PROPIEDADES DE LOS LOGARITMOS
3log(x+2)+4log(x-4)- 2log(x+5)-3log(x-9)

Answer:

CD = 15

Step-by-step explanation:

We are given two quadrilaterals: CDEF and GIJH.

We know that CD = 3x - 6, and GI = x + 8.

We want to find the length of CD.

Notice how CD and GI both have one tick mark on them.
This indicates that these two are congruent, meaning that they have the same length.

Because of that, CD = GI.

If we substitute 3x - 6 for CD and x + 8 for GI, we get:

3x - 6 = x + 8

Now, we can solve this like a regular equation.

Add 6 to both sides.

3x - 6 = x + 8

    +6       +6

_________________

3x = x + 14

Subtract x from both sides.

3x = x + 14

-x    -x

_____________-

2x = 14

Divide both sides by 2.

2x = 14

÷2    ÷2

____________

x = 7

We found the value of x.

Now, substitute 7 as x in 3x-6 (the length of CD).

CD = 3x - 6 = 3(7) - 6 = 21 - 6 = 15

Therefore, CD = 15.

The bisector angle is angle PQT which is equal to angle RQT.

Angle bisector or a bisector angle is a type of angle obtained after dividing the initial angle into two equal parts.

The bisected angle can be obtained using a pair of compass and a pencil attached to it.

To bisect the given angle RQP; we will take the following steps;

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Answer:

96.25%

Step-by-step explanation:

The empirical rule regarding mean and standard deviation is that

Therefore between mean and +2 standard deviation or between mean and -2 standard deviation you will find  approximately 95/2 = 47.5% of the values

Between mean and ± 3 standard deviations you will find approximately 97.5/2 = 48.75% of the values

Therefore between 2 standard deviations above and 3 standard deviations below you will find approximately 47.5 + 48.75 = 96.25% of values

Answer: 14.94 subscribers/year

Step-by-step explanation:

To calculate the rate of change, we need to take the first derivative of the equation:

\(y^{'} = \frac{dy}{dx} = 14.94\)

Answer:

The 8-pack is a better value

Step-by-step explanation:

When viewed through the magnifying glass, the termite appears to be approximately 1.58 mm in length.

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Answer:

It's the second option

Step-by-step explanation:

The x moves over to the right for a positive 3

The y moves up for a positive 4.

Hope this helps! :)

Answer:

6.16.

Step-by-step explanation:

hope this helps.

Answer:

37/6

Step-by-step explanation:

The logically equivalent statement to p → q is:

~q → ~p

The conditional statement:

p → q

Assuming p and q are propositions, the conditional statement may be expressed as:

"If p holds true, then q follows suit. "

'

Whenever p is true, q is true as well. This implies that if q is false, then p must also be false.

We can rephrase this statement cleverly using the negative propositions, which include the opposite or contradictory statements.

~p  and ~q

These mean:

Not p and Not q respectively.

Then the statement:

"If q is not true, then p is not true"

Is written as:

~q → ~p

So this is the logically equivalent statement.

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The Complete Question

Given a conditional statement p → q, which statement is logically equivalent?

~p → ~q

~q → ~p

q → p

p → ~q

Answer:

can u put the entire problem so i can help? :)

Step-by-step explanation:

Question:

Kenia spent 270$ on 6 chairs to find out how much she spent on each chair she did the following work in long division.

045

6  /  270

− 0    

 27  

− 24  

  30

−  30

   0

Did she do the problem correctly? Why or why not?

Multiple choice answers:

A. No, because there is a remainder of 0.

B. Yes, she worked the problem correctly.

C. No, because the first digit in the quotient should be 5, not 4.

D. No, because the problem should be 270 / 6.

Answer:

B. Yes, she worked the problem correctly.

The Domain: (-∞, -3) ∪ (-3, 6) ∪ (6, ∞) and Range: (-∞, 0) ∪ (0, ∞).

What is domain?

The domain of a function refers to the set of all possible input values (also known as the independent variable) for which the function is defined.

According to question:

In this case, the denominator of the function is a quadratic expression, and we know that dividing by zero is undefined. Therefore, we need to find the values of x that make the denominator equal to zero, and exclude those values from the domain.

To find the values that make the denominator equal to zero, we can factor it as follows:

x² - 3x - 18 = 0

(x - 6)(x + 3) = 0

So, the denominator is equal to zero when x = 6 or x = -3. Therefore, the domain of the function is all real numbers except x = 6 and x = -3.

Domain: (-∞, -3) ∪ (-3, 6) ∪ (6, ∞)

The range of a function consists of all possible output values of the function, given the domain of the function.

To find the range of this function, we need to analyze the behavior of the function as x approaches positive or negative infinity.

As x approaches positive infinity, both the numerator and denominator of the function approach positive infinity. Therefore, the function approaches zero.

As x approaches negative infinity, both the numerator and denominator of the function approach negative infinity. Therefore, the function approaches zero.

