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3 years ago

REASONING IN ALGEBRA AND GEOMETRY Fill in the reason that justifies each step

Mathematics

1 answer:

pantera1 [17]3 years ago

5 0

9514 1404 393

Answer:

1a. multiplication property of equality

1b. distributive property

1c. subtraction property of equality

1d. division property of equality

2a. distributive property

2b. addition property of equality

2c. division property of equality

Step-by-step explanation:

The properties that let you do the same thing to both sides of an equation are the properties of equality. These are usually given an additional qualifier according to the operation being performed: addition property ..., subtraction property ..., multiplication property ..., division property .... The property that lets you add or eliminate parentheses is the distributive property (of multiplication over addition).

To answer these questions, you need to compare each line to the previous to see what operation was performed. It will generally be use of one of the properties described above, or "simplification," in which like terms are combined.

1a. both sides are multiplied by 3: multiplication property of equality

1b. parentheses are eliminated: distributive property

1c. 18 is subtracted from both sides: subtraction property of equality

1d. both sides are divided by 2: division property of equality

2a. parentheses are eliminated: distributive property

2b. 24 is added to both sides: addition property of equality

2c. both sides are divided by 2: division property of equality

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PLEASE HELP ASAP ILL GIVE BRAINLIEST!!!!! find measure of arc MK

Gwar [14]

Answer:

Arc length MK = 15.45 units (nearest hundredth)

Arc measure = 58.24°

Step-by-step explanation:

Calculate the measure of the angle KLN (as this equals m∠KLM which is the measure of arc MK)

ΔKNL is a right triangle, so we can use the cos trig ratio to find ∠KLM:

$\sf \cos(\theta)=\dfrac{A}{H}$

where:

$\theta$ is the angle
A is the side adjacent the angle
H is the hypotenuse (the side opposite the right angle)

Given:

$\theta$ = ∠KLM
A = LN = 8
H = KL = 15.2

$\implies \sf \cos(KLM)=\dfrac{8}{15.2}$

$\implies \sf \angle KLM=\cos^{-1}\left(\dfrac{8}{15.2}\right)$

$\implies \sf \angle KLM=58.24313614^{\circ}$

Therefore, the measure of arc MK = 58.24° (nearest hundredth)

$\textsf{Arc length}=2 \pi r\left(\dfrac{\theta}{360^{\circ}}\right) \quad \textsf{(where r is the radius and}\:\theta\:{\textsf{is the angle)}$

Given:

r = 15.2
∠KLM = 58.24313614°

$\implies \textsf{Arc length MK}=2 \pi (15.2)\left(\dfrac{\sf \angle KLM}{360^{\circ}}\right)$

$\implies \textsf{Arc length MK}=\sf 15.45132428\:units$

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2 years ago

Which is the equation of the line with a slope of 9 that goes through the point (1,10.6)?

Lilit [14]

Answer: y - 10.6 = 9(x-1)

Step-by-step explanation:

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4 years ago

I'LL GIVE BRAINLIEST TO WHOEVER ANSWERS THE QUESTION CORRECTLY!!

GrogVix [38]

Answer:

(a) show all sides to be congruent

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3 years ago

George bought a lawnmower which had a list price of $360. If he got a 20% discount on the purchase, how much did he pay for the

julia-pushkina [17]

Answer:

$288.00

Step-by-step explanation:

$360.00

20%

=$288.00

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4 years ago

Find the volume of the frustrum of the right circular cone generated by rotating the line y = 3x+1 about the x-axis between x =

Juli2301 [7.4K]

Answer:

38π cubic units

Step-by-step explanation:

The volume V = ∫₀²πy²dx

Since y = 3x + 1, dy = 3dx ⇒ dx = dy/3

So, when x = 0, y = 3(0) + 1 = 0 + 1 = 1

when x = 2, y = 3(2) + 1 = 6 + 1 = 7

So, changing the variable to y and the limits of integration from y = 1 to y = 7, we have

V = ∫₀²πy²dx

V = π∫₁⁷y²dy/3

V = π[y³/3]₁⁷/3

V = π[y³]₁⁷/9

V = [7³ - 1³]π/9

V = [343 - 1]π/9

V = 342π/9

V = 38π cubic units

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3 years ago