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3 years ago

If y varies directly with x, write an equation for the direct variation. Then find each value,

Mathematics

2 answers:

Shalnov [3]3 years ago

5 0

I think 3, because 15 is half of 30 and 3 is half of 6. Hope this helps

lukranit [14]3 years ago

3 0

Just a guess Bc I’ve no idea what you’re talking abt, but 3. Would set 30/6 and 15/y cross multiply, solve for y and get y =3

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Find the value of the trig function indicated.

jekas [21]

Answer:

$\displaystyle cos\theta = \frac{2\sqrt{13}}{13}$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality

Trigonometry

[Right Triangles Only] Pythagorean Theorem: a² + b² = c²

a is a leg
b is another leg
c is the hypotenuse

[Right Triangles Only] SOHCAHTOA

[Right Triangles Only] cosθ = adjacent over hypotenuse

Step-by-step explanation:

Step 1: Define

Identify variables

a = 8

b = 12

c

Step 2: Solve for c

Substitute in variables [Pythagorean Theorem]: 8² + 12² = c²
Evaluate exponents: 64 + 144 = c²
Add: 208 = c²
[Equality Property] Square root both sides: √208 = c
Rewrite: c = √208
Simplify: c = 4√13

Step 3: Define Pt. 2

Identify variables

Angle θ

Adjacent leg = 8

Hypotenuse = 4√13

Step 4: Find

Substitute in variables [Cosine]: $\displaystyle cos\theta = \frac{8}{4\sqrt{13}}$
Rationalize: $\displaystyle cos\theta = \frac{2\sqrt{13}}{13}$

6 0

3 years ago

Read 2 more answers

Complete the two-column proof by providing the missing statements or reasons.

navik [9.2K]

The diagonals of a rhombus bisect each other perpendicularly, making the

angles formed by the intersecting diagonals to be 90°.

Correct Response:

∠1 and ∠2 are corresponding angles of congruent triangles ΔAOD and ΔAOB, therefore, ∠1 = ∠2

<h3>Method used to prove that ∠1 = ∠2</h3>

Given:

The quadrilateral represented by ABCD = A rhombus

Required:

To prove that ∠1 = ∠2

Solution:

From the diagram, we have;

The measure of ∠AOD = ∠1, the measure of ∠AOB = ∠2

The two column proof is presented as follows;

Statement ${}$ Reasons

1. ABCD is a rhombus ${}$ 1. Given

2. AB = BC = CD = DA ${}$ 2. Definition

3. AO = OC, BO = OD ${}$ 3. Diagonals of a rhombus bisect each other

4. ΔAOD ≅ ΔAOB ${}$ 4. SSS congruency postulate

5. ∠1 ≅ ∠2 ${}$ 5. CPCTC

6. ∠1 = ∠2 ${}$ 6. Definition of congruency

SSS (Side-Side-Side) congruency postulate states that if the three sides of

one triangle are congruent to the three sides of another triangle, the two

triangles are congruent.

CPCTC is an acronym for Corresponding Parts of Congruent Triangles are Congruent.

Learn more about the properties of a rhombus and congruency here:

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5 0

3 years ago

The first two terms of an arithmetic sequence are a1 = 2 and a2 = 4. What is a10,the tenth term?

qaws [65]

A(1) = 2
a(2) = 4

You can see that the terms are increasing by +2.
so

a(1) = 2
a(2) = 4
a(3) = 6
a(4) = 8
a(5) = 10
a(6) = 12
a(7) = 14
a(8) = 16
a(9) = 18
a(10) = 20

your answer is a(10) = 20.

7 0

3 years ago

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Which statement is true about the value of the expression below?

Rashid [163]

Answer:It is between one and zero

Step-by-step explanation:

8 0

3 years ago

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The number of potholes in any given 1-mile stretch of freeway pavement in Pennsylvania has a Normal distribution. This distribut

Iteru [2.4K]

Answer:

83.85% of 1-mile long roadways with potholes numbering between 22 and 58

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 49

Standard deviation = 9

Using the Empirical Rule, what is the approximate percentage of 1-mile long roadways with potholes numbering between 22 and 58?

22 = 49 - 3*9

So 22 is three standard deviations below the mean.

Since the normal distribution is symmetric, 50% of the measures are below the mean and 50% are above the mean.

Of those 50% which are below the mean, 99.7% of those are within 3 standard deviations of the mean, that is, greater than 22.

58 = 49 + 9

So 58 is one standard deviation of the mean.

Of those which are above the mean, 68% are within 1 standard deviation of the mean, that is, lesser than 58.

Then

0.997*0.5 + 0.68*0.5 = 0.8385 = 83.85%

83.85% of 1-mile long roadways with potholes numbering between 22 and 58

5 0

3 years ago