How many ms in a second?

Since beta is in the first quadrant, the final answer will be positive.

To find cos(beta) so we can use the half angle identity, we can substitute into the Pythagorean identity. Doing so gives us that

[tex] \sin( \beta ) = \frac{ \sqrt{17} }{5} [/tex]

So, this means that

[tex] \sin( \frac{ \beta }{2} ) = \sqrt{ \frac{1 - \frac{ \sqrt{17} }{2} }{2} } = \sqrt{ \frac{2 - \sqrt{17} }{4} } = \frac{ \sqrt{2 - \sqrt{17} } }{2} [/tex]

Answer:

6 hours.

Step-by-step explanation:

Speed = distance / time.

Carla travels  3 * 12 = 36 miles before Zari leaves the shop.

So Zari travels x miles in the same time as Carla travels x- 36 miles.

So 18 = x/t and 12 = (x - 36)/t

From first equation x = 18t so we have the equation

12 = (18t - 36/t

18t - 36 = 12t

6t = 36

t = 6 hours.

The theorem which justifies that two lines are parallel when cut by a transversal k is converse of the alternate interior angles theorem.

Given that two lines m and n are parallel.

We have to find the theorem which justifies that the lines m and n are parallel when cut by a transversal k.

Parallel lines are those lines which do not meet each other at any point on the surface.

If we know that the alternte interior angles are equal,then m and n become parallel to each other.

So the converse of the alternate interior angles theorem correctly justifies that the lines are parallel if cut by a transversal k.

Hence to justify that two lines are parallel if they are cut by a transversal k, we have to use converse of the alternate interior angles theorem.

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Question is incomplete as it should include the following options:

1) converse of the corresponding angles theorem,

2) converse of the alternate interior angles theorem.

3) converse of the same side interior angles theorem,

4) converse of the alternate exterior angles theorem.

Answer:

Second choice

Step-by-step explanation:

Analyse each sentences: The sum of x and y is 5 can be mathematically expressed as [tex]\displaystyle{x+y = 5}[/tex] since both are sum together and equal to 5.

Next, the value of y is one more than value of x can be mathematically expressed as [tex]\displaystyle{y=x+1}[/tex] because value of y is one more than value of x so y will be the value of x add with 1.

Therefore, form the simultaneous equation:

[tex]\displaystyle{\left \{ {{x+y=5} \atop {y=x+1}} \right}[/tex]

Hence, the answer is second choice.

Answer:

Step-by-step explanation:

cos A = √( 1 - (5/13)²) = √( 1 - 25/169) = √(144/169) = - 12 /13

in 2 A = 2 sin A cos A

sin 2 A = 2 *5/13 ( - 12/13 ) = - 120 / 169

the answer is -120/169

Answer: 18 years

Work Shown:

[tex]f(\text{x}) = 2.56(1.04)^\text{x}\\\\5 = 2.56(1.04)^\text{x}\\\\5/2.56 = (1.04)^\text{x}\\\\1.953125 = (1.04)^\text{x}\\\\\log(1.953125) = \log(1.04^\text{x})\\\\\log(1.953125) = \text{x}*\log(1.04)\\\\\text{x} = \frac{\log(1.953125)}{\log(1.04)}\\\\\text{x} \approx 17.0682937693249\\\\[/tex]

The steps above show f(x) replaced with 5. Then you'd use logarithms to isolate the variable x. The relevant useful log rule is [tex]\log(A^B) = B\log(A)[/tex] so we can pull down the exponent.

From here it seems your teacher wants you to round up to the nearest integer.

If we plugged in x = 17, then f(x) = 4.99 which is one cent too small.

While x = 18 leads to f(x) = 5.19

Therefore, x = 18 has the price reach or exceed $5

Answer:

See below

Step-by-step explanation:

If the car has 4 wheels    480/4 = 120 cars

If the car has 3 wheels    480/3 = 160 cars

If the car has 6 wheels ( like a dual truck)  480 / 6 = 80

The thousand of miles across the United states from the east coast to the west coast.

In order to find the number of miles across the United states from the east coast to the west coast.

Hence, the thousand of miles across the United states from the east coast to the west coast.

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she bought 20 items at price of 0.01$, 6 items at cost $2, 4 items at cost $3.

According to the statement

Janice bought total items = 30

Price of items are 30 cents, 2 dollars, or 3 dollars.

Total purchase price of Janice = 30$

If we let she bought 10 items at price of 3$, Then it is not possible

So, Number of items which are bought by her at price of $3 is less than 10. Similarly Number of items which are bought by her at price of $2 is less than 10.

we know that 1 CENT = 0.01 $

We also know that 10 30-cents will worth 3 dollars, so the number of cents which are bought by her at price of $0.01 is greater than 10.

Now, Let she bought 20 items at price of 0.01$

Then 20*0.3 = 6$

It means 30$-6$ = 24$

24$ are left to purchase the things which are at price of 2$ and 3$.

If we let she purchase 4 items at cost $3 then

Then 4*$3 = 12$

It means 24$-12$ = 12$

Now, with remaining money she bought 6 items at cost $2.

So, she bought 20 items at price of 0.01$, 6 items at cost $2, 4 items at cost $3.

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she bought 20 items at price of 0.01$, 6 items at cost $2, 4 items at cost $3.

According to the statement

Janice bought total items = 30

Price of items are 30 cents, 2 dollars, or 3 dollars.

Total purchase price of Janice = 30$

If we let she bought 10 items at price of 3$, Then it is not possible

So, Number of items which are bought by her at price of $3 is less than 10. Similarly Number of items which are bought by her at price of $2 is less than 10.

we know that 1 CENT = 0.01 $

We also know that 10 30-cents will worth 3 dollars, so the number of cents which are bought by her at price of $0.01 is greater than 10.

Now, Let she bought 20 items at price of 0.01$

Then 20*0.3 = 6$

It means 30$-6$ = 24$

24$ are left to purchase the things which are at price of 2$ and 3$.

If we let she purchase 4 items at cost $3 then

Then 4*$3 = 12$

It means 24$-12$ = 12$

Now, with remaining money she bought 6 items at cost $2.

So, she bought 20 items at price of 0.01$, 6 items at cost $2, 4 items at cost $3.

Answer:

V≈3053.63

A≈1017.88

Step-by-step explanation:

V=[tex]\frac{4}{3}[/tex]π [tex]r^{3}[/tex]=[tex]\frac{4}{3}[/tex]·π·[tex]9^{3}[/tex] ≈3053.62806

A=4π[tex]r^{2}[/tex]=4·π·[tex]9^{2}[/tex] ≈1017.87602

For a person to be able to create a coordinate proof to show that the two triangles are congruent by the SSS Triangle Congruence Theorem one can simply use the distance formula.

Given that the distance formula =

[tex]\sqrt{(x_{2} -x_{1})^{2} + (y_{2} - y_{1}^{2} )}[/tex]

Let say that Angle ABC has the vertices of A (-4, -2),  B (-5,1). C (0,2) and Angle DEF   has the vertices of D (7, -4), E (4,-5), F (3,0)

So lets prove it:

AC = [tex]\sqrt{(x_{2} -x_{1})^{2} + (y_{2} - y_{1}^{2} )}[/tex]

=[tex]\sqrt{(-4-0)^2 + (-2-2)^2}[/tex]

=[tex]\sqrt{32}[/tex]

= 4[tex]\sqrt{2}[/tex]

Do the same for DF:

DF = [tex]\sqrt{(x_{2} -x_{1})^{2} + (y_{2} - y_{1}^{2} )}[/tex]

= [tex]\sqrt{(7-3)^2 + (-4-0)^2}[/tex]

=[tex]\sqrt{32}[/tex]

= 4[tex]\sqrt{2}[/tex]

Looking at the above, one can see the values are the same and as such this proves that AC is the same to DF. If you do the same for the other part of the angles, you will see that they are congruent.

Therefore, For a person to be able to create a coordinate proof to show that the two triangles are congruent by the SSS Triangle Congruence Theorem one can simply use the distance formula.

