Expand the logarithm as much as possible. Rewrite the expression as a sum, difference, or product of logs.



ln(1/4k)


Enclose arguments of functions in parentheses and include a multiplication sign between terms. For example, c*ln(h).



ln(1/4k)=

Answer:

Step-by-step explanation:

2x + 3y = 2

x = 2 - 3y /2

x + y = 0

substitute the value of x

[tex]\frac{2 \\- 3y}{2}[/tex] + y = 0

2 - 3y + 2y = 0

2 = y

again,substitute the value of y

x = 2 - 3y / 2

=2 - 3*2 / 2

=2 - 6 / 2

=-2

Answer:

x = 2, y = -2

Step-by-step explanation:

This is an alternate way. You can also solve simultaneous equations using matrices. First, rewrite the simultaneous equations in matrix form.

[tex]\displaystyle \large{\left[\begin{array}{ccc}2&3\\1&1\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] =\left[\begin{array}{ccc}2\\0\end{array}\right]}[/tex]

Let:

[tex]\displaystyle \large{A= \left[\begin{array}{ccc}2&3\\1&1\end{array}\right]}\\\displaystyle \large{X = \left[\begin{array}{ccc}x\\y\end{array}\right]}\\\displaystyle \large{B =\left[\begin{array}{ccc}2\\0\end{array}\right]}[/tex]

So now we have [tex]\displaystyle \large{AX = B}[/tex] and we have to solve for X which:

[tex]\displaystyle \large{A^{-1}AX = A^{-1}B}\\\displaystyle \large{X = A^{-1} B}[/tex]

Where:

[tex]\displaystyle \large{A^{-1}=\frac{1}{ad-bc}\left[\begin{array}{ccc}d&-b\\-c&a\end{array}\right]}[/tex]

**ad-bc is determinant of 2*2 matrices and shortened as det(var) or |var|**

Therefore, from A:

Find detA:

[tex]\displaystyle \large{\det A = |A| = ad-bc = 2(1)-3(1) = 2-3 = -1}[/tex]

Therefore, detA = -1. Hence:

[tex]\displaystyle \large{A^{-1}=-1\left[\begin{array}{ccc}1&-3\\-1&2\end{array}\right]}[/tex]

And [tex]\displaystyle \large{X = A^{-1}B}[/tex]:

[tex]\displaystyle \large{X = -1\left[\begin{array}{ccc}1&-3\\-1&2\end{array}\right] \left[\begin{array}{ccc}2\\0\end{array}\right] }[/tex]

Evaluate the matrices:

[tex]\displaystyle \large{X = -1\left[\begin{array}{ccc}1 \cdot 2-3 \cdot 0\\-1 \cdot 2+2\cdot 0\end{array}\right] }\\\displaystyle \large{X = -1\left[\begin{array}{ccc}2-0\\-2+0\end{array}\right] }\\\displaystyle \large{X = -1\left[\begin{array}{ccc}2\\-2\end{array}\right] }\\\displaystyle \large{X = \left[\begin{array}{ccc}-2\\2\end{array}\right] }\\\displaystyle \large{\left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}-2\\2\end{array}\right] }[/tex]

Therefore, x = -2 and y = 2.

Answer:

y=−2x+5

Use the slope-intercept form to find the slope and y-intercept.

The slope-intercept form is

y=mx+b , where m is the slope and b is the y-intercept.

y=mx+b

Find the values of

m and b

using the form

y=mx+b.

m=−2b=5

The slope of the line is the value of m , and the y-intercept is the value of

b.

Slope: −2

y-intercept:

(0,5)

Any line can be graphed using two points. Select two x values, and plug them into the equation to find the corresponding y values.

Graph the line using the slope and the y-intercept, or the points.

Slope:  −2

y-intercept:  (0,5)

X|Y

0 5

1  3

Step-by-step explanation:

The required graph of the equation y = -2x +5 has been shown.

The graph is a demonstration of curves that gives the relationship between the x and y-axis.

Here,
As the given equation y = -2x+5 represents a straight line,
in order to graph the line,
We must know, the two points on the line,
So,
Put x = 0 on the equation,
y = 5,

And put y = 0,
0 = -2x + 5
x = 2.5,

Now, locate the points (0, 5) and (2.5, 0) on the graph and draw the straight curve joining these two points will be the required graph of the equation,

Thus, the required graph of the equation y = -2x +5 has been shown.

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Answer:

44.58

Step-by-step explanation:

[tex]v=\frac{4}{3}\pi r^{3}\\ given r= 2.2\\\pi =3.14\\hence:v=\frac{4}{3} (3.14)(2.2)^3=44.58[/tex]

Answer:

600,000

Step-by-step explanation:

Your answer would be 600,000 because in the hundred thousands place there is a 6.

