Answer:
14
Step-by-step explanation:
f(x)=3x²+1
f(2) = 3 x 2² + 1 = 13
g(x) =1-x
g(2) = 1 - 2 = -1
(f-g)(2) f(2) - g(2) = 13 - (-1) = 14
Answer:
x = -7/4
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
- Subtract Property of Equality
<u>Algebra I</u>
Step-by-step explanation:
<u>Step 1: Define</u>
5x + 3 - 2x = 12 + 7x - 2
<u>Step 2: Solve for </u><em><u>x</u></em>
- Combine like terms: 3x + 3 = 7x + 10
- [SPE] Subtract 3x on both sides: 3 = 4x + 10
- [SPE] Subtract 10 on both sides: -7 = 4x
- [DPE] Divide 4 on both sides: -7/4 = x
- Rewrite: x = -7/4
<u>Step 3: Check</u>
<em>Plug in x into the original equation to verify it's a solution.</em>
- Substitute in <em>x</em>: 5(-7/4) + 3 - 2(-7/4) = 12 + 7(-7/4) - 2
- Multiply: -35/4 + 3 + 7/2 = 12 - 49/4 - 2
- Add: -23/4 + 7/2 = 12 - 49/4 - 2
- Add: -9/4 = 12 - 49/4 - 2
- Subtract: -9/4 = -1/4 - 2
- Subtract: -9/4 = -9/4
Here we see that -9/4 does indeed equal -9/4.
∴ x = -7/4 is the solution to the equation.
First step: name the sides according to geometry standards, namely, the sides are named the same lowercase letter as the opposing angle. A revised diagram is shown.
Second step: we need to know the relationships of the trigonometric functions.
cosine(A)=cos(63) = adjacent / hypotenuse = AC/AB .................(1)
sine(A)=sin(63) = opposite / hypotenuse = CB/AB .......................(2)
We're given AB=7, so
using (1)
AC/AB=cos(63)
AC=ABcos(63)=7 cos(63) = 7*0.45399 = 3.17993 = 3.180 (to three dec. figures)
Using (2)
BC/AB=sin(63)
BC=ABsin(63) = 7 sin(63) = 7*0.89101 = 6.237 (to three dec. figures).
Answer:
C
Step-by-step explanation:
Rectangle base, tiny triangle sides, but rectangle top
Using rigid motion, both of these triangles will be congruent. The reason is because rigid motions include reflections, translations, and rotations.
None of these transformations will affect the size or shape of the figure, therefore keeping them congruent.
