All categories

3 years ago

John is 3 years younger than twice Monica's age. If m represents Monica's age, which equation can be used to find j, John's age?

Mathematics

1 answer:

AnnZ [28]3 years ago

7 0

Answer:

J =2m -3

Step-by-step explanation:

2m is twice Monica's age

-3 represents 3 years younger

You might be interested in

For the following right triangle, find the side length x.

never [62]

Answer:

x = 10

Explanation:

Using Pythagoras Theorem:

a² + b² = c²

Solve:

8² + 6² = x²

x² = 64 + 36

x² = 100

x = √100

x = 10

8 0

2 years ago

Read 2 more answers

Simplify 2m - [n - (m - 2n)]. -3m - n 3m - n -3m - 3n 3m - 3n

zhenek [66]

Answer:

3m-3n

Step-by-step explanation:

We want to simplify the expression;

2m - [n - (m - 2n)].

We expand the parenthesis to obtain;

2m - (n - m + 2n)

2m - ( - m + 3n)

Expand further to get;

2m +m -3n

Combine the first two terms;

3m-3n

4 0

3 years ago

Read 2 more answers

Find a polynomial with integer coefficients that satisfies the given conditions. R has degree 4 and zeros 3 − 3i and 2, with 2 a

dolphi86 [110]

Answer:

The required polynomial is $P(x)=x^4-10x^3+46x^2-96x+72$ .

Step-by-step explanation:

If a polynomial has degree n and $c_1,c_2,...,c_n$ are zeroes of the polynomial, then the polynomial is defined as

$P(x)=a(x-c_1)(x-c_2)...(x-x_n)$

It is given that the polynomial R has degree 4 and zeros 3 − 3i and 2. The multiplicity of zero 2 is 2.

According to complex conjugate theorem, if a+ib is zero of a polynomial, then its conjugate a-ib is also a zero of that polynomial.

Since 3-3i is zero, therefore 3+3i is also a zero.

Total zeroes of the polynomial are 4, i.e., 3-3i, 3_3i, 2,2. Let a=1, So, the required polynomial is

$R(x)=(x-3+3i)(x-3-3i)(x-2)(x-2)$

$R(x)=((x-3)+3i)((x-3)-3i)(x-2)^2$

$R(x)=(x-3)^2-(3i)^2((x-3)-3i)(x-2)^2$ $[a^2-b^2=(a-b)(a+b)]$

$R(x)=(x^2-6x+9-9(i)^2((x-3)-3i)(x-2)^2$

$R(x)=(x^2-6x+18)(x^2-4x+4)$ $[i^2=-1]$

$R(x)=(x^2-6x+18)(x^2-4x+4)$

$R(x)=x^4-10x^3+46x^2-96x+72$

Therefore the required polynomial is $P(x)=x^4-10x^3+46x^2-96x+72$ .

3 0

3 years ago

IM RUNNING OUT IF TIME CAN SOMEONE PLEASE HELP

Elenna [48]

Answer:

the third option

Step-by-step explanation:

hope this helps! have a good day and stay safe!

3 0

3 years ago

Write the equation for the line whose slope is -1/4 and goes through the point (-2,6)

Kryger [21]

Answer:

$y = -\frac{1}{4} + \frac{11}{2}$

Step-by-step explanation:

use y = mx + b where:

y = y-coordinate = 6

m = slope = -1/4

x = x-coordinate = -2

b = y-intercept = what we're solving for to complete the equation

plug the values into the equation

$6 = -\frac{1}{4}(-2) + b$ multiply $-\frac{1}{4}$ and 2

$6 = \frac{1}{2} + b$ subtract $\frac{1}{2}$ from both sides

$b = \frac{11}{2}$

now we plug m and b into the equation and leave x and y as variables to get the final equation:

$y = -\frac{1}{4} + \frac{11}{2}$

8 0

3 years ago