please help due soon

Area of the region inside the circle r=4cos(theta) and outside the circle r=2 is 4π/3 + 2√3

A form created using the polar coordinate system is called a polar curve. Points on polar curves have varying distances from the origin (the pole), depending on the angle taken off the positive x-axis to calculate distance. Both well-known Cartesian shapes like ellipses and some less well-known shapes like cardioids and lemniscates can be described by polar curves.

r = 1 − cosθsin3θ

Polar curves are more useful for describing paths that are an absolute distance from a certain point than Cartesian curves, which are good for describing paths in terms of horizontal and vertical lengths. Polar curves can be used to explain directional microphone pickup patterns, which is a useful application. Depending on where the sound is coming from outside the microphone, a directional microphone will take up sounds with varied tonal characteristics. A cardioid microphone, for instance, has a pickup pattern like a cardioid.

The area between two polar curves can be found by subtracting the area inside the inner curve away from the area inside the outer curve.

The figure attached shows the bounded region of the two graphs. The red curve is  r=4cos⁡(θ) and the blue curve is r=2.

The points of intersection of the two curves are

θ = π/3 and 5π/3

The area is calculated as follows:

Since the bounded region is symmetric about the horizontal axis, we will find the area of the top region, and then multiply by 2, so as to get the total area.

A = 2 \(\(\int_{0}^{\pi /3}\) ½ (4 cos (θ)² − ½ (2)² dθ

  =  \(\(\int_{0}^{\pi /3}\) 16 cos2 (θ) − 4dθ

  = \(\(\int_{0}^{\pi /3}\) 8 (1+cos(2θ)) − 4dθ

  =\(\(\int_{0}^{\pi /3}\) 4 + 8 cos (2θ) dθ

  = [4θ + 4sin (2θ)] \(\(\int_{0}^{\pi /3}\)

  = 4π/3 + 2√3

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Answer:

x = -3

Step-by-step explanation:

The equation is : -1.3x=3.9

We can divide both sides by -1.3

-1.3x/-1.3=-3.9/-1.3

We get

x=-3

Answer:

x =-3

Step-by-step explanation:

divide -1.3 to both sides

The domain and the range of the function are (-∝, ∝) and (0, ∝), respectively

From the question, we have the following parameters that can be used in our computation:

The graph

The above graph is an exponential function

The rule of an function is that

The domain is the set of all real values

In this case, the domain is (-∝, ∝)

For the range, we have

Range = (0, ∝)

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Answer:

24 miles

Step-by-step explanation:

In order to calculate Judy's estimation, we would simply have to multiply the actual distance in kilometers of the tour by the number of miles that Judy believes are in a single mile. This would give us Judy's estimation for how long the tour would be in miles.

40 km. * 0.6 miles = 24 miles

Finally, we can see that Judy's estimation would be that the tour is 24 miles long. Using Judy's believed conversion rate.

Answer:

4

Step-by-step explanation:

use the formula to get the answer but i got 785.71.

The width of the new rectangular field would be 0 meters, which means it would essentially be a line segment.

To find the length and width of another rectangular field that has the same perimeter but a larger area, we can use the following steps:

1. Calculate the perimeter of the given rectangular field:

  Perimeter = 2 * (Length + Width)

            = 2 * (120 meters + 80 meters)

            = 2 * 200 meters

            = 400 meters

2. Divide the perimeter by 2 to find the equal sides of the new rectangular field. Since the perimeter is divided equally into two sides, each side would be half of the perimeter length:

  Side length = Perimeter / 2

             = 400 meters / 2

             = 200 meters

3. Now, we have the side length of the new rectangular field. However, we need to determine the length and width that would yield a larger area. One way to achieve this is to make one side longer and the other side shorter.

4. Let's assume the length of the new rectangular field is 200 meters. Since both sides have the same length, the width can be calculated using the formula for the perimeter:

  Width = Perimeter / 2 - Length

        = 400 meters / 2 - 200 meters

        = 200 meters - 200 meters

        = 0 meters

5. Therefore, the width of the new rectangular field would be 0 meters, which means it would essentially be a line segment. However, note that the question asks for a rectangular field with a larger area. Since the width cannot be zero, we can conclude that it is not possible to have a rectangular field with the same perimeter but a larger area than the given field.

In summary, it is not possible to find another rectangular field with the same perimeter but a larger area than the rectangular field with dimensions 80 meters wide and 120 meters long.

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A. The mean and the standard deviation for the numbers of peas with green pods in the groups of 24 is 18 and 2.1213.

B. The values separating results that are significantly low and significantly high is 13.76  and 22.24.

C. The result of 3 peas with green pods a result is significantly​ low.

What is the probability?

