Use the GCF and the Distributive property to find the sum of 66+78

-10 sin(x) = -4 csc(x) + 3

Recall that csc(x) = 1/sin(x) :

-10 sin(x) = -4/sin(x) + 3

Multiply both sides by sin(x) :

-10 sin²(x) = -4 + 3 sin(x)

Move everything to one side:

10 sin²(x) + 3 sin(x) - 4 = 0

Factorize the left side:

(2 sin(x) - 1) (5 sin(x) + 4) = 0

Then we have two cases,

2 sin(x) - 1 = 0   or   5 sin(x) + 4 = 0

Solve for sin(x) :

sin(x) = 1/2   or   sin(x) = -4/5

Solve for x :

• if sin(x) = 1/2, then

x = arcsin(1/2) + 2nπ   or   x = π - arcsin(1/2) + 2nπ

x = π/6 + 2nπ   or   x = 5π/6 + 2nπ

• if sin(x) = -4/5, then

x = arcsin(-4/5) + 2nπ   or   x = π - arcsin(-4/5) + 2nπ

x = -arcsin(4/5) + 2nπ   or   x = π + arcsin(4/5) + 2nπ

(where n is any integer)

Answer:

Plan One: y=4x+40

Plan Two: y=12x

Step-by-step explanation:

Answer:

C(t)=0.10t + 25

Step-by-step explanation:

gradient = change in y/ change in x = 5/50 = 0.10

the y intercept is 25

so the equation is y = 0.1t + 25

Answer:

40cm

Step-by-step explanation:

volume of a cylinder= πr²h

V=24litres, Area=πr²=600cm², height=?

converting litres to cm³

1litre=1000cm³

24litres= 24×1000

=24000cm³

24000=600× h

h= 24000/600

= 40cm

Answer:

it should be 21 if I did this right.

Step-by-step explanation:

you multiply the width times the length (6 × 7) =42 then 882 divided by 42 to get 21

Answer:

This answer would be c

Step-by-step explanation:

Answer:

Step-by-step explanation:

it is two left night

Answer:

$8x + $12y = $120

Step-by-step explanation:

x = amount of juice

y = amount of pizza

$120 = his total money

Answer:

x = 65

Step-by-step explanation:

2x + 2(2x-15) = 360

2x + 4x - 30 = 360

6x = 390

x = 65

Answer:

18394

Step-by-step explanation:

9197 × 2 = 18394 You double 91972

to work out the profit in December

Answer:

31%

Step-by-step explanation:

hope this helps

Answer:

i think the answer to this question is positive correlation

Step-by-step explanation:

this image below may help u

Answer:

The answer is A.

Step-by-step explanation:

It is A because both sides match up except for the last pair, where they are the same. Hope this helped!

Answer:

i think factor the expression (r+7)(r+14) is answer

Step-by-step explanation:

Answer:

(r + 14)

Step-by-step explanation:

When factoring a trinomial in the form of:

[tex]ax^2+bx+c[/tex]

you need to find 2 numbers that multiply to make ac and add to make b. Here, we need to find 2 numbers that multiply to 98 and add to 21. First, list the factors of 98:

1, 98

2, 49

7, 14

and the reverse of all of those is also true.

Now find factors that add to 21. In this case, those are 7 and 14. You need to break the middle term in the trinomial into those 2 numbers:

[tex]r^2+21r+98\\r^2+7r+14r+98[/tex]

Finally, you can factor each half of this individually.

[tex](r^2+7r)+(14r+98)\\r(r+7)+14(r+7)\\(r+14)(r+7)[/tex]

We were already given (r + 7), so the answer is (r + 14).

Answer:

The answer is below.

Step-by-step explanation:

4x<-6-6

4x<-12

x= -3

Inequality form:

x< -3

Interval Notion:

(-8,-3)

Note: Turn the -8 on the sideways on the right, because its not 8.

Answer: x < -3

Step-by-step explanation: 4x+6=-6

                                                   -6  -6

                                                     4x/4      -12/4

                                                            x<-3

Answer:

Not including circles in total shapes: 1 circle to every 4 squares or 1:4

Including circles in total shapes: 1 circle to every 5 shapes or 1:5

Step-by-step explanation:

16 ÷ 4 = 4

20 ÷ 4 = 5

Answer: 1:5

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

4 is of course not equal to 5 so no values of x make the equation true.

