Solving multi-step equations<br><br> 8- 5y = -3y

Use cubic regression to find a function that fits the following points.

8090 [49]

Answer:

y = 2x³ + x² - 4x + 6

Step-by-step explanation:

General formula:

y = ax³ + bx² + cx + d

If you replace point (0, 6) in the general formula, you get:

6 = a(0)³ + b(0)² + c(0) + d

6 = d

If you replace points (-1, 9), (1, 5) and (2, 18) in the general formula, you get the following system of equations:

9 = a(-1)³ + b(-1)² + c(-1) + 6

9 = -a + b - c + 6 (eq. 1)

5 = a(1)³ + b(1)² + c(1) + 6

5 = a + b + c + 6 (eq. 2)

18 = a(2)³ + b(2)² + c(2) + d

18 = 8a + 4b + 2c + 6 (eq. 3)

Adding equation 1 to equation 2:

14 = 2b + 12

(14 - 12)/2 = b

b = 1

Multiplying equation 1 by 2:

18 = -2a + 2b - 2c + 12 (eq. 4)

Adding equation 4 to equation 3, and replacing with b value:

36 = 6a + 6b + 18

36 = 6a + 6 + 18

(36 - 6 - 18)/6 = a

a = 2

Replacing a and b values in equation 1:

9 = -2 + 1 - c + 6

c = -2 + 1 + 6 - 9

c = -4

8 0

3 years ago

Read 2 more answers

HELP I DONT GET #10! PLZ HELP!

zhenek [66]

Yes, there will be more than 100 inches because there are 12 inches in a foot so it’s 100x12 which means it’s going to be 1,200 inches per second

8 0

3 years ago

2 (x - 2/3) = 0<br><br>solve for x

Rama09 [41]

X would equal 2/3 or in decimal form, 0.6 repeated

6 0

3 years ago

Read 2 more answers

the equation is -2x² = 4-3 (x + 1) and the question is justify that it is a 2nd degree equation with the unknown x complete.

Serggg [28]

Answer:

Please check the explanation.

Step-by-step explanation:

Given the equation

-2x² = 4-3 (x + 1)

-2x² = 4-3x-3

-2x² = -3x -7

0 = 2x² -3x -7

We know that the degree of the equation is the highest power of x variable in the given equation.

In the equation 0 = 2x² -3x -7 the highest power of x variable in the given equation is 2.

Thus, the degree of the equation is 2.

Also in the equation 0 = 2x² -3x -7, the unknown variable is 'x'.

Let us determine the value 'x'

2x² -3x -7 = 0

Add 7 to both sides

$2x^2-3x-7+7=0+7$

$2x^2-3x=7$

Divide both sides by 2

$\frac{2x^2-3x}{2}=\frac{7}{2}$

$x^2-\frac{3x}{2}=\frac{7}{2}$

Add (-3/4)² to both sides

$x^2-\frac{3x}{2}+\left(-\frac{3}{4}\right)^2=\frac{7}{2}+\left(-\frac{3}{4}\right)^2$

$x^2-\frac{3x}{2}+\left(-\frac{3}{4}\right)^2=\frac{65}{16}$

$\left(x-\frac{3}{4}\right)^2=\frac{65}{16}$

$\mathrm{For\:}f^2\left(x\right)=a\mathrm{\:the\:solutions\:are\:}f\left(x\right)=\sqrt{a},\:-\sqrt{a}$

solving

$x-\frac{3}{4}=\sqrt{\frac{65}{16}}$

$x-\frac{3}{4}=\frac{\sqrt{65}}{\sqrt{16}}$

$x-\frac{3}{4}=\frac{\sqrt{65}}{4}$

Add 3/4 to both sides

$x-\frac{3}{4}+\frac{3}{4}=\frac{\sqrt{65}}{4}+\frac{3}{4}$

$x=\frac{\sqrt{65}+3}{4}$

similarly solving

$x-\frac{3}{4}=-\sqrt{\frac{65}{16}}$

$x=\frac{-\sqrt{65}+3}{4}$

So the solution of the equation will have the values of x such as:

$x=\frac{\sqrt{65}+3}{4},\:x=\frac{-\sqrt{65}+3}{4}$

6 0

3 years ago

A store is selling 5 types of hard candies: cherry, strawberry, orange, lemon and pineapple. How many ways are there to choose:(

Volgvan

Answer:

The number of ways of selecting of n items form r different items = $^{(n+r-1)}C_{(r-1)}$

A store is selling 5 types of hard candies: cherry, strawberry, orange, lemon and pineapple.

A) How many ways are there to choose 32 candies?

So, n = no. of items = 32

r = no. of types of items = 5

So, No. of ways to choose 32 candies = $^{(32+5-1)}C_{(5-1)}$

= $^{36}C_{4}$

= $\frac{36!}{4!(36-4)!}$

= $58905$

So, No. of ways to choose 32 candies is 58905

B)32 candies with at least a piece of each flavor?

Out of 32 you choose 5 candies of different types

So, Remaining candies = 32 - 5 = 27

So, No. of ways to choose 27 candies = $^{(27+5-1)}C_{(5-1)}$

= $^{31}C_{4}$

= $\frac{31!}{4!(31-4)!}$

= $31465$

So, No. of ways to choose 32 candies with at least a piece of each flavor is 31465

C) 32 candies with at least 4 cherry and at least 6 lemon?

So, you already choose 6+4= 10

So, remaining candies = 32-10 = 22

So, No. of ways to choose 22 candies = $^{(22+5-1)}C_{(5-1)}$

= $^{26}C_{4}$

= $\frac{26!}{4!(26-4)!}$

= $14950$

Hence No. of ways to choose 32 candies with at least 4 cherry and at least 6 lemon is 14950

8 0

4 years ago

Solving multi-step equations 8- 5y = -3y - 31