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Leni [432]
3 years ago
9

The function f(x) is shown on the graph

Mathematics
2 answers:
PilotLPTM [1.2K]3 years ago
7 0

Answer:

A) -6

Step-by-step explanation:

f(0) means that the line x=0 passes through the function and only touches the x-coordinate -6

Bess [88]3 years ago
4 0
It -6 only, because it’s the only value that the function passes through the y axis
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Find the equation of the sphere centered at (-9,9, -9) with radius 5. Normalize your equations so that the coefficient of x2 is
olganol [36]
<h2><u>Answer</u>:</h2>

(a) x² + y² + z² + 18(x - y + z) + 218 = 0

(b) (x + 9)² + (y - 9)² + 56 = 0

<h2><u>Step-by-step explanation:</u></h2>

<em>The general equation of a sphere of radius r and centered at C = (x₀, y₀, z₀) is given by;</em>

(x - x₀)² + (y - y₀)² + (z - z₀)² = r²               ------------------(i)

<em>From the question:</em>

The sphere is centered at C = (x₀, y₀, z₀) = (-9, 9, -9) and has a radius r = 5.

<em>Therefore, to get the equation of the sphere, substitute these values into equation (i) as follows;</em>

(x - (-9))² + (y - 9)² + (z - (-9))² = 5²

(x + 9)² + (y - 9)² + (z + 9)² = 25      ------------------(ii)

<em>Open the brackets and have the following:</em>

(x + 9)² + (y - 9)² + (z + 9)² = 25

(x² + 18x + 81) + (y² - 18y + 81) + (z² + 18z + 81) = 25

x² + 18x + 81 + y² - 18y + 81 + z² + 18z + 81 = 25

x² + y² + z² + 18(x - y + z) + 243 = 25

x² + y² + z² + 18(x - y + z) + 218 = 0    [<em>equation has already been normalized since the coefficient of x² is 1</em>]

<em>Therefore, the equation of the sphere centered at (-9,9, -9) with radius 5 is:</em>

x² + y² + z² + 18(x - y + z) + 218 = 0

(2)  To get the equation when the sphere intersects a plane z = 0, we substitute z = 0 in equation (ii) as follows;

(x + 9)² + (y - 9)² + (0 + 9)² = 25

(x + 9)² + (y - 9)² + (9)² = 25

(x + 9)² + (y - 9)² + 81 = 25        [<em>subtract 25 from both sides</em>]

(x + 9)² + (y - 9)² + 81 - 25 = 25 - 25

(x + 9)² + (y - 9)² + 56 = 0

The equation is therefore, (x + 9)² + (y - 9)² + 56 = 0

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3 years ago
Question 6 of 10 Multiple Choice: Please select the best answer and click "submit." What is the greatest number of acute angles
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2. it can't have three because one of them is a right triangle do D doesn't add up. It can't have 0 because an obtuse angle plus a right angle would go over 180 degrees. So, the most it can have is 2 acute for example 90(right angle) 30(acute) and 60 (acute) is a possible answer. Also, a right angle can only have two acute angles since an obtuse angle would put it over 180 which was already stated
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The statements below can be used to prove that the triangles are similar. ? △ABC ~ △XYZ by the SSS similarity theorem. Which mat
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Solution:

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⇒\frac{AB}{XY}=\frac{BC}{ZY}=\frac{AC}{XZ}

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Answer:

A=202

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A=2(wl+hl+hw)

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Use a drawing of counters to show 5 and then +7
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