Prove: (sin α + cos β)^2 + (cos β + sin α)(cos β − sin α) = 2 cos β(sin α + cos β)

Using an exponential function, it is found that there will be 8290 landlines in 5 years.

A decaying exponential function is modeled by:

[tex]A(t) = A(0)(1 - r)^t[/tex]

In which:

In this problem, we have that the initial value and the decay rate are given as follows:

A(0) = 25300, r = 0.2.

Hence the function is given by:

[tex]A(t) = 25300(0.8)^t[/tex]

In t = 5 years, the amount of landlines will be given by:

[tex]A(5) = 25300(0.8)^5 = 8290[/tex]

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Answer:

96

Step-by-step explanation:

12 ÷ 3 = 4 (therefore he is saving $24 four times in 12 weeks)

24 × 4 = 96

Answer:

she is 66

Step-by-step explanation:

you multiply the age she as when you were born with 3 and get 66

ur wlcm :)

brainliest?

Answer:

A

Step-by-step explanation:

10-7= 7-4= 3

That's it!

Answer:weight and the Oz would be the same for both problems

Step-by-step explanation:

Answer:

Faces = 12

Step-by-step explanation:

Answer:

the answer is A

Step-by-step explanation:

Given x2-2y= stock value

and

2x+5y= purchases

stock value must stay at or more than 6000

while purchases must stay under 2000

Step-by-step explanation:

If we let the width be w, then the length is w+3.5.

This means that w(w+3.5)=11

w^2 + 3.5w - 11 = 0

2w^2 + 7w - 22 = 0 (multiply both sides by 2)

(2w+11)(w-2)=0

w = -11/2 or w = 2 (disregard w = -11/2 as distance is positive)

This means that w=2, and thus the length is 2+3.5=5.5

Answer: C and D

Step-by-step explanation:

√36 = ±6

Answer:

(-4, 2), (-1, -3), (2,0), (4,3).

Answer:

See below ~

Step-by-step explanation:

Solutions :

6. Domain of the graph

⇒ Minimum value : x = -2

⇒ Maximum value : x = 6

⇒ Domain = [-2, 6]

===============================================================

7. Range of the graph

⇒ Minimum value : y = 0

⇒ Maximum value : y = 5

⇒ Range = [0, 5]

=============================================================

8. Function increasing

⇒ It is increasing from x = -2 to x = 1

⇒ Interval is : [-2, 1]

=============================================================

9. Function decreasing

⇒ It decreases from x = 4 to x = 6

⇒ Interval is : [4, 6]

=============================================================

10. Function constant

⇒ It remains constant from x = 1 to x = 4

⇒ Interval is : [1, 4]

1) Domain of a graph lies in the x axis: -2 ≤ x ≤ 6

In Interval Notation: [-2, 6]

2) Range of a graph lies in the y axis: 0 ≤ f(x) ≤ 5

In Interval Notation: [0, 5]

3) Interval where the function is increasing: -2 ≤ x ≤ 1

Interval Notation: [-2, 1]

4) Interval where the function is increasing: 4 ≤ x ≤ 6

Interval Notation: [4, 6]

5) Interval where the function is constant: 1 ≤ x ≤ 4

Interval Notation: [1, 4]

Answer:

$2.39

Step-by-step explanation:

to find the cost of 1 pound , divide the cost of 4 pounds by 4

$9.56 ÷ 4 = $2.39

The statement that is not true is the walkways will create a 90 degree angle when they intersect.

The shape shown is a rectangle. A rectangle is a four sided quadrilateral with opposite equal sides. The walkway is along the diagonals of the rectangle.

The diagonals are of equal length. The diagonals bisect each other and form to two congruent right angle triangles.

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Answer:

[tex]\sf 2\sqrt{2}[/tex]

Step-by-step explanation:

First find h(10)

   h(x) = 2x - 8

   h(10) = 2*10 - 8

           = 20 - 8

           = 12

[tex]\sf g(x)=\sqrt{x-4}\\\\ g(h(10) = g(12) = \sqrt{12-4}\\[/tex]

                         [tex]\sf = \sqrt{8}\\\\ = \sqrt{2*2*2}\\\\ = 2\sqrt{2}[/tex]

Answer:

$239.68

Step-by-step explanation:

Given

Solving

Coordinate pairs are organized like (x,y).

