For a circle of radius 3 feet, find the arc length s subtended by a central angle of 21°.

Answer:

[tex]y = \frac{1}{2}x+\frac{5}{2}[/tex]

Step-by-step explanation:

The perpendicular bisector of a line passes through the mid-point of the line and the product of slopes of the line and perpendicular bisector will be -1.

So,

[tex]Mid-point\ of\ BC = (\frac{6+8}{2},  \frac{8+4}{2})\\= (\frac{14}{2},  \frac{12}{2})\\= (7,6)[/tex]

The line will pass through (7,6)

Now,

[tex]Slope\ of\ BC = m_1 = \frac{y_2-y_1}{x_2-x_1} \\=\frac{4-8}{8-6}\\= \frac{-4}{2}\\= -2[/tex]

Let

m_2 be the slope of perpendicular bisector

So,

m_1*m_2 = -1

-2 * m_2 = -1

m_2 = -1/-2 = 1/2

The standard equation of line is:

y=mx+b

Where m is slope

So putting the value of slope and point to find the value of b

[tex]6 = \frac{1}{2}*7 +b\\ 6 = \frac{7}{2} + b\\b = 6 - \frac{7}{2}\\ b = \frac{12-7}{2}\\b = \frac{5}{2}\\So,\ the\ equation\ of\ perpendcular\ bisector\ of\ BC\ is:\\y = \frac{1}{2}x+\frac{5}{2}[/tex]

..

[tex]\bf \textit{Logarithm Cancellation Rules} \\\\ log_a a^x = x\qquad \qquad \stackrel{\textit{we'll use this one}}{a^{log_a x}=x} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ e^{\ln(3x)}\implies e^{\log_e(3x)}\implies 3x[/tex]

Answer:

3x

Step-by-step explanation:

e^ln3x

We know that e and ln are inverses of each other, so when we take e to the power ln, they cancel

e^ ln 3x

3x

The range of the function y=3/x+8 is all real numbers except 8, since the function approaches 8 but never reaches it due to the vertical asymptote at x=0.

The range of the function y=3/x+8 refers to all possible output values (y-values) that the function can produce. To find the range, it is essential to consider the values that x can take. Since x is in the denominator, x cannot be 0, as division by zero is undefined. Therefore, the function has a vertical asymptote at x=0.

As x approaches both positive and negative infinity, y approaches the constant 8, because the term 3/x approaches 0. Thus, the function can get close to, but never equal, the value of 8. Also, since 3/x can take any value except 0, the range of the function is all real numbers, excluding 8.

The final range of the function y=3/x+8 is therefore: {y | y ≠ 8}, meaning all real numbers that are not equal to 8.

Answer:

51/7 = [tex]\frac7 {2}{7}[/tex]  31/9 = [tex]\frac3{4}{9}[/tex]

Step-by-step explanation: I hope this helps you!

Answer:

Step-by-step explanation:

51/7 = 7 2/7

31/9 = 3 4/9

Hope this helps!

Answer:

t = 1

Step-by-step explanation:

Given

16 - 2t = 5t + 9 ( subtract 5t from both sides )

16 - 7t = 9 ( subtract 16 from both sides )

- 7t = - 7 ( divide both sides by - 7 )

t = 1

Answer:

2.43

Step-by-step explanation:

16-2t=5t+2t

16-9=5t+2t

17÷7=7t

t=2.43

Hello There!

the distance between 0 and -53 on a number line would be 53 spaces. This is because they are exactly 53 spaces away from each other.

Answer:

[tex]x=e^3+4[/tex] (exact)

x = 24.0855 (rounded)

Step-by-step explanation:

We need to remember 3 rules:

1. ln means log_e (ln is log base e)

2. [tex]a^b=x\\SameAS\\log_ax=b[/tex]

3. [tex]aLogx=Logx^a[/tex]

Now we can write the equation as:

[tex]3Ln(x-4)=9\\3Log_e(x-4)=9\\Log_e(x-4)^3=9[/tex]

Now, we can convert it to exponential and solve:

[tex]Log_e(x-4)^3=9\\(x-4)^3=e^9\\\sqrt[3]{(x-4)^3}=\sqrt[3]{e^9} \\ x-4=e^3\\x=e^3+4[/tex]

This is the exact value of x, in 4 decimal places (by using calculator), it would be

x = 24.0855

Answer:

An important property of every line is its steepness, or slope.

