Solve each equation.
9^(x+2)=2^(5x-4)

He collected 936 US stamps.

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

Total number of stamps - 1170

US stamps - 4 times as many as foreign stamps

Let x be the number of foreign stamps.

4x as the number of US stamps.

To find the number of US and foreign stamps Peter collected, we are going to represent the given data as:

x + 4x = 1170.

x + 4x = 1170

5x = 1170

5x/5 = 1170/5

x = 234

Peter collected 234 foreign stamps.

US stamps = 4x

= 4(234)

= 936

Peter collected 936 US stamps.

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Answer:

Step-by-step explanation:

I'm impressed that they make you do this in H.S.    Linear Algebra.   it's good for more complex math .   so that's why i'm impressed.   Is this an AP class?  

Ax=B is our formula.   we need to know something about x,  it's size

so we look at rows and columns of A,   2x2   , also we need to know about B as well it's also 2x2

so now we know, that   a matrix  A, of  size  2x2,  *x = B of size 2x2

2x2*x=2x2   ....   2x2|2x2   since the two inside number match, we can do this multiplication,  and the two ouside numbers tell us the size of  x... it's also a 2x2.  I know, a lot of explaining to just get 2x2.   Maybe that is obvious, and i'm mansplaining,  :DD  ,  but I don't know what you know.

I'll put big subscripts on my matrix variable so you can see it well.  You understand the subscript is the element location in the matrix , right?  1,1 is just the top left corner element of the matrix.  ect , ect.

so now we need,  a1,1 * x1,1 + a1,2 * x2,1   = 2  in b1,1

then we need   a2,1 * x1,1 + a2,2 * x2,1 = 7  in b2,1

next we need a1,1 * x1,2 + a1,2 * x2,2   = 3  in b1,2

finally we need a2,1 * x2,1 + a2,2 * x2,2   = 8  in b2,2

X =  [tex]\left[\begin{array}{ccc}\frac{3}{2} &1\\\frac{1}{2} &2\end{array}\right][/tex]   I did that by observation.   have you learned any RREF methods yet?

Dan's sales for the next month if he wants his monthly average for the year to be 25,000 is 36430.

Since for the first 11 months of this year , Dan's sales averaged 24,870 a month. The total amount will be:

= 11 × 24870

= 273570

Since Dan's sales for the next month if he wants his monthly average for the year to be 25,000, the amount will be:

= 12 × 25000

= 300000

Therefore, the amount for the next month will be:

= 300000 - 273570

= 26430

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a) The revenues for both items will be the same after 1 day.

b) The graph with the solution is given by the image at the end of the answer.

The functions defining the revenues for the selling of x brownies and of x cookies are presented as follows:

The revenues will be the same after x days, for which:

B(x) = C(x).

Hence:

2x² + 8x - 4 = 2x + 4

2x² + 6x - 8 = 0.

x² + 3x - 4 = 0.

The quadratic function can be factored as follows:

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

Applying the Factor Theorem, the solutions are given as follows:

The graph shows the intersection of the two curves, B(x) and C(x).

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You walked 16 blocks in a time of 28 minutes. At this rate you walk 1 block in 1 minute 75 seconds.

In Science, distance can be defined as the amount of ground that is covered (travelled) by a physical object over a particular period of time and speed, irrespective of its direction, starting point or ending point.

Mathematically, the distance traveled by a physical object (body) can be calculated by using this formula:

Distance = speed (rate) × time

Note: Let the variable x represent the halfway distance.

Since it takes the same amount of time to walk each block and halfway there, half of the berries are gone. Therefore, we have the following:

At point x, the number of strawberries that is left is equal to 12 strawberries while the distance after walking 3 more blocks, you still have 5 blocks to go would be given by:

1/2 × x = (3 + 5) = 8

1/2 × x = 8

Distance, x = 8 × 2

Distance, x = 16 blocks.

Now, we can determine the rate at which this person walks a block:

Rate (speed) = 28/16

Rate (speed) = 1.75 minutes.

