Answer:
t = 5/2
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtraction Property of Equality
<u>Algebra I</u>
Step-by-step explanation:
<u>Step 1: Define</u>
3t + 7 = 2 + 5t
<u>Step 2: Solve for </u><u><em>t</em></u>
- [Subtraction Property of Equality] Isolate <em>t</em> terms: 7 = 2 + 2t
- [Subtraction Property of Equality] Isolate <em>t</em> term: 5 = 2t
- [Division Property of Equality] Isolate <em>t</em>: 5/2 = t
- Rewrite: t = 5/2
A) There are a number of ways to compute the determinant of a 3x3 matrix. Since k is on the bottom row, it is convenient to compute the cofactors of the numbers on the bottom row. Then the determinant is ...
1×(2×-1 -3×1) -k×(3×-1 -2×1) +2×(3×3 -2×2) = 5 -5k
bi) Π₁ can be written using r = (x, y, z).
Π₁ ⇒ 3x +2y +z = 4
bii) The cross product of the coefficients of λ and μ will give the normal to the plane. The dot-product of that with the constant vector will give the desired constant.
Π₂ ⇒ ((1, 0, 2)×(1, -1, -1))•(x, y, z) = ((1, 0, 2)×(1, -1, -1))•(1, 2, 3)
Π₂ ⇒ 2x +3y -z = 5
c) If the three planes form a sheath, the ranks of their coefficient matrix and that of the augmented matrix must be 2. That is, the determinant must be zero. The value of k that makes the determinant zero is found in part (a) to be -1.
A common approach to determining the rank of a matrix is to reduce it to row echelon form. Then the number of independent rows becomes obvious. (It is the number of non-zero rows.) This form for k=-1 is shown in the picture.
5200 - 700 = 4500
25 words per minute
25 × 60 = 1500 words (1 hour)
4500 ÷ 1500 = 3
Answer: 3 hours
What number is multiplied by 2 in left parentheses to get 8 in original expression? That is j, the coefficient for x^2. Follow the same pattern to find k, the middle coefficient.
j= x^2 coefficient
k= x coefficient
= 8x^3 – 125
= (2x−5)(4x^2+10x+25)
ANSWER: j= 4; k= 10
Hope this helps! :)
Answer:
(Exponential) Growth
Step-by-step explanation:
Given that the growth rate is greater than 1, this is exponential growth where the growth rate is 2%.