cos^2a + tan^2a cos^2a

Answer:

x=120

Step-by-step explanation:

There are 84 boats in the marina using algebraic equation.

We shall represent the number of boats in the marina with the letter x so that we derive an algebraic equation to solve for x as follows:

number of white boats = 3x/4

number of blue boats = 4/7 of (x - 3x/4)

number of blue boats = 4/7 × x/4

number of blue boats = x/7

number of red boats = 9

so that;

3x/4 + x/7 + 9 = x

LCM of the denominators is 28

(21x + 4x + 252)/28 = x

25x + 252 = 28x {cross multiplication}

28x - 25x = 252 {collect like terms}

3x = 252

x = 252/3 {divide through by 3}

x = 84.

Therefore, There are 84 boats in the marina using algebraic equation.

Know more about algebra here:https://brainly.com/question/13818690

#SPJ1

By using linear inequation it can be calculated that-

One possible solution is Aiden has 8 quarters and 14 dimes

What is linear inequation?

Inequation shows the comparision between two algebraic expressions by connecting the two algebraic expressions by >, <, ≥, ≤

A one degree inequation is known as linear inequation

Aaden has z quarters and y dimes.

He has no more than 22 coins

z + y ≤ 22

z ≤ -y + 22 .... (1)

He has no less than $3.60 combined.

0.25z + 0.1y ≥ 3.60

5z  + 2y ≥ 45

5z ≥ -2y + 45

z ≥ -0.4y + 9 .... (2)

This system of linear inequation is solved graphically

From the graph it is clear that

one solution is z = 8 and y = 14

One possible solution is Aiden has 8 quarters and 14 dimes.

To learn more about linear inequation, refer to the link-

https://brainly.com/question/25799000

#SPJ1

Answer:

\( \boxed{f = -6} \)

Step-by-step explanation:

\( = > - 7f - 9 = 9 - 4f \\ \\ = > - 7f + 4f - 9 = 9 \\ \\ = > - 3f = 9 + 9 \\ \\ = > - 3f = 18 \\ \\ = > 3f = - 18 \\ \\ = > f = - \frac{18}{3} \\ \\ = > f = - 6\)

\(\huge\fcolorbox{blue}{aqua}{Answer:}\)

═════════════════════

\( \frac{5}{6}x = 35\)

\(x=35\times \left(\frac{6}{5}\right) \)

\(x=\frac{35\times 6}{5} \)

\(x=\frac{35\times 6}{5} \)

\(x=\frac{210}{5} \)

\(x=42 \)

══════════════════════

Step-by-step explanation:

#Carry on learning

9514 1404 393

Answer:

  cos(θ) = (5√74)/74

Step-by-step explanation:

The length of the hypotenuse is given by the Pythagorean theorem:

  h = √(5² +7²) = √74

The cosine of the angle is the ratio of the adjacent leg to the hypotenuse:

  cos(θ) = 5/√74 = (5√74)/74

Answer:

more than 168 tickets

Step-by-step explanation:

4 weeks = 28 days

5 x 28 = 140

1 week = 7 days

4 x 7 = 28

140 + 28 = 168

In order for hector to sell more than Danielle he has to sell a # of tickets that is greater then 168.

Answer:

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

We have intersecting secants here, use relevant theorem:

Apply it our question to obtain the following equation:

Answer:

Step-by-step explanation:

One pump will fill 200l in 20 minutes

So the rate of filling per pump will be 10l/minute (200/20)

Let the number of minutes it will take to fill the 600l be x minutes

Now, since the rate of filling per pump is 10 l/minute

Then in x minute, they would have filled 10l/minute * x = 10x liters

So it is now this 10x liters that will be equal to 600

To find x, we simply divide

10x = 600

x= 600/10

x = 6 minutes

Answer:

To find the volume of a figure, we need to know the shape of the figure. Without this information, I cannot provide an answer. Please provide more details about the shape of the figure.

Answer:

y=0.25x^2−2x

Step-by-step explanation:

You have to use the disruptive property.

