Determining a Local Maximum and Minimum

Analyze the table of values for the continuous function,
f(x), to complete the statements.
A local maximum occurs over the interval __
A local minimum occurs over the interval ___

Answer:

y = -5/6x + 6

Step-by-step explanation:

Since we have 2 points, (6,0) and (6,1), we can calculate for the slope by using the formula

Slope = m = (y2 - y1)/(x2-x1) = (1-6)/(6-0) = -5/6

Then plug in m, x(from one of the point), and y(from one of the point) to the equation y = mx + b which get us 0 = -5/6*6+b if we use the point (6,0). Now we'll get b = 6. And then plug in -5/6 for m and 6 for b into the equation y = mx + b we'll get y = -5/6x + 6

Answer:

4x + 5y = 19 - (x + 5y = 16)

4x - x = 3x

5y - 5y = 0

19 - 16 = 3

3x = 3

x = 1

4x + 5y = 19

4(1) + 5y = 19

4 + 5y = 19

5y = 15

y = 3

Solution: (1,3)

Step-by-step explanation:

4x + 5y = 19 - (x + 5y = 16)

4x - x = 3x

5y - 5y = 0

19 - 16 = 3

3x = 3

x = 1

4x + 5y = 19

4(1) + 5y = 19

4 + 5y = 19

5y = 15

y = 3

Solution: (1,3)

Hope this helps! :)

Answer:

the can contained a total of 69.6 oz

Step-by-step explanation:

First, we find the total amount he used.

2/3 + 1/6 = 4/6 + 1/6 = 5/6

He used 5/6 of the can.

He used 58 oz.

That means that 5/6 of the can equals 58 oz.

We don't know the size of the can, so let x = original number of ounces in can.

5/6 of can = 58

5/6x = 58

Multiply both sides of the equation by 6/5 to find x.

6/5 × 5/6x = 6/5 × 58

x = 69.6

Answer: the can contained a total of 69.6 oz

varables:

O= omar songs\

S= total # of songs

equation:

2o+37= S

Hoped that helped:)

Answer:

  b.  f(x) = -2x +2

Step-by-step explanation:

The graph has a negative slope (m < 0) and a positive y-intercept (b > 0). The only equation with those characteristics is ...

  f(x) = -2x +2

_____

Additional comment

The line on the graph appears to fall by 2 grid squares for each 3 to the right. That means it has a slope of ...

  m = rise/run = -2/3

None of the offered equations have that slope. We have to assume the graph is "not to scale". Hence we can only comment on the signs of slope and intercept, and not their values.

You may want to discuss this question with your teacher.

its a ratio i think .......

Answer:

(-1,1)

Step-by-step explanation:

To find where both lines intersect, solve for x and y with substitution.

Equation 1.

-8x+3y=11

Equation 2.

y=3x+4

Substitute y from equation 2 into equation 1.

-8x+3(3x+4)=11

-8x+9x+12=11

x=-1

Now plug x into the second equation to solve for y.

y=3(-1)+4

y=-3+4

y=1

Both lines intersect at (-1,1)

Answer:

  (-1, 1)

Step-by-step explanation:

It's somewhat difficult to find the point of intersection when graphing these by hand, but a graphing calculator can show it easily.

The lines intersect at (-1, 1).

__

You are given an expression for y, which makes it easy to use substitution as a solution method. Using the second equation to substitute for y in the first equation, we get ...

  -8x +3(3x +4) = 11

  x +12 = 11 . . . . simplify

  x = -1 . . . . . . . subtract 12

Substituting back into the second equation, we find y to be ...

  y = 3(-1) +4 = 1

The lines intersect at (x, y) = (-1, 1).

_____

Additional comment

The slopes are 8/3 and 3. When hand-drawn lines have nearly the same slope, it is difficult to tell exactly where they intersect. Of course, a graphing calculator does not have the problem of finite line width and an apparent long region of intersection. It can pinpoint the intersection exactly.

Of course, "substitution" is not the only way this system of equations can be solved. However, for this system, it is one of the easiest when doing the solution by hand.

According to it's asymptotes, the function represented by the graph is:

[tex]y = \frac{3x + 5}{x + 1}[/tex]

The vertical asympotes of a function f(x) is the points which are outside the function domain.

In this problem, there is a vertical asymptote at x = -1, which is a zero of the denominator, hence the denominator is x + 1.

The horizontal asymptotes are the values of the function as x goes to infinity.

In this problem, they are given by:

[tex]\lim_{x \rightarrow -\infty} f(x) = -3[/tex]

[tex]\lim_{x \rightarrow \infty} f(x) = 3[/tex]

Hence, the option that satisfies it is:

[tex]y = \frac{3x + 5}{x + 1}[/tex]

To learn more about asymptotes, you can take a look at https://brainly.com/question/16948935.

The interpretation that describes a line of best fit of y = 9.5x for the data in the scatterplot is (a) For each 1 minute, the runner ran 9.5 miles

The equation of the line of best fit is given as:

[tex]y = 9.5x[/tex]

The line of best fit is represented as:

[tex]y = mx + b[/tex]

Where m represents the rate or slope.

So, by comparison:

[tex]m = 9.5[/tex]

This means that, the number of miles travelled every minute is 9.5

Hence, the true statement is (a)

Read more about regression equations at:

https://brainly.com/question/4333650

Answer:

I think it's 25 meters.

