log8​x+log8​(x+7)=1
step bye step please​

Step-by-step explanation:

8x² - 10x - 3 = (2x - 3)(4x + 1)

(2x - 3)(4x + 1) = 0

2x = 3 Or 4x = -1

x = 3/2 x = -1/4

Answer:

The answer is 15.71

Step-by-step explanation:

All you have to do is multiply Pie or 3.14 with 5 from the sphere. 3.14 x 5 = 15.7. If you use the Pie symbol when multiplying you'll get this answer -> 15.70796327. But I recommend using the pie symbol and just rounding it off. When rounding 15.70796327 to the hundredth place, do you know the saying 5 & up moves up and 4 & below stays??? Will it's the same thing here. 7 in 15.707 will move the 0 to a 1 instead of a 0.

The price elasticity of demand for x is -1.25.

Price elasticity of demand (PED) is a measure of how responsive quantity demanded is to changes in price. It is calculated as follows:

```

PED = (% change in quantity demanded)/(% change in price)

```

In this case, the price of x increases by 12% and the quantity demanded decreases by 15%. Therefore, the PED is -1.25.

A PED of -1.25 means that the quantity demanded is relatively inelastic. This means that a change in price will have a relatively small effect on quantity demanded.

The demand for x is a normal good. This means that as the price of x increases, the quantity of value demanded of x will decrease.

The demand for x is relatively inelastic. This is because the PED is -1.25, which is less than -1. A PED of -1 or less indicates that the demand is inelastic.

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Answer:

6000 meters per minute

Answer:

This race car can reach 6,000 meters per minute.

Step-by-step explanation:

There are 60 seconds in one minute, so multiply 100×60. The product is 6,000. I hope this helps you. Please give Brainliest :)

30.625 rounded to the nearest hundredth is 30.630, because there is a five at the end, it jumps +5.

The value of x is 6.67 degrees.

The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.

The (5x + 9)° angle on line m and the (7x -  9)° angle on line n are corresponding angles.

We have given that Line m and Line n are parallel.

t line is the transversal line on the two parallel lines, line m and line n.

We see that,

(5x + 9)° angle on line m is corresponding to the  (7x -  9)° angle on line n.

So,

(5x + 9)° +  (7x -  9)° = 180

12x = 180

x = 80 /12

x = 6.67

Thus, The value of x is 6.67 degrees.

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If I read this right,

you put the numbers where the letters go

2 (8) (-4)

since they are in parenthesis, you multiply them.

= -64

$140.75

Step-by-step explanation:

$350 minus $165.65 is $184.35 . $184.35 minus 43.60 is 140.75 :)

With a credit card balance of $17,426, a minimum monthly payment of $461, and an interest rate of 15.5%, we need to calculate the number of years it will take to pay off the card without adding any additional debt.

To determine the time required to pay off the credit card, we consider the monthly payment and the interest rate. Each month, a portion of the payment goes towards reducing the balance, while the remaining balance accrues interest.

To calculate the time needed for repayment, we track the decreasing balance each month. First, we determine the interest accrued on the remaining balance by multiplying it by the monthly interest rate (15.5% divided by 12).

We continue making monthly payments until the remaining balance reaches zero. By dividing the initial balance by the monthly payment minus the portion allocated to interest, we obtain the number of months needed for repayment. Finally, we divide the result by 12 to convert it into years.

In this scenario, it will take approximately 3.81 years to pay off the credit card (17,426 / (461 - (17,426 * (15.5% / 12))) / 12).

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The value of Tan( A) = 53.1°

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

sin(tetha) = opp/hyp

cos( tetha) = adj/hyp

tan ( tetha) = opp/adj

The opposite to the angle A is a which is 8, the adjacent is 6 and hypotenuse 10

Tan(A) = 8/6

Tan(A) = 1.33

A = tan^-1 ( 1.33)

A = 53.1°

therefore the value of tan A is 53.1°

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Answer:

They get 4 good points!

Step-by-step explanation:

21-17= 4:)

Answer:

2.364646461616161616

Answer:

2.364646461616161616

Step-by-step explanation:

There are infinitely many such numbers, so I'll give some examples.

\(\sqrt{25}=5\\\sqrt{27}\approx5.196\)

Therefore, such numbers can be \(5.19,5.03,5.\overline{17},5.\overline{045},\dfrac{77}{15},\dfrac{22937}{4500}\).

Answer:

25 = 5

27 = 5.196152422706632

Step-by-step explanation:

if we divide the number with prime number .

25/5 = 5

5/5 = 0

5*5 = 25

5 is repeating two times so it is a square root of 25

in 27 is not square

if we divide the prime number repeating 3 times so if we have another prime number we can calculate the square root of a number

Answer:

10 Joules/second

Step-by-step explanation:

To find the power needed to get up the stairs, we need to divide the amount of work done (30 Joules) by the time it took to do the work (3 seconds):

Power = Work / Time

Power = 30 Joules / 3 seconds

Power = 10 Joules/second

Therefore, it takes 10 Joules/second of power to get up the stairs.