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The approximate probability that a 47% shooter makes 5 or more shots in 10 attempts is 12/25

Given,

Number of trials of the simulation were performed = 25

Number of set of simulated shots = 10

We have to find the approximate probability that a 47% shooter makes  5 or more shots in 10 attempts;

The dots in the 5 shot mark is 9, 6 shot mark is 2, and 7 shot mark is 1.

Now the approximate probability that a 47% shooter makes 5 or more shots in 10 attempts can be calculated below:

P(x5) = (dots in 5 short mark + dots in 6 shot mark + dots in 7 short mark) / 25

= (9 + 2 + 1) / 25

 = 12 / 25

Therefore, the approximate probability that a 47% shooter makes 5 or more shots in 10 attempts is 12/25

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Answer:

FALSE

Step-by-step explanation:

3.6ft is 43.2

3ft 6in is 42 in

For the given equation the solution would be

                          [tex]r=-7t-3,\:s=\frac{-6t-7}{3}[/tex]

What is the system of linear equations in three variables?

Three-variable equation systems are only slightly more difficult to solve than two-variable equation systems. Substitution and the use of 3x3 matrices are the two most straightforward methods for solving these types of equations.

The given equations are

                  r - 3s + t = 4 ------------(I)

                  3r - 6s +9t = 5 ---------(II)

                  4r - 9s + 10t = 9--------(III)

from equation (I), we get

                  r = 4 + 3s - t ------------(IV)

Now put the value of 'r' in equations (II) and (III), and we get

               3(4 + 3s - t) - 6s + 9t = 5

               4(4 + 3s - t) - 9s + 10t = 9

Solving the above equations, we get

             3s + 6t + 12 = 5 --------(V)

             3s + 6t + 16 = 9 --------(VI)

 Now isolate the value of 's' from equation (IV), we get

              3s = - 6t + 5 -12

             [tex]s=\frac{-6t-7}{3}[/tex]

Now put the value of 's' in equation (IV), and we get

           [tex]r=4 +3s -t\\r=4+3\cdot(\frac{-6t-7}{3}) -t\\ r=4-6t-7-t\\r=-7t-3[/tex]

Hence, For the given equation the solution would be

                   [tex]r=-7t-3,\:s=\frac{-6t-7}{3}[/tex]

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The volume of the prism with area 41 cm^2 and height 11 cm is 451 cm^3

Volume refers to three dimensional solid. The three dimensions include some elements which are

While area is 2 dimensional which is solved by length * width

In the figure the area is already solved to be 41 cm^2 and height is given to be 11 cm

The volume of the solid is given

= length * width * height

= area * height

= 41 * 11

= 451 cm^3

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..........................................

[tex]\displaystyle\\Answer: \frac{-11-12i}{15}[/tex]

Step-by-step explanation:

[tex]\displaystyle\\\frac{-7+2i}{3-6i}=\\\\\frac{(-7+2i)(3+6i)}{(3-6i)(3+6i)}=\\\\ \frac{-21-42i+6i+12i^2}{3^2-(6i)^2} =\\\\\frac{-21-36i-12}{9+36}=\\\\\frac{-33-36i}{45} =\\\\\frac{3(-11-12i)}{3(15)} =\\\\\frac{-11-12i}{15}[/tex]

Answer:f^-1(x)= square root x-1 over 4 and square root -square root over 4

Step-by-step explanation:

interchange the variables and solve for y

Answer: ( 4 , 8 )

Step-by-step explanation:

3x - 2y = -4

y = 2x

Substitute the second equation into the first

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

y = 2(4)
y=8

( 4 , 8 )

a) The linear equation that represents the total amount of snow, y, after x number of hours is: y = 2 + 0.25x.

b) 3 inches is the amount of snow that is on the ground after four hours.

c) The time until the snow reaches 6 inches is of 16 hours, which is enough to finish the hike, as they usually take at most five hours.

The slope-intercept representation of a linear function is shown by the equation as follows:

y = mx + b

In which the parameters m and b of the linear equation are explained as follows:

Thus the values of these parameters are given as follows:

m = 0.25, b = 2.

The equation that represents the total amount of snow, y, after x number of hours is:

y = 0.25x + 2.

