Find the value of x which satisfies the following equation.
log2(x−1)+log2(x+5)=4

Answer:

the type of growth defined by the equation is Exponential growth.

Step-by-step explanation:

Exponential growth :-Exponential growth is a pattern of data that shows greater increases with passing time, creating the curve of an exponential function. It occurs when the instantaneous rate of change of a quantity with respect to time is proportional to the quantity itself

expression for exponential growth -

f(x) = k(1+t)^x

f(x) = exponential growth

k = initial amount

t = rate of growth

x = no  of time interval

therefor,

the equation shown in the question represents exponential growth with increasing time.

hence, Exponential growth is the correct answer.

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Answer:

-26

Step-by-step explanation:

2 is 14 away from -12. The other number that is 14 away from -12 is -26.

-12 + x = 2

x  = 14

-12 - 14 = -26

Based on the stated annual interest rate and the face value of the bond, the semiannual payments will be $1,000,000.

The formula to find the semiannual payment is:

= (Face value x Stated annual interest rate) / 2 semi-annual periods per year

Solving gives:

= (50,000,000 x 4%) / 2

= 2,000,000 / 2

= $1,000,000

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The function that includes the given points of (0,−2),(5,13),(−2,−8),(4,10) is the second encircled option by the top right in the image attached.

Note that all function of  (0,−2),(5,13),(−2,−8),(4,10)  can be seen as all the brackets are placed in the form (X, Y), Y=P(x)

In the case above, how we arrived at the answer, you have to fill up the X's in the brackets using the X's in the Options.

Then since P(x) is the number one see in place of Y in the brackets, then that the top Right option is correct as it has −2.

Therefore, The function that includes the given points of (0,−2),(5,13),(−2,−8),(4,10) is the second encircled option by the top right in the image attached.

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Substituting in p = 1/2,

[tex]\frac{1}{2}=\frac{8}{v}\\ \\ v=\boxed{16}[/tex]

The length of the arc given in the question is; 4.1r

We are given;

Angle at which arc is subtended; θ = 235°

Formula for arc length subtended at an angle θ is;

Arc Length = (θ/360) * 2πr

where r is radius of circle.

Thus;

Arc Length = (235/360)  * 2πr

Arc Length = 4.1r

The complete question is;

Find the value of the length of an arc that subtends an angle of 235 degrees to the circle's center.

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The cost of one ft² of sod is $2 and the cost of one geranium is $9.

9s + 2g = 36 equation 1

9s + 5g = 63 equation 2

Subtract equation 1 from equation 2:

3g = 27

g = 27 / 3

g = $9

Substitute for g in equation 1

9s + (2 x 9) = 36

9s + 18 = 36

9s = 36 - 18

9s = 18

s = 18 / 9

s = $2

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Answer:

[tex]\displaystyle{f(x+1)=|x-6|-4}[/tex]

Step-by-step explanation:

To evaluate [tex]\displaystyle{f(x+1)}[/tex], substitute [tex]\displaystyle{x}[/tex] to [tex]\displaystyle{x+1}[/tex] so we should have:

[tex]\displaystyle{f(x+1) = |x+1-7|-4}[/tex]

Evaluate the expression and finally, we have:

[tex]\displaystyle{f(x+1)=|x-6|-4}[/tex]

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Answer:

Aprism =  483.246 yd2

Step-by-step explanation:

The surface area is the sum of the 2 circles areas and the rectangle area.

Ac1 = PI*r2

Ac1 = (3.14)*(11.4/2)2

Ac1 = 102.0186 yd2

Ac1 = Ac2 then

Ac2 = 102.0186 yd2

Now the perimeter of the circle is one the sides of the rectangle:

Pc = 2PI*r

Pc = 2*3.14*(11.4/2)

Pc = 35.796 yd

Now the area of the rectangle is:

Ar = 7.8yd*35.796yd

Ar = 279.2088 yd2

Then, the surface area of prism is:

Answer:

A intersection B = ( elements which are common in both)

= ( 2,4,7,19)

A union B = ( all the elements which are either in A or in B).