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The slant height of the hexagonal pyramid is: B. 14 inches.

Area of a regular hexagon = 3√3/2(s²)

First, find the area of the regular hexagon:

Area = 3√3/2(s²) = 3√3/2(10²) = 150√3 in.².

Surface area is given as 420 + 150√3 in.².

Area of the 6 triangles = surface area - area of hexagonal base = 420 + 150√3 - 150√3

Area of the 6 triangles = 420 in.²

Area of 1 triangle = 420/6 = 70 in.²

Use the area of a triangle to find the slant height (h):

70 = 1/2(10)(h)

2(70) = 10(h)

140/20 = h

h = 14 in.

The answer is B. 14 inches.

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Answer:

125

Step-by-step explanation:

y = 1k/x^3  I am trying to find the constant k.  I will use the information that I have been given to find k

1 = k/5^3

1 = k/125  Multiply both sides by 125

125 = k

Now, we will find y when x = 1

y = 125/1^3

y = 125

The value of y is 125 when x is 1.

Write the function y as a function of x, i.e., y = f(x), and then solve for x as a function of y, to determine the inverse of a function.

y = 1k/x^3  I am trying to find the constant k.  I will use the information that I have been given to find k

1 = k/5^3

1 = k/125

Multiply both sides by 125

125 = k

Now, we will find y when x = 1

y = 125/1^3

y = 125

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Answer:

A because of the average length showed

What is one major limitation of the Social Readjustment Rating Scale?

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The functions f(x) = -4x + 11 and f(x) = 2/3x - 8 are having the range of {y ∈ R | -∞ < y < ∞}.

Step 1: Finding the range for the function f(x) = -(x + 1)² - 4

The given function is quadratic in the form of a(x - h)² + k,

So, the range of the function is y ≤ k if a < 0 or y ≥ k if a > 0

For the given function, a = -1 so, a < 0. thus, the range of the given function is y ≤ k, where k = -4

∴ Range of f(x) = -(x + 1)² - 4 is: (-∞ -4], {y | y ≤ -4}

Step 2: Finding the range for the function f(x) = -4x + 11

This is a linear function. So, the range is R.

∴ Range of f(x) = -4x + 11: (-∞, ∞), { y | y ∈ R}

Step 3: Finding the range for the function f(x) = 2/3x - 8

This is also a linear function. So, the range is R.

∴ Range of f(x) = 2/3x - 8: (-∞, ∞), { y | y ∈ R}

Step 4: Finding the range for the function f(x) = 2^x + 3

This is an exponential function. So, the range is y > k

Here k = 3.

∴ Range of f(x) = 2^x+3: (3, ∞), {y | y > 3}

Step 5: Finding the range for the function f(x) = x² + 7x - 9

This is a quadratic function.

we can write it as,

f(x) = x² + 2 × x × (7/2) + (7/2)² - (7/2)² - 9

     = (x + 7/2)² - 85/4

This is in the form of a(x - h)² - k. where a = 1 > 0 and k = -85/4

Since a > 0, the range of the function is y ≥ -85/4

∴ Range of f(x) = x² + 7x - 9: [-85/4, ∞), {y | y ≥ -85/4}

Therefore, the functions f(x) = -4x + 11 and f(x) = 2/3x - 8 are having the given range {y ∈ R, -∞ < y < ∞}

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Because It is quicker and fast.

Sampling:

Sampling is a process used in statistical analysis in which a predetermined number of observations are taken from a larger population. The methodology used to sample from a larger population depends on the type of analysis being performed, but it may include simple random sampling or systematic sampling.

Sampling is the selection of a subset of the population of interest in a research study. In the vast majority of research endeavors, the participation of an entire population of interest is not possible, so a smaller group is relied upon for data collection.

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Answer:

y=-2x+5

Step-by-step explanation:

For every increase in x, y decreases by 2

so the slope is -2

You can solve for the y-intercept by going backward, 1-1=0, 3+2=5

the y-intercept is (0,5)

Using the slope intercept equation format, the answer is y-2x+5

By definition and properties of the absolute value used on the quadratic equation we conclude that F(|- 4|) = 12.