The probability of an occurrence is a number used in science to describe how likely it is that the event will take place. In terms of percentage notation, it is expressed as a number between 0 and 1, or between 0% and 100%. The higher the likelihood, the more likely it is that the event will take place.

Here, we have

Given: Assume that hybridization experiments are conducted with peas having the property that for​ offspring, there is a 0.75 probability that a pea has green pods.

This is a binomial probability distribution problem.

Where n = 24 [groups of 24, total trials]

p = 0.75 [probability of success]

a) Mean = np =24×0.75 = 18

and std deviation =(np(1-p))1/2 = 2.1213

b) from a range rule of thumb; 2 std deviation values above and below the mean are significantly low AND significantly high

Hence significantly low value = mean -2×std deviation = 13.76 or lower values

Significantly high value =mean +2*std deviation = 22.24 or higher values

c) As 3 falls in significantly low values cause it is below 2 std deviations from the mean hence it is significantly​ low.

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The first runner ran 2750 meters and second runner ran 2250 meters

Solution:

Given that,

Relay Races Two runners ran as a team in a 5,000-m relay race

Let "a" be the distance ran by first runner

Let "b" be the distance ran by second runner

The first runner ran 500 m farther than the second runner

Therefore,

distance ran by first runner = 500 + distance ran by second runner

a = 500 + b

a - b = 500

Thus the difference between the distance ran by first runner and distance ran by second runner is 500

Now lets try out different pairs of numbers with a sum of 5000 and the difference between that numbers should be 500

2500 + 2500 = 5000 [ But the difference is 2500 - 2500 = 0]

3000 + 2000 = 5000 [ But the difference is 3000 - 2000 = 1000 ]

2750 + 2250 = 5000 [The difference is 2750 - 2250 = 500 ]

Thus the pair of number is a = 2750 and b = 2250

Thus first runner ran 2750 meters and second runner ran 2250 meters.

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complete question:

Relay Races Two runners ran as a team in a 5,000-m relay race. The first runner ran 500 m farther than the second runner. How many meters did each run?

To forecast using data that has seasonality, one commonly used method is seasonal decomposition of time series (STL). This method separates the time series data into three components: trend, seasonality, and residuals. By isolating the seasonal component, you can forecast future values by extrapolating the pattern observed in previous seasons.

Another approach is the use of seasonal autoregressive integrated moving average (SARIMA) models. SARIMA models are an extension of ARIMA models that incorporate seasonal patterns. These models capture both the trend and seasonality in the data and can be used to make forecasts.

To control volatility in various time series models, a common technique is to use a volatility model, such as the generalized autoregressive conditional heteroskedasticity (GARCH) model. This model estimates the volatility of the time series by incorporating past volatility and squared residuals. By modeling and forecasting the volatility, you can better understand and manage the potential fluctuations in the time series data.

A simple moving average method is a technique used to smooth out fluctuations and identify trends in time series data. It involves calculating the average of a fixed number of data points, often referred to as the window size or period. As new data becomes available, the oldest data point in the window is dropped, and the newest data point is included in the calculation. This process is repeated for each subsequent data point. The resulting moving average values can provide insights into the overall trend of the data, helping to identify patterns or changes over time.

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The basis of the null space is the empty set, as there are no vectors in the null space.

To find a basis of the null space (also known as the kernel) of a matrix, we need to solve the homogeneous equation Ax = 0, where A is the given matrix and x is a vector.

a.) Let's find the basis of the null space for the matrix:

⎡⎣⎢​2 1 1​−1 2 −2​0 −1 −1​−10 −2​⎤⎦⎥​

We can set up the following augmented matrix:

⎡⎣⎢​2 1 1 0​−1 2 −2 0​0 −1 −1 0​−1 0 −2 0​⎤⎦⎥​

Next, we perform row operations to bring the matrix into row-echelon form:

R2 = R2 + R1

R3 = R3 - R1

R4 = R4 + (1/2)R1

⎡⎣⎢​2 1 1 0​0 3 -1 0​0 -1 -1 0​0 1 -1 0​⎤⎦⎥​

R3 = R3 + (1/3)R2

R4 = R4 - (1/2)R2

⎡⎣⎢​2 1 1 0​0 3 -1 0​0 0 -2 0​0 0 -1 0​⎤⎦⎥​

R3 = R3 / (-2)

R4 = R4 / (-1)

⎡⎣⎢​2 1 1 0​0 3 -1 0​0 0 1 0​0 0 1 0​⎤⎦⎥​

R2 = R2 - 3R3

R1 = R1 - R3

⎡⎣⎢​2 1 0 0​0 3 0 0​0 0 1 0​0 0 1 0​⎤⎦⎥​

R1 = R1 - (1/2)R3

R2 = (1/3)R2

⎡⎣⎢​1 1 0 0​0 1 0 0​0 0 1 0​0 0 1 0​⎤⎦⎥​

We can see that the matrix is now in row-echelon form. The variables corresponding to the columns without leading 1's (i.e., columns 3 and 4) are the free variables. Let's denote these variables as t1 and t2, respectively.

