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3 years ago

A house was bought 20 years ago for $160,00. Due to inflation, its value had increased by 5% each year.

Mathematics

1 answer:

erik [133]3 years ago

4 0

320,000 You have to add 5% then multiply by 20

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Write the equation of the line that has undefined slope and passes through the point(-5,9)

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Write the equation of the circle with center (3, 2) and radius r = 7. Use the ^ key for the exponents. Write your answer as the example: (x - 4)^2+(y+8)^2=25

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3 years ago

NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!! THIS IS NOT A TEST OR AN ASSESSMENT!! Please help me with these math questions

Art [367]

Answer:

See below

Step-by-step explanation:

3. What are two ways that a vector can be represented?

Considering a vector $\vec{v}$ in some vector space $\mathbb R^n$ we have

$\vec{v} = \langle a,b\rangle$

This is the component form. I don't like that way. It is probably used in high school, but

$\vec{v} = \begin{pmatrix} a\\ b\\ \end{pmatrix}$

is preferable because the inner product on $\mathbb R^n$ is defined to be

$\langle a,b\rangle := \sum_{i = 1}^n a_i b_i$

You can also write it using linear form such as $\vec{v} = 2i+2j$

For this question, I think you meant

vectors

$\vec{u_1} = (-8, 12)$

$\vec{u_2} = (13, 15)$

Once

$\cos(\theta)=\dfrac{\vec{u_1} \cdot\vec{u_2}}{||\vec{u_1}||||\vec{u_2}||}$

Considering that the dot product is

$\vec{u_1}\cdot \vec{u_2} = (-8)\cdot 13 + 12\cdot 15 = -104+180= 76$

and the norm of $\vec{u_1}$ is $||\vec{u_1}|| = \sqrt{(-8)^2 + 12^2} = \sqrt{64 + 144}= \sqrt{208}$

and the norm of $\vec{u_2}$ is $||\vec{u_2}|| = \sqrt{13^2 + 15^2} = \sqrt{169 + 225}= \sqrt{394}$

Thus,

$\cos(\theta)=\dfrac{76}{\sqrt{208} \sqrt{394}} = \dfrac{19}{\sqrt{13}\sqrt{394}}=\dfrac{19}{\sqrt{5122}}$

$\therefore \theta = \arccos \left(\dfrac{19}{\sqrt{5122}} \right)$

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3 years ago

A regular octagonal pyramid has a base edge of 3m and a lateral area of 60m^2. Find its slant height.

Olin [163]

Octagon = 8-side polygon

<u>Find area of 1 triangle:</u>
Area of one side triangle = 60 ÷ 8 = 7.5 m²

<u>Given area and length, find height:</u>
Area of each triangle = 7.6 m²
Length of each triangle = 3m

Area = 1/2 x base x height
7.5 = 1/2 x 3 x height
Heigth = 5m

Answer: Slanted Height = 5 m

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3 years ago

On a map, 1 in. represents 12 mi. Two cities are 6 1/2in. apart on the map.

olasank [31]

1 inch = 12 miles

so 6 1/2 inches (or 6.5 inches) = 6.5 * 12 = 78 miles <===

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3 years ago

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