10 and two tens, and then double the amount, and 5, 3, and 2. How much now?

The map shows the location of the airport and a warehouse in a city. Though not displayed on the map, there is also a factory 10

kipiarov [429]

step 1

find the coordinates of the factory

the factory is 104 miles due north of the warehouse

the coordinates of the warehouse are (39,-52)

coordinates of the factory------> (39,-52+104)------> (39,52)

step 2

find the distance warehouse to airport

let

A coordinates of warehouse-------> A( 39,-52)

B coordinates of airport---------> B(-39,52)

C coordinates of factory-------> C(39,52)

distance AB=√[(52+52)²+(-39-39)²]------> distance AB=130 miles

step 3

find the distance airport to factory

B(-39,52)

C(39,52)

distance BC=√[(52-52)²+(39+39)²]-----> distance BC=39 miles

the total number of miles=distance AB+distance BC---> 130+39

the total number of miles=169 miles

<em>Thus</em> the answer is 169

4 0

3 years ago

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Use a half-angle identity to find the exact value

Tatiana [17]

Given:

$\cos 15^{\circ}$

To find:

The exact value of cos 15°.

Solution:

$$\cos 15^{\circ}=\cos\frac{ 30^{\circ}}{2}$

Using half-angle identity:

$$\cos \left(\frac{x}{2}\right)=\sqrt{\frac{1+\cos (x)}{2}}$

$$\cos \frac{30^{\circ}}{2}=\sqrt{\frac{1+\cos \left(30^{\circ}\right)}{2}}$

Using the trigonometric identity: $\cos \left(30^{\circ}\right)=\frac{\sqrt{3}}{2}$

$$=\sqrt{\frac{1+\frac{\sqrt{3}}{2}}{2}}$

Let us first solve the fraction in the numerator.

$$=\sqrt{\frac{\frac{2+\sqrt{3}}{2}}{2}}$

Using fraction rule: $\frac{\frac{a}{b} }{c}=\frac{a}{b \cdot c}$

$$=\sqrt{\frac {2+\sqrt{3}}{4}}$

Apply radical rule: $\sqrt[n]{\frac{a}{b}}=\frac{\sqrt[n]{a}}{\sqrt[n]{b}}$

$$=\frac{\sqrt{2+\sqrt{3}}}{\sqrt{4}}$

Using $\sqrt{4} =2$ :

$$=\frac{\sqrt{2+\sqrt{3}}}{2}$

$$\cos 15^\circ=\frac{\sqrt{2+\sqrt{3}}}{2}$

5 0

4 years ago

The first three terms of a geometric sequence are

Lisa [10]

Answer:

a4 = 128

a5 = -512

Step-by-step explanation:

a1= -2

q= (-1)^(n+1) × 4

a4 = a1q³ = (-2) (-4)³ = -2 × -64 = +128

a5 = a1q⁴ = (-2) (-4)⁴ = -2 × 256 = -512

3 0

2 years ago

Last year's computer models are discounted 20%. What was the original price to the nearest dollar of a computer that now costs $

Alisiya [41]

Answer:

Step-by-step explanation:

<h3>If the Original price was $ X , Then </h3>

$x - 0.20x \: = 1480$

$0.8x = 1480$

$x = 1480 \div 0.8$

<h3>So , X = 1850 dollars .</h3>

<h2>Hope this helps you !!! </h2>

3 0

2 years ago

Two functions, P and Q, are described as follows: Function P y = 5x + 3 Function Q The rate of change is 2 and the y-intercept i

Svetach [21]

Function P . . . . . y = 5x + 3

Function Q . . . . . y = 2x + 4

Function P rate of change = 5
Function Q rate of change = 2

The first one is => 3 <= more than second one.

7 0

3 years ago

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