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The derivative of [tex]y = 3x^4 - 2x^3 - 7x + 5[/tex] with respect to x is

dy/dx = 12x³ - 6x² - 7.

We have,

The power rule states that if we have a term of form a[tex]x^n[/tex], the derivative with respect to x is given by [tex]d/dx(ax^n) = nax^{n-1}.[/tex]

Applying the power rule, we differentiate each term as follows:

[tex]d/dx(3x^4) = 3 \times 4x^{4-1} = 12x^3\\d/dx(-2x^3) = -2 \times 3x^{3-1} = -6x^2\\d/dx(-7x) = -7 \times 1x^{1-1} = -7[/tex]

d/dx (5) = 0 (since 5 is a constant)

Combining these derivatives, we get:

dy/dx = 12x³ - 6x² - 7

Therefore,

The derivative of [tex]y = 3x^4 - 2x^3 - 7x + 5[/tex] with respect to x is

dy/dx = 12x³ - 6x² - 7.

Learn more about derivatives here:

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Answer:

the answer is 6

Step-by-step explanation:

Answer:

The equation of the line in standard form is y = -1/2·x - 3

Step-by-step explanation:

From the given graph, the "x" and "y" coordinates points through which the line of the graph passes are;

(-4, -1), (-2, -2), and (2, -4)

The slope, m, of the graph is given as follow;

[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Therefore, by substituting the values of the coordinates for two known points, we have;

[tex]Slope, \, m =\dfrac{(-4) -(-1)}{2-(-4)} = \dfrac{(-4) + 1}{2+4 } = \dfrac{-3}{6} = -\dfrac{1}{2}[/tex]

The slope of the graph, m = -1/2

The equation of the graph on point and slope form is given as follows;

y - (-4) = -1/2(x - 2)

y = -x/2 + 1 - 4 = -x/2 - 3

The equation of the line in standard form, y = m·x + c  is y = -1/2·x - 3.

Answer:

70x+4^2+3

Step-by-step explanation:

Answer:

Third option

[tex]y-3=4(x-1)[/tex]

Step-by-step explanation:

Equation of straight line in point slope form is given as

[tex]y-y_1=m(x-x_1)[/tex]

Here

slope=m=4 and [tex](x_1, y_1) = ( 1, 3 )[/tex]

Equation of straight line having slope 4 and crossing from point (1, 3) is given as

[tex]y-3=4(x-1)[/tex]

Answer:

4t

Step-by-step explanation:

Answer:

10.75

Step-by-step explanation:

Answer:

6:8:10:12

Step-by-step explanation:

Scale factor of 2-

3:4:5:6

multiply each number by 2

6:8:10:12

Answer:

(x - 2) (x + 2) (x + 3)

Step-by-step explanation:

Dont know the full thing but hope some of this helps!

Answer:

(x - 2) (x + 2) (x + 3)

Step-by-step explanation:

Answer:

Step-by-step explanation:

1) Determine the GCF of the numbers 96 and 88

=> Decompose each number in their prime numbers:

=> 96 = (2^5)(3)

=> 88 = (2^3) (11)

=> GCF of 96 and 88 = 2^3 = 8

2) Determine the GCF of the letters, x^2 and x

=> x

3) Conclude the GCF of the terms is 8x

4) Now you can factor the expression by dividing each term by the GCF, 8x:

96 x^2 / (8x) = 12x

88x / (8x) = 11

The factored form is (8x) (12x + 11)

Answer:

Factor the GCF from 96x2 + 88x. Use the drop-down menus to complete the statements.

The GCF of 96x2 and 88x  ✔ 8x

Each term is written as a product, where one factor is the GCF, is ✔ 8x(12x) + 8x(11)

The factored form of the expression is ✔ 8x(12x + 11)

Answer:82feet tall

Step-by-step explanation:

Answer:

Step-by-step explanation:

incomplete question

Answer:

1. 5

2. [tex]\sqrt{85}[/tex]

3. [tex]\sqrt{26}[/tex]

Step-by-step explanation:

1. just count the units: 5 units

2. Find the slope = rise/run = -7/6

you now have a right triangle, one side is 7 units (from the rise), and the other is 6 units (from the run)

use the pythagorean theorem to find the hypotenuse.

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

[tex]7^{2} + 6^{2} = c^{2}[/tex]

49 + 36 = [tex]c^{2}[/tex]

85 = [tex]c^{2}[/tex]

[tex]\sqrt{85} = \sqrt{ c^{2}[/tex]

[tex]\sqrt{85} = c[/tex]

Simplify the radical, but [tex]\sqrt{85}[/tex] is farthest that it can go, so that is the answer.

