<4 and <5 are alternate interior angles, find the measure of <5

The derivative of the given function y= ∛(x²-3x+5)

is calculated as :  \(\frac{2x-3}{3(x^2-3x+5)^{\frac{2}{3} }}\) .

A derivative is the instantaneous rate at which a function alters in relation to another variable according to calculus.

Differentiation is the process of determining a function's derivative. The derivative of a function is equivalent to its tangent slope, rate of change, etc. It is possible to broaden the application of derivatives as functions of numerous real variables. This interpretation reinterprets the derivative as a linear transformation whose graph is the closest linear approximation of the graph of the original function (after an appropriate translation).

The given function is of the form y= ∛(x²-3x+5)

We will now find the derivative of the function by using the power rule of differentiation .

\(or, \frac{dy}{dx} = \frac{d}{dx}\sqrt[3]{x^2-3x+5} \\\\or, \frac{dy}{dx}=\frac{1}{3}(x^2-3x+5)^{-\frac{2}{3}}(2x-3)\\\\or, \frac{dy}{dx}=\frac{2x-3}{3(x^2-3x+5)^{\frac{2}{3} }}\)

Hence the derivative of the function is given as: \(\frac{2x-3}{3(x^2-3x+5)^{\frac{2}{3} }}\)

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Answer: 102cm²

Step-by-step explanation:

Area of base = 6 × 7 ÷ 2 = 21

Area of lateral face = 6 × 9 ÷ 2 = 27

Since all of the sides of the base are equal, we can multiply the area of 1 lateral face by 3 to get the area of all the lateral faces.

27 × 3 = 81.

Now we add up the area of the base and the lateral faces.

21 + 81 = 102cm²

I am not a professional, simply using prior knowledge!

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Answer:

40.6

Step-by-step explanation:

Step 1:  Convert 52% to a decimal:

Thus, 52% as a decimal is 0.52.

Step 2:  Multiply 0.52 by 78 and round to one decimal place:

Now we can multiply 0.52 by 78 and round to one decimal place to find 52% of 78:

0.52 * 78

40.56

40.6

Thus, 52% of 78 is about 40.6,

The value of x from the inequality is x < 3

An inequality is defined as a statement of an order relationship between two numbers or algebraic expressions.

Given the inequality;

3x + 1 < 10

To determine the solution, we take the followings steps;

collect like terms

3x < 10 - 1

Find the difference between the terms

3x < 9

Make 'x' the subject of formula

x < 9/ 3

x < 3

Thus, the value of x from the inequality is x < 3

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Answer:

4

Step-by-step explanation:

2/3÷1/6

Flip the 1/6 to make it a reciprocal and then multiply

2/3•6/1

simplify by crossing out

2•2 =4

Answer:

b= \(\frac{416}{y}\)    =  59.429

Answer:

b = 416/7

Step-by-step explanation:

b = 416/7 or you could say 59.4

Answer:

Step-by-step explanation:

a

Answer:

Step-by-step explanation:

The first time:

The second time and each time after, half of the previous distance

This is a GP with the first 6 terms:

Sum of the distances:

Answer:

Solution given:

For first time:

ball goes 16 m up and 16 m down = 32 m

The second time and each time after, half of the previous distance

since it is in a GP with the first 6 terms:

32, 16, 8, 4, 2, 1

now

Sum of the distances:32 + 16 + 8 +4+2+1= 63 m

63 m is your answer.

Answer: Half of them are even and half of them are odd.

Step-by-step explanation:

The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.

The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.

Therefore, out of the given numbers, half of them are even and half of them are odd.

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The length of the rectangle is twice its width. If its perimeter is 7 1/3 cm, its length will be 22/9 cm, and the width is 11/9 cm.

Let's assume the width of the rectangle is "b" cm.

According to the given information, the length of the rectangle is twice its width, so the length would be "2b" cm.

The formula for the perimeter of a rectangle is given by:

Perimeter = 2 * (length + width)

Substituting the given perimeter value, we have:

7 1/3 cm = 2 * (2b + b)

To simplify the calculation, let's convert 7 1/3 to an improper fraction:

7 1/3 = (3*7 + 1)/3 = 22/3

Rewriting the equation:

22/3 = 2 * (3b)

Simplifying further:

22/3 = 6b

To solve for "b," we can divide both sides by 6:

b = (22/3) / 6 = 22/18 = 11/9 cm

Therefore, the width of the rectangle is 11/9 cm.

To find the length, we can substitute the width back into the equation:

Length = 2b = 2 * (11/9) = 22/9 cm

So, the length of the rectangle is 22/9 cm, and the width is 11/9 cm.