The volume of the solid whose base is a circle centered at the origin with a radius r is 16r³/3 cubed unit.

The equation of the circle is the equation which is used to represent the circle in the algebraic equation form, with the value of center point in the coordinate plane and measure of radius.

The equation of the circle can be given as,

\(x^2+y^2=r^2\)

Here, (r) is the radius of the circle.

Rewrite this equation as,

\(y^2=r^2-x^2\\y=\sqrt{r^2-x^2}\)

This will give you the half the length of the side. Thus, the length of the side of the square is,

\(s=2y=2\sqrt{r^2-x^2}\)

The area of the square it square of its side. Thus, the area of the square is,

\(A(x)=s^2\\A(x)=(2\sqrt{r^2-x^2})^2\\A(x)=4(r^2-x^2})\)

The volume of the solid can be got by integrating the area of the cross-section.

\(V=\int\limits {A(x)} \, dx\)

Here, A(x), provides the area of the square at the point x. Thus,

\(V=\int\limits {A(x)} \, dx\\V=\int\limits_{-r}^r {4(r^2-x^2)} \, dx\\V=[ {4(r^2x-\dfrac{x^3}{3})}]^r_{-r}\\V= {4(r^2(r)-\dfrac{(r)^3}{3})}- {4(r^2(-r)-\dfrac{(-r)^3}{3})}\\V=4[r^3-\dfrac{r^3}{3}}+ {r^3-\dfrac{r^3}{3}]\\V=\dfrac{16r^3}{3}\)

Thus, the volume of the solid whose base is a circle centered at the origin with a radius r is 16r³/3 cubed unit.

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The interval of convergence for the given power series is (2, 8).

To find the interval of convergence for the given power series. We have the power series:

∑(n=2 to ∞) ((x-5)ⁿ)/(3ⁿ)

To find the interval of convergence, we'll use the Ratio Test. For the Ratio Test, we need to compute the limit:

L = lim (n → ∞) |(a_(n+1)/a_n)|

For our series, a_n = ((x-5)ⁿ)/(3ⁿ). Therefore, a_(n+1) = ((x-5)(n+1))/(3(n+1)). Now, let's compute the ratio:

|(a_(n+1)/a_n)| = |(((x-5)(n+1))/(3(n+1))) / (((x-5)ⁿ)/(3ⁿ))|

Simplify the expression:

|(a_(n+1)/a_n)| = |(x-5)/3|

The series converges if L < 1. So we have:

|(x-5)/3| < 1

Now, we'll solve for x to find the interval of convergence:

-1 < (x-5)/3 < 1

Multiply each term by 3:

-3 < x-5 < 3

Add 5 to each term:

2 < x < 8

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Answer: width = 82.50 m

Step-by-step explanation:

P = 2l x 2w

425 = 2(130) + 2w

425 - 260 = 2w

w = 165 / 2 = 82.50

The required width of the rectangular field is 82.5 meters.

A rectangular field is 130m long and requires 425 m of fencing to enclose it. The width of the field is to be determined.

rectangle is four sided polygon whose opposites sides are equal and has angle of 90° between its sides.

Here,
Perimeter of rectangle = 2 length + 2 width
                           425  = 2x 130 + 2 x width
                           165 = 2 x width
                           width = 165/2
                           width = 82.5

Thus, the required width of the rectangular field is 82.5 meters.
   

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Answer:

76

Because 11*8=88 and 4*3=12

88-12=76

The answer is random sampling in my thinking.

please mark me brainliest<3

The standard deviation is 7.35.

Standard deviation is used to determine how the values in a group differs from the mean of the values in the group

In order to determine the standard deviation, take the following steps:

Determine the mean of the observation: (87 + 91 + 74 + 73 + 80 + 84 + 68 + 75) / 8 =79

Determine the difference between each value and the mean and then square the result:

(87 - 79)² + ( 91 - 79) ² + (74 - 79)² + (73 - 79)² + (80 - 79)²  + (84- 79)²  + (68 - 79)²  +( 75- 79) ²

64 + 144 + 25 + 36 + 1 + 25 + 121 + 16 = 432

Determine the mean of the sum of the squared differences and then find the square root of the mean:

√432 / 8 = 7.35

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Answer:

\(x+3>27\\ x-8>12\\ 7x\leq 14\\ x+15\geq 4\)

Answer:

96 u

Step-by-step explanation:

area of a triangle is base * height all divided by 2. 24*8/2

In part A, the problem involves a tank containing water with dissolved salt, where brine is continuously added and removed. By considering the rate of salt entering and leaving the tank, we can determine the amount of salt in the tank after 3 hours.

In part B, the problem asks to solve a second-order linear differential equation using power series. By assuming a power series solution and substituting it into the given equation, we can determine the coefficients of the power series and find the solution.

