What is this expression in simplified form?

1) m∠1 = 62°, lines t and l intersect (given)

2) ∠1 and ∠4 are vertical angles (intersecting lines form vertical angles)

3) ∠1 and ∠4 are congruent (vertical angles are congruent)

4) m∠1 = m∠4 (congruent angles have equal measure)

5) 62° = m∠4 (substitution)

6) m∠4 = 62° (symmetric property of equality)

Using the quotient rule, the derivative of [tex]y[/tex] is

[tex]y' = \dfrac{(x^2-1) x' - x(x^2-1)'}{(x^2-1)^2} = \dfrac{(x^2-1) - x(2x)}{(x^2-1)^2} = -\dfrac{x^2+1}{(x^2-1)^2}[/tex]

as you're shown in the picture.

If [tex]y[/tex] has any local extrema, they occur at critical points where [tex]y'=0[/tex] or possibly when [tex]y'[/tex] is undefined.

In this case, [tex]y'[/tex] is undefined when [tex]x=1[/tex], but this is outside the domain of [tex]y[/tex] anyway, so we can ignore that.

That leaves us with the zero-case. For [tex]x\neq1[/tex], the denominator is always positive, so the numerator must be zero. But this never happens, since

[tex]-(x^2+1) = 0 \implies x^2 = -1[/tex]

but [tex]x^2\ge0[/tex] for all real [tex]x[/tex]. Therefore [tex]y[/tex] has no critical points and thus no extrema.

Answer:

4

Step-by-step explanation:

[tex]In(e^4)[/tex] =  [tex]4In(e)[/tex]
          = 4 x 1
          = 4

The value of the expression ln([tex]e^4[/tex]) is 4.

Option D is the correct answer.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

The natural logarithm (ln) is the inverse function of the exponential function,

[tex]e^x[/tex].

ln([tex]e^4[/tex]) = 4,

since ln([tex]e^4[/tex]) "undoes" the exponentiation of [tex]e^4[/tex].

So the value of ln([tex]e^4[/tex]) is 4.

Thus,

The value of the expression ln([tex]e^4[/tex]) is 4.

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Answer:

7, 11, 2, 18, -7, 25

The test statistic z  is 2.33, the p-value corresponding to the test statistic z value is 0.0099.

Probability is the measure of the likeliness of happening of an event.

The mean of the data is 15.07 centimeters

The standard deviation of the data is 0.26 centimeters.

n = 75

Significance Level ∝ = 0.01

According to the null and alternative hypothesis

Hₐ : [tex]\rm \mu[/tex] ≤15  vs H₁ : [tex]\rm \mu[/tex] >15

The test statistic z  is given by

[tex]\rm Z = \dfrac{(X-\mu)}{\sigma/\sqrt{n}}[/tex]

Z = ( 15.07 -15)/(0.26/√75)

Z = 2.33

The p-value corresponding to z value is 0.0099

as p-value < significance level, therefore the H₁ : [tex]\rm \mu[/tex] >15 is acceptable.

No, significant evidence is not present to tell that the length of bolts is actually greater than the mean value at a significance level of 0.01.

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The equation that represents the given problem is (n-30) + n = 210. The correct option is the first option (n-30) + n = 210

From the question, we are to write an equation for the given problem

From the given information,

n = Tom's weight in pounds

If Jim weighs 30 pounds less than Tom

Then,

Jim weighs (n - 30)

Thus,

The sum of their weight is

(n-30) + n

∴ (n-30) + n = 210

Hence, the equation that represents the given problem is (n-30) + n = 210. The correct option is the first option (n-30) + n = 210

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Answer:

its 20, because I said it

Step-by-step explanation:

so 5+5=10

30-10=20

Answer:

54y+78

Step-by-step explanation:

6*3y+ 18y

6*7=42

4*9=36

4*9y=36y

18y+36y+42+36= 54y+78

See the graph in the attached image.

The amount of paper that are needed to line the bottom of 3 drawers with paper is equal to 2,160 square inches.

First of all, we would calculate the area of the bottom of each drawer as follows:

Area = length × width

Area = 36 × 20

Area = 720 square inches.

Next, we would multiply this area by 3:

Total area = 720 × 3

Total area = 2,160 square inches.

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Complete Question:

A decorator wants to line the bottom of 3 drawers with paper. If the bottom of each drawer measures 36 inches by 20 inches, how many square inches of paper are needed?

A. 1,040

B. 1,080

C. 2,040

D. 2,160

Answer:

20

Step-by-step explanation:

According to Euclidian theorem:

h^2 = AD*CD (h is the height, DB in this case)

rewrite the equation by using given values

10^2 = 5*CD find the square value of 10

100 = 5*CD divide both sides by 5

20 = CD

Answer:

48000

Step-by-step explanation:

After rounding each number to the criteria stated, we get the question 800 * 60. Multiply the 8 and the 6 and add the same number of zeros that are there right now. this is 48 + "000" so 48000.

Answer:

to find the value of x

x=(8x28)÷4

Answer: x=56

x/y 28/4=x/8

reduce 28/4 to 7/1

7/1 = x/8

cross multiply

x=56

Step-by-step explanation:

Answer:

  C.  c is less than zero

Step-by-step explanation:

The parent radical function y=x^(1/n) has its point of inflection at the origin. The graph shows that point of inflection has been translated left and down.

The transformation of the parent function y=x^(1/n) into the function ...

  f(x) = a(x +k)^(1/n) +c

represents the following transformations:

The location of the inflection point at (-3, -4) indicates it has been shifted left 3 units, and down 4 units. In the transformed function equation, this means ...

