please put answers for sin, cos, tan, cot, sec, and csc

Please Put Answers For Sin, Cos, Tan, Cot, Sec, And Csc

Answers

Answer 1

If we measure the angle in the clockwise direction:

Therefore, this point is:

[tex](-1,0)[/tex]

Since the cosine and sine functions are given by:

[tex]\begin{gathered} \sin (\theta)=\frac{opposite}{_{\text{ }}hypotenuse} \\ \cos (\theta)=\frac{adjacent}{_{\text{ }}hypotenuse} \end{gathered}[/tex]

Therefore:

[tex]\begin{gathered} \sin (-\pi)=\frac{0}{1}=0 \\ \cos (-\pi)=\frac{1}{-1}=-1 \end{gathered}[/tex]

Since:

[tex]\begin{gathered} \cot (\theta)=\frac{adjacent}{_{\text{ }}opposite}\to\cot (-\pi)=-\frac{1}{0}=_{\text{ }}undefined \\ \csc (\theta)=\frac{hypotenuse}{_{\text{ }}opposite}\to\csc (-\pi)=\frac{1}{0}=_{\text{ }}undefined \end{gathered}[/tex]

Therefore, we can conclude that cotangent and cosecant are undefined for - π

[tex]\begin{gathered} \tan (\theta)=\frac{opposite}{_{\text{ }}adjacent}=\frac{0}{-1}=0 \\ \sec (\theta)=\frac{hypotenuse}{_{\text{ }}adjacent}=\frac{1}{-1}=-1 \end{gathered}[/tex]

Please Put Answers For Sin, Cos, Tan, Cot, Sec, And Csc

Related Questions

The math class is selling raffle tickets to raise money for the fall ball the raffle tickets cost them $0.08 each at the office supply store and they spent $55 making T-shirts for the club members to wear. they are selling the raffle tickets for two dollars each if X represents the number of raffle tickets they sell ,the following functions can be used to present the situation where c(x) is the clubs cost and r(x) is the amount of money they make selling the tickets

Answers

We have the next information

x is the number of raffle tickets

the Profit function is R(x) function minus C(x)

C(x)=0.08x+55

R(x)=2x

P(x)=R(x)-C(x)=2x-(0.08x+55)=2x-0.08x-55

We sum similar terms

P(x)=1.92x-55

Sam takes 4 hours to peel 32 potatoes, while Josh takes 5 hours to peel 30 potatoes. How mnay potatoes will they peel together in 12 hours

Answers

To determine the amount of potato peeled in 12 hours:

Sam takes 4 hours to peel 32 potatoes

Sam take 1 hour to peel 32 / 4 potato

[tex]\begin{gathered} 4\text{ hour }\Rightarrow\text{ 32 potato} \\ 1\text{ hour }\Rightarrow\text{ }\frac{32}{4} \\ 1\text{ hour }\Rightarrow\text{ 8 potato} \\ \end{gathered}[/tex]

Josh takes 5 hours to peel 30 potatoes

Josh takes 1 hour to peel 30 / 5 potato

[tex]\begin{gathered} 5\text{ hour }\Rightarrow\text{ 30 potato} \\ 1\text{ hour }\Rightarrow\text{ }\frac{30}{5} \\ 1\text{ hour }\Rightarrow\text{ 6 potato} \end{gathered}[/tex]

Sam peels 8 potato

They will peel hepotatoeel together in 12 hours

Answer:

168

Step-by-step explanation:

Determine the sum of the measure of the interior angle of the specified polygon (octagon)A/720B/900C/1080D/1440

Answers

Solution:

The sum of interior angles of a polygon is calculated using the formula below

[tex]=(n-2)\times180[/tex]

Since the polygon is an octagon,

[tex]n=8[/tex]

By substituting the values, we will have

[tex]\begin{gathered} (n-2)\times180 \\ (8-2)\times180 \\ =6\times180 \\ =1080^0 \end{gathered}[/tex]

Hence,

The final answer is

[tex]\Rightarrow1080^0[/tex]

OPTION C is the right answer

After filling the ketchup dispenser at the snack bar where she​ works, Kelley measures the level of ketchup during the day at different hourly intervals.

