1-Determine a solução dos sistemas abaixo pelo método de adição: a) {x + y = 5 {2x- y=9 b) {3x - y = 10 {x + y =18 Prfvr gente

Answers

Answer 1

a)

X + Y = 5

2X - Y = 9      

X + 2X + Y - Y = 5 + 9

3X = 14

X = 14/3

Para Y, basta substituir o valor de X em qualquer uma das 2 equacoes - arbitrariamente. Escolhendo a primeira:

X+ Y = 5

14/3 + Y = 5

Y = 5 - 14/3

Y = 1/3

.........................

b)

3X - Y = 10

X + Y = 18        

3X + X - Y + Y = 10 + 18

4X = 28

X = 7

Para Y, basta substituir o valor de X em qualquer uma das 2 equacoes - arbitrariamente. Escolhendo a segunda:

X + Y = 18

7 + Y = 18

Y = 18 - 7

Y = 11

Related Questions

Plz Help I Will Mark Brainliest If Right f(x) = x^2 + 3 A). y > -3 B). All real numbers C). y ≥ 3 D). y ≤ 3

Answers

Answer:

  C)  y ≥ 3

Step-by-step explanation:

The answer choices suggest that you're interested in the range of the function. x^2 cannot be negative, so its value will be 0 or greater. Adding 3 to x^2 ensures that the value of f(x) will be 3 or greater.

  y ≥ 3 . . . . matches C

PLEASE ANSWER QUICKLY ASAP
READ QUESTIONS CAREFULLY ​

Answers

Answer:

see details below

Step-by-step explanation:

a) week 1 :  #10" / (#10"+#12") = 509 / 736 =  69% (to nearest percent)

b) week 2 :  #10" / (#10"+#12") = 766 / 1076 = 383/538 = 71% (to nearest percent)

A).69% for week 1

B)71% for week 2

What is the difference between a matrix and a determinant?

Answers

Answer:

Step-by-step explanation:

A matrix is a set of numbers organized in rows and columns to represent the variables in a situation, and the determinant is used to find the inverse of a matrix which helps you solve for different variable values.

Answer: A matrix or matrices is a rectangular grid of numbers or symbols that is represented in a row and column format. A determinant is a component of a square matrix and it cannot be found in any other type of matrix. ... A determinant is a number that is associated with a square matrix.

Step-by-step explanation:

A line passes through the point (4,8) and has a slope of -3/2

Write an equation in Ax+By=C

Answers

Answer:

The answer is

3x + 2y = 28

Step-by-step explanation:

To find an equation of the line using a point and the slope we use the formula

y - y1 = m(x - x1)

where

m is the slope

(x1 , y1) is the point

From the question

slope = -3/2

Point = (4,8)

So the equation of the line is

[tex]y - 8 = - \frac{3}{2} (x - 4)[/tex]

Multiply through by 2

2y - 16 = -3( x - 4)

2y - 16 = - 3x + 12

3x + 2y = 16 + 12

We have the final answer as

3x + 2y = 28

Hope this helps you

What is a21 of the arithmetic sequence for which a7=−19 and a10=−28? A. -35 B. 35 C. -58 D. -61

Answers

Answer:

a21 = -61

Step-by-step explanation:

[tex]a_{n}=a_{1}+(n-1)d[/tex]

[tex]-19=a_{1}+(7-1)d[/tex]

[tex]-28=a_{1}+(10-1)d[/tex] (subtract to eliminate a₁)

9 = -3d

d = -3

-19 = a₁ + (6)(-3)

-1 = a

a21 = -1 + (21 - 1)(-3)

= -61

Answer:

-61 (Answer D)

Step-by-step explanation:

The general formula for an arithmetic sequence with common difference d and first term a(1) is

a(n) = a(1) + d(n - 1)

Therefore, a(7) = -19 = a(1) + d(7 - 1), or a(7) = a(1) + d(6) = -19

and a(10) = a(1) + d(10 - 1) = -28, or a(1) + d(10 - 1) = -28

Solving the first equation a(1) + d(6) = -19 for a(1) yields a(1) = -19 - 6d.  We substitute this result for a(1) in the second equation:

-19 - 6d + 9d = -28.  Grouping like terms together, we get:

3d = -9, and so d = -3.

Going back to an earlier result:  a(1) = -19 - 6d.

Here, a(1) = -19 - 6(-3), or a(1) = -1.

