5. Write the following inequality in slope-intercept form. −8x + 4y ≥ −52 y ≤ 2x − 13 y ≥ 2x − 13 y ≤ 2x + 13 y ≥ 2x + 13

Your answers seem to be on the right track. These online homework apps can be picky about the answer they accept, though.

Given [tex]f(x) = x^4 - 2x^2 + 3[/tex], we have derivative

[tex]f'(x) = 4x^3 - 4x = 4x (x^2 - 1) = 4x (x - 1) (x + 1)[/tex]

with critical points when [tex]f'(x) = 0[/tex]; this happens when [tex]x=0[/tex] or [tex]x=\pm1[/tex].

We also have second derivative

[tex]f''(x) = 12x^2 - 4 = 12 \left(x^2-\dfrac13\right) = 12 \left(x - \dfrac1{\sqrt3}\right) \left(x + \dfrac1{\sqrt3}\right)[/tex]

with (possible) inflection points when [tex]x=\pm\frac1{\sqrt3}=\pm\frac{\sqrt3}3[/tex].

Intercept

If "intercept" specifically means [tex]y[/tex]-intercept, what you have is correct. Setting [tex]x=0[/tex] gives [tex]f(0) = 3[/tex], so the intercept is the point (0, 3).

They could also be expecting the [tex]x[/tex]-intercepts, in which case we set [tex]f(x)=0[/tex] and solve for [tex]x[/tex]. However, we have

[tex]x^4 - 2x^2 + 3 = \left(x^2 - 1\right)^2 + 2[/tex]

and

[tex]x^2-1\ge-1 \implies (x^2-1)^2 \ge (-1)^2 = 1 \implies x^4-2x^2+3 \ge 2[/tex]

so there are no [tex]x[/tex]-intercepts to worry about.

Relative minima/maxima

Check the sign of the second derivative at each critical point.

[tex]f''(-1) = 8 > 0 \implies \text{rel. min.}[/tex]

[tex]f''(0) = -4 < 0 \implies \text{rel. max.}[/tex]

[tex]f''(1) = 8 > 0 \implies \text{rel. min.}[/tex]

So we have two relative minima at the points (-1, 2) and (1, 2), and a relative maximum at (0, 3).

Inflection points

Simply evaluate [tex]f[/tex] at each of the candidate inflection points found earlier.

[tex]f\left(-\dfrac{\sqrt3}3\right) = \dfrac{22}9[/tex]

[tex]f\left(\dfrac{\sqrt3}3\right) = \dfrac{22}9[/tex]

The correct equation is [tex]x\cdot6=3x-4[/tex].

Let the number be [tex]x[/tex].

According to the question,

Number multiplied by [tex]6[/tex] [tex]=6x[/tex].

[tex]4[/tex] less than thrice the number  [tex]=3x-4[/tex].

Hence, the correct equation will be [tex]x\cdot6=3x-4[/tex].

To learn more about equations, refer: https://brainly.in/question/19089782.

#SPJ2

Answer:

A = 8000

B = 4000

C = 12000

Step-by-step explanation:

$24000 = A,B and C

A = 2B

B = 1/3C

solve for the letter that gets described the most

that letter is B

A =2B

B = 1/3C -> C = 3B

24000 = A + B + C

24000 = 2B + B + 3B

24000 = 6B

B = 4000

A =2B = 8000

C = 3B = 12000

Given the area and perimeter of the rectangular dining room, the dimensions of the dining room are 8m by 8m.

The area of rectangle is expressed as;

A = l × b

The perimeter of a rectangle is expressed as;

P = 2( l + b )

Given that;

We use the information given to form a system of equations.

A = l × b

64 = l × b

P = 2( l + b )

32 = 2( l + b )

Hence, we have;

64 = l × b --------- equ 1

32 = 2( l + b )-----equ 2

Lets make l the subject of the formula in equation 1

64 = l × b

l = 64/b -------------equ 3

Substitute equation 3 into equation 2

32 = 2( l + b )

32 = 2l + 2b

32 = 2(64/b) + 2b

32 = 128/b + 2b

Now, we solve for b.

