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3 years ago

Find two consecutive integers such that the smaller integer is six more than twice the larger integer

Mathematics

1 answer:

ZanzabumX [31]3 years ago

8 0

Let the integers be x and x+1.

x = 6 + 2(x + 1)

x = 6 + 2x + 2

x = -8

Hence, the integers are -8 and -7.

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tammy is 14 years old. she has a younger sister and an older brother. her sister is 12. the mean of all their ages is 14. how ol

mafiozo [28]

Answer:

Step-by-step explanation:

To solve, we can use an equation finding the average of the siblings'ages.

$\frac{14 + 12 + x}{3} = 14 \\ \ 14 + 12 + x = 42 \\ x = 42 - 14 - 12 \\ x = 16$

7 0

3 years ago

Find a polynomial function of degree 3 with 2, i, -i as zeros.

sergiy2304 [10]

Answer:

$p(x)= x^3-2x^2+x-2$

Step-by-step explanation:

Here we are given that a polynomial has zeros as 2 , i and -i . We need to find out the cubic polynomial . In general we know that if $\alpha , \ \beta \ \& \ \gamma$ are the zeros of the cubic polynomial , then ,

$\sf \longrightarrow p(x)= (x -\alpha )(x-\beta)(x-\gamma)$

Here in place of the Greek letters , substitute 2,i and -i , we get ,

$\sf\longrightarrow p(x)= (x -2 )(x-i)(x+i)$

Now multiply (x-i) and (x+i ) using the identity (a+b)(a-b)=a² - b² , we have ,

$\sf \longrightarrow p(x)= (x-2)\{ x^2 - (i)^2\}$

Simplify using i = √-1 ,

$\sf \longrightarrow p(x)= (x-2)( x^2 + 1 )$

Multiply by distribution ,

$\sf \longrightarrow p(x)= x(x^2+1) -2(x^2+1)$

Simplify by opening the brackets ,

$\sf\longrightarrow p(x)= x^3+x-2x^2-2$

Rearrange ,

$\sf\longrightarrow \underline{\boxed{\blue{\sf p(x)= x^3-2x^2+x-2}}}$

4 0

2 years ago

The sum of three numbers is 102. The first number is 6 more than the second. The third number is 4 times the second. What are th

const2013 [10]

Answer:

1st number: 22

2nd number: 16

3rd number: 64

Step-by-step explanation:

x + y + z = 102

x = 6 + y

z = 4y

plug that in!

(6 + y) + y + (4y) = 102

get rid of the parenthesis (I added them so you could see what I was replacing) and add like terms.

6 + 6y = 102

move 6 to the other side.

6y = 96

y = 16

now that you know one number, you can solve the equations for the rest!

x = 6 + (16)

z = 4(16)

__________________________________________________________

x = 22

y = 16

z = 64

6 0

2 years ago

Given the function h(x) = – x2 + 4x + 10, determine the average

Nonamiya [84]

Answer:

x = 1

Step-by-step explanation:

4 0

2 years ago

How would you read the expression, 4^3? CLEAR CHECK four to the third power four to the three power three-fourths four-thirds

Vlad1618 [11]

Answer:

4 to the power of three

Step-by-step explanation:

5 0

2 years ago