Unit 8: right triangles & trigonometry date: ________________________ per: _______ homework 2: special right triangles.

Answer:

2.1

Step-by-step explanation:

The point at which the y axis is passed through is (0,1).

Answer:   Reduce the expression, if possible, by cancelling the common factors.

Exact Form:

1/40

Decimal Form: 0.025

Step-by-step explanation:

Answer:

[tex]22 \frac12[/tex] acres

Step-by-step explanation:

We need to find 3/4 of 30.

Method 1

30 by 3/4:

[tex]\implies 30 \times \dfrac34=\dfrac{30}{1}\times \dfrac34= \dfrac{30\times3}{1 \times4}=\dfrac{90}{4}=22 \frac12[/tex]

Method 2

Divide 30 by 4:  30 ÷ 4 = [tex]\frac{15}{2}[/tex]

Multiply the result by 3: [tex]\frac{15}{2}[/tex] x 3 = [tex]\frac{45}{2}[/tex] = [tex]22 \frac12[/tex]

Answer:The solution is in the attached file

Step-by-step explanation:

Answer:The answer is in the attached file

Step-by-step explanation:

Answer:

No solution:  [tex]4(0.6x-0.9)=2.4x-2.8[/tex]

One solution:  [tex]0.5(3x-8)=0.8x+0.9[/tex]

Many solutions:  [tex]4.2x-3.8=7(0.6x-0.7)+1.1[/tex]

Step-by-step explanation:

[tex]4.2x-3.8=7(0.6x-0.7)+1.1[/tex]

[tex]\implies 4.2x-3.8=4.2x-3.8[/tex]

Therefore, true for all [tex]x[/tex] so many solutions

[tex]4(0.6x-0.9)=2.4x-2.8[/tex]

[tex]\implies 2.4x-3.6=2.4x-2.8[/tex]

[tex]\implies -3.6=-2.8[/tex]

Therefore, no solution

[tex]0.5(3x-8)=0.8x+0.9[/tex]

[tex]\implies 1.5x-4=0.8x+0.9[/tex]

[tex]\implies 0.7x=4.9[/tex]

[tex]\implies x=7[/tex]

Therefore, one solution

Answer:

11.20cm

11 cm=the height of the cylinder

A 2-column table that has 3 rows. The first column is labeled x with entries 0, 1, 2. The second column is labeled P x (x) with entries 0. 25, 0. 5, 0. 25.

The probability helps us to know the chances of an event occurring.

[tex]\rm{Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

We know about the probability, therefore, let's find the probability of each of the cases.

When the number of success of the spinner landing on blue is none, therefore, the spinner does not land on the blue color at all.

[tex]\rm{Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

Now, as it is given that there is only one case when the spinner does not land on the blue side(RR) in the set, S = {RR, RB, BR, BB}. therefore,

[tex]\rm{Probability(X=0)=\dfrac{1}{4} = 0.25[/tex]

When the number of success of the spinner landing on blue is just once, therefore, the spinner does land on the blue color only once out of the two spin.

[tex]\rm{Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

Now, as it is given that there are two cases when the spinner does land on the blue side(RB, BR) in the set, S = {RR, RB, BR, BB}. therefore,

[tex]\rm{Probability(X=1)=\dfrac{2}{4} = 0.25[/tex]

When the number of success of the spinner landing on blue is twice, therefore, the spinner does land on the blue color both the times the spinner is spun.

[tex]\rm{Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

Now, as it is given that there is only one case when the spinner does land on the blue side twice(BB) in the set, S = {RR, RB, BR, BB}. therefore,

[tex]\rm{Probability=\dfrac{1}{4} = 0.25[/tex]

Now, if we draw the table of the data and the probability we will get the following table,

x             P(X)

0           0.25

1            0.50

2           0.25

Hence, the table that is correct is table A, which is  A 2-column table that has 3 rows. The first column is labeled x with entries 0, 1, 2. The second column is labeled P x (x) with entries 0. 25, 0. 5, 0. 25.