Hope that helps. x

Answer:

I think it will be 25 meters

Answer:

5/3

Step-by-step explanation:

let the number be x

3/5×[x] = 3x/5

3x/5=1

x=1÷3/5

x=5/3

Step-by-step explanation:

To solve both questions you will have to use the Pythagoras theorem

[tex] {c}^{2} = {a}^{2} + {b}^{2} [/tex]

c being the hypotenuse

so to find AB we say

[tex] {ap}^{2} = {pb}^{2} + {ab}^{2} [/tex]

To make AB the subject of the formula, we take PB over. Therefore:

[tex] {ab}^{2} = {ap}^{2} - {pb}^{2} [/tex]

now we just substitute

[tex] {ab}^{2} = {13}^{2} - {5}^{2} [/tex]

[tex] {ab}^{2} = 169 - 25[/tex]

[tex] {ab}^{2} = 144[/tex]

square root both sides of the equation

[tex]ab = 12[/tex]

We then use the same formula to find AQ(which is a hypotenuse)

[tex] {aq}^{2} = {ab}^{2} + {bq}^{2} [/tex]

[tex] {aq}^{2} = {12}^{2} + {9}^{2} [/tex]

[tex] {aq}^{2} = 144 + 81[/tex]

[tex] {aq}^{2} = 225[/tex]

square root both sides

[tex]aq = 15[/tex]

Answer:

y = -9

Step-by-step explanation:

Combine like terms first; 6y-8y=-2y and -8-6=-14  

-2y-14=4.

Then add 14 to both sides.

-2y=18

Lastly, divide both sides by -2

y=-9

Answer: = -9

Step-by-step explanation:

1. subtract -8-6 which equals -14

2. Combine like terms which are -8y and 6y and you should get -2y

3. Add 14 on both sides eliminate the -14 on one side. it should be -2y = 18

4. Now you want to get y all on its own so you divide -2 on both sides -2y/2 = 18/-2

5. and you should be able to cancel out -2y and get y= -9

Answer:

50 grams

Step-by-step explanation:

You simply subtract 70 from 120, and get 50.

Answer:

40 Grams!! i got it wrong and this was the answer

Step-by-step explanation:

[tex] \: \: \: \: \: \: [/tex]

If a value is greater than 100% of the original value, then it is larger than the original value. For example, 150% of 6 is 6 150% = 61.5 =9> 6. -

If a value is greater than 100% of the original value, then it is larger than the original value. For example, 150% of 6 is 6 150% = 61.5 =9> 6. -If the value is less than 1% of the original value, then it is smaller than the original value. For example, 0.1% of 6 is 6 0.1% = 6 0.001 0.006 < 6.

Answer: The value of R is 6.

Explanation: I recommend you go to these two links for an easier understanding:

https://www.wikihow.com/Find-the-Y-Intercept

https://www.wikihow.com/Find-the-X-Intercept

If the pair of points (5, 6) and (10, y) lie on a line with slope 4/5, then the value of y is 10

The slope m of the line passing through the points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is calculated as:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

For the line passing through points (5, 6) and (10, y)

[tex]x_1=5, y_1=6, x_2=10, y_2=y[/tex]

The slope, m = 4/5

Substitute these value into the slope formula and solve for y

[tex]m=\frac{y_2-y_1}{x_2-x_1} \\\\\frac{4}{5}=\frac{y-6}{10-5} \\\\\frac{4}{5}=\frac{y-6}{5}[/tex]

Cross  multiply:

4(5)  =  5(y-6)

4   =  y  -  6

Collect like terms

y  =  4  +  6

y  =  10

Learn more here: https://brainly.com/question/13763238

Answer:

84 and 144

Step-by-step explanation:

If the two numbers are  a  and  b  and their LCM is  x  and their HCF is  y  then there is a rule that is  a×b=x×y

in this case:

a×b=x×y

a×b=(504)×(24)

a×b=12096

when finding factors of 12096 that are between 60 and 160, we can see that 84 and 144 is the best pair.

hope this helps! :D

have a miraculous day!! <3

Answer:

Step-by-step explanation:

from the given information, I would say they are all false since congruent means they are identical in form, whereas these are similar parrellelograms since potentially if you upscaled one it would be close to the other

Answer:

30$ is 15% of 200$

Step-by-step explanation:

To find how much percent Jennie spent let's first find how much one percent of $200 is.

∴200/100=2

so one percent of 200 is 2

now let's find how much percent 30$ is of 200$

∴30/2=15

meaning that 30$ is 15% of 200$

Answer:

There is 7 students in each group

Step-by-step explanation:

So it's basically easy math 42 divided by 6 equals 7 :)

Hopes This Helps :)

Answer: 24 of 80 is 30%

Step-by-step explanation:

24 of 80 can be written as: 24/80

To find percentage, we need to find an equivalent fraction with denominator 100. multiply both numerator & denominator by 100: 24/80 x 100/100

= (24x100 / 80 ) x 1/10 = 30/100

Therefore, the answer is 30%

If you are using a calculator, simply enter 24÷80×100 which will give you 30 as the answer.

Answer:

option C can be used.

Step-by-step explanation:

hope this helps you.

Answer:

f(x) = x^2 is a classic example

f( 3 ) = 9 and

f( -3 ) = 9, but

f^(-1)[9] is undefined because the result can be 3 and -3

h(x)=3x−3, find h(3)

h(3)= 3(3)−3

= 9-3

= 6