The numeric value of function after four hours is found replacing the lone instance of x on the function by 4, hence:

y = 0.25(4) + 2 = 3 inches.

To find when the amount will be of six inches, we have to solve for x when y = 6, hence:

2 + 0.25x = 6

0.25x = 4

x/4 = 4

x = 16 hours.

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the question was already answered but here you go

Based on the rate the number of songs being downloaded is decreasing, in 2030, the number of songs downloaded will be 7,792 songs.

The number of songs downloaded in 2010 is 18,000.

To find the number of downloads in 2030, use the formula:

= Songs in 2010 x ( 1 - Rate of decrease) ^ number of years

Number of years = 2030 - 2010 = 20 years

= 18,000 x (1 - 4.1%)²⁰

= 7,791.92

= 7,792 songs

In conclusion, 7,792 songs will be downloaded in 2030.

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The equation of line is y = -1/4x + 11/12.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx

where, m is the slope

Given:

line passing through P(-1, 3) that is perpendicular to y = 4x - 7.

Now, the slope of perpendicular line is

slope= -1/ 4

and, the lines passes through (-1, 3)

Thus, using slope- intercept form

y- 3 = m( x + 1)

y- 3 = -1/4 ( x+ 1)

y- 3 = -1/4x - 1/4

y = -1/4x + 11/12

Hence, the equation of line is y = -1/4x + 11/12

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Answer: 3p-q-2

Step-by-step explanation:

Perimeter is the sum of all the sides.

Add the known sides together:

(p-3) + (2p+3q) = 3p + 3q - 3

To find the unknown side, subtract the sum of the 2 known sides from the perimeter (combine like terms):

(6p+2q-5) - (3p+3q-3) = 3p-q-2

Add all 3 sides together as a check of your answer!

For the given condition the x distribution is normal. Option B is correct.

It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.

[tex]\rm \sigma = \sqrt{\dfrac{ \sum (x_i-X)}{n}[/tex]

σ is the standard deviation

xi is each value from the data set

X is the mean of the data set

n is the number of observations in the data set.

n=64

√n=8

μ=8

σ=16

The sample size (n > 30) is enough. Using the Central Limit Theorem

¯X∼N(8,16²/64)

The formulas below give the mean and standard deviation of the mean value of x:

The sampling distribution of x has a mean value of 8.

The following equation gives the sampling distribution's standard deviation:

=σ/√n

=16/√64

=16/8

=2

The sample distribution's standard deviation is 2.

Yes, this distribution can be regarded as normal as it roughly follows the normal distribution (By using CLT)

Thus, for the given condition the x distribution is normal. Option B is correct.

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Answer: Brittany can buy 10 fish

Step-by-step explanation:

If you divide 15 by 1.50 you get 10 meaning Britanny can buy 10 fish. Apologies if this is incorrect.

The equation represents the line that passes through the points (6, -12) and (16,-10) is y = 1/5x - 13.2

The first point = (6, -12)

The second point = (16, -10)

The slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the values in the equation

The slope of the line m = (-10 -(-12) / (16 - 6)

= (-10 +12) / 10

= 2/10

= 1/5

The slope intercept form is

y = mx + b

Consider the point (6, -12)

-12 = (1/5)6 + b

-12 = 6/5 + b

b = -12 - 6/5

b = -13.2

The equation will be

y = 1/5x - 13.2

Hence, the equation represents the line that passes through the points (6, -12) and (16,-10) is y = 1/5x - 13.2

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Answer:

3n+6 May i pls have the crown

Step-by-step explanation:

If you use the PEMDAS rule

3 * n= 3n

and 3*2= 6

The lengths of the major and minor axis are 4√6 and 4√3.

A point on a curve is described by an ellipse if its location is such that the sum of the distances between its two focal points is a constant.