To determine a coordinate pair, we can determine each coordinate individually, then put them together.

Notice how the red point sits on the very edge of the graph.

When we look at the x-axis, we can see that it occurs at the number 0 on the x-axis. In other words, the red point occurs when x=0.

When we look at the y-axis, we can see that it lines up with the number 2. In other words, the red point occurs when y=2.

Therefore, when we put the two coordinates together like (x,y), we get (0,2).

(0,2)

A. The rolls of groovy wallpaper is needed to cover the apartment bedroom. 9 rolls

B.The cost to re-wallpaper the apartment room $143.10

Based on the question, we have to assume there are no windows and no doors in that bedroom... to calculate how much less wallpaper we really need, and we cover completely from the floor to the ceiling.

A. If one rolls covers 50 sq ft, how many rolls do we need?

First, let's calculate the perimeter of that room, which is 16'x10'.

P = 16 + 10 + 16 + 10 = 52 feet of perimeter.

Now, the walls are 8 feet high... so, let's see just how big is the area to cover.

A = 52 feet * 8 feet = 416 sq feet to cover all walls.

Since we know each roll covers 50 sq ft, we will need:

416 / 50 = 8.32 rolls.

When talking about quantity you need to buy or to fill something, you always have to round up to the next unit.  Because you usually can't buy a portion of a unit and if you round it down, you'll miss material to cover your walls.

So, we will need 9 rolls.

B. Total cost, based on $15.90 per roll.

We already know we need 9 rolls... so how much will it cost us?

C = 9 * $15.90 = $143.10

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Answer:

152.5

Step-by-step explanation:

Step-by-step explanation:

f(x) = y= -x²-x+6

When y is max, f'(x) = 0

f'(x) = -2x-1

Equating to 0,

-2x-1= 0

x= -1/2

Put the value of x in f(x)

y = -(-1/2)² -(-1/2) +6

= -1/4+1/2+6

= 6+1/2

y= 13/2

Answer:

1.28

Step-by-step explanation:

4/10 + 88/100

so this is unlike denominators so

4 times 10 and 10 times 10 equal to 40/100

so 40/100 + 88/100 equal to 128/100 so we simplify 128÷2 and 100÷2 equal to 64/50 and 64÷2 and 50÷2 equals 32/25 we do long division then it is equal to 1.28

Answer: Choice C

f(x) = x+5

===========================================

Explanation:

The input x = -3 has 5 added to it to get x+5 = -3+5 = 2

The diagram shows the "-3" in the input oval pointing to "2" in the output oval.

Through similar steps, we have the input -2 map to the output 3. Also, the input 0 points to the output 5.

The input -5 should map to 0, but 0 isn't in the output list. So we ignore -5 in the input oval.

Answer:

108

Step-by-step explanation:

five times a number x decreased by 2 can be expressed as by 5x- 2

Answer:

x=6, y=5

Step-by-step explanation:

plug it in!

Answer:

Step-by-step explanation:

-5x + 5y = -5

6x - 5y = 11

x = 6

6 - y = 1

-y = -5

y = 5

(6, 5)

Answer:34a

Step-by-step explanation:

because 6a-4=2a

4a+28=32a

2a+32a=34a

Answer:

119.32

Step-by-step explanation:

Answer:

  D.  Symmetric

Step-by-step explanation:

The symmetric property of congruence says, for objects A and B, ...

  if A ≅ B, then B ≅ A.

__

The symmetric property of congruence makes your statement true:

  if ΔHXA ≅ ΔRGI, then ΔRGI ≅ ΔHXA

__

Additional comment

The other answer choices involve other properties:

  Reflexive -- an object is congruent to itself: ΔHXA ≅ ΔHXA

  Commutative -- certain operations allow the order of their operands to be reversed: A +B = B +A for addition; AB = BA (for scalar multiplication)

  Transitive -- if A ≅ B and B ≅ C, then A ≅ C.

The property which is illustrated by the given statement is Symmetric property.

Reflexive property states that for any number, c, the number is equal to itself.

Or in case of expressions, a + b = a + b.

Symmetric property states that, for any numbers m and n,

If m = n then n = m.

Transitive property states that, for any numbers m, n and o,

If m = n and n = o, then m = o.

Commutative property is for operation of numbers.

a + b = b + c

Given statement is If, ΔHXA ≅ ΔRGI, then ΔRGI ≅ ΔHXA.

This is symmetric statement.

Hence the correct option is D.

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Answer:

  a +7d = 11

Step-by-step explanation:

The sum of an arithmetic series is given by the formula ...

  Sn = (n/2)(2·a1 +d(n -1))

where n is the number of terms, a1 is the first term, and d is the common difference.

__

Here, you are given n=15, S = 165, a1=a, and asked to find a relation for 'a' and 'd'. Substituting the known values, we have ...

  165 = (15/2)(2a +d(14))

  11 = a +7d . . . . . . . . simplify and divide by 15

We have found the relation to be ...

  a +7d = 11 . . . . . as required

Answer:

x = 6

Step-by-step explanation:

As the function f(x) is an exponencial function, it will grow faster than g(x), that is a linear function.

For small values of x, we have that f(x) < g(x). For example:

f(1) = 1/2 * 2 = 1

g(1) = 5*1 + 2 = 7

f(2) = 1/2 * 4 = 2

g(2) = 5*2 + 4 = 14

So we just need to check some integer values and see when f(x) will be bigger than g(x). It will not be a big value, as the exponencial function grows very fast.

For x = 5, we have:

f(5) = 1/2 * 32 = 16

g(5) = 5*5 + 4 = 29

For x = 6, we have:

f(6) = 1/2 * 64 = 32

g(6) = 5*6 + 4 = 34

For x = 7, we have:

f(7) = 1/2 * 128 = 64

g(7) = 5*7 + 4 = 39

So the largest integer value of x for f(x) ≤ g(x) is x = 6.

Another way to solve this is by plotting both equations, and then checking where they cross, that is, where f(x) = g(x).

Answer:

  x = 6

Step-by-step explanation:

We assume your functions are ...

In general, mixed polynomial and exponential functions have no algebraic solution. That means we need to solve f(x) = g(x) using a table of values, or by graphing.

__

Attached is a graphical solution. It shows the largest value of x for which f(x) = g(x) is x=6.

Check: f(6) = 1/2(2^6) = 32 = g(6) = 5(6) +2

__

Additional comment

We can start with f(x) = g(x) and subtract g(x) from both sides of the equation. This gives ...

  f(x) -g(x) = 0

Many graphing calculators readily identify the zeros of a function or expression. We have used that fact to find the two values of x where these functions are equal: ≈0.32 and 6.

For x>6, the exponential function increases without bound, so the graphs never cross again. Likewise, for x < -0.32, the linear function decreases without bound, so the graphs never cross again.

The lower value of x where the graphs cross is an irrational number near −0.319886722135.

Answer:

y = 30 + 3.25c

(where y is the total cost in dollars, and c is the number of balloon bouquets)

Step-by-step explanation:

Let y = total cost (in dollars)

Let c = number of balloon bouquets

Given:

⇒ y = 30 + 3.25c

Y inetercept:-

Rate of change=3.25

So

Cost be Y

Answer:

x = - 43.5

Step-by-step explanation:

Step 1 : Simplify the given equation.

(8x - 20) - 16 = 10x + 51

8x - 20 - 16 = 10x + 51

8x - 36 = 10x + 51

Step 2 : Add/Subtract the alphabetical terms and numerical terms separately.

8x - 36 = 10x + 51

Step 3 : Add 36 on both sides.

8x = 10x + 51 + 36

8x = 10x + 87

Step 4 : Subtract 10x on both sides.

8x - 10x = 87

- 2x = 87

Step 5 : Divide - 2 on both sides.

x = 87/-2

x = - 87/2 (answer in terms of fraction)

x = - 43.5 (answer in terms of decimal)

Hence,

The value of x is - 43.5