MATHEMATICS HIGH SCHOOL

Mr. Morgan has five daughters. They were all born the number of years apart as the youngest daughter is old. The oldest daughter is 12 years older than the youngest. What are the ages of Mr. Morgan's daughters?

Answers

Answer 1

Answer:

Representing the scenario as an equation,the ages of Mr. Morgan's daughters are 3,6,9,12 and 15.

Given the parameters:

Number of daughters = 5

owing to constant difference between their ages :

Let 'oldest' = 5a , 'youngest' = a

Since we are told that the difference between the ages of the youngest and oldest is 12 :

5a - a = 12

5a - a = 12

4a = 12

a = 12/4

a = 3

Youngest is 3 ;

oldest = 5(3) = 15

The ages of the other 3 will be ;

3 * 2 = 6
3 * 3 = 9
3 * 4 = 12

Hence, their ages are 3,6,9,12 and 15.

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Answer 2

Answer: x, 2x, 3x, 4x, 5x

5x - x = 12

x = 3

The youngest is 3 and the oldest is 15.

The ages are: 3, 6, 9, 12, 15

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What is the initial value of the equation shown?y = −7x − 6

A. −13
B. −7
C. −6
D. −1

Answers

Answer:

Option C $-6$

Step-by-step explanation:

we know that

The initial value is the value of the function when the value of x is equal to zero

The initial value is the y-intercept of the function

In this problem we have

$y=-7x-6$ -----> equation of the line into slope intercept form

therefore

$m=-7$ -----> the slope

$b=-6$ ----> the y-intercept

The initial value is $-6$

C. −6, is the best option

(x − 2) is a factor of x4 + 2x3 − 7x2 − 8x + 12.

Answers

(x + 3) • (x + 2) • (x - 1) • (x - 2)

If f(x) = x - 2, what is f(-1)?

Answers

Step-by-step explanation:

f(x) = x - 2

f(-1) = -1 -2

= -3

Is √(9+16 ) the same as √(9 ) + √(16 ).

Answers

Answer:

Step-by-step explanation:

$√((9+16))$ = $√(25)$ = 5

compared to

$√(9)$ + $√(16)$ = 3 + 4 = 7

Thus

$√((9+16))$ ≠ $√(9)$ + $√(16)$

Put the following equation of a line into slope-intercept form, simplifying all fractions: 6x + 2y = -4.

Answers

Answer:

y = - 3x - 2

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given the equation

6x + 2y = - 4 ( subtract 6x from both sides )

2y = - 6x - 4 ( divide through by 2 )

y = - 3x - 2 ← in slope- intercept form

Final answer:

To put the equation 6x + 2y = -4 into slope-intercept form, subtract 6x from both sides of the equation. Then, divide both sides by 2 to isolate y. The resulting equation is y = -3x - 2.

Explanation:

To put the equation 6x + 2y = -4 into slope-intercept form, we need to solve for y. First, subtract 6x from both sides of the equation: 2y = -6x - 4. Then, divide both sides of the equation by 2 to isolate y: y = -3x - 2. This is now in slope-intercept form, where the slope is -3 and the y-intercept is -2. The question asks to put the equation 6x + 2y = -4 in slope-intercept form and simplify all fractions. Slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Here are the steps to follow: Isolate y on one side of the equation: 2y = -6x - 4

Divide all terms by 2 to solve for y: y = -3x - 2

So, the equation in slope-intercept form is y = -3x - 2. The slope (m) is -3 and the y-intercept (b) is -2.