Please help due ASAP
I really need help

Answer:

there are no real solutions

Step-by-step explanation:

\(\log_5(x-1)+\log_5(x+3)-1=0\\\\\log_5(x-1)+\log_5(x+3)=1\)

there is a rule that says

\(\log_b(a)+\log_b(c)=\log_b(ac)\)

so we have

\(\log_5(x-1)+\log_5(x+3)=\log_5((x-1)(x+3))=1\)

and we have the definition

\(\log_a(b)=c\\\\a^{c} =b\)

so we have

\(5^{1} = (x-1)(x+3)\\\\5=x^{2} -1x+3x-3\\\\5=x^{2} +2x-3\\\\0=x^{2} +2x-3-5\\\\0=x^{2} +2x-8\\\\\)

and using the quadratic formula we get that

there are no real solutions

The value of log5(x - 1) + log5(x + 3) - 1 = 0 is x = 1 and x = -3.

The logarithm is exponentiation's opposite function in mathematics.

This indicates that the exponent to which b must be raised in order to obtain a number x is the logarithm of x to the base b. For instance, because 100 = 10², the logarithm of 100 in base 10 is 2, or log10 = 2.

Given, log5(x - 1) + log5(x + 3) - 1 = 0.

As log + log b = log(ab).

∴ log5(x - 1) + log5(x + 3) - 1 = 0.

log5{(x - 1)(x + 3)} = 1.

(x - 1))x + 3) = 0.  (as any value to the power zero is 1)

x - 1 = 0 Or x + 3 = 0.

x = 1 Or x = - 3.

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Answer:

rational

Step-by-step explanation:

Answer:

it's Rational Number

Step-by-step explanation:

since each integer can't be written in the fraction form or for this example it would be thus 5 so it would be a rational number

Answer:

6

Step-by-step explanation:

All triangles equal 180 degrees to this is what I did:

8x + 2 + 70 + 60 = 180

8x + 2 + 130 = 180

8x + 132 = 180

subtract 132 from each side

8x = 48

now divide each side by 8 to isolate the x

x = 6.

Answer:

it would be 0.7 got it right when i done it

Step-by-step explanation:

Answer: real answer is 0.278

Step-by-step explanation:

Charles Darwin predicted that tetrapods evolved from lobe-finned fishes. The observation that led to this hypothesis is the similarity of the limb structure of tetrapods to lobe-finned fish fins. He observed that the fin structure of the fish contained a similar bone pattern as the limb structure of tetrapods.

To support the hypothesis, the evidence that we can expect to find are fossils that have the transitional structures between the two organisms. We can also expect to find evidence of how the fins in fishes changed over time and how they evolved into the limb structures that we see in tetrapods. This could be in the form of fossils with intermediate stages between the two groups, showing how the structure of the fins changed over time and how that might have influenced the development of tetrapod limbs.

To find such fossils, we would look for rocks from the Devonian period, which lasted from around 419 to 359 million years ago. This is because this is the time period when tetrapods are believed to have evolved from lobe-finned fishes. It was during this period that the early tetrapod species such as Ichthyostega and Acanthostega evolved. As such, fossils of these early tetrapods and the fish they evolved from, as well as any intermediate fossils, would be most likely found in rocks from this time period.

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By using the unitary method , the cost of one shotgun shell to determine that the cost of shooting the last 6 ducks would be $6.86.

The unitary method involves finding the value of one unit and then using that value to find the value of a given number of units. In this problem, we can use the number of shotgun shells as the unit of measurement. Let's say Bill used x shotgun shells to shoot 8 ducks on his previous hunting trip. Therefore, the cost of shooting 8 ducks would be the cost of x shotgun shells.

Now, we know that Bill shot 14 ducks using the same amount of shotgun shells he used on his previous trip. Therefore, the cost of shooting 14 ducks would be the cost of x shotgun shells. We can use a proportion to find the value of x.

8 ducks can be shot using x shotgun shells, so 14 ducks can be shot using (14/8) x x shotgun shells.