Complete parts a to c.

Question content area bottom

Part 1

a. Assuming the ketchup is used at a constant​ rate, write a linear equation that can be used to determine the level of ketchup in the dispenser after x hours. Let y represent the level of ketchup in inches.


y equals negative five eighths x plus 15

​(Type an​ equation.)

Part 2

b. How can the equation from part a be used to find the level of ketchup when the dispenser is​ full?

A.

Identify the slope of the line represented by the equation.

B.

Find the difference between the slope and the​ y-intercept of the line represented by the equation.

C.

Substitute 0 for x in the equation and solve for y.​ Equivalently, find the​ y-intercept.

D.

Substitute 0 for y in the equation and solve for x.​ Equivalently, find the​ x-intercept.

Part 3

c. If Kelley fills the ketchup dispenser just before the snack bar opens and the snack bar is open for 18​ hours, will the dispenser need to be refilled before closing​ time? Explain.

If the ketchup is used at a constant​ rate, then the equation from part a indicates the dispenser will become empty


enter your response here hours after the snack bar opens. This means that the dispenser



will become empty before closing time,

will become empty exactly at closing time,

still has ketchup in it at closing time,

and so it



will not

will

need to be refilled before closing time.

Answers

The answer is c because it’s showing in the text with a lot of information that’s related to it.

Answer:

Answers

Step-by-step explanation:

Got it from SAVVAS

Find two points on the line.4y + 2x = 7

Answers

Given the equation of a line:

4y +2x = 7

It's required to find two points on the line.

Solving for y:

[tex]y=\frac{7-2x}{4}[/tex]

We give x any value and calculate the corresponding value of y.

For example, for x = 1:

[tex]y=\frac{7-2(1)}{4}=\frac{5}{4}[/tex]

The point is (1, 5/4)

Now for x = -4:

[tex]y=\frac{7-2(-4)}{4}=\frac{15}{4}[/tex]

The point is (-4, 15/4)

What is type of angle is it vertical complementary supplementary or none of the above I will reward you greatly if you answer

Answers

In the given figure,

∠a and ∠b are complementary angles.

This is because ∠CXB + ∠a + ∠b = 180° .........(as they form linear pairs)

∠CXB = 90° ..........(given)

Hence,

∠a + ∠b = 90°

What are Complementary Angles?Two angles whose total is 90 degrees are referred to as complementary angles in geometry. To put it another way, complimentary angles are two angles whose sums equal 90 degrees. 60° and 30°, for illustration. By adding up the two angles' measurements, one can determine the complement and supplement of the two angles. Complementary angles are those where the sum of the two angles equals the measurement of a right angle. They are referred to as adjacent complementary angles if they share a vertex and an arm. It is referred to as non-adjacent complementary angles when two complementary angles are NOT contiguous.

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A professional football prospect runs a 40 yard dash in 5 seconds.What is the player's average speed over this distance?a.) 8 yards per secondb.) 0.625 yards per secondc.) 0.125 yards per secondd.) 5 yards per second

Answers

[tex]\begin{gathered} Spe\text{ ed =}\frac{dis\tan ce}{\text{time}} \\ Spe\text{ ed =}\frac{40}{5} \\ \text{Spe ed = 8 yards per second} \\ \text{The correct option is the first option} \end{gathered}[/tex]

. Find the Value of x. SHOW YOUR WORK OR NO CREDITIMI

Answers

we can use pythagoras to solve the triangle

[tex]a^2+b^2=h^2[/tex]

where a and b are sides and h the hypotenuse on this case we use half triangle to make a rigth triangle and apply pythagoras

a is 9, b is 20 and h the x

so replacing

[tex]\begin{gathered} 9^2+20^2=x^2 \\ \end{gathered}[/tex]

solve for x

[tex]x=\sqrt[]{9^2+20^2}[/tex]

and do the operatios

[tex]\begin{gathered} x=\sqrt[]{81+400} \\ x=\sqrt[]{481}\approx21.93 \end{gathered}[/tex]

the value of x is 21.93 units

The distance to the grocery store is 13.456 miles round this distance to the nearest tenth

