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3 years ago

The parabola y = x² - 4 opens: A.) up B.) down C.) right D.) left

Mathematics

1 answer:

fomenos3 years ago

3 0

Answer:

Step-by-step explanation:

Here the easy rules to remember the orientation of the parabolas are

a) If x is squared it opens up or down. And its coefficient of { $x^{2}[tex] is negative it opens down.b) If y is squared it opens side ways right or left. It its coefficient of [tex]y^{2}$

Hence in our equation of parabola

$y = x^ 2-4$

x is squared and its coefficient is positive , hence it opens up towards positive y axis.

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Let h(x)=e−x+kx, where k is any constant. For what value(s) of k does h have (a) No critical points? (b) One critical point? (c)

mrs_skeptik [129]

Answer:

a) for k≤0 , h has no critical point

b) for k>0 , h has a critical point

c) for k=0 , has a horizontal asymptote

Step-by-step explanation:

for the function

h(x)=e^(−x)+k

h has a critical point when the first derivative is =0 or is undefined. Since e^(−x) and k*x are continuos functions for all x then the second case is discarded. Then

dh/dx = -e^(−x)+k = 0

k = e^(−x)

x = ln (1/k)

since ln (1/k) should be possitive then k should be >0 . Thus h(x) has a critical point when k>0 and do not have any when k≤0

h has a horizontal asymptote when

lim h(x)=a when x→∞ (or -∞)

then

when x→∞, lim h(x)= lim e^(−x)+k*x = lim e^(−x) + k* lim x = 0 + k*∞ = ∞

on the other hand , when k=0 , lim h(x)= lim e^(−x)= 0 , then h has a horizontal asymptote for k=0

for x→(-∞) , e^(-x) rises exponentially , thus there is no k such that h has an horizontal asymptote when x→(-∞)

6 0

4 years ago

Hellp me solve this thanks

stellarik [79]

Answer:

c. 10 cm

Step-by-step explanation:

The parallel sides of trapizium are the bases so

base 1(B1) =9cm , base(B2)= 12cm

$area(a) = 105 {cm}^{2}$

the perpendicular distance means the height so lets find the height

area of trapizium= B1 + B2 × h

2

${105cm}^{2}(the \: given \: area) = \frac{9cm(the \: given \: base) + 12cm(the \: given \: base)}{2} \times h$

${105cm}^{2} = \frac{21cm}{2} \times h$

now we crisscross

${105cm}^{2} \times 2 = 21cm \times h$

${210cm}^{2} = 21cm \times h$

$\frac{ {210cm}^{2} }{21cm} = \frac{21cm \: }{21cm} \times h$

h = 10 cm

hope u like it ‍❤️‍‍❤️‍‍❤️‍

For any question comment me

4 0

3 years ago

What is the least common denominator of 7/9 and 1/12

kvv77 [185]

You could find this by going and doing:
9: 9,18,27,36,45,54,63,72...
12:12,24,36,48,60,72...
36 is the first # that pops up so you could do 36 as a common denominator

8 0

4 years ago

Describe how to draw a line that passes through the origin and has a slope of -2/-3?

Sophie [7]

First of all you know it wiill be a positive slope as both the rise and the run are negative. a negative divided by a negative equals a positive. so you can plot the points (2,3) and (-2,-3) as they will be points on this line. next you take a straight line and place it so that both points are intercepted. then extend the line outwards.

7 0

4 years ago

Suppose that a child in France pays five euros to visit the zoo. Five euros is the same as $6.80 in the U.S. In France, an adult

GarryVolchara [31]

6.8/5 = 1.36
1.36 x 8 = 10.88
This means that the cost of an adult is $10.88

3 0

3 years ago

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