Help picture below problem 18 will give brainlest

The tan θ and cos θ values of 17π/12 are illustrations of trigonometry ratios

The values of tan θ and cos θ are 2 + √3 and (√2 - √6)/4, respectively

We have:

θ = 17π/12

Express as sum

θ = 9π/12 + 8π/12

Simplify

θ = 3π/4 + 2π/3

The above becomes

tan(17π/12) = tan(3π/4 + 2π/3)

Using the sum formula, we have:

tan(A + B) = [tan(A) + tan(B)]/[1 - tan(A)tan(B)]

Substitute known values

tan(3π/4 + 2π/3) = [tan(3π/4) + tan(2π/3)]/[1 - tan(3π/4)tan(2π/3)]

Evaluate the expression

tan(3π/4 + 2π/3) = [-1 - √3]/[1 - (-1)(-√3)]

Evaluate the product

tan(3π/4 + 2π/3) = [-1 - √3]/[1 - √3]

Rationalize

[tex]tan(\frac{3\pi}4 + \frac{2\pi}3) = \frac{-1 - \sqrt3}{1 - \sqrt3} * \frac{1 + \sqrt3}{1 + \sqrt3}[/tex]

Evaluate the product

[tex]tan(\frac{3\pi}4 + \frac{2\pi}3) = \frac{-(1 + \sqrt3)^2}{1 - 3}[/tex]

This gives

[tex]tan(\frac{3\pi}4 + \frac{2\pi}3) = \frac{-(1 + 3 + 2\sqrt 3)}{-2}[/tex]

[tex]tan(\frac{3\pi}4 + \frac{2\pi}3) = \frac{-(4 + 2\sqrt 3)}{-2}[/tex]

Divide

[tex]tan(\frac{3\pi}4 + \frac{2\pi}3) = 2 + \sqrt 3[/tex]

So, we have:

tan(17π/12) = 2 + √3

We have:

θ = 17π/12

Express as difference

θ = 9π/4 - 5π/6

The above becomes

cos(17π/12) = cos(9π/4 - 5π/6)

Using the difference formula, we have:

cos(A - B) = cos(A)cos(B) + sin(A)sin(B)

So, we have

cos(17π/12) = cos(9π/4)cos(5π/6) + sin(9π/4)sin(5π/6)

Evaluate

[tex]cos(\frac{17\pi}{12}) = \frac{\sqrt 2}{2} * - \frac{\sqrt 3}{2} + \frac{\sqrt 2}{2} * \frac 12[/tex]

Evaluate

[tex]cos(\frac{17\pi}{12}) = \frac{\sqrt 2}{2} (- \frac{\sqrt 3}{2} + \frac 12)[/tex]

Evaluate the difference

[tex]cos(\frac{17\pi}{12}) = \frac{\sqrt 2}{2} (\frac{1 - \sqrt 3}{2})[/tex]

Expand

cos(17π/12) = (√2 - √6)/4

Hence, the values of tan θ and cos θ are 2 + √3 and (√2 - √6)/4, respectively

Read more about trigonometry ratios at:

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Answer:

1/5

Step-by-step explanation:

jack + 4 friends = 5 people

5 people would each get 1 slice

[tex]\sqrt{ { (x2 - x1)}^{2} + {(y2 - y1)}^{2} } \\ \\ = \sqrt{( {5 - ( - 1)}^{2} + {( - 9 - ( - 1)}^{2} )} \\ \\ = \sqrt{ {(5 + 1)}^{2} + {( - 9 + 1)}^{2} } \\ \\ = \sqrt{ {(6)}^{2} + {( - 8)}^{2} } \\ \\ = \sqrt{36 + 64} \\ \\ = \sqrt{100} \\ \\ = 10 \: units[/tex]

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

According to angle sum property of a quadrilateral, Sum of all angles of a quadrilateral measures 360°

So, let's solve for x ~

[tex]\qquad \tt \dashrightarrow \:68 + 126 + 106 + x = 360[/tex]

[tex]\qquad \tt \dashrightarrow \:300+ x = 360[/tex]

[tex]\qquad \tt \dashrightarrow \:x = 360 - 300[/tex]

[tex]\qquad \tt \dashrightarrow \:x = 60 \degree[/tex]

Step-by-step explanation:

for me it is best as a first step to combine this all to one big fraction, and then simplify the whole expression.

you do know that when multiplying the same variable with exponent we simply add the exponents. and she we divide the same variable with exponents, we subtract them from each other (as the overlapping exponent parts cancel each other out).

