(2x+5)a + (x+3)b = 2x+4 calcule (a-b)^2

The given exponential function will grow at 7.1%

We have to given that;

The exponential function is,

⇒ y = 25 (1.071)ˣ

Now, For identify whether the change represents growth or decay, and to determine the percentage rate of increase or decrease.

Since, We have,

⇒ y = 25 (1.071)ˣ

Here, The equation represents exponential growth because the growth factor is 1.071 which is greater than 1.

Since, The general form equation is:

⇒ y(x) = a(1 + r)ˣ

such that r is the growth percent.

Hence,

⇒ 1 + r = 1.071

⇒ r = 0.071 = 7.1%

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After 1 year, you have invested $977.28. The Option B

To find the total amount, we have to determine monthly investment required.

Let's represent monthly investment as M.

After 12 months of compounding, the final amount will be $1000. We will use formula for compound interest [tex]A = P(1 + r/n)^{nt}[/tex]

To solve for monthly investment (M), we rearrange the formula as follows: [tex]A = M * ((1 + r/n)^{nt} - 1) / (r/n)[/tex]

[tex]1000 = M * ((1 + 0.05/12)^{12*1} - 1) / (0.05/12)\\M = $1000 * (0.05/12) / ((1 + 0.05/12)^{12*1} - 1)\\M = $81.4408151 \\M = $81.44[/tex]

To get total amount invested after 1 year, we will multiply investment by 12 months:

= $81.44 * 12

= $977.28.

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Based on the information, we can infer that the area of the prism is: 981.3m²

To calculate the area of the prism we must calculate the area of each of the faces and then add them as shown below:

Now we must multiply each value by 2 because we have two faces of each in the prism. Additionally, we must add the results to obtain the total area:

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To calculate Keith's take-home pay, we need to subtract the taxes deducted from his total earnings.

Regular pay: $896

Overtime pay: $672

Total earnings: $896 + $672 = $1568

Taxes deducted: $275

Take-home pay: Total earnings - Taxes deducted

Take-home pay: $1568 - $275 = $1293

Therefore, Keith's take-home pay is $1293.

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No, Tyler is wrong.

Given that according to Tyler all parallelograms can be classified as trapezoids, the diagonals of all trapezoids must intersect at their midpoints.

A parallelogram is a quadrilateral in which the opposite sides are parallel and equal.

Parallelograms are classified into three main types: square, rectangle, and rhombus, and each of them has its own unique properties.

A parallelogram is a special kind of quadrilateral that is formed by parallel lines. The angle between the adjacent sides of a parallelogram may vary but the opposite sides need to be parallel for it to be a parallelogram. A quadrilateral will be a parallelogram if its opposite sides are parallel and congruent.

Tyler's comment on trapezoids is totally wrong, because no trapezoid is considering as a parallelogram.

However, a trapezoid has one pair of parallel sides, but to be a parallelogram it should have both pairs of sides equal and parallel like a rectangle.

Hence Tyler is wrong.

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The value of the missing sides are;

1. 12. 9

2. 2. 0

3.  4. 6

4. 5. 3 degrees

We have that their are six trigonometric identities. These identities are;

From the information given, we have that;

Using sine identity

sin 57 = 10.8/x

cross multiply the values

x = 12. 9

2. Using cosine identity

cos 47 = x/3

cross multiply

x = 2. 0

3. Using the tangent identity;

tan 41 = 4/x

cross multiply

x = 4. 6

4. The angle of depression is ;

sin X = 27.6/300

sin X = 0. 092

X = 5. 3 degrees

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Option (A) Names of TV shows taped in New York are an example of qualitative data. Qualitative data is descriptive in nature and does not involve numerical values or measurements.

It deals with qualities or attributes that cannot be expressed numerically. In this case, the names of TV shows are characteristics that describe the nature of the data. Quantitative data, on the other hand, is numerical data that can be measured and expressed in numbers. A parameter is a measurable factor or variable that can be used to define a system, while statistics is a branch of mathematics that deals with data collection, analysis, and interpretation. In conclusion, since the names of TV shows are descriptive in nature and do not involve numerical values, they are an example of qualitative data.