Learn more about Probability:

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Answer:

its A

Step-by-step explanation:

Answer:

x=3

Step-by-step explanation:

12*3=36

8*3=24 +12= 36

36=36

Answer:

x= 3

Step-by-step explanation:

12x=8x+12

combine like terms

12x-8x=12

4x=12

x=

[tex] \frac{12}{4} [/tex]

x=3

Check:

12x-8x=12

since x=3

12(3)-8(3)=12

36-24=12

Answer:

i think the answer is 39,366

Step-by-step explanation:

sorry if im wrong

Answer:

The 4th shape (rectange) is a parallelogram.

Step-by-step explanation:

Rectangle also has opposite sides equal and parallel. The difference between the two is that sides of rectangles form 90° while that of parallelogram don't. So rectangle can be called a parallelogram because they fulfill all the requirement of a parallelogram.

Answer:

D

Step-by-step explanation:

D is right(not the left! the right)and right is always right

Answer:

A

Step-by-step explanation:

Please mark brainlest

Answer:

A

Step-by-step explanation:

π[tex]\sqrt{3}[/tex] - 8π[tex]\sqrt{3}[/tex] ← factor out [tex]\sqrt{3}[/tex] π from each term

= [tex]\sqrt{3}[/tex] π (1 - 8)

= [tex]\sqrt{3}[/tex]π (- 7)

= - 7[tex]\sqrt{3}[/tex] π → A

Answer:

x = 55° (nearest degree)

Step-by-step explanation:

Trig ratios:

[tex]sin(\theta)=\dfrac{O}{H} \ \ \ cos(\theta)=\dfrac{A}{H} \ \ \ tan(\theta)=\dfrac{O}{A} \ \ \[/tex]

where [tex]\theta[/tex] is the angle, O is the side opposite the angle, A is the side adjacent to the angle, and H is the hypotenuse of a right triangle

Given:

[tex]\implies cos(x)=\dfrac{3.3}{5.7}[/tex]

[tex]\implies x=\arccos \dfrac{3.3}{5.7}=54.623459...[/tex]

⇒ x = 55° (nearest degree)

Answer:

54.6° OR 55° rounded up.

Step-by-step explanation:

So it is a fact that 3.3 is adjacent to x. And 5.7 is the hypotenuse.

Now, let's think of SOHCAHTOA: *Always remember that*

SOH: Sin = Opp/Hyp

CAH: Cos = Adj/Hyp

TOA: Tan = Opp/Adj

We will be using CAH since we have the adjacent and the hypotenuse.

Now, you need to plug in the numbers to the correct placement, in this case, it will look like this:

Cos(x) = 3.3/5.7

*If I were you, I'd use a Cosine calculator online or just your handy-dandy standard calculator because you can't just plug in 3.3/5.7 like that and expect to get the answer.*

*In order to find the cosine on a regular calculator, you must press the inverse button, followed by the cos button. Or just use the "arccos" button if it's on there*

REMEMBER SOHCAHTOA FOR THE FUTURE

Step-by-step explanation: 20/100 × x =60

1/5 × x = 60

× = 300

brainliest please

Answer:

x = 300

Step-by-step explanation:

i hope this helps! have a wonderful rest of ur day :)

and if its not too much to ask could you mark me as brainliest pls, im trying to rank up by the end of the month and i only need 2 more, if not its ok! ty and let me know if theres anything else you need help with!!

[tex] = 20 \frac{ {..144y. \frac{ \leqslant y.}{?} }^{?} }{?} 5 \time41s \frac2{9} < .40.2{0} {. \times \frac{?}{?} }^{?} [/tex]

Answer:

6.34

Explanation:

6.34615384615  rounded is 6.34

so therefore 6.34*26 is 164.84 which is more closer to 165. But if you happen to multiply 6.35*26 it is 165.1 but it goes over the right number by 0.01. So stick to 6.34 and have under exceeded amount.