3. same process as 2

slope = -1/5

[tex]1^{2} + 5^{2} = c^{2}[/tex]

1 + 25 = [tex]c^{2}[/tex]

26 = [tex]c^{2}[/tex]

[tex]\sqrt{26} = c[/tex]

That is the farthest it can go, so that will be the answer.

[tex]4c \: + 18 = 74[/tex]

[tex] \implies \: 4c = 74 - 18[/tex]

[tex] \implies \: 4c = 56[/tex]

[tex] \implies \: c = \cancel \dfrac{56}{4} [/tex]

[tex] \implies \: c = 14[/tex]

The value of c is 14 .

Answer:

14

Step-by-step explanation:

move all terms that don't contain c then solve.

Answer:

2.5

Step-by-step explanation:

10 / 4 = 2.5

Answer:

12x+20

Step-by-step explanation:

Perimeter of a garden = 4s, s being the length of the side

In this case, s = 3x+5

substitute the equation

4(3x+5)

=12x+20

Answer:

m=10

w=15

Step-by-step explanation:

m + w = 25

3m + 4w = 90

Let's do substitution, first by solving the first equation for m.

m = 25 - w

Substitute!

3(25 - w) + 4w = 90

75 - 3w + 4w = 90

w = 15

m = 25 - 15 = 10

Answer:

161.75

Step-by-step explanation:

45.28 divided by 7 = 6.47

6.47 per cande

6.47 times 25 = 161.75

Step-by-step explanation:

(x - 4)(x - 1)

= x² - x - 4x + 4

= x² - 5x + 4.

Answer:

[tex]\huge(x - 4)(x - 1) \\ \huge= {x}^{2} - x - 4x + 4 \\ \huge = {x}^{2} - 5x + 4[/tex]

Answer:

(1)  4

Step-by-step explanation:

Isolate x.

[tex]\frac{x-2}{3}[/tex] + [tex]\frac{1}{6}[/tex] = [tex]\frac{5}{6}[/tex]

[tex]\frac{x-2}{3}[/tex] = [tex]\frac{5}{6}[/tex] - [tex]\frac{1}{6}[/tex]

[tex]\frac{x-2}{3}[/tex] = [tex]\frac{2}{3}[/tex]

[tex]\frac{x-2}{3}[/tex] × 3 = [tex]\frac{2}{3}[/tex] × 3

x - 2 = 2

x = 2 + 2

x = 4

Answer: 3 1/2

Step-by-step explanation:

Yes

Answer:3 1/2

Step-by-step explanation:

Answer:

you didnt attach anything

Step-by-step explanation:

Answer:

6b + 8 = 7

Step-by-step explanation:

The proper translation of the sentence is 6b + 8 = 7.

Solving for b, we get 6b = -1 and b = -1/6

How is "6 - 0" part of this problem?  

Answer:

Step-by-step explanation:

The angles (2x- 10) and (4x+ 16) are consecutive interior angles and therefore are corresponding

Corresponding angles sum to 180

Answer:

2 block east from home

Step-by-step explanation:

Given an expression for how many blocks east Robert is from his home after finding his wallet as the sum 7+​(−​5),

Simplifying the given expression

7+(-5) = 7-5 (note that the product of a plus and minus sign will give a minus sign)

7-5 = 2

Hence Robert will be 2 block east from home

Answer:

[tex]\frac{5}{12}[/tex]

Step-by-step explanation:

[tex]\frac{3}{4} -\frac{1}{3}[/tex]

Find the common denominator and multiply each side by that number

[tex]\frac{9}{12} -\frac{4}{12}[/tex]

[tex]\frac{5}{12}[/tex]

For bolded part in explanation: 4·3=12 3·3=9

                                                    3·4=12 1·4=4

Answer:

2:55 P.M.

Step-by-step explanation:

First, add the amount of time Jim played outside; 45+55=100

100 minutes is equal to 1 hour 40 minutes.

If he left the playground at 4:35 P.M., then you have to subtract in order to find out when he arrived there.

Subtract 1 hour 40 minutes from 4:35 P.M. to then get 2:55 P.M.

To confirm your answer, you can add back the 1 hour and 40 minutes to 2:55 P.M. and you'll get 4:35 P.M.; back with what you started with.

Hope this helped !!!