9514 1404 393
Answer:
(b) Ingrid’s claim is correct, but her steps are incorrect
Step-by-step explanation:
As nearly as we can tell from the problem statement, Ingrid's table looks like the one attache. We have highlighted the incorrect steps.
Step 3 should read ...
0·cos(y) -(-1)·sin(y) = sin(y) . . . . . . . . . sin(-π/2) = -1
Step 4 should read ...
0 + sin(y) = sin(y)
So, Ingrid's conclusion is correct, but her steps are incorrect.
Answer: Dimes= 20, Nickels= 15
Step-by-step explanation:
Since we are looking for the amount of coins, we can use system of equations to solve for the amount of coins.
Equation 1:
0.1x+0.05y=2.75
This equation comes from the total cost. x stands for dimes and y stands for nickels. 0.1 is the worth of a dime and 0.05 is the worth of a nickel.
Equation 2:
x=2y-10
This equation comes from 10 less than twice the number of nickels.
We can use substitution to find x and y.
0.1(2y-10)+0.05y=2.75
0.2y-1+0.05y=2.75
0.25y-1=2.75
0.25y=3.75
y=15
There are 15 nickels.
Now that we have y, we can plug it back into the equation to find x.
x=2(15)-10
x=30-10
x=20
There are 20 dimes.
Answer:
A
Step-by-step explanation:
if it is at least -27 it will be greater than or equal to -27
Answer:
(-9,-2)
x= -9
y= -2
Step-by-step explanation:
x+5y=-19
x-5y=1
solve the equation
x+5y=-19
x=1+5y
substitute the value of x into an equation
1+5y+5y=-19
add 5y to 5y
1+10y=-19
subtract 1 to -19
10y=-20
divide both sides by 10
y= -2
substitute the value of y into an equation
x=1+5•(-2)
multiply 5 to -2
1+-10
add 1 to -10 but since 10 is a negative the equation is subtraction.
x= -9
(-9,-2)
Mickey's bowling score is 167 and Minnie's bowling score is 61
Step-by-step explanation:
The given is:
1. Mickey's bowling score is 16 less than 3 times Minnie's score
2. The sum of their scores is 228
We need to find the score of each one
Assume that the score of Minnie is x
∵ Minnie's score = x
∵ Mickey's score is 16 less than 3 times Minnie's score
- That means subtract 16 from 3 times Minnie's score
∴ Mickey's score = 3 x - 16
∵ The sum of their scores is 228
- Add their scores and equate the sum by 228
∴ x + 3 x - 16 = 228
- Add like terms in the left hand side
∴ 4 x - 16 = 228
- Add 16 for both sides
∴ 4 x = 244
- Divide both sides by 4
∴ x = 61
Substitute the value of x to find their scores
∵ Minnie's score is x
∴ Minnie's score = 61
∵ Mickey's score is 3 x - 16
∴ Mickey's score = 3(61) - 16 = 167
Mickey's bowling score is 167 and Minnie's bowling score is 61
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