Question 3 (1 point)
(03.06 LC)

Determine if the sequence is arithmetic or geometric, and find the common difference or ratio

Answer:

16.4 cm  

Step-by-step explanation:

In a right triangle :

cosine 43 = adjacent leg / hypotenuse = 12/x

SO:

cosine 43 = 12/x        then x   =   12 / cos 43  = 16.4 cm

Answer:

Step-by-step explanation:

Equations:

Recall the identities:

Now find a and b, then find their product.

The time taken by the ball to reach the ground is 0.067 seconds

Given,

The initial velocity of the ball (speed) = 35 feet/second

The height of the ball (distance), h = -16t² + 35t + 6

We have to find the time, (t in seconds) taken by the ball to reach the ground.

Speed = distance/time

So, Time = distance/speed

Here,

Time = (-16t² + 35t + 6) / 35

We have to solve the equation first.

-16t² + 35t + 6 = 0 is in quadratic form. So, we can solve this by using quadratic formula.

Quadratic formula = [tex]\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}[/tex]

Here,

a = -16, b = 35, c = 6

Now,

[tex]\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}[/tex]

= [tex]\frac{-35(+-)\sqrt{35^{2}-4(-16)(6) } }{2(-16)}[/tex]

= [tex]\frac{-35(+-)\sqrt{1225 +384} }{-32}[/tex]

= (-35±√1609) / -32

= (-35±40.11) / -32

Now,

Solve for:

(-35 + 40.11) / -32 = 5.11/-32 = -0.15

Solve for

(-35 - 40.11) / -32 = -75.11 / -32 = 2.35

Lets take the height as 2.35 feet.

Now,

Time = distance/speed

Time = 2.35/35 = 0.067

Therefore, the time taken by the ball to reach the ground is 0.067 seconds.

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Coplanar lines are referred to as parallel lines because they may be extended indefinitely without ever intersecting. || is the sign meaning "parallel to." If two lines are drawn, they don't have to be parallel, and a third line runs across them as seen in the diagram below. We may obtain eight distinct angles by drawing two parallel lines, and then drawing a transverse line through them.

Four pairs of matching angles will be created from all eight angles. One of the pairings is represented by angles F and B in the preceding diagram. If the two lines are parallel, corresponding angles are congruent.

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The equation of the line that passes through the point; (-4, 8) and is parallel to x + y = 6 as required in the task content is; x + y = 4.

It follows that the equation of the line that passes through the given point and is parallel to the given line is to be determined.

By expressing the given linear equation in slope-intercept form; it follows that we have;

x + y = 6

y = -x + 6

Hence, the slope of the equation by comparison with; y = mx + c is; -1.

Therefore, the slope of the required equation is same as the two lines are said to be parallel.

Ultimately, the required equation from point-slope form of an equation is;

( y - 8) = -1 ( x - (-4))

y - 8 = -x - 4

x + y = -4 +8

x + y = 4.

Ultimately, the required equation is; x + y = 4.

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Answer:

Thr equation is y=x-1

Step-by-step explanation:

The y intercept is negative 1 so that eliminates options 1 and 3 and the slope goes up which leaves only option 2 left

Answer:

=[tex]\frac{78139}{5}[/tex]

Step-by-step explanation:

[tex]-\frac{3}{15}-(-3)+25^{3} \\=\frac{78139}{5}[/tex]

The postulate that could be used is the: linear pair postulate.

If two angles share a common side and also a common vertex lie on a straight line, they both form a special angle relationship that is called the linear pair.

Based on the linear pair postulate, it is proven that angles that form a linear pair add up to 180 degrees and are therefore regarded as supplementary.

Angle CAD and angle CAB have a common side, side CA, and a common vertex, angle A. They are also on the straight line, line AB.

Thus, it can be proved that the angles CAB and CAD are supplementary based on the linear pair postulate.

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Answer:

Formula for slope is given as (y2-y1)÷(x2-x1) or (y1-y2)÷(x1-x2).

Slope of line = (14-8)÷(7-10)

                     = 6÷(-3)

                     = -2

A
-------------------------------------------------------

bc it is an integer but not whole numbers

Answer:

$569.80

Step-by-step explanation:

She worked $12.95 per hour for 6 hours of overtime, meaning we would multiply $12.95 by 6 which is equal to $77.70, since she worked for 38 hours that week, we would multiply $12.95 by 38 which is $492.10, so now we add how much she earned for the total. Her overtime pay was $77.70 + her regular pay was $492.10 which adds up to $569.80

Fred's overtime pay is $16.50 an hour. He put in extra time this week on Monday and Thursday. The equation is $123.75-4 times the x value =h and h value is 57.75 and the working hours are 3.5 hours.

