Find the gradient of the curve y =2x³-7x+4when x=-2

Answer:

[tex]x=-2\\[/tex]

Step-by-step explanation:

[tex]8^x=\frac{1}{64}\\xlog8=log\frac{1}{64}\\x=\frac{log\frac{1}{64}}{\log8}\\x=-2[/tex]

First we write the equation given

Next we take the log of both sides. This turns [tex]x[/tex] into a normal term instead of an exponent, but turns [tex]8[/tex] and [tex]64[/tex] into the log version of themselves.

Next we can divide both sides by [tex]log8[/tex] to isolate [tex]x[/tex].

This gives us our answer of [tex]\boxed{-2}[/tex]

Answer:

x=2.7

Step-by-step explanation:

tan34 = x/4

x = 4tan34 = 2.7

If Larry is measuring the object's mass, the object he is most likely measuring is; D: A horse.

There are different units of measurement for different parameters such as meters for length, seconds for time, Amperes for current e.t.c.

Now, we are talking about measurement of an object mass in grams. This means it has to be a living thing and as such from the options, the only living thing is a horse.

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the lowest mileage rate is 25 miles per gallon.

Multiply 25 by 15 gallons

25 x 15 = 375 miles

Answer: B. 375 miles

Answer:

The measure of <YXP and <YZQ are 35 and 65 degrees respectively

Equilateral triangles are triangles that has equal sides and angles.

From the given diagram;

<YZQ + 90 + 25 = 180

<YZQ =180 -115

<YZQ = 65degrees

Determine the measure of <YXP

<YXP = 60 - 25 (XYZ is a 60degrees triangle)

<YXP = 35 degrees

Hence the measure of <YXP and <YZQ are 35 and 65 degrees respectively

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Answer:

y=586.4

Step-by-step explanation:

64^2= 64x64 = 4096

4096-7y+9=0

4105-7y=0    1. +7y on both sides

4105=7y       2. /7 on both sides

y=586.4

Answer:

490,000 grams

Step-by-step explanation:

To convert from kilograms to grams - multiply the number of kilograms by 1000. (there are 1000 grams in a kilogram)

[tex]490 * 1000 = 490,000[/tex]

Answer:

490000

Step-by-step explanation:

1 kg : 1000 gram

So,

490 kilograms : 490 ×1000 grams

: 490000 grams

Division is one of the four fundamental arithmetic operations. The number of pints of water Scott drank yesterday is 4.2 pints.

Division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.

A rope was 14.35 inches long. Megean cut the rope into 7 pieces of equal length. Therefore, the length of each piece of rope in inches will be,

Length of piece = 14.35 inches/7 = 2.05 inches

Scott drank 3.5 bottles of water yesterday . Each bottle contained 1.2 pints of water. Therefore, the number of pints of water Scott drank yesterday is,

Number of pints = 3.5 bottles × 1.2 pints = 4.2 pints

Hence, The number of pints of water Scott drank yesterday is 4.2 pints.

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Reason:

The largest sin(x) can get is 1, and the same goes for sin(3x).

Consequently, the largest 2sin(3x) can get is 2.

You can visually verify these claims by graphing each function with a tool like Desmos. Take note of the y coordinate of the highest points. See below.

Therefore, the largest f(x) = 2sin(3x)+C can get is 2+C or C+2

Answer:

Step-by-step explanation:

Givens

Comment

This is a proportion. A proportion is 2 equal ratios. If you know 3 parts of a proportion, you can solve for the 4th.

Equation

wage/time = wage2/time2                   Substitute values.

Solution

367.40 /22 = 584,50 /x                        Cross multiply

367.40x = 22 *584.50                          Simplify the right

367.40x = 12859                                   Divide both sides by 367.40

x = 12859/367.40

x = 35

Answer

Genesis will have to work 35 hours.

The product that is  undefined is known a CD, where C is a 3 x 1 matrix and D is a 1 x 2 matrix.

Looking at the product of matrix, note that to multiply  the two matrix, the column of the first matrix needs to have the same or equal to the row of the 2nd matrix.

And in this case (propensity), it is not satisfied by the first  option because:

C =  3 x 1  and

O= 2 x 1  matrix

In this case CD is therefore undefined.

So we can say that The product that is  undefined is known a CD, where C is a 3 x 1 matrix and D is a 1 x 2 matrix.