Then the formula specifically for this case is a(n) = -1 - 3(n - 1)

and so a(21) = -1 - 3(20) = -61 (Answer D)

Write and solve an equation to answer the question. How many people must attend the third show so that the average attendance per show is 3000?

Answers

Answer:

3250

Step-by-step explanation:

so for the first and 2nd show, the attendance is 2580 and 2920.

The average of both these numbers is 2750

the if the third show had 3000 people, the average attendance would only be 2875.

We need the average number to be 3000.

2750 is 250 less than 3000, so the other number must be 250 more.

3250 is how many people should go to the last show.

Answers:First box = (5500+x)/3Second box = 3500

=====================================

Explanation:

We have 2580 people attend the first show and 2920 attend the second. So far, that's 2580+2920 = 5500 people. Add on another x people to get 5500+x, which represents the sum of all three days attendance figures. Divide this sum by 3 to get the average attendance

average attendance = (sum of individual attendance values)/(number of days)

average attendance = (5500+x)/3

So that's why (5500+x)/3 goes in the first box. The parenthesis are important to ensure that you divide all of "5500+x" over 3. If you just wrote 5500+x/3, then the computer would think you just want to divide x only over 3.

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

We set (5500+x)/3 equal to 3000 as we want the average of the three days to be 3000

(5500+x)/3 = 3000

5500+x = 3*3000

5500+x = 9000

x = 9000-5500

x = 3500

We need 3500 people to show up on day 3 so that the average of all three days is 3000.

3500 goes in the second box.

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

Check:

The figures for the three days are 2580, 2920, and 3500

They add to 2580+2920+3500 = 9000

Which divides to 9000/3 = 3000, which is the average we're after. So the answer is confirmed.

kofi and kweku are two brothers. Kofi is older than kweku. Given that kofi's age is (5x-4) years and kweku's age is (2x+1) years.
a. write down an expression, interns of x,for how much old is Kofi than kweku.
b. if Kofi is tens years older than kweku, find the value of x and the ages of Kofi and kweku

Answers

Answer:

Kindly check explanation

Step-by-step explanation:

Given the details :

Kofi is older than kweku

kofi's age = (5x-4) years

kweku's age = (2x+1) years

a. write down an expression, interns of x,for how much old is Kofi than kweku

Equate the ages of Kofi and kweku

(5x - 4) = (2x + 1)

5x - 4 = 2x + 1

5x - 2x = 1 + 4

3x = 5

3x - 5

B.) if Kofi is tens years older than kweku, find the value of x and the ages of Kofi and kweku

Then,

(5x-4) = (2x + 1) + 10

5x - 4 = 2x + 1 + 10

5x - 2x = 1 + 10 + 4

3x = 15

x = 5

Kofi's age : 5x - 4

5(5) - 4 = 25 - 4 = 21 years

Kweku's age : (2x + 1)

2(5) + 1 = 10 + 1 = 11 years

Which number is in the 3rd position after ordering in
descending order. V220,-10, V100, 11.5

Answers

Answer:

√100

Step-by-step explanation:

Given the following numbers: √220, -10, √100, 11.5,

Let's arrange the numbers from the largest to the smallest (in descending order).

Note: √220 ≈ 14.8

√100 = 10

From the largest to the smallest number, we have: √220, 11.5, √100, -10

Therefore, the number in the third position is √100

Can someone pls help and explain it

Answers

Answer:

(7,-4) ; 12

Step-by-step explanation:

Basically, three corners of a rectangle are already on the graph. If you put a dot at (7,-4), that is the last corner(vertex) that finishes the rectangle

Then to find base of the rectangle, you find the length of the longer side, (the distance between the x coordinates). So you would subtract -5 from 7 and get 12, and 12 is the length of your base.

what is the value of this expression when g= -3.5?
8-|2g-5|
a. 20
b. 10
c. 6
d. -4​

Answers

Answer:

d. -4

Step-by-step explanation:

Let's plug in g

8 - |2(-3.5) - 5|

8 - |-7-5|

8 - |-12|

The absolute value is always positive of any number,

8 - 12

= -4

Answer:

D. -4

Step-by-step explanation:

We are given this expression:

[tex]8-|2g-5|[/tex]

and asked to evaluate when g= -3.5 Therefore, we must substitute -3.5 in for g.

[tex]8-|2(-3.5)-5|[/tex]

First, multiply 2 and -3.5

2 * -3.5 = -7

[tex]8-|-7-5|[/tex]

Next, subtract 5 from -7.

-7-5= -12

[tex]8-|-12|[/tex]

Next, evaluate the absolute value of -12. The absolute value is how far away a number is from 0, and it is always positive. The absolute value of -12 is 12.