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According to the solving the capacity of the tank is  = 500

The term 'volume' in mathematics refers to the amount the three-dimensional space occupied by such an item or a closed surface. The volume is measured in cubic units like as m3, cm3, in3, and so on. Volume is also referred to as capacity at times.

Volume is the amount of three-dimensional space inhabited by a liquid, solid, or gas. Volume is commonly expressed in liters, cubic meters, gallons, milliliters, teaspoons, and ounces, while many additional units exist.

fuel storage tank is 3/4 full.

75 liters have been drawn off.

it is 3/5 full.

The capacity of the tank = ?.

So,

3/4x - 75 = 3/5x

3/4x - 3/5x = 75

Multiplying by 20 both the side:

15x - 12x = 1,500

3x = 1500

x = 1500/3

x = 500

According to the solving the capacity of the tank is  = 500

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The solution to the inequality is x >= -2 for inequality 3x-5≥-11

The given inequality is 3x-5≥-11

Three times of x greater than or equal to minus eleven

x is the variable

3x - 5≥ -11:

Adding 5 to both sides, we get:

3x ≥ -6

Dividing both sides by 3, we get:

solution is  x≥-2

Therefore, the solution to the inequality is x >= -2.

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It depends on the number of variables, if the inequality has one variable, then it is graphed on a number line.

The type of diagram that we need to use depends on the number of variables that we have.

That is the main reason, for example:

x > 2

Is graphed on a number line.

y > 3x + 4

is graphed on a coordinate plane.

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The probability of the four events are: Event 1: 1/84Event 2: 3/14Event 3: 15/28 Event 4: 5/21

The total number of drinks = 9The number of sweet teas = 3The number of unsweetened teas = 6If you select 3 drinks at random, the following events can take place:

Event 1: All three drinks are sweet teas. The probability of event 1 = (Number of ways in which all three drinks can be sweet teas) / (Number of ways to select 3 drinks)The number of ways in which all three drinks can be sweet teas = 3C3 = 1 (because all three sweet teas are already fixed)The number of ways to select 3 drinks = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84Therefore, the probability of event 1 = 1/84 = 1/84

Event 2: Exactly two drinks are sweet teas. The probability of event 2 = (Number of ways in which two drinks are sweet teas and one is an unsweetened tea) / (Number of ways to select 3 drinks)The number of ways in which two drinks are sweet teas and one is an unsweetened tea = (3C2 × 6C1) = 18 (because you can choose 2 sweet teas from 3 and 1 unsweetened tea from 6)The number of ways to select 3 drinks = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84Therefore, the probability of event 2 = 18/84 = 3/14

Event 3: Exactly one drink is a sweet tea. The probability of event 3 = (Number of ways in which one drink is a sweet tea and the other two are unsweetened teas) / (Number of ways to select 3 drinks)The number of ways in which one drink is a sweet tea and the other two are unsweetened teas = (3C1 × 6C2) = 45 (because you can choose 1 sweet tea from 3 and 2 unsweetened teas from 6)The number of ways to select 3 drinks = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84Therefore, the probability of event 3 = 45/84 = 15/28

Event 4: All three drinks are unsweetened teas. The probability of event 4 = (Number of ways in which all three drinks can be unsweetened teas) / (Number of ways to select 3 drinks)The number of ways in which all three drinks can be unsweetened teas = 6C3 = 20 (because you can choose 3 unsweetened teas from 6)The number of ways to select 3 drinks = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84 Therefore, the probability of event 4 = 20/84 = 5/21

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Answer:

Step-by-step explanation:

-14 - 73 i

Answer:

-28i^2-73i-42

Step-by-step explanation:

(−7)(6)+(−7)(7i)+(−4x)(6)+(−4i)(7i)

= −42−49i−24i−28i^2

= -28i^2-73i-42

\({\huge{\fbox{\tt{\blue{ANSWER}}}}}\)

______________________________________

The probability of answering a single problem correctly by randomly guessing is 1/4, since there are 4 answer choices and only one correct answer. Since the student randomly guessed the answer to both problems, the probability of answering both problems correctly is:

(1/4) x (1/4) = 1/16

Therefore, the probability that the student answered both problems correctly is 1/16.

Answer:

12%

Step-by-step explanation:

each shares 12% because 100-28=72

72÷6=12%

The product of the secondary diagonal is 13 in this example of a second order determinant .

A determinant is a scalar quantity in mathematics that is a function of the entries of a square matrix. It describes various aspects of the matrix and the linear map that the matrix represents. In particular, the matrix must be invertible and the linear map it represents must be an isomorphism for the determinant to be nonzero.

Determinants can also be described by some of their characteristics, such as the four following: The determinant is the sole function defined on the n× n matrices.

