Angle α is in quadrant III, and angle β is in quadrant II. If sin α = –4∕5 and sin β = 1∕2, find cos (α + β).

Answer:

4.

[tex]$x=\frac{2}{3} \pm \frac{1}{6}i \sqrt{158}$[/tex]

Step-by-step explanation:

[tex]18x^2-24x+87=0[/tex]

Using Quadratic Formula

[tex]$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$[/tex]

[tex]$x=\frac{-\left(-24\right)\pm \sqrt{\left(-24\right)^2-4\cdot \:18\cdot \:87}}{2\cdot \:18}$[/tex]

Solving the discriminant:

[tex]\Delta = \left(-24\right)^2-4\cdot \:18\cdot \:87\\\Delta = 576-6264\\ \Delta=-5688[/tex]

[tex]$x= \frac{24 \pm \sqrt{-5688} }{36} $[/tex]

[tex]$x= \frac{24 \pm \sqrt{5688i} }{36} $[/tex]

Once [tex]\sqrt{5688} =\sqrt{2^3\cdot \:3^2\cdot \:79}=6\sqrt{158}[/tex]

[tex]$x=\frac{24\pm6\sqrt{158}i}{36}$[/tex]

Dividing the denominator and numerator by 6

[tex]$x=\frac{4\pm \sqrt{158}i}{6}$[/tex]

Now rewrite it:

[tex]$x=\frac{4}{6} \pm i\frac{\sqrt{158}}{6}$[/tex]

[tex]$x=\frac{2}{3} \pm i \frac{\sqrt{158}}{6}$[/tex]

or

[tex]$x=\frac{2}{3} \pm \frac{1}{6}i \sqrt{158}$[/tex]

Answer:

6

Step-by-step explanation:

We can make:

A 3 sided shape and a 13 sided shape (3 + 13 = 16)

A 4 sided shape and a 12 sided shape (4 + 12 = 16)

A 5 sided shape and an 11 sided shape

A 6 sided shape and a 10 sided shape

A 7 sided shape and a 9 sided shape

2 8 sided shapes

Therefore the answer is 6.

Answer:

1/16

Events A+B are written (P) yellow : 1/4 * (P) green : 1/4

Ao event = (P) 1/4 * 1/4 = 1/16

Step-by-step explanation:

The probability of event A and event B is 1/16.

We have given that,

Event A: lands on yellow.

Event B: lands on green

Events A+B are written  

yellow(P) = 1/4 * (P) green= 1/4

Probability is defined as the likelihood of something occurring or the chance of something happening.

Ao event (P)=1/4 * 1/4

Event = 1/16

Therefore the probability of event A and event B is 1/16.

To learn more about the probability visit:

https://brainly.com/question/25870256

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Answer:

20

Step-by-step explanation:

1.75 x 6 = 10.5

10.5 + 9.5 = 20

Answer:

20 is the answer im 100% sure ask me for a picture if u want my work shown

Step-by-step explanation:

Answer:

100 divided by 40 is 14

Step-by-step explanation:

just dived 100 by 40 is 14 then add  7 to 14 they give you 21

Answer:

1

Step-by-step explanation:

8(y^0) + (-7)(y^0)

Remove parentheses: (a)=a

= 8[tex]y^{0}[/tex]-7[tex]y^{0}[/tex]

Add similar elements: 8[tex]y^{0}[/tex]-7[tex]y^{0}[/tex]= [tex]y^{0}[/tex]

= [tex]y^{0}[/tex]

Apply rule [tex]a^{0}[/tex] = 1, [tex]\alpha \neq 0[/tex]

= 1

Answer:

7 units to the right and 2 units up

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

Alr so correct me if I'm wrong but I think you made a mistake. It says find 44 of those rectangles. You found just 1 in that case which the area is 3/11. You have to do 3/11 X 44 which is

3/11 x 44/1 = 132/11 = 12.

As I said, correct me if I'm wrong.

Hope this Helps!

Answer:

7

Step-by-step explanation:

1 Simplify  -2-4−2−4  to  -6−6.

2-19-(-6)\times (-5-(-7))\times 22−19−(−6)×(−5−(−7))×2

2 Remove parentheses.

2-19-(-6)\times (-5+7)\times 22−19−(−6)×(−5+7)×2

3 Simplify  -5+7−5+7  to  22.

2-19-(-6)\times 2\times 22−19−(−6)×2×2

4 Simplify  (-6)\times 2\times 2(−6)×2×2  to  -24−24.

2-19-(-24)2−19−(−24)

5 Remove parentheses.

2-19+242−19+24

6 Simplify  2-192−19  to  -17−17.

-17+24−17+24

7 Simplify.

7

Answer:

P

Step-by-step explanation:

It passes through -2 on the y-axis

HOPE THIS HELPS! (:

Answer: -8x^3 - x - 7

Answer:

First open parenthesis:

x^5-9x^3+7x+x^3-x^5-7-x

-8x^3+6x-7

Answer:

A. a point that shows the y-intercept

Step-by-step explanation:

the statement (l4x-2l = -6) is false (no solution) for any value of x because the absolute value function is always positive or 0

Answer:

-180 is your answer.

