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4 years ago

Simplify the given expression below:

Mathematics

2 answers:

Zina [86]4 years ago

4 0

The answer will be C. OR 3. 11−<span>13<span>i</span></span>

WINSTONCH [101]4 years ago

4 0

Answer:

The correct option is 3.

Step-by-step explanation:

The given expression is

$(7-3i)\cdot(2-i)$

We need to find the simplified form of given expression.

Using distributive property, the given expression can be written as

$7\cdot(2-i)-3i\cdot(2-i)$

$7(2)+7(-i)-3i(2)-3i(-i)$

On further simplification we get

$14-7i-6i+3i^2$

$14-13i+3(-1)$ $[\because i^2=-1]$

$14-13i-3$

On combining like terms we get

$(14-3)-13i$

$11-13i$

The simplified form of given expression is 11-13i. Therefore the correct option is 3.

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If there are 40 entries to the science fair how man ways can the students get 1st, 2nd, and 3rd

djyliett [7]

40 choices for 1st slot
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3 0

4 years ago

Geometry Problem. Please help I don't understand this question! The diameter AC of circle O is 24 cm. Arcs AB and CD are congrue

In-s [12.5K]

Answer:

A. $\text{Measure of arc DC}=60^o$

B. $\text{Measure of arc AB}=60^o$

C. $m\angle ACB=30^o$

D. $m\angle AOD=120^o$

E. $m\angle ABC=90^o$

F. $\text{Measure of Arc BC}=120^o$

Step-by-step explanation:

We have been given that the diameter AC of circle O is 24 cm. Arcs AB and CD are congruent. Angle DOC = 60° .

A. Since we know that the degree measure of an arc is equal to the measure of the central angle that intercepts the arc.

We can see that angle DOC is central angle and $m\angle DOC=60^o$ and arc DC subtends to central angle, therefore, the measure of arc DC will be 60 degrees.

B. Since we are told that arcs AB and CD are congruent and measure of arc DC is 60 degrees, therefore, measure of arc AB will be 60 degrees as well.

C. The Inscribed Angle Theorem states that the measure of an inscribed angle is half the measure of its intercepted arc. Measure of Arc AB is 60 degrees, so by inscribed angle theorem the measure of angle ACB will be half the measure of AB.

$m\angle ACB=\frac{1}{2}\times \text{The measure of arc AB}$

$m\angle ACB=\frac{1}{2}\times 60^o$

$m\angle ACB=30^o$

Therefore, measure of angle ACB will be 30 degrees.

D. We can see that angle DOC and AOD form a linear pair of angles, so they will add up-to 180 degrees.

$m\angle DOC+m\angle AOD=180^o$

Upon substituting measure of angle DOC we will get,

$60^o+m\angle AOD=180^o$

$60^o-60^o+m\angle AOD=180^o-60^o$

$m\angle AOD=120^o$

Therefore, measure of angle AOD will be 120 degrees.

E. Since we know that angle inscribed in a semicircle is always a right angle. We can see that angle ABC is angle inscribed in the semicircle as AC is the diameter of our given circle, therefore, measure of angle ABC will be 90 degrees.

F. Since we know that arc measure of a semicircle is 180 degrees. We can see that arc ABC is arc of the semicircle, so we can set an equation as:

$\text{Measure of arc AB+ Measure of Arc BC}=180^o$