Answers

Answer:

Your answer is 13.50

The measures of 6 interior angles of a heptagon are: 111, 110, 121, 135, 139 and 92.Find the measure of the seventh interior angle. show work please:)

Answers

The sum of the interior angles of a heptagon 900º, if you know 6 of the 7 interior angles of the heptagon, you can determine the measure of the seventh angle as follows:

[tex]\begin{gathered} 900=111+110+121+135+139+92+x \\ 900=708+x \end{gathered}[/tex]

Subtract 708 from both sides of the equal sign to reach the measure of the seventh angle:

[tex]\begin{gathered} 900-708=708-708+x \\ 192=x \end{gathered}[/tex]

The seventh interior angle has a measure of 192º

Which relation is a function? 4 15 O -6- 7 C fy 0 -H O O O -2 -4 ​

Answers

The most appropriate choice for functions will be given by -

Third option is correct

Third relation is a function.

What is a function?

A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.

There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.

Here,

For a function a point in the domain has a unique image.

Here values of x axis represents domain and values of y axis represents the range

For the first option,

x = -1 has two images, y = -1 and y = 3

so x = -1 do not have a unique image

So the first relation is not a function

For the second option,

x = 0 has two images, y = -1 and y = 2

so x = 0 do not have a unique image

So the second relation is not a function

For the third option,

Every point of the domain has a unique image

So the third relation is a function

For the fourth option,

x = -2 has two images, y = 1 and y = -2

so x = -2 do not have a unique image

So the fourth relation is not a function

so, Third option is correct

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Suppose you choose four booksto read from a summer readinglist of 12 books. How manydifferent combinations of booksare possible?Note: nCrn!r!(n-r)!

Answers

Answer

495 different combinations of books are possible.

Explanation

The different combinations of books possible can be known using the given formula

[tex]_nC_r=\frac{n!}{r!(n-r)!}[/tex]

Choosing four books to read from a list of 12 books means r = 4 and n = 12

Therefore

[tex]\begin{gathered} _nC_r=\frac{n!}{r!(n-r)!}=\frac{12!}{4!(12-4)!}=\frac{12!}{4!\times8!}=\frac{12\times11\times10\times9\times8!}{4\times3\times2\times8!}=495 \\ \\ \end{gathered}[/tex]

Hence, there are 495 different combinations of books are possible

of the arithmetic sequence -10, -25, -40, ...
Find the 81st term

Answers

The 81st term of the arithmetic sequence -10, -25, -40, ... is -1210

Here is a step-by-step explanation The common difference in this sequence,

d = a2 -a1

let a2 = -25 and a1 = -10

d= -25 - (-10)

d = -15

the common difference (d) = -15

To find the n term we use :

an= a1+ (n-1)d

Therefore,

a81 = -10 + (81-1)(-15)

= -1210

The 81stterm of the arithmetic sequence -10, -25, -40, ...    -1210

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what sentence represent the number of poins in the problem below

Answers

hello

to solve this question, we can write out two sets of equation and solve them

let the short answers be represented by x

let the multiple-choice questions be represented by y

we know that the test has 60 points

multiple-choice carries 2 points

short answers carries 5 points

[tex]2x+5y=60[/tex]

now we have a total of 15 questions which comprises of multiple-choice questions and short answers

[tex]x+y=15[/tex]

now we have two set of equations which are

[tex]\begin{gathered} 2x+5y=60\ldots\text{equ}1 \\ x+y=15\ldots\text{equ}2 \end{gathered}[/tex]

now let's solve for x and y

from equation 2, let's make x the subject of formula

[tex]\begin{gathered} x+y=15 \\ x=15-y\ldots\text{equ}3 \end{gathered}[/tex]

put equation 3 into equation 1

[tex]\begin{gathered} 2x+5y=60 \\ x=15-y \\ 2(15-y)+5y=60 \\ 30-2y+5y=60 \\ 30+3y=60 \\ \text{collect like terms} \\ 3y=60-30 \\ 3y=30 \\ \text{divide both sides by the coeffiecient of y} \\ \frac{3y}{3}=\frac{30}{3} \\ y=10 \end{gathered}[/tex]

now we know the value of y which is the number of multiple-choice question. we can use this information to find the number of short answer through either equation 1 or 2

from equation 2

[tex]\begin{gathered} x+y=15 \\ y=10 \\ x+10=15 \\ \text{collect like terms} \\ x=15-10 \\ x=5 \end{gathered}[/tex]

from the calculations above, the number of short answers is equal to 5 and multiple-choice questions is equal to 10.