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The equation 3+7+2=+2 is actually not true, but false.

The equation 3+7+2=+2 is actually not true, but false. This is because the sum of 3, 7, and 2 is 12, not 2.

In general, an equation is considered true if the expressions on both sides of the equal sign are equivalent in value. In this case, the expressions on the left-hand side (3+7+2) and the right-hand side (+2) are not equivalent, and therefore the equation is false.

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The sum of the infinite geometric series –288 –216 –144 –72 is -1152.

The sum of an infinite number of terms having a constant ratio between successive terms is called as infinite geometric series.

Given series, -288, -216, -144, -72, ...

The sum of the infinite geometric series can be calculated as:

Sum = [tex]\dfrac{a}{1 -r}[/tex]

Here, 'a' is the first term of the series and 'r' is the common ratio.

a = -288

The common difference can be calculated as:

r = [tex]\dfrac{(-216)}{(-288)}[/tex]

= [tex]\dfrac{3}{4}[/tex]

Substitute the values in the sum formula:

Sum = [tex]\dfrac{-288}{1 - \dfrac{3}{4}}[/tex]

It can be simplified as:

Sum =  -288 [tex]\times[/tex] 4

             = -1152

So, the sum of the infinite geometric series is -1152.

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The remainder after dividing 2x³ + 5x² - 3x + 1 by x+4 is 9x+1

We have to find the remainder when we divide 2x³ + 5x² - 3x + 1 by x+4

Dividend is the number which is getting divided by some other number

2x² - 3x + 15 is the dividend

Divisor is the number which divides a number

x+4 is the divisor

In the given division the

       2x² - 3x + 15

       ------------------

x + 4|2x³ + 5x² - 3x + 1

    - (2x³ + 8x²)

       --------------

            -3x²- 3x

            +(-3x² - 12x)

            --------------

                       9x + 1

Hence, the remainder  is 9x+1 when we divide 2x³ + 5x² - 3x + 1 by x+4

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Answer:

6.37 x 10^5

This is it

In conclusion, the correct answer is d) Straight.

The correct answer is d) Straight.

In geometry, an angle is formed by two rays that have a common endpoint. Angles can be classified based on the measure of their degree. A straight angle measures 180 degrees, which is the same as a straight line. It is formed by two opposite rays that point in opposite directions, and they create a straight line.

Therefore, an angle that measures 180 degrees is called a straight angle. In a straight angle, the two rays point in opposite directions and form a straight line. This angle is not acute, obtuse, or right because it doesn't form a triangle, and the degree measure is not less than 90 degrees or greater than 90 degrees.

In conclusion, the correct answer is d) Straight.

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For linear trigonometric equations involving only sine or cosine, there will be solutions if the constant term on the other side of the equation falls within the range of -1 to 1.

When solving linear trigonometric equations in terms of only sine or cosine, we can determine whether there will be solutions by considering the range of values that sine and cosine can take.

For sine (sin) and cosine (cos), their values range from -1 to 1. If the equation involves only sine or cosine and is linear, it means the variable is not squared or involved in any higher powers. In such cases, the equation will have solutions if the constant term on the other side of the equation is within the range of -1 to 1.

For example, if we have the equation sin(x) = 0.5, it will have solutions because 0.5 is within the range of -1 to 1. However, if we have the equation sin(x) = 2, it will not have any solutions because 2 is outside the range of -1 to 1.

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Answer:

Justin is packing a container with books the dimension of each book are 8 in by 6 in by 2 in the dimensions of the container are 16 in by 12 in by 12 in all of the books in the container are rectangular prisms how many books can fit in the container if the books are packed so that there is no unused space in the container

1. 2x = 14 --> divide both sides by 2 --> x = 14/2 --> x = 7

2. x + 4 = 3 --> subtract 4 from both sides --> x = 3-4 --> x = -1

3. 3x + 6 = 12 --> subtract 6 from both sides --> 3x = 12-6 --> 3x = 6

4. 2x + 8 = 14 --> factor 2 out on the left side --> 2(x+4) = 14 --> divide both sides by 2 --> x + 4 = 14/2 --> x + 4 = 7

5. x + 5 = 4 --> factor -1 out on the left side --> -(-x-5) = 4 --> divide both sides by -1 --> -x-5 = 4/-1 --> -x-5 = -4

6. 2x + 4 = 3x - 5 --> subtract 2x from both sides --> 4 = 3x - 5 - 2x --> add 5 on both sides --> 4 + 5 = 3x - 2x --> 3x - 2x = 9

7. x - 8 = 24 --> add 8 on both sides --> x = 24 + 8 --> x = 32

8. 21 - 5x = 2 --> subtract 21 from both sides --> -5x = 2 - 21 --> -5x = -19 --> divide both sides by -1 --> 5x = -19/-1 --> 5x = 19

9. 4x + 2 = 8 --> add 2 on both sides --> 4x + 2 + 2 = 8 + 2 --> 4x + 4 = 10 --> factor 4 out on the left side --> 4(x+1) = 10 --> divide both sides by 4 --> x + 1 = 10 / 4 --> x + 1 = 2.5

10. (x-5) / 7 = 10 --> multiply both sides by 7 --> x-5 = 10 * 7 --> x-5 = 70

The value of the length f is 6. 7

To determine the value, we have to know the different trigonometric identities.

These trigonometric identities are enumerated as;

To determine the length of f

Let us use the tangent identity, we have that;

tan θ = opposite/adjacent

substitute the values, we have;

tan 24 = f/15

Multiply the values, we get;

f = 0. 4452(15)

multiply the values

f = 6. 7

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A 4.2 earthquake's energy release is 10 times more than a 3.2 earthquake's energy release despite the 3.2 earthquake's amplitude being 10 times smaller.

Now, A 3.2- to 6.5-magnitude earthquake has a substantial difference in intensity.

In actuality, a 6.5 earthquake has a magnitude almost 1000 times greater than a 3.2 earthquake.

The Richter scale, which uses a logarithmic scale to assess earthquake intensity, is the reason behind this.

Since, the Richter scale uses a seismograph to estimate the amplitude of earthquake waves, it is a logarithmic equation.

Each unit increase on the Richter scale causes an exponential increase in the energy released by the earthquake, which is proportional to the amplitude of the earthquake waves.

For instance, a 4.2 earthquake's energy release is 10 times more than a 3.2 earthquake's energy release despite the 3.2 earthquake's amplitude being 10 times smaller.

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Answer:

13) 225

14) 289

15) 64

16) 8

To find the length of the curve r(t) = sqrt(2)ti, we need to use the arc length formula:L = ∫[a,b] ||r'(t)|| dt,where ||r'(t)|| is the magnitude of the derivative of the curve.

First, we need to find r'(t):

r'(t) = (d/dt) [sqrt(2)ti] = sqrt(2)i

The magnitude of r'(t) is ||r'(t)|| = sqrt(2).

So, the length of the curve is:

L = ∫[0,1] sqrt(2) dt = sqrt(2) * [t] [0,1] = sqrt(2)

Therefore, the length of the curve r(t) = sqrt(2)ti is sqrt(2).

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Answer:

Step-by-step explanation:

x + [tex]\frac{y}{3}[/tex] = 0         ------    ( 1 )

6x - 2y = 6     ------    ( 2 )

6x + 2y = 0    ----- ( 3 )

6x - 2y = 6    ------ ( 4 )

Adding ( 3 ) and ( 4 ) ; we get ,

12x = 6

x = 1/2

putting value of x in (3) , we get ,

3 + 2y = 0

2y = -3

x + 2y = (1/2) - 3

= - 5/2

Answer: 80

Step-by-step explanation:

10x5=50      10x2=20 2x5=10

The corresponding IQ score for a z-score of 1.86 is 127.9.

Option A.

If IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. Given a z-score of 1.86, the corresponding IQ score is calculated as follows;

The formula for IQ score is given as;

IQ = (z-score x standard deviation) + mean

Substituting the given values, the value of IQ score is calculated as;

IQ = (1.86 x 15) + 100

IQ = 27.9 + 100

IQ = 127.9

Therefore, the corresponding IQ score for a z-score of 1.86 is 127.9. The answer is A.

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Answer:

Step-by-step explanation:

1. Put the equations in order:

-14x+y=4(1)

-6x+y=8(2)

2. Eliminate a variable.

In this case, we want to eliminate y, so subtract the second equation from the first

(1)-(2)    -8x=-4

x=-4/8

x=1/2

3. Now that we have one variable, we can use it to solve for y:

6(1/2) + 8=y

3+8=y

y=11

(1/2,11) is the answer.

Another way to do this is to set the first equation equal to the second equation:

6x+8=14x+4

8x=4

x=1/2

y=11

(1/2,11) is the answer!

We used elimination and equal values!

The cost of running the electric water heater for one month (30 days) would be $36, assuming the electricity costs 12 cents per kilowatt-hour.

To calculate the cost of running the electric water heater for one month, we need to determine the total energy consumption and multiply it by the cost per kilowatt-hour.

The water heater consumes 5 kW for 2 hours per day, so the daily energy consumption can be calculated as follows:

Daily energy consumption = Power (kW) × Time (hours) = 5 kW × 2 hours = 10 kWh

Next, we calculate the total energy consumption for one month (30 days):

Total energy consumption = Daily energy consumption × Number of days = 10 kWh/day × 30 days = 300 kWh

Finally, we multiply the total energy consumption by the cost per kilowatt-hour (12 cents/kWh) to find the cost of running the water heater for one month:

Cost = Total energy consumption × Cost per kilowatt-hour = 300 kWh × $0.12/kWh = $36

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The area of the shaded region ( sector ) rounded to the nearest hundredth is 38.47 cm².

A sector of a circle is simply part of a circle made up of an arc and two radii.

The area of a sector of a circle can be expressed as:

A = (θ/360º) × πr²

Where θ is the sector angle in degrees, and R is the radius of the circle.

From the diagram:

The sector angle θ = 90 degrees

Radius r = 7cm

Plug these values into the above formula and solve for the area.

Area = (θ/360º) × πr²

Area = (90/360º) × 3.14 × (7 cm)²

Area = (90/360º) × 3.14 × 49 cm²

Area = 38.465 cm²

Area = 38.47 cm²

Therefore, the area of the sector is 38.47 cm².

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The range of the function f include the following: [-20, ∞].

In Mathematics and Geometry, a range is the set of all real numbers that connects with the elements of a domain.

Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following range and domain:

Range = [-20, ∞] or -20 ≤ y ≤ ∞.

Domain = [-∞, ∞] or -1 < x < ∞.

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Yes, -0.614035088 is a rational number.

We know, A rational number is any number that can be expressed as a fraction, where the numerator and denominator are both integers.

We have the number -0.614035088.

In this case, -0.614035088 can be expressed as the fraction -1227/1999, where both the numerator and denominator are integers.

Thus, Yes, -0.614035088 is a rational number.

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Vlad should sample 1733 soldiers to estimate the proportion with a margin of error of less than 0.007 and a 97% confidence level.

We can use the formula for the margin of error of a proportion:

ME = zsqrt(p(1-p)/n)

where ME is the margin of error, z is the critical value for a 97% confidence interval (which can be found using a table or calculator and is approximately 2.17), p is the estimated proportion (0.62), and n is the sample size.

We want to find n, so we can rearrange the formula and solve for n:

n = (z^2 * p * (1-p)) / ME^2

Substituting the values given, we get:

n = (2.17^2 * 0.62 * 0.38) / 0.007^2

n ≈ 1732.92

Since we need a whole number of soldiers, we round up to n = 1733.

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Answer:

See attached. ∠A is a right angle, ∠B and ∠D are acute, ∠C is obtuse.

Step-by-step explanation:

     A right angle is defined as an angle equal to 90 degrees.

     An acute angle is defined as an angle less than 90 degrees.

     An obtuse angle is defined as an angle greater than 90 degrees.

     Using this information we will classify all of the four given angles.

∠A is a right angle, 90 = 90

∠B is acute angle, 60 < 90

∠C is obtuse angle, 160 > 90

∠D is acute angle, 70 < 90