a big storage tank contains 1680 gallons of gasoline. 25 cars filled their tanks with 24 gallons of gas each. 35 trucks put 30 gallons of gas in each of their tanks. how many gallons of gas are left in the big storage tank?

We have proved the given trigonometric equations by using trigonometric identities.

What are the trigonometric identities?

Pythagorean identities, reciprocal identities, sum and difference identities, and double-angle and half-angle identities are the most important trigonometric identities. We'll need to apply the sine and cosine rules to non-right-angled triangles.

For the first equation:

The given equation is

              [tex]sec(x)[sec(x)-cos(x)]+\frac{sin(x) + cos(x)}{sin(x)}-cotx=sec^2(x)[/tex]

Now simplifying the given equation, we can write

[tex]LHA= sec(x)[sec(x)-cos(x)]+\frac{sin(x) + cos(x)}{sin(x)}-cotx\\\\LHS=sec^2(x)-sec(x)cos(x)+\frac{sin(x)}{sin(x)}+\frac{cos(x)}{sin(x)}-cot(x)\\\\LHS=sec^2(x)-1+1+cot(x)-cot(x)\\\\LHS=sec^2(x)[/tex]

LHS = RHS.

Hence proved.

For the second equation:

     cos(π - Θ) + sin(π/2 + Θ) = 0

LHS = cos(π - Θ) + sin(π/2 + Θ)

      = -cosΘ + cosΘ

      = 0

LHS = RHS

Hence, we have proved the given trigonometric equations by using trigonometric identities.

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1. It is an experiment and the kind of study is the case - control study.

2. We can't conclude that shorter men are at higher risk of dying from a heart attack ad D. No, since there may be lurking variables, such as patient age or weight.

It should be noted that a case control study is an observational study where there are two groups that are compared based on certain attribute.

It should also be noted that it's an experiment as a research was made to get some needed information about heart attack.

Lastly, we can't conclude that shorter men are at higher risk of dying from a heart attack as some other variables are missing from the information provided.

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The area in square feet is 180.

Given:

There is a rectangular floor is 5 yd long and 4 yd wide.

Required:

Jessica wants to tile the floor with tile sold by the square foot

Now, According to the question:

First of all we need to convert the given data in foot from yd.

We know that:

1 yd = 3feet

4 yd = 12 feet

5 yd = 15 feet

Now find the area of rectangular floor

Length of the floor = 5 yd = 15 feet

Breadth of the floor = 4 yd = 12 feet

Area = l x b

Area of the rectangular floor is :

15 x 12 = 180 feet sq.

Hence, The area in square feet is 180.

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The quadratic function has a maximum value of 0 at x = 3

Here, the maximum value f(x) at x = 1 is called the absolute maximum value, global maximum or greatest value of the function f on the closed interval [0, 1]. Similarly, the minimum value of f(x) at x = 0 is called the absolute minimum value, global minimum or least value of the function f on the closed interval [0, 1].

In the function given f(x) = -3x² + 18x + 3

dy/dx = -6x + 18

For stationary values

0 = -6x + 18

6x = 18

x = 3

d²y/dx² = -6

for maximum or minimum value

d²y/dx² = -6x + 18

-6(3) + 18 = 0

The function has a maximum value of 0 at x = 3

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Step-by-step explanation:

let the first number be x &

the second number be y

x+2y=10×2

2x+y=26×1

2x+4y=20

2x+y=26

subtract

3y=6

divide both sides by 3

3y/3 = 6/3

y=2

put y=2 in x+2y=10

x+2(2)=10

x+4=10

x=10-4

x=6

the smallest number is 2

Answer:

0.3115264797507,0.1610305958132,0.7,1.4

Using metric units, the cost of rice in London is ₤0.85 per pound

To solve this problem, we need to convert the price per kilogram to price per pound.

We can use the conversion factor of

1 pound = 0.454kg

And

$1 = ₤1.18

Let's proceed to convert from kilogram to pounds since the currency is already in the desired unit.

1lb = 0.454kg

x = 1kg

x = 1 / 0.454

x = 2.2lb

This implies that

₤1.88 = 2.2lb

x = 1lb

x = (1.88 * 1) / 2.2

x = 0.85

This becomes ₤0.85 per pound

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The gas bill exceeded $87 from last month to this month.

We know simple interest (SI) is given by SI = (p×r×t)/100, where

p = principle, r = rate in percentage, and t = time in years.

Given, The Haddad expected the automatic withdrawal of their gas bill to

be more than last month's bill of $215.85 but did not know by how much.

Their account showed a previous balance of $417.80, $350.00 in deposited checks, and an automatic deposit of $150.00.

∴ Their current balance is (417.80 + 250 + 150) = $817.8 and $5.25 in interest which is (105/100)×$817.7 = $858.69.

Haddads' present balance is $555.82,

∴ The gas bill is $(858.69 - 555.82) = $302.87.