The important property of every line is its steepness, or slope.

In terms of mathematics, the slope or gradient of a line represent the number that explained both the direction and the steepness of the line.

The steepness, incline, or grade of a line should be determined by the absolute value of the slope. A slope should have a greater absolute value indicates a steeper line.

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Answer:

a=1, b=-12

Step-by-step explanation:

This is a rational function with a hole at x=3 and a vertical asymptote at x=-4.

The denominator of this rational function must be:

[tex](x - 3)(x + 4)[/tex]

When we expand using the distributive property, we get:

[tex] {x}^{2} + 4x -3 x - 12[/tex]

This simplifies to

[tex] {x}^{2} + x - 12[/tex]

Therefore the graphed rational function is:

[tex]f(x) = \frac{ {x}^{2} - 4x + 3 }{ {x}^{2} + x - 12 } [/tex]

Comparing this to

[tex]f(x) = \frac{ {x}^{2} - 4x + 3 }{ {x}^{2} +a x + b} [/tex]

We have

[tex]a = 1[/tex]

and

[tex]b = - 12[/tex]

Answer:

C. The scientific revolution

Step-by-step explanation:

The scientific revolution led to new ways of studying and  thinking about the natural world.

The Scientific Revolution is the modern movement that led to new ways of studying and thinking about the natural world. It was characterized by advances in various fields of science, and marked a transformation in scientific thought and practice.

Among the options provided, option C -- The Scientific Revolution -- represents the modern movement that led to new ways of studying and understanding the natural world. The Scientific Revolution, which took place during the 16th and 17th centuries, was characterized by significant advances in physics, astronomy, biology, human anatomy, and chemistry. It marked a crucial period of transformation in scientific thought and practice, with philosophers and scientists starting to challenge traditional beliefs about nature and the universe, leading to the adoption of the scientific method.

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Answer:

Question 1: 8

Question 2: -32.5

Step-by-step explanation:

Laura gets paid 8 dollars an hour to baby sit

8x represents how much Laura gets paid by the hour.

Laura owes her friend 32.50

-32.50 represents the amount she owes her friend

Combine

y = 8x - 32.50

Answer

Question 1: 8

Question 2: -32.5

Answer:

y = 8x-32.50

Step-by-step explanation:

She makes 8 dollars an hour babysitting.  She will work x hours

She makes 8x

She owes 32.50 to her friend.  This will be subtracted because she owes it

The amount of money she has at the end, y, is given by

y =8x-32.50

Answer:

0

Step-by-step explanation:

Each time two cubes are rolled, the sum can be a number from 2 (rolling 1 and 1) to 12 (rolling 6 and 6). It is impossible to get a sum of more than 12, so there is zero probability of getting a sum of 47.

Answer: 0

(b^2+5)(−b^2+7)

Use the FOIL METHOD to expand.

-b^4 + 7b^2 - 5b^2 + 35

-b^4 + 2b^2 + 35

Did you follow?

Standard form (b^2+5)(−b^2+7) polynomial is = -b⁴+2b²+35

Using FOIL METHOD to expand.

(b²+5)(−b²+7)

=(b²+5)(7-b²)

=7b²-b⁴+35-5b²

=2b²-b⁴+35

= -b⁴+2b²+35

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Answer:

y = - 3x + 3

Step-by-step explanation:

Assuming you require the equation of the line

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = - 3 and c = 3, hence

y = - 3x + 3 ← equation of line

Hey there!

What I am assuming you are looking to do is convert this into a linear equation. I will guide you on how to do just that.

The linear equation form is:

y = mx + b

Note in particular m represents the slope and b represents the y-intercept.

Our answer would be y = -3x + 3

Answer:

Its a kite

Step-by-step explanation:

Answer:

kite

Step-by-step explanation:

try not to get it confused with a rhombus

Answer:

D) 800

Step-by-step explanation:

5609/7 = 801.285

rounding to the nearest would be 800.

Anything below a 5 will go to the lower anything above a 5 will go higher:

ex: 804 would round nearest to 800

807 would round nearest to 810

Answer:

Part 1) The price will decrease $5,548

Part 2) The price of the next model is $32,452

Step-by-step explanation:

Let

x ----> the price of the next model

we know that

The current model costs $38,000 -----> represent the 100%

step 1

To find the price decrease in dollars multiply the current model price by 14.6%

14.6%=14.6/100=0.146

so

0.146*($38,000)= $5,548

step 2

Find the price of the next model

To find the price of the next model subtract the price decrease from the price of the current model

so

x=$38,000-$5,548=$32,452

Answer: Last Option

[tex]P=0.4125[/tex]

Step-by-step explanation:

In this case we have a uniform probability. In the graph the horizontal axis represents the possible values of the variable x and the vertical axis represents the probability P(x).

To calculate the probability that x is between 4.71 and 7.4 we calculate the area under the curve.

The horizontal length between 4.71 and 7.4 is:

[tex]7.4-4.1 = 3.3[/tex].

Then notice that the vertical length in this interval is 0.125.

Then the area of a rectangle is:

[tex]A = lw[/tex]

Where l is the length and w is the width.

In this case we have to:

[tex]l = 3.3[/tex]

[tex]w = 0.125[/tex]

So

[tex]P = A = 3.3 * 0.125[/tex]

[tex]P=0.4125[/tex]

Answer:

C. positively skewed

Step-by-step explanation:

If a data set has more extremely large data values, the distribution is said to be positively skewed.

Have a great day!

A data set with more extremely large data values is said to be skewed right or positively skewed. This describes a distribution where the tail on the right side is extended due to a few high extreme values.

If a data set has more extremely large data values, the distribution is said to be skewed right or positively skewed. This occurs because the tail of the distribution on the right-hand side is longer or more drawn out compared to the left-hand side.

In a right-skewed distribution, the mean is typically larger than the median, and the mode lies to the left of the median. This asymmetry indicates a larger number of lower values and a few extreme higher values in the data set. For example, if we have a data set with the histogram showing a longer tail on the right, it suggests there are some very large values stretching the scale, resulting in a skewed right distribution.

Step-by-step explanation:

[tex]rise=y_2-y_1\\\\run=x_2-x_1\\\\slope=\dfrac{rise}{run}`\\\\\text{We have}\ (4,\ 6),\ (8,\ -8).\ \text{Substitute:}\\\\rise=-8-6=-14\\\\run=8-4=4\\\\slope=\dfrac{-14}{4}=-\dfrac{7}{2}[/tex]

Answer:

-11x-4 is the answer if the expression to simplify is (-7x+1)-(4x+5).

Step-by-step explanation:

We are first going to distribute to get rid of the ( ):

-7x+1-4x-5

Pair up like terms:

-7x-4x+1-5

Combine the like terms:

-11x-4

Correct. We need a balance in order to answer the question.

Answer:

the rest of the question but the answer is $555.37

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Evaluate (h + k)(x) then substitute x = 2 into the result

(h + k)(x) = h(x) + k(x)

h(x) + k(x) = x² + 1 + x - 2 = x² + x - 1, thus

(h + k)(2) = 2² + 2 - 1 = 4 + 2 - 1 = 5

To find the value of (h + k)(2), substitute x = 2 into h(x) and k(x) and then add the results. The result is 5.

To find the value of (h + k)(2), we first need to find the values of h(2) and k(2). To find h(2), we substitute x = 2 into the function h(x) = x² + 1. h(2) = (2)² + 1 = 4 + 1 = 5. Next, to find k(2), we substitute x = 2 into the function k(x) = x - 2. k(2) = 2 - 2 = 0. Now, we can find (h + k)(2) by adding the values of h(2) and k(2). (h + k)(2) = h(2) + k(2) = 5 + 0 = 5.

