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professor190 [17]

3 years ago

11

amy purchases 27 teeshirts for a certain amount of money. using m for the total amount of money in dollars that amy spent on tee

shirts, write an expression that represents how much one teeshirt costs.

1 answer:

Sophie [7]3 years ago

4 0

<span>One T-shirt is m dollars. The number of T-shirts is n. Amy bought 27 T-shirts.

27n = m, so n = m/27.</span><span>
Hope that helps! (:</span>

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Given f(x)=cos c and g(x)=cot x, what are the domain and range of f(g(x))?

Evgesh-ka [11]

Answer:

Option C

Step-by-step explanation:

We know that the function $y = cos(x)$ has as its domain all real numbers, and as a range $-1\leq y\leq 1$

We know that the function $cot(x) = \frac{cos(x)}{sin(x)}$

The denominator of the function can not be equal to 0. But $sin(x) = 0$ for all $x = n\pi$ where n is an integer number.

Therefore the domain of cot(x) are all real numbers except $x = n\pi$

The range of cot(x) are all real numbers

Then, the domain of f(g(x)) is:

x ∈ Domain g and g(x) ∈ Domain of f

Where:

Domain of g: All reals except $x = n\pi$

Domain of f: All reals.

This is:

Domain of f(g(x)):

All real numbers except $n\pi$

Range of f(g(x)):

$-1\leq y\leq 1$

Therefore the correct option is:

C. Domain: All real numbers x except x does not equal npi for all integers n; Range: -1 is less than or equal to and is less than or equal to 1.

7 0

3 years ago

The Supremacy Clause makes what the

Andrej [43]

Answer:

B. The United States Constitution

3 0

2 years ago

Students were asked to use the distributive property to write an equivalent expression for the expression (x-5)(x-2).

andre [41]

Answer:

x^2-7x+10

Step-by-step explanation:

the answer is x^2-2x-5x+10=

5 0

3 years ago

Read 2 more answers

The highest point in the United States is Mount McKinley in Alaska. Its summit is 20,335 feet above sea level. Badwater, a basin

miss Akunina [59]

Answer:

20,053

Step-by-step explanation:

20,335 - 282 = 20,053

5 0

3 years ago

Read 2 more answers

Hey! Can someone check my answers?

Andrew [12]

The greatest common factor is the biggest number taken from the values.

Q1. The answer is <span>A. 5y^6
</span>
$20 y^{9} +5 y^{6}= 4*5 y^{9}+5 y^{6}$
Since $x^{a}* x^{b} =x^{a+b}$ , then $x^{9}= x^{3}* x^{6}$

Back to our expression:
$4*5 y^{9}+5 y^{6}=4*5 y^{3}*y^{6}+5 y^{6}=4 y^{3}*5y ^{6}+ 5y ^{6}*1=5 y^{6} (4y ^{3} +1)$
The greatest common factor is thus $5 y^{6}$

Q2. The answer is <span>D. 12xy^2
</span>
$12x y^{5}+60 x^{4} y^{2} -24 x^{3} y^{3}=12x y^{5}+5*12 x^{4} y^{2} -2*12 x^{3} y^{3}$
We will use the rule $x^{a}* x^{b} =x^{a+b}$ to factorise the exponents:
$12x y^{5}+5*12 x^{4} y^{2} -2*12 x^{3} y^{3}= \\ =12x*y^{2}*y^{3}+5*12*x* x^{3} *y^{2}-2*12x* x^{2} *y*y^{2}= \\ =12xy^{2}*y^{3}+12xy^{2}*5 x^{3} -12xy^{2}*2 x^{2} y= \\ =12xy^{2}(y^{3}+5 x^{3}-2 x^{2} y)$
The greatest common factor is thus $12xy^{2}$

3 0

3 years ago