All categories

2 years ago

Given that (-5,-6) is on the graph of f(x), find the corresponding point for this function -1/3f(x).

Mathematics

1 answer:

masya89 [10]2 years ago

5 0

<h3>Answer: (-5, 2)</h3>

Explanation:

We multiply the y coordinate by -1/3 because of the notation (-1/3)*f(x). Recall that y = f(x). The x coordinate stays the same.

You might be interested in

A recipe for a cake needs 2 1/4 cups of cake. You are making 1/2 of the recipe. How many cups of flour do you need?

vazorg [7]

Answer:

4.5 or 1 1/8

Step-by-step explanation:

2 1/4 is a full box to back 1/2 of the flour you need to divide 2 1/4 in half

Half of 2 is 1 & half of 1/4 is 1/8

3 0

3 years ago

Read 2 more answers

Determine all prime numbers a, b and c for which the expression a ^ 2 + b ^ 2 + c ^ 2 - 1 is a perfect square .

kogti [31]

Answer:

The family of all prime numbers such that $a^{2} + b^{2} + c^{2} -1$ is a perfect square is represented by the following solution:

$a$ is an arbitrary prime number. (1)

$b = \sqrt{1 + 2\cdot a \cdot c}$ (2)

$c$ is another arbitrary prime number. (3)

Step-by-step explanation:

From Algebra we know that a second order polynomial is a perfect square if and only if $(x+y)^{2} = x^{2} + 2\cdot x\cdot y + y^{2}$ . From statement, we must fulfill the following identity:

$a^{2} + b^{2} + c^{2} - 1 = x^{2} + 2\cdot x\cdot y + y^{2}$

By Associative and Commutative properties, we can reorganize the expression as follows:

$a^{2} + (b^{2}-1) + c^{2} = x^{2} + 2\cdot x \cdot y + y^{2}$ (1)

Then, we have the following system of equations:

$x = a$ (2)

$(b^{2}-1) = 2\cdot x\cdot y$ (3)

$y = c$ (4)

By (2) and (4) in (3), we have the following expression:

$(b^{2} - 1) = 2\cdot a \cdot c$

$b^{2} = 1 + 2\cdot a \cdot c$

$b = \sqrt{1 + 2\cdot a\cdot c}$

From Number Theory, we remember that a number is prime if and only if is divisible both by 1 and by itself. Then, $a, b, c > 1$ . If $a$ , $b$ and $c$ are prime numbers, then $2\cdot a\cdot c$ must be an even composite number, which means that $a$ and $c$ can be either both odd numbers or a even number and a odd number. In the family of prime numbers, the only even number is 2.

In addition, $b$ must be a natural number, which means that:

$1 + 2\cdot a\cdot c \ge 4$

$2\cdot a \cdot c \ge 3$

$a\cdot c \ge \frac{3}{2}$

But the lowest possible product made by two prime numbers is $2^{2} = 4$ . Hence, $a\cdot c \ge 4$ .

The family of all prime numbers such that $a^{2} + b^{2} + c^{2} -1$ is a perfect square is represented by the following solution:

$a$ is an arbitrary prime number. (1)

$b = \sqrt{1 + 2\cdot a \cdot c}$ (2)

$c$ is another arbitrary prime number. (3)

Example: $a = 2$ , $c = 2$

$b = \sqrt{1 + 2\cdot (2)\cdot (2)}$

$b = 3$

4 0

3 years ago

Hello could you please help me

seropon [69]

I think .. correct me if i’m wrong
1. 3x+75=165
2. 3x+200

7 0

2 years ago

Change x + 2y = 6 into slope-intercept form.

mart [117]

Answer:

The slope intercept form involves solving for y, such that the equation looks like this: y = mx + b, where m is a constant representing the slope of the line, and b is a constant representing the value of the y-intercept.

Starting with the equation x+2y=6 and subtracting x from both sides gives 2y = -x + 6.

If we then divide each term by 2, we get the final result of y = -1/2x + 3.

Here we see that the slope (m) is equal to -1/2, and the y-intercept (b) is 3.

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Common ratio of fraction in geometric sequence? <br> 5/12,-1/6,1/15,-2/75,4/375

mestny [16]

To find the common ratio, u take ur 2nd term, and divide it by ur 1st term
(-1/6) / (5/12) =
-1/6 * 12/5 =
- 2/5 <== ur common ratio

6 0

3 years ago