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3 years ago

Simplify the expression to a + bi form: (-7 - 3i) + (-5 + 10i)

Mathematics

2 answers:

Harman [31]3 years ago

6 0

Answer:

-12+7i

Step-by-step explanation:

(-7-3i)+(-5+10i)

-7-3i-5+10i

-7-5-3i+10i

-12-3i+10i

-12+7i

Please mark me as Brainliest if you're satisfied with the answer.

nignag [31]3 years ago

6 0

Answer:

$→( - 7 - 3i) +( - 5 + 10i) \\ = - 7 - 3i - 5 + 10i \\ = - 7 - 5 - 3i + 10i \\ = \boxed{ - 12 + 7i}✓$

-<u>12 + 7i</u> is the right answer.

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Is this linear relationship a direct variation?

Talja [164]

Since the ratio of of second variable to the ratio of first variable remains constant i.e y/x =8 so, the linear relationship is direct variation.

Step-by-step explanation:

A relationship is said to have direct variation if ratio of second variable to the ratio of first variable remains constant.

A relationship is direct variation if $y=kx\,\,or\,\, \frac{y}{x} =k$ where k is the constant.

Now checking if the given data is having direct variation or not.

x y

3 24

4 32

5 40

6 48

Now finding y/x

if y=24 and x = 3 then y/x = 24/3 = 8

if y=32 and x = 4 then y/x =32/4=8

if y=40 and x = 5 then y/x =40/5 =8

if y=48 and x = 6 then y/x =48/6= 8

Since the ratio of of second variable to the ratio of first variable remains constant i.e y/x =8 so, the linear relationship is direct variation.

Keywords: Direct Variation

Learn more about Direct Variation at:

#learnwithBrainly

5 0

3 years ago

A circle is defined by the equation given below.

tatyana61 [14]

Answer:

(1/2, 1)

Step-by-step explanation:

x² + y² − x − 2y − 11/4 = 0

x² − x + y² − 2y = 11/4

Complete the squares.

x² − x + 1/4 + y² − 2y + 1 = 11/4 + 1/4 + 1

(x − 1/2)² + (y − 1)² = 4

The center of the circle is (1/2, 1) and the radius of the circle is 2.

5 0

3 years ago

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

3 years ago

From base camp, a hiker walks 3.5 miles west and 1.5 miles north. Another hiker walks 2 miles east and 0.5 miles south. To the n

levacccp [35]

Answer:

The hikers are 5.9 miles apart.

Step-by-step explanation:

Let O represents the base camp,

Suppose after walking 3.5 miles west, first hiker's position is A, then after going 1.5 miles north from A his final position is B,

Similarly, after walking 2 miles east, second hiker's position is C then going towards 0.5 miles south his final position is D.

By making the diagram of this situation,

Let D' is the point in the line AB,

Such that, AD' = CD

In triangle BD'D,

BD' = AB + AD' = 1.5 + 0.5 = 2 miles,

DD' = AC = AO + OC = 3.5 + 2 = 5.5 miles,

By Pythagoras theorem,

$BD^2 = BD'^2 + DD'^2$

$BD = \sqrt{2^2 + 5.5^2}=\sqrt{4+30.25}=\sqrt{34.25}\approx 5.9$

Hence, the hikers are 5.9 miles apart.

8 0

3 years ago

1.3/4 - 5 3/7 <br> 2.-9 3/10 - 2/11

kodGreya [7K]

$1)\\\\\frac{3}{4}-5\frac{3}{7}\\\\\frac{3}{4}-\frac{38}{7}\\\\\frac{3}{4}*\frac{7}{7}-\frac{38}{7}*\frac{4}{4}\\\\\frac{21}{28}-\frac{152}{28}\\\\\frac{-131}{28}\\\\-4\frac{19}{28}\\\\\\2)\\\\-9\frac{3}{10}-\frac{2}{11}\\\\\frac{-93}{10}-\frac{2}{11}\\\\\frac{-93}{10}*\frac{11}{11}-\frac{2}{11}*\frac{10}{10}\\\\\frac{-1023}{110}-\frac{20}{110}\\\\\frac{-1043}{110}\\\\-9\frac{53}{110}$

3 0

3 years ago