The standard form of the equation of a circle is (x−3)^2+(y−1)^2=16.

Sample Work Help Needed! Please answer these questions and show the steps used to solve them. NO DECIMAL ANSWERS (except on thre

anygoal [31]

1. Using the exponent rule (a^b)·(a^c) = a^(b+c) ...

$\left(-2x^3y^4\right)\left(5x^9y^{-2}\right)=(-2)(5)\left(x^{(3+9)}y^{(4-2)}\right)\\\\=-10x^{12}y^{2}$

Simplify. Write in Scientific Notation

2. You know that 256 = 2.56·100 = 2.56·10². After that, we use the same rule for exponents as above.

$8 \left(32\times 10^{11}\right)=(8)(32)\times 10^{11}=256\times 10^{11}=2.56\times 10^{13}$

3. The distributive property is useful for this.

(3x – 1)(5x + 4) = (3x)(5x + 4) – 1(5x + 4)

... = 15x² +12x – 5x –4

... = 15x² +7x -4

4. Look for factors of 8·(-3) = -24 that add to give 2, the x-coefficient.

-24 = -1×24 = -2×12 = -3×8 = -4×6

The last pair of factors adds to give 2. Now we can write

... (8x -4)(8x +6)/8 . . . . . where each of the instances of 8 is an instance of the coefficient of x² in the original expression. Factoring 4 from the first factor and 2 from the second factor gives

... (2x -1)(4x +3) . . . . . the factorization you require

8 0

3 years ago

3. ms. Johnson placed two different orders with TR's special item store. each order was for 40 jars with the circus logo imprint

denis23 [38]

1.The height is 6 inches ad the width (diameter) is 3 inches!
2. So the jars are Volume ≈ 42.41 inches so each boy needs 200 / 42.41 which equals approximately 4.72 inches per jar. So if wach boys have half the amount of jars which is 20 you multiply 20 by 4.72 which is 94.4 inches for each boy!

3 0

3 years ago

Help me please asap I need to know fully how to solve this problem

vivado [14]

Consider the absolute value, because we only worry about the quadrant later.

$\text{Consider: } sin(A) = |-\frac{\sqrt{3}}{4}|$
$sin(A) = \frac{\sqrt{3}}{4}$

Thus, we know that the hypotenuse has a length of 4 units, and the side opposite the angle, A is √3, because this is the nature of the sine function in relation to its triangular component.

The missing side can be found using Pythagoras' Theorem:
4² - (√3)² = x²
16 - 3 = x²
13 = x²
x = √13

$\therefore tan(A) = \pm \sqrt{\frac{3}{13}}$

Since angle A is in the third quadrant, the tangent function will produce a positive angle.

$tan(A) = \sqrt{\frac{3}{13}}$
$\text{Rationalise the denominator: } \frac{\sqrt{3}}{\sqrt{13}} \cdot \frac{\sqrt{13}}{\sqrt{13}}$

$tan(A) = \frac{\sqrt{39}}{13}$