The answer to this question is option C

A 17 m guy wire attached to the top of a tower (the height of the tower is not yet known) is anchored on the ground, 8 m away from the base of the tower. A second guy wire needs to be attached to the centre of the tower and then anchored to the same ground-anchor as the first wire.Draw and label a diagram.How long does the second guy wire need to be?Determine the measure of the angle formed between the two wires.

Answers

Solution

Step 1:

Draw the diagram to illustrate the information.

Step 2:

Use the Pythagoras theorem to find the height of the pole.

[tex]\begin{gathered} 17^2\text{ = h}^2\text{ + 8}^2 \\ 289\text{ = h}^2\text{ + 64} \\ h^2\text{ = 289 - 64} \\ h^2\text{ = 225} \\ h\text{ = }\sqrt{225} \\ \text{h = 15m} \end{gathered}[/tex]

Step 3

b) The height of the second guy wire = d

[tex]\begin{gathered} \text{Apply the pythagoras theorem} \\ d^2=\text{ \lparen}\frac{15}{2}\text{\rparen}^2+\text{ 8}^2 \\ d^2\text{ = 56.25 + 64} \\ d^2\text{ = 120.25} \\ \text{d = }\sqrt{120.25} \\ \text{d = 10.97m} \end{gathered}[/tex]

c)

[tex]\begin{gathered} sin(\theta\text{ + }\alpha)\text{ = }\frac{Opposite}{Hypotenuse} \\ sin(\theta\text{ + }\alpha)\text{ = }\frac{15}{17} \\ \theta\text{ + }\alpha\text{ = sin}^{-1}(\frac{15}{17}) \\ \theta\text{ + }\alpha\text{ = 61.9}^o \end{gathered}[/tex][tex]\begin{gathered} sin\alpha\text{ = }\frac{7.5}{10.97} \\ \alpha=\text{ sin}^{-1}(\frac{7.5}{10.97}) \\ \alpha\text{ = 43.1} \end{gathered}[/tex]

The angle between the two guys' wires = 61.9 - 43.1

Measure of the angle formed between the two wires = 18.8

Which set of expressions are not equivalent?(4 1\2 a + 2) + 3 and 5 + 4 a18 a + 14 and 6 a + 12 + 2 + 1 2a0.5 a + 3.5 + 4 a and 3.5 + 4.5 a3 a + 7 +2 a and 7 a + 5

Answers

Solution:

Solution:

To find which of given expressions are equivalent

For the first expressions

[tex](4\frac{1}{2}a+2)+3\text{ and 5}+4\frac{1}{2}a[/tex]

Solving the expression

[tex]\begin{gathered} 4\frac{1}{2}a+2+3=5+4\frac{1}{2}a \\ 5+4\frac{1}{2}a=5+4\frac{1}{2}a \end{gathered}[/tex]

The expressions are equivalent

For the second expression

[tex]18a+14\text{ and 6a}+12+2+12a[/tex]

Solving the expression

[tex]\begin{gathered} 18a+14=6a+12a+12+2 \\ 18a+14=18a+14 \end{gathered}[/tex]

The expressions are equivalent

For the third expression

[tex]0.5a+3.5+4a\text{ and 3.5}+4.5a[/tex]

Solving the expression

[tex]\begin{gathered} 3.5+0.5a+4a=3.5+4.5a \\ 3.5+4.5a=3.5+4.5a \end{gathered}[/tex]

The expressions are equivalent

For the fourth expression

[tex]3a+7+2a\text{ and 7a}+5[/tex]

Solving the expression

[tex]\begin{gathered} 3a+2a+7=7a+5 \\ 5a+7\ne7a+5 \end{gathered}[/tex]

The expressions are not equivalent.