Based on the given clues, we can determine the person, drink, and price paid for each individual:

Calvin: Root Beer, $4.99

Dean: Lemonade, $7.99

Kelli: Water, $6.99

Lee: Iced Tea, $5.99

From clue 1, we know that either Calvin or the person who got the Root Beer paid $4.99. Since Calvin paid more than Lee according to clue 4, Calvin cannot be the one who got the Root Beer. Therefore, Calvin paid $4.99.

From clue 2, Kelli paid $6.99.

From clue 3, the person who got the water paid $1 less than Dean. Since Dean paid the highest price, the person who got the water paid $1 less, which means Lee paid $5.99.

From clue 5, the person who got the Root Beer paid $1 less than the person who got the Iced Tea. Since Calvin got the Root Beer, Lee must have gotten the Iced Tea.

Therefore, the final assignments are:

Calvin: Root Beer, $4.99

Dean: Lemonade, $7.99

Kelli: Water, $6.99

Lee: Iced Tea, $5.99

Learn more about word problems at https://brainly.com/question/21405634

#SPJ1

Start-fraction 2 over start root 5 end root end-fraction (2/√5) after simplification is 2√5/5.

To simplify the expression 2/√5, we can rationalize the denominator by multiplying both the numerator and the denominator by the conjugate of the denominator, which is √5.

Here's how it works, multiply the numerator and denominator by √5,

(2/√5)(√5/√5) = (2√5)/(5)

Now the denominator no longer contains a square root. Therefore, the simplified expression is 2√5 / 5.

This expression represents a number that is 2 times the square root of 5, divided by 5. It is a simplified form of the original expression 2/√5, making it easier to work with in calculations or further mathematical operations.

To know more about fractions, visit,

https://brainly.com/question/78672

#SPJ4

Complete question - Simplify start-fraction 2 over start root 5 end root end-fraction 2/√5.

Answer: D

A store had 500 apples to be placed in bags with an equal number of apples in each bag. If n is the number of bags to be used, then 500n is the number of apples in each bag.

Step-by-step explanation: It´s correct, I took the test. Trust me. If I got it right, please rate a 5 star and a thanks

The expected value of the distribution is 7.

To find the expected value of a uniform distribution using Excel, you can use the formula:

E(X) = (b + a) / 2

where a and b are the lower and upper bounds of the distribution.

For this problem, a = 2 and b = 12, so we can plug these values into the formula:

E(X) = (12 + 2) / 2

E(X) = 7

Therefore, the expected value of the distribution is 7.

In Excel, you can simply enter the formula "=AVERAGE(2,12)" in a cell to calculate the expected value of the distribution.

To know more about Uniform Distribution using Excel refer here:

https://brainly.com/question/14509120

#SPJ11

Answer:

angle b = 41.4°

Step-by-step explanation:

Answer:

true

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

1) origin point is (0;0);

2) the required distance is:

\(d=\sqrt{(-3-0)^2+(4-0)^2} =5.\)

A mathematical expression known as an algebraic expression includes variables, constants, and algebraic operations (addition, subtraction, etc.). Expressions include terms. Here, y=3x.

The idea behind algebraic expressions is to represent numbers using letters or alphabets rather than giving their exact values. In algebraic basics, we learned how to express an unknown number using letters like x, y, and z. We will refer to these letters as variables from now on. An algebraic expression may have both constants and variables. Any amount that is added to a variable before it is multiplied by another is known as a coefficient.

A mathematical expression known as an algebraic expression includes variables, constants, and algebraic operations (addition, subtraction, etc.). Expressions include terms.

There are 3 main types of the algebraic expressions which include:

For the above question:

4x3=12 , 5x3=15 , 6x3=18 ,.....

To know more about algebraic expression visit: https://brainly.com/question/550129

#SPJ9

The complete question:

"Write an equation that represents the pattern in the table

x 4,5,6,7,8

y 12,15,18,21,24 y = __ x"

Answer:

yes

Step-by-step explanation:

A quadratic function has the general form

fx) = ax² + bx + c ( a ≠ 0 )

f(x) = x² - 2x + 3 ← is in this form and is a quadratic function

Cos 12° * cos 12° is approximately equal to 0.9568.