There are no solutions to this equation.

Answer:

5 feet + 12 inches = 2 yards

48 inches = 1 foot + 1 yard

5 feet = 3 feet + 24 inches

Step-by-step explanation:

To help solve these equations, you must know how to convert feet to inches, inches to yards, etc. Use the information below:

1 feet = 12 inches

3 feet = 1 yard

To solve 5 feet + 12 inches = blank yard(s), convert 5 feet & 12 inches to yards. Since 5 feet would be complicated to convert, let's convert 12 inches to feet first.

12 inches = 1 feet

Instead of 12 inches, we can substitute it as 5 feet + 1 feet = blank yard(s). That would be 6 feet = ? yards. 3 feet = 1 yard, which tells us we must divide both sides by 3. Thus, 5 feet + 12 inches = 2 yards.

Blank inches = 1 foot + 1 yard

To find the # of inches in a yard, you must first know that 3 feet = 1 yard. If there are 12 inches in a foot, we must multiply 3 by 12, getting us 36. You add 12 inches (1 foot), getting us 48 inches in total. Thus 48 inches = 1 foot + 1 yard.

Blank feet = 3 feet + 24 inches

Since 3 feet is already feet, we do not need to convert it. If 12 inches is 1 foot, we must divide 24 inches by 12. So, there is 2 feet in 24 inches. 2 + 3 is 5. Thus, 5 feet = 3 feet +24 inches.

Answer: 0.1(1000 + 300m)

Use the distributive property: a x (b + c) = a x b + a x c

0.1 x 1000 + 0.1 x 300m

Evaluate both products: 100 + 30m (1)

Note: Multiplying a number by 0.1 is the same as dividing the number by 10.

We need to determine the profit when 50 pieces are sold.

Substitute m with 50 in equation (1).

100+30(50)

Evaluate product: 100 + 1500

Evaluate sum" 1600

Thus the profit is $1600.

Step-by-step explanation: I hope this helps you on any other problem! :)

Good Luck!

Answer:

y = -8

Step-by-step explanation:

-7y + 11 = 75 + y

Bring the "y" variable on one side, and rest on the other.

Rearranging, we get,

-7y - y = 75 - 11

-8y = 64

-y = 8

y = -8

Hope it helps :)

Answer:

43 messages

Step-by-step explanation:

Given:

146 messages = $21.90

x messages = $6.45

Finding x by cross-multiplication:

x = 146*6.45/21.90 = 43

Hope this helps! :)

Answer:

p=1

Step-by-step explanation:

[tex]\frac{4-p}{1-0}[/tex]=3

4-p=3

p=1

Answer:

  35.4 years

Step-by-step explanation:

The annual consumption (in billions of units) is described by the exponential function ...

  f(t) = 45.5·1.026^t

The accumulated consumption is described by the integral ...

  [tex]\displaystyle\int_0^t{f(x)}\,dx=45.5\int_0^t{1.026^x}\,dx=45.5\left(\dfrac{1.026^t-1}{\ln{1.026}}\right)[/tex]

We want to find t such that the value of this integral is 2625, the estimated oil reserves.

  2625 = 45.5/ln(1.026)·(1.026^t -1)

  2625·ln(1.026)/45.5 +1 = 1.026^t ≈ 1.480832 +1 = 1.026^t

Taking natural logs, we have ...

  ln(2.480832) = t·ln(1.026)

  t ≈ ln(2.480832)/ln(1.026) ≈ 35.398

After about 35.4 years, the oil reserves will run out.

Answer:

y=2x-1

Step-by-step explanation:

Because this equation is in point-slope form and we need it in slope-intercept form, all we need to do is simplify y-5=2(x-3).

y-5=2x-6     Distribute.

 +5     +5     Add 5 to both sides of the equation.

y=2x-1

Hope this helped! Have a great day ♥

Answer:

A.

Step-by-step explanation: