(a) 95% of what is 57?

(b) What number is 35% of 40?

a) The value of [tex]k'(0)[/tex] is [tex]\frac{3\sqrt{3}}{2}[/tex].

b) The value of [tex]m'(5)[/tex] is approximately -0.034.

c) The value of [tex]x[/tex] is approximately 0.622.

a) [tex]f(x)[/tex] is a piecewise function formed by two linear functions, whose form is defined by the following definition:

[tex]f(x) = \frac{y_{2}-y_{1}}{x_{2}-x_{1}} \cdot x + b[/tex] (1)

Where:

Now we proceed to determine the linear functions:

Line 1: [tex]x \in [-1, 2)[/tex]

[tex](x_{1}, y_{1}) = (0, 3)[/tex], [tex](x_{2}, y_{2}) = (1, 5)[/tex], [tex]b = 3[/tex]

[tex]f(x) = \frac{5-3}{1-0}\cdot x + 3[/tex]

[tex]f(x) = 2\cdot x + 3[/tex]

Line 2: [tex]x \in [2, 8][/tex]

[tex](x_{1}, y_{1}) = (2, 7)[/tex], [tex](x_{2}, y_{2}) = (8, 3)[/tex]

First, we determine the slope of function:

[tex]m = \frac{3-7}{8-2}[/tex]

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

Now we proceed to determine the intercept of the linear function:

[tex]7 = -\frac{2}{3}\cdot 2 + b[/tex]

[tex]b = \frac{25}{3}[/tex]

[tex]f(x) = -\frac{2}{3}\cdot x +\frac{25}{3}[/tex]

The first derivative of a linear function is its slope, and the first derivative of a product of functions is defined by:

[tex]k'(x) = f'(x)\cdot g(x) + f(x)\cdot g'(x)[/tex]

If we know that [tex]f(x) = 2\cdot x + 3[/tex], [tex]f'(x) = 2[/tex], [tex]g(x) = \sqrt{x^{2}-x+3}[/tex], [tex]g'(x) = \frac{2\cdot x - 1}{2\cdot \sqrt{x^{2}-x+3}}[/tex] and [tex]x = 0[/tex], then:

[tex]k'(x) = 2\cdot \sqrt{x^{2}-x+3}+\frac{(2\cdot x +3)\cdot (2\cdot x - 1)}{2\cdot \sqrt{x^{2}-x+3}}[/tex]

[tex]k'(0) = 2\sqrt{3}-\frac{3}{2\sqrt{3}}[/tex]

[tex]k'(0) = \frac{12-3}{2\sqrt{3}}[/tex]

[tex]k'(0) = \frac{9}{2\sqrt{3}}[/tex]

[tex]k'(0) = \frac{3\sqrt{3}}{2}[/tex]

The value of [tex]k'(0)[/tex] is [tex]\frac{3\sqrt{3}}{2}[/tex].

b) The derivative is found by means of the formulas for the derivative of the product of a function and a constant and the derivative of a division between two functions:

[tex]m'(x) = \frac{f'(x)\cdot g(x)-f(x)\cdot g'(x)}{2\cdot [g(x)]^{2}}[/tex] (2)

If we know that [tex]f(x) = -\frac{2}{3}\cdot x +\frac{25}{3}[/tex], [tex]f'(x) = -\frac{2}{3}[/tex], [tex]g(x) = \sqrt{x^{2}-x+3}[/tex], [tex]g'(x) = \frac{2\cdot x - 1}{2\cdot \sqrt{x^{2}-x+3}}[/tex] and [tex]x = 5[/tex], then:

[tex]f(5) = 5[/tex]

[tex]f'(5) = -\frac{2}{3}[/tex]

[tex]g(5) = \sqrt{23}[/tex]

[tex]g'(5) = \frac{9\sqrt{23}}{46}[/tex]

[tex]m'(5) = \frac{\left(-\frac{2}{3} \right)\cdot \sqrt{23}-\left(-\frac{2}{3} \right)\left(\frac{9\sqrt{23}}{46} \right)}{3\cdot 25}[/tex]

[tex]m'(5) \approx -0.034[/tex]

The value of [tex]m'(5)[/tex] is approximately -0.034.

c) In this case we must find a value of [tex]x[/tex], so that [tex]h'(x) = 2[/tex]. Hence, we have the following formula below:

[tex]5\cdot e^{x}-9\cdot \cos x = 2[/tex]

A quick approach is using a graphing tool a locate a point so that [tex]5\cdot e^{x}-9\cdot \cos x = 2[/tex]. According to this, the value of [tex]x[/tex] is approximately 0.622.

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Answer:

Step-by-step explanation:

The top left angle is 55 (alternate interior angles).

x + 100 + 55 = 180                     All triangles are made up of 180 degrees

x + 155 = 180                             Subtract 155 from both sides.

x = 180 - 155                              Combine

x = 25

Hence, 'x = 25°' is the value of 'x'

Hoped this helped.

[tex]-BrainiacUser1357-[/tex]

Answer:

I need help with this too!!!

Step-by-step explanation:

Answer:

what does it mean?

Step-by-step explanation:

I do not understand.

Answer:

4th on should be the correct

The probability of getting an odd number on the first roll and less than 3 on the second roll is 1/6.

It is a branch of mathematics that deals with the occurrence of a random event.

The probability of getting an odd number on the first roll is 3/6

since there are three odd numbers (1, 3, 5) out of six possible outcomes (1, 2, 3, 4, 5, 6).

The probability of getting less than 3 on the second roll is 2/6, since there are two possible outcomes (1, 2) out of six.

To find the probability of both events happening, we multiply the probabilities:

P(odd on first roll and less than 3 on second roll) = P(odd on first roll) × P(less than 3 on second roll)

= (3/6)×  (2/6)

= 1/6

Therefore, the probability of getting an odd number on the first roll and less than 3 on the second roll is 1/6.

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Answer:

c. m < 13

Step-by-step explanation:

13 - 7 is equal to 6 so m must be less than 13 to be less than 6.

Step-by-step explanation:

1550 - 395 = 1155

1155 / 82.5 = 14

Answer should therefore be 14 weeks.

Not my usual way of doing this sort of question but I'm interested to see if it's right. Alternatively you can subtract $82.50 from $1550 until/before you reach $395. Do not go below $395 though.

Answer:

K12 Answer

Step-by-step explanation:

Evaluate the following division: (3b-6a)÷(30a-15b) is -1/5.

~ Algebraic Forms and their Elements

Algebraic form is a mathematical form whose presentation involves symbols or letters to represent unknown numbers.

Elements of Algebra:

1. Variables, Constants and Coefficients

Pay attention to the algebraic form 3x + 2y + 3

From the algebraic form above, x and y are variables (variables), while the number 3 is a constant. A variable is a substitute symbol for a number whose value is not clearly known. While constants are terms of an algebraic form in the form of numbers and do not contain variables.

And what is meant by the coefficient is the constant factor of a term in algebraic form. The coefficient on the 3x term is 3, on the 2y term it is 2.

2. Terms and Factors

» The term is part of the algebraic form which is limited by the operation of addition (+) or difference (-). The term one is an algebraic form that is not connected by the operation of addition or difference.

Example: 2x, 2a², -4xy, . . .

» Term two is an algebraic form that is connected by an operation of sum or difference.

Example: 2x + 3, a² - 4, 3x² - 4x, . . .

» Similar terms in algebraic form are terms that have the same variable and the same power.

Example:

2a is similar to 3a, 4a, etc.

» Factors are part of the algebraic form that is restricted to multiplication operations.

Example: 5n = 5 × n, 5 and n are factors of 4n, respectively.

Calculation Operations on Algebraic Forms

1. Addition and subtraction of algebraic forms can only be done on similar terms.

2. Multiplication and division of algebraic forms.

Multiply two terms by constants or variables.

Example:

3 (4y + 5)

= (3 × 4y) + (3 × 5)

= 12y + 15

Division of two terms with a variable or constant, for example:

(8y+4)/2 = 8y/2 + 4/2 = 4y + 2

(3b-6a)÷(30a-15b)

= (-6a + 3b) ÷ (-5(-6a+3b))

= (-6a+3b)/(-5(-6a+3b))

= -1/5

So, Evaluate the following division: (3b-6a)÷(30a-15b) is -1/5.

(mampir ke indo:v)

_____________

Class: 7 Middle School

Subject: Math

Material: Chapter 2.1 -Operations of Algebraic Forms

Categorization Code: 7.2.2.1

Keywords: Simple form of algebra

Answer:

x=4

Step-by-step explanation:

you take both equations, and make them equal to each other. so....

5x-6=3x+2 subtract 3x from both sides

2x-6=2 then add 6 to the other side.

2x=8 then divide 8 by 2.

X=8

Answer:

94.74

Step-by-step explanation:

Hope this helps!

Answer:

94.74

Step-by-step explanation:

Answer:

6cm

Step-by-step explanation:

let height of ladder be x

so if height of ladder is x then the distance from the base of the ladder to the base of the slide is x+2

Assuming this is a right angle triangle, the slide is the longest lenght (c)

so

x²+(x+2)²=10²

x²+x²+4x+4=100

2x²+4x+4=100

2x²+4x+4-100=0

2x²+4x-96=0

2(x²+2x-48)=0

x²+2x-48=0 -- Factor

(x+8)(x-6)=0

x=-8 and x=6

since height cannot be a negative number

height of ladder is 6 cm

The base length is 8 feet. Then the height of the triangle will be 6 feet.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as

H² = P² + B²

The length of a slide on a swing set is 10 ft.

The distance from the base of the ladder to the base of the slide is 2 ft more than the height of the ladder.

Let x be the length of the height of the triangle. Then the base of the triangle will be (x + 2).

10² = (x + 2)² + x²

100 = x² + 4x + 4 + x²

96 = 2x² + 4x

48 = x² + 2x

0 = x² + 2x - 48

0 = (x - 6)(x + 8)

x = 6, -8

Then the base length is 6 ft. Then the height of the triangle will be

B = x + 2

B = 6 + 2

B  = 8 ft

More about the Pythagoras theorem link is given below.

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Answer:

add the two then subtract the two and put those answers in each box :)

Step-by-step explanation:

hope this helped! happy holidays!

Answer:

1. <  2. < 3. > 4. = 5. >

Step-by-step explanation:

Answer:

[tex]\sqrt 10y[/tex]

Step-by-step explanation:

10*[tex]\sqrt{y}[/tex] is [tex]\sqrt 10y[/tex]

[tex]\sqrt{100y}[/tex]

Step-by-step explanation:

Recall that

[tex]10 = \sqrt{100}[/tex]

So we can write our original expression as

[tex]10\sqrt{y} = \sqrt{100}\sqrt{y}[/tex]

[tex]\;\;\;\;\;\;\;\;\;=\sqrt{100y}[/tex]

a) If f(y) is a probability density function, then both f(y) ≥ 0 for all y in its support, and the integral of f(y) over its entire support should be 1. eˣ > 0 for all real x, so the first condition is met. We have

[tex]\displaystyle \int_{-\infty}^\infty f(y) \, dy = \frac14 \int_0^\infty e^{-\frac y4} \, dy = -\left(\lim_{y\to\infty}e^{-\frac y4} - e^0\right) = \boxed{1}[/tex]

so both conditions are met and f(y) is indeed a PDF.

b) The probability P(Y > 4) is given by the integral,

[tex]\displaystyle \int_{-\infty}^4 f(y) \, dy = \frac14 \int_0^4 e^{-\frac y4} \, dy = -\left(e^{-1} - e^0\right) = \frac{e - 1}{e} \approx \boxed{0.632}[/tex]

c) The mean is given by the integral,

[tex]\displaystyle \int_{-\infty}^\infty y f(y) \, dy = \frac14 \int_0^\infty y e^{-\frac y4} \, dy[/tex]

