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2 years ago

Which of the following is equivalent to the expression below? 7(3+4i)

Mathematics

1 answer:

vodomira [7]2 years ago

3 0

$7(3+4i)$ is equivalent to $21+28i$

Option D is correct option

Step-by-step explanation:

We need to find the equivalent to the given expression:

$7(3+4i)$

To solve the expression multiply 7 with the terms inside the bracket

$7(3+4i)\\=7(3)+7(4i)\\=21+28i$

So, $7(3+4i)$ is equivalent to $21+28i$

Option D is correct option

Learn more about complex numbers at:

brainly.com/question/10736268

brainly.com/question/4678474

Keywords: Complex Numbers

#learnwithBrainly

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A LINE SEGMENT IS 5 INCHES MORE THAN FOUR TIMES THE LENGTH OF ANOTHER. THE DIFFERENCE IN THEIR LENGTHS IS 35 INCHES. HOW LONG AR

Georgia [21]

<h3>Answer:</h3>

One line segment is 10 cm and the other one is 45 cm

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6 0

2 years ago

Expand the given power by using Pascal’s triangle. (9a - 10b)^6

xxMikexx [17]

Answer:

$531441a^6-3542940a^5b+9841500a^4b^2-14580000a^3b^3+12150000a^2b^4-5400000ab^5+1000000b^6$

Step-by-step explanation:

1 n=0

1 1 n=1

1 2 1 n=2

1 3 3 1 n=3

1 4 6 4 1 n=4

1 5 10 10 5 1 n=5

1 6 15 20 15 6 1 n=6

This is where n is the exponent in

$(x+y)^n$ .

$(x+y)^6=1x^6+6x^5y+15x^4y^2+20x^3y^3+15x^2y^4+6xy^5+1y^6$

Now we want to expand:

$(9a-10b)^6$ or we we can rewrite as $(9a+(-10b))^6$ .

Let's replace $x$ with $(9a)$ and $y$ with $(-10b)$ in the expansion:

$(x+y)^6=1x^6+6x^5y+15x^4y^2+20x^3y^3+15x^2y^4+6xy^5+1y^6$

$((9a)+(-10b))^6$

$=1(9a)^6+6(9a)^5(-10b)+15(9a)^4(-10b)^2+20(9a)^3(-10b)^3+15(9a)^2(-10b)^4+6(9a)(-10b)^5+1(-10b)^6$

Let's simplify a bit:

$=9^6a^6-60(9)^5a^5b+15(-10)^2(9)^4a^4b^2+20(9)^3(-10)^3a^3b^3+15(9)^2(-10)^4a^2b^4+6(9)(-10)^5ab^5+(-10)^6b^6$

$=531441a^6-3542940a^5b+9841500a^4b^2-14580000a^3b^3+12150000a^2b^4-5400000ab^5+1000000b^6$

8 0

3 years ago

Last summers, students who worked earned an average of $80 a week with a standard deviation of $12. What percentage of students

Roman55 [17]

Answer:

2.28%

Step-by-step explanation:

<u>Given:</u>

μ = 80
σ = 12
x = 104

<u>Find z-score:</u>

z = (x - μ)/σ
z = (104 - 80)/12 = 2

Percent value corresponding to 2 as per z-table is 0.9772. This is corresponding to 97.72%.

<u>Percentage of students earned more than $104:</u>

100 - 97.72 = 2.28

5 0

2 years ago

Diego is solving the equation x^2-12x = 21

uysha [10]

Answer:

The solutions to the quadratic equations will be:

$x=\sqrt{57}+6,\:x=-\sqrt{57}+6$

Step-by-step explanation:

Given the expression

$x^2-12x\:=\:21$

Let us solve the equation by completing the square

$x^2-12x\:=\:21$

Add (-6)² to both sides

$x^2-12x+\left(-6\right)^2=21+\left(-6\right)^2$

simplify

$x^2-12x+\left(-6\right)^2=57$

Apply perfect square formula: (a-b)² = a²-2ab+b²

i.e.

$x^2-12x+\left(-6\right)^2=\left(x-6\right)^2$

so the expression becomes

$\left(x-6\right)^2=57$

$\mathrm{For\:}f^2\left(x\right)=a\mathrm{\:the\:solutions\:are\:}f\left(x\right)=\sqrt{a},\:-\sqrt{a}$

solve

$x-6=\sqrt{57}$

add 6 to both sides

$x-6+6=\sqrt{57}+6$

Simplify

$x=\sqrt{57}+6$

also solving

$x-6=-\sqrt{57}$

add 6 to both sides

$x-6+6=-\sqrt{57}+6$

Simplify

$x=-\sqrt{57}+6$

Therefore, the solutions to the quadratic equation will be:

$x=\sqrt{57}+6,\:x=-\sqrt{57}+6$

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2 years ago

In a bag of sweets, 6 are orange and 9 are lime. Jodi chooses a sweet at random, eats it an

Digiron [165]

Answer: $\frac{17}{35}$

Step-by-step explanation:

Given

The bag contains 6 orange and 9 lime sweets

For both sweets of the same flavor, Jodi must either choose orange or lime

No. of ways it can be done is $^6C_1\times^5C_1+^9C_1\times^8C_1$

The total no of ways of selecting two sweets out of 15 is $^{15}C_1\times^{14}C_1$

The probability that both sweets are the same flavor

$P=\dfrac{^6C_1\times^5C_1+^9C_1\times^8C_1}{^{15}C_1\times^{14}C_1}=\frac{102}{210}=\frac{51}{105}=\frac{17}{35}$

3 0

2 years ago