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4 years ago

Simplify exponents. A, B, or C and explain.

Mathematics

2 answers:

kramer4 years ago

7 0

Answer:

$8^{-3}$

Step-by-step explanation:

$\frac{8^3}{8^6}$

in division f the base are same u can subtract their exponents

8^3-6

8^-3

Zina [86]4 years ago

5 0

8^-3 is the answer.. when two numbers of the same base in a fraction form are stacked on top of each other, the exponents always SUBTRACT.. so 3-6 is -3 and the base stays the same :)

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Write 9x² - 36x = 4y² + 24y + 36 in standard form

Kisachek [45]

Answer:

9·x² - 36·x = 4·y² + 24·y + 36 in standard form is;

(x - 2)²/2² - (y + 3)²/3² = 1

Step-by-step explanation:

The standard form of a hyperbola is given as follows;

(x - h)²/a² - (y - k)²/b² = 1 or (y - k)²/b² - (x - h)²/a² = 1

The given equation is presented as follows;

9·x² - 36·x = 4·y² + 24·y + 36

By completing the square, we get;

(3·x - 6)·(3·x - 6) - 36 = (2·y + 6)·(2·y + 6)

(3·x - 6)² - 36 = (2·y + 6)²

(3·x - 6)² - (2·y + 6)² = 36

(3·x - 6)²/36 - (2·y + 6)²/36 = 36/36 = 1

(3·x - 6)²/6² - (2·y + 6)²/6² = 1

3²·(x - 2)²/6² - 2²·(y + 3)²/6² = 1

(x - 2)²/2² - (y + 3)²/3² = 1

The equation of the hyperbola is (x - 2)²/2² - (y + 3)²/3² = 1.

5 0

3 years ago

Which equation is equivalent to y = x² + 24x - 18?

stira [4]

(X+12)^2 -18-(24/2)^2

(X+12)^2 -18-144

(X+12)^2-162

Your answer is 1.

7 0

3 years ago

A is the point (2, 3) and B is the point (7,-5).Find the equation of the line

madam [21]

Step-by-step explanation:

Find the gradient of AB

-2.5

Find the gradient of perpendicular

0.4

Make the equation

y= 0.4x + c

Apply point A

3= 0.4*2+c

3-0.8= c

c= 2.2

y= 0.8x + 2.2

5 0

3 years ago

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EMERGENCY PLEASE HELP STRUGGLING! The triangles in each pair are similar.

Ludmilka [50]

Answer: The missing length is 120 {option C}

Step-by-step explanation: What we have in the question is a triangle placed on top of another triangle and as shown in the attached diagram we can separate them into triangles BFC and GFH.

A close observation shows that line BC is parallel to line GH. Hence we have two similar triangles, and we can determine their similarity ratios as follows;

BF/FC = GF/FH

Similarly BF/BC = GF/GH

We can also express the following ratio

FC/FH = BC/GH

Therefore to calculate the missing side, which is GF, we can use the ratio

FC/FH = FB/FG

30/100 = 36/FG

By cross multiplication we now have 30 (FG) = 100 (36)

30FG = 3600

Divide both sides of the equation by 30

FG = 120

5 0

3 years ago

On Monday, 284 students went on a trip to the zoo. All 5

77julia77 [94]

Answer:

Step-by-step explanation:

$(284 - 4) \div 5 = 280 \div 5 = 56$

3 0

3 years ago

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