1) If the hats cost $12.50 each and the materials cost $5.50, then the fashion designer makes ($12.50 - $5.50 =) $7 per hat. So, to work out how many hats you must make, you need to divide how much you spend on advertising by how much you make per hat so, $1,400 ÷ $7 = 200 hats.
$12.50 - $5.50 = $7
$1,400 ÷ $7 = 200 hats
and your variable and equation is:
y = number of hats needed to sell
advertising = earnings of 1 hat x number of hats
1,400 = 7y
1,400÷7 = y
200 = y
∴ The fashion designer must make and sell 200 hats to break even and get back her $1,400 spent on advertising.
2) So, you do the same on this one as well. If he makes $2 per book, and binding and packaging cost $0.80, then you need to $2 - $0.80 to find how much each book will make you, the answer is $1.20 per book. Then you need to $864 ÷ $1.20 which equals 720 books.
$2 - $0.80 = $1.20
$864 ÷ $1.20 = 720 books.
and your variable and equation would be:
y = unknown number of books needed to sell
initial costs = earnings of 1 book x number of books
864 = 1.20y
864 ÷ 1.20 = y
720 = y
∴ The puzzle expert must sell 720 books to break even and earn back his initial costs of $864.
** I hope that's what you meant (putting it in an algebraic equation) and I hope is correct **
Answer:
A = 169π/4
Step-by-step explanation:
From these two given points we find the length of the diameter of this circle, using the Pythagorean Theorem:
d^2 = (8 - 3)^2 + (13 - 1)^2, or
d^2 = 25 + 144 = 169
Thus, the diameter, d, of this circle is √169, or 13.
The radius is thus 13/2 units.
The area formula is A = πr^2. Here the area is
A = π(169/4), or A = 169π/4
Answer:
<h2>3.6</h2>
Step-by-step explanation:
It can be seen from the diagram that ΔDAC and ΔABD are right angled triangle.
Using the SOH, CAH, TOA trigonometry identity on ΔDAC where;
AC is the hypotenuse = 5.1
CD is the opposite (since it faces the angle directly)
According to SOH;
Sin = opp/hyp
sin
∠DAC = ∠BAD = 38.9°
According to ΔABD, the opposite side is DB which is unknown and the hypotenuse id AB i.e 5.7
Using SOH;
BD ≈ 3.6 to one dp
Answer:
x=7.5
Step-by-step explanation:
To show that the triangles are similar, we simply need to show that all sides are proportionate.
So, we create a proportion
Then we plug in the values
and can be simplified to , so that is our ratio of similarity
then we know
Now solve
1. Cross multiply
2×(2x-5) = 22
2. Distribute
4x-8 = 22
4x=30
x=7.5
There is your answer, x=7.5
Hope this helped.
Answer:
4 runs
Step-by-step explanation:
Set up the average equation as follows:
Remember 12 will be on the bottom since you have to add an extra score; they have 11 games already. Now, just solve for x.
6 x 12 = 68 + x
72 = 68 + x
4 = x
Hope this helps!