Answer:
2b < 56
n = b - 2
b = n + 2
n < 27
b < 28
No, because the difference between Brittany and Nate's age is 2years
Step-by-step explanation:
A.)
Twice Brittany’s age is less than the age of Abraham Lincoln when he died. President Lincoln was 56 years old at the time of his death
Let Brittany's age = b
Twice Brittany's age = 2 × b = 2b
Lincoln's age = 56
2b < 56
B.)
Nate's age = n
Nate is 2 years younger than brittany who is aged 'b'
n = b - 2
C.) b = n + 2
D.)
If 2b < 56 and b = n + 2
2(n + 2) < 56
2n + 2 < 56
2n < 56 - 2
2n < 54 ; n < 27
2b < 56
b < 56/2
b < 28
No, because the difference between Brittany and Nate's age is 2years
Answer: radius = 47.8 inches
Step-by-step explanation:
An arc is a portion of the circumference of the circle. The formula for determining the length of an arc is expressed as
Length of arc = θ/360 × 2πr
Where
θ represents the central angle.
r represents the radius of the circle.
π is a constant whose value is 3.14
From the information given,
θ = 60 degrees
Length of arc = 50 inches
Therefore,
50 = 60/360 × 2 × 3.14 × r
Cross multiplying by 360, it becomes
18000 = 376.8r
r = 18000/376.8
r = 47.8 inches
Supposing that the trail mix was 5/8 pound, and Lisa gave 1/8 pound, then to know what is left we only have to subtract those fractions:
5/8 - 1/8 = 4/8
that is because we only subtract the numerators (upper part) of the fractions due to the fact that the denominators are equal, now, 4/8 can also simplify to 1/2
therefore there are left 4/8 pound of trail mix or, what is the same, 1/2 pound of it
To factor a trinomial, first we should factor out the GCF, or greatest common factor, shared by all of the coefficients and constants. The greatest common factor of -3, -21, and -30 is -3, therefore, this is the number we must factor out first.
When we factor out the GCF of -3, we get:
-3(q^2 + 7q + 10)
Next, we must look for two numbers that will serve as coefficients for the variables in factored form. These two numbers must add to 7 (the middle term) and multiply to 10 (the constant or last term). The two numbers that satisfy these parameters are 5 and 2.
Therefore, we must use these numbers to create factors of the innermost factor that we have left, to get:
-3(q+5)(q+2)
The above expression is your final answer, because you cannot factor any more. And remember: you can always check to make sure that your factoring is correct by multiplying out the factors and making sure you get your original trinomial.
I hope this helps!