[tex]8-12[/tex]

Subtract 12 from 8.

[tex]-4[/tex]

The value of the expression is -4 and D is the correct answer.

7.006 x 10^-3 in standard notation

Answers

Answer:

7.006*10⁻³ = 0.007006

Step-by-step explanation:

7.006*10⁻³ = 0.007006

Question 1 (
Multiple Choice Worth 3 points)
(07.04)
The cost of 3 slices of pizza is $4.89. What is the cost of each slice of pizza?
O $1.63
$1.89
O $2.45
O $2.88​

Answers

Answer:

Each slice of pizza cost:

$1.63

Step-by-step explanation:

4.89/3 = 1.63

Answer:

$1.63

Step-by-step explanation:

We want to find the cost per slice of pizza. Therefore, we must divide the total cost by the number of slices of pizza.

cost / slices

It costs $4.89 for 3 slices.

$4.89 / 3 slices

Divide 4.89 by 3 (4.89/3=1.63)

$1.63 / slice

The cost of each slice of pizza is $1.63

the product of 5 and z

Answers

Answer:

5z

Step-by-step explanation:

As product = multiplication =>

5 x z --> 5(z)

[tex]\text{Find the product of 5 and z}\\\\\text{The key term in this questions is product, and in math it translates to}\\\text{the answer when multiplled}\\\\\text{In this case, you would multiply them together to get your "product"}\\\\\text{Solve:}\\\\5\cdot z\\\\\boxed{5z}[/tex]

41 =12d-7 d= Math is not my strong suit. I love to read and write but I can not do math without a little bit of help.

Answers

Answer:

[tex]\huge\boxed{d = 4 }[/tex]

Step-by-step explanation:

41 = 12d - 7

Adding 7 to both sides

41+7 = 12d

48 = 12 d

Dividing both sides by 12

4 = d

OR

d = 4

Answer:

[tex]\large \boxed{{d=4}}[/tex]

Step-by-step explanation:

[tex]41 =12d-7[/tex]

Add 7 on both sides.

[tex]41 +7=12d-7+7[/tex]

[tex]48=12d[/tex]

Divide both sides by 12.

[tex]\displaystyle \frac{48}{12} =\frac{12d}{12}[/tex]

[tex]4=d[/tex]

Find b.
Round to the nearest tenth:

Answers

Answer:

always b is equal to 9 is rhdx forum post in is ek of

Answer:

6.7 cm

Step-by-step explanation:

A+B+C=180°

55°+B+82°=180°

B=43°

Using the formulae

(Sin A)/a = (Sin B)/b

(Sin 55)/8 = (Sin 43)/b

b = [8(Sin 43)]/(Sin 55)

b= 6.7 cm

This table represents a quadratic function.
y
x
0
14
1
10.5
2
8
3
6.5
4
5
6.5
What is the value of a in the function's equation?
A.2
B.1/2
C.-1/2
D.1

Answers

Answer:

B. 1/2

Step-by-step explanation:

y = ax^2 + bx + c

14 = a(0)^2 + b(0) + c

c = 14

10.5 = a(1)^2 + b(1) + 14

10.5 = a + b + 14 ____(i)

8 = a(2)^2 + b(2) + 14

8 = 4a + 2b + 14

4 = 2a + b + 7 ___ (ii)

i - ii

10.5 - 4 = -a + 7

6.5 = -a + 7

a = 7- 6.5

a = 0.5

Value of a in the quadratic function is 0.5

What is Quadratic function?

In algebra, a quadratic function, a quadratic polynomial, a polynomial of degree 2, or simply a quadratic, is a polynomial function with one or more variables in which the highest-degree term is of the second degree

Given,

Quadratic function

y = [tex]ax^{2}+bx+c[/tex]

Consider values in the table x= 0 and  y =14

[tex]14=a(0)^{2}+b(0)+c\\ c=14[/tex]

Consider x=1 and y = 10.5

[tex]10.5=a(1^{2})+b(1)+c\\ a+b=10.5-14\\a+b=-3.5[/tex]

Consider x=2 and y =8

[tex]8=a(2^{2})+b(2)+c\\ a\\8=4a+2b+14\\4a+2b=-6\\2a+b=-3[/tex]

Subtract a + b= -3.5 from 2a + b= -3

a=-3--3.5=0.5

Hence, the Value of a in the quadratic function is 0.5

Learn more about Quadratic function here

https://brainly.com/question/5975436

#SPJ2

Anyone who answers will be marked brainiest answer. If u don't understand anything just ask.

