Write an equation of a line in slope-intercept form for the table

The equation that is used to prove 1 + tan²(x) = sec²(x) is Cos²(x)/Cos²(x) + Sin²(x)/Cos²(x) = 1/Cos²(x)  , the correct option is (d) .

In the question ,

a trigonometric equation is given as 1 + tan²(x) = sec²(x) ,

we have to find the equation that will be used in proving .

the equation is 1 + tan²(x) = sec²(x)

rewriting the equation ,

we get ,

1+Sin²(x)/Cos²(x) = 1/Cos²(x)...because tan(x) = Sinx/Cosx and Secx = 1/cosx

taking the LCM as Cos²(x) , and solving further ,

we get ,

Cos²(x)/Cos²(x) + Sin²(x)/Cos²(x) = 1/Cos²(x)

that is option (d) .

Therefore , the equation is Cos²(x)/Cos²(x) + Sin²(x)/Cos²(x) = 1/Cos²(x) .

The given question is incomplete , the complete question is

Which equation can be used to prove 1 + tan²(x) = sec²(x) from the options given in the image below  ?

Learn more about Equation here

https://brainly.com/question/14331885

#SPJ4

Answer:

  7.6

Step-by-step explanation:

You want to know the number of 360 ft football fields tall the 2722 ft Burj Khalifa building is.

The ratio of height to football field length is ...

  (2722 ft)/(360 ft/field) ≈ 7.6 fields

The height of the building is about 7.6 football field lengths.

Answer:

5

Step-by-step explanation:

If a boy grows 5 inches, he will be one half a tall as his sister , his sister is 68 inches tall. So the height of the boy is 29 inches

In mathematics, the opposite of multiplication is the process called division. Finding the number of times one quantity is included within another is the procedure. The letters "/" or "" are typically used to denote this. For instance, 8 boys divided by 2 may be expressed as 8/2 or 82. The outcome in this situation would be 4, which is the quantity that 2 may be found in 8 times. The quotient, or outcome of the division, and the remainder, or quantity remaining after dividing, may both be found using division. Calculus, algebra, geometry, and other branches of mathematics all make use of the crucial mathematical notion of division.

How to solve?

If the boy grows 5 inches, he will be 68/2 =34 inches tall

The boy's current height is 34 - 5 = 29 inches

To learn more about division, visit:

https://brainly.com/question/2273245

#SPJ4

The​ manager's likely​ error is $20 if a store is instructed by corporate headquarters to put a markup of ​11% on all items. An item costing ​$18 is displayed by the store.  

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

It is given that:

A markup of ​11% on all items. An item costing ​$18 is displayed by the store manager at a selling price of ​$2.

The manager’s likely error was forgetting to add the $2 back to the $18.

$2= 11% of $18 = 1.98(=2)

For a markup,

= $2 + $18

= $20

Thus, the​ manager's likely​ error is $20 if a store is instructed by corporate headquarters to put a markup of ​11% on all items. An item costing ​$18 is displayed by the store.

Learn more about the percentage here:

brainly.com/question/8011401

#SPJ1

The required quadratic equation is x² - 12x + 36 Or (x - 6)².

A quadratic equation is an algebraic expression in the form of variables and constants.

A quadratic equation has two roots as its degree is two.

We know (a - b) = a² - 2ab + b².

Given, An expression 36 - 12x + __

now, here b² = 36 ⇒ b = 6,

∴ - 2ab = - 2(a)(6).

So, a = 1.

∴ The required quadratic equation is x² - 12x + 36 Or (x - 6)².

learn more about quadratic equations here :

https://brainly.com/question/17177510

#SPJ1

Answer: y= -2/3x + 0

Step-by-step explanation: y=mx+b

The Y-intercept is at (0,0), so b is 0

Slope is -2/3

So the equation is y=-2/3x + 0

The answer to this Question based on Profits is No they cant make 5000$ profit

What is profit?

Profit is simply the extra money we earn on selling good etc things and there are tonnes of different ways of making money and profit

Solution:

Here Diego high school soccer team started a fundraiser selling treats at their games

Initial money spent = 1000$

They decided to make 0.3$ revenue on both candy and soda hence total 0.6$ revenue in one pack

one pack costs for 2$ where 0.6$ is revenue and actual cost is 1.4$

Total packs to sell = 1000/1.4

= 714 packs

hence total profit = 714 * 0.6 = 428$

hence maximum revenue they can make is 428$ and it is maximum

hence they cant make 5000$ profit

To learn more about revenue:

https://brainly.com/question/8645356

#SPJ1

Answer:

x=64/39

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

Step 2: Subtract 2/13 from both sides.

