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2 years ago

What is the range of y = (x - 5)^2 – 1?

Mathematics

1 answer:

Setler79 [48]2 years ago

8 0

1. The graph is a parabola.

2. The parabola opens up, because there's no negative number in front of $(x-5)^2$ .

3. The vertext is (5,-1), because of the vertex form.

This means that that -1 will be the least y-value used on the graph and the garph will open up from there.

The range is (-1, infinity) or { y | y > -1 }.

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Find a vector equation and parametric equations for the line through the point (7,4, 5) and parallel to the vector 3i 2j-k .

aleksley [76]

Answer: vector equation r = (7+3t)i + (4+2t)j + (5 - 5t)k

parametric equations: x = 7 + 3t; y = 4 + 2t; z = 5 - 5t

Step-by-step explanation: The vector equation is a line of the form:

r = $r_{0}$ + t.v

where

$r_{0}$ is the position vector;

v is the vector;

For point (7,4,5):

$r_{0}$ = 7i + 4j + 5k

Then, the equation is:

r = 7i + 4j + 5k + t(3i + 2j - k)

r = (7 + 3t)i + (4 + 2t)j + (5 - 5t)k

The parametric equations of the line are of the form:

x = $x_{0}$ + at

y = $y_{0}$ + bt

z = $z_{0}$ + ct

So, the parametric equations are:

x = 7 + 3t

y = 4 + 2t

z = 5 - 5t

4 0

2 years ago

Given f(c)=2x^2-3x and g(x)=4x+1 Evaluate (g•f)(x)

natulia [17]

The answer is
8x^4-10x^3-3x^2

6 0

2 years ago

Reynaldo rode his bike 2 miles north and 3 miles east. Which equation should he ise to find the distance, d, that takes him dire

ValentinkaMS [17]

Pythagorean theorem - a^2 + b^2 = c^2

2^2+3^2 = d^2
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6 0

2 years ago

Read 3 more answers

Solve.and show your work

Marysya12 [62]

Answer:

a) x > − 24 $\frac{3}{4}$

b) x < − 3

c) q < 56

Step-by-step explanation:

a) −2/5x−9<9/10

<=> 2/5x + 9 > − 9/10

<=> 2/5x > − 9/10 − 9

<=> 2×2/2×5x > − 9/10 − 9×10/10

<=> 4/10x > − 99/10

<=> x > − 99/4

<=> x > − 24 $\frac{3}{4}$

b) 4x+6<−6

<=> 4x < − 6 − 6

<=> 4x < − 12

<=> x < − 12/4

<=> x < − 3

c) q+12−2(q−22)>0

<=> q+12−2q −2×(−22)>0

<=> (q−2q) + (12+ 44) >0

<=> −q + 56 >0

<=> q < 56

8 0

2 years ago

11 The net force on a vehicle that is accelerating at a rate of 1.5 m/s² is 2,800 newtons. What is

ololo11 [35]

Answer:

$Mass = 1867kg$

Step-by-step explanation:

Given

$Force = 2800N$

$Acceleration = 1.5m/s^2$

Required

Determine the mass of the vehicle

This question will be answered using Newton's second law

$Force = Mass * Acceleration$

Substitute values for Force and Acceleration

$2800 = Mass * 1.5m/s^2$

Make Mass the subject

$Mass = \frac{2800N}{1.5m/s^2}$

$Mass = 1866.6667kg$

$Mass = 1867kg$ ---- approximated

Hence, the mass of the vehicle is 1867kg

4 0

2 years ago