Hence, the set of expressions that are not equivalent is

[tex]3a+7+2a\text{ and 7a}+5[/tex]

Mimstoon started with at most 2 boondins (y). Every day (x), he
bought at most 1/2 more of them.
Write an inequality to model this relationship.

Answers

Step-by-step explanation:

y <= x/2 + 2

the maximum is to have 2 boondins and add 1/2 boondin every day.

but every time Mimstoon did not use the max. possible, the resulting total sum of boodins stays smaller that the maximum, and is therefore a valid data point.

(6, 7) is not in the inequality relationship.

because the max. boondins after 6 days is 2 (from the beginning) and 1/2 every day = 2 + 1/2 × 6 = 2 + 3 = 5.

but the data point shows 7 as y value (which is larger than the allowed max. of 5).

therefore the inequality is false for this data point, and therefore the data point is not in the inequality relationship.

how do I solve Tan-1(0.577)?

Answers

In the given fexpressionwe have,

Tan-1(0.577)

[tex]\begin{gathered} \text{Tan}^{-1}(0.577) \\ \text{Let x = Tan}^{-1}(0.577) \\ \text{Multiply both side by Tan} \\ \text{Tan x=0.577} \\ \text{ From the trignometric table find at what degr}e\text{ the tangent will be 0.577} \\ \text{ SO, }from\text{ Trignometric table we have, Tan 29.98}=0.577 \\ So,Tan^{-1}(0.577)\text{ = 29.98} \end{gathered}[/tex]

Answer : 29.98 degress

if you can't read it, it says : Add -7d-3 and 10d-6. Show all steps

Answers

-7 d - 3 + 10d - 6

First step

Group in parenthesis and

Add both letter terms

(-7d + 10d)= -3d

Second step

Group and add numbers only

(-3 - 6) = -9

Now add both results

=-3d - 9

Answer is -3d - 9

Stores on the verbal Graduate Record Exam (GRE) have a mean of 462 and a standard deviation of 119. Scores on the quantitative GRE have a mean of 584 and a standard deviation of 151. Assuming the scores are normally distributed, what quantitative scores are required for an applicant to score at or above the 90th percentile

Answers

We need Z-score here.

The formula is:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

A normal curve (with 90th percentile), looks like the one below:

We need a standard normal table to move further.

When we go to the table, we find that the value 0.90 is not there exactly, however, the values 0.8997 and 0.9015 are there and correspond to Z values of 1.28 and 1.29, respectively

(i.e., 89.97% of the area under the standard normal curve is below 1.28).

The exact Z value holding 90% of the values below it is 1.282.

--------------- Now, we work backwords and find the value of x:

Verbal GRE:

[tex]\begin{gathered} \mu=462 \\ \sigma=119 \\ z=\frac{x-\mu}{\sigma} \\ 1.282=\frac{x-462}{119} \\ x-462=1.282(119) \\ x=614.558 \end{gathered}[/tex]

So, a 90th percentile on Verbal GRE is a score above 614.56

Quantitative GRE:

[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ 1.282=\frac{x-584}{151} \\ x=777.582 \end{gathered}[/tex]

So, a 90th percentile on Quantitative GRE is a scoer above 777.58

I need help with this problem. The table below shows that the number of miles driven by Samuel is directly proportional to the number of gallons he used. \text{Gallons Used}Gallons Used \text{Miles Driven}Miles Driven 3030 10411041 4646 1596.21596.2 4848 1665.61665.6 \text{What is the rate of gas usage, in miles per gallon?} What is the rate of gas usage, in miles per gallon?

Answers

The rate of gas usage, in miles per gallon is 34.7 miles per gallon.

What is a direct proportion?

A direct proportion is used to show the constant of proportionality.

In this case, at 30 gallons, the miles used was 1041. Therefore the rate of gas usage will be:

= Miles travelled / Number of gallons

= 1041 / 30

= 34.7 miles per gallon

This shows the rate.