(3ac³f³)/(8a²bcf⁴) × (12ab²c)/(18ab³c²f) =

= (3×12a²b²c⁴f³)/(8×18a³b⁴c³f⁵) =

= (3×12c)/(8×18ab²f²) = 12c / (8×6ab²f²) =

= 2c / (8ab²f²) = c / (4ab²f²)

Answer:

D. marginal credit is right one

Answer:

45 fireflies

Step-by-step explanation:

Because,

Sheri caught 70 and Robert caught 35.

150-35-70= 35

35+10 is equal to 45.

Following the rules given is the right answer

furthering dendritic untiring s very crushed iridium rushes Rivendell ft Zarathustra

Answer:

the answer is 30..........

Answer:

Vertex is (-1/3, -1/3) and the axis of symmetry is x = -1/3

Hope this helps :)

Answer:

P(M &C) = 0.24

Step-by-step explanation:

Chemistry book will be denoted by C

Mathematics book will be denoted by M

5C2 = 10

There are 10 possible ways in which she can choose two books from the 5 books.

The probability of choosing a chemistry book:

P(C) = 2/5

The probability of choosing a mathematics book:

P(M) = 3/5

Probability of choosing a chemistry book and a mathematics book:

P(M &C) = (2/5) × (3/5)

P(M &C) = 0.24 or 24%

The probability that she pulls out a math book and a chemistry book will be 0.24.

The term probability refers to the likelihood of an event occurring

Given that;

Julia has 2 chemistry books and 3 math books.

Now,

Since, Julia has 2 chemistry books and 3 math books.

Hence, Total number of books = 2 + 3 = 5

So, The probability to choosing a chemistry book = 2/5

And, The probability to choosing a math book = 3/5

Thus, The probability that she pulls out a math book and a chemistry book is,

⇒ 2/5 × 3/5

⇒ 6/25

⇒ 0.24

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Answer:

45.5 and 17.5

Step-by-step explanation:

a)

b)

Answer:

e

Step-by-step explanation:

Answer:

a, e

Step-by-step explanation:

a would round to 110,000 because 113,450 rounded to the ten thousand round down to 110,000

95,678 would round up to 100,000 not 110,000

104,298 would round down to 100,000 not 110,000

94,560 would round down to 90,000

106,789 would round up to 110,000 because 6 rounds up because 5 and up is rounded up

Answer:

See below ↓↓

Step-by-step explanation:

Important facts given [needed to solve]

Solving :

Interest paid

well, at the beginning of the 6th year, you've been there for 5 whole years, so you've gotten 5 increases hmmm

[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &16000\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ t=years\dotfill &5\\ \end{cases} \\\\\\ A=16000(1 + 0.03)^{5}\implies A=16000(1.03)^5\implies A\approx 18548.39[/tex]

Pythagorean Theorem:

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

Since 10 and 24 are the legs, "x" has to be the hypoteneuse.  "a" and "b" are the legs (10 and 24).

Now, replace the values in.

[tex]10^2+24^2 = x^2[/tex]

[tex]x^2 = 100+576\\x^2 = 676\\x = 26[/tex]

Hope this helped! :)

Answer

Since 3 is greater than 0 we know that 7.835 is greater than 7.8. We follow the same process to find that 7.35 is less than 7.358. Then we can put the number

There you go I hope that helps and have a great day

Answer:

x=4 (Vertical angles have to be equal to each other! If one side is 46 then the side vertical to it is 46!) **Plug number in for x to verify once again!**

Step-by-step explanation:

You need to understand vertical angles!!

Vertical Angles must be congruent and equal to each other!

You need to do:

10x+6=46

Subtract 6 from both sides

10x=40

Do 40 divided by 10

x=4

To verify: plug 4 for x which should be 40 added to 6 is 46!

Answer:

-c is the blank and a+b is variables of real numbers.

Step-by-step explanation:

A real number is a value of a continuous quantity that can represent a distance.

However equality is a relationship between two quantities or, more generally two mathematical expressions, asserting that the quantities have the same value, or that the expressions represent the same mathematical object.

Answer:

The correct answer is Choice C.

Step-by-step explanation:

I drew a diagram of all the triangles to compare the statements given to each other

I marked the triangle sides with lines to show congruency in length.

One line for AB = DF

Two lines for AB = GI

Three lines for BC = HI

Four lines for DE = HI

The angles are all marked for the last sentence we are given.

The first and third triangles are the only ones similar. This is because of SAS congruence as given in the Diagram. AB = GI, angle B = angle I, BC = IH

The second triangle is different from the rest, and even if we tried to rotate it ad compare it, it would still be wrong.

