Which of the following is a simpler way to write startfraction cosine theta over sine theta endfraction? tan theta sec theta csc theta cot theta

The growth of the town is an illustration of exponential growth function

The population of the town in 15 years is 125651

The given parameters are:

An exponential growth function is represented as:

y = a * (1 + r)^t

So, we have:

y =75000 * (1 + 3.5%)^15

Evaluate

y =125651

Hence, the population in 15 years is 125651

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Answer:

Domain [0,50] and Range [0,100]

Step-by-step explanation:

The domain of a graph is the values that x takes on in the graph.

We see the x values for the graph go from 0 to 50.

Since both ends of the graph are closed circles we will use brackets:

D [0,50]

The range of a graph is the values that y takes on in the graph.

We see the y values for the graph go from 100 to 0.

R [0,100]

We can also write them in interval notation:

Domain: [tex]0\leq x\leq 50[/tex]

Range: [tex]0\leq y\leq 100[/tex]

Answer:

[tex]\orange{ \rule{100pt}{999999pt}}[/tex]

Answer:

115.395 min

Step-by-step explanation:

First we find the volume of 6 cm of water. We use the formula:

[tex]\pi *radius^2 *height[/tex]

[tex]\pi *35^2*6 = 23,079 cm^3[/tex]

1 L/min = 1000 cm^3 / min

0.2 L/min = 200 cm^3 /min

[tex]\frac{23,079}{200} = 115.395 min[/tex]

5 1/3 - 2/3

= (5 – 0) + (1/3-2/3)

= 5 + 1-2/3

= 5 +-1/3

 = 4 2/3

in fraction:

= 4 2/3

in decimal:

= 4.6666666666667

[tex]\\ \rm\Rrightarrow -42z^2=14z[/tex]

[tex]\\ \rm\Rrightarrow 42z^2=-14z[/tex]

[tex]\\ \rm\Rrightarrow 3z^2=-z[/tex]

[tex]\\ \rm\Rrightarrow 3z=-1[/tex]

[tex]\\ \rm\Rrightarrow z=-1/3[/tex]

Answer:

[tex] - \frac{844}{29} z[/tex]

Step-by-step explanation:

I hope to help

Step-by-step explanation:

radius = 14cm

area of circle = [tex]\pi[/tex]r^2

                      = 22/7 *(14)^2

                      = 616 cm^2

Answer:

196π cm² or 615.44 cm²

Step-by-step explanation:

Substitute:

A = πr²

A = 3.14*14²

A = 3.14*196

A = 615.44 cm²

Therefore, the area of the cake is 196π cm² or 615.44 cm²

Hope this helps!

Answer:

the area would be 11/6 yards^2

or 1 5/6 yards^2 or 1.8333333...yards^2

Step-by-step explanation:

turn 2 3/4 into 11/4 and multiply with 2/3 to get 22/12 divide by 2 to get 11/6 then simplify

Step-by-step explanation:

Turn 2 3/4 into an improper fraction

11/4

Multiply both fractions

2/3 × 11/4 = 22/12

Simplified is 11/6 (you divide 22/12 by 2)

Answer:

8 cm

Step-by-step explanation:

Squares have equal side lengths so if we call each side x, then x × x gives us the area (32 cm²). This means that x² = 32 and therefore, one side is √32 cm.

Next, to work out the diagonal we can use Pythagoras' theory, since we can form a right-angled triangle. a² + b² = c² (c is the diagonal or the hypotenuse)

(√32)² + (√32)² = c²

(note: the square and the square root cancel out)

32 + 32 = 64

c² = 64 ∴ c = √64 which is 8

Hope this helps!

Answer:

The length of the diagonal is 8 cm.

Step-by-step explanation:

The side length of the square is √32 cms.

The diagonal divide the square into 2 congruent right triangles.

We use Pythagoras Theorem here:

d^2 = (√32)^2 +  (√32)^2

d^2 = 32 + 32 = 64

d = √64 = 8.

Answer:

Each one of the little squares is called a unit. they count in a line how many units are on the base. they did the same upward for the height

Step-by-step explanation:

Answer:

ik my head be harding so much

Step-by-step explanation:

like take it out

(.25x)+5 ≤10 or .25x ≤5 i believe both should work.

20 is how many toppings....

you need four quarters to make a dollar and honestly i just counted with my fingers even though i could have just multiplied 5 x 4

sorry for missing the inequality part at first.........

#1

#2

Convert to Vertex form of parabola y=a(x-h)²+k

We need calculator now

On comparing

As a is negative so parabola is opening downwards hence vertex is maximum

#3

When h(t) is 0 ball hits the ground

On solving we get t=-1/16 or 4

Take it positive

At 4s it reach the ground

#4

Domain is set of all t values (Time axis)

Here

ball starts from 0s and hits 0 again at 4s

So domain=[0,4]

Answer:

(a)  66 ft

(b)  66.015625 feet

(c)  4 s

(d)  0 ≤ t ≤ 4

Step-by-step explanation:

[tex]h(t)=-16t^2+63t+4[/tex]

Part (a)

[tex]t=2 \implies h(2)=-16(2)^2+63(2)+4=66[/tex]

Therefore, the height of the ball after 2 seconds is 66 feet

Part (b)

The maximum height will be the turning point of the parabola.

To find the turning point, differentiate the function:

[tex]\implies h'(t)=-32t+63[/tex]

Set it to zero:

[tex]\implies h'(t)=0[/tex]

[tex]\implies-32t+63=0[/tex]

Solve for t:

[tex]\implies 32t=63[/tex]

[tex]\implies t=\dfrac{63}{32}=1.96875[/tex]

Input found value of t into the function and solve for h:

[tex]\implies h(1.96875)=-16(1.96875)^2+63(1.96875)+4=66.015625[/tex]

Therefore, the maximum height of the ball is 66.015625 feet

Part (c)

The ball will hit the ground when h(t) = 0

[tex]\implies -16t^2+63t+4=0[/tex]

[tex]\implies 16t^2-63t-4=0[/tex]

[tex]\implies 16t^2+t-64t-4=0[/tex]

[tex]\implies t(16t+1)-4(16t+1)=0[/tex]

[tex]\implies (t-4)(16t+1)=0[/tex]

[tex]\implies t=4, t=-0.0625[/tex]

As time is positive, t = 4s only

Part (d)

As time is positive, and the ball hits the ground when t = 4 s, the domain should be restricted to:  0 ≤ t ≤ 4

Answer:(x+5)(x-2) I Dont know what a special product is sry

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The square root of 100 is 10, and 10 is a rational number.

Answer:

13 or 14 pictures

Step-by-step explanation:

there are 27 students who has decided to be grouped in pair. pair means 2, so mathematically

27 = 2 *x 27 can't make a pair

where x is the one student is removed

number of 26 is left

pictures x = 26 \ 2

x = 27 \ 2 OR x = 13 pictures

x = 13.5

x = 14 pictures

hope it help

There are 13 or 14 pictures can be taken.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

We have,

Total students at booth= 27 students

Number of person in a group = 2

Then, the possible number of pictures can be

x = 26/2

x= 13

Since one person is left and have a single photo which shows total 14 pictures.

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#SPJ2

Answer:

The answer is 3 and (-4).

Step-by-step explanation:

We are given an equation 2x² + 2x – 24.

Let us assume that the equation is equal to zero.

2x² + 2x – 24 = 0

Now, divide whole equation by 2 we get,

x² + x – 12 = 0

x² + 4x – 3x – 12 = 0

x(x + 4) – 3(x + 4) = 0

(x – 3) (x + 4) = 0

x = 3, -4

Thus, The actual roots of f(x) are 3 and (-4).

Answer:

-4 AND 3

Step-by-step explanation:

The answer is 410

Hope this helps!!

Answer:

30% also means 30/100 in fraction form.

(Think of the root 'per' in percent to be per a 100.)

The keyword 'of' means multiplication.

'X' will be the unknown number aka the part that says ('-what number').

And 123 will represent the result.

Set up equation;

Then solve for x;

So your answer is 410.

The amount of the tip was computed first, and it was then used to find then percentage of the tip that was given at the restaurant

Given Data

Let us find the amount of the tip

= 17.78 -14

= $3.78

Let us find the percentage tip

= 3.78/14 * 100

= 0.27 * 100

= %27

Learn more about percentages here:

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Answer:

All are complementary angles

Step-by-step explanation:

See attachment

Answer:

Below in bold.

Step-by-step explanation:

x /18 = 12/10

10x = 18*12

x = 216/ 10

= 21.6.

10/w = 18/24

10/w =  3/4

3w = 40

w = 40/3 =  13 33   to the neaest hundredth.

Answer:B.a= -2

2.2(44a+5)=1.8a-3

8.8a+11=1.8a-3

8.8a-1.8a=-3-11

7a=-14

:a=-2

Step-by-step explanation:

Answer:

  a/(a-4)

Step-by-step explanation:

Simplifying generally means expressing the rational function over a common denominator. Factoring the second term can help us see what that common denominator should be.

___

  [tex]\dfrac{3a}{a+4}-\dfrac{2a^2-16a}{a^2-16}=\dfrac{3a(a-4)}{(a-4)(a+4)}-\dfrac{2a(a-8)}{(a-4)(a+4)}\\\\=\dfrac{a(3(a-4)-2(a-8))}{(a-4)(a+4)}=\dfrac{a(3a-12-2a+16)}{(a-4)(a+4)}\\\\=\dfrac{a(a+4)}{(a-4)(a+4)}=\boxed{\dfrac{a}{a-4}}[/tex]

Answer: Rs. 3120

Step-by-step explanation:

So...

rs. 2400 is the cost as of when it was overpriced by 20%

10%=240

20%= (240+240)= 480

Rs. 2400-480= Rs. 1920 which is the original price before the 20% was added making the price 2400 INR

Now we need to find what 30% is to find out the price if 30% was added to the original cost

so...

If 10%=240

30%=(240+240+240)= Rs. 720

Rs. 2400+720= Rs. 3120

Rs. 3120 is the price the watch was sold at when 30% was added onto the original price and the owner gained 30%.

Adjacent angles in parallelograms are supplementary angles thus :

[tex]x + 130 = 180[/tex]

[tex]x = 180 - 130[/tex]

[tex]x = 50[/tex]

Answer:

The total of the discount would be 1,360.

Step-by-step explanation:

If a 6,800$ item had a 20% discount, subtract 6,800 by 20 in percentage, therefore the result would be 1,360 in discount.