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OverLord2011 [107]

3 years ago

9

What is the distance between -10 and 5 on the number line?

1 answer:

stiks02 [169]3 years ago

8 0

Answer:

the distance is 15

Step-by-step explanation:

because if we take away the negative on the -10 and make it positive 10 and add 5 it would be 15 spaces

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HELP WITH ALL <br> Determine the composite functions of the following set of functions

elixir [45]

QUESTION 1

i) Given $f(x)=5x-2$ and $g(x)=x^2$ .

$(f\circ g)=f(g(x))$

$(f\circ g)=f(x^2)$

We plug in $x^2$ into $f(x)=5x-2$

$(f\circ g)=5x^2-2$

ii) Given $f(x)=5x-2$ and $g(x)=x^2$ .

$(g\circ f)=g(f(x))$

$(g\circ f)=g(5x-2)$

We plug in $5x-2$ into $g(x)=x^2$

$(g\circ f)=(5x-2)^2$

$(g\circ f)=25x^2-10x-10x+4$

$(g\circ f)=25x^2-20x+4$

QUESTION 2

i) Given $g(x)=x^2-4$ and $h(x)=\sqrt{2x+1}$ .

$(h\circ g)=h(g(x))$

$(h\circ g)=h(x^2-4)$

We plug in $x^2-4$ into $h(x)=\sqrt{2x+1}$

$(h\circ g)=\sqrt{2(x^2-4)+1}$

$(h\circ g)=\sqrt{2x^2-8+1}$

$(h\circ g)=\sqrt{2x^2-7}$

ii) Given $g(x)=x^2-4$ and $h(x)=\sqrt{2x+1}$ .

$(g\circ h)=g(h(x))$

$(g\circ h)=g(\sqrt{2x+1})$

We plug in $\sqrt{2x+1$ into $g(x)=x^2-4$

$(g\circ h)=(\sqrt{2x+1})^2-4$

$(g\circ h)=2x+1-4$

$(g\circ h)=2x-3$

QUESTION 3

i) Given $g(x)=x+5$ and $h(x)=\sqrt{x-4}$ .

$(g\circ h)=g(h(x))$

$(g\circ h)=g(\sqrt{x-4})$

We plug in $\sqrt{x-4}$ into $g(x)=x+5$

$(g\circ h)=\sqrt{(x-4)+5}$

ii) Given $g(x)=x+5$ and $h(x)=\sqrt{x-4}$ .

$(g\circ g)=g(g(x))$

$(g\circ g)=g(x+5)$

We plug in $x+5$ into $g(x)=x+5$

$(g\circ g)=(x+5)+5}$

$(g\circ g)=x+10}$

QUESTION 4

The given functions are;

$f(x)=-2x+1$ and $g(x)=-x^2$

$f\circ f=f(f(x))$

$f\circ f=f(-2x+1)$

$f\circ f=-2(-2x+1)+1)$

$f\circ f=4x-2+1)$

$f\circ f=4x-1)$

ii)

$g\circ g=g(g(x))$

$g\circ g=g(-x^2)$

$g\circ g=-(x^2)^2$

$g\circ g=-x^4$

QUESTION 5

$f(x)=5x-2;g(x)=x^2;h(x)=-3x$

$h\circ g\circ f=h\circ (g(f(x))$

$h\circ g\circ f=h\circ (g(5x-2))$

$h\circ g\circ f=h\circ ((5x-2)^2)$

$h\circ g\circ f=h\circ (25x^2-20x+4)$

$h\circ g\circ f=h(25x^2-20x+4)$

$h\circ g\circ f=-3(25x^2-20x+4)$

$h\circ g\circ f=-75x^2+60x-12)$

ii.

$f\circ f\circ g=f\circ (f(g(x))$

$f\circ f\circ g=f\circ (f(x^2)$

$f\circ f\circ g=f\circ (5x^2-2)$

$f\circ f\circ g=f(5x^2-2)$

$f\circ f\circ g=5(5x^2-2)-2$

$f\circ f\circ g=25x^2-10-2$

$f\circ f\circ g=25x^2-12$

7 0

3 years ago

Write -2/9 as a decimal.

Inessa [10]

-2/9 is equal to -0.222222222 and it keeps on going hope it helps!

5 0

3 years ago

Read 2 more answers

How to do this question plz answer me step by step plzz

solniwko [45]

Answer:

25deg 55deg 100deg

Step-by-step explanation:

There are 180deg in a triangle. We know one angle is 30deg more and the other 75deg more than the smallest angle so we subtract that from 180.

180-75-30 = 75

We divide 75deg by 3 because there are 3 angles.

75/3 = 25

So we know the smallest angle is 25deg. We have to add 30deg to one angle and 75 to the other in oder to find the remaining angles.

25+30 = 55deg

25+75 = 100deg

So the angles are 25deg, 55deg, and 100deg.

5 0

3 years ago

Pizzas for a party cost $48 plus a tip of $8 for the delivery person. Seven people split the bill equally. Which expression show

marusya05 [52]

In total the amount of money needed to be paid is 56 (you get it from 48 plus 8)

then divide it by seven to split the bill evenly

the answer is C

6 0

3 years ago

15 is at least the quotient of a number and 6 increased by 3

crimeas [40]

Answer:

The number is $x\geq 72$

Step-by-step explanation:

Given:

Quotient $\geq$ 15

Let the number be $x$

The quotient is 15 of a number and 6 which is increaase by 3

Hence forming the inequality expression from the question given we get;

$\frac{x}{6}+3\geq 15$

Now Solving the above equation we get,

$\frac{x}{6}+3\geq 15\\\\\frac{x}{6}\geq 15-3\\\\\frac{x}{6}\geq 12\\\\x\geq 12\times6\\x\geq 72$

Hence the number is $x\geq 72$

4 0

3 years ago