At what point does the terminal side of the angle 7pi /4 in standard position intersect the unit circle

Answer:

Step-by-step explanation:

To find the roots/zeros, set

2

x

3

+

x

2

−

x

equal to

0

and solve.

2

x

3

+

x

2

−

x

=

0

Factor the left side of the equation.

Tap for more steps...

x

(

2

x

−

1

)

(

x

+

1

)

=

0

If any individual factor on the left side of the equation is equal to

0

, the entire expression will be equal to

0

.

x

=

0

2

x

−

1

=

0

x

+

1

=

0

Set the first factor equal to

0

.

x

=

0

Set the next factor equal to

0

and solve.

Tap for more steps...

x

=

1

2

Set the next factor equal to

0

and solve.

Tap for more steps...

x

=

−

1

The final solution is all the values that make

x

(

2

x

−

1

)

(

x

+

1

)

=

0

true. The multiplicity of a root is the number of times the root appears.

x

=

0

(Multiplicity of

1

)

x

=

1

2

(Multiplicity of

1

)

x

=

−

1

(Multiplicity of

1

)

Answer:

  -1, 0, 1/2

Step-by-step explanation:

The function can be factored as ...

  y = x(2x^2 +x -1)

  y = x(2x -1)(x +1)

The factors are unique, so each zero has multiplicity 1. The zeros are the values of x that make the factors zero:

  -1, 0, 1/2 . . . . zeros of the function; each with multiplicity 1

Answer:

  f(x) = x⁵ +4x⁴ +x³ -10x² -4x+8

Step-by-step explanation:

If p is a zero, then (x -p) is a factor. The multiplicity of the zero tells you how many times that is a factor (its exponent).

  f(x) = (x -1)²(x +2)³ = (x² -2x +1)(x³ +6x² +12x +8)

  f(x) = x⁵ +4x⁴ +x³ -10x² -4x+8

_____

Additional comment

You can use the distributive property to write out the 12 terms of the product of the two expanded factors, or you can do a little mental arithmetic based on what you know about the exponent of a product term. (It is the sum of the exponents of its factors.)

The mental exercise can be made easier by writing the coefficients of the factors as though they were two cubics. It works well to write them in two rows:

  [tex]\left[\begin{array}{cccc}0&1&-2&1\\1&6&12&8\end{array}\right][/tex]

The columns are in order of decreasing powers of x. A relatively simple and symmetrical pattern of sums of cross products is used to find the coefficients of the final polynomial. Working in order of decreasing exponents, we have ...

coefficient of x^6 = (0)(1) = 0

coefficient of x^5 = (0)(6) +(1)(1) = 1

coefficient of x^4 = (0)(12) +(1)(-2) +(1)(6) = 4

coefficient of x^3 = (0)(8) +(1)(1) +(1)(12) +(6)(-2) = 1

coefficient of x^2 = (1)(8) +(6)(1) +(-2)(12) = -10

coefficient of x^1 = (-2)(8) +(12)(1) = -4

coefficient of x^0 = (1)(8) = 8

Since "p" represents the number of pounds of peanuts and:  

4.05p + 14.40 = 4.50(p + 3) [then by distributing we have:

4.05p + 14.40 = 4.50p + 13.5 [then by subtracting 13.5 from both sides we have:

4.05p + 0.9 = 4.50p [then by subtracting 4.05p from both sides we have:

0.9 = 0.45p [then by dividing both sides by 0.45 we have:

2 = p

So there are 2 pounds of peanuts needed for the trail mix.

Answer:

7 out of 10

Step-by-step explanation:

if you have 10 in the cup then you add

4 vanilla 3 chocolate = 7

and add all scoops together and you get 10

so your probability would be 7 out of 10

another way to say it is

the probability of getting chocolate or vanilla ice cream from the cup would be 7 out of 10

Answer:

Generally, the algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division. To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.