So the gas bill s exceeded by $(302.87 - 215.85) = $87.

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Answer:

Oh this is easy

Dela made 21

all of them is 12 ounce

so to know each of them

21/12

So the answer is 1.75ounce of peanut butter per sandwich

Step-by-step explanation:

I think i got it right

The constant of proportionality that relates the quantities x and y is 2.25.

An equation that relates the quantities is, y = 2.25x.

What is constant of proportionality?

The ratio connecting two given numbers in what is known as a proportional relationship is the constant of proportionality. Constant ratio, constant rate, unit rate, constant of variation, and even rate of change are other names for the constant of proportionality.

1) From the given table,

   4.5 / 2 = 2.25

   11.25 / 5 = 2.25

   15.75 / 7 = 2.25

2) The constant of proportionality that relates the quantities x and y is,

y / x = 2.25

3)  An equation that relates the quantities is,

y = kx,

where, k is constant of proportionality.

Here, k = 2.25

Therefore,

y = 2.25x

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Answer:

2x + 5y = -10

Step-by-step explanation:

Y = -2/5x - 2

5Y = 5(-2/5x - 2)

5Y = -2x - 10

2x + 5Y = -10

The given function is linear and constant because your equation is represented by the standard form for the linear equation.

A linear function can be represented by an equation. The standard form for the linear equation is: y= mx+b , for example, y=6x+4. Where:

m= the slope.

b= the constant term that represents the y-intercept

For the given example: m=6 and b=4.

An equation is classified as nonlinear when it is not represented by the standard form for the linear equation. For example, 2x²+x+10, x², x³, x³ +2, etc.

The given equation is  4y=24. Firstly, you should rewrite it  to the standard form for the linear equation is: y= mx+b. Therefore,

4y=24

y=24/4

y=6

If the standard form for the linear equation is y= mx+b, for the given equation m=0 and b=6. Thus, the given equations is linear and constant. It can be classified for constant because for any value of x, the value of y always be equal to 6.

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Answer:

y=-3/2x +2

Step-by-step explanation:

Answer:

y = 1.50x +2

Step-by-step explanation:

First, we must find two points.

Equation of a straight line:

y = mx + b ------(i)

Step 1: Calculating Slope (m).

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{2-0.500}{1-0}[/tex]

[tex]m=\frac{1.50}{1}[/tex]

[tex]m=1.50[/tex]

Now putting value of m in equation (i)

                             y = 1.50x + b -----(ii)

Step 2: Calculating Y-intercept (b).

Lets choose the first point, (0,2) for calculating y-intercept:

2 = 1.50(0) + b

2 = 0 + b

2 = b

b = 2

Now putting value of b in equation (ii)

y = 1.50x + 2

Grape Juice (cups) 6 8 10 Rainbow Sherbet (cups) 0.75 1 1.25 represents the correct relationship.

A ratio is a comparison between two similar quantities in simplest form.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

Given, The proportional relationship for 6 cups of grape juice for every three-fourths cup of rainbow sherbet.

So, the ratio of grape to rainbow sherbet is 3/4 : 6 = 3 : 24.

Which is (24/3) = 8 times.

Now checking the options Grape Juice (cups) 6 8 10 Rainbow Sherbet (cups) 0.75 1 1.25 is the correct relationship.

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The time taken for the rocket to reach its maximum height as determined from the given information is; 2.25 seconds.

The maximum height reached by the toy rocket is; 88 feet.

It follows from the task content that the maximum height reached by the rocket is to be determined.

The given function is; h (t) = -16 t² + 72t + 7.

Since it follows from evaluation that; at maximum height, the rate of change of height to time is equal to 0.

Therefore; at maximum height;

h'(t) = 0

h'(t) = -32t + 72 = 0

-32t = -72

t = -72/-32

t = 2.25 seconds.

Therefore, the time taken for the rocket to reach its maximum height is; 2.25 seconds.

Also, the maximum height reached by the rocket is at; h (2.25);

h(2.25) = -16(2.25)² + 72 (2.25) + 7

= -81 + 162 + 7

= 88.

The maximum height reached is; 88 feet.

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Any vector can be rotated via a 60 degree angle in the clockwise direction using the linear transformation from R2 to R2, and the corresponding matrix is

[tex]\left[\begin{array}{ccc}\frac{1}{2} &\frac{\sqrt{3} }{2} \\\frac{\sqrt{3} }{2}&\frac{1}{2} \end{array}\right][/tex]

What does a matrix for an angle alpha that is counter-clockwise mean?

An angle's matrix for counter clockwise rotation is

[tex]\left[\begin{array}{ccc}cos (alpha) &-sin (alpha) \\-sin (alpha)&cos (alpha)\end{array}\right][/tex]

Alpha angle matrix for a clockwise direction

Put alpha = -alpha in the matrix shown above.

The matrix above becomes

[tex]\left[\begin{array}{ccc}cos (alpha) &sin (alpha) \\sin (alpha)&cos (alpha)\end{array}\right][/tex]

if alpha = 60 degrees

The matrix above becomes

[tex]\left[\begin{array}{ccc}\frac{1}{2} &\frac{\sqrt{3} }{2} \\\frac{\sqrt{3} }{2}&\frac{1}{2} \end{array}\right][/tex]

Consequently, the matrix for the linear transformation from R2 to R2 that rotates any vector by 60∘ degrees in the clockwise direction.

is .[tex]\left[\begin{array}{ccc}\frac{1}{2} &\frac{\sqrt{3} }{2} \\\frac{\sqrt{3} }{2}&\frac{1}{2} \end{array}\right][/tex]

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The trigonometric expression tan² x + 1 = sec² x is proved by using the fundamental trigonometric formula and the definition of tangent and secant.

In this problem we must prove the existence of a trigonometric formula by means of definitions of trigonometric functions and the fundamental trigonometric formula.

Step 1 - Introduce the fundamental trigonometric formula and the definitions of tangent and secant:

sin² x + cos² x = 1, tan x = sin x / cos x, sec x = 1 / cos x

Step 2 - Divide each side of the formula by cos² x:

sin² x / cos² x + cos² x / cos² x = 1 / cos² x

(sin x / cos x)² + 1 = (1 / cos x)²

Step 3 - Use the definition of the two trigonometric functions:

tan² x + 1 = sec² x

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Answer:

Im not sure but I think the answer is 6, but only if the total amount is for sure 17

Step-by-step explanation:

This is because we know that whatever the number is is five more than the unknown number and equals 17. This can be written as n + (5 + n) = 17, which can be simplified to x = 6.

Answer:

x=7y+x

Step-by-step explanation:

Isolate x on one side

x-7y=8

 +7y.  +7y

x=7y+8

Hopes this helps please mark brainliest

Answer:

Step-by-step explanation:

Answer:

Answer:

y - 4 = - 3(x + 1)

Step-by-step explanation:

Point- slope form

y - y₁ = m(x - x₁), where m- slope, (x₁, y₁) - the point on the line

Step-by-step explanation:

Answer: 72.5%

Step-by-step explanation: Since you want the percent of the paid amount of the received amount this will be your equation: paid/received. So if you do 412/567.89, you get ≈ .725 or 72.5%.

Answer: -13.35

Step-by-step explanation:

Trust the process

Answer:

it's answer D

Step-by-step explanation:

because it is the angle postulate theorem

Answer:

it's answer D

Step-by-step explanation:

By reviewing Damon's work, the true statement is, Damon used the subtraction property of equality.

what is true statement?

A statement is true if the assertion it makes is true, and it is false if the assertion it makes is untrue. For example, the statement "The trains are always late" is only accurate if the situation it describes—that is, if the trains are indeed always late—actually exists.

As given, Damon is saving for a vacation.

He estimates that he’ll need about $2,500 for the trip.

He created an equation last week to model his savings plan to determine how many more months of saving it will take to reach his goal.

In the equation Damon created, x represents the number of months since last week and y represents the total amount he’s saved for the vacation.

The statements are,

Step 1: y = 500 + 400x

Step 2: y - 500 = 500 + 400x - 500

Step 3: y - 500 = 400x

Step 4: y - 500/400 = 400x/400

Step 5: y - 500/400 = x

Step 6: 2500 - 500/400 = x

Step 7: 5 = x

Therefore, the true statement is Damon used the subtraction property of equality in step 3.

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Answer: There are 151200 permutations

Answer:

In the word "bookkeeping" there are approximately 151,200 permutations.

Step-by-step explanation:

Permutations:

Is a way, especially one of several possible variations, in which a set or number of things can be ordered or arranged.

May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!

6) The missing angles and lengths are; x = 14, T = 14, AB = WY = 60

7) The missing angles and lengths are; X = 7, ∠A = ∠Z =31°, T = 9, YZ = AB = 28

6) We are told that;

ΔABC ≅ ΔYWZ

That means triangle ABC is congruent to triangle YWZ

Thus;

∠C ≅ ∠Z

5x - 4 = 66

5x = 70

x = 14

Similarly, AB = WY

5T - 10 = 4T + 4

5T - 4T = 10 + 4

T = 14

AB = 5(14) - 10

AB = 60 = WY

7) We are told that;

ΔABC ≅ ΔZYW

That means triangle ABC is congruent to triangle ZYW

Thus;

∠A ≅ ∠Z

5X - 4 = 3X + 10

2X = 14

X = 7

∠A = 5(7) - 4 = 31° = ∠Z

Similarly;

2T + 10 = 4T - 8

T = 18/2

T = 9

YZ = 4(9) - 8

YZ = 28 = AB

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