solve the following equations and check your answers: a) log (x+1) - log (x-1)=2 b) 7^x/2 = 5^-1x

Answer:

Answer is 726 cm2.

Step-by-step explanation:

I hope it's helpful!

Answer:

86

Step-by-step explanation:

Since ∆JKL is an isosceles triangle, it's base angles (<L and <J) would be equal to each other.

<L is opposite to side JK, <J is opposite to side KL.

m<J is given as 47°. Therefore,

m<L = m<J = 47°

m<L = 47°

m<J + m<L + m<K = 180° (sum of triangle)

47° + 47° + m<K = 180° (substitution)

94° + m<K = 180°

m<K = 180° - 94°

m<K = 86°

Answer:

0.8686

Step-by-step explanation:

= 1 - (area under -1.12)

= 1 - 0.1314 = 0.8686

Answer:

1 m^3

Step-by-step explanation:

Assume hight 4 and ength 4.

2, 1, 1 = 1

It doesn't have any direct relationship with the slope of the line. The correct answer is (c) increase of $1 in advertising is expected to result in an increase of $5 in sales.

This can be determined by looking at the coefficient of the advertising variable in the regression equation, which is 5. This means that for every one-unit increase in advertising (in thousands of dollars), we can expect a five-unit increase in sales (in thousands of dollars).

It's important to note that the intercept term in the regression equation, which is $80,000, represents the estimated sales when advertising is zero. However, it doesn't have any direct relationship with the slope of the line. The slope tells us the rate of change in sales for a given change in advertising, whereas the intercept tells us the baseline level of sales when there is no advertising. So, we cannot use the intercept to answer this question. Instead, we need to focus on the coefficient of the advertising variable.

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Answer:

Find the relative frequency for the event ​"heads​" for each friend:

Friend 1: 0.59 (41/70)

Friend 2: 0.7 (49/70)

Friend 3: 0.37 (26/70)

If the friends combine their results to get 116 heads and 94 ​tails, what is the relative frequency for the event ​"heads​"?

0.55 (116/210)

Suppose each friend flips a coin 700 times. Is there a value you would expect the relative frequency for the event ​"​heads" to be close​ to?

For Friend 1, basing it off the 0.59 frequency from earlier, I would expect the heads to be around 413.

Friend 2, 490

Friend 3, 259

Answer:

\(\boxed {\boxed {\sf d=\sqrt{170} \ or \ d\approx 13.04}}}\)

Step-by-step explanation:

We are asked to find the length of a segment or the distance between the 2 points. The formula for distance is:

\(d= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2\)

where (x₁ y₁) and (x₂, y₂) are the points. We are given the points ( -5, 4) and (6, -3). If we match the number and the corresponding variable, it is:

Substitute the values into the formula.

\(d= \sqrt{(6--5)^2+(-3-4)^2\)

Solve inside the parentheses.

\(d= \sqrt{(11)^2+(-7)^2\)

Solve the exponents.

\(d= \sqrt {(121)+(49)\)

Add.

\(d= \sqrt {170}\)

\(d=13.0384048104\)

Even though it's not specified, we could round to the nearest hundredth to make the answer more concise. The 8 in the thousandth place tells us to round the 3 to a 4 in the hundredth place.

\(d\approx 13.04\)

The length of the segment is √170 or approximately 13.04.

Hope this helps

Answer:

£21

€28 = £21

Answer:

48

Step-by-step explanation:

Answer:

Average of 3mph

Step-by-step explanation:

If Sarah goes uphill at 2mph and downhill at 4mph.

Then to find the average you can:

Add 2 plus 4

which equals 6

Then divide the sum of 6 by the number of values given, there are two values (2 and 4)

6 divided by 2 equals 3

So the average is 3mph

The length of the displaced threshold for runway 22 at Toledo (TDZ) is 380 feet. Option C) is correct.

A displaced threshοld is a pοrtiοn οf a runway where landing aircraft are nοt allοwed tο tοuch dοwn. It is typically marked by white arrοws οr lines οn the runway surface.

The purpοse οf a displaced threshοld is tο prοvide additiοnal clearance fοr οbstacles, such as buildings οr terrain, that may be lοcated at the beginning οf the runway. By mοving the tοuchdοwn pοint further dοwn the runway, the usable length οf the runway is effectively shοrtened.

Displaced threshold is half of clearance,

Therefore, we calculate the clearance and divide it by 2

(1000 - 620) / 2 = 380

Thus, The length of the displaced threshold for runway 22 at Toledo (TDZ) is 380 feet. Option C) is correct.