1. One is the identity matrix's determinant.

2. The sign of a matrix's determinant changes if two rows (or columns) are switched.

3. The determinant of a matrix is multiplied by k if any row (or column) is multiplied by a scalar.

4. The determinant of a matrix is zero if any two rows (or columns) are proportionate.

Hence, we may determine the value of the determinant if we are aware that the product of the secondary diagonal is 13.

Assume that the matrix A has the following elements: a, b, c, and d. Then,

A = [a b] [c d]

Cd is the result of the secondary diagonal. As we are aware, cd = 13.

A = ad - bc3 is the value of the second-order determinant. Therefore,

A = ad-bc

= ad-(cd/d)*b

= d(a-(c/d)*b)

Given that cd = 13, we may replace it in the equation above:

A = d(a - (13 / d) * b)

The product of the secondary diagonal is 13 in this example of a second order determinant.

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Answer: 0.628

Step-by-step explanation:

Probability of U.S. smartphone owners have made an effort to limit their phone use in the past : p = 0.4702

Sample size : n= 54

Mean : \(\mu =(54)(0.4702)=25.39\)

Standard deviation:

\(\sigma=\sqrt{(54)(0.4702)}=\sqrt{25.39}\\\\\approx5.039\)

The probability that between 22 and 29 (inclusively) will have attempted to limit their cell phone use in the past will be :

\(P(22\leq x\leq29)=P(21<x<30)=P(\dfrac{21-25.39}{5.039}<\dfrac{X-\mu}{\sigma}<\dfrac{30-25.39}{5.039})\\\\=P(-0.8712<z<0.914864)\ \ \ \ [z=\dfrac{X-\mu}{\sigma}]\\\\=P(z<0.914864)-P(z<-0.8712)\\\\=P(z<0.914864)-(1-P(z<0.8712))\\\\=0.8198685-(1-0.8081775)\ \ \ [\text{ By p-value table}]\\\\=0.628046\)

Hence, the required probability = 0.628

The equivalent expression is log (yz/x²)

We have,

Using the logarithmic concept.

log a + log b = log ab

log a - log b = log (a/b)

log x² = 2 log x

Now,

We will use,

log_2 x = log x

Now,

-2 log x + 4 log y + 4 log z

= (4 log y + 4 log z) -2 log x

= log (yz) - log x²

= log (yz/x²)

Thus,

The equivalent expression is log (yz/x²)

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Answer:

b = 4

Step-by-step explanation:

4/6 is equivalent to 2/3, so with the slopes and y-intercepts being the same, there will be infinitely many solutions

Answer:

mode is 10 as it is repeated more

Answer:

I think it's b I'm not sure I'm sorry if it's wrong

Answer:

If f(-5) = 7, then the point P(-5, 7) will be on the graph of f

where -5 is the x-coordinate and 7 is the y-coordinate

Step-by-step explanation:

Answer:

4vwg5 htdc7vagvt4#=3#!3$:\&,=4/&&&;,;;;;;;;::£::::;&;;

Answer:

1

Step-by-step explanation:

1111111

Is this the problem?

\(18x^{2+4+4} = 18^{9x+18}\)

Answer

The Answer is C                    

x=-2 and x=7                      

Using the information in the given diagram, the value of the missing angle is: m∠1 = 75°

The transverse line theorem states that If two parallel lines are cut by a transversal, then corresponding angles are congruent. Two lines cut by a transversal are parallel IF AND ONLY IF corresponding angles are congruent.

Now, when we draw a horizontal line parallel to lines a and b and directly cutting across the vertex of angle 1, we can see that angle 1 will be composed of two angles.

Now, for the transverse line theorem we can say that:

Angle 1 will be composed of two angles namely:

48 degrees and (180 - 153) degrees.

Thus:

m∠1 = 48° + 27°

m∠1 = 75°

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Answer:

$7.00

Step-by-step explanation:

'-'

okay thanks for the free points but i dont know the awnser

The equivalent expressions to \(24^{-7}\) are given as follows:

C. \(\left(\frac{1}{24^{-7}}\right)^{-1}\)

F. \((24^3 \times 24^4)^{-1}\)

Equivalent expressions are expressions that have the same value for all possible values of the variables. In other words, equivalent expressions are different ways of writing the same mathematical idea.

The exponent in the denominator can be moved to the numerator with the changed signal, hence:

\(\left(\frac{1}{24^{-7}}\right)^{-1} = (24^7)^{-1}\)

Applying the power of power rule, we multiply the powers, hence:

\((24^7)^{-1} = 24^{-7}\)

When two terms with the same base and different exponents are multiplied, we add the bases and keep the exponents, hence:

\((24^3 \times 24^4)^{-1} = (24^7)^{-1} = 24^{-7}\)

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