Angle A =x
Angle B is represented as 4x
Angle C is expressed as 5x-30
Hence, the correct responses are A, C, and D
Let’s define x as the amount invested by Sam in the first year.
Here are the corresponding expressions derived from the provided descriptions for Sam's investments.
For Sam:
2nd year: investment = 5x/2 - 2000
3rd year: investment = x/5 + 1000
The total Sam invested is:
x + (5x/2 - 2000) + (x/5 + 1000)
Next, we can form the expressions for Sally’s investments.
For Sally
1st year: investment = 3x/2 - 1000
2nd year: investment = 2x - 1500
3rd year: investment = x/4 + 1400
Thus, Sally's total investment is,
total = (3x/2 - 1000) + (2x - 1500) + (x/4 + 1400)
Setting both totals equal gives us:
(x) + (5x/2 - 2000) + (x/5 + 1000) = (3x/2 - 1000) + (2x - 1500) + (x/4 + 1400)
Solving for x,
x = 2000
For Sally's investment for the third year:
investment = x/4 + 1400 = (2000/4 + 1400) = 1900
RESULTS:
Sam's first year = $2000
Sally's third year = $1900
The total number of bills and coins is 14.
Step-by-step explanation:
To minimize the count of bills and coins, start with the largest denominations that fit within the amount.
The change due is $39.49.
Start with:
-$20 bill (largest under $39.49)
Remaining: $19.49
-$10 bill (largest under $19.49)
Remaining: $9.49
-$5 bill (largest under $9.49)
Remaining: $4.49
Then:
4 × $1 bills (to cover $4.49)
Remaining: $0.49
-$0.25 coin (quarter)
Remaining: $0.24
2 × $0.10 coins (dimes)
Remaining: $0.04
4 × $0.01 coins (pennies)
The final composition includes:
1 twenty-dollar bill
1 ten-dollar bill
1 five-dollar bill
4 one-dollar bills
1 quarter
2 dimes
4 pennies
Totaling 14 pieces.
Let x represent the hot dogs
and y represent the snacks
The equation x + y = 175
Rewrite x as 175 - y
And the second equation: 2.50x + 0.75y = 262.50
Substitute to get 2.50(175 - y) + 0.75y = 262.50
Which simplifies to 437.50 - 2.50y + 0.75y = 262.50
Rearranging gives -1.75y = -175
Hence, solving for y results in y = -175 / -1.75 = 100
Thus, 100 snacks and 75 hot dogs were sold
Solution: 49°, 49°, 82°
Detailed explanation:
Let x denote the base angles
and therefore the vertex angle is expressed as 2x - 16.
According to the Triangle Sum Theorem, the angles in a triangle total 180°
(x) + (x) + (2x - 16) = 180
4x - 16 = 180
4x = 196
x = 49
Base angles are: x = 49
The vertex angle: 2(49) - 16 = 82
