Solve the equation y+5=-12

Find the distance between the points (9, –6) and (–4, 7). Question 15 options: A) B) C) D)

Verdich [7]

Answer:

$\huge \boxed{ \boxed{ \tt \sqrt{170} }}$

Step-by-step explanation:

<h3>to understand this</h3><h3>you need to know about:</h3>

coordinates
PEMDAS

<h3>given:</h3>

point:(9,-6),(-4,7)

<h3>tips and formulas:</h3>

$d = \sqrt{(x _{2} - x _{1} ) ^{2} + (y_{2} - y_1 {)}^{2} } \atop$

<h3>let's solve:</h3>

$\sf substitute \: the \: value \: o f \:x _{2} \: x _{1} \: y_{2} \: y_1 \: respectively : \\ \sqrt{(9-(-4) ) ^{2} + (-6 - (-7){)}^{2} }$
$\sf simplify : \\ \sqrt{(9-(-4) ) ^{2} + (-6 - (-7){)}^{2} } \\ \sqrt{(9 + 4 {)}^{2} + ( - 6 + 7 {)}^{2} } \\ \sqrt{ {13}^{2} + {1}^{2} } \\ \sqrt{169 + 1} \\ \sqrt{170} \\$

7 0

3 years ago

Find the arc length of the given curve between the specified points.

yuradex [85]

Answer:

4.25

Step-by-step explanation:

Given:

$f(x) = \frac{x^3}{12} + \frac{1}{x} \\\\Arc Length = \int\limits^a_b {\sqrt{1 + (f'(x))^2} } \, dx \\f '(x) = \frac{x^2}{6} - \frac{1}{x^2}\\\\f'(x)^2 = (\frac{x^2}{6} - \frac{1}{x^2})^2 = \frac{x^4}{36} + \frac{1}{x^4} - \frac{1}{3}\\\\1 + f'(x)^2 = \frac{x^4}{36} + \frac{1}{x^4} + \frac{2}{3}\\\\\= \frac{x^8 + 36 + 12x^4}{36x^4}\\\\= \frac{(x^4 + 6)^2}{36x^4}\\\\=\sqrt{1 + f'(x)^2} = \sqrt{ \frac{(x^4 + 6)^2}{36x^4}}\\\\= \frac{x^2}{6} + \frac{1}{x^2} \\\\$

$ArcLength = \int\limits^4_1 {\frac{x^2}{6} + \frac{1}{x^2} } \, dx \\= (\frac{x^3}{18} - \frac{1}{x})\limits^4_1\\\\= (\frac{64}{18} - \frac{1}{4}) - (\frac{1}{18} - 1)\\\\= \frac{17}{4}= 4.25$

8 0

3 years ago

What is the difference between earth's highest mountain and its deepest ocean canyon?what is the difference between mars highest

irinina [24]

Earth's Highest Mountain: Mount Everest = 29,029 ft
Earth's Deepest Ocean Canyon: Challenger Deep = - <u>(-)36,070 ft
</u>Total Difference ----------------------------------------------------- 65099 ft

Mars' Highest Mountain: Olympus Mons = 69,650 ft Mars' Deepest Ocean Canyon: Valles Marineris = - <u>(-) 23000 ft
</u>Total Difference ----------------------------------------------------- 92650 ft

<em>ANSWER: Mars has greater difference of Highest Mountain - Deepest Ocean Canyon. It differ with that of Earth's by 27, 551 ft</em>

6 0

3 years ago

Which graph best represents the solution to the system of equations below?

xxTIMURxx [149]

Hey.. the answer is Graph 2. y=-4x+19....(7)=-4(3)+19

8 0

4 years ago

Katie is buying a refrigerator for her apartment. She's choosing between a regular fridge and a gigantic fridge . She notices th

Anuta_ua [19.1K]

Answer:

Volume of the gigantic fridge is 2.5 times the volume of regular fridge.

Step-by-step explanation:

This question is incomplete; here is the complete question.

Katie is buying a refrigerator for her apartment. She's choosing between a regular fridge and a gigantic fridge (details are shown in the table below). She notices that the gigantic fridge costs 3 times as much as the regular fridge.

How many times as great is the volume of the gigantic fridge as the volume of the regular fridge?

Area of the base, Height, Price

Regular Fridge: 1m² / 2m / $200

Large Fridge: 2m² / $\frac{5}{2}$ m / $600

In this question cost of the large fridge is 3 times as much as the regular fridge.

Area of the base of regular fridge = 1m²

Height of the regular fridge = 2m

So volume of this fridge = 1×2 = 2m³

Area of the base of the large fridge = 2m²

Height of the large fridge = $\frac{5}{2}$ m

Volume of the large fridge = $\frac{5\times 2}{2}$ = 5m³

Ratio of the volumes of the large and regular fridge = $\frac{5}{2}=2.5:1$

Therefore, volume of the gigantic fridge is 2.5 times the volume of regular fridge.

3 0

3 years ago