Answer:
Dimensions are 12 , 5
Step-by-step explanation:
Area of rectangular mural = length * width
length * width = 60 square feet
(x + 10)(x + 3) = 60
Use FOIL method
x*x + x*3 + 10*x + 10*3 = 60
x² + <u>3x + 10x</u> + 30 = 60 {Combine like terms}
x² +<u> 13x</u> + 30 - 60 = 0
x² + 13x - 30 = 0
Sum = 13
Product = -30
Factors = 15 , -2 (15+ (-2) = 13 ; 15*(-2) = -30)
x² + 15x - 2x - 30 =0 {Rewrite middle terms}
x(x + 15) - 2(x + 15) = 0
(x + 15)(x - 2) =0
x - 2 = 0 {Ignore (x +15) as dimensions wont have a negative value}
x = 2
x + 10 = 2 + 10 = 12
x + 3 = 2 + 3 = 5
Dimensions are 12 , 5
Divide the total amount she has by how much she needs per batch.
When dividing fractions, flip the second one over and then multiply straight across.
9/10 / 1/4 becomes: 9/10 x 4/1
9/10 x 4/1 = 36/10 = 3 6/10 = 3 3/5
She can make 3 more batches and have 3/5 of a teaspoon left over.
Composite is a number that is NOT prime. So we want to find an odd perfect square that IS prime to be a counterexample.
√36 = Not odd
√49 = 7 Factors only 1 * 7 so it is prime
√81 = 9 Factors 1, 3, 9 composite
√225 = 15 Factors 1,3, 5,9,15, 25, 45, 75, 225 composite
Counterexample for 2∧n - 1 Is prime
2^6 - 1 = 64 - 1 = 63 NOT PRIME Factors are: 1, 3, 7, 9,21, 63
2^5 - 1 = 32 - 1 = 31 Prime
2^3 - 1 = 8 - 1 = 7 Prime
2^2 - 1 = 4 - 1 = 3 Prime
Answer:
1 in 30
Step-by-step explanation:
1 in 6 chance Mary picks the red marble in the first place. After this there is a 1 in 5 chance her sister picks the blue one. 5 multiplied by 6 is 30.
Divide both sides by -0.7 to get rid of that pesky thing in the front
0.3x-0.8=6.4
add 0.8 to both sides
0.3x=7.2
divide both sides by 0.3
x=24