And that 6 in the hundred thousands place is asking the ten thousands place for help also the digit in the ten thousands place is a 1.

So if you know the rule the 6 can't round up because the 1 is below 4./the rule is 4 and below keep it low 5 or more give it one more.

Ok so the 1 is below 4 and can't bring 6 up so 6 has to stay in it's lane at 600,000

Hope this helps have a great afternoon:)

Answer:

Its 600000

Step-by-step explanation:

Hundred thousand refers to 6 numbers so we look at the number after 6 and its less than 5 so we round it back to 0

Answer:

(B) 10

Step-by-step explanation:

x = 15

y = 3

---------------------------------

9(5) - x / y =

The value of the given expression [tex]\dfrac{9(5)-x}{y}[/tex] is 10 when x = 15 and y = 3. So, the correct answer is (b) 10.

An expression is a combination of numbers, variables, mathematical operations, and many more.

To obtain the value of the given expression, the values of x and y will be inserted in the expression and the concepts of PEMDAS will be used.

Let's assume that the given expression is as follows:

[tex]z = \dfrac{9(5)-x}{y}[/tex]

Substitute x = 15 and y = 3 in the given expression:

[tex]z = \dfrac{9(5)-x}{y}\\z = \dfrac{9(5)-15}{3}\\z = \dfrac{45-15}{3}\\z = \dfrac{30}{3}\\z = 10[/tex]

Therefore, option (d) is correct, i.e., for x = 15 and y = 3, the value of the given expression is 10.

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Answer:

Angles in a triangle adds to 180

Step-by-step explanation:

Hope this helps!

Answer:

Step-by-step explanation:

first of all you need to do is make a lemonade stand and make the lemonade taiste good then you can sell it for 15 dollars which is a good price to get you started with your life

Using the normal probability distribution and the central limit theorem, it is found that the probabilities are given by:

a) 0.0119 = 1.19%.

b) 0.121 = 12.1%.

c) 0.9257 = 92.57%.

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In this problem:

Item a:

The probability is the p-value of Z when X = 42600, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{42600 - 45000}{1060}[/tex]

[tex]Z = -2.26[/tex]

[tex]Z = -2.26[/tex] has a p-value of 0.0119.

The probability is of 0.0119 = 1.19%.

Item b:

The probability is the 1 subtracted by the p-value of Z when X = 46240, hence:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{46240 - 45000}{1060}[/tex]

[tex]Z = 1.17[/tex]

[tex]Z = 1.17[/tex] has a p-value of 0.879.

1 - 0.879 = 0.121.

The probability is of 0.121 = 12.1%.

Item c:

The probability is the p-value of Z when X = 46980 subtracted by the p-value of Z when X = 43190, hence:

X = 46980:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{46980 - 45000}{1060}[/tex]

[tex]Z = 1.87[/tex]

[tex]Z = 1.87[/tex] has a p-value of 0.9693.

X = 43190:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{43190 - 45000}{1060}[/tex]

[tex]Z = -1.71[/tex]

[tex]Z = -1.71[/tex] has a p-value of 0.0436.

0.9693 - 0.0436 = 0.9257.

The probability is of 0.9257 = 92.57%.

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Answer:

So basically what you have to is divide the log as you see the word quotient, therefore you need to take log^6 30 and divide 30 by 5 which will give you 6 right. Do you understanding so far? Moreover, you see log^6 2 so 15x2=30 it just basically itself breaking down.

Hence, it will take [tex]75seconds[/tex] to meet both the cars at the same place.

What is the time?

Time can be defined as an ongoing and continuous sequence of events that occur in succession, from past through the present, and to the future.

Here given that,

Two toy cars race around a circular track (both go in the same direction). One car can travel around the track in [tex]30[/tex] seconds. The other car travels around the track in [tex]50[/tex] seconds.

Case 1 :-

Track length every [tex]30[/tex] seconds. In [tex]x[/tex] seconds, travels [tex]\frac{x}{30}[/tex] of the track.

Case 2:-

Track length every [tex]50[/tex] seconds. In [tex]x[/tex] seconds, travels [tex]\frac{x}{50}[/tex] of the track.

Combining case 1 and case 2, we get

[tex]\frac{x}{30}=\frac{x}{50}+1\\\\\\frac{x}{30}-\frac{x}{50}=1\\\\\\frac{50x-30x}{1500}=1\\\\20x=1500\\\\x=\frac{1500}{20}\\\\x=75seconds[/tex]

Hence, it will take [tex]75seconds[/tex] to meet both the cars at the same place.

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Answer:

Step-by-step explanation:

There will be a +1 becuase the lines y intercept is +1.

We can then take two points on the line and then find the slope through them.

(0,1) and (4,2). 4-0 and 2-1.