Since the function approaches zero as x approaches positive or negative infinity, we can say that the range of the function is all real numbers except zero.

Range: (-∞, 0) ∪ (0, ∞).

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Answer:

480

Step-by-step explanation:

Lets break this down to make it even easier

(24x2)x10

=(48)x10

=480

Answer:

If you are looking for the simplest form of 24/20 it is basically 6/5.

because if you multiply 6/5 by 4/4 you could get the answer which is 24/20.

and the same thing if you divide

I hope that I helped

Answer:

2 products a second.

Step-by-step explanation:

Answer:

166

Step-by-step explanation:

$15.00-$5.00= $10.00 (subtract five dollars because aiden wants to have at least five dollars left)

10.00 divided by 0.06=  166

I hope this helps! :)

B. Lin can make 2 batches of blueberry muffins.

C. Lin needs to make 2/3 of a batch of blueberry muffins to use all of the blueberries.

What is mixed fraction?

A mixed number is one that contains both a whole number and a fraction. The fraction is written after the whole number, with a space or plus sign placed between them. The mixed number 2 1/4 serves as an explanation for how the numbers 2 and 1/4 were added. Objects that aren't whole numbers but are close to them, such length or time measurements, are typically represented by mixed numbers.

a) Diagram

   4 cups of blueberries

    __ __ __ __

    |    |     |    |    |

    |__|__|__|__|

Each batch uses 3/2 cups of blueberries

B) To find the number of batches Lin can make, we need to divide the total amount of blueberries by the amount of blueberries per batch:

4 cups of blueberries ÷ (3/2 cups of blueberries per batch)

= (4 cups of blueberries) × (2/3 batches per cup of blueberries)

= 8/3 batches

Therefore, Lin can make 8/3 or approximately 2.67 batches of blueberry muffins using all of the blueberries.

C) To find the fraction of a batch Lin will need to make in order to use all of the blueberries, we need to subtract the number of whole batches from the total number of batches:

8/3 batches - 2 batches = 2/3 of a batch

Therefore, Lin will need to make 2/3 of a batch in order to use all of the blueberries.

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Try this option:

1) if csc(u)=9, then 1/sin(u)=9 and sin(u)=1/9;

2) if sin(u)=1/9, then cos(u):

\(cos(u)=\sqrt{1-sin^2(u)}=\sqrt{1-\frac{1}{81}}=\frac{4\sqrt{5}}{9};\)

3) \(if \ sin(u)=\frac{1}{9} \ and \ cos(u)=\frac{4\sqrt{5}}{9}, then\)

\(sin(2u)=2sin(u)*cos(u)=\frac{8\sqrt{5}}{81};\)

\(cos(2u)=cos^2(u)-sin^2(u)=\frac{80}{81}-\frac{1}{81}=\frac{79}{81};\)

\(tan(2u)=\frac{sin(2u)}{cos(2u)}=\frac{\frac{8\sqrt{5}}{81}}{\frac{79}{81} }=\frac{8\sqrt{5}}{79}.\)

Answer:

d=9.899495 or √98

Step-by-step explanation:

√(7-0)^2 + (2-(-5))^2

√(7)^2+(7)^2

√98

Answer:

Step-by-step explanation:

the answer is : 4,8,6,6,6

= 6

Answer:

$90.83

Step-by-step explanation:

Because each yard of fabric is $8.65, and she's buying 10.5 yards, you need to multiply 10.5 by 8.65 to get 90.825. Because you then have to round that, the answer turns into 90.83 (as the 5 in the 1000th place makes you round up).

Step-by-step explanation:

the area (length × width) is

A = (x² - 4)/2x in² = (x + 2)(x - 2)/2x

length = (x + 2)²/2 = (x + 2)(x + 2)/2

width = A/length = 2(x+2)(x-2) / 2x(x+2)(x+2) =

= (x-2)/x(x+2) = (x-2)/(x²+2x)

Solution :

The null and the alternate hypothesis can be stated as :

Null hypothesis

\($H_0:\mu_1 \geq \mu_2$\)

Alternate hypothesis

\($H_a:\mu_1 \leq \mu_2$\)

We known;

\($\overline x_1=\frac{\sum_{i=1}^n X_i}{n_1}$\)

   \($=\frac{43+....+75}{7}$\)

   = 62.286

\($\overline x_2=\frac{\sum_{i=1}^n X_i}{n_2}$\)

   \($=\frac{66+....+81}{16}$\)

   = 72.125

\($s_1^2=\frac{\sum_{i=1}^n(X_i- \overline X_1)^2}{n_1-1}$\)

    \($=\frac{(43-65.5)^2+....+(75-65.5)^2}{7-1}$\)

   = 116.571

\($s_2^2=\frac{\sum_{i=1}^n(X_i- \overline X_2)^2}{n_2-1}$\)

    \($=\frac{(66-72.13)^2+....+(81-72.13)^2}{16-1}$\)

