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3 years ago

Factor 18p-36 to identify the equivalent expression

Mathematics

1 answer:

Novay_Z [31]3 years ago

4 0

Answer:

9(2p-4)

Step-by-step explanation:

To factor an expression, find the GCF of each term. 18p and 36 share in common the factor 9. Divide each term by 9 to get the factor.

18p - 36 = 9(2p-4)

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Question: A canary's beak is, at most, 20mm long. Which algebraic inequality represents this situation?

Paul [167]

Answer:

Option (1).

Step-by-step explanation:

Statement given states that "A canary's beak is, at most 20 mm long."

Word "at most" means "the maximum".

So at most length of the beak means "length of the beak is less than equal to 20 mm".

And the expression representing this statement algebraically will be,

x ≤ 20

Therefore, option (1) will be the correct option.

8 0

3 years ago

9. A circle has an arc of length 56pi that is intercepted by a central angle of 120 degrees. What is the radius of the circle?

SSSSS [86.1K]

Answer:

Part 4) $r=84\ units$

Part 9) $sin(\theta)=-\frac{\sqrt{5}}{3}$

Part 10) $sin(\theta)=-\frac{9\sqrt{202}}{202}$

Step-by-step explanation:

Part 4) A circle has an arc of length 56pi that is intercepted by a central angle of 120 degrees. What is the radius of the circle?

we know that

The circumference of a circle subtends a central angle of 360 degrees

The circumference is equal to

$C=2\pi r$

using proportion

$\frac{2\pi r}{360^o}=\frac{56\pi}{120^o}$

simplify

$\frac{r}{180^o}=\frac{56}{120^o}$

solve for r

$r=\frac{56}{120^o}(180^o)$

$r=84\ units$

Part 9) Given cos(∅)=-2/3 and ∅ lies in Quadrant III. Find the exact value of sin(∅) in simplified form

Remember the trigonometric identity

$cos^2(\theta)+sin^2(\theta)=1$

we have

$cos(\theta)=-\frac{2}{3}$

substitute the given value

$(-\frac{2}{3})^2+sin^2(\theta)=1$

$\frac{4}{9}+sin^2(\theta)=1$

$sin^2(\theta)=1-\frac{4}{9}$

$sin^2(\theta)=\frac{5}{9}$

square root both sides

$sin(\theta)=\pm\frac{\sqrt{5}}{3}$

we know that

If ∅ lies in Quadrant III

then

The value of sin(∅) is negative

$sin(\theta)=-\frac{\sqrt{5}}{3}$

Part 10) The terminal side of ∅ passes through the point (11,-9). What is the exact value of sin(∅) in simplified form?

see the attached figure to better understand the problem

In the right triangle ABC of the figure

$sin(\theta)=\frac{BC}{AC}$

Find the length side AC applying the Pythagorean Theorem

$AC^2=AB^2+BC^2$

substitute the given values

$AC^2=11^2+9^2$

$AC^2=202$

$AC=\sqrt{202}\ units$

$sin(\theta)=\frac{9}{\sqrt{202}}$

simplify

$sin(\theta)=\frac{9\sqrt{202}}{202}$

Remember that

The point (11,-9) lies in Quadrant IV

then

The value of sin(∅) is negative

therefore

$sin(\theta)=-\frac{9\sqrt{202}}{202}$

5 0

3 years ago

How to write 4/6 in unit fraction

omeli [17]

U write it as 1/6+1/6+1/6+1/6=4/6

5 0

3 years ago

A scientist is investigating whether percent concentration can be used to predict density in apple juice. A scientist selected a

USPshnik [31]

Answer:

The most appropriate inference procedure for the investigation is;

a. A linear regression t-interval for the slope

Step-by-step explanation:

Given that the slope of an horizontal line is zero, we have that there is no change in the y (dependent) variable when there is a change in the x-variable, therefore, it is important to find the true relationship between the two variables, 'x', and 'y'

The confidence interval of the slope is calculated and analyzed to determine if it excludes or includes, 0, such that, if the confidence interval exclude 0, then, it is unlikely that the slope is 0, therefore, there the relationship between the variables, 'x', and 'y' is significant

Therefore, a linear regression t-interval for the slope is most appropriate.

3 0

3 years ago

I need help with truth tables

Lerok [7]

The complete table of truth value for the composite proposition:

p q ¬ q p ∨ ¬ q (p ∨ ¬ q) ⇒ q

T T F T T

T F T T F

F T F T T

F F T T F

<h3>How to fill a truth table with composite propositions</h3>

In mathematics, propositions are structures that contains a truth value. There are two truth values in classic logics: True, False. Composite propositions are the result combining simpler propositions and operators. There are the following logic operators and rules:

Negation changes the truth value of the proposition into its opposite.
Disjunction brings out "true" value when at least one of the two propositions is so.
Conjunction brings out "true" value when the two propositions are so.
Conditional form brings out "true" value when both propositions are true or only the consequent is true or both propositions are false.

Now we present the complete table of truth value for the composite proposition:

p q ¬ q p ∨ ¬ q (p ∨ ¬ q) ⇒ q

T T F T T

T F T T F

F T F T T

F F T T F

To learn more on truth values: brainly.com/question/6869690

#SPJ1

7 0

2 years ago