Given that,

Fred's overtime pay is $16.50 an hour. He put in extra time this week on Monday and Thursday. He put in four hours of extra on Monday. He received $123.75 in overtime compensation in total for the week.

We have to determine how many overtime hours, h, Fred worked on Thursday, write an equation and solve it.

We can write the equation as

$123.75-4 times the x value =h

Here,

x value is $16.50

We get,

$123.75-4×$16.50=h

h=57.75

To check hours working

57.75/16/50

=3.5 hours.

Therefore, the equation is $123.75-4 times the x value =h and h value is 57.75 and the working hours are 3.5 hours.

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Answer:

[tex](1)\;\;\;\text{Slope }= \dfrac{3}{5}\\[/tex]

(2) Equation of line in slope-intercept form is
[tex]y = \dfrac{3}{5}x + 3[/tex]

(3) Equation of line in standard form is:
[tex]5y - 3x = 15[/tex]

Step-by-step explanation:

Equation of a line in slope-intercept form is
y = mx + b

where m = slope and b = y-intercept

Slope = [tex]\dfrac{y2 - y1}{x2-x1}[/tex]

where (x1, y1) and (x2, y2) are two points on the line.

y2 - y1 is known as the rise
x2 - x1 is known as the run
Slope is also defined as rise/run

We are given x-intercept = -5.
The ex-intercept is the point at which the line crosses the x-axis. At this point the y-value = 0.

So we get one of the points (-5, 0)

We are given y-intercept = 3
The y-intercept is the point at which the line crosses the y-axis. At this point the x-value is 0

So another point on the line is (0, 3)

Knowing this we can compute rise and run
rise = y2 - y1 = 3 - 0 = 3

run = x2 - x1 = 0 - (-5) = 0+5 = 5

[tex](1)\;\;\;\text{Slope = $\dfrac{3}{5}$}[/tex]

(2) Equation is
y = mx + b where m = slope and b = y-intercept
Slope = 3/5 from (1) and y-intercept = 3

So equation of line in slope-intercept form is
[tex]y = \dfrac{3}{5}x + 3[/tex]

(3) Equation in standard form
In (2) subtract (3/5)x from both sides.

[tex]y - \dfrac{3}{5}x = 3[/tex]

We can multiply both sides by 5 to get
[tex]5(y - \dfrac{3}{5}x )= 5 \times 3\\\\= 5y - 3x = 15[/tex]

Answer: c=1

Step-by-step explanation:

Move the variable to the left side

2c+8−10c=0

Subtract the terms

−8c+8=0

Move the constant to the right side

−8c=0−8

Subtract the terms

−8c=−8

Divide both sides

−8c  = −8

−8       -8

Simplify

Answer:

The volume would be [tex]396cm^3[/tex].

Step-by-step explanation:

Answer:

792 cm

Step-by-step explanation:

99*8

Soyala travelled for 3 hours with a speed of 25 mph and 5 hours with a speed of 15 mph

We know that Distance = Rate x Time. The distance traveled to the library is assumed to be same as the distance traveled on the way to home from the library. Let t be the time it took to travel to the library after which (8 - t) = the time it took to travel back home. We can write following two equations using the formula for distance:

d = 25t ---------> (1)

d = 15(8 - t) = 120 - 15t -----------> (2)

Since the distance d is equal for both trips, let's set the two expressions of time t equal to each other.

25t = 120 - 15t

40t = 120

t = 3 hours

Therefore, Soyala travelled for 3 hours at 25 mph and for 8 - 3 = 5 hours at 15 mph. Each rate will yield a distance traveled of 125 miles.

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Answer:

540

Step-by-step explanation:

Answer:

slope = 0

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (7, - 6 ) and (x₂, y₂ ) = (6, - 6 )

m = [tex]\frac{-6-(-6)}{6-7}[/tex] = [tex]\frac{-6+6}{-1}[/tex] = [tex]\frac{0}{-1}[/tex] = 0

The slope of the parallel line to line MN -6

From the question, the line is given as

Line MN

Also, we have the slope of line MN to be

Slope of MN = -6

As a general rule in linear functions and parallel lines

The slopes of parallel lines are equal

This means that any line that is parallel to the line MN and the line MN would have the same slope of -6

Hence, the slope of the line segments that are parallel to line MN is -6

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Answer:

I'll assume z3 is actually z^3

z = 2

Step-by-step explanation:

z*z*z = 8

(2)*(2)*(2) = 8

Answer:

1 7/8 inches is 1.875 in decimal form.