= ( 2, 4, 7 , 13, 14, 19, 20 , 3, 5, 6, 10,11, 12 , 15,17 , 18 , 19 )

Answer:  The price per ton of topsoil is $179

and price per ton of mulch is $248.

Step-by-step explanation:

Let price of 1 ton of topsoil be x

and price 1 ton of mulch be y

According to question

4x + 3y = $1460   -(i)

and 5x + 2y = $1391    -(ii)

Now solving these linear equations

By multiply (i) equation with 5 and divide it by 4

we get 5x + [tex]\frac{15}{4}[/tex]y = $1825  -(iii)

Subtract equation (ii) from equation (iii)

5x +[tex]\frac{15}{4}[/tex] y - 5x - 2y = $1825-$1391

[tex]\frac{7}{4}[/tex]y=$434

y = $434х[tex]\frac{4}{7}[/tex] = $248

put value of y in equation (i)

4x + 3($248) = $1460

4x - $744 =$1460

4x = $716

x = $179

The price per ton of topsoil is $179

the price per ton of mulch is $248.

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0.70 -0.50 = 0.20 cent mark up

0.20/0.50 = 0.40 = 40% markup

Answer:

17.5 mph

Step-by-step explanation:

Let the speed of the boat in still water be B mph
Let the rate of the current be R mph

When going upstream the effective speed is B-R mph. In terms of values given effective upstream speed = 42/3 = 14 mph

So,

B-R = 14  ... (1)

Similarly downstream speed is  B + R (faster downstream)

B + R = 42/2 = 21 ....  (2)

(1) + (2) ==> 2B = 35

B = 35/2 = 17.5 mph

Answer:

n^2 -10n + 24

Step-by-step explanation:

Given expression:

(n-6)(n-4)

Solution:

Apply distributive property,then simplifying using PEMDAS,we obtain

Hence,n^2 -10n -24 is the answer.

Answer:

B. △RTS

Step-by-step explanation:

△MON ≅ △RTS

Answer:

Hamish earns $20 per hour, and Harry earns $26 per hour.

Step-by-step explanation:

Harry earns

$1+(5/4)•x and also (7/5)•x-$2

$1+(5/4)•x = (7/5)•x-$2

$1+$2= (7/5)•x-(5/4)•x

3=(7•4•x-5•5•x)/20

3=3x/20

3•20=3x

X=20, Hamish earns $20

Substitute x in one of the expressions

1+(5/4)•20=1+25=26, Harry earns $26

There are 245 gallons of antifreeze solution required.

Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100.

Here, Let 60% antifreeze solution  volume = x

15% antifreeze solution volume = 15%

Final concentration 50%

Process

             0.6x + 0.15(70) = 0.5(70 + x)

Simplification

                 0.6x + 10.5 = 35 + 0.5x

                 0.6x - 0.5x = 35 - 10.5

                          0.1x = 24.5

                             x = 24.5/0.1

                            x = 245 gallons

Thus, There are 245 gallons of antifreeze solution required.

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Using the binomial distribution, it is found that there is a 0.0001 = 0.01% probability that the airplane will be in serious trouble the next time it goes up.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

The values of the parameters are given as follows:

p = 0.1, n = 2.

The plane is in serious trouble if both engines fail, that is, the probability is P(X = 2), hence:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 2) = C_{2,2}.(0.1)^{2}.(0.9)^{0} = 0.0001[/tex]

0.0001 = 0.01% probability that the airplane will be in serious trouble the next time it goes up.

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Answer:

-4(-2)+2(3)-(-4)

8+6+4

16 is the answers

Step-by-step explanation:

please mark me as brainlest

Answer:

Using the concept of number line, we find that Libby owes more than Daniel.

Step-by-step explanation:

Given that the account balance of Daniel is -$1.25 and of Libby is -$2.00. Sandra has as much savings in her account as the amount Daniel owes the bank. So, her account balance is +$1.25.

