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3 years ago

A dolphin is 9 below the surface of the ocean.if it’s position can be recorded as -9 what word the position of 0 represent?

Mathematics

1 answer:

pashok25 [27]3 years ago

5 0

Answer: 0 represents the surface of the ocean

Step-by-step explanation: Words like 'below' indicate a negative number. Since the dolfin's positions is -9 below the sea level, the equation x-9=-9 can be created (let x = ocean surface level). Add 9 to both sides to cancel out -9 on the left side and isolate x. You have x = 0, so the ocean surface is 0.

Of course, you don't have to do all that! That was a in-depth explanation. Just make sure to look at the wording :P

You might be interested in

A researcher collects data on the relationship between the amount of daily exercise an individual gets and the percent body fat

fredd [130]

Answer: approximately 24

Step-by-step explanation:

We need to plot a regression line.

So we fit a model using the regression of Y on X, that an equation that predict Y for a given X using:

(Y -mean(Y ))= a(X-meanX)...........1

Where the formular of a is given the attachment.

N= the of individuals = 5

Y = amount of fat

X = time of exercise

mean(X )= sum of all X /N

= 131/5 = 26.2

mean(Y) = sum of all Y/N

= 104/5 = 20.8

a = N(SXY) - (SX)(SY)/ NS(X²) -(SX)²......2

SXY = Sum of Product X and Y

SX= sum of all X

SY = Sum of all Y

S(X²)= sum of all X²

(SX) = square of sum of X

a = -0.478

Hence we substitute into 1

Y-20.8 = -0.478 (X-26.2)

Y -20.8 = -0.478X - 12.524

Y = -0.478X + 33.324 or

Y = 33.324 - 0.478X (model)

When X = 20

Y = 33.324 - 0.478 × 20

Y = 33.324 - 9.56

Y = 23. 764

Y =24(approximately)

Carefully meaning of formula used in attachment to the solution they are the same.

4 0

3 years ago

Find all the zeros of the polynomial function p(x) = x3 – 5x2 + 33x – 29

hram777 [196]

Answer:

$\large \boxed{\sf \ \ x=1, \ \ x=2+5i, \ \ x=2-5i \ \ }$

Step-by-step explanation:

Hello,

I assume that we are working in $\mathbb{C}$ , otherwise there is only one zero which is 1. Please consider the following.

First of all, <u>we can notice that 1 is a trivial solution</u> as

$p(1) = 1^3-5\cdot 1^2 + 33\cdot 1-29=1-5+33-29=0$

It means that (x-1) is a factor of p(x) so we can find two real numbers, a and b, so that we can write the following.

$p(x)=(x-1)(x^2+ax+b)=x^3+ax^2+bx-x^2-ax-b=x^3+(a-1)x^2+(b-a)x-b$

Let's identify like terms as below.

a-1 = -5 <=> a = -5 + 1 = -4

b-a = 33

-b = -29 <=> b = 29

$\boxed{ \ p(x)=(x-1)(x^2-4x+29) \ }$

Now, we need to find the zeroes of the second factor, meaning finding x so that:

$x^2-4x+29=0 \ \text{ complete the square, 29 = 25 + 4} \\ \\ x^2-2\cdot 2 \cdot x+2^2+25=0 \\ \\ (x-2)^2=-25=(5i)^2 \ \text{ take the root } \\ \\x-2=\pm 5i \ \text{ add 2 } \\ \\ x = 2+5i \ \text{ or } \ x = 2-5i$