A. To find the amount of salt in the tank after 3 hours, we consider the rate of salt entering and leaving the tank. Since 5 gallons of brine, each containing 31 pounds of salt, enter the tank per minute, the rate of salt entering the tank is 5 * 31 = 155 pounds per minute. The rate of salt leaving the tank is the same since the mixture is kept uniform by stirring. Therefore, the net rate of salt change in the tank is 155 - 0 = 155 pounds per minute. To find the amount of salt after 3 hours (180 minutes), we multiply the net rate of salt change (155 pounds/minute) by the time in minutes (180 minutes): 155 * 180 = 27900 pounds. Hence, the amount of salt in the tank after 3 hours is 27900 pounds.

B. To solve the differential equation y" - xy' - xy = 0 using power series, we assume a power series solution of the form y(x) = ∑(n=0 to ∞) a_n * x^n. We substitute this series into the differential equation and equate coefficients of like powers of x to obtain a recurrence relation for the coefficients a_n. By differentiating y(x) twice and substituting it into the differential equation, we can collect terms with the same powers of x and solve for the coefficients a_n. The recurrence relation will involve the coefficients a_n, a_(n-1), and a_(n-2).

By solving the recurrence relation, we can find the values of the coefficients a_n in terms of the initial conditions or known coefficients. The power series solution y(x) will be the sum of the terms with the determined coefficients. The power series solution allows us to find the solution to the given differential equation in terms of an infinite series, providing a more general and flexible form of the solution compared to specific analytic functions.

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five out of of the twenty-five top-grossing films of 2017 in the united states were part of a movie franchise

If you were to attribute this film, that means you'd say that (something) caused the success of the movie Rocky. This question is basically asking what do you think made this movie a big hit? Personally, I'd say it's because of how the storyline and plot turned out. It's very intriguing and it doesn't just make the movie about boxing. The film adds some love between the protagonist and some other character, and not only that, but the movie teaches you something. Because Rocky lost to Apollo, Rocky didn't care. At least he still had Adrian. So, the movie teaches you that, even if you do lose, at least you still have something and/or someone with you.

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\(\huge \rm༆ Answer ༄\)

In the given question, the two sides of the given triangles are parallel, so the the two corresponding angles of the Triangles are equal to one another.

Therefore, the Triangles are similar by AA similarity criteria ~

And since they are similar, the ratio of sides of one Triangle will be equal to ratio of corresponding sides of the other Triangle.

that is ~

Hence, value of l = 15.4 units ~

Option 2 is correct that is 1.79

When presented in ascending order, the value that 75% of data points fall within is known as the higher quartile, or third quartile (Q3).

The quartiles formula is as follows:

Upper Quartile (Q3) = 3/4(N+1)

Lower Quartile (Q1) = (N+1) * 1/3

Middle Quartile (Q2) = (N+1) * 2/3

Interquartile Range = Q3 -Q1,

1.74, 0.24, 1.56, 2.79, 0.89, 1.16, 0.20, and 1.84 are available.

Sort the data as follows: 0.20, 0.24, 0.89, 1.16, 1.56, 1.74, 1.84, 2.79 in ascending order of magnitude.

The data set has 8 values.

hence, n = 8; third quartile: 3/4 (n+1)th term

Q3 =3/4 of a term (9) term

Q3 =27/4 th term

Q3 = 1.74 + 1.84 / 2 (average of the sixth and seventh terms)

equals 1.76

Thus Q3 is 1.76 that is option 2

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Answer: \(y= -3x+11\)

Step-by-step explanation:

Given equation: \(y=\dfrac13x-3\)

By comparing this to intercept form \(y=mx+c\)  , where m= slope , c=y-intercept.

\(m=\dfrac13\)

Let n= slope of required line.

\(n\times m =-1\)[Product of slope of two per perpendicular line =-1 ]

\(\Rightarrow\ n=\dfrac{-1}{m}\\\\\Rightarrow\ n=\dfrac{-1}{\dfrac13}=-3\)

Equation of line passes through (a,b) and have slope m:

\((y-b)=m(x-a)\)

Equation of required line :

\((y-2)=-3(x-3)\\\\\Rightarrow\ y-2=-3x+9\\\\\Rightarrow\ y= -3x+11\)

Hence, equation of the required line: y= -3x+11

Answer:

D. 195

Step-by-step explanation:

dx/dt = 4+3√3 in the case of the circle with radius 4 and the equation x²+y²=16.

The method of finding an implicit function's dependent variable's derivative by differentiating each term individually, symbolizing the derivative, and then solving the resulting expression for the symbol.

Without having to solve the provided equation for y, you may use the implicit differentiation technique to determine the derivative of y with respect to x.

Because we assume that y may be written as a function of x, the chain rule must always be applied when differentiating the function y.

So, the dx/dt will be:

The circle's equation is: x² + y² = 16

Assuming that x = 2, then:

2² + y²   = 16

y² = 12

y = ±√12

Hence, the first quadrant is positive:

y = √12

y = 2√3

When implicit differentiation is used, we get that:

2x dx/dt + 2y dy/dt = 16

If fracdydt = -3, as is the case, then

2(2) dx/dt - 12√3 = 16

4 dx/dt = 16 + 12√3

dx/dt = 16+12√3/4

dx/dt = 4+3√3

Therefore, dx/dt = 4+3√3 in the case of the circle with radius 4 and the equation x² + y² = 16.

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