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The stem-and-leaf plots for both data set are shown in the attachment below.

Stem 5 would have 10 leaves.

For example, if 23, 24, 25, 28 are data points in a data distribution, 2 would be represented as a stem while 3, 4, 5, 8 would be the leaf of the stem. The data would be represented on the stem-and-leaf plot as: 2 | 3, 4, 5, 8.

Given the data, 42, 51, 56, 55, 51, 54, 51, 60, 62, 43, 55, 56, 61, 52, 69, 64, 46, 54, the stem-and-leaf plot is shown in the image attached below.

Stem 5 would have 10 leaves, as shown in the stem-and-leaf plot attached below.

The numbers 4 and 89 are represented on the second stem-and-leaf plot in the attachment below.

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Answer:

P = 20 cm

Step-by-step explanation:

the perimeter (P) is the sum of the 4 sides (s)  of the square

the sides of a square are congruent , then

P = 4s = 4 × 5 = 20 cm

Answer: 6.7 units for the diagonal from J to L

Step-by-step explanation:

you can use the Pythagorean theorem to find the diagonal (hypotenuse)

a^2 + b^2 = c^2

by counting units from M to J you have a length of 3 for the "a" value

by counting units from M to L you have a length of 6 for the "b" value

3^2 + 6^2 = c^2

9 + 36 = c^2

45 = c^2

take square root of both sides

6.7 = c

the diagonal is 6.7 units

The equation to represent the proportional relationship is c = 0.25d

Let c = the number of cans

Let d = the number of days

So, we have:

c = kd

Where k represents the constant of proportionality.

From the given parameters, we have:

3 = 12k

Divide both sides by 12

k = 0.25

Substitute k = 0.25 in c = kd

c = 0.25d

Hence, the equation to represent the proportional relationship is c = 0.25d

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Answer:

the original price of the product is $109.20

Answer:

109.2

Step-by-step explanation:

First multiply: 78 × 40 = 3120

Then Divide by 100: 3120 ÷ 100 = 31.2

Then add 31.2 to the sales price: 78 + 31.2 = 109.2

Answer:

p = 5

Step-by-step explanation:

Given equation:

2p - 3 = p+2

To Find:

Soln:

2p - 3 = p + 2

Subtract p from both sides:

=>2p-3−p = p+2-p

=>p-3 = 2

Add 3 to both sides:

=>p−3+3 = 2+3

=>p = 5

Hence,the value of p would be 5.

We can plug the value we got to the original equation to verify:

=> 2p - 3 = p + 2

=> 2(5) -3 = 5 + 2

=> 10 - 3 = 7

=> 7 = 7 [Proved]

Hence,this equation is true.

[tex]\rule{225pt}{2pt}[/tex]

Acronym PEMDAS rule means:

Answer:

p = 5

Step-by-step explanation:

First we add 3 to both sides to make :

2p = p + 5

Now we subtract p from both sides :

p = 5

Hope this helped and brainliest please

Answer:

[tex]\sf y = -\dfrac{1}{2} x +4[/tex]

Find slope (m):

[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]

[tex]\rightarrow \sf slope \ (m): \dfrac{0-4}{4-0} = -\dfrac{1}{2}[/tex]

Now, find equation:

[tex]\sf y -y_1 = m(x - x_1) \ \ \ \ \textsc where \ (x_1, y_1 ) \ are \ points[/tex]

[tex]\rightarrow \sf y - 4 = -\dfrac{1}{2} (x - 0)[/tex]

[tex]\rightarrow \sf y = -\dfrac{1}{2} x +4[/tex]

The income tax for the married couples under filing a joint return receives a standard deduction of $25,100.

An income tax is a type of tax that governments impose on income generated by businesses and individuals within their jurisdiction.

In this case, the income tax for the married couples filing a joint return receives a standard deduction of $25,100

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Answer:

(x-1)^2

=x^2 - 2x + 1

Step-by-step explanation:

hope this helps

Answer:

The area and the perimeter of the square barn which has each side 9 meters long is 81 m² and 36 m.

Step-by-step explanation:

The height of the cylinder will be 5 units based on the information given.

The cylinder has a volume of 45π cubic meters and the radius is 3 units.

The height will be calculated thus:

Volume of a cylinder = πr²h

45π = πr²h

45π = π(3²)h

45π = 9πh

h = 45π/9π

h = 5

Therefore, the height of the cylinder will be 5. units.

