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3 years ago

Type the correct answer in the Box use numerals instead of words if necessary use / for the fraction bar find the missing term

2 answers:

8 0

The roots of the given equation are 5 + 3i, 5 - 3i.

This means the two factors of the given polynomial are x - (5+3i) and x - (5 - 3i). The product of the factors must result in the original expression. So, we can write:

x² - (answer) + 34 = (x - 5 -3i)(x - 5 + 3i) (Equation 1)

Simplifying the right hand side:

$(x - 5 -3i)(x - 5 + 3i) \\ \\ = x^{2} -5x+3xi-5x+25-15i-3xi+15i-9i^{2} \\ \\ = x^{2} -10x+25-9i^{2} \\ \\ = x^{2} -10x+25-9(-1) \\ \\ = x^{2} -10x+25+9 \\ \\ = x^{2} -10x+34$

Thus, we can write the Equation 1 as:

x² - (answer) + 34 = x² - 10x + 34

Comparing the two sides, we can conclude that the answer to this question is 10x.

Dvinal [7]3 years ago

6 0

Answer:

Type the correct answer in the box. Use numerals instead of words.

Find the area of this shape.

The area of the shape is

square centimeters.

Step-by-step explanation:

You might be interested in

Equation for geometric sequence 6,12,24,48,96

Alex_Xolod [135]

Answer:

a(n)=6*2^(n-1)

Step-by-step explanation:

a(n)=a(1)r^(n-1)

a(1) = 6

a(2)=6r^1=12

r=2

a(n)=6*2^(n-1)

7 0

3 years ago

Read 2 more answers

The following function is probability mass function. f left-parenthesis x right-parenthesis equals StartFraction 2x plus 1Over 2

lora16 [44]

Answer:

a) Mean = 2.6

B) Variance = 9.2

Step-by-step explanation:

We are given the following probability mass function in the question:

$F(x) = \dfrac{2x+1}{25}, x = 0,1,2,3,4$

a) Mean of random variable

$\mu = \displaystyle\sum x_iF(x_i)\\\\=0(\dfrac{1}{25}) + 1(\dfrac{2+1}{25}) + 2(\dfrac{4+1}{25}) + 3(\dfrac{6+1}{25}) + 4(\dfrac{8+1}{25})\\\\=\dfrac{3+10+21+36}{25} = \dfrac{70}{25} = 2.8$

b) Variance of the random variable

$\sigma^2 = \displaystyle\sum x_i^2F(x_i)\\\\=0^2(\dfrac{1}{25}) + 1^2(\dfrac{2+1}{25}) + 2^2(\dfrac{4+1}{25}) + 3^2(\dfrac{6+1}{25}) + 4^2(\dfrac{8+1}{25})\\\\=\dfrac{3+20+63+144}{25} = \dfrac{230}{25} = 9.2$

6 0

3 years ago

A gardener is planting two types of trees:

Scrat [10]

It will take 4 years for these trees to be the same height

Step-by-step explanation:

A gardener is planting two types of trees:

Type A is 6 feet tall and grows at a rate of 12 inches per year

Type B is 2 feet tall and grows at a rate of 24 inches per year

We need to find exactly how many years it will take for these trees to be the same height

Assume that it will take x years for these trees to be the same height

Type A:

∵ The initial height of the tree is 6 feet

∵ 1 foot = 12 inches

∴ 6 feet = 6 × 12 = 72 inches

∴ The initial height of the tree is 72 inches

∵ It grows at a rate of 12 inches per year

∵ The number of years is x

∴ The height of the tree in x years = 72 + 12 x

Type B:

∵ The initial height of the tree is 2 feet

∴ 2 feet = 2 × 12 = 24 inches

∴ The initial height of the tree is 24 inches

∵ It grows at a rate of 24 inches per year

∵ The number of years is x

∴ The height of the tree in x years = 24 + 24 x

Equate The heights of the two types

∴ 72 + 12 x = 24 + 24 x

- Subtract 2 from both sides

∴ 48 + 12 x = 24 x

- Subtract 12 x from both sides

∴ 48 = 12 x

- Divide both sides by 12

∴ x = 4

It will take 4 years for these trees to be the same height

Learn more:

You can learn more about the word problems in brainly.com/question/10557938

#LearnwithBrainly

3 0

3 years ago

What is the volume of the container below?

zheka24 [161]

Answer:

Step-by-step explanation:

Split the figure into two rectangles
The dimensions of the smaller rectangle on top are: length = 6 width = 10 height = 4
V = 6(10)(4) = 240
The dimensions of the larger rectangle on the bottom are: length = 6 width = 14 height = 16
*You can find the height by subtracting 20 - 4 = 16*
V = 6(14)(16) = 1,244
Add the volumes: 240 + 1,244 = 1,584
The sum, 1,584, is the total volume

4 0

3 years ago

I am confused in this can someone help?

fgiga [73]

Answer:

$\huge\boxed{\sf a = -12 , b = 8}$

Step-by-step explanation:

<u>Given polynomial is:</u>

$f(x) = ax^3+ b^2 + 3x + 4$

$\rule[225]{225}{2}$

First factor is (x-1)

Let x - 1 = 0 => x = 1

Putting this in the above polynomial

$f(1) = a(1)^3 + b(1)^2 + 3(1) + 4$

Given that it's remainder is 3

$3 = a + b + 3 + 4$

$3 = a + b + 7$

Subtracting 7 to both sides

$-4 = a + b\\OR \\$

$\rule[225]{225}{2}$

Second Factor is 2x + 1

Let 2x + 1 = 0 => x = - 1 / 2

Putting in the above polynomial

$f(-\frac{1}{2} ) = a (-\frac{1}{2} )^3 + b (-\frac{1}{2} )^2 + 3 (-\frac{1}{2} ) + 4$

The remainder is 6

$6 = -\frac{a}{8} + \frac{b}{4} - \frac{3}{2} + 4\\6 - 4 = -\frac{a}{8} + \frac{b}{4} - \frac{3}{2}\\2 = \frac{-a + 2b -12 }{8} \\-a + 2b - 12 = 16\\-a + 2b = 16 + 12\\$

$\rule[225]{225}{2}$

Adding both equations

a + b - a + 2b = -4 + 28

3b = 24

Dividing both sides by 3

b = 8

$\rule[225]{225}{2}$

Putting b = 8 in Equation (1)

a + 8 = -4

a = - 4 - 8

a = -12

$\rule[225]{225}{2}$

8 0

4 years ago