + 5m²[tex]n^{4}[/tex] + 9m²[tex]n^{4}[/tex] - m³n³   - 4m³n³ +  [tex]n^{6}[/tex] - 4[tex]m^{6}[/tex] - 2[tex]m^{6}[/tex]

=7m[tex]n^{5}[/tex]  + 14m²[tex]n^{4}[/tex]  - 5m³n³ - 6 [tex]m^{6}[/tex] +  [tex]n^{6}[/tex]

now, arranging according to their powers

[tex]n^{6}[/tex] + 7m[tex]n^{5}[/tex] + 14m²[tex]n^{4}[/tex] - 5m³n³ -6[tex]m^{6}[/tex] - 2[tex]m^{6}[/tex]

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see the attached figure to better understand the problem

we know that

[tex]0.65\ (65\%)[/tex] of the buyers buy paperback and [tex]0.45\ (45\%)[/tex] of them buy fiction.

Hence

The probability that they buy both fiction and paperback is equal to

[tex]0.65*0.45=0.2925[/tex]

the answer is

[tex]0.2925[/tex]

Answer:

[tex](x+6)^{2}+2x=189[/tex]  

and

[tex]x^{2}+14x+36=189[/tex]

Step-by-step explanation:

Let

x -----> the number

we know that

The equation that represent the situation is

[tex](x+6)^{2}+2x=189\\ \\x^{2} +12x+36+2x=189\\ \\x^{2}+14x+36=189[/tex]

therefore

The equations that could be used are

[tex](x+6)^{2}+2x=189[/tex]  and [tex]x^{2}+14x+36=189[/tex]

Answer:

(x+6)^{2}+2x=189  

and

x^{2}+14x+36=189

Step-by-step explanation:

Answer:

1/4

Step-by-step explanation:

It is given that on Tuesday, apples were on sale for 20% off. Now, we know that on Monday Mrs. Wise bought 3 lbs of apples at $4 per lb. This means that if we have a 20% off on Tuesday then this must be with respect to the price on Monday which is $4. Thus the price of Tuesday can be calculated as:

[tex] 4-\frac{20}{100}\times 4=4-0.8=3.2 [/tex]

Thus, the per pound price of apples on Tuesday was $3.2

Answer:

Cassandra is likely to qualify for Chapter 7 bankruptcy.

Step-by-step explanation:

Given scenario is : Cassandra lives in Oklahoma and makes $60,000 a year. The median annual income in Oklahoma is $64,105.

A person qualifies for chapter 7 bankruptcy, if his annual median income is below the median income of his state. So, here the annual median income of Cassandra is below the median income of her state, Oklahoma.

So, she will qualify for chapter 7 bankruptcy.

In this question it has been clearly indicated that AZB is to be taken as an arc. This is because there is the arc symbol on top of AZB. Thus, we have [tex] \overarc{AZB} [/tex] and we need to answer what does the arc [tex] \overarc{AZB} [/tex] represent.

As we can see from the diagram, by visual inspection, that AZ is the chord which is lesser than the diameter and AZB is the segment on that lesser side of the circle. Therefore, the arc [tex] \overarc{AZB} [/tex] must be the minor arc.

Therefore, Option A, minor arc is the correct answer.

Solution :

To factor completely

[tex] a^{2} + 3a-28 [/tex]

To factor it completely , first take the product of first and third term, and then break the second term in two parts in such a way that its sum equals the second term and the product equals the product of first and third term.

Product of first and third term is [tex] (a^{2})(-28) = -28 a^{2} [/tex]

Second term is 3a, Re-write 3a as sum of 7a and -4a.

Lets check it Product of 7a and -4a is [tex] -28 a^{2} [/tex] wich is eaqual to product of first and third term and sum of 7a and -4a is 3a which is the second term.

Now factorise, we get

[tex] a^{2}+3a-28\\\\ = a^{2} +7a-4a-28\\\\=a(a+7)-4(a+7)\\\\=(a+7)(a-4) [/tex]

Hence, [tex] (a+7)(a-4) [/tex] is the factor of [tex] a^{2}+3a-28 [/tex].

Answer:

5ft

Step-by-step explanation:

The required greatest distance, in feet, a person could be from the lamp and be detected is 5 ft. Option A is correct.

The circle is the locus of a point whose distance from a fixed point is constant i.e center (h, k). The equation of the circle is given by

(x - h)² + (y - k)² = r²

where h, k is the coordinate of the center of the circle on the coordinate plane and r is the radius of the circle.

Here,
Given equation

(x+15)²+(y−12)²=25

The above equation is the equation of the circle, so the longest distance that person could be from the lamp and be detected is the radius of the circle,

Which is given as,
r² = 25
r = √25
r = 5

Thus, the required greatest distance, in feet, a person could be from the lamp and be detected is 5 ft. Option A is correct.

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Answer:

The slope intercept form of the required line is [tex]y=\frac{-3}{2}x[/tex].

Step-by-step explanation:

If a line is defined as

[tex]Ax+By+C=0[/tex]        ... (1)

Then the slope of the line is

[tex]m=\frac{-A}{B}[/tex]

The given equation is

[tex]3x+2y-6=0[/tex]       .... (2)

From (1) and (2), we get

[tex]A=3, B=2, C=-6[/tex]

The slope of the line is

[tex]m=\frac{-3}{2}[/tex]

The slope of parallel line is same. So, the slope of required line is -3/2.

The slope intercept form of a line is

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

Where, m is slope and b is y-intercept.

The slope of required line is -3/2 and y-intercept is at (0,0).

[tex]y=\frac{-3}{2}x+0[/tex]

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

Therefore the slope intercept form of the required line is [tex]y=\frac{-3}{2}x[/tex].

APEX APEX APEX APEX APEX APEX APEX APEX APEX APEX

More than $0 but less than $4100

The slope - intercept form of the equations are : [tex]y = \frac{3}{4} x - 7 [/tex] and [tex]y = - \frac{2}{5} x + 2[/tex]

Given the standard form of the equations :

The General form of a slope - intercept equation :

For equation (1) :

3x - 4y = 28

Make y the subject

-4y = 28 - 3x

Divide both sides by - 4 to isolate y

y = -7 + 3/4x

[tex]y = \frac{3}{4} x - 7 [/tex]

For equation (2) :

4x + 10y = 20

Make y the subject

10y = 20 - 4x

Divide through by 10 to isolate y

y = 2 - 2/5x

[tex]y =- \frac{2}{5} x + 2[/tex]

Hence, the slope - intercept equations are : [tex]y = \frac{3}{4} x - 7 [/tex] and [tex]y = - \frac{2}{5} x + 2[/tex]

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