Simplifying this expression, we get:

(14/8) x x = 14 ducks

x = (8/14) x 14 ducks

x = 8/7 ducks

So, Bill used 8/7 shotgun shells to shoot 1 duck on his previous hunting trip.

Now, to find the cost of shooting the last 6 ducks, we need to determine how many shotgun shells he would need. Using the unitary method again, we can say:

1 duck can be shot using 8/7 shotgun shells, so 6 ducks can be shot using 6 * (8/7) shotgun shells.

Simplifying this expression, we get:

6 x (8/7) = 48/7 shotgun shells

Therefore, to shoot the last 6 ducks, Bill would need 48/7 shotgun shells. To determine the cost, we need to know the cost of one shotgun shell. Let's say the cost of one shotgun shell is $1. Then the cost of shooting the last 6 ducks would be:

(48/7) x $1 = $6.86 (rounded to the nearest cent)

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9514 1404 393

Answer:

  2/15

Step-by-step explanation:

The given expression for θ can be rewritten to ...

  5sin(θ + arctan(-3/4)) = 0

This will have solutions ...

  θ +arctan(-3/4) = nπ

  θ = nπ - arctan(-3/4) = nπ + arctan(3/4)

__

The corresponding values of sine and cosine will be ...

  sin(arctan(3/4)) = 3/5

  cos(arctan(3/4) = 4/5

or both values may be negative. Either sign will give the same result in the expression we're to find.

  (2sin(θ) -cos(θ))/(sin(θ) +3cos(θ)) = (2(3/5) -(4/5))/(3/5 +3(4/5))

  = ((6 -4)/5)/((3+12)/5) = 2/15

  \(\boxed{\dfrac{2\sin\theta-\cos\theta}{\sin\theta+3\cos\theta}=\dfrac{2}{15}}\)

A cat weighing 5 lb and fed at a rate of 40 calories/lb/day should be fed a certain number of cups of commercial cat food at each meal if fed twice a day. We need to calculate this based on the given information that the cat food has 120 kcal/cup.

To determine the amount of cat food to be fed at each meal, we can follow these steps:

1. Calculate the total daily caloric intake for the cat:

  Total Calories = Weight (lb) * Calories per lb per day

                 = 5 lb * 40 calories/lb/day

                 = 200 calories/day

2. Determine the caloric content per meal:

  Since the cat is fed twice a day, divide the total daily caloric intake by 2:

  Caloric Content per Meal = Total Calories / Number of Meals per Day

                          = 200 calories/day / 2 meals

                          = 100 calories/meal

3. Find the number of cups needed per meal:

  Caloric Content per Meal = Calories per Cup * Cups per Meal

  Cups per Meal = Caloric Content per Meal / Calories per Cup

                = 100 calories/meal / 120 calories/cup

                ≈ 0.833 cups/meal

Therefore, the cat should be fed approximately 0.833 cups of commercial cat food at each meal if fed twice a day.

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Divide vat by price

40/400 = 0.1

Multiply by 100

0.1 x 100 = 10%

Rate of vat is 10%

Answer:

29839150

Step-by-step explanation:

$1= 124.85

$23,9000= 124.85*239000

=RS.29839150

Answer:

677 seats

Step-by-step explanation:

There are 26 letters in the alphabet.

26 × 26 possible combinations of first and last name initials

To guarantee that there are at least two people having the same first and last initials:

26 × 26 + 1 = 677 seats

a) Using the Euclidean algorithm, we can find gcd (707,413) as follows:707 = 1 · 413 + 294413 = 1 · 294 + 119294 = 2 · 119 + 562119 = 2 · 56 + 71356 = 4 · 71 + 12 71 = 5 · 12 + 11 12 = 1 · 11 + 1

Thus, gcd (707,413) = 1.