Answer:

8x+10y=-8

Step-by-step explanation:

5x+3x=8x

4y+6y=10y

-14+6=-8

Answer:

Hope the picture will help you. Make sure to mark my answer brilliant

Answer:

2

Step-by-step explanation:

using the rules of logarithms

logx + logy = log(xy)

logx - logy = log ([tex]\frac{x}{y}[/tex] )

log[tex]x^{n}[/tex] ⇔ nlogx

[tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex]

given

3log2 + log200 - log16

= log 2³ + log200 - log16

= log8 + log200 - log16

= log(8 × 200) - log16

= log1600 - log16

= log ([tex]\frac{1600}{16}[/tex] )

= log100

let [tex]log_{10}[/tex] 100 = n , then

100 = [tex]10^{n}[/tex] = 10²

thus value of expression is n = 2 , that is 2

[tex]2 \cdot 1[/tex]Answer:

Equal to 2

Step-by-step explanation:

1. Apply log rule: [tex]alog_c(b) = log_{c}(b^a)[/tex]

[tex]3log_{10}(2) = log_{10}(2^3)[/tex]

[tex]= log_{10}(2^3) + log_{10}(200) - log_{10}(16)[/tex]

2. Apply log rule: [tex]log_c(a) + log_c(b) = log_c(ab)[/tex]

[tex]log_{10}(2^3) + log_{10}(200) = log_{10}(2^3 \cdot 200)[/tex]

[tex]= log_{10}(2^3 \cdot 200) - log_{10}(16)[/tex]

[tex]2^3 \cdot 200 = 1600[/tex]

[tex]= log_{10}(1600) - log_{10}(16)[/tex]

3. Apply log rule: [tex]log_c(a) - log_c(b) = log_c(\frac{a}{b})[/tex]

[tex]log_{10}(1600) - log_{10}(16) = log_{10}(\frac{1600}{16})[/tex]

Divide the numbers: [tex]\frac{1600}{16} = 100[/tex]

[tex]= log_{10}(100)[/tex]

Rewrite 100 in power - base form: [tex]100 = 10^2[/tex]

[tex]= log_{10}(10^2)[/tex]

4. Apply log rule: [tex]log_a(x^b) = b \cdot log_a(x)[/tex]

[tex]log_{10}(10^2) = 2log_{10}(10)[/tex]

[tex]2log_{10}(10)[/tex]

5. Apply log rule: [tex]log_a(a) = 1[/tex]

[tex]log_{10}(10) = 1[/tex]

[tex]= 2 \cdot 1 = 2[/tex]

Answer:

  87%

Step-by-step explanation:

The percentage of normally-distributed data between 45 and 77 in a data set with mean 63 and standard deviation 10.4 can be found by any of a number of calculators, apps, web sites, or spreadsheets.

The percentage is 87%.

Answer: (-4, -6)

Step-by-step explanation:

Solving by graphing

[] See attached

    () The only point in the required range is point (-4, -6)

Solving by plugging-in

        I will figure out what the correct option is by plug them into the first equation. Since only one of these options is true, I do not need to do the second equation.

[✗] Let's check point (4, 10)

    () 10 < (1/4)4 - 4

       10 < 1 - 4

       10 < -3 is false, so this answer is incorrect

[✗] Let's check point (-4, 5)

    () 5 < (1/4)-4 - 4

       5 < -1 -4

       5 < -5 is false, so this answer is incorrect

[✗] Let's check point (-4, -4)

    () -4 < (1/4)-4 - 4

       -4 < -1 -4

       -4 < -5 is false, so this answer is incorrect

[✓] Let's check point (-4, -6)

    () -6 < (1/4)-4 - 4

       -6 < -1 - 4

       -6 < -5 is true, so this answer is correct      

Answer:

Step-by-step explanation:

The angle formed by two secants is half the difference of intercepted arcs.

Correct choice is C

Let that be y

Option C

Answer:

72 yd²

Step-by-step explanation:

area of this figure = area of 1st rectangle + area of 2nd rectangle

= l×b + L×B

= 6 × 5 + 14 × 3

=30 + 42

= 72 yd²

Answer:

the answer c 72 yd2

Step-by-step explanation:

Answer:

14[tex]w^{8}[/tex] + 63[tex]w^{4}[/tex]

Step-by-step explanation:

7w³ (2[tex]w^{5}[/tex] + 9w) ← multiply each term in the parenthesis by 7w³

= 14[tex]w^{8}[/tex] + 63[tex]w^{4}[/tex]

[ using rule of exponents

[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex] ]

Answer:

7w⁴ (2w⁴ + 9)

Step-by-step explanation:

Given

Let's simplify.