We can use the identity:

cos(2θ) = 2cos²(θ) - 1

Applying this identity, we have:

cos 12° * cos 12° = (cos 24° + 1) / 2

Cos 24° is not a well-known number, so we will use a calculator to determine a rough estimate of it:

cos 24° ≈ 0.9135

Substituting this value back into the expression:

(cos 24° + 1) / 2 ≈ (0.9135 + 1) / 2 ≈ 1.9135 / 2 ≈ 0.9568

Therefore, cos 12° * cos 12° is approximately equal to 0.9568.

Learn more about expression here : brainly.com/question/723406

#SPJ4

Answer:

If Mia has to work 10 hours total, and she works 3 days a week each for 1 hour, she needs to work for 10/3 = 3.33 weeks.

Step-by-step explanation:

If Mia has to work 10 hours total, and she works 3 days a week each for 1 hour, she needs to work for 10/3 = 3.33 weeks.

Answer:

\(\frac{x^{2} }{576y^4}\)

Step-by-step explanation:

Anything to the power of 0 becomes the number 1

\(-3x^3\\2(36x^2y^2 )\\\\-x\\2*12y^2\\\\-x^2\\24^2y^2*^2\\\\x^2\\576y^4\)

The width of each column is 2 inches.

Width is the measurement of something from side to side.

Let x = width of each column.

If a "gutter" is one eighth as wide as each column, then the width of the gutter can be expressed as

gutter = (1/8)x

If the document is 8.5 in. wide, then the sum of the widths of the left and right margins, the 3 columns and the 2 gutters in between columns is equal to 8.5 in.

left margin + right margin + 3 columns + 2 gutters = 8.5in

1 in + 1 in + 3x + 2(1/8)x = 8.5 in

3x + 2(1/8)x = 8.5 in - 1 in - 1 in

3 1/4 x = 6.5 in

x = 2 in

width of each column = 2 inches

Learn more about width here: https://brainly.com/question/11434049

#SPJ4

The tree has at least 3n-2 nodes and 2n-2 edges. It has n leaves, each with a parent node, and then one internal node for each additional edge. This means that the total number of nodes is 3n-2 and the total number of edges is 2n-2.

A tree with n leaves is composed of a number of nodes and edges. Each leaf node has one parent node and one edge connecting it to the parent node. Each internal node has at least 3 children, meaning it has 3 edges connecting it to 3 different child nodes. This means that the total number of nodes in the tree is at least 3n-2, where n is the number of leaves. Similarly, there are at least 2n-2 edges in the tree, where n is the number of leaves. This is because each leaf has 1 edge and each internal node has 3 edges. Therefore, the total number of nodes in the tree is 3n-2 and the total number of edges is 2n-2.

Learn more about number here

https://brainly.com/question/10547079

#SPJ4

Given :

The value of the surface area of the cylinder is equal to the value of the volume of the cylinder.

To Find :

The relation between height and radius.

Solution :

\(S.A=2\pi rh+2\pi r^2=2\pi r(h+r)\)

\(V=\pi r^2h\)

Now ,

\(S.A=V\\\\2\pi r(h+r)=\pi r^2h\\\\2(h+r)=rh\\\\2h+2r=rh\\\\h(2-r)=-2r\\\\h=\dfrac{2r}{r-2}\)

Hence, this is the required solution.

Answer:

Options (1), (5), and (6)

Step-by-step explanation:

See attached image

Three pairs of measurements which are possible side lengths for the triangle are,

1.  AB = 4, BC = 4√3

5 AB = 7, AC = 14.

6. AB = 11, BC = 11√3

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Now, We get;

The sides of this triangles has lengths in the ratio x : √3x : 2x

where 2x is the hypotenuse.

Now, When C = 30,  the side AB is the small leg (=x).

When B = 90, the hypotenuse is AC ( =2x).

When A =  60, the larger leg is BC (=√3x).

1.  AB = 4, BC = 4√3 :- Are possible legs.

5 AB = 7, AC = 14. :-  AB = small leg, AC = hypotenuse.

6. AB = 11, BC = 11√3:-   AB = small, BC = larger leg.

Learn more about the triangle visit;

brainly.com/question/1058720

#SPJ5