Answer:
<D = 100
<E =30
<F =50
Step-by-step explanation
Given that triangles triangle ABC and triangle DEF are similar, this means that their angles are congruent i.e
<A = <D
<B = <E
<C = <F
Given
<A = 100 then <D = 100
<B = 30°, then <E = 30°
To get <F, we will use the expression
<D+<E+<F = 180 (sum of angles in a triangle is 180°)
100+30+<F = 180
130+<F = 180
<F = 180-130
<F = 50°
Hence the measure of <F is 50°
First you want to turn 1/3 into 5/15.
You can multiply 5/15 x 2 = 10/15. Thats as far as you get.
12/15
-10/15
__________
2/15 Pounds of granola left.
Answer:
B.) 1/7
Step-by-step explanation:
you have a total of 15 the you subtract one so you have
15-1= 14
you had 3 dimes and you took one out so you have
3-1=2
so you have 2/14 and in simplest for that is 1/7 because you divide both by 2
I hope this was good enough:
Answer:
Step-by-step explanation:
The formula for volume of a cylinder is
V = πr²h where r is the radius and h is the height.
We are given r = 5 and h = 2.5, plug those values in and simplify...
V = π(5²)(2.5)
V = π(25)(2.5)
V = 62.5π
Answer:
There are 24 nickels
Step-by-step explanation:
Let x represent the number of nickels
Let y represent the number of quarters
—————————————————————
Value Value
Type Number of of
of of each all
Coin Coin Coin Coin
—————————————————————
Nickels | x | $0.05 | $0.05x
Quarters | y | $0.25 | $0.25y
—————————————————————
Totals 28 ——— $2.20
•••••••••••••••••••••••••••••••••••••••••••••••••
The first equation comes from the “Number of coins” column.
(Number of nickels) + (Number of quarters) = (total number of coins)
Equation: x + y = 28
—————————————————————
The second equation comes from the “value of all coins” column.
(Value of all nickels) + (Value of all quarters) = (Total value of all coins)
0.05x + 0.25y = 2.20
Remove the decimals by multiplying each term by 100:
5x + 25y = 220
—————————————————————
So we have the system of equations:
{x + y = 28
{5x + 25y = 202
Solve by substitution. Solve the first equation for y:
x + y = 28
y = 28 - x
Substitute (28 - x) for y in 5x + 25y = 220
5x + 25 (28 - x) = 220
5x + 700 - 25x = 220
-20x + 700 = 220
-20x = -480
x = 24
The number of nickels is 24.
————————————————————
Substitute in y = 28 - x
y = 28 - (24)
y = 4
The number of quarters is 4.
————————————————————
Checking:
24 nickels is $1.20 and 4 quarters is $1.00
That’s 28 coins.
Indeed $1.20 + $1.00 = $2.20
————————————————————