32 = 128/b + 2b

32 - 2b = 128/b

32b - 2b² = 128

2b² - 32b + 128 = 0

We factor out 2

2( b² - 16b + 64) = 0

From perfect square rule

2( 8-b )² = 0

divide both side by 2 and take the square root of both side

( 8-b )² = 0

8-b = 0

b = 8

Substitute b=8 into equation 1

64 = l × b

64 = l × 8

l = 64/8

l = 8

Given the area and perimeter of the rectangular dining room, the dimensions of the dining room are 8m by 8m.

Learn more about area of rectangle here: brainly.com/question/12019874

#SPJ1

Answer:

choice C. Yes, this image proves the pythagorean theorem is true because 9 + 16 = 25

Step-by-step explanation:

Answer:

Each Cat video gets 750 comments

Each dog video gets 450 comments

Hope this helps you!

Answer:

He gets 750 comments on the cat videos and 450 on the dog videos the answer to the second question is yes

Step-by-step explanation:

khan :)

Answer: u - 8 = -9

Step-by-step explanation:

Given equation

-7u - 5 = 2

Add 5 on both sides

-7u - 5 + 5 = 2 + 5

-7u = 7

Divide -7 on both sides

-7u / (-7) = 7 / (-7)

u = -1

Substitute values into the goal expression

u - 8 = (-1) - 8 = [tex]\Large\boxed{-9}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

The answer is -9.

First, let's find the value of u.

Now, substitute in the expression.

Step-by-step explanation:

it's 2x²+8x

and I cannot understand your question

Answer:

x = - 6, x = - 1

Step-by-step explanation:

[tex]\frac{2x}{x+2}[/tex] = - [tex]\frac{6}{x+4}[/tex] ( cross- multiply )

2x(x + 4) = - 6(x + 2) ← distribute parenthesis on both sides )

2x² + 8x = - 6x - 12 ( subtract - 6x - 12 from both sides )

2x² + 14x + 12 = 0 ( divide through by 2 )

x² + 7x + 6 = 0 ← in standard form

(x + 6)(x + 1) = 0 ← in factored form

equate each factor to zero and solve for x

x + 6 = 0 ⇒ x = - 6

x + 1 = 0 ⇒ x = - 1

Answer:

Step-by-step explanation:

The radius of the base is the distance between the center of the circle and the edge of the base, therefore in this case it is equal to 3 in.

The volume of a cone is given by:

V = π * r² * h / 3

V = π * (3)² * 10 / 3

V = 94. 25 in³

Therefore, The volume of is 94. 25 in³.

Step-by-step explanation:

6.25 points

Find the GCF for the list.

10m4, 40m⁹

10m5

40m4

10m4

6.25 points

list

Expanding the desired form, we have

[tex]A \sin(\omega t + \phi) = A \bigg(\sin(\omega t) \cos(\phi) + \cos(\omega t) \sin(\phi)\bigg)[/tex]

and matching it up with the given expression, we see that

[tex]\begin{cases} A \sin(\omega t) \cos(\phi) = 2 \sin(4\pi t) \\ A \cos(\omega t) \sin(\phi) = 5 \cos(4\pi t) \end{cases}[/tex]

A natural choice for one of the symbols is [tex]\omega = 4\pi[/tex]. Then

[tex]\begin{cases} A \cos(\phi) = 2 \\ A \sin(\phi) = 5 \end{cases}[/tex]

Use the Pythagorean identity to eliminate [tex]\phi[/tex].

[tex](A\cos(\phi))^2 + (A\sin(\phi))^2 = A^2 \cos^2(\phi) + A^2 \sin^2(\phi) = A^2 (\cos^2(\phi) + \sin^2(\phi)) = A^2[/tex]

so that

[tex]A^2 = 2^2 + 5^2 = 29 \implies A = \pm\sqrt{29}[/tex]

Use the definition of tangent to eliminate [tex]A[/tex].

