We are given : The cost of tools for building wind chimes = $130.
Cost of material for each wind chime = $10.
We need to find the total cost of making 100 wind chimes.
Please note : $130 is the fix cost and $10 is the variable cost of each wind chime.
<em>In order to find the cost of 100 wind chimes, we need to multiply 100 by cost of making one wind chime and add the fix cost for tools for building wind chimes.</em>
Therefore, total cost of making 100 wind chimes = 10×100 + 130
= 1000+130
=1130.
<h3>Therefore, the total cost to make 100 wind chimes is $1130.</h3>
Answer:
The length of s is 5.1 inches to the nearest tenth of an inch
Step-by-step explanation:
In Δ RST
∵ t is the opposite side to ∠T
∵ r is the opposite side to ∠R
∵ s is the opposite side to ∠S
→ To find s let us use the cosine rule
∴ s² = t² + r² - 2 × t × r × cos∠S
∵ t = 4.1 inches, r = 7.1 inches, and m∠S = 45°
→ Substitute them in the rule above
∴ s² = (4.1)² + (7.1)² - 2 × 4.1 × 7.1 × cos(45°)
∴ s² = 16.81 + 50.41 - 41.1677568
∴ s² = 26.0522432
→ Take √ for both sides
∴ s = 5.10413981
→ Round it to the nearest tenth
∴ s = 5.1 inches
∴ The length of s is 5.1 inches to the nearest tenth of an inch
We can use linear combinations of the equations to eliminate variables.
3x - 4y = 1
-2x + 3y = 1
To eliminate y we'll make the linear combination of 3 times the first equation minus four times the second.
9x - 12y = 3
-8x + 12y = 4
Adding,
x = 7
We could solve for y directly but let's use another linear combination, twice the first plus three times the second:
2(3x - 4y) + 3(-2x + 3y)= 2(1)+3(1)
y = 5
Check: 3(7)-4(5)=1 good. -2(7)+3(5)=1 good.
Q18 Answer: (7,5)
y = -3x + 5
5x - 4y = -3
4y +1(5x - 4y) = 4(-3x + 5) + 1(-3)
5x = -12x + 20 -3
17 x = 17
x = 1
y = -3(1) + 5 = 2
Check: 5(1) - 4(2) = -3 good
Q19 Answer (1,2)
6x + 5y = 25
x = 2y + 24
6x = 12y + 144
5y = 25 - 12y - 144
17y = -119
y = -119/17= -7
x = 2y+24= 10
Check: 6(10)+5(-7)=25 good 2y+24=2(-7)+24=10=x good
Q20 Answer (10,-7)
3x + y = 18
-7x + 3y = -10
9x + 3y = 54
9x - -7x = 54 - -10
16x = 64
x=4
y = 18 -3x = 18-12=6
Check: 3(4)+6=18 good, -7(4)+3(6)=-10 good
Q21 Answer: (4,6)
Answer:
<em>Any width less than 3 feet</em>
Step-by-step explanation:
<u>Inequalities</u>
The garden plot will have an area of less than 18 square feet. If L is the length of the garden plot and W is the width, the area is calculated by:
A = L.W
The first condition can be written as follows:
LW < 18
The length should be 3 feet longer than the width, thus:
L = W + 3
Substituting in the inequality:
(W + 3)W < 18
Operating and rearranging:
Factoring:
(W-3)(W+6)<0
Since W must be positive, the only restriction comes from:
W - 3 < 0
Or, equivalently:
W < 3
Since:
L = W + 3
W = L - 3
This means:
L - 3 < 3
L < 6
The width should be less than 3 feet and therefore the length will be less than 6 feet.
If the measures are whole numbers, the possible dimensions of the garden plot are:
W = 1 ft, L = 4 ft
W = 2 ft, L = 5 ft
Another solution would be (for non-integer numbers):
W = 2.5 ft, L = 5.5 ft
There are infinitely many possible combinations for W and L as real numbers.
Answer:
Step-by-step explanation:
The volume of a rectanguiar shape like this one is V = L * W * H, where the letters represent Length, Width and Height. Here L is the longest dimension and is 28 - 2x; W is the width and is 22-2x; and finally, x is the height. Thus, the volume of this box must be
V(x) = (28 - 2x)*(22 - 2x)*x
and we want to maximize V(x).
One way of doing that is to graph V(x) and look for any local maximum of the graph. We'd want to determine the value of x for which V(x) is a maximum.
Another way, for those who know some calculus, is to use the first and second derivatives to identify the value of x at which V is at a maximum.
I have provided the function that you requested. If you'd like for us to go all the way to a solution, please repost your question.
