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1 year ago

Determine intervals when the graph is concave up or concave down

Mathematics

1 answer:

topjm [15]1 year ago

5 0

The graph is concave has two curved part as follows;

The graph is concave up between;(0, 1), and (1, 0)

The graph is concave down between; (0, 1), and (-a, 2)

<h3>How can the direction of concavity be found?</h3>

The direction the concave part of the graph faces is given as follows;

The graph is concave up when the concave part faces up

It is concave down when the concave part faces down

From the given diagram, we have;

The graph is concave up between;

(0, 1), and (1, 0)

The graph is concave down between; (0, 1), and (-a, 2)

Where <em>a </em>is in the range; 1 < a < 2

Learn more about graphs here:brainly.com/question/17136458

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When you subtract 8from 10 what is the different

Alinara [238K]

Answer:

Step-by-step explanation:

Difference = 10 - 8 = 2

Hope it helps you in your learning process.

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3 years ago

The speeds of cars on a given i street we are normally distributed with a mean of 72 miles per hour and a standard deviation of

Ostrovityanka [42]

Answer: 72.78% of the drivers are traveling between 70 and 80 miles per hour based on this distribution.

Step-by-step explanation:

Let X be a random variable that represents the speed of the drivers.

Given: population mean : M = 72 miles ,

Standard deviation: s= 3.2 miles

The probability that the drivers are traveling between 70 and 80 miles per hour based on this distribution:

$P(70\leq X\leq 80)=P(\frac{70-72}{3.2}\leq \frac{X-M}{s}\leq\frac{80-72}{3.2})\\\\= P(-0.625\leq Z\leq 2.5)\ \ \ \ \ [Z=\frac{X-M}{s}]\\\\=P(Z\leq2.5)-P(Z\leq -0.625)\\\\\\ =0.9938-0.2660\ \ \ [\text{Using p-value calculator}]\\\\=0.7278$

Hence, 72.78% of the drivers are traveling between 70 and 80 miles per hour based on this distribution.

3 0

3 years ago

Determine the number of real solutions for each of the given equations. Equation Number of Solutions y = -3x2 + x + 12 y = 2x2 -

rosijanka [135]

Answer:

Step-by-step explanation:

Our equations are

$y = -3x^2 + x + 12\\y = 2x^2 - 6x + 5\\y = x^2 + 7x - 11\\y = -x^2 - 8x - 16\\$

Let us understand the term Discriminant of a quadratic equation and its properties

Discriminant is denoted by D and its formula is

$D=b^2-4ac\\$

Where

a= the coefficient of the $x^{2}$

b= the coefficient of $x$

c = constant term

Properties of D: If D

i) D=0 , One real root

ii) D>0 , Two real roots

iii) D<0 , no real root

Hence in the given quadratic equations , we will find the values of D Discriminant and evaluate our answer accordingly .

Let us start with

$y = -3x^2 + x + 12\\a=-3 , b =1 , c =12\\D=1^2-4*(-3)*(12)\\D=1+144\\D=145\\D>0 \\$

Hence we have two real roots for this equation.

$y = 2x^2 - 6x + 5\\$

$y = 2x^2 - 6x + 5\\a=2,b=-6,c=5\\D=(-6)^2-4*2*5\\D=36-40\\D=-4\\D$

Hence we do not have any real root for this quadratic

$y = x^2 + 7x - 11\\a=1,b=7,-11\\D=7^2-4*1*(-11)\\D=49+44\\D=93\\$

Hence D>0 and thus we have two real roots for this equation.

$y = -x^2 - 8x - 16\\a=-1,b=-8,c=-16\\D=(-8)^2-4*(-1)*(-16)\\D=64-64\\D=0\\$

Hence we have one real root to this quadratic equation.

7 0

3 years ago

Two roots of a third degree polynomial function f(x) are 4 and 4. Which statement describes the number and nature of all roots

VladimirAG [237]

Answer:f(x) has three real roots

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Write a unit rate for the situation. 880 calories in 8 servings

enyata [817]

Answer:

It would be 110 calories per serving

Step-by-step explanation:

So a unit rate is measuring how much of something is there if one unit of another thing is present. In this case, there are 8 servings and 880 calories. Now, simply divide both sides by 8 in order to get the unit rate for each serving:

880/8 ---> 110 calories per serving

5 0

3 years ago