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krok68 [10]
3 years ago
9

Consider the given function.

Mathematics
1 answer:
Arturiano [62]3 years ago
8 0

Answer:


Step-by-step explanation:

To find the intercept with the x axis, we make h (x) = 0.

0 = (x + 1) ^ 2 - 4

0 = x ^ 2 + 2x + 1 -4

0 = x ^ 2 + 2x - 3

0 = (x +3) (x-1)

x = 1

x = -3

To find the intercept with the y axis, we make x = 0.

y = (0+1)^2 -4

y = -3

For a quadratic equation of the form ax ^2 + bx+ c

The vertex is calculated with the formula x = -b/2a

So:

x = -2/2(1)

x = -1

Finally the axis of symmetry of a quadratic function always passes through the vertex.

So:

x = -1

Below is a graph for this function, where you can see the cut points with the axes, the vertex and axis of symmetry


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The table gives the boiling point of water at different altitudes.
stich3 [128]
Slope = raise / run

(211.1 - 212.0) / (0.5-0) = - 1.8

(210.2 - 211.1) / (1.0-0.5) = - 1.8

(208.4 - 210.2) / (2.0 - 1.0) = - 1.8

You can check, the other points. The slope is constant because the function is a linear equation,

Answer: - 1.8
4 0
3 years ago
Five less than the product of 3 and a number of 40 . Write in an equation
vagabundo [1.1K]

Answer:

I don't get the "number of 40" part, but here's my best shot!

3(40x)-5

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
George and Paula are running around a circular track. George starts at the westernmost point of the track, and Paula starts at t
arsen [322]

Answer:

George is 43.20 ft East of his starting point.

Step-by-step explanation:

Let Paula's speed be x ft/s

George's speed = 9 ft/s

Note that speed = (distance)/(time)

Distance = (speed) × (time)

George takes 50 s to run a lap of the track at a speed of y ft/s

Meaning that the length of the circular track = y × 50 = 50y ft

George and Paula meet 14 seconds after the start of the run.

Distance covered by George in 14 seconds = 9 × 14 = 126 ft

Distance covered by Paula in 14 seconds = y × 14 = 14y ft

But the sum of the distance covered by both runners in the 14 s before they first meet each other is equal to the length of the circular track

That is,

126 + 14y = 50y

50y - 14y = 126

36y = 126

y = (126/36) = 3.5 ft/s.

Hence, Paula's speed = 3.5 ft/s

Length of the circular track = 50y = 50 × 3.5 = 175 ft

So, in 4 minutes (240 s), with George running at 9 ft/s, he would have ran a total distance of

9 × 240 = 2160 ft.

2160 ft around a circular track of length 175 ft, means that George would have ran a total number of laps (2160/175) = 12.343 laps.

Breaking this into 12 laps and 0.343 of a lap from the starting point. 0.343 of a lap = 0.343 × 175 = 60 ft

So, 60 ft along a circular track subtends an angle θ at the centre of the circle.

Length of an arc = (θ/360°) × 2πr

2πr = total length of the circular track = 175

r = (175/2π) = 27.85 ft

Length of an arc = (θ/360) × 2πr

60 = (θ/360°) × 175

(θ/360°) = (60/175) = 0.343

θ = 0.343 × 360° = 123.45°

The image of this incomplete lap is shown in the attached image,

The distance of George from his starting point along the centre of the circular track = (r + a)

But, a can be obtained using trigonometric relations.

Cos 56.55° = (a/r) = (a/27.85)

a = 27.85 cos 56.55° = 15.35 ft

r + a = 27.85 + 15.35 = 43.20 ft.

Hence, George is 43.20 ft East of his starting point.

Hope this Helps!!!

6 0
3 years ago
3/8 or 11/12 which one is greater
Mazyrski [523]

Answer:11/12

Step-by-step explanation:

3 0
3 years ago
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Lucy reads 450 words in 3 minutes.
AnnyKZ [126]

Answer:

3000 words

Step-by-step explanation:

450 words in 3 minutes is 150 words in 1 minute. 20 minutes = 1 times 20.          

1 minute = 150 words so 150 words times 20 minutes = 3000 words.

5 0
3 years ago
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