4 and 1. The slope is 1/4.

y = mx + b

y = 1/4x + 1

Answer:

124

Step-by-step explanation:

350 times 35.5% = 124.25 and obviously .25 of a person cant go to a movie so you round down to 124.

Answer: 25.5 feet

Step-by-step explanation:

if each hat requires 30 inches of material, then 3 hats will require 3(30) = 90 inches.

if each scarf requires 2 yds of material, then 3 scarfs will need 3(2) = 6 yds.

The question wants us to give our answer in feet, so we will be converting:

Using 12in = 1ft:

90 in = 90/12 feet = 7.5 feet

Using 1 yd = 3 ft:

6 yds = 6(3) = 18 feet.

Now that the units are the same, we can add them up to get our answer:

7.5 + 18 = 25.5 feet

So Terry will need 25.5 feet of material to make 3 sets of hat and scarves.

Answer:

First, you find the volume of each box

Volume = Length * Width * Height

Box A

V = 13 * 40 * 5

V = 2600 cm^3

Box B

V = 8 * 10 * 25

V = 2000 cm ^3

Box C

V = 11 * 20 * 30

V = 6600 cm ^3

Since 7400, the cubes trying to be packed, is bigger than any of the volumes of the boxes, 2 boxes must be used

The boxes with volumes that add up to a number greater than 7400 are Box C with Box A or B (either works, as long as C is one of them)

The total volume of the boxes together can be found with simple addition

2600 + 2000 + 6600 = 11200 cm ^3

Answer:

42.5 or 43

Step-by-step explanation:

Since you need to travel 850 miles, and you can travel 20 miles per gallon, you should divide 850 by 20 to get the number of gas cans needed. In doing so, you get 42.5 gas cans, but since it may be asking for whole cans rather than part of a gas can, you might want to write 43 instead. If you were to round down to 42, you would not have enough gas to finish the trip, so you should round up to 43. So, it is up to you if you want to write 42.5 or 43.

Hope this helped somewhat! ;(

Answer:

x<3

Step-by-step explanation:

The answer is x<3.

If the point were filled it would be one of these for example ≥

Answer: 37.5%

Step-by-step explanation:

Answer:

Mari watch died of eating Boba drinks

Answer:

1. (4,5)  2. D  3. J  4.D  5. 64.8 oz

Step-by-step explanation:

math

Considerando la definición de número complejo, su opuesto, conjugado y afijo, siendo z= -2-2i, se obtiene:

Los números complejos son combinaciones de números reales y números imaginarios. Su representación más común es la suma de una parte real y una parte imaginaria. Al mismo tiempo, la parte imaginaria se divide entre la parte imaginaria y la unidad imaginaria.

Esto es: z= a +bi

donde:

Dado un número complejo z = a+bi, se llama opuesto de z al número -z = -a-bi.

Esto es, el opuesto de un número complejo se calcula cambiando el signo de la parte real y de la parte imaginaria.

Dado un número complejo z = a+bi, se llama conjugado de z al número z = a-bi.

Esto es, el conjugado de un número complejo se obtiene al cambiar el signo de la parte imaginaria.

Los números complejos se representan mediante vectores. Al extremo del vector se le llama afijo del complejo. Esto es, el afijo del número complejo z=a +bi es (a,b)

Considerando las correspondientes definiciones:

Aprende más sobre números complejos:

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The answer is 40cm in cube 3

Answer:

[tex]\huge\boxed{\sf 58\ m\²}[/tex]

Step-by-step explanation:

The figure is made up of two rectangles.

Area of the larger rectangle:

Length = 5 m

Width = 10 m

= Length × Width

= 5 × 10

= 50 m²

Area of smaller rectangle:

Length = 4 m

Width = 2 m

= Length × Width

= 4 × 2

= 8 m²

Area of the figure:

= Area of larger rectangle + Area of smaller rectangle

= 50 + 8

= 58 m²

[tex]\rule[225]{225}{2}[/tex]

Answer:

BFG

Step-by-step explanation:

The segment BF is the diagonal of the top face of the cube (GBCF)

Therefore, it is the hypotenuse of ΔBFG and ΔBFC

See attached diagram for visual of the cube.

Answer: Coach Lopez wants to divide his soccer team into a smaller, equal-sized group of players for practice. He noticed that he divided his team evenly into groups of 3.

Coach Lopez can form smaller equal-sized groups because the number of students on his team is a prime number.

This means that the number of players on the team has three factors.

Coach Lopez could possibly have 12 players on his team.

Answer:

3.

Step-by-step explanation:

Since angle DBC and DBA are supplementary (they add up to a straight angle-180 degrees) we can subtract 121 from 180 and find out the answer of  angle DBA.

Answer:

3.............

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