[tex]\tan(\phi) = \dfrac{\sin(\phi)}{\cos(\phi)} = \dfrac{A\sin(\phi)}{\cos(\phi)}[/tex]

so that

[tex]\tan(\phi) = \dfrac52 \implies \phi = \tan^{-1}\left(\dfrac52\right)[/tex]

We end up with

[tex]y(t) = 2 \sin(4\pi t) + 5 \cos(4\pi t) = \boxed{\pm\sqrt{29} \sin\left(4\pi t + \tan^{-1}\left(\dfrac52\right)\right)}[/tex]

where

• amplitude:

[tex]|A| = \boxed{\sqrt{29}}[/tex]

• angular frequency:

[tex]\boxed{4\pi}[/tex]

• phase shift:

[tex]4\pi t + \tan^{-1}\left(\dfrac 52\right) = 4\pi \left(t + \boxed{\frac1{4\pi} \tan^{-1}\left(\frac52\right)}\,\right)[/tex]

Using the combination formula, it is found that 436,270,780 different selections are possible.

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this problem, 7 numbers are taken from a set of 61, hence the number of different selections is given by:

C(61,7) = 61!/(7! x 54!) = 436,270,780

More can be learned about the combination formula at https://brainly.com/question/25821700

#SPJ1

The given number of balloons, green = 10, purple = 4, red = 5, tie-dye = 2, black = 3, gives;

a. 5/138

b. 25/276

c. 5/1012

d. 35/46

Given parameters;

Number of balls;

Green = 10

Purple = 4

Red = 5

Tie-dye = 2

Black = 3

Mode of selection = Without replacement

Number of balloons = 10+4+5+2+3 = 24

a. Probability of popping a red balloon = 5/24

Probability of popping a second red balloon = 4/23

Therefore;

Probability of popping two reds consecutively = 5/24 × 4/23 = 5/138

b. Probability of popping a red balloon = 5/24

Probability of popping a green balloon next = 10/23

Therefore;

Probability of popping a red and then a green balloon = 5/24 × 10/23 = 25/276

c. Probability that the first balloon that pops is a red = 5/24

Next balloon is a black = 3/23

Third balloon is red = 4/22

The probability, P, is therefore;

d. The probability that the first balloon is a tie-dye = 2/24 = 1/12

Therefore;

Probability that the first balloon is not a tie-dye = 1 - 1/12 = 11/12

Probability that the second balloon is not a tie-dye = 21/23

Similarly;

Probability that the third balloon is not a tie-dye = 20/22 = 10/11

Which gives;

The probability, P, of popping anything but a tie-dye on three consecutive throws is therefore;

Learn more about probability theory in mathematics?

https://brainly.com/question/13604758

#SPJ1

The upper quartile for the given data is 51 .

Given data: {51,49,52,46,50,38,38,45,34,52,46}

Data in arranged form: {34,38,38,45,46,46,49,50,51,52,52}

Find the median first, then the upper quartile. There are eleven data points, thus look at term six to determine the median as there are five data points on any side. The median is 46 because the sixth term is 46.

The upper extreme, 52, and the median are then used to determine the upper quartile; make sure not to include the median data point when dividing the groups. The upper quartile is the third term (between the median and upper extreme) because there would be two data points on each side if there were only five data points from the median to the upper extreme. The third term, which is 51, falls into the upper quartile.

Learn more about upper quartile here:

https://brainly.com/question/10005803

#SPJ1

Answer:

0.45 per egg

Step-by-step explanation:

since it's 3 dozen that mean it's gonna be 36 eggs divided by 16.20 so it's 0.45 per egg

Answer: an improper fraction

Step-by-step explanation:  An improper fraction is a fraction that is larger than 1 7/3 is larger than one because 7, the numerator is larger than the denominator so 7/3 is an improper fraction

Based on the stem and leaf plots given, the correct stem and leaf plot for the first table on per capita income is the third stem and leaf diagram.

For the table on the basketball tornament, the correct stem and leaf plot would be the last one.