We can find the coefficients s and t that solve the equation 707s + 413t

= 1 as follows:1 = 12 - 11 = 12 - (71 - 5 · 12) = 6 · 12 - 71 = 6 · (119 - 2 · 56) - 71

= - 12 · 56 + 6 · 119 - 71

= - 12 · 56 + 6 · (294 - 2 · 119) - 71 = 18 · 119 - 12 · 294 - 71

= 18 · 119 - 12 · (413 - 294) - 71 = 30 · 119 - 12 · 413 - 71

= 30 · (707 - 1 · 413) - 12 · 413 - 71 = 30 · 707 - 42 · 413 - 71

Thus, s = 30, t = -42. So we have found that 707(30) + 413(−42) = 1.

b) Since 707s + 413t = 1 and 9 does not divide 1, the equation 707x + 413y = 9 has no integer solutions. Therefore, we can conclude that there are no such integers x and y.

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Statement Problem: Calculate the percentage of the income based on the amount used to start the business.

Solution:

The percentage income is;

Thus, we have;

A higher slope indicates a stronger relationship between the variables, and the sign (positive or negative) indicates the direction of the relationship (positive: both variables increase together, negative: one variable increases while the other decreases).

When comparing the slopes of the regression lines for two models, you're essentially looking at the differences in their unstandardized coefficients. These coefficients represent the change in the dependent variable for each unit change in the independent variable, keeping all other variables constant.

In the unstandardized model you mentioned, the slope of 0.96 means that for every one-unit increase in the independent variable, the dependent variable is expected to increase by 0.96 units, on average. This helps us understand the strength and direction of the relationship between the two variables in the model.

To compare the slopes between two models, simply examine their unstandardized coefficients.

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To take a systematic sample of 100 companies from a population of 1,803 companies, determine the sampling interval (k) which is N/n, choose a random starting point between 1 and k, and select every kth company until 100 companies are sampled.

To take a systematic sample of 100 companies from the 1,803 companies that are members of an industry trade association, follow these steps

Determine the sampling interval (k), which is the number of companies in the population divided by the desired sample size. In this case, k = 1803/100 = 18.03. Round this number up or down to the nearest whole number based on your sampling preferences.

Choose a random starting point between 1 and k. For example, you could randomly select a number between 1 and 18.

From the starting point, select every kth company in the list of members until you have 100 companies. For example, if the starting point is 4, you would select companies 4, 22, 40, 58, 76, 94, 112, and so on until you reach 100 companies.

Important numerical values used in this process are:

Population size (N) = 1,803 companies

Desired sample size (n) = 100 companies

Sampling interval (k) = N/n = 1803/100 = 18.03

Random starting point (any number between 1 and k, depending on sampling preference)

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Answer: 8/10

Step-by-step explanation: so you have to multiply 5 times x u till you get 10 so you’ll multiply it 2 times and since you multiplied the left 5 times two you have to multiply the 4 by 2 also to keep everything equal so the final answer is 8/10

Answer:

30. 540

31. 720

32.360

33. 540

34. 180

35.900

Step-by-step explanation:

Sum of the angles = number of sides in the polygon -  two, all multiplied by 180 degrees.

*if you want to  find the measure of one interior angle, take that same formula and divide by the number of sides n: (n - 2) * 180 / n.

30 .

sum of the angles = (5-2)180

sum of the angles =540

31.

sum of the angles = (6-2)180

sum of the angles =720

32.

sum of the angles = (4-2)180

sum of the angles =360

33.

sum of the angles = (5-2)180

sum of the angles= 540

34. sum of the angles = (3-2)180

sum of the angles = 180

35.

sum of the angles = (7-2)180

sum of the angles = 900

The tree should be 22.5 feet tall in the mural.

To determine the height of the tree in the mural, we can set up a proportion based on the scale ratio between Devon's height and the height of the tree.

Let's denote the height of the tree in the mural as 'x'.

According to the given information:

Devon's actual height: 6 feet

Devon's height in the mural: 4.5 feet

Tree's actual height: 30 feet

Setting up the proportion:

(Devon's height in the mural) / (Devon's actual height) = (Tree's height in the mural) / (Tree's actual height)

Substituting the given values:

4.5 feet / 6 feet = x / 30 feet

To solve for 'x', we can cross-multiply:

4.5 feet * 30 feet = 6 feet * x

135 feet = 6x

Divide both sides by 6:

x = 135 feet / 6

Simplifying the division:

x = 22.5 feet

Therefore, in the painting, the tree should stand 22.5 feet tall.