The graph says the value of c is less than zero.

__

Additional comment

Apparently, the value of 'a' is 2, and the value of n is 3. The equation of the graph seems to be ...

  f(x) = 2(x +3)^(1/3) -4

Answer:

mine was D

Step-by-step explanation:

mine was D unless its diffrent

Answer:

1/2

Step-by-step explanation:

We are given the expression 3b²-c, and we want to evaluate it if b is 1/2 and c is 1/4.

Because b and c are given values, we can substitute them into the expression as so:

Replace b with 1/2 in the expression.

3(1/2)²-c

Now replace c with 1/4 in the expression.

3(1/2)²-1/4

Now to solve this, we need to use the order of operations, which is usually known as PEMDAS (parentheses, exponents, multiplication, division, addition, subtraction) in the United States, although other countries have different abbreviations.

Regardless, the order of operations tells us that we should start with what is inside parentheses (i.e. if we need to do anything, like multiplying or dividing any numbers that are inside parentheses).

In this case, we don't have anything. So, we should go next to exponents, and we do have an exponent here (1/2 is raised to the second power).

So let's evaluate that.

Raise 1/2 to the second power (multiply it by itself).

1/2 * 1/2 = 1/4

We can substitute (1/2)² with 1/4:

3(1/4) - 1/4

Next, we should take care of any multiplication / division, making sure that we should work left to right

There is one multiplication thing to do: the 3(1/4), which will be 3/4

Replace 3(1/4) with 3/4.

3/4 - 1/4

Now, we can subtract 1/4 from 3/4, as the final two things in PEMDAS are addition and subtraction (A and S). Note that even though while addition is written first, we should always be working left to right, so for example if we had 3 - 4 + 6, we should do 3 - 4 first, THEN add 6 to the result of that. The same is true for multiplication and division.  

3/4 - 1/4 = 2/4 = 1/2

Answer:

$9.66 isb15% of $64.40

Step-by-step explanation:

64.40×15%

Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. Both the cards have the same cost of credit.

Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. It is calculated with the help of the formula,

SI = PRT

where SI is the simple interest, P is the principal amount, R is the rate of interest, and T is the time period.

The interest on $12,000 will be,

SI = $12,000 × 3 × 0.212 = $7,632

The interest on $24,000 will be,

SI = $24,000 × 3 × 0.106 = $7,632

Hence, both the cards have the same cost of credit.

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The interest you will earn from the loan of 500 dollars at rate of 6% and 6 months is $15.

He borrowed $500 and she will pay at the end of 6 months.

The interest rate is 6%.

Therefore,

I = prt / 100

where

Therefore,

I = 500 × 6 × 0.5 / 100

I = 1500 / 100

I = $15

Therefore, the interest you will earn from the loan is $15.

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The required value of δ = 1/4.  

0< |x-1| < δ
| f(x) - 4 | < 1/2 where f(x) = 6 - 2x

Inequality can be define as the relation of equation contains the symbol of ( ≤, ≥, <, >) instead of equal sign in an equation

now

| f(x) - 4 | < 1/2
|6 - 2x - 4 | <1/2
| 2-2x | < 1/2
| 1 - x | < 1/4
| x - 1 | < 1/4
since modulus function always give positive values.
0 < | x - 1 | < 1 /4

The required value of δ = 1/4.

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Answer:

second one listed

Step-by-step explanation:

second one given--he can buy between 3 and 6 albums; and 0 to 30 songs

(if he were to buy exactly 3 albums, he could not buy more than 30 songs; which is why that portion of the graph is not shaded)

(shaded = possible)

hope this helps!

The functions that have a maximum and are transformed are:

This is the rule in mathematics that is used to show the relationship that is in existence between variables.

In order to check for the minimum and the maximum, we have to check on the coefficient of the x square. When it is negative, we have a maximum. When it is positive it is a minimum.

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Answer: b and e

Step-by-step explanation: algebra edge 2022 :)

Answer:

3906

Step-by-step explanation:

(125-1):2+1=63

63x(125+1):2=3906

Answer:

c=y×z

Step-by-step explanation:

the answer is this because z would be the number of dozens you have times y the cost of one by multiplying those together you will get the cost of the z dozens of eggs

Answer: 140

Step-by-step explanation:

Answer:

r = 163 --> C

Step-by-step explanation:

In a right triangle, the remaining angle is = 180-73-90 = 17

Because n // p so acute angle created by n = 17

r+17 =180 --> r = 180-17 = 163

Answer:

hope it helps. good day .in case of any question please ask.

Answer:

  the numbers are 3, 5, 4

Step-by-step explanation:

The given relations can be written as a system of equations. These are conveniently solved using elimination.

Let the three numbers be represented by x, y, z. The given relations are ...

  x +y +z = 12

  x -y +z = 2

  x +y -z = 4

Subtracting the second equation from the first gives ...

  (x +y +z) -(x -y +z) = (12) -(2)

  2y = 10 . . . . . . . . . simplify

  y = 5 . . . . . . . . divide by 2

Subtracting the third equation from the first gives ...

  (x +y +z) -(x +y -z) = (12) -(4)

  2z = 8 . . . . . . . . . simplify

  z = 4 . . . . . . . . divide by 2

Using these values of y and z in the first equation lets us find x:

  x +5 +4 = 12

  x = 3 . . . . . . . . . subtract 9

The numbers, in order, are (3, 5, 4).