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3 years ago

1. Use "decomposing" to answer the question bellow.

Mathematics

1 answer:

snow_lady [41]3 years ago

7 0

Answer:

1A: 29 units²

1B: √29 units

2, 3, 4. see below

5. between 8 and 8.5

Step-by-step explanation:

1A: Split the given square up into 4 triangles and a square in the centre. You'll get 4 triangles of sides 5 and 2, and a centre square of sides 3.

Area = 4(0.5)(5 x 2) + (3²) = 29 units²

1B: Square root your answer in 1A. √29 units

Alternatively you can use Pythagoras' theorem on one of the triangles. √(5² + 2²) = √29 units

2. The area is exactly 17 units, because the area of a square is the length of its side squared. (√17)² = 17, hence the square's area is 17 units.

3. A number that can be expressed as a fraction (includes whole numbers). E.g. 1/2, 1/7, 4

4. A number that cannot be expressed as a fraction. E.g. π, e, √3

5. Consider the closest square numbers to 70. 70 is closer to 64 than 81 (difference of 6 vs 11). Hence √70 should be closer to 8 than 9. Your answer should be between 8 and 8.5.

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Terry evaluates 6 divided by 1/8 by using a related multiplication expression. Which multiplication expression should he use ?

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3 years ago

What is the equation of the quadratic graph with a focus of (8, −8) and a directrix of y = −6?

sp2606 [1]

Answer:

$y=-\frac{223}{28}(x-8)^2-7$

Step-by-step explanation:

we are given a quadratic equation

we know that quadratic equation is same as equation of parabola

so, we can use formula

$y=a(x-h)^2+k$

Focus is

$(h,k+\frac{1}{4a} )$

now, we can compare it with given focus

=(8,-8)

we get

$h=8$

$k+\frac{1}{4a}=-8$

Directrix is

$y=k-\frac{1}{4a}$

we are given directrix =-6

$k-\frac{1}{4a}=-6$

we got two equations as

$k+\frac{1}{4a}=-8$

$k-\frac{1}{4a}=-6$

now, we can add both equations

and we get

$k+\frac{1}{4a}+k-\frac{1}{4a}=-8-6$

$2k=-8-6$

$2k=-14$

$k=-7$

now, we can find 'a'

$k+\frac{1}{4\times -7}=-8$

$k=-\frac{223}{28}$

now, we can plug back all values

and we get

So, equation of parabola is

$y=-\frac{223}{28}(x-8)^2-7$

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3 years ago

The graph of a line with the following slope and y-intercept

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Answer:

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