Herein we must apply the definition of absolute value prior to evaluating the quadratic equation defined in the statement. From algebra we know that absolute values are defined as:

|x| = x, when x ≥ 0 or - x, when x < 0. (1)

Then, we apply (1) on the quadratic equation:

F(|x|) = |x|² - 2 · |x| + 4

As x < 0, by absolute value properties:

F(|x|) = x² + 2 · x + 4

F(|- 4|) = (- 4)² + 2 · (- 4) + 4

F(|- 4|) = 16 - 8 + 4

F(|- 4|) = 12

By definition and properties of the absolute value used on the quadratic equation we conclude that F(|- 4|) = 12.

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Answer:

Step-by-step explanation:

[tex](g+f)(x)=g(x)+f(x)=x-1+x^2 +4=x^2 +x+3[/tex][tex]x^2 +x+3[/tex]

Answer:

30

Step-by-step explanation:

Since ABC is isosceles, BC = CA.

So, AB = 9(3)+3 = 30.

Answer:

A little less than 320

Step-by-step explanation:

Round the miles to 168 and 150

Add together 168 + 150 = 318

Answer: a. a little less than 320

Answer:

The slope is -2

Step-by-step explanation:

To find the slope, we can use the slope formula

m = ( y2-y1)/(x2-x1)

    = (-1 -3)/(-1 - -3)

   = ( -1-3)/(-1+3)

   = -4/2

   = -2

The slope is -2

Answer:

875

Step-by-step explanation:

1-0.32=0.68 so its 0.68 of its original price.

x*0.68=595 x is the original price

x=595/0.68

x=875

If f(x) = 2x + 3 then Δy/Δx = 2 and g(x) = 2² +3 then Δy/Δx = 2.33.

The correct answer is option A.

f(x) has a rate of change of 2

g(x) has a rate of change of 2.33

So g(x) is growing faster

Let f(x) = 2x + 3 and g(x) = 2² +3

Let, ∆y /∆x denotes the ratio of y change and x change when x change exists relatively large.

If f(x) = 2x + 3

Δy/Δx = [f(3) - f(0)]/3 - 0

f(3) [tex]= 2*3+3 = 9[/tex]

f(0) [tex]= 2*0+3 = 3[/tex]

[f(3) - f(0)]/3 - 0 = (9 - 3)/3

= 6/3 = 2

g(x) = 2² +3

Δy/Δx = [g(3) - g(0)]/3 - 0

[tex]$= (2^3 +3)-(2^0 +3)/3[/tex]

[tex](2^3 +3)-(2^0 +3) = 7[/tex]

[tex](2^3 +3)-(2^0 +3)/3[/tex] = 7/3 = 2.33

Therefore, the correct answer is option A.

f(x) has a rate of change of 2

g(x) has a rate of change of 2.33

So g(x) is growing faster

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Answer:

Slope: 1

Y-intercept: -1

Step-by-step explanation:

The line passes the y-axis at -1, the rise/run, which is used to calculate the slope is 2/2, and it equals to 1, so the slope is 1.

I hope it helps! Have a great day!

bren~  

The equation can be used to find other combinations of x and y is  y^2 = (1/16)x^3

The direct variation from the square of y to the cube of x is represented as:

y^2 = kx^3

Where k represents the variation constant.

When x = 4, y = 2.

So, we have:

2^2 = k * 4^3

This gives

4 = 64k

Divide both sides by 64

k = 1/16

Substitute k = 1/16 in y^2 = kx^3

y^2 = (1/16)x^3

Hence, the equation can be used to find other combinations of x and y is  y^2 = (1/16)x^3

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Answer:

8 books per box.

Step-by-step explanation:

One must assume that the books are evenly distributed among the boxes.  Ryan has 3 books already and adds 4 boxes to reach a total of 35 books:

3 books + 4 boxes = 35 books

4 boxes = 35 books-3 books

4 boxes = 32 books

1 box = 8 books

There are 8 books per box.