First look at the key to the bottom right of the plot to see how to interpret the data.

The key on the third stem and lead plot says 1 I 2 = 12,000. This means that every steam and lead pairing is in thousands.

Based on the income per capita being in thousands, this is the most likely stem and lead plot for the first table on income per capita.

The second table about basketball tornament appearances is on single and double digits. Only a small stem and leaf key will do.

Look at the number of appearances. The minimum is 1. On a stem and leaf, this is shown as 0 I 1. Options A and B don't have this so we go to Options C and D.

As established, Option C is for data in their thousands so it is out. The correct stem and leaf plot is therefore Option D.

Find out more on stem and leaf plots at https://brainly.com/question/8649311

#SPJ1

Probability has to do with the possibility that an event may or may not happen.

The term probability has to do with the possibility that an event may or may not happen. The value of probability always ranges from zero to one.

Now;

Total number of fishes = 32 + 14 + 10 + 3 = 59

a) probability of catching a bass and then a carp = 32/59 * 10/59 = 320/3481

b) probability of catching two consecutive bull sharks= 3/59 * 3/59 = 9/3481

c) probability of catching  a fluke and then any different type of fish 14/59 * (32/59 + 10/59 + 3/59) = 14/59 * 45/59 = 630/3481

d) probability of catching  a bass, another bass, and a bull shark =  32/59 * 32/59 * 3/59 = 3072/205379

Learn more about probability:https://brainly.com/question/11234923

#SPJ1

Using the Central Limit Theorem, the standard error of the distribution of differences in sample means is of 1.97.

According to the Central Limit Theorem, it is given by the standard deviation of the sample divided by the square root of the sample size, hence:

It is given by the square root of the sum of the standard errors of each sample squared, hence:

s = sqrt(1.1² + 1.63²) = 1.97.

More can be learned about the Central Limit Theorem at https://brainly.com/question/16695444

#SPJ1

Answer:

5w^2 + 6w - 32

Step-by-step explanation:

Subtract as needed and combine like terms

(-2w^2 + 6w - 19) - (-7w^2 +13) dont forget to distribute the negative

so you get this:

-2w^2 + 7w^2 = 5w^2

6w

-19 - 13 = - 32

your answer is 5w^2 + 6w - 32

hope this helps :)

Hi :)

Let's solve by combining like terms

Combining like terms means you add or subtract

Solve by combining like terms

[tex]\implies\darkblue\sf{-2w^2+6w-19-(-7w^2+13)}\\\implies\darkblue\sf{-2w^2+6w-19+7w^2-13}\\\implies\darkblue\sf{-2w^2+7w^2+6w-19-13}\\\implies\darkblue\sf{\underline{5w^2+6w-32}}[/tex]

[tex]\tt{Learn\:More;Work\:Harder}[/tex]

:)

The amount of money invested in stocks was $50000, $90000 was invested in bonds and $75000 was invested in CDs

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depend on other variables while a dependent variable is a variable that depends on other variables.

Let x represent the amount of money invested in stocks, y represent bonds and z represent CDs, hence:

x + y + z = 215000     (1)

Also:

0.0225z + 0.02y + 0.092x = 8087.5    (2)

And:

y = 15000 + z    (3)

The solution of the equation is:

x = 50000, y = 90000 and z = 75000

The amount of money invested in stocks was $50000, $90000 was invested in bonds and $75000 was invested in CDs

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Sim wants to increase his waist size to 32.4 inches.

Sim wants the increase to be 8% of 30 inches.

The amount of increase Sim wants in his waist size exists

8% × 30 inches.

= 0.08 × 30 inches.

= 2.4 inches.

Adding the wanted increase to his present size would create Sim's waist size to be

30 in + 2.4 in = 32.4 inches.

Sim wants to increase his waist size to 32.4 inches.

Therefore, the correct answer is 32.4 inches.

