All categories

4 years ago

Check all the equations that are examples of joint variation. A) a= 3bc

Mathematics

2 answers:

nlexa [21]4 years ago

6 0

Answer:

A, C and E.

Step-by-step explanation:

Joint variation means that the dependent variable varies directly as 2 or more independent variables.

spin [16.1K]4 years ago

5 0

Answer:

For the Second Question: Which of these statements are true for joint variations? Check all that apply.

Answer: B and C

Step-by-step explanation:

You might be interested in

the diagram shows 3 identical circles inside a rectangle. each circle touches the other two circles and the sides of the rectang

Sergio [31]

Answer:

2640mm

Step-by-step explanation:

I'm assuming you need the area of the rectangle which the circles don't take up.

First, to find the area of the whole rectangle:

length x width

to find length:

the length is 1 circle, therefore it is the diameter of the circle, which is 32 x 2 = 64mm

to find width:

the width is 3 circles, which is the radius 6 times, so 32 x 6 = 192mm

So, area of rectangle = 64 x 192 = 12288mm

Now to find the area the circles take up:

area of 1 circle =

$\pi \times {r}^{2}$

$\pi \times {32}^{2}$

$1024\pi$

As we have 3 circles, we multiply this by 3:

$1024\pi \times 3 = 3072\pi$

Finally we subtract the area of the three circles from the area of the rectangle:

$12288mm - 3072\pi = 2637$

As we need to round it to 3 significant figures, the answer is 2640mm

7 0

2 years ago

(4a^3-6a^2)-(a^3-3a^2)

frozen [14]

7 0

4 years ago

Read 2 more answers

There you go beuty :)

Oxana [17]

Answer:

Thank you so much I appreciate all of your support for me

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Riley is half as old as Henry. The sum of their ages is 72. How old is henry going tobe nextyear?

AVprozaik [17]

Henry will be 37 next year. If Riley is half as old as Henry then you would divide 72 by 2. That gives you 36 which is how old they both are. Next year Henry will be 37. ( Riley would be too but it doesn't ask for her)

3 0

4 years ago

Can anyone help me do the questions that are circled with red and you don't need to do the graphing calculator thing, please

creativ13 [48]

Answer:

There are six problems circled in red.

As requested, only the analytical solutions are shown.

Question 16. Factor the polynomial

$44+15h+h^2$

Answer: (h + 4) (h + 11)

Question 17. Factor the polynomial

$40-22x+x^2$

Answer: (x - 2) (x -20)

Question 18. Factor the polynomial

$-24-10x+x^2$

Answer: (x - 12) (x + 2)

Question 19. Factor the polynomial

$-42-m+m^2$

Answer: (m - 7) (m + 6)

Question 20. Solve the equation

$x^2-7x+12=0$

Answer: x = 4 and x = 3

Question 22. Solve the equation

$x^2-6x=27$

Answer: x = 9 and x = - 3.

Explanation:

Question 16. Factor the polynomial

$44+15h+h^2$

1. Rearrange the terms:

$h^2+15h+44$

2. Open two parenthesis and place the common variable, h, as the first term of each.

$(h+a)(h+b)$

You are going to determine the values of a and b.

3. The values of a and b must satisfy that their product is 44 and their sum is 15.

a + b = 15 and a × b = 44

11 and 4 meet those conditions: 11 + 4 = 15, and 11 × 4 = 44.

So, the factored polynomial is:

$(h+4)(h+11)$

Question 17. Factor the polynomial

$40-22x+x^2$

1. Rearrange the terms:

$x^2-22x+40$

2. Write two binomials; each with first term x

(x-a)(x-b)

The negative sign for a comes from the negative sign before 22x; the negative sign of b comes from the product of the signs of -22x and + 40.

3. Find a and b such that a + b = 22 and a × b = 40

20 + 2 = 22 and 20 × 2 = 40, so the binomials are (x - 2) and (x - 20)

And the factored polynomial is:

$(x-2)(x-20)$

Question 18. Factor the polynomial

$-24-10x+x^2$

1. Rearrange the terms

$x^2-10x-24$

2. Sketch two binomials

$(x-a)(x+b)$

The negative sign for a corresponds to the negative sign for -10x, and the positive sign for b corresponds to the multplication of the signs of -10x and -4.

3. Find a and b such that their product is -24 and their aum is - 10.

Those numbers are - 12 and + 2:

- 12 + 2 = - 10
- 12 × (2) = - 24

Thus, the two factors are (x - 12) and (x +2).

And the factored polynomial is:

$(x-12)(x+2)$

Question 19. Factor the polynomial

$-42-m+m^2$

1. Rearrange the terms

$m^2-m-42$

2. Sketch the factors:

$(m-a)(m+b)$

The negative sign for a corresponds to the negative sign in front of m, the positive sign for b corresponds to the product of the signs of -m and -42.

3. Find two numbers, a and b, such that - a + b = - 1, and a × b = - 42

Those numbers are 6 and 7:

- 7 + 6 = - 1
-7 × 6 = - 42

Then, the factors are m - 7 and m + 6.

The factored polynomial is:

$(m-7)(m+6)$

Question 20. Solve the equation

$x^2-7x+12=0$

1. Factor the left side:

Find two numbers that sum -7 and their product is + 12. Those two numbers are - 4 and - 3.

$(x-4)(x-3)=0$

2. Use the zero product rule

x - 4 = 0 or x - 3 = 0

x = 4 or x = 3

Both, x = 4 and x = 3 are solutions.

Hence, the solutions are x = 4 and x = 3.

Question 22. Solve the equation

$x^2-6x=27$

1. Move 27 to the left side (using subtraction property of equalities):

$x^2-6x-27=0$

2. Factor the polynomial.

Find two numbers whose sum is - 6 and their product is - 27.

Those numbers are - 9 and + 3:

- 9 + 3 = - 6
- 9 × 3 = 27

$(x-9)(x+3)=0$

3. Zero product rule

$x-9=0\\ \\ x=9\\ \\ x+3=0\\ \\ x=-3$

The two solutions are: x = 9 and x = -3

3 0

4 years ago