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2 years ago

Simplify (3 + 2i)(7 − 5i).

2 answers:

8 0

Rule needed: i^2 = -1
Standard form a + bi

(3 + 2i)(7 - 5i) FOIL
3 * 7 = 21
3 * - 5i = - 15i
2i * 7 = 14i
2i * -5i = - 10i^2 = - 10 * -1 = 10
Putting it all back together.
31 - i

swat322 years ago

3 0

(3+2i)(7-5i) = 21 - 15i + 14i + 10 = 31 - i

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Karen's city took a survey about a plan for a new park. Of the people surveyed, 380 liked the plan for the park and 120 did not.

Law Incorporation [45]

Answer:

Step-by-step explanation:

Survey response

Those who liked the proposed plan=380 persons

Those who didn't like the proposed plan=120 persons

We assume that the these are the only people who participated, with those who never took sides being zero

Total number of people surveyed=380 persons+120 persons=500 persons

Percentage of those who liked = $\frac {380}{500}*100%=76%$

Therefore, the percentage that liked the plan is 76%

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2 years ago

Select all the points that are on the line through (0 5) and (2 8) A.(5 11) B.(5 10) C.(6 14) D.(30 50) E.(40 60)

mihalych1998 [28]

Answer:

Options C. and D. are correct.

Step-by-step explanation:

Let $(x_1,y_1)=(0,5),\,(x_2,y_2)=(2,8)$

Equation of a line is given by $y-y_1=(\frac{y_2-y_1}{x_2-x_1})(x-x_1)$

$y-5=(\frac{8-5}{2-0})(x-0)\\\\y-5=\frac{3}{2}x\\\\2y-10=3x\\3x-2y+10=0$

Put $(x,y)=(5,11)$

$3(5)-2(11)+10=15-22+10=3\neq 0$

Put $(x,y)=(5,10)$

$3(5)-2(10)+10=15-20+10=5\neq 0$

Put $(x,y)=(6,14)$

$3(6)-2(14)+10=18-28+10=0$

Put $(x,y)=(30,50)$

$3(30)-2(50)+10=90-100+10=0$

Put $(x,y)=(40,60)$

$3(40)-2(60)+10=0\\120-120+10=10\neq 0$

So, points $(6,14),\,(30,50)$ satisfy the equation $3x-2y+10=0$

Therefore,

points $(6,14),\,(30,50)$ lie on the line through $(0,5)$ and $(2,8)$

Options C. and D. are correct.

8 0

2 years ago

Triangle MNP has vertices N(2, 2) and P(0, –2). The triangle is symmetric about the y-axis. What is the approximate measure of t

Evgesh-ka [11]

Point M of the triangle is (-2,2) to make triangle MNP as shown in the attached image

Triangle MNP has a base of 4 units and a height of 4 units. We can work out the angle x and angle y using trigonometry ratio

We use tan ratio to find both angles

$Tan (x) = \frac{opposite}{adjacent}$
$Tan(x)= \frac{4}{2}$
$Tan(x)=2$
$Tan^{-1}(2)=63.43494882$
$Angle x=63.43$

$Tan(y)= \frac{opposite}{adjacent}$
$Tan(y)= \frac{2}{4}$
$Tan^{-1}(0.5)=26.56505118$
$Angle y=26.6$

Angle MNP = Angle NMP = 63.43 degrees (this is based on the fact that the triangle is an isosceles triangle)

Angle MPN = 2×26.6 = 53.2 degrees (we multiply by 2 as angle y is only a half of angle MPN - as shown in the diagram)