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how to write the standard equation for the hyperbola that is on the graph

Answers

[tex]=\text{ }\frac{y^2}{25}-\frac{x^2}{9}[/tex]Explanation:

The standard form of the hyperbola:

[tex]\frac{(y-k)^2}{a^2}-\frac{(x-h)^2}{b^2}\text{ = }1[/tex]

The center of the hyperbola is at (h, k) = The point where the lines intersect

(h, k) = (0, 0)

For hyperbola:

c² = a² + b²

b is gotten by tracing the value of a to the intersecting line. Trace 3 down to the x axis. you get 5.

[tex]\begin{gathered} a\text{ = distance from center to vertex} \\ \text{the hyperbola coordinate = (0, a) = }(0,\text{ 3)} \\ \text{the other one = (0, -a) = (0, -3)} \\ \text{Hence, a = 3} \end{gathered}[/tex][tex]\begin{gathered} c\text{ = distance from the center to the focus point} \\ b\text{ = 5 and -b = 5} \\ c^2=3^2+5^2 \end{gathered}[/tex][tex]\begin{gathered} c^2\text{ = 9+25 = 34} \\ c\text{ = }\sqrt[]{34} \\ c\text{ = 5.83} \end{gathered}[/tex]

The equation becomes:

[tex]\begin{gathered} \frac{(y-k)^2}{5^2}-\frac{(x-h)^2}{3^2}=\text{ }\frac{(y-0)^2}{5^2}-\frac{(x-0)^2}{3^2} \\ =\text{ }\frac{y^2}{25}-\frac{x^2}{9} \end{gathered}[/tex]

the cost price of 24 articles is the selling price of 15 articles find the gain percentage

Answers


Let cost price of one article be x.
So cost price of 15 articles will be 15*x=15x.

Cost price of 24 articles=selling price of 15 articles.

So selling price of 15 articles= 24*x=24x.
Cost price of 15 articles=15x.
Gain= 24x-15x= 9x.
So gain%= gain/CP ×100.
= 9x/15x *100 .
= 3/5 ×100 .
= 3×20=60%

Answer:

Step-By step explanation:

Helena is watching a movie on television she notices that there are 9 1/4 min of commercial for every 1/2 hour of the movie

Answers

If Helena watches a movie that shows a commercial for 9 1/4 mins of every 30 minutes (half hour), then the unit rate of commercials per hour is derived as;

[tex]\begin{gathered} \text{Com /30 mins=9}\frac{1}{4} \\ \text{Com /60 mins=9}\frac{1}{4}\times2 \\ \text{Com /hour=}\frac{37}{4}\times2 \\ \text{Com /hour=}\frac{37}{2} \\ Com\text{ /hour=18}\frac{1}{2} \end{gathered}[/tex]

The unit rate of commercials per hour is 18 1/2 minutes (eighteen and half minutes)

Solve the quadratic equation by completing the square.x^2-14x+46=0First choose the appropriate form and fill in the blanks with the correct numbers. Then solve the equation. If there’s more than one solution, separate them with commas.

Answers

x² - 14x + 46 = 0

subtract 46 from both-side

x² - 14x = -46

Add the square of the half of the co-efficient of x

x² - 14x + (-7)² = -46 + 7²

(x-7)² = -46 + 49

(x-7)² =3

Take the square root of both-side

x-7 = ±√3

x-7= ±1.732

Add 7 to both-side of the equation.

x= 7 ± 1.732

Eithe x= 7 + 1.732 or x= 7 - 1.732

x=8.732 or x=5.268

Therefore x = 8.732 , 5.268

the statement below always sometimes or never true give at least two examples to support your reasoning the LMC of two numbers is the product of the two numbers discuss with a partner

Answers

[tex]\begin{gathered} \text{LMC for 4 and 6} \\ Multiples\text{ of 4 = 4, 8, 12, 16, 20, 24}\ldots \\ Multiples\text{ of 6 = 6, 12, 18, 24, 30, 36}\ldots \\ \text{LMC for 4 and 6 is 12} \\ but\text{ 12 is 3x4 or 6x2 or 12x1, so the LMC of two numbers is the product of thw two nombers.} \end{gathered}[/tex]

The Jacksons bought a $276,000 condominium. They made a down payment of S43,000 and took out a mortgage for the rest. Over the course of 30 years theymade monthly payments of $1396.96 on their mortgage until it was paid off.Х$?(a) What was the total amount they ended up paying for the condominium(including the down payment and monthly payments)?si(b) How much interest did they pay on the mortgage?si

Answers

(a) What was the total amount they ended up paying for the condominium

(including the down payment and monthly payments)?