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Answer:

1) y = -1.5x - 1     ||   2) y = -1.5x + 1    ||  3. D ( 2 , -8 )

Step-by-step explanation:

1)

two coordinates: ( 0 , -1 ) , ( 2 , -4 )

slope = ( y2-y1 )÷(x2-x1) = (-4--1)÷(2-0) = -1.5

then find equation using: y - y1 = m ( x - x1 )

                                        : y - - 1 = -1.5 ( x - 0 )

                                        : y = -1.5x - 1

2)

two coordinates: ( 0 , 1 ) , ( -2 , 4 )

slope = ( 4 - 1) ÷ (-2-0) = -1.5

Find equation using y = mx +b ........where m is slope and b is y-intercept

y = -1.5x + 1

3)

y + 8 = 3(x -2 )

y = 3x -14  ..........main equation in slope intercept form.

A)

y = 3(-2)-14

y = -20 .therefore option A is incorrect

B)

y = 3(8)-14

y = 10 .therefore option B is incorrect

C)

y = 3(-8)-14

y = -38.therefore option C is incorrect

D)

y = 3(2)-14

y = 6 -14

y = -8 . therefore it matches and is correct answer.

the line crosses D( 2 , -8 )

As per your questions,

IMAGE 1 :-

The equation is

\(y = - \frac{3}{2}x - 1\)

(Explanation attached as 1st image. Check it!)

IMAGE 2 :-

The equation is

\(y = - \frac{3}{2}x + 1 \)

(Explanation attached as 2nd image. Check it!)

IMAGE 3 :-

When the point is (2,-8)

\(y + 8 = 3(x - 2)\)

\( = > - 8 + (- 8) = 3 \times (2 - 2)\)

\( = > 0 = 0\)

Therefore, (2,-8) is true.

So, the answer is the option (2,-8)

~ Benjemin360

Answer:

The y coordinate is 3

Step-by-step explanation:

Here, we want to find the y-coordinate of the line that divides the line segment in the given ratio.

To calculate this, we shall be using the internal division formula;

It is as follows;

( (mx2 + nx1) /m + n , (my2 + ny1)/( m + n))

In this question;

m = 3 and n = 4

x1 = 0 , y1 = 6

x2 = -10, y2 = -1

Now substituting these values into the equation, we have;

(3(-10) + 4(0)/(3 + 4) , (3(-1) + 4(6)/(3+4))

= -30/7 , (-3 + 24)/7

= -30/7 , 21/7

= -30/7 , 3

Answer:

15 miles= 3 hours

   x         =    2.5

37.5/3= 3x/3

         12.5 miles   =  x

Answer: x=3 or x=5

Step-by-step explanation:

0 = 0=(x-4)²-1

(x -4)^2-1=0

Factor the expression using

a^2-b^2= ( a + b ) ( a - b )

Apply zero Product Property

( (x -4 ) + 1 ) ( (x - 4 ) - 1 ) = 0

( x - 4 ) + 1 = 0

Determine the sign

x - 3 = 0

Rearrange variables to the left side of the equation

x = 3

( x - 4 ) + 1 = 0

Determine the sign

x - 5 - 1 = 0

Combine like terms

x - 5 = 0

Rearrange variables to the left side of the equation

x = 5

The projectile hit the ground approximately at t = 5.3 seconds.

It is given that projectile with an initial velocity of 48 feet per second is launched from a building 190 feet tall.

It is required to find when will the projectile hit the ground if the projectile equation is \(\rm h(t)= -16t^2+48t+190\)

It is defined as the graph of a quadratic function that has something bowl-shaped.