The following ordered pairs are the solutions to 5x+2y=-1 :

(1,-3) and (-3,7)

Given we have the ordered pairs and the equation.

To find out whether the ordered pair is a solution or not, we just need to replace the x and y values from the ordered pair (x,y) and check if both the sides equate.

a. (1,-3)

5x+2y=-1

5(1)+2(-3) = -1

consider L.H.S

5-6

= -1

Therefore, L.H.S = R.H.S

hence the ordered pair (1,-3) is a solution to 5x+2y=-1.

b. (2,8)

5x+2y=-1

5(2)+2(8) = -1

consider L.H.S

10+16

= 16

Therefore, L.H.S ≠ R.H.S

hence the ordered pair (2,8) is not a solution to 5x+2y=-1.

c. (-4,-6)

5x+2y=-1

5(-4)+2(-6) = -1

consider L.H.S

-20-12

= -32

Therefore, L.H.S ≠ R.H.S

hence the ordered pair (-4,-6) is not a solution to 5x+2y=-1.

d. (-3,7)

5x+2y=-1

5(-3)+2(7) = -1

consider L.H.S

-15+14

= -1

Therefore, L.H.S = R.H.S

hence the ordered pair (2,8) is a solution to 5x+2y=-1.

Therefore the ordered pairs which are solutions to 5x+2y=-1 are:

(1,-3) and (-3,7)

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Answer: The equation of line parallel to given line passing through (8,-7) is:

Step-by-step explanation:

Given line is:

5x+4y=16

first of all, we have to convert the equation of given line in slope-intercept form

Dividing both sides by 4

Slope intercept form is:

The slope of given line is:

Let m1 be the slope of line parallel to given line

"The slopes of two parallel lines are equal"

The equation of line parallel to given line will be:

Putting the value of slope

Putting the point (8,-7) in the equation

Putting the value of b

Hence,

The equation of line parallel to given line passing through (8,-7) is:

First you need to ubicate those vertices in a plane as follow:

Then you link the vertices with lines to form the triangle:

Knowing that a right triangle must have one angle of 90º

The answer is that yes, it is a right triangle because it has an angle of 90º in the vertice H(8,5)

Answer: D (last bubble)

Step-by-step explanation:

slope of f is 2/3

inverse of 2/3 is 3/2

that is graph h

these graphs are symmetrical around the line y = x

Answer:

  2a.  ((500x +200)x +600)x

  2b.  $1350.68

  3.  -1

Step-by-step explanation:

2. You want to know the balance in an account at the end of 3 years with deposits at the beginning of successive years being $500, $200, and $600, and with deposits having an annual growth factor of x. You want (a) an expression for the balance in terms of x, and (b) the balance when x=1+2%.

3. You want the value of p(-2) for p(x) = 5x³ +8x² -3x + 1.

$500 is deposited at the beginning of the first year. The problem statement tells us that this has been multiplied by growth factor x by the end of the year, so the balance at that point is 500x.

At the beginning of the second year, $200 is added to the account, and the entire amount is multiplied by the growth factor for the year. That makes the balance at the end of the second year be ...

  (500x +200)x

Then $600 is added, and again the account grows by a factor of x. At the end of the third year, the balance is ...

  balance = ((500x +200)x +600)x

The growth factor is given as x = 1 +r. When r = 2%, this becomes x = 1.02. Then the balance at the end of year 3 is ...

  ((500·1.02 +200)·1.02 +600)·1.02 = 1350.68

The amount in the account at the end of three years is $1350.68.

__

The value of p(x) = 5x³ +8x² -3x +1 for x=-2 is found by substituting -2 where x is found. Evaluation can be easier by rewriting the polynomial to Horner form:

  p(x) = ((5x +8)x -3)x +1

  p(-2) = ((5(-2) +8)(-2) -3)(-2) +1 = ((-2)(-2) -3)(-2) +1 = (1)(-2) +1 = -1

The value of the function for x=-2 is -1.

__

Additional comment

You will note that the expression in problem 2 is also written in Horner form. If it were expanded, it would be 500x³ +200x² +600x. Evaluation takes fewer steps when Horner form is used.

ANSWER

x - 6

EXPLANATION

We want to write an algebraic expression that matches the statement:

Six less than a number.

First, let that unknown number be x.

So, 6 less than x.

Since it means that we are taking 6 from x, we subtract 6 from x.

That will be:

x - 6