Step-by-step explanation:

The cost of each campstools, tent and sleeping bag is $20, $100 and $26

let

tent = 1

sleeping bags = 2

campstools = 3

Total cost = $212

tent = t

sleeping bags = s

campstools = c

If

t = 5c

s = c + 6

Total = t + 2s + 3c

212 = 5c + 2(c + 6) + 3c

212 = 5c + 2c + 12 + 3c

212 = 10c + 12

212 - 12 = 10c

200 = 10c

c = 200/10

c = 20

t = 5c

= 5 × 20

= 100

s = c + 6

= 20 + 6

= 26

Therefore, the cost of each campstools, tent and sleeping bag is $20, $100 and $26

Learn more about equation:

https://brainly.com/question/4916384

Answer:

y=3x+5

Step-by-step explanation:

y=mx+b

-y=-5-3x

divide each term

y=5+3x

reorder 5 and 3x

answer:y=3x+5

Answer:

C. two times a number n added to one

Answer:

3 cups

Step-by-step explanation:

3/4 times 4 equals 12/4. divide and get 3.

Answer:1/16 squared

Step-by-step explanation:

1/4*1/4

4*4=16

1/16

The segments on triangle HJK are illustrations of equivalent ratios

The length of line AJ is 8.75 inches

The given parameters are:

[tex]H A = 5.25[/tex]

[tex]HB = 3[/tex]

[tex]BK = 5[/tex]

Because lines AB and JK are parallel lines, then we have the following equivalent ratios

[tex]HA:HB = AJ:BK[/tex]

Substitute values for length HA, HB and BK.

[tex]5.25:3 = AJ:5[/tex]

Express both ratios as fractions

[tex]\frac{5.25}{3} = \frac{AJ}5[/tex]

Multiply both sides by 5

[tex]\frac{5.25}{3} \times 5= AJ[/tex]

[tex]8.75= AJ[/tex]

Rewrite as:

[tex]AJ = 8.75[/tex]

Hence, the length of line AJ is 8.75 inches

Read more about equivalent ratios at:

https://brainly.com/question/2328454

Answer:

You could substitute the point (5,-4) into each equation

Step-by-step explanation:

x=5    y=-4

3x-2y=23

3(5)-2(-4)=23

15+8=23

23=23

2x+y=6

2(5)+(-4)=6

10-4=6

6=6

The points go into each equation which proves that the point (5,-4) is the solution.

(i don't know if I did this right, I apologize if I didn't

Answer:

yw

Step-by-step explanation:

Answer:

the answer to the question is 15$

Answer:

b=24, please give Brainliest if this helped you

Step-by-step explanation:

[tex] =( \frac{1}{2} \times 10.4 \times 16.9) {ft}^{2} \\ = (5.2 \times 16.9) {ft}^{2} \\ = 87.88 {ft}^{2} [/tex]

Answer:

The area of the triangle is 87.88 square feet.

Hope you could get an idea from here.

Doubt clarification - use comment section.

Answer:

[tex]k\le \:-18[/tex]

Step-by-step explanation:

First, you add 66 to both sides so then the equation you are trying to solve will be: [tex]k-66+66\le \:-84+66[/tex]

Finally, you simplify and get: [tex]k\le \:-18[/tex]

Hope this helped!

Looking at the first system of equations,

16x - 10y = 10

-8x - 6y = 6

If we multiply both sides of the second equation by 2, the coefficient of x is exactly the negative of the coefficient of x in the first equation.

-8x - 6y = 6

⇒   2 (-8x - 6y) = 2 (6)

⇒   -16x - 12y = 12

By combining this new equation with the first one, we can eliminate x and solve for y :

(16x - 10y) + (-16x - 12y) = 10 + 12

⇒   -22y = 22

⇒   y = -1

Then we just solve for x by replacing y in either equation.