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Complete question:

(Refer to Figure 63.) What is the length of the displaced threshold for runway 22 at Toledo (TDZ)?

A) 25 feet.

B) 100 feet.

C) 380 feet.

The evolution of the Korean fashion industry has had strategic implications for Korean fashion firms' global expansion strategies. As the market has become stagnant and global luxury and SPA brands have aggressively entered the market, local fashion firms have faced challenges in sustaining their growth momentum.

To overcome these challenges, Korean fashion firms have adopted diverse strategies, including direct entry, licensing, and acquisitions, to successfully tap into the global market. Kolon FnC, one of the five affiliates of Kolon Industries, has focused on its strength in the sports and outdoor segment to differentiate itself from its global competitors.

Kolon FnC has implemented several strategic moves to enhance its global expansion. Firstly, it has diversified its fashion portfolio by acquiring small-sized designer shops and fashion accessory shops since 2010. This allows the company to offer a wider range of products and create a young and vibrant brand image.

Additionally, Kolon FnC has collaborated with artists to create new value and attract consumers. By leveraging its R&D capability for new garment materials, led by its sister affiliate Kolon Fashion Material, the company can stay innovative and meet the demands of the global market.

In comparison to its major local competitors, Kolon FnC's global expansion strategy stands out. While Korean fashion firms typically focus on licensing or acquiring foreign brands, Kolon FnC has taken a different approach by acquiring small-sized designer shops and fashion accessory shops. This unique strategy allows them to have more control over their brand image and product offerings.

Based on the comparative analyses of Kolon FnC and its competitors, future strategic directions for Kolon FnC can be recommended. Firstly, the company should continue to focus on attracting talented young designers in Korea to differentiate itself from global competitors. This can be a viable source of competitive advantage in the global fashion industry.

Additionally, Kolon FnC should further enhance its R&D capability to develop new garment materials. This will enable the company to stay ahead in terms of innovation and meet the changing demands of consumers.

Overall, the strategic implications of the evolution of the Korean fashion industry have prompted Korean fashion firms, including Kolon FnC, to adopt diverse global expansion strategies. By focusing on their strengths, diversifying their fashion portfolio, collaborating with artists, and enhancing their R&D capability, these firms can position themselves competitively in the global market.

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Answer:

Step-by-step explanation:

Net monthly income = 3218 +3218 = $ 6436

$ 1817 is the fixed expense for net income $6436. So, to find the percentage, multiply by 100

\(Percentage \ of \ fixed \ expenses = \dfrac{1817}{6436}*100\)

                                   = 28%

Answer:

Step-by-step explanation:

The slope is - 2/3 and the point on the line is (-3, -1).

Find the y-intercept:

The line is:

Correct choice is D

Equation in point slope form

Option D

Answer:

(a) Equation:  (x + 7) + (4x - 3) + (3x) = 180

(b) m ∠D = 29°, m ∠E = 85°, and m ∠F = 66°

Step-by-step Explanation:

(a):  According to the triangle sum theorem, the sum of the interior angles of a triangle equals 180°.  Thus, setting the sum of the angles equal to 180 allows us to find x:

m ∠D + m ∠E + m ∠F = 180

Equation:  (x + 7) + (4x - 3) + (3x) = 180°

(b):

Step 1:  First, we need to find x:

(x + 7) + (4x - 3) + (3x)

(x + 4x + 3x) + (7 - 3) = 180

8x + 4 = 180

8x = 176

x = 22

Step 2:  Now we can plug in 22 for x for each expression representing the angle measures:

Plugging in 22 for x in ∠D expression:

m ∠D =  (22 + 7)

m ∠D = 29°

Plugging in 22 for x in ∠E expression:

m ∠E = 4(22) -3

m ∠E = 88 - 3

m ∠E = 85°

Plugging in 22 for x in ∠F expression:

m ∠F = 3(22)

m ∠F = 66°

Optional Step 3:  We can check that the sum of the three angles we've found equals 180:

29 + 85 + 66 = 180

114 + 66 = 180

180 = 180

Answer: 3x + 5

Step-by-step explanation:

First, we need to understand that x is a variable, an unknown number. Think back to how you would do multiplication with numbers that you know. Here are some examples:

If you want to multiply 2 by 3, you would write 3 × 2.

If you want to multiply 3 by 256, you would write 3 × 256.

If you want to multiply 3 by x, you would write 3 × x.

If you want, you can simplify 3 × x to 3x. 3x just means that you are multiplying three by x.

Now we have finished the first step. 3x means three times a number. Now, what about the plus 5?

For the next part, we need to add five to this expression. Think back to how you know how to do addition.

If you want to add 5 to 9, you would write 9 + 5.