Step 3: Multiply both sides by 2/(-1).

Answer:

1 25/39

Step-by-step explanation:

on my test

The class intervals appropriate to use in creating a histogram of the data are 0 – 30, 30 – 55, 55 – 80, 80 – 105, and 105 – 130. The correct option is B.

A histogram is used to represent data graphically. the histogram is made up of rectangles whose area is equal to the frequency of the data and whose width is equal to the class interval.

The width of the intervals must be equal. This means that the difference between the lower bound and the upper bound must be equal. Also, the upper bound of the preceding interval must be the same as the lower bound of the next interval.

This means that the intervals must be overlapping. Of all the options, it is 0 – 30, 30 – 55, 55 – 80, 80 – 105, and 105 – 130 that satisfy both conditions.

To learn more about histograms, please check: brainly.com/question/14473126

#SPJ1

Answer:first option

Step-by-step explanation:

Answer: About 20.82 liters.

Step-by-step explanation:

         To go from gallons to liters, we will multiply by 3.785. Since we are in half gallons, we will multiply 11 by 0.5 for 5.5 full gallons. Now, we will multiply;

        5.5 gallons * 3.785 = 20.8198 ≈ 20.82 liters

[tex]\begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} ~\hspace{4em} \begin{array}{llll} \textit{Logarithm of rationals} \\\\ \log_a\left( \frac{x}{y}\right)\implies \log_a(x)-\log_a(y) \end{array} \\\\\\ \begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \log_3(y)=11.03\hspace{5em}\log_3(z)=7.74\hspace{5em}\log_3(t)=5.44 \\\\[-0.35em] ~\dotfill[/tex]

[tex]12\log_3\left( \cfrac{z^7}{y^5 t^2} \right)\qquad \textit{let's nevermind the 12 for now} \\\\\\ \log_3\left( \cfrac{z^7}{y^5 t^2} \right)\implies \log_3(z^7)-\log_3(y^5 t^2)\implies \log_3(z^7)-[\log_3(y^5)+\log_3(t^2)] \\\\\\ \log_3(z^7)-\log_3(y^5)-\log_3(t^2)\implies 7\log_3(z)-5\log_3(y)-2\log_3(t) \\\\\\ 7(7.74)-5(11.03)-2(5.44)\implies \stackrel{\textit{let's put back the 12}}{12 ~~ [7(7.74)-5(11.03)-2(5.44)]} \\\\\\ ~\hfill \text{\LARGE -142.2}~\hfill[/tex]

Applying the definition of supplementary angles, the reasons that complete the two-column proof that proves x = 15 are:

a. Substitution property

b. Combine like terms

c. Division property of equality.

Two angles are supplementary angles if their sum is equal to 180 degrees when they are added together.

Given that m∠RST = 5x° and m∠UVW = 7x°, and both angles are supplementary angles, the two-column proof that proves x = 15 is shown below.

Statement                                  Reason                                            

m∠RST = 5x°; m∠UVW = 7x°    Given

∠RST and ∠UVW are

supplementary angles.

m∠RST + m∠UVW = 180          Definition of supplementary angles

5x + 7x = 180                             Substitution property

12x = 180                                   Combine like terms

x = 15                                         Division property of equality

Learn more about supplementary angles on:

https://brainly.com/question/12919120

#SPJ1

Answer:

Step-by-step explanation:

(-3)(k) = -15

-3k = -15

k = -15/-3

k = 5

(2x+3)(x+5) = 0

2x + 3 = 0

2x = -3

x = -3/2

x+ 5 = 0

x = -5

The simplified form of the given expression has a numerator of (x + 9)(2x + 1) and the denominator of (x + 7) and the expression does exist when (x = 9) and this can be determined by factorizing the given expression.

By identifying the biggest factors that the terms in the equation have in common, factoring is a technique used in mathematics to simplify algebraic expressions.