Step-by-step explanation:

Answer: -180

Step-by-step explanation: I uh, used the calculator app on my phone.

a squared + b squared = c squared

576+100=c squared

676=c squared

c squared = 26

hope it helps

Answer:

Step-by-step explanation:

Answer: 24

Step-by-step explanation:

Take the factorial of that number.

4! = 4*3*2*1=24

Answer: a = 17/6

Step-by-step explanation:

I will use two laws of indices to solve this question

1. x^a / x^b = x^(a-b)

2. x^a = x^b, => a = b

Using both laws

x³/x^1/6 = x^a

x^(3-1/6) = x^a

3 - 1/6 = a

a = 3 - 1/6

a = (18 - 1)/6 using LCM

a = 17/6

Answer:

The slope is 4

Step-by-step explanation:

Everytime x goes up by 1, y goes up by 4.

4/1=1

The slope of line is 4.

Therefore,the table represents the slop relationship between the lines....

please see the attached picture for full solution

hope it helps

Answer:

I think it is c

Step-by-step explanation:

I just worked it out but I am not sure if I am 100% right.

hope this helped at all!!!

Answer:

y = 3/2x - 1

Step-by-step explanation:

Slope intercept form = y = mx + b

m = slope of the line = -2/3

y = -2/3x + b

Plug in (-2, -2) and the perpendicular line is

y = 3/2x - 1

You are welcome and don't for get to click THANKS

Answer: #1 his school is out

Step-by-step explanation: #2 bcuz all sides equal to 66cm.

Please mark me brainlest.✌✌

Answer:

Yes, they are equilateral because all of the sides have the same length of 5

Step-by-step explanation:

The Triangle has 3 sides and each side measures up to be 5 so its an equilateral triangle

Answer:

Jason Inherit a land with a 45% chance of having oil.

Step-by-step explanation:

 The probability of the land having oil is = P ( O) = 45 /100

The probability of the land having oil is= Q(O ) =55/100

The machine has an accuracy of 80%. This suggests that 8 out of 10 times the machine will give a wrong reading.

The probability of the correct reading is=  P(M)=80/100

The probability of the incorrect reading is=Q(M)=20/100

The case when the machine predicts there is no oil and there is indeed oil can be calculated:Probability=Probability of oil present  ×  probability of the incorrect reading

Probability=P(O) x Q(M)

Probability=45/100 x 20/100

Probability=9/100

The probability of the test predicting no oil in land and the land has oil is  0.09 or 9%

Answer:

The center is (-1,0) and the radius is 10

Step-by-step explanation:

We can write the equation of a circle as

(x-h)^2 + (y-k)^2 = r^2

where the center is (h,k) and the radius is r

(x+1)^2+y^2=100

(x - -1)^2+(y-0)^2=10^2

The center is (-1,0) and the radius is 10

Answer:

radius = 10

center = (- 1, 0)

Step-by-step explanation:

eqn. of the circle = (x - h)^2 + (y - k)^2 = r^2

= (x + 1)^2 + y^2 = 100

(x - (-1))^2 + (y - 0)^2 =10^2

The center is (- 1, 0) and the radius is 10

Hope this helps!

Answer:

Approximately 3.8 seconds

Step-by-step explanation:

H(x)=-16x^2+60x+4

We want to find when the ball hits the ground, or where the zeros are

0 =-16x^2+60x+4

Using the quadratic formula

-b ±sqrt(b^2 -4ac)

---------------------------

   2a

-60 ±sqrt(60^2 -4*-16*4)

---------------------------

   2(-16)

-60 ±sqrt(3600+256)

---------------------------

   -32

-60 ±sqrt(3856)

---------------------------

-32

We want the positive value for time

-60-62.09669879

---------------------------    

  -32

3.815521837

Approximately 3.8 seconds

Answer:

4

Step-by-step explanation:

4 times 4 = 16

Answer:

sqrt(16) = +4 and -4

Step-by-step explanation:

A square root has a positive and a negative square root

sqrt(16) = +4 and -4

Answer:

50 feet

Step-by-step explanation:

[tex]\mid -20 \mid +\mid 30\mid = \\\\20+30= \\\\50[/tex]

Hope this helps!

Answer:

50 feet

Step-by-step explanation:

hope this helps

Answer:

x=7

Step-by-step explanation:

CE = 36

CE = 9+(3x+6) = 9+6+3x = 15+3x

36= 15+3x

36-15 = 15-15+3x (removing 15 from left side also means removing 15 from right side)

21 = 3x

x= 21/3 = 7

Answer:

x=7

Step-by-step explanation:

First, I wrote down the equation.

3x+6=36-9

Then, I simplified it.

3x+6=27

Then, I moved the six from the right to the left.

3x=21

After that, I divided both sides by 3.

x=7

Yay! You got your answer!