If you want to add 5 to 24, you would write 24 + 5.

If you want to add 5 to x, you would write x + 5

If you want to add 5 to 3x, you would write 3x + 5.

In conclusion, 3x + 5 means three times a number (x) plus five. If this doesn't make sense yet, don't worry. You have got this. Don't give up. For more information, search "How to write an expression."

ANSWER

C = -4

EXPLANATION

Given:

15x +20y= -10

6x + 8y= c

Thus we have:

a1 = 15x, b1 = 20y, c1 = -10

and

a2 = 6x, b2 = 8y, c2 = c

The condition now is:

i.e:

Determine c using the x

Determine c using the y

Hence, the value of C that will make the systems a dependent system is -4.

Mountain Mack can carve 30 fishing lures and 36 duck decoys in a week.

Mountain Mack spends his time carving fishing lures and duck decoys. It is stated that if he spends all of his time carving fishing lures, he can carve 30 lures in a week. Similarly, if he spends all of his time carving duck decoys, he can carve 25 decoys in a week. Additionally, for every 5 duck decoys Mountain Mack carves, he must give up 6 fishing lures.

To determine the number of fishing lures and duck decoys Mountain Mack can carve in a week, we need to consider the trade-off between the two activities. Let's assume that Mountain Mack spends x amount of time carving fishing lures and y amount of time carving duck decoys in a week.

From the given information, we know that if Mountain Mack spends all of his time carving fishing lures, he can carve 30 lures in a week. Therefore, we can set up the equation:

x = 30

Similarly, if Mountain Mack spends all of his time carving duck decoys, he can carve 25 decoys in a week. Hence, we can set up another equation:

y = 25

Now, let's consider the trade-off between fishing lures and duck decoys. For every 5 duck decoys carved, Mountain Mack must give up 6 fishing lures. This means that for every 5 units of y (duck decoys), he loses 6 units of x (fishing lures). We can express this relationship as:

(5/6)y = x

Now we have a system of equations:

x = 30

y = 25

(5/6)y = x

To solve this system, we can substitute the value of x from the first equation into the third equation:

(5/6)y = 30

y = (6/5) * 30

y = 36

Now that we have the value of y, we can substitute it back into the second equation to find x:

x = 30

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The properties of eclipsing binary systems are detected by examining a light curve.

Eclipsing binary systems are a type of binary star system where the stars orbit each other in such a way that they periodically pass in front of each other from the perspective of an observer on Earth. This results in periodic variations in the total amount of light observed from the system, which is known as the light curve.

By studying the shape and timing of the light curve, astronomers can determine a number of properties of the binary system, such as the orbital period, the sizes and masses of the stars, and their distance from Earth.

For example, the duration and depth of the eclipses can be used to estimate the sizes of the stars, while the timing of the eclipses can reveal information about their orbital period and any changes in their orbit over time. By analyzing the light curve in detail, astronomers can gain valuable insights into the structure, behavior, and evolution of binary star systems.

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Answer:

the answer is  4.979

Step-by-step explanation:

Answer:

The answer is 4.979

Step-by-step explanation:

Answer:

5 4/5 or 5.8

Step-by-step explanation:

convert 29/5 to 5 4/5

or

divide 29/5 is 5.8

\(\qquad\) \(\purple{\twoheadrightarrow\bf 2cos^2A = 1 + cos2A }\)

\(\qquad\) \(\purple{\twoheadrightarrow\bf a^3 +b^3 = (a+b)^3 -3ab(a+b)}\)

\(\qquad\) \(\purple{\twoheadrightarrow\bf 2 sinA cosA = sin2A}\)

________________________________________

1)

\(\qquad\) \(\twoheadrightarrow\bf L.H.S\)

\(\qquad\) \(\pink{\twoheadrightarrow\bf cos^4 x}\)

\(\qquad\) \(\twoheadrightarrow\sf \dfrac{1}{4} (2cos^2x)^2\)

\(\qquad\) \(\twoheadrightarrow\sf \dfrac{1}{4}(1+cos2x)^2\)

\(\qquad\) \(\twoheadrightarrow\sf \dfrac{1}{4}(1+2cos2x+cos^22x)\)

\(\qquad\) \(\twoheadrightarrow\sf \dfrac{1}{4}+\dfrac{1}{2}cos2x+\dfrac{1}{8}\times 2cos^22x\)

\(\qquad\) \(\twoheadrightarrow\sf \dfrac{1}{4}+\dfrac{1}{2}cos2x+\dfrac{1}{8}\times(1+cos4x)\)

