MATHEMATICS HIGH SCHOOL

A rope attached to the top of a tent is staked into the ground.The rope is 4.5 ft long.The angle formed by the rope and the ground is 46 degrees.How far from the center of the base of the tent is the rope staked.

Answers

Answer 1

Answer:

Length of base = 3.126ft

Step-by-step explanation:

Using the SOHCAHTOA

We are looking for the length .

Lets call the length a,

Length of hypotenuse = 4.5ft

cos46 = a/4.5

4.5 x cos46 = a

a = 3.126

Length of base = 3.126ft

Answer 2

Answer: cos46 = a/4.5
4.5 x cos46 = a

a = 3.1 ft

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Use the functions f(x) = 3x – 4 and g(x) = x2 – 2 to answer the following questions. Complete the tables.

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For what value of the what value of the domain {–3, –1, 0, 2, 5} does f(x) = g(x) {–3, –1, 0, 2, 5} does f(x) = g(x)? Answer:

consider the relation {(–4, 3), (–1, 0), (0, –2), (2, 1), (4, 3)}.Graph the relation.
State the domain of the relation. State the range of the relation. Is the relation a function? How do you know? Answer:

2. graph the function f(x) = |x + 2|.

Answer:

consider the following expression. Rewrite the expression so that the first denominator is in factored form. Determine the LCD. (Write it in factored form.) Rewrite the expression so that both fractions are written with the LCD. Subtract and simplify.

Answer:

Answers

$1)\nf(x)=3x-4\n|\ \ \ x\ \ \ |\ \ -3\ \ \ |\ \ -1\ \ \ |\ \ \ 0\ \ \ |\ \ \ 2\ \ \ |\ \ \ 5\ \ \ |\n=========================\n|\ f(x)\ |\ \ -13\ \ |\ \ -7\ \ |\ -4\ \ |\ \ \ 2\ \ \ |\ \ \ 11\ \ |\n\nf(-3)=3\cdot(-3)-4=-9-4=-13\nf(-1)=3\cdot(-1)-4=-3-4=-7\nf(0)=3\cdot0-4=0-4=-4\nf(2)=3\cdot2-4=6-4=2\nf(5)=3\cdot5-4=15-4=11$

$g(x)=x^2-2\n|\ \ \ x\ \ \ |\ \ -3\ \ \ |\ \ -1\ \ \ |\ \ \ 0\ \ \ |\ \ \ 2\ \ \ |\ \ \ 5\ \ \ |\n=========================\n|\ g(x)\ |\ \ \ \ \ 7\ \ \ \ |\ \ -1\ \ \ |\ -2\ \ |\ \ \ 2\ \ |\ \ \ 23\ \ |\n\ng(-3)=(-3)^2-2=9-2=7\ng(-1)=(-1)^2-2=1-2=-1\ng(0)=0^2-2=0-2=-2\ng(2)=2^2-2=4-2=2\ng(5)=5^2-2=25-2=23\n\nf(x)=g(x)\ \ \ \Leftrightarrow\ \ \ x=2,\ \ \ \ because\ \ \ \ f(2)=2\ \ \ and\ \ \ g(2)=2$

$2)\nthe\ relation:\ \{(-4, 3), (-1, 0), (0, -2), (2,1), (4, 3)\}.\n\nthe\ domain:\ D=\{-4,-1,0,2,4\}\nthe\ range:\ R=\{3,0,-2,1\}\n\nThis\ relation\ is\ the\ function,\ because\ \ each\ number\n of\ the\ domain\ D\ has\ exactly\ one\ value\ in\ the\ range\ R.$

$3)\nf(x)=|x+2|\n\n|x+2|= \left \{ {\big{x+2\ \ \ \ \ if\ \ \ x \geq -2} \atop \big{-x-2\ \ \ if\ \ \ x<-2}} \right.$

Answer:

-11 and 0 for EDGE2020

f(4)= -11

If g(x)=2, x= 0

Step-by-step explanation:

Joshua went kayaking. It cost him $ 15 to rent the kayak. It also cost $ 6 for each hour spent on the lake kayaking. Joshua spent 2 $\frac{1}{2}$1
2 hours on the lake. How much was his total bill for the kayak rental and hours kayaking on the lake?

Answers

Step-by-step explanation:

The total bill will be the sum of the rent and the cost for the total time spent.

$15 + $6 * 2.5

$15 + $15

$30

a rectangle has a length that is nine feet less than four times its width. Its area is 90 ft. Algebraically determine the length of its width and length. Show work

Answers

Ok... after much confusion, I've come to the conclusion that you must have written the question wrong and it's actually the perimeter that is 90 feet so that's how I'm going to work it...

Width = w
Length = 4w - 9

P = 2w x 2L
90 = 2w + 2(4w - 9)
90 = 2w + 8w - 18
90 = 10w - 18
108 = 10w
108/10 = w
10 4/5 = w

Width is 10 4/5 ft

Length = 4w - 9
L = 4(10 4/5) - 9
L = 43 1/5 - 9
L = 34 1/5 ft

Length 34 1/5 ft Width 10 4/5 ft or
Length 34.2 ft and width 10.8 ft

What is the value of the function at x = -2?
y = -4
y = 0
y=2
y = 3

Answers

Answer:

Given the graph:
When x = -2, the value of y is 3
When y = -4, the value of x is -37
When y = 0, the value of x is -17
When y = 2, the value of x is -7
When y = 3, the value of x is -2

Step-by-step explanation:

To find the values of y = -4, 0, 2, and 3, we need to find the slope of the line:
Given that at x = -2, y = 3 and at x = 3, y = 4:
we can find the slope using these two given points on the graph:
slope = y2 - y1/x2 - x1

4-3/3-(-2) = 1/5
We can then write the equation in slope intercept form to find the value of b.

Substitute a point on the graph for the x and y to find b:
y = 1/5x + b
4 = 1/5(3) + b

4 - 3/5 = b
b = 3.4

y = 1/5x + 3.4
Plug in the values of y to find x
y = -4, x = -37
y = 0, x = -17
y = 2, x = -7
y = 3, x = -2

8 is 50% 0f what number

Answers

'is' in mathematics means equal
'of' in mathematics means multiplication

Translating 8 is 50% of what number into an equation, we get:

8 = 50% * x

50%, or 50 percent, is nothing but 50 over 100 or 50/100, which is the same as 1/2.

8 = 1/2 * x

Multiply 2 on both sides.

8 * 2 = 1/2 * 2 * x

16 = x

x = 16

8 is 50% of 16.

x=is the number.
50% of x=8
(50/100)x=8
x=(8*100)/50=16

Answer: 8 is 50% of 16

Simplify 6x - 4 - 6x

Answers

If you combine like terms, positive 6 x and negative 6 x cancel each other out and you are left with -4.

6x - 4 - 6x = = -4

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