Can I please have brainliest.

Answer:

the answer is 4.7

Step-by-step explanation:

you calculate the height and the weight and it will equal 4,712.388980, to the nearest tenth equals 4.7

hope it helps!

45% of 78 = [tex]\frac{45}{100}*78 = 35.1[/tex]

Hope that helps!

Answer:

[tex](2x + 5) * (x^{2} + 6x - 10)\\= 2x (x^{2} + 6x - 10) + 5 (x^{2} + 6x - 10)\\= 2x^{3} + 12x^{2} - 20x + 5x^{2} +30x - 50\\= 2x^{3} + 12x^{2} + 5x^{2} - 20x + 30x - 50\\= \boxed{2x^{3} + 17x^{2} + 10x - 50}[/tex]

Hope it helps ⚜

[tex](2x + 5) × (x² + 6x − 10)[/tex]

[tex]\bold\pink{↪}\small\bold\red{2x(x² + 6x − 10) +5(x² + 6x − 10)}[/tex]

[tex]\bold\pink{↪}\bold\red{2x³ + 12x² - 20x + 5x² + 30x - 50}[/tex]

[tex]\bold\pink{↪}\bold\red{2x³ + 12x² + 5x² - 20x + 30x - 50}[/tex]

[tex]\bold\pink{↪}\bold\red{2x³ + 17x² + 10x - 50}[/tex]

Answer:

10 gallons

Step-by-step explanation:

Multiply 20 by 1/2.

20 x 1/2 = 10

Hope it helps!

Let me know if it doesn't, I can make it right.

It would equal

6a^2-19a-20

Answer:

6a^2−25a−25 this is the answer to number 5

Answer:

Isolate the variable by dividing each side by factors that don't contain the variable.

[tex]x=\frac{7}{2f} -3[/tex]

My gratitude attitude  - THANKS!

Answer:

you are right

Step-by-step explanation:

1 1/3 is greater than 1 so that means he rode more miles this week.

Answer: c) he rode more miles this week

Clockwise from the top left, the angles are ∠1, ∠2, ∠3, ∠4, ∠5, ∠6, ∠7, ∠8 are 96°, 84°, 96°, 84°, 56°, 124°, 56°, 124° respectively. Then the correct option is A.

Angle is the space between the line or the surface that meets.  And the angle is measured in degree. For complete 1 rotation, the angle is 360 degrees.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

Vertically opposite angle - When two lines intersect, then their opposite angles are equal.

In the diagram, the measure of angle ∠8 is 124°, and the measure of angle ∠2 is 84°.

Angle ∠1 and ∠2 are supplement angles.

∠1 + ∠2 = 180°

∠1 + 84° = 180°

        ∠1 = 96°

Similarly, angles ∠7 and ∠8 are supplement angles.

∠7 + ∠8 = 180°

∠7 + 124° = 180°

          ∠7 = 56°

By the property of the opposite angles, we have

∠1 = ∠3 = 96°

∠2 = ∠4 = 84°

∠5 = ∠7 = 56°

∠6 = ∠8 = 124°

Clockwise from the top left, the angles are ∠1, ∠2, ∠3, ∠4, ∠5, ∠6, ∠7, ∠8 are 96°, 84°, 96°, 84°, 56°, 124°, 56°, 124° respectively.

Then the correct option is A.

More about the angled link is given below.

https://brainly.com/question/15767203

Answer:

Clockwise from the top left, the angles are ∠1, ∠2, ∠3, ∠4, ∠5, ∠6, ∠7, ∠8 are 96°, 84°, 96°, 84°, 56°, 124°, 56°, 124° respectively. Then the correct option is A.

What is an angle?

Angle is the space between the line or the surface that meets.  And the angle is measured in degree. For complete 1 rotation, the angle is 360 degrees.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

Vertically opposite angle - When two lines intersect, then their opposite angles are equal.