We need to calculate the total monthly payments, plus the down payment.

[tex]=1396.96\cdot30\cdot12+43000=545905.60[/tex]

So, the total amount they ended up paying was $545,905.60

(b) How much interest did they pay on the mortgage?

The interest they pay is: $269,905.60

[tex]=545905.60-276000.00=269905.60[/tex]

A student has 30 dimes and nickels. Their total value is $2.70. If d = number of dimes and n = number of nickels, this system of equations represents the situation:
d + n = 30
0.10d + 0.05n = 2.70
How many of each type of coin are there? Solve the system to answer the question.

A.
24 dimes and 6 nickels

B.
20 dimes and 10 nickels

C.
10 dimes and 20 nickels

D.
6 dimes and 24 nickels

Answers

Taking into account the definition of a system of linear equations, a student has 24 dimes and 6 nickels.

System of linear equations

A system of equations is a set of equations in which there are two or more variables, the goal of which is to find all ordered pairs (x, y) that satisfy the equation, where x and y are real numbers.

In other words, a system of linear equations is a set of two or more first degree equations that relate two or more unknowns, in which it is desired to find the value of each unknown so that all the equations of the system are satisfied.

This case

In this case, a system of linear equations must be proposed taking into account that:

d = number of dimes.n = number of nickels.

You know that:

A student has 30 dimes and nickels. The total value is $2.70.

The system of equations to be solved is

d + n = 30

0.10d + 0.05n = 2.70

It is decided to solve it using the substitution method. This method consists of isolate one of the variables in one of the equations of the system and substituting its value in the other equation.

In this case, isolating the variable "d" from the first equation:

d= 30 -n

Replacing the expression in the second equation:

0.10×(30 - n) + 0.05n = 2.70

Solving:

0.10×30 - 0.10n + 0.05n = 2.70

3- 0.10n + 0.05n = 2.70

- 0.10n + 0.05n = 2.70 -3

-0.05n= -0.3

n= (-0.3)÷ (-0.05)

n= 6

Remembering that d=30 -n you get:

d= 30 - 6

d= 24

There are 24 dimes and 6 nickels.

Learn more about system of equations:

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Susan works as a Hostess where she makes $8.75 per hour she also babysitting earns $10 per hour last week she made $165 if she works 6 hours more as a Hostess than she did babysitting how many hours did she babysit last week?

Answers

6 hours as babysitter last week

1) Gathering the data

Hostess

8.75h

Babysitting

10h

2) Based on that, we can write out the following equation, considering that Susan worked 6 hours more:

8.75(h+6) +10h= 165 Distribute the factor 8.75

8.75h +52.5 +10h = 165 Combine like terms

18.75h = 165 -52.5 Subtract from both sides 52.5

18.75h = 112.5 Divide both sides by 18.75

h =6

3) Hence, we can conclude that Susan worked as a hostess for 12 hours and as a baby sitter 6 hours last week

Show where the expression in number 8 would be on a unit circle

Answers

Solution

Step 1:

Write the expression

[tex]cos270\text{ }[/tex]

Step 2

[tex]\begin{gathered} cos270\text{ = 0} \\ sin270\text{ = -1} \\ (0,\text{ -1\rparen} \end{gathered}[/tex]

Question 8 Second part

[tex]\begin{gathered} sin(\frac{16\pi}{3})\text{ = sin960 = sin\lparen960 - 2}\times360)\text{ = sin240} \\ sin(\frac{16\pi}{3})\text{ = }\frac{-\sqrt{3}}{2} \\ cos(\frac{16\pi}{3})\text{ = }\frac{-1}{2} \end{gathered}[/tex][tex](\frac{-1}{2},\text{ }\frac{-\sqrt{3}}{2})[/tex]

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