We have the projectile equation:

\(\rm h(t)= -16t^2+48t+190\) .....(1)

When it hit the ground the value of h(t) = 0, equate the equation(1) with 0

We get:

\(\rm 0= -16t^2+48t+190\)

or

\(\rm 16t^2-48t-190= 0\)

It is a quadratic equation,

Compare with the equation \(ax^2+bx+c=0\)

a = 16, b = -48, and c = -190

By using the formula:

\(\rm x= \frac{-b\pm\sqrt{b^2-4ac} }{2a}\)

\(\rm t= \frac{-(-48)\pm\sqrt{(-48)^2-4(16)(-190)} }{2(16)}\\\\\rm t= \frac{48\pm{(120.266)} }{32}\\\)

t = -2.25  or t = 5.25

Time can not be a negative quantity, so leave the negative value of 't'.

So, t = 5.25 ≈ 5.3 seconds

Thus, the projectile hit the ground at t = 5.3 seconds.

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Answer:

7.74cm ^2

Step-by-step explanation:

a=pie * r ^2

3.14*3^2=3.14*9=28.26  then you know all sides of a square are equal and 3 is half of 1 side so 6*6-=36 36-28.26=7.74

the answer to ur question is 156

The median represents the middle value of the data 5.8 feet will be the middle value.

The median represents the middle value in a dataset. The median is important because it gives us an idea of where the center value is located in a dataset. The median tends to be more useful to calculate than the mean when a distribution is skewed and/or has outliers.

Given that apod of dolphins contains 800 dolphins of different ages and lengthens. The median length of dolphins in this pod is 5.8 feet.

From the definition, we can see that of the 800 dolphins the length of the middle dolphin is 5.8 feet because it is a median and the upper values will be greater than 5.8 feet and below it all the dolphins will have smaller lengths.

Therefore, the median represents the middle value of the data 5.8 feet will be the middle value.

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The approximate altitude of the rocket is 34.45 km (rounded to the nearest kilometer).

Given:

Angle of elevation from station A = 41°

Angle of elevation from station B = 75°

Distance between station A and station B = 20 km

Using the tangent function to calculate the altitude 'h' for each station:

For station A:

h = 20 * tan(41°) ≈ 17.39 km (rounded to two decimal places)

For station B:

h = 20 * tan(75°) ≈ 74.64 km (rounded to two decimal places)

Taking the average of the two altitudes,

(h from station A + h from station B)/2 = (17.39 + 74.64)/2 ≈ 34.45 km (rounded to two decimal places)

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\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$9651\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.10\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &4 \end{cases} \\\\\\ A = 9651\left(1+\frac{0.10}{1}\right)^{1\cdot 4}\implies A=9651(1.1)^4 \implies A \approx 14130.03\)

There are $13,511.4 amount in 4 years.

A quick and easy method of calculating the interest charge on a loan is called a Simple interest.

Given that;

Lamar deposited $9,651 in an account earning 10% interest compounded annually.

Here, We have;

Principle amount = $9,651

Rate = 10%

Time = 4 years

Hence, Value of interest is,

Interest = 9651 × 4 × 10 / 100

            = 3860.4

Therefore, Total amount he have after 4 years is,

⇒ $9,651 + $3,860.4

⇒ $13,511.4

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Answer:

w = 11

Step-by-step explanation:

Solve for w by simplifying both sides of the equation, then isolating the variable.

Answer:

w = 11

Step-by-step explanation:

To solve for w, simplify both sides, then isolate the variable.

Hope I could help.

Answer: -12 -10i

Step by step:

(-9 -8i) - (3 +2i)

-9 -8i -3 -2i distribute negative to the 3 and 2i

-9 -3 -8i -2i combine like terms

-12 -10i

The difference of the given expression is -12-10i. Therefore, option C is the correct answer.

Given that, (3 + 2i) from (–9 – 8i).

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

Now, subtract the expression (3 + 2i) from (–9 – 8i)

That is -9-8i-(3+2i)

= -9-8i-3-2i

= -12-10i

The difference of the given expression is -12-10i. Therefore, option C is the correct answer.

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