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3 years ago

3 questions 50 points

Mathematics

2 answers:

wolverine [178]3 years ago

7 0

rational numbers

(3x-7)+35

6x + 3

it's ok

saul85 [17]3 years ago

7 0

Question 3.

First lets multiply the fractions. We do this by multiplying the numerators together and by multiplying the denominators together:

$\frac{1}{3}$ × $\frac{5}{6}$ = $\frac{5}{18}$

(Numerator: 1 x 5 = 5 Denominator: 3 x 6 = 18)

Now that we know that the product is $\frac{5}{18}$ we know that it is not an integer or a natural number, since the product is a fraction and not a whole number. Also, fractions are never irrational numbers - they are always rational.

So the Answer is D) Rational numbers

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Question 4

We can re-write $(\frac{3x}{5} -7) +7$ as $\frac{3x}{5} -7 + 7$

This makes it clear that the -7 and the +7 cancel out ( -7 + 7 = 0)

This means that we are left with $\frac{3x}{5}$ as the Answer

Answer: $\frac{3x}{5}$ (option 2)

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Question 5

The perimeter of a rectangle is just all the 4 sides added up together.

Since the shape is a rectangle, all the long sides (lengths) are the same and all the short sides (widths) are the same.

So for example, if the length the rectangle was 4, and the width was 2, then the perimeter would be 4 + 4 + 2 + 2 = 12

Now lets do the same with the rectangle in your question:

[4x + 3] + [4x + 3] + [2x] + [2x]

Now we collect all of the similar terms. For example we add up all of the x values and all of the normal numbers:

Answer: 4x + 3 + 4x + 3 + 2x + 2x = 12x + 6 (The last option)

(4x + 4x +2x + 2x = 12x and 3 + 3 = 6. So the answer is 12x +6)

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3 years ago

Use the Rational Zeros Theorem to write a list of all potential rational zeros. (5 points)

yawa3891 [41]

So the Rational Zeros Theorem states that the potential zeros are ± P/Q, with P = factors of the constant and Q = factors of the leading coefficient.

In this case, the constant is -3 and the leading coefficient is 2.

P = 1,3
Q = 1,2

With P and Q established, divide them all as such:

$\pm \frac{1}{1}, \pm \frac{3}{1}, \pm \frac{1}{2}, \pm \frac{3}{2}\\\\\pm 1,\pm 3, \pm \frac{1}{2}, \pm \frac{3}{2}$

In short, your potential zeros are ± 1/2, ± 3/2, ± 1, and ± 2.

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3 years ago

Read 2 more answers

Write the expression as a single logarithm with a coefficient of 1. 3 ln x − 8 ln y

viva [34]

Answer:

$\ln(\frac{x^3}{y^8})$

Step-by-step explanation:

$3 \ln(x)-8\ln(y)$ is the given.

The instructions is to write as a single logarithm.

Let's use the power rule first:

$\ln(x^3)-\ln(y^8)$

Now we see the minus between the natural logs so we can use the quotient rule:

$\ln(\frac{x^3}{y^8})$

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3 years ago

20 points

djverab [1.8K]

Answer:

To solve the system below by substitution, replace y in the second equation with 7−6x.

==> False

This statement is false. To solve the system by substitution, replace x in the second equation with 7−6x.

==> False.

This statement is false. To solve the system by substitution, replace y in the first equation with 7−6x.

==> False

This statement is false. To solve the system by substitution, replace y in the second equation with 6x−7.

==> True.

From the first equation, 6x-y=7

y= 6x-7

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3 years ago

The junior and senior class officers are sponsoring a homecoming dance. The total cost for the facilities and catering is $45 pe

larisa86 [58]

Answer:

Domain is (0,∞)

Range is (45, ∞)

Step-by-step explanation:

Let x represents the number of persons and f(x) represents the average cost per person,

∵ Fixed cost = $ 2500

Also, additional cost is $ 45 per person,

So, the total cost for x persons ( in dollars ) = fixed deposit + additional cost for x persons,

= 2500 + 45x

$\text{Average cost for x persons}=\frac{\text{Total cost}}{x}$

$\implies f(x)=\frac{2500+45x}{x}$

Which is a rational function,

∵ A rational function is defined for all real numbers except those for denominator = 0

Denominator of f(x) = x

So, f(x) is defined for all real numbers except x ≠ 0,

Now, the cost can not be negative,

⇒ x > 0

Hence, the domain for f(x) is (0, ∞)

Again,

$f(x)=45+\frac{2500}{x}$

If $x\rightarrow \infty$

$f(x)\rightarrow 45$

So, 45 < f(x) < ∞

i.e., range of f(x) is (45, ∞)

5 0

3 years ago