Integrate by parts, with

[tex]u = y \implies du = dy[/tex]

[tex]dv = e^{-\frac y4} \, dy \implies v = -4 e^{-\frac y4}[/tex]

Then

[tex]\displaystyle \int_{-\infty}^\infty y f(y) \, dy = \frac14 \left(\left(\lim_{y\to\infty}\left(-4y e^{-\frac y4}\right) - \left(-4\cdot0\cdot e^0\right)\right) + 4 \int_0^\infty e^{-\frac y4} \, dy\right)[/tex]

[tex]\displaystyle \cdots = \int_0^\infty e^{-\frac y4} \, dy[/tex]

[tex]\displaystyle \cdots = -4 \left(\lim_{y\to\infty} e^{-\frac y4} - e^0\right) = \boxed{4}[/tex]

Answer:

22, 40, 40, and 41

Step-by-step explanation:

happy to help have a nice day

Answer:

Step-by-step explanation:

Rational number ,because it can be written as 37 which is a ratio

Answer:

C their speeds are equal

Answer: C) Their speeds are equal

Step-by-step explanation:

Use the speed-distance equation

Dog - s=d/t = 100/4 = 25m/s

Lion - s=d/t = 250/4 = 25m/s

Answer:

1 2/3

Step-by-step explanation:

5 pizzas divided by 3 people = 1 2/3

Answer:

0.6

Step-by-step explanation:

3/5=0.6

Answer:

An easy way to solve this problem is divide $23.25 by 3 or $54.25 by 7. Either way, you get $7.75. This number represents the amount of money he makes for 1 hour. So with that in mind, the correct equation is:

$7.75x = y

Step-by-step explanation:

Answer: y = 7.75x

Step-by-step explanation:

Find the difference of charges between 6 hours and 8 hours

62-46.5 = 15.5 for 2 hours

15.5/2 = 7.75/hr

62 = 7.75 x 8

Therefore there is no initial charge, and that the relationship is linear

so y = 7.75x

Answer:

I don't know sorry

Answer:

y=4x-3

Step-by-step explanation:

Answer:

DO i care... no ask your dam teacher won der why u aint pass

Step-by-step explanation:

[tex]\text{Given that,}\\\\f(x) = x^3+ax^2-7x+b \\\\\text{Since}~ (x+2)~ \text{and}~ (x-3)~ \text{are factors of f(x),}\\\\f(-2) = 0 ~ \text{and}~ f(3)=0\\\\\\ \text{Now,}\\\\f(-2)=0\\\\\ \implies (-2)^3+a(-2)^2-7(-2)+b =0\\\\\implies -8 +4a +14+b =0\\\\\implies 4a +b +6 =0~~~....(i)\\\\\\f(3) = 0\\\\\implies 3^3+a(3^2) -7(3) +b =0\\\\\implies 27 +9a -21 +b =0\\\\\implies 9a +b +6 =0~~....(ii)\\\\\\(ii)-(i):\\\\9a+b+6 - 4a-b - 6 = 0\\\\\implies 5a =0\\\\\implies a = 0\\[/tex]

[tex]\text{Substitute a=0 in equation (i):}\\\\4(0) +b +6 =0\\\\\implies b+6 =0\\\\\implies b =-6\\\\\text{Hence, a = 0 and}~ b =-6[/tex]

subtract 6 from both sides of the equation and simplify and your answer should be f = 55 over 2

Answer:

y = 2x + -3

Step-by-step explanation:

Use the equation y=mx+b

m is the slope (2 in this case)

b is the y intercept (-3 in this case)

The equation of the line would be y = 2x + -3

Answer:

y=1x-2

Step-by-step explanation:

Well this one is already given

When x=0, it's the y intercept

and it gives the slope, so we got it :D

Answer:

y=x-2

Step-by-step explanation:

y-y1=m(x-x1)

y-(-2)=1(x-0)

y+2=1(x)

y+2=x

y=x-2