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3 years ago

For what value of "a" will the product shown below have a purely imaginary value? (Show work please)

1 answer:

5 0

If you expand out the brackets you get this,

(4+5i)(a+2i) = 4a + (5a)i + 8i - 10

The -10 comes from 5i * 2i.
Squaring i becomes -1.

Let's group the real stuff together,
and imaginary separately,

(4a - 10) + (5a + 8)i

For this to be purely imaginary,
the real part needs to be zero.

Therefore 4a - 10 = 0

Solve for a.

You might be interested in

Simplify and solve this equation for q: 3q + 5 + 2q – 5 = 65.

gladu [14]

3q+5+2q-5 = 65

5q = 65

q = 13

3 0

3 years ago

Triangle PQR is transformed to triangle P'Q'R'. Triangle PQR has vertices P(4, 0), Q(0, −4), and R(−8, −4). Triangle P'Q'R' has

Whitepunk [10]

Answer:

Please find attached the required plot accomplished with an online tool

Part A:

1/4

Part B:

P''(-1, 0), Q''(0, -1), and R''(2, -1)

Part C:

Triangle PQR is similar to triangle P''Q''R'' but they are not congruent

Step-by-step explanation:

Part A:

Triangle ΔPQR has vertices P(4, 0), Q(0, -4), R(-8, -4)

Triangle ΔP'Q'R' has vertices P'(1, 0), Q'(0, -1), R'(-2, -1)

The dimensions of the sides of the triangle are given by the relation;

$l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}$

Where;

(x₁, y₁) and (x₂, y₂) are the coordinates on the ends of the segment

For segment PQ, we place (x₁, y₁) = (4, 0) and (x₂, y₂) = (0, -4);

By substitution into the length equation, we get;

The length of segment PQ = 4·√2

The length of segment PR = 4·√10

The length of segment RQ = 8

The length of segment P'Q' = √2

The length of segment P'R' = √10

The length of segment R'Q' = 2

Therefore, the scale factor of the dilation of ΔPQR to ΔP'Q'R' is 1/4

Part B:

Reflection of (x, y) across the y-axis gives;

(x, y) image after reflection across the y-axis = (-x, y)

The coordinates after reflection of P'(1, 0), Q'(0, -1), R'(-2, -1) across the y-axis is given as follows;

P'(1, 0) image after reflection across the y-axis = P''(-1, 0)

Q'(0, -1) image after reflection across the y-axis = Q''(0, -1)

R'(-2, -1) image after reflection across the y-axis = R''(2, -1)

Part C:

Triangle PQR is similar to triangle P''Q''R'' but they are not congruent as the dimensions of the sides of triangle PQR and P''Q''R'' are not the same.

6 0

3 years ago

Factor the following expression using Reverse Distribution: 6n-24

harkovskaia [24]

Answer:C 2(3n + 12)

Step-by-step explanation:

2 x 3n = 6n

2 x 12 = 24

8 0

2 years ago

the half-life of bismuth-210 is 5 days. if 25 grams of bismuth-210 are present initially, how much will remain after 10 days?

Jet001 [13]

10 days is twice the half-life. After 5 days, can expect $\dfrac{25}2$ grams to remain; after another 5 days, you'd be left with $\dfrac{25}4$ grams.

3 0

2 years ago

Use the equation below to find T, if w=85, m= 12, and a=3. T=w-ma T = 3,060 X ?

saw5 [17]

Answer:

T = 49

Step-by-step explanation:

T = w - ma

w = 85

m = 12

a = 3

Plug in the corresponding numbers to the corresponding variables:

T = (85) - (12) * (3)

Remember to follow PEMDAS. PEMDAS is the order of operations, and stands for:

Parenthesis

Exponents (& Roots)

Multiplications

Divisions

Additions

Subtractions

First, multiply, then subtract:

T = 85 - (12 * 3)

T = 85 - 36

T = 49

T = 49 is your answer.

6 0

1 year ago