MATHEMATICS HIGH SCHOOL

Cambridge has a job mowing lawns. He mowed 5 lawns last week and earned $82.50. The table shows his earnings for the week. Which coordinate pair represents the unit rate for this situation?A) (0, 0)
B) (1, 16.5)
C) (3, 49.5)
D) (5, 82.5)

Answers

Answer 1

Answer:

Answer:

Option B.

Step-by-step explanation:

Consider the below table attached with this question.

It is given that Cambridge has a job mowing lawns. He mowed 5 lawns last week and earned $82.50.

We need to find the coordinate pair that represents the unit rate for this situation.

Unit rate represent the value of dependent variable when the value of independent variable is 1.

In the given situation, dependent variable is earnings and independent variable is number of lawns.

5 lawns = $82.50

Divide both sides by 5.

1 lawns = $16.5

So, the unit rate rate is $16.5 and the required coordinates are (1,16.5).

Therefore, the correct option is B.

Answer 2

Answer: i think so its B 82.50÷5=16.5

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Solve the quadratic equation by completing the square.x^2+4x-6=0

First, choose the appropriate form and fill in the blanks with the correct numbers.
Then, solve the equation. Round your answer to the nearest hundredth.
If there is more than one solution, separate them with commas.

Answers

1.16, - 5.16

Working
Take 6 to the other side
x^2+4x = 6
Find the 3rd for the left hand side:
x^2+4x+ (4/2)^2= 6 + (4/2)^2
Factoring the LHS gives
(x+2)^2=10
Finding square roots on both sides:
x+2=square root of 10
x+2= +3.1623 or - 3.1623
x=3.1623-2
=1.16
or
x= -3.1623 - 2
= - 5.16

Let f(x) = x2 + x + 2 and g(x) = 2x2 + 5. Find f(g(x)). Show each step of your work.

Answers

For given functions f(x) and g(x) the composite function f(g(x)) is $f(g(x))=4x^4+22x^2+32$

What is function?

"It defines a relation between input values and output values."
"In function, for each input there is exactly one output."

What is composition of function?

"It is applying one function to the results of another."
"It is written is $\( f\circ g(x)=f(g(x))$ "
"First apply function f, then apply function g on the result of function f "

For given question,

We have been given two functions,

$f(x) = x^2 + x + 2,~g(x) = 2x^2 + 5.$

We need to find f(g(x))

This means we need to find composite function $\( f\circ g(x)=f(g(x))$

We have, $g(x) = 2x^2 + 5$

We find the value of f(x) for x = g(x)

$f(g(x))\n\n=f(2x^2 + 5)\n\n=(2x^2 + 5)^2 + (2x^2 + 5) + 2\n\n=[(2x^2)^2+2(2x^2)(5)+5^2]+2x^2+5+2\n\n=[4x^4+20x^2+25]+2x^2+7\n\n=4x^4+20x^2+2x^2+25+7\n\n=4x^4+22x^2+32$

Therefore, for given functions f(x) and g(x) the composite function f(g(x)) is $f(g(x))=4x^4+22x^2+32$

Learn more about compositefunction here:

brainly.com/question/20379727

#SPJ3

$f(g(x))=(2x^2+5)^2+2x^2+5+2\nf(g(x))=4x^4+20x^2+25+2x^2+7\nf(g(x))=4x^4+22x^2+32$

Leann makes an average of 36 cookies per week. About how many cookies will she make in a year

Answers

Answer:

The answer is 1872 cookies.

Step-by-step explanation:

First we know that in one year there are 52.18 weeks or 52 weeks. You take that number of weeks and multiply it by 36.

If you multiply 36 by 52 you get 1872 cookies.

Or, if you multiply 52.18 by 36 you get 1878.48

the hypotenuse of a right triangle is 16 and one of the angle is 45 . find the length of the side opposite to that angle ?

Answers

In a 90 45 45 triangle, the 2 legs each have a
length = hypotenuse / square root of 2
length = 16 / square root of 2
length =16 / 1.4142135624
length =11.313708499

Solving Trig. Equations:

csc^2x-2cot^2x=0

Answers

$csc^2x-2cot^2x=0;\ D:x\neq k\pi\ (k\in\mathbb{Z})\n\n(1)/(sin^2x)-2\cdot(cos^2x)/(sin^2x)=0\n\n(1-2cos^2x)/(sin^2x)=0\iff 1-2cos^2x=0\n\n-2cos^2x=-1\ \ \ /:(-2)\n\ncos^2x=(1)/(2)\n\ncosx=\sqrt(1)/(2)\ \vee\ cosx=-\sqrt(1)/(2)\n\ncosx=(\sqrt2)/(2)\ \vee\ cosx=-(\sqrt2)/(2)$

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A rectangle has length (x-3) cm and width 4 cm. The perimeter of the rectangle is 40 cm. Find the length.

Answers

we actually don't need to solve for x, just legnth

P=2(L+W)
40=P
L=x-3=L (since we are solving for Legnth not specifically x)
W=4

40=2(L+4)
divide both sides by 2
20=L+4
minus 4 both sides
16=L

legnth=16 cm (x=19 just fyi)

2(x-3)+2(4)=40
2x-6+8=40
2x+2=40
2x=38
x=19
Length=(x-3)=(19-3)=16 cm

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