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Readme [11.4K]
3 years ago
9

Urgent!! will mark brainliest!

Mathematics
1 answer:
Jlenok [28]3 years ago
5 0

Answer:

1) secФ = √2 ⇒ 2nd answer

2) The best identity is 1 + cot²Ф = csc²Ф ⇒ 4th answer

3) The expression 1/(-3/8) is equivalent to cotФ ⇒ 1st answer

Step-by-step explanation:

* The angle Ф lies in the 4th quadrant because 2π/3 < Ф < 2π

∴ The values of cosФ and secФ only positive

* Use the identity sec²Ф = tan²Ф + 1

∵ tanФ = -1

∴ sec²Ф = (-1)² + 1 = 1 + 1 = 2 ⇒ take √ in both sides

∴ secФ = ± √2

∵ Ф lies in the 4th quadrant

∴ secФ = √2

* Remember if we have the value of cotФ, we can use the identity

 cot²Ф + 1 = csc²Ф to find the value of cscФ

∵ cscФ = 1/sinФ

∴ sinФ = 1/cosФ

* In the problem Fatma know that cotФ = 4/7

∵ She wants to know the value of sinФ

∴ She can use the identity cot²Ф + 1 = csc²Ф

* The best identity is cot²Ф + 1 = csc²Ф

* We know that cotФ = 1/tanФ

∵ tanФ = -3/8

∴ cotФ = 1/(-3/8)

∴ The expression 1/(-3/8) is equivalent to cotФ

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kenny6666 [7]

General Idea:

When simplifying a rational expression, we need to do the below steps:

(i) Factor the Denominator of each fraction

(ii) Identify the Least Common Denominator (It is the product of prime factors involved with its highest exponent)

(iii) Identify and rewrite the equivalent fraction with the desired LCD.

(iv) Once the denominator are same, Combine the numerator.

Applying the concept:

What is the difference x/x^2-16-3/x-4

I assume that you mean to type the expression \frac{x}{x^{2}-16}  -\frac{3}{x-4}

Step 1: Factoring x^{2} -16

x^{2} -16=x^{2} -4^{2} =(x+4)(x-4)

Step 2: Identifying the LCD, we get (x+4)(x-4)

Step 3: Rewriting the second fraction by multiplying x+4 on both top and bottom of second fraction so that we get the LCD.

\frac{x}{x^2-16}-\frac{3}{x-4}=\frac{x}{(x+4)(x-4)}   -\frac{3*(x+4)}{(x-4)*(x+4)} Step 4: Combine like terms since the denominators are same[tex] \frac{x-3(x+4)}{(x+4)(x-4)} =\frac{x-3x-12}{(x+4)(x-4)}=\frac{-2x-12}{(x+4)(x-4)} =\frac{-2(x+6)}{(x+4)(x-4)}

Conclusion:

In factored form the simplified expression =\frac{-2(x+6)}{(x+4)(x-4)}

In expanded form the simplified expression =\frac{-2x-12}{x^2-16}

8 0
3 years ago
Which is the solution set of the inequality<br> -15y+9&lt;-36
liraira [26]

Answer:

-15y+93\:\\ \:\mathrm{Interval\:Notation:}&\:\left(3,\:\infty \:\right)\end{bmatrix}

Therefore, the first choice is correct.

The graph of the inequality is also attached below.

Step-by-step explanation:

Considering the inequality

-15y+9

solving

-15y+9

\mathrm{Subtract\:}9\mathrm{\:from\:both\:sides}

-15y+9-9

-15y

\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}

\left(-15y\right)\left(-1\right)>\left(-45\right)\left(-1\right)

15y>45

\mathrm{Divide\:both\:sides\:by\:}15

\frac{15y}{15}>\frac{45}{15}

y>3

In other words,

-15y+93\:\\ \:\mathrm{Interval\:Notation:}&\:\left(3,\:\infty \:\right)\end{bmatrix}

Therefore, the first choice is correct.

The graph of the inequality is also attached below.

6 0
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Answer: 9

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Likurg_2 [28]
7 out of 50 people so to find the whole amount u must multiply 50x8 to =400 and multiply 7x8 =56 therefore 56 out of 400 have traveled to a foreign country. however 56 is not MORE THAN 56. if it said 56 or more he would be correct but because he says more than 56 he is incorrect. hope that helps!
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