To learn more about sizes refer to:

https://brainly.com/question/6285404

#SPJ9

a) The target cost for Model J20, assuming that the historical markup on product cost and selling price is maintained, is $200 per unit.

b) The required cost reduction per unit is $30 per unit ($230 - $200).

c) An evaluation of the three engineering improvements together to determine if the required cost reduction (drift) can be achieved as follows:

While the calculated cost reduction, including direct materials, is $25, the required reduction to achieve the target markup cost is $30.

Thus, the expected target cost reduction does not add up with the calculated cost reduction, envisaged by the engineers.

Model J20 Selling price per unit = $460

Direct materials $175

Direct labor 40

Factory overhead 15

Total $230

Direct labor rate = $30 per hour

Direct labor rate per minute = $0.50 ($30/60)

Direct labor hours per unit = 1¹/₃ hours ($40/$30) or 80 minutes

Normal direct labor time = 80 minutes

Plastic printer cover =        -15 minutes

Total new direct labor time = 65 minutes

Direct labor rate per unit = $32.50 ($0.5 x 65)

Additional inspection time = 6 minutes

Injection molding machine = 1 minute

Direct materials cost = $155 ($175 - $20)

Historical markup = 200% ($460/$230 x 100)

Target cost based on historical markup = $200 ($400 x 100/200)

Required cost reduction per unit is $30 per unit ($230 - $200)

1. Direct labor reduction of $7.50 per unit ($40 - $32.50)

2. Additional inspection $3 per unit (6 x $0.50)

3. Injection molding productivity improvement $0.50 per unit

4. Material cost reduction = $20

Total savings are $25 per unit ($7.50 - $3 + $0.50 + $20).

Learn more about target costing at https://brainly.com/question/20534175

#SPJ1

Answer:4 1/12.

Step-by-step explanation: First, you add 3 and a half with a quarter. A half equals two quarters so it equals 3 and 3/4.  Then, you add 3 3/4 with 1/3. A common denominator here is 12. 3/4 times 3/3 = 9/12. 1/3 times 4/4 = 4/12. 9+4 = 13. The answer is more than one so we carry and get 4 and 1/12.

Answer:

A:The Reqd. No. of Permutations=3360

Step-by-step explanation:

I couldn’t find the answer to B..sorry

The coordinates of the center is at (1, 0) and the length of the radius is 4 units.

An equation is an expression that shows the relationship between two or more variables and numbers.

The standard form of a circle is:

(x - h)² + (y - k)² = r²

Where (h, k) is the center of the circle and r is the radius.

The coordinates of the center is at (1, 0) and the length of the radius is 4 units.

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Answer:

Consider the table for y= |x+1| :

x   |   y

---------

0      1

1       2

2      3

-1      2

-2     3

This would give us the parent function of y=|x| but translated up one unit. It should look like a v starting at (0, 1)

Answer: -2

Step-by-step explanation:

The graph passes through (-2, 3) and (4, -9).

So, the average rate of change is [tex]\frac{-9-3}{4-(-2)}=\boxed{-2}[/tex]

1. To determine the better option between a 10% off coupon versus a $10 off coupon, it is necessary to determine the coupon price.

2. On the other hand, the $10 off coupon becomes better when the coupon price is less than $100.

3. The 10% off coupon and the $10 off coupon do not give the same amount of discount unless the coupon or list price is $100 in both situations.

A discount is a monetary reduction in the cost of a good or service offered to customers to increase trade.

Offering discounts enhances sales but not profitability.  So, there is a trade-off that must be considered properly.

Ordinarily, if the coupon price is more than $100, the 10% off coupon becomes better than the $10 off coupon.

For instance, if the coupon price is $110, the 10% off coupon will yield a discount amount of $11 ($110 x 10%), which is more than $10.

For instance, if the coupon price is $99, the discount amount will be $9.90, which is less than $10.

Thus, a 10% off coupon and a $10 off coupon do not offer the same discount amount unless the list price is $100, no more, no less.

Learn more about discounts at https://brainly.com/question/15407093

#SPJ1

Compare the discounts you would receive with a 10% off coupon versus a $10 off coupon.