Now, we can express the solutions in terms of these free variables:

x1 = -t1 - t2

x2 = t1

x3 = t2

x4 = 0

Thus, the general solution to Ax = 0 is:

⎡⎣⎢​x1​x2​x3​x4​⎤⎦⎥​ = ⎡⎣⎢​-t1 - t2​t1​t2​0​⎤⎦⎥​ = t1 ⎡⎣⎢​-1​1​0​0​

⎤⎦⎥​ + t2 ⎡⎣⎢​-1​0​1​0​⎤⎦⎥​

Therefore, the basis of the null space is the set of vectors ⎡⎣⎢​-1​1​0​0​⎤⎦⎥​ and ⎡⎣⎢​-1​0​1​0​⎤⎦⎥​.

b.) Let's find the basis of the null space for the matrix:

⎡⎣⎢​1 0 -1​0 1 -2​2 -2 -3​-1 -1 0​0 2 -1​⎤⎦⎥​

We can set up the following augmented matrix:

⎡⎣⎢​1 0 -1 0​0 1 -2 0​2 -2 -3 0​-1 -1 0 0​0 2 -1 0​⎤⎦⎥​

Next, we perform row operations to bring the matrix into row-echelon form:

R3 = R3 - 2R1

R4 = R4 + R1

R5 = R5 - 2R1

⎡⎣⎢​1 0 -1 0​0 1 -2 0​0 -2 -1 0​0 -1 1 0​0 2 -1 0​⎤⎦⎥​

R3 = R3 + 2R2

R4 = R4 + R2

R5 = R5 - 2R2

⎡⎣⎢​1 0 -1 0​0 1 -2 0​0 0 -5 0​0 0 -1 0​0 0 -3 0​⎤⎦⎥​

R5 = R5 / (-3)

⎡⎣⎢​1 0 -1 0​0 1 -2 0​0 0 -5 0​0 0 -1 0​0 0 1 0​⎤⎦⎥​

R3 = R3 / (-5)

⎡⎣⎢​1 0 -1 0​0 1 -2 0​0 0 1 0​0 0 -1 0​0 0 1 0​⎤⎦⎥​

R1 = R1 + R3

R2 = R2 + 2R3

R4 = R4 + R3

R5 = R5 - R3

⎡⎣⎢​1 0 0 0​0 1 0 0​0 0 1 0​0 0 0 0​0 0 0 0​⎤⎦⎥​

We can see that the matrix is now in row-echelon form. There are no free variables, which means the only solution to Ax = 0 is the trivial solution.

Therefore, the basis of the null space is the empty set, as there are no vectors in the null space.

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The value of logm 4/m is 1.139 - 2 logm m. This means that we can express logm 4/m in terms of other logarithmic values without finding the exact value of m.

Given that logm 3 = 0.903, logm 4 = 1.139, and logm 7 = 1.599. We are to find logm 4/m.

Using the properties of logarithm, we have,

logm 4/m = logm 4 - logm m

               =1.139 - logm m               .....................................(1)

Again, using the properties of logarithm, we know that:

logm 4 = logm (2 × 2)  

        = logm 2 + logm 2

         = 1.139 = 2logm 2                    ..................................(2)

Substituting equation (2) into (1) gives:

logm 4/m = 2logm 2 - logm

           m = 2logm (2/m)          ..................................................(3)

Using the property of logarithm once again, we know that:

loga b = logc b / logc a                     ............................................(4)

Substituting equation (4) into equation (3), we have:

logm 4/m = 2 logm 2 - logm

m= logm [(2/m)² / m]                       .............................................(5)

Now, we are to find logm 4/m by substituting the given values.

Using equation (2), we have:

logm 2 = (1.139)/2

     = 0.5695

Using equation (5), we get:

logm 4/m = logm [(2/m)² / m]

logm 4/m = logm [4/m²m]

 logm 4/m = logm 4 - logm

logm 4/m = 1.139 - 2 logm m

Therefore, by using the properties of logarithm, we have found that logm 4/m = 1.139 - 2 logm m. This means that we can express logm 4/m in terms of other logarithmic values without finding the exact value of m.

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Therefore , the solution of the given problem of volume comes out to be false we must first know the cylinder's radius and height.