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Answer:

The correct answer is 8cm.

Step-by-step explanation:

Vol. Of cone= 1/3pi r²h

= 1/3×3.14× 8²×15

= 8×8×5×3.14

64× 5×3.14

= 320×314/100

=16×314=5024 cm³

Hope this helps:) Goodluck!

Answer:

The correct answer is 8cm.

Step-by-step explanation:

Vol. Of cone= 1/3pi r²h

= 1/3×3.14× 8²×15

= 8×8×5×3.14

64× 5×3.14

= 320×314/100

=16×314=5024 cm³

Hope this helps:) Goodluck!

There is more variability on glasses of doctor B's dataset than the glasses of doctor A's dataset

The dataset of doctor A is given as:

643 634 670 658 636 624 641 655 649 629

The dataset of doctor B is given as:

651 625 622 624 631 621 653 647 646 646

Using a statistical calculator, we have:

Doctor A

Hence, the mean absolute deviation is 11.28 for Doctor A’s and 12 for Doctor B’s data set on glasses

In a dataset, the larger the mean absolute deviations value, the larger the variation.

By comparison, 12 is greater than 11.28

Hence, there is more variability on glasses of doctor B's dataset than the glasses of doctor A's dataset

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Answer:

1. 4/12, 3/9, 2/6, 5/15

2. 4/8, 8/16, 6/12

3. 2/8, 4/16, 3/12

4. 6/8, 9/12, 4/16

Step-by-step explanation:

I'm assuming your question is about all 4 problems shown so I'll explain how to solve all of them.

1. The question is asking you to find an equivalent fraction to 1/3. The easiest way to do this is to reduce all of the options given.

To reduce fractions, first determine if the numerator and denominator share any factors. If they do, divide both terms by the shared factors until you no longer get whole numbers.

Step 1: reduce answer choices

6/16 = 3/8 (done by dividing both terms by 2)

4/10 = 2/5 (divide both by 2)

3/8 = 3/8 (fully reduced)

2/5 = 2/5 (fully reduced)

4/12 = 1/3 (divide both by 4)

5/10 = 1/2 (divide both by 5)

1/2 = 1/2 (fully reduced)

3/9 = 1/3 (divide both by 3)

2/6 = 1/3 (divide both by 2)

5/15 = 1/3 (divide both by 5)

3/8 = 3/8 (fully reduced)

3/4 = 3/4 (fully reduced)

2. This question is solved the same way as question 1.

Step 1: reduce answer choices

2/5 = 2/5

6/9 = 2/3

4/8 = 1/2

3/9 = 1/3

8/16 = 1/2

8/10 = 4/5

7/12 = 7/12

6/12 = 1/2

3. This question is solved the same way as questions 1 and 2.

Step 1: reduce answer choices

3/8 = 3/8

2/8 = 1/4

4/9 = 4/9

2/7 = 2/7

4/16 = 1/4

10/14 = 5/7

6/9 = 2/3

3/12 = 1/4

4. This question is solved the same way as questions 1, 2, and 3.

Step 1: reduce answer choices

6/8 = 3/4

4/9 = 4/9

4/6 = 2/3

9/12 = 3/4

10/12 = 5/6

6/9 = 2/3

12/16 = 3/4

7/9 =7/9

If your bottom time is 25 minutes, general rules recommend that you ascend immediately to 15 feet then remain there for 8 minutes. You should then go to the surface and not dive for 6 hours.

The recommended bottom time is 24 minutes which means that staying there for 25 minutes will have exceeded this recommendation.

You should immediately ascend to 15 feet or 5 meters, and then wait there for 8 minutes. Then return to the surface and avoid diving for the next 6 hours.

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The equation of the function is y = sec(2(x + π/6)) + 2

From the graph, we have the following parameters:

A secant function is represented as:

y = A sec(b(x + c)) + d

Where:

A = 0.5 * (max - min) = 0.5 * (3 - 1) = 1

b = Period = 2

c = Phase shift = π/6

d = 0.5 * (max + min) = 0.5 * (3 + 1) = 2

So, we have:

y = 1 * sec(2(x + π/6)) + 2

Evaluate

y = sec(2(x + π/6)) + 2

Hence, the equation of the function is y = sec(2(x + π/6)) + 2

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Answer

The answer is B on Edgenuit

Step-by-step explanation:

Desmos