Answers

Answer:

7/2 pi

or approximately 10.99557429

Step-by-step explanation:

2 pi sqrt( a/b)

let a = 49 and b = 16

2 pi sqrt( 49/16)

We know that sqrt( a/b) = sqrt(a) /sqrt(b)

2 pi sqrt(49) / sqrt(16)

2pi ( 7) / (16)

2 pi ( 7/4)

7/2 pi

This is the exact answer

We can make an approximation for pi

Using the pi button on the calculator

10.99557429

Please answer. I need this to be done, Thanks. Will give brainliest

Answers

Answer:

The answer is s^26/pq59

Step-by-step explanation:

Answer:

p^ -1 q ^ -59  s ^26

or without negative exponents

s^ 26 /(p q^ 59)

Step-by-step explanation:

When multiplying , we can add the exponents when the bases are the same

p^0 q ^ -60 r^-1 s^25  * p^-1 qrs

When there is no exponent written, there is an implied 1

p^ (0+-1) q^(-60+1) r ^( -1 +1) s ^ ( 25+1)

p^ -1 q ^ -59 r ^0 s ^26

r^0 = 1

p^ -1 q ^ -59  s ^26

If you need  the negative exponents written as positive

a^-b = 1/ a^b

s^ 26 /(p q^ 59)

An important factor in selling a residential property is the number of people who look through the home. A sample of 17 homes recently sold in the Buffalo, New York, area revealed the mean number looking through each home was 19 and the standard deviation of the sample was 4 people.
Develop a 98 percent confidence interval for the population mean. (Round your answers to 2 decimal places.)
Confidence interval for the population mean is between and ?

Answers

Answer:

Confidence interval for the population mean is between 15 homes and 19 homes

Step-by-step explanation:

Given that:

Sample (n) = 17 homes, mean (μ) = 19 homes, standard deviation (σ)= 4 people and confidence (C) = 98% = 0.98

α = 1 - C = 1 - 0.98 = 0.02

α/2 = 0.02/2 = 0.01.

The z score of 0.01 (α/2) corresponds to the z score of 0.49 (0.5 - 0.01) which from the normal distribution table is 2.33

The margin of error (E) is:

[tex]E=z_{0.01}*\frac{\sigma}{\sqrt{n} } =2.33*\frac{4}{\sqrt{19} }=2[/tex]

The confidence interval = μ ± E = 17 ± 2 = (15, 19)

Confidence interval for the population mean is between 15 homes and 19 homes

Please answer this question now

Answers

Answer:

11 yd

Step-by-step explanation:

To find the volume of a rectangular prism, we multiply the width, length and height.

We already know the length, 18, and the height, 11, and the volume, 2178, so we can easily solve for y.

[tex]18\cdot y\cdot11=2178\\192y=2178\\y = 11[/tex]

Hope this helped!

hi there can you please help me

[tex]t = \sqrt{ \frac{ab - s}{r + ak} } [/tex]

Answers

[tex]t=\sqrt{\dfrac{ab-s}{r+ak}}\\\\t^2=\dfrac{ab-s}{r+ak}\\\\rt^2+akt^2=ab-s\\\\akt^2-ab=-rt^2-s\\\\a(kt^2-b)=-(rt^2+s)\\\\a=-\dfrac{rt^2+s}{kt^2-b}\\\\a=-\dfrac{rt^2+s}{-(b-kt^2)}\\\\a=\dfrac{rt^2+s}{b-kt^2}[/tex]

Consider the function represented by 9x + 3y = 12 with x as the independent variable. How can this function be
written using function notation?
O FID = - Šv
O f(x) = - 3x + 4
Of(x) = -x +
O fly) = -34+4​

Answers

Answer:

f(x) = - 3x + 4

Step-by-step explanation:

Note that y = f(x)

Rearrange making y the subject

9x + 3y = 12 ( subtract 9x from both sides )

3y = - 9x + 12 ( divide all terms by 3 )

y = - 3x + 4 , that is

f(x) = - 3x + 4

Ahmad has some files.
زرا
He gave
of the files and had 14 files left.
5
How many files did he have at first?​

Answers

Step-by-step explanation:

why did u add the 5 in the question?.