The numbers to be plotted on the number line are -2.00, -1.25 and 1.25.

The number line is in the attachment.

These numbers are related as: -2 < -1.25 < 1.25.

From the number line, all the names that come left to the origin owe some amount to the bank while all the names that come right to the origin have some money as savings in their account.

Clearly, Daniel and Libby owe the bank.

But since Libby comes before Daniel, Libby owes more than Daniel.

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Answer:

5

Step-by-step explanation:

Using the mean concept, the expression that gives the average of the low and high temperatures is:

(-3 + 8)/2.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.

In this problem, the two observations are -3 and 8, hence their average is given by:

(-3 + 8)/2.

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The value(s) for which the rational expression −5u+12−2u+2 is undefined is u = 1.

The expression or an equation which can be undefined at some point is a celled the radial expression.

f(u) = -5u +12 / -2u +2

For the function to be undefined, denominator must be equal to zero.

-2u +2 =0

-2u =-2

u = 1

Thus, the value for which the given expression is undefined is 1.

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Answer: [tex]4.5 \text{ cm}^{2}[/tex]

Step-by-step explanation:

[tex]A=\frac{1}{2} bh\\\\A=\frac{1}{2}(3)(3)\\\\\boxed{A=4.5 \text{ cm}^{2}}[/tex]

The area of the triangle will be equal to 4.5 square centimeters.

The space occupied by any two-dimensional figure in a plane is called the area. The space covered by the triangle in the two-dimension is called an area of the triangle.

The area of the triangle ABD will be calculated as:-

Area = [tex]\dfrac{1}{2}[/tex] x Base x height

Area = [tex]\dfrac{1}{2}[/tex] x 3 x 3

Area = 4.5 cm.

Therefore the area of the triangle will be equal to 4.5 square centimeters.

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There are 540 fuses in total and the original price of the internet is $55.91

a) We know that 5% of the fuses are faulty, and there are 27 faulty fusses, then we can write:

5% = 27

100% = x

We want to find x, to do that, we can write:

x = 27*(100%/5%) = 27*20 = 540

There are 540 fuses in total.

b) Now we know that the original price is P, and when we decrease it by 7%, then new price is $52.00

Then we can write:

$52.00 = P*(1 - 7%/100%)

$52.00 = P*(0.93)

$52.00/0.93 = P = $55.91

The original price is $55.91

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The standard deviation of the data to the nearest hundredth is 173.01.

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

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

Determine the mean of the observation: 185

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

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

Following these steps, the standard deviation is 173.01

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Answer:

Step-by-step explanation:

The width of the cooling tower at the base of the structure will be A. 36 meters.

From the information given, the towers walls are modeled by x²/324 - (y² - 90)²/1600.

Therefore, the width of the cooling tower at the base of the structure will be:

= 2 × ✓324

= 2 × 18

= 36

In conclusion, the width is 36 meters.

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Answer:

It is actually D

Step-by-step explanation:

The multiplicative rate of change of the function f(x) = 2 × 5ˣ is 5.

An exponential function is a type of function in math that involves exponents. A basic exponential function is of the form f(x) = bˣ, where b > 0 and b ≠ 1.

The function is given as:

f(x) = 2 X 5ˣ

The above function is an exponential function.

An exponential function is represented as:

f(x) = abˣ

Where b represents the multiplicative rate

By comparison;

b = 5

Thus, the multiplicative rate of change of the function is 5.

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Answer:

B!!!!!!!!!!!!!!!!!!!!!!!

Step-by-step explanation:

Answer:

The x-intercept is 2.

Step-by-step explanation:

[tex]2 \sqrt[3]{x - 10} + 4 = 0[/tex]

[tex]2 \sqrt[3]{x - 10} = - 4[/tex]

[tex] \sqrt[3]{x - 10 } = - 2[/tex]

[tex]x - 10 = - 8[/tex]

[tex]x = 2[/tex]