16x - 10y = 10

⇒   16x - 10 (-1) = 10

⇒   16x + 10 = 10

⇒   16x = 0

⇒   x = 0

The main idea behind elimination is combining the given equations in just the right amount so that one of the variables disappears. The "right amount" involves using the LCM of the coefficients of a given variable. In this example, the x-coefficients had LCM(8, 16) = 16, so we only had to scale one of the equations (the one with -8x) to cancel all the x terms.

If we wanted to eliminate y first instead, we first note that LCM(6, 10) = 30. To get 30 as a coefficient on y, in the first equation we would have multiplied by 3:

16x - 10y = 10

⇒   3 (16x - 10y) = 3 (10)

⇒   48x - 30y = 30

And in the second equation, we would have multiplied by -5 (negative so that upon combining the equations, we end up with -30y + 30y = 0):

-8x - 6y = 6

⇒   -5 (-8x - 6y) = -5 (6)

⇒   40x + 30y = -30

Now combining the two scaled equations gives

(48x - 30y) + (40x + 30y) = 30 + (-30)

⇒   88x = 0

⇒   x = 0

We then solve for y :

16x - 10y = 10

⇒   -10y = 10

⇒   y = -1

so we end up with the same solution as before.

Answer:

L

Step-by-step explanation:

Answer:

y = (2/3)x + 1/3

Step-by-step explanation:

Check that a single straight line will actually go through all four of these points.  Going from (1, 1) to (4, 3), the 'rise' is 2 and the 'run' is 3, which would make the slope, m, equal rise/run = 2/3.  Going from (4,3) to (10, 7), m = rise/run = 4/6 = 2/3 (again).

Let's find the slope-intercept form of the equation of this line:  y = mx + b

Arbitrarily choose the point (1, 1).  Here x = 1, y = 1 and m = 2/3.  Then

we have

1 = (2/3)(1) + b, or 1 = 2/3 + b, so that b must be 1/3.

The equation in question is y = (2/3)x + 1/3

Answer: 8 or -6

Step-by-step explanation:

x^2 - 2x = 48

x^2 - 2x - 48 = 0

(x-8)(x+6) = 0

x = 8 or -6

Answer:

i need help too

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

x = - 3 is a vertical line parallel to the y- axis.

A line perpendicular to it will therefore be a horizontal line parallel to the x- axis with equation

y = c

where c is the value of the y- coordinates the line passes through.

The line passes through (6, - 4 ) with y- coordinate - 4 , then

y = - 4 ← equation of perpendicular line

Answer:

y=5/3x+b

Step-by-step explanation:

Supposing CD uses the equation y=mb (meaning CD passes through the origin) and passes through (3,5), we then know the slope if 5/3 and the y intercept is 0. We can then write CD's equation as y=5/3x+0, or just y=5/3x.

So if AB is parallel to CB, then their equation is y=5/3x+b, as we don't the y-intercept yet.

Thank you!

Answer:

B

Step-by-step explanation:

Answer:

Your answer would be C

Step-by-step explanation:

Because its a ratio of integers with a nonzero denominator.

Answer:

16

Step-by-step explanation:

y = mx+b, where y is cost x is # of movies, m is $ per rental and b is the flat charge.

y = 1.50x+15

40 = 1.50x+15

25 = 1.50x

16.666... = x

You can rent about 16 movies

Hope that helps

Answer:

40 = 1.50x+15

25=1.50x

x=16

16 movies

Step-by-step explanation:

Answer:

The answer is  $22.79. Hope this helped! If the answer is wrong i'm super sorry!

Step-by-step explanation:

$13.50 + $8 = $21.50

0.06 x 21.50 = $1.29

$1.29 + $21.50 = $22.79

Answer:

 B

Step-by-step explanation:

The incorrect tables each have at least one flaw that makes it not match the histogram.

A. The relative frequency associated with 4 of 86 is about 0.047, not 0.055. The relative frequencies are incorrect.

B. this table matches the histogram

C. The "bins" are not of uniform width, nor are they centered on the same values as shown in the histogram.

D. The values in a cumulative frequency table should be non-decreasing. The table value of 24 should be 54.