(x−h)²/ b² +(y- k)² /a² = 1

Given:

(x−3)²/ 27+(y+4)² /45=1

The above equation can be compared to the standard equation of an ellipse

(x−h)²/ b² +(y- k)² /a² = 1

where, (h, k) = coordinates of the center of the ellipse

a =  length of the semi major axis

b = length of the semi minor axis

By comparison, we have;

(h, k) = (3, -4)

a = √(24) = 2 x√6

b = √(12) = 2 x√3

and, length of the major axis = 2a

length of the minor axis = 2b

Thus, The length of the major axis is

2x a = 2 × 2 x √6 = 4√6

and, length of the minor axis is

2•b = 2 × 2√3 = 4√3

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Answer: 6sqrt(5) and 6sqrt(3)

Step-by-step explanation:

I took the test and these were the correct answers.

Answer:

lo siento soy muy malo para las matemáticas y además soy nuevo en este aplicación

The area of each of the patios is 1600 m².

The mason builds two patios with the same area. One of the patios is square, and the other is rectangular. The rectangular patio is 10 m longer but 8 m less wide than the square patio. We need to find the area of each patio.

Let the side length of the square patio be denoted by the variable "x". The area of the square can be calculated as follows.

A1 = x²

The length and breadth of the rectangular patio is "x + 10" and "x - 8", respectively. The area of the rectangular patio is calculated below.

A2 = (x + 10)*(x - 8)

A2 = x² + 2x - 80

We know that the areas of both patios are equal.

A1 = A2

x² = x² + 2x - 80

2x = 80

x = 40

Hence, the area of each patio is A = x² = 40² = 1600 m².

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The equation is y = -3

Since, the line parallel to the line y=5, its slope is zero.

so, the equation has the form

y = constant

it passes through (-2,-3), the equation is

y = -3

Slope of a Line :

In mathematics, a line's slope is defined as the ratio of the change in the y coordinate to the change in the x coordinate.

The net change in the y-coordinate and the net change in the x-coordinate are denoted by the letters Y and X, respectively.

Since the slope of a line is denoted by "m," the formula for the change in y-coordinate with respect to the change in x-coordinate is m = change in y/change in x = y/x.

The slope, intercept, and y-intercept values on the graph of the equation y = mx + c are all equal to m. M and C are real integer values in the slope-intercept version of the linear equation.

Complete question:

find an equation of the line parallel to the line y=5 and passing through -2,-3

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The insurance cost now is £449.204.

Given:

Brian pays £465. 98 a year on his car insurance. The insurance company reduces the price by 3. 6%.

Insurance  = 465.98*3.6%

= 465.98*3.6/100

= 465.98*36/10*100

= 46598/100 * 36/1000

= 46598*36 / 100000

= 1677528/100000

= 16.77528

Insurance cost now = 465.98 - 16.77528

= £449.20472

Therefore the insurance cost now is £449.204.

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Answer:

0.96 inches

Step-by-step explanation:

The first step is to find the diameter given the circumference. This is the formula for circumference:

[tex]C=\pi d[/tex]

In terms of d, the formula looks like this:

[tex]d=\frac{C}{\pi}[/tex]

For the softball, the diameter is approximately:

[tex]d=\frac{12}{\pi} =3.82[/tex]

For the baseball:

[tex]d=\frac{9}{\pi } =2.86[/tex]

Find the difference:

[tex]3.82-2.86=0.96[/tex]

The approximate difference in diameters is 0.96 inches!

Answer: 0.96 inches

Step-by-step explanation:

"If we assume that 57% of Americans says that GM foods are generally unsafe to eat, then there is an 8.8% chance that random sample results will show 60%or more who says that GM foods are generally unsafe to eat" is valid interpretations of this p-valid.

Given info;

Genetically modified foods: A 2016 Pew Research survey found that 56% of Americans believe that eating genetically modified (GM) food is generally harmful. This month, a survey of 500 randomly chosen American citizens found that 60% believe gm foods are typically dangerous to consume. We examine the possibility that more people than 56% believe that eating GM food is generally unsafe this year. 0.084 is the p-value.

If we assume that 57% of Americans say that GM foods are generally unsafe to eat, then there is an 8.8% chance that random sample results will show 60% or more who say that GM foods are generally unsafe to eat” is a good interpretation of the P-value. The P-value is the probability that results will be as or more extreme than those from the latest survey if opinions have not changed since 2014.

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