   = 23.45

Therefore, calculating the test statics :

\($t=\frac{\overline x_1 - \overline x_2}{\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}}$\)

\($t=\frac{62.29-72.125}{\sqrt{\frac{116.571}{7}+\frac{23.45}{16}}}$\)

\($t=\frac{-9.839}{4.2566}$\)

 = -2.312

Now calculating the P-value for the test as follows :

P=T.DIST(t, df)

\($df=\frac{\left(\frac{s_1^2}{n_1}+\frac{s^2_2}{n_2}\right)^2}{\frac{1}{n_1-1}\left(\frac{s^2_X}{n_1}\right)^2+\frac{1}{n_2-1}\left(\frac{s^2_Y}{n_2}\right)^2}$\)

\($df=\frac{\left(\frac{116.571}{7}+\frac{23.45}{16}\right)^2}{\frac{1}{7-1}\left(\frac{116.571}{7}\right)^2+\frac{1}{16-1}\left(\frac{23.45}{16}\right)^2}$\)

    \($=\frac{328.2868}{46.36395}$\)

   \($\approx 7$\)

P=T.DIST(t, df)

 =T.DIST(-2.31, 7)

 = 0.0270

Thus, the \($\text{P-value}$\) of the test is P = 0.0270 is \($\text{less}$\) than the level of significance \($\alpha= 0.05$\). Hence the researcher can reject the null hypothesis.

Conclusion: The mean launch temperature for the flights with O ring damages less than that for the flights with no O rings.

Answer and  explanation:

(a) Classify a call as long, lasts more than three minutes. What is P [L)?

Given probability of event a call lasts more than three minutes, M the probability and B is denoted as the event that a call is billed minutes.

P (L) = 1 – P (3 or less than three minutes)

        =1 – P (Bm) – P (Bm) –P (Bm)                                for m=1,2,3

         =1 – P(B1) – P(B2) – P(B3)                                                       as P (Bm) = a (1-a) m-1

        =1 –  a(1 –a)1-1 – a (1-a)2-1– a (1-a)3-1                          

        = (1-a) 3

        = 0.57

(b)

Probability of billed for nine minutes or less= P (nine minutes or less)

                                                                            = ∑i=19 a (1-a)i-1

                                                                      = 1 – (0.57)3

Given:

P (L) = 1 – P (3 or less than three minutes)

       =1 – P (Bm) – P (Bm) –P (Bm)    for m=1,2,3

        =1 – P(B1) – P(B2) – P(B3)                                                      

P (Bm) = a (1-a) m-1

           =1 –  a(1 –a)1-1 – a (1-a)2-1– a (1-a)3-1                          

           = (1-a) 3

           = 0.57

The probability that a call will be billed for nine minutes or less :

Probability of billed for nine minutes or less= P (nine minutes or less)

                                                                           = ∑i=19 a (1-a)i-1

                                                                           = 1 – (0.57)3

                                                                           =0.814

The probability that a call will be billed for nine minutes is less .

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Answer:

\(Model = 6.05ft\)

Step-by-step explanation:

Given

\(Space\ Needle = 605ft\)

\(Scale\ Model = \frac{1}{100}\)

Required

Determine the height of the model.

To do this, we simply multiply the scale model by the height of the space needle.

\(Model = Scale\ Model * Space\ Needle\)

\(Model = \frac{1}{100} * 605ft\)

\(Model = \frac{605ft}{100}\)

\(Model = 6.05ft\)

Hence, the height of the model is 6.05ft

Answer:

Fact

Step-by-step explanation:

It is according to the school report so it is based off of facts so it is real

Hopes this helps!

The amount of force used to pull the cart from 60 N to 90 N, the new acceleration of the cart is, 1.5 m/s²

The definition of force is the pushing or pulling of anything. Push and pull are the result of two things interacting with one another. Stretch and crush are two more phrases that can be used to describe force.

Formula of force,

F = ma

Given that,

A man pulled a cart filled with stones that had a total mass of 60 kg

He increased the amount of force used to pull the cart from 60 N to 90 N

New acceleration of cart = ?

F  = ma

Old acceleration,

60  = 60a

a   =  1 m/s²

New acceleration,

90 = 60a

a   = 90/60

a   =  3/2

a   =  1.5 m/s²

Hence, the new acceleration is 1.5 m/s²

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Answer:

In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

Step-by-step explanation:

The first five terms of the given sequence are:

C: 18, 30, 42, 54, 66

The formula for the nth term of an arithmetic sequence is expressed as:

aₙ = a + (n - 1)d

where:

a is first term

d is common difference

n is number of term

The formula for the sequence is 12x + 6. Thus:

First term = 12(1) + 6 = 18

Second term = 12(2) + 6 = 30

Third term = 12(3) + 6 = 42

Fourth term = 12(4) + 6 = 54

Fifth term = 12(5) + 6 = 66

Thus, the sequence is : 18, 30, 42, 54, 66

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