11,9,7,5,3,1,
B) Common Difference:
Recursive Function:
D) Explicit
Function:​

Answers

Answer:

The terms 11, 9, 7, 5, 3, 1 have a common difference of -2 therefore, the correct option defining the relationship between the terms is

B) Common difference

Step-by-step explanation:

The common difference between a series of numbers is found by subtracting a number from the next number following and a common difference exists  when the difference between successive adjacent number pairs is the same

A sequence that has a common difference is an arithmetic sequence or arithmetic projection.

The given sequence, 11, 9, 7, 5, 3, 1, is an arithmetic sequence.

the number of states that entered the union in 1889 was half the number of states "s" that entered in 1788. which expression shows the number of states that entered the union in 1889

Answers

Answer:

x = s/2

Step-by-step explanation:

● s states have joined the union in 1788

● half of s have joined in 1889

Let x be the number of states that have joined in 1889

● x = (1/2)× s

● x = s/2

Evaluate. Write in standard form.

Answers

Answer:

-i

Step-by-step explanation:

(-i)^0 = 1

(-i)^1 = -i

(-i)^2 = -1

(-i)^3 = -i

(-i)^4 = 1

(-i)^5 = -i

etc.

From this pattern, you see that when the exponent is a multiple of 4, you get 1. When the exponent is a multiple of 4 plus 1, you get -i, etc.

213 = 4 * 53 + 1

213 is 1 more than a multiple of 4.

(-i)^213 = (-i)^1 = -i

State if the triangles are similar. If so, how do you know they are similar and complete the similarity statement. Triangle LKJ≈____

Answers

Answer: C) similar, SAS similarity, triangle LQR

==============================================

Explanation:

The vertical angles KLJ and QLR are congruent. This forms the "A" in "SAS". The angles in question are between the marked sides.

KL = 18 is twice that of QL = 9, or put another way, KL/QL = 18/9 = 2. The ratio of the sides is 2. Also, JL/RL = 16/8 = 2 is the same ratio. Because both pairs of sides have the same ratio, the sides are in proportion. This helps form the two "S" letters of "SAS".

The original triangle has LKJ mentioned at the top. Note the order as its important. We start with L and move to K, so LK is the first segment mentioned. LK = 18 pairs up with LQ = 9, meaning that LQ must be the first segment mentioned of the answer triangle. Therefore LQR is the correct letter sequence if we start with point L. Writing QLR is not correct because Q is the first letter here but Q does not pair up with L.

Company a samples 16 workers, and their average time with the company is 5.2 years with a standard deviation of 1.1. Company b samples 21 workers and their average time with the company is 4.6 years with a standard deviation 4.6 years

Answers

Company a samples 16 workers, and their average time with the company is 5.2 years with a standard deviation of 1.1. Company b samples 21 workers and their average time with the company is 4.6 years with a standard deviation 4.6 years

The populations are normally distributed.  Determine the:

Hypothesis in symbolic form?

Determine the value of the test statistic?

Find the critical value or value?

determine if you should reject null hypothesis or fail to reject?

write a conclusion addressing the original claim?

Answer:

Step-by-step explanation:

GIven that :

Company A

Sample size n₁ = 16 workers

Mean [tex]\mu[/tex]₁ = 5.2

Standard deviation [tex]\sigma[/tex]₁ = 1.1

Company B

Sample size n₂ = 21 workers

Mean [tex]\mu[/tex]₂ = 4.6

Standard deviation [tex]\mu[/tex]₂ = 4.6

The null hypothesis and the alternative hypothesis can be computed as follows:

[tex]H_o : \mu _1 = \mu_2[/tex]

[tex]H_1 : \mu _1 > \mu_2[/tex]

The value of the test statistics can be determined by using the formula:

[tex]t = \dfrac{\overline {x_1}- \overline {x_2}}{\sqrt{\sigma p^2( \dfrac{1}{n_1}+\dfrac{1}{n_2})}}[/tex]

where;

[tex]\sigma p^2= \dfrac{(n_1 -1) \sigma_1^2+ (n_2-1)\sigma_2^2}{n_1+n_2-2}[/tex]

[tex]\sigma p^2= \dfrac{(16 -1) (1.1)^2+ (21-1)4.6^2}{16+21-2}[/tex]

[tex]\sigma p^2= \dfrac{(15) (1.21)+ (20)21.16}{35}[/tex]

[tex]\sigma p^2= \dfrac{18.15+ 423.2}{35}[/tex]

[tex]\sigma p^2= \dfrac{441.35}{35}[/tex]

[tex]\sigma p^2= 12.61[/tex]

Recall:

[tex]t = \dfrac{\overline {x_1}- \overline {x_2}}{\sqrt{\sigma p^2( \dfrac{1}{n_1}+\dfrac{1}{n_2})}}[/tex]

[tex]t = \dfrac{5.2- 4.6}{\sqrt{12.61( \dfrac{1}{16}+\dfrac{1}{21})}}[/tex]

[tex]t = \dfrac{0.6}{\sqrt{12.61( \dfrac{37}{336})}}[/tex]

[tex]t = \dfrac{0.6}{\sqrt{12.61(0.110119)}}[/tex]

[tex]t = \dfrac{0.6}{\sqrt{1.38860059}}[/tex]

[tex]t = \dfrac{0.6}{1.178388981}[/tex]

t = 0.50917

degree of freedom df = ( n₁ + n₂ - 2 )

degree of freedom df = (16 + 21 - 2)

degree of freedom df = 35

Using Level of  significance ∝ = 0.05, From t-calculator , given that t = 0.50917 and degree of freedom df = 35

p - value =  0.3069

The critical value [tex]t_{\alpha ,d.f}[/tex] = [tex]t_{0.05 , 35}[/tex] = 1.6895

Decision Rule: Reject the null hypothesis if the test statistics is greater than the critical value.

Conclusion: We do not reject the null hypothesis because, the test statistics is lesser than the critical value, therefore we conclude that there is  no sufficient information that the claim that company a retains it workers longer than more than company b.

Suppose the population of a country is 100 people: 40 work full-time, 20 work half-time but would prefer to work full-time, 10 are looking for a job, 10 would like to work but are so discouraged they have given up looking, 10 are not interested in working because they are full-time students, and 10 are retired. What is the number of unemployed

Answers

Answer:

10

Step-by-step explanation:

Those people who are actively seeking for a job are counted as unemployed. Underemployment is not considered as unemployment. Those who have given up looking for jobs are also not considered as unemployed as well. Hence there are 10 unemployed people.

PLZ HELP !!!!!! ASAP!!!

Answers

Part (a)

BC = opposite side (furthest leg from the reference angle)

AB = adjacent side (closest leg from the reference angle)

AC = hypotenuse (always opposite the 90 degree angle)

=============================================

Part (b)

i. False. Angle B is 90 degrees as shown by the square angle marker.

ii. False. Side AB is opposite angle C. Note how "C" is part of "BC", so that means we cannot have BC be opposite C.

iii. True. Leg AB is the closer leg to angle A. We have "A" in "AB" to see this without having to draw the diagram. Refer to part (a) above.

iv. False. The longest side of any right triangle is always the hypotenuse. The longest side of any triangle is always opposite the largest angle.

==============================================

Part (c)

cos(theta) = adjacent/hypotenuse = AB/AC

tan(theta) = opposite/adjacent = BC/AB

Refer back to part (a) to determine the opposite,adjacent and hypotenuse side lengths.

==============================================

Part (d)

The reference angle has changed, so the opposite and adjacent sides swap. The hypotenuse remains the same regardless of what reference angle you pick.

sin(C) = opposite/hypotenuse = AB/AC

cos(C) = adjacent/hypotenuse = BC/AC

tan(C) = opposite/adjacent = AB/BC

Note the tangent ratio is the reciprocal of what we found back in part (c).

Answer & Step-by-step explanation:

(a)

The hypotenuse is on line CA (the hypotenuse is always opposite the 90° angle (marked by a little square))

The adjacent is on the line BA (adjacent is next to the given angle, but NOT the hypotenuse)

The opposite is on the line CB (this is opposite the given angle)

(b)

i.   false (b is a right angle)

ii.  false (the side opposite C is BA)

iii. true

iv. false (the side opposite B is the hypotenuse, and the hypotenuse is always the longest side in a triangle)

(c)

cosine ratio: [tex]cos=\frac{adjacent}{hypotenuse}[/tex]

tangent ratio: [tex]tan=\frac{opposite}{adjacent}[/tex]

The cosine and tangent ratios of the given angle:

[tex]cos0=\frac{AB}{CA} \\\\tan0=\frac{CB}{AB}[/tex]

(d)

Remember SOH-CAH-TOA:

Sine=Opposite/Hypotenuse

Cosine=Adjacent/Hypotenuse

Tangent=Opposite/Adjacent

Using the angle C, plug in the appropriate sides:

[tex]sinC=\frac{BA}{CA}\\\\ cosC=\frac{CB}{CA}\\\\ tanC=\frac{BA}{CB}[/tex]

:Done

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