In the diagram, the measure of angle ∠8 is 124°, and the measure of angle ∠2 is 84°.

Angle ∠1 and ∠2 are supplement angles.

∠1 + ∠2 = 180°

∠1 + 84° = 180°

       ∠1 = 96°

Similarly, angles ∠7 and ∠8 are supplement angles.

∠7 + ∠8 = 180°

∠7 + 124° = 180°

         ∠7 = 56°

By the property of the opposite angles, we have

∠1 = ∠3 = 96°

∠2 = ∠4 = 84°

∠5 = ∠7 = 56°

∠6 = ∠8 = 124°

Clockwise from the top left, the angles are ∠1, ∠2, ∠3, ∠4, ∠5, ∠6, ∠7, ∠8 are 96°, 84°, 96°, 84°, 56°, 124°, 56°, 124° respectively.

Then the correct option is A.

More about the angled link is given below.

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Answer:

(a) 3/28

(b) 5/28

(c) 5/7

Step-by-step explanation:

(a) To find 3/8 ths of 2/7, multiply the fractions:

[tex]\implies \dfrac38 \textsf{ of } \dfrac27=\dfrac27 \times \dfrac38=\dfrac{2 \times3}{7 \times8}=\dfrac{6}{56}=\dfrac{3}{28}[/tex]

(b)  The sum of the probabilities of all possible outcomes is 1.

Therefore, if 3/8 of the children are girls, then 1 - 3/8 are boys:

[tex]\implies 1-\dfrac38=\dfrac88-\dfrac38=\dfrac{8-3}{8}=\dfrac58 \textsf{ of children are boys}[/tex]

So again, multiply 5/8 by 2/7 to find 5/8ths of 2/7:

[tex]\implies \dfrac58 \textsf{ of } \dfrac27=\dfrac27 \times \dfrac58=\dfrac{2 \times5}{7 \times8}=\dfrac{10}{56}=\dfrac{5}{28}[/tex]

(c) The sum of the probabilities of all possible outcomes is 1.

Therefore, if 2/7 of the people watching the football game are children, then 1 - 2/7 are not children:

[tex]\implies 1-\dfrac27=\dfrac77-\dfrac27=\dfrac{7-2}{7}=\dfrac57 \textsf{ of people watching the football are NOT children}[/tex]

Answer:

0

Step-by-step explanation:

6x-12-6x+12=

0x-12+12=0

Answer:

x is the number of books

2.25x≤10

Hope This Helps!!!

The expression representing the total number of books that can be purchased for $10 is [10/2.25],  a step function.

A Step function or the greatest integer function is of the form f(x) = [x] gives us the value of f(x) as the first integer less than or equal to x, that is, x-1≤ f(x) ≤ x, f(x) ∈ I.

We are informed that the cost of each book is $2.2.5, and the total money with the person is $10.

∴ The total number of books that can be purchased for $10, will e a step function, as the number of books needs to be an integer, with the total amount in hand divided by the cost of each book.

∴ The total number of books that can be purchased for $10 = [10/2.25].

Learn more about Step functions at

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Answer: y=x+3

Step-by-step explanation: First, I drew a line that equally divided the two points. It looks like R was moved 4 points tot he right and then 4 points down, so draw the line in that direction.

Then I picked 2 points on the line, where the line intersects the graph.

I chose (-3,0) and (2,5) and used those to solve for the equation of the line.

Gradient=>  [tex]\frac{y2-y1}{x2-x1} = \frac{5-0}{2-(-3)}=\frac{5}{5}=1[/tex]

y = mx+c => 5 = 1(2) +c

c= 5-2 =3

Therefore, equation of the line is y = 1(x) + 3 => y = x + 3

Hope this helped! Please give brainliest :)

the area is 40 square meters

You are welcome

Answer:

40 square meters

Step-by-step explanation: