(17 points)
Determine if line AB is tangent to the circle

Answer:

x = 127°

Step-by-step explanation:

We are given a polygon which has six sides but all the sides and angles are not equal so it is an irregular hexagon.

We know that the sum of the measures of the interior angles of a polygon with n sides is given by: [tex](n-2)\times180[/tex].

[tex](6-2)\times180 = 112+133+128+100+120+x[/tex]

[tex] 7 2 0 = 5 9 3 + x [/tex]

[tex] x = 7 2 0 - 5 9 3 [/tex]

x = 127°

Answer:

35.25

Step-by-step explanation:

There are 4 data:

262, 313, 393, and 323

The formula for MAD (mean absolute deviation) = [tex]\frac{SUM(|x_{i}-XBar|)}{n}[/tex]

Where x_i are the each individual values (stated)

XBar is the average value

n is the number of data

First, let's find XBar, or the average. We add up all the 4 numbers and divide by 4 to get:

XBar = (262+313+393+323)/4=322.75

Now, let's calculate MAD:

MAD = [tex]\frac{|262-322.75|+|313-322.75|+|393-322.75|+|323-322.75|}{4}\\=35.25[/tex]

MAD = 35.25

Answer:

31.5

Step-by-step explanation:

Answer is

New perimeter = 112

See photo

Answer:

X = 20.6 inches

Step-by-step explanation:

Pythagorean Theorem: [tex]A^{2} =B^{2} +C^{2}[/tex]

A = 41.2 in, while B = 35.7 in and we are solving for C.

[tex]41.2^{2} = 35.7^{2} +C^{2}[/tex]

[tex]1697.44 = 1274.49 + C^{2}[/tex]

Now solve for C

[tex]422.95 = C^{2}[/tex]

Take the square root

[tex]20.5657482237 = C[/tex]

Answer:

The answer is D

Answer:

The answer is A

Answer:

9.2 kilo grams

Step-by-step explanation:

Answer:

m∠2 = 56°

Step-by-step explanation:

Given;

m∠1 = 10x + 4 and m∠2 = 5x - 4

Angles 1 and 2 are supplementary angles meaning that they add up to 180°

i.e,

(10x + 4) + (5x - 4) = 180°

10x + 5x + 4 - 4 = 180°

15x = 180°

x = 180/15 = 12

m∠2 = 5(12)° - 4° = 60° - 4° = 56°

Answer:

The approximate difference in the growth rate of the two populations is 40%.

Step-by-step explanation:

The general exponential growth model is

[tex]y=a(1+r)^t[/tex]

Where, a is initial value, r is growth rate and t is time.

In the given graph, red curve passing through the points (2,22.5) and (3,33.75).

[tex]22.5=a(1+r)^2[/tex]           .... (1)

[tex]33.75=a(1+r)^3[/tex]           .... (2)

Divide the equation (2) by equation (1).

[tex]1.5=1+r[/tex]

[tex]0.5=r[/tex]

The graph rate of red curve is 50%.

In the given graph, purple curve passing through the points (7,19.4) and (8,21.4).

[tex]19.4=a(1+r)^7[/tex]           .... (3)

[tex]21.4=a(1+r)^8[/tex]           .... (4)

Divide the equation (4) by equation (3).

[tex]1.1031=1+r[/tex]

[tex]0.1031=r[/tex]

[tex]0.1\approx r[/tex]

The graph rate of red curve is 10%.

The approximate difference in the growth rate of the two populations is

[tex]50-10=40\%[/tex]

Therefore the approximate difference in the growth rate of the two populations is 40%.

Answer:

B. The price for each student ticket is the same at both theaters

Correct Option is B.

System of Linear equations:

A system of linear equations is a set of equations which are satisfied by the same set of variables.

Ex : 2x - y = 12 , x - 2y = 48

Here,

Let's take adult ticket price in theatre A = x

And the student ticket price in theatre A = y

So, (Given), 3x + 2y = $42.50 (Melanie paid)

=> 2y = $42.50 - 3x --(1)

Also given, 2x + 4y = $47 (Drew paid)

=> 4y = $47 - 2x

2(2y) = $47 - 2x

Now, substitute 2y value from eq-(1), we get

2($42.50 - 3x) = $47 - 2x

$85 - 6x = $47 - 2x

=>  $85 - $47 = 6x - 2x

=> $38 = 4x

=> x = ($38)/4 => 9.5

Substitute x value in eq-(1), we get

2y = $42.50 - 3(9.5) => y = $7.

In the given options only Option B is the correct answer.

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Answer:

factors of [tex] x^{12}y^{18}+1 = (x^4y^6+1) (x^8y^{12} -x^4y^6 +1)[/tex]

Step-by-step explanation:

We need to find factors of [tex]x^{12}y^{18}+1 can\,\,be\,\, written\,\, as\,\,\\(x^2y^3)^6 + 1\\It\,\, can\,\, be\,\, further\,\, written\,\, as\\((x^2y^3)^2)^3 +1\\Using\,\, the\,\, formula\,\, a^3+b^3 = (a+b)(a^2-ab+b^2)\\Here \,\, a = (x^2y^3)^2 and y = 1\\((x^2y^3)^2)^3 +(1)^3= ((x^2y^3)^2+1) (((x^2y^3)^2)^2 -(x^2y^3)^2 +1)\\= (x^4y^6+1) (x^8y^{12} -x^4y^6 +1)[/tex]

So, factors of [tex] x^{12}y^{18}+1 = (x^4y^6+1) (x^8y^{12} -x^4y^6 +1)[/tex]

Answer:

Step-by-step explanation:

f(x) = x⁵ – 8x⁴ + 16x³

As x approaches +∞, the highest term, x⁵, approaches +∞.

As x approaches -∞, x⁵ approaches -∞ (a negative number raised to an odd exponent is also negative).

Now let's factor:

f(x) = x³ (x² – 8x + 16)

f(x) = x³ (x – 4)²

f(x) has roots at x=0 and x=4.  x=4 is a repeated root (because it's squared), so the graph touches the x-axis but does not cross at x=4.

The graph crosses the x-axis at x=0.

Answer:

Part 1. B

Part 2. 4, 0

Step-by-step explanation: Edge 2023

Answer:

A (0,0)

Step-by-step explanation:

When a function intersects the y-axis then the point of intersection is called y-intercept of the function,

Also, for y-intercept x = 0.

That is, if f(x) is the function then its y-intercept is (0, f(0) )

By the given table for x = 0, f(x) = 0

Hence, the y-intercept of the given function is (0,0),

Option A is correct.

Answer:

A trust

Step-by-step explanation:

Answer:

x is less than or equal to 3.5

Step-by-step explanation:

For this you can any variable but let’s use d representing the distance that Jonathan ran.

Hmm

D_>3.5+5

In other words d is less than or equal to 3.5 plus 5

Hope this helped u :)

Answer:

Step-by-step explanation:

the lawn above is 40 x 60= 2400 ft^2

one bag of seed that costs $2.50 and it covers 1200 ft^2

if your lawn is 2400 ft^2 you divide it by the 1200 ft^2

                            2400 ft^2 / 1200 ft^2 = 2

so if 1 bag covers 1200 ft^2 then you will need 2 bags to cover 2400 ft^2.

at $2.50 a bag your answer will be, B.

Answer is B

Area = area of rectangle + area of that small areched shape

Area is little bit more than (60*40)=2400

Which is covered by 2 bags (2400/1200) =2

Cost of 2 bags is 2.5*2=5

So..you have to choose what is more than 5 with little amout..which is 5.51

Answer:

see explanation

Step-by-step explanation:

Given

q = [tex]\frac{p}{r}[/tex] + s ( subtract s from both sides )

q - s = [tex]\frac{p}{r}[/tex]

Multiply both sides by r

r(q - s) = p

Answer:

Step-by-step explanation:

Put x = -4 to f(x) = -x - 2:

f(-4) = -(-4) - 2 = 4 - 2 = 2

Answer:

See below.

Step-by-step explanation:

The graph of the quadratic equation is a parabola or u shaped graph. It has a vertex at (-1,-3) since h=-1 and k=-3 in the vertex form. It is also facing down since the leading coefficient is negative.

The graph of the equation y = -(x + 1)2 -3 is a downward opening parabola with the vertex at (-1, -3).

The graph of the equation y = -(x + 1)2 -3 is a downward opening parabola. The coefficient in front of the quadratic term, in this case, -1, determines the direction of the opening. If the coefficient is negative, the parabola opens downward.

Additionally, the vertex of the parabola is (-1, -3) since the equation is in vertex form. The vertex is the highest or lowest point on the graph. Therefore, the graph of the equation y = -(x + 1)2 -3 will be a downward opening parabola with the vertex at (-1, -3).

hope it helps you!!!!!!!!!!!

Answer: option B

Step-by-step explanation:

The circumference of a circle can be calculated with this formula:

[tex]C=2\pi r[/tex]

Where "C" is the circumference of the circle and "r" is the radius of the circle.

The area of a circle can be calculated with:

[tex]A=\pi r^2[/tex]

Where "r" is the radius.

Knowing the area, you can solve for the radius:

[tex]r^2=\frac{9\pi cm^2}{\pi }\\\\r=\sqrt{\frac{9\pi cm^2}{\pi } }\\\\r=3cm[/tex]

Substituting into  [tex]C=2\pi r[/tex], you get that the circumference of this circle is:

 [tex]C=2\pi (3cm)=6\pi\ cm[/tex]

Answer:

B

Step-by-step explanation:

The area (A) of a circle = πr² ← r is the radius

here A = 9π, hence

πr² = 9π ( divide both sides by π )

r² = [tex]\frac{9\pi }{\pi }[/tex] = 9

r = [tex]\sqrt{9}[/tex] = 3

The circumference (C) of a circle is C = 2πr, hence

C = 2π × 3 = 6π → B

The best-fit line for a data set is found using the least-squares regression method, which identifies the linear equation that minimizes the residual errors. The equation is in the form y = mx + b, where m is the slope, and b is the y-intercept.

The question seeks to determine the linear function equation that best fits a given data set. To find the best-fit line, also known as the least-squares regression line, we typically analyze data points and use statistical methods to determine the equation that minimizes the sum of the squares of the residuals (the differences between the observed values and the values predicted by the model). The given options suggest that we are looking for a linear equation of the form y = mx + b, where m is the slope and b is the y-intercept.

The equation of the best-fit line provided in the reference material, ý = -173.51 + 4.83x, indicates the method to determine both the slope (4.83) and the y-intercept (-173.51). This can be compared with the provided options to identify which one has a slope (or multiplier for x) closest to 4.83 and y-intercept closest to -173.51. In practice, students would use numerical and conceptual methods rather than graphing to interpret the data in multi-dimensional space when there are more than two variables involved.

Answer:

6

Step-by-step explanation:

Given data:

x=area

f(x)=the length of one side of the square

Also the model of f(x)= [tex]\sqrt{x-1} +1[/tex]

Now determining length of one side of the square f(x), when Area x of square is 26:

Putting the value x=26 in given equation of f(x)

f(x)= [tex]\sqrt{26-1} +1[/tex]

   = [tex]\sqrt{25} +1[/tex]

  = 5 +1

   = 6

Hence length of one side of the square f(x) is 6, when Area x of square is 26 !

Answer with explanation:

x= Area

f(x)= The length of one side of the square

Model Determined by Sam to approximate the side of a square is

    [tex]f(x)=\sqrt{x-1} +1[/tex]

It is given that , Area(x) = 26 Square Unit

 Substituting the value of , x in above equation

    [tex]f(x)=\sqrt{26-1} +1\\\\f(x)=\sqrt{25} +1\\\\f(x)=5+1\\\\f(x)=6[/tex]

So, Side length of Square According to model created by Sam = 6 unit

Answer:

see explanation

Step-by-step explanation:

The exponential function is of the form

y = a [tex]b^{x}[/tex]

Substitute the given points into the equation to find a and b

Using (0, 4), then

4 = a[tex]b^{0}[/tex] ⇒ a = 4

Using (1, 24), then

24 = 4 [tex]b^{1}[/tex] ⇒ b = 6

Exponential function is

y = 4 × [tex]6^{x}[/tex]

The equation of the exponential function that passes through the points (0,4) and (1,24) is y = 4(6)^x.

To find the equation of the exponential function that passes through the points (0,4) and (1,24), we can use the general form of an exponential function: y = ab^x, where a is the initial value and b is the growth/decay factor.

Using the point (0,4), we plug in x=0 and y=4 to get the equation 4 = ab^0, which simplifies to a = 4.

Using the point (1,24), we plug in x=1, y=24, and a=4 to get the equation 24 = 4b^1, which simplifies to b = 6.

Therefore, the equation of the exponential function is y = 4(6)^x.

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Go 6 units in X axis and 1 unit in Y axis and you get V.

Alternative B

Answer:

B, Point V

Step-by-step explanation:

find 6 on the x-axis and go up 1, you will find point V

Answer:

Flat 12,885.68

Compound 13,876.90

Step-by-step explanation:

Flat rate (6% of only the amount you invested originally per year (based on investment) -

(8706.54*.06)*8+8706.54=12885.68 (rounded)

Compound interest (6% interest on total money earned per year(based on amount invested previous year).)

(((((((8706.54*1.06)*1.06)*1.06)*1.06)*1.06)*1.06)*1.06)*1.06)=13,876.90

The future value of the investment is $13876.90 and the interest earned is $5170.36.

We can use the following formulas:

Future value = [tex]Principal * (1 + Interest rate)^N^u^m^b^e^r ^o^f^ y^e^a^r^s[/tex]

Interest earned = Future value - Principal

Substituting the known values into the formulas, we get:

Future value =[tex]$8706.54 * (1 + 0.06)^8 = $13876.90[/tex]

Interest earned = $13876.90 - $8706.54 = $5170.36

Therefore, the future value of the investment is $13876.90 and the interest earned is $5170.36.

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Answer:

47%

Step-by-step explanation:

you would take the number of palomino horses and divide that by the total number of horses like this:

7 / 15 = 0.46666667

which would be rounded to 0.47

which equals 47%

so the probability of randomly choosing a palomino horse would be about 47%

i hope this helps :)

Still second graph from top down is the good one

Answer:

2 31/32   cups used

Step-by-step explanation:

We have 4 3/8 cups cherries

Change this to an improper fraction

4 3/8 = (8*4+3)/8 = 38/8

We use 5/8 of the cherries

38/8 *5/8

190/64

Change this back to a mixed number

64 goes into 190 2 times

190 - 128 =62  left over

2 62/64

2 31/32   cups used

ANSWER

[tex]g(x) = \sin(x +4) - 4[/tex]

EXPLANATION

The basic sine function is

[tex]f(x) = \sin(x) [/tex]

The transformed sine function has equation

[tex]g(x) = a \sin(bx +c ) + d[/tex]

where a=1 is the amplitude

2π/b=2π is the period

c/b= 4 is the horizontal shift 4 units left.

d=-4 is a downward vertical shift of 4 units.

The required sine function is:

[tex]g(x) = \sin(x +4) - 4[/tex]

Answer:

A = 36.75 cm^2

Step-by-step explanation:

The area of a trapezoid is found by

A = 1/2 (b1+b2) *h

where b1 and b2 are the bases and h is the height

A = 1/2 (12+9) *3.5

A = 1/2(21)*3.5

A = 36.75 cm^2

Answer:

How is that possible

Step-by-step explanation:

So..... what is the question ?