\(\qquad\) \(\pink{\twoheadrightarrow\bf \dfrac{1}{4}+\dfrac{1}{2}cos2x+\dfrac{1}{8}\times cos4x} \)

\(\qquad\) \(\twoheadrightarrow\bf R.H.S\)

______________________________________

2)

\(\qquad\) \(\twoheadrightarrow\bf L.H.S\)

\(\qquad\) \(\pink{\twoheadrightarrow\bf cos^6\theta +sin^6\theta }\)

\(\qquad\) \(\twoheadrightarrow\sf (cos^2\theta)^3 +(sin^2\theta)^3\)

\(\twoheadrightarrow\sf (cos^2\theta +sin^2\theta)^3 -3cos^2\theta sin^2\theta (cos^2\theta +sin^2\theta)\)

\(\qquad\) \(\twoheadrightarrow\sf 1-3\times \dfrac{1}{4}\times 4(sin\theta cos\theta) ^2\)

\(\qquad\) \(\twoheadrightarrow\sf 1-\dfrac{3}{4}(2sin\theta cos\theta) ^2\)

\(\qquad\) \(\pink{\twoheadrightarrow\sf 1-\dfrac{3}{4}sin^22\theta}\)

\(\qquad\) \(\twoheadrightarrow\bf R.H.S\)

Answer:

all 3 options are true : A, B, C

Step-by-step explanation:

warning : it has come to my attention that some testing systems have an incorrect answer stored as right answer for this problem.

they say that A and C are correct.

but I am going to show you that if A and C are correct, then also B must be correct.

therefore, my given answer above is the actual correct answer (no matter what the test systems say).

originally the information about the alignment of the point F in relation to point E was missing.

therefore, I considered both options :

1. F is on the same vertical line as E.

2. F is not on the same vertical line as E.

because of optical reasons (and the - incomplete - expected correct answers of A and C confirm that) I used the 1. assumption for the provided answer :

the vertical line of EF is like a mirror between the left and the right half of the picture.

A is mirrored across the vertical line resulting in B. and vice versa.

the same for C and D.

this leads to the effect that all 3 given congruence relationships are true.

if we consider assumption 2, none of the 3 answer options could be true.

but if the assumptions are true, then all 3 options have to be true.

now, for the "why" :

remember what congruence means :

both shapes, after turning and rotating, can be laid on top of each other, and nothing "sticks out", they are covering each other perfectly.

for that to be possible, both shapes must have the same basic structure (like number of sides and vertices), both shapes must have the same side lengths and also equally sized angles.

so, when EF is a mirror, then each side is an exact copy of the other, just left/right being turned.

therefore, yes absolutely, CAD is congruent with CBD. and ACB is congruent to ADB.

but do you notice something ?

both mentioned triangles on the left side contain the side AC, and both triangles in the right side contain the side BD.

now, if the triangles are congruent, that means that each of the 3 sides must have an equally long corresponding side in the other triangle.

therefore, AC must be equal to BD.

and that means that AC is congruent to BD.

because lines have no other congruent criteria - only the lengths must be identical.

6x

Step-by-step explanation:

1.2(4x-1)=8x-2=6x

The value of the angle x in the given polygon image is: x = 54°

The formula to find the interior angles of a polygon is:

θ = 180(n - 2)/n

Thus, for a pentagon with 5 sides, we have:

θ = 180(5 - 2)/5

θ = 540/5

θ = 108°

Interior angle of a square is 90 degrees and since angle at a point is 360 degrees then we have:

x + 108 + 108 + 90 = 360

x = 360 - 306

x = 54°

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Answer:

523.33 cm³

Step-by-step explanation:

Volume of sphere is given by the formula :

V = (4/3)×pi×r³

= (4/3)×3.14×125

= 523.33 cm³

Answer:

The degree of the power function is 3

Step-by-step explanation:

Let the power function be f(x) = b × xᵃ

Therefore, from the table, we have;

40 = b × (-2)ᵃ

5 =  b × (-1)ᵃ

0 = b × 0ᵃ

-5 = b × (1)ᵃ

-40 = b × (2)ᵃ

From -5 = b × (1)ᵃ, we have;

1ᵃ = 1, which gives;

-5 = b × 1

b = -5

From -40 = b × (2)ᵃ, where b = -5, we have;

-40 = -5 × (2)ᵃ

(2)ᵃ = -40/(-5) = 8

(2)ᵃ = 8 = (2)³

∴ a = 3

㏑(2)ᵃ = ㏑(8)

a·㏑(2) = ㏑(8)

a = ㏑(8)/(㏑(2)) = 3

a = 3

The power function is f(x) = -5 × x³

∴ The degree of the power function is 3.