Given :

Expression - [tex]\frac{3x^2 - 27x}{2x^2+13x-7}[/tex] ÷ [tex]\frac{3x}{4x^2-1}[/tex]

First, factorize the expression, [tex]4x^2-1[/tex]

So, [tex]4x^2-1[/tex] = [tex](2x-1) (2x+1)[/tex]

Now, factorize the equation: [tex]2x^2+13x-7[/tex]

[tex]2x^2+13x-7[/tex] = [tex]2x^2+14x -x -7[/tex]

                     = [tex]2x(x+7) -1(x+7)[/tex]

                     = [tex](2x-1) (x+7)[/tex]

Now, factorize the equation: [tex]3x^2-27x[/tex]

So, [tex]3x^2-27x[/tex] = [tex]3x(x-9)[/tex]

Now, substitute the factorized terms in the given expression:

= [tex]\frac{3x(x-9)}{(2x-1) (x+7)}[/tex] ÷ [tex]\frac{3x}{(2x-1) (2x+1)}[/tex]

= [tex]\frac{(x+9) (2x+1)}{(x+7)}[/tex]

To know more about factorizing refer to:

brainly.com/question/25834626

#SPJ4

The complete question is as follows:

Select the correct answer from each drop down menu. The simplest form of this quotient has a numerator of... and a denominator of.... The expression does exist when x=......

Answer: To solve the equation "-5/8x + 10" for x when x equals -8, we can first substitute -8 for x in the equation:

-5/8(-8) + 10

Next, we can simplify the expression by performing the calculations within the parentheses:

-5/8(-8) + 10 = 5/8(8) + 10 = 5(8)/8 + 10 = 40/8 + 10 = 5 + 10 = 15

Therefore, the value of "-5/8x + 10" when x equals -8 is 15.

If Kareem has 3.5 cups of sugar then the amount of flour that Kareem need to make the muffins is 7 cups  .

In the question ,

it is given that ,

the ratio that Kareem uses to make the muffin is 3.5 cups of flour for every 1.75 cups of sugar .

let the number of cups of flour be "y" and

the number of cups of sugar be "x" .

So , y ∝ x ,

y = k*x , where k is the constant of proportionality .

From the given data ,

3.5 = k*1.75

k = 3.5/1.75

k = 2 .

we have to find the cups of flour that Kareem needs , if he has 3.5 cups of sugar .

the equation becomes ,

y = 2*3.5

y = 7

Therefore , Kareem needs 7 cups of flour .

The given question is incomplete , the complete question is

Kareem makes muffins using a ratio of 3. 5 cups of flour for every 1. 75  cups of sugar. If he has 3. 5 cups of sugar, how much flour does he need to make the muffins ?

Learn more about Ratio here

https://brainly.com/question/24955784

#SPJ4

The function y = (x + 2)^(1/2) + 3 belongs to the family of square root functions. A square root function is a type of function in which the independent variable (in this case, x) is under the radical sign.

In mathematics, a function is a relationship between a set of potential inputs and an equally likely set of outputs, with the condition that each input is associated to just one possible outcome. In other terms, a function is a category of mathematical action that accepts one or more parameters for input and generates a return result. Equations or graphs are frequently used to depict functions, which are useful for both modeling and solving mathematical issues.

In computer programming, a function is a block of code that completes a particular task and can be used repeatedly throughout a program. Programmers have the option of creating their own functions or using ones that are already included in the language.

To learn more about functions, visit:

https://brainly.com/question/21145944

#SPJ4

Answer:

y = 4x + 2

Step-by-step explanation:

24 coins gained after 6 weeks

24 / 6 = 4 coins a week

y = 4x + 2

Not enough information to answer

Option C is the correct answer.

Speed is the ratio of distance and time.

It shows how fast an object is moving at a given time.

We have,

A roller-coaster goes over a 12 m tall hill and then approaches a 30 m hill.

The minimum velocity the roller-coaster would need when going over the 12 m hill to make it to the top of the 30 m hill.

To find the minimum velocity we need to know the acceleration of the roller coaster that comes down the 12 m tall hill.

The value of the acceleration is not given.

So,

We can not find the minimum velocity.

Thus,

Not enough information to answer

Option C is the correct answer.

Learn more about speed here:

https://brainly.com/question/7359669

#SPJ1

Answer:

y + 9 = 2(x + 5): slope is 2

y - 4 = -3(x - 3): slope is -3

(12/5, 29/5)

Step-by-step explanation:

y + 9 = 2(x + 5)

y + 9 - 9 = 2(x + 5) - 9   ==> subtract both sides by 9 to isolate y

y = 2(x + 5) - 9 ==> simplify

y = 2x + 2*5 - 9  ==> distribute x and 5 by multiplying them by 2

y = 2x + 10 - 9

y = 2x + 1  ==> slope is 2

y - 4 = -3(x - 3)

y - 4 + 4 = -3(x - 3) + 4  ==> add both sides by 4 to isolate y

y = -3(x - 3) + 4

y = -3x - 3(-3) + 4  ==> multiply x and -3 by -3 by distributive property

y = -3x - (-9) + 4

y = -3x + 9 + 4  ==> simplify

y = -3x + 13  ==> slope is -3

Since y = -3x + 13 and y = 2x + 1:

2x + 1 = -3x + 13  ==> solve for x

2x + 3x + 1 = -3x + 3x + 13

5x + 1 = 13

5x + 1 - 1 = 13 - 1

5x = 12

x = 12/5

y = 2x + 1

y = 2(12/5) + 1  ==> plug in 12/5 for x

y = 24/5 + 1  ==> solve for y

y = 24/5 + 5/5

y = (24+5)/5  ==> y = 29/5   ==> (x, y) = (12/5, 29/5)

Khadija has 8 nickels and 2 quarters

From the question, we have the following parameters that can be used in our computation:

Worth of coins = $0.90

Type of coins = Dimes and quarters

Represent the nickels with n and the quarters with q

So, we have the following representation

n + q = 10

0.05n + 0.25q = 0.9

Make n the subject

n = 10 - q

So, we have

0.05(10 - q) + 0.25q = 0.9

Evaluate the products

0.5 - 0.05q + 0.25q = 0.9

This gives

0.2q = 0.4

Divide both sides by 0.2

q = 2

Recall that

n = 10 - q

So, we have

n = 10 - 2

Evaluate

n = 8

Hence, the number of nickels is 8

Read more about system of equations at

brainly.com/question/13729904

#SPJ1

Answer:

ANS:- = -25/18

Step-by-step explanation:

= (5/6)/(-3/5)

=5*5/6*(-3)

=25/-18

= -25/18

Answer: It should not be able to

Step-by-step explanation:

It should always be in the middle, aka its name, "Median"

Answer:

Step-by-step explanation:

12

x=12y

2:3

3:14

nope-60/2=30

495/9=55

Time required to spread the rumor so that half of the given heard the rumor is equal to 15 hours (approximately).

As given in the question,

Number of people among whom rumor is spread = 400

Number of people is represented by N(t)

Time is represented by 't' hours

Function representing relation between number of people who heard about the rumor and time

N(t) = 400/ ( 1+ 399 × e^(-0.4t) )

Condition : Half of the given number of people heard the rumor

N(t) = 400/2

      = 200

Substitute the value in the function we get,

200 = 400/ ( 1+ 399 × e^(-0.4t) )

⇒ ( 1+ 399 × e^(-0.4t) ) = 400 ÷ 200

⇒  1 +  399 × e^(-0.4t)  = 2

⇒  399 × e^(-0.4t)  = 2 - 1

⇒ e^(-0.4t)  = 1 ÷ 399

⇒ e^(-0.4t) = 0.002506

⇒ -0.4t = [tex]log _{e}[/tex] (0.002506)

⇒ t= 14.97 hours

⇒ t= 15 hours (round off)

Therefore, time required to spread the rumor among half of the given number of people is equal to 15hours(approximately).

The complete question is:

A rumor spreads among a group of 400 people. The number of people, N(t), who have heard the rumor by the time t in hours since the rumor started to spread can be approximated by a function of the form

N(t) = 400 / (1+399e^(-0.4t))

Approximately how long will it take until half the people have heard the rumor?

Learn more about time here

brainly.com/question/28050940

#SPJ4

The values of sin2x, cos2x and tan2x is  [tex]-\frac{3\sqrt{13}}{11}[/tex], 2/11 and  [tex]-\frac{3\sqrt{13}}{2}[/tex] respectively.

What is tan function?

The tan function, one of the primary six trigonometric functions, is typically expressed as tan x. It is the ratio of the angle's opposite and adjacent sides when a right-angled triangle is being considered.

Tangent is a verb that means "to touch" in Latin, from the root tangere. A circle is precisely the point at which a line tan to it intersects. In trigonometry, the tan function, a periodic function, is crucial. Utilizing the unit circle will make understanding the tangent function the simplest possible.

To learn more about the tan function, use the link given
https://brainly.com/question/7966290
#SPJ1

The original price of the T.V is 350 dollars

a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.

le the original price of T.V be x.

so if the t.v was sold 40% off, I means that the sale price of T.V  = 60x/100

0.6x.

if the original price is 140 more than sale price, it means sale price is 140 less = x - 140

Equating both expressions we have

x - 140 = 0.6x

x - 0.6x = 140

0.4x = 140

x = 140/0.4

x = 350 dollars

In conclusion, the original price of tv is 350 dollars

Learn more about Percentage: https://brainly.com/question/24304697

#SPJ1