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Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}y=-3x+6\\y=9\end{array}\right\ \text{put the value of}\ y\ \text{to the first equation}\\\\9=-3x+6\qquad\text{subtract 6 from both sides}\\3=-3x\qquad\text{divide both sides by (-3)}\\-1=x\to x=-1[/tex]

Answer:

The answer would be 6.

just a quick note, that triangle is misleading some, since the HG side of 6 units, shows longer than GE which is 8, and of course 8 > 6.

Since GE is a perpendicular bisector, that means the angle at G is 90°.

Check the picture below.

To find the length of HE, we utilize the properties of a perpendicular bisector and trigonometry. Knowing that GE halves HF into two equal parts, we calculate HF using trigonometric concepts, then halve it to find HE.

In the question, it's mentioned that GE is a perpendicular bisector of HF. This means that GE bisects HF into two equal lengths. Therefore, the length of HE will be equivalent to half of the length of HF.

Since, HF can be calculated using trigonometry as mentioned. By definition, cose = x/h, so if we know the height 'h' and the angle, we can find 'x' which in this case would be HF, and subsequently HE would be HF/2.

Moreover, in trigonometry, the length of side opposite to the right angle in a right-angled triangle is calculated by the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. We use this to find out HF if other two sides are known.

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Answer:

Step-by-step explanation:

{z+1}/{z-1} = i.

z+1 = i (z-1)

z+1 =iz -i

z - iz  = -1 -i

z ( 1 -i) = - 1 -i

z = (- 1 - i ) /(1-i) = - (1+i)/(1-i)

z = - (1+i)(1+i)/(1-i)(1+i)

z = - (1+2i +i²)/ ( 1²-i²).........i² = -1

z =-2i/2

z = - i      (one solution)

All the complex numbers z satisfying the equation {z+1}/{z-1} = i is z = -i.

Complex numbers are numbers which are of the form [tex]a + ib[/tex], where a and b are real numbers and i is the imaginary number called iota whose value is [tex]i^2[/tex]= -1.

Given equation is,

(z + 1) / (z - 1) = i

Multiplying both sides by (z - 1),

z + 1 = i (z - 1)

Let z = (a + bi)

Substituting,

(a + bi + 1) = i (a + bi - 1)

(a + bi + 1) - i (a + bi - 1) = 0

a + bi + 1 - (ai + b(i)² - i) = 0

a + bi + 1 - ai - b(i)² + i = 0

Now i² = -1

a + bi + 1 - ai + b + i = 0

Combining the like terms,

(bi - ai + i) + (a + 1 + b) = 0

i (b - a + 1) + (a + b + 1) = 0

Left hand side is a complex number.

A complex number is a + bi = 0, when a = 0 and b = 0.

So, we get,

(b - a + 1) = 0 and (a + b + 1) = 0

b - a = -1 and a + b = -1

So, combining,

a + b = b - a

a + a = b - b

2a = 0

a = 0

Substituting,

b = -1

So the complex number, z = a + bi = -i

Hence the complex number z = -i.

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Answer:

B 0.55

Step-by-step explanation:

the student is a sophomore - so youre looking at the sophomore row, 77 sophomores total

the student attended the volleyball game - 42 sophomores attended the game

42 / 77 students total = about 0.55

Option: B is the correct answer.

              B.   0.55

Let A denote the event that the student is a sophomore.

and B denote the event that the student attend the volleyball game.

and A∩B denote the event that the student is a sophomore and attend volleyball game.

Let P denote the probability of an event.

We are asked to find the probability : P(B|A)

We know that:

[tex]P(B|A)=\dfrac{P(A\bigcap B)}{P(A)}[/tex]

Based on the table provided to us we have:

[tex]P(A)=\dfrac{77}{137}[/tex]

and

[tex]P(A\bigcap B)=\dfrac{42}{137}[/tex]

Hence, we have:

[tex]P(B|A)=\dfrac{\dfrac{42}{137}}{\dfrac{77}{137}}[/tex]

i.e.

[tex]P(B|A)=\dfrac{42}{77}=0.55[/tex]

Answer:

the answer is 12 days

Step-by-step explanation:

3×4=12

Answer:

w=6

Step-by-step explanation:

P=2(L)+2(w)

48= 2(18)+2w

48=36+2w

12=2w

w=6

checking;

48= 2(18)+2(6)

48= 36+12

48= 48