A three-dimensional object's volume, which is expressed in cubic units, indicates how much space it takes up. The symbols cm3 and in3 stand for cubic dimensions. However, you can use an object's bulk to estimate its dimensions. Usually, the weight of the item is converted into mass measures like kilograms and kilos.

Here,

The capacity of a cylinder and a cone that are the same height and radius are not the same.

The formula V = πr²h,

where r is the radius of the base and h is the height, determines the volume of a cylindrical. Contrarily, the equation

=> V = (1/3)r²h gives the volume of a cone.

To calculate the volume of a cone with the same measurements if the cylinder's volume is 99 cubic cm,

False we must first know the cylinder's radius and height.

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Upper

daysThe(a) The time for an individual to recover from an infectious disease, is estimated to be between 4.02 and 5.98 days. (d) The structured SIR model assumes homogeneous mixing, constant population, recovered immunity.

(a) To calculate the time for an individual to recover with a 95% confidence level, we can use the properties of the normal distribution. The 95% confidence interval corresponds to approximately 1.96 standard deviations from the mean in both directions.

Given:

Mean (μ) = 5 days

Standard deviation (σ) = 0.5 days

The confidence interval can be calculated as follows:

Lower limit = Mean - (1.96 * Standard deviation)

Upper limit = Mean + (1.96 * Standard deviation)

Lower limit = 5 - (1.96 * 0.5)

= 5 - 0.98

= 4.02 days

Upper limit = 5 + (1.96 * 0.5)

= 5 + 0.98

= 5.98 days

Therefore, the time for an individual to recover from the infectious disease with a 95% confidence level is between approximately 4.02 and 5.98 days.

(b) To simulate the epidemic using the SIR model, we need additional information about the transmission rate and the duration of infectivity.

(c) Without the transmission rate and duration of infectivity, we cannot determine the fraction of the total population that will have come down with the infectious disease once the epidemic is over.

(d) The structured model in this case is the SIR (Susceptible-Infectious-Recovered) model, which is commonly used to study the dynamics of infectious diseases. The major assumptions associated with the SIR model include:

Homogeneous mixing: The model assumes that individuals in the population mix randomly, and each individual has an equal probability of coming into contact with any other individual.

Constant population: The model assumes a constant population size, without accounting for birth, death, or migration rates.

Recovered individuals develop immunity: The model assumes that individuals who recover from the infectious disease gain permanent immunity and cannot be reinfected.

No vaccination or intervention: The basic SIR model does not incorporate vaccination or other intervention measures.

These assumptions simplify the model and allow for mathematical analysis of disease spread dynamics. However, they may not fully capture the complexities of real-world scenarios, and more sophisticated models can be developed to address specific contexts and factors.

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Answer:

To experimentally verify that the base angles of an isosceles triangle are equal, we will need two isosceles triangles of different sizes.

Materials needed:

Two sheets of paper

Ruler

Pencil

Protractor

Scissors

Experiment:

Draw a large isosceles triangle on one sheet of paper by drawing a straight line at least 20 cm long. Then draw two additional lines from each end of the first line to meet at the top, forming an isosceles triangle. Label the base as "AB" and the other two sides as "AC" and "BC."

Measure and mark the midpoint of the base "AB."

Using a ruler, draw a perpendicular bisector through the midpoint of the base. This line should create two congruent segments.

Measure each angle formed by the intersection of the perpendicular bisector and the two sides of the triangle. Use a protractor to measure these angles.

Repeat steps 1-4 with a smaller isosceles triangle on the second sheet of paper. The smaller triangle should have a base of at least 10 cm and two sides of equal length.

Compare the measurements of the angles of both triangles. If the triangles are truly isosceles, then the two angles opposite the base (ACB) should measure the same in both triangles.

Cut out both isosceles triangles along their outlines.

Fold each triangle along the perpendicular bisector line drawn in step 3 so that the two congruent segments come together.

If the angles opposite the base are indeed equal, then the two sides of each triangle should match up perfectly when folded along the perpendicular bisector. If they do not match up, then the triangles are not truly isosceles.

By repeating this experiment with different sized isosceles triangles, we can verify that the base angles of any isosceles triangle are always equal.

Therefore , the solution of the given problem of angles comes out to be following about a normal 16-gon is FALSE:

The top but also bottom of wall separate the two circular edges that make the sides of a skew in Euclidean space. A junction point may develop when two beams collide. Another result of two things interacting is an angle. They most closely resemble dihedral shapes. Two line beams can be arranged in different ways at their extremities to form a two-dimensional curve.

Here,

The following about a normal 16-gon is FALSE:

c. The internal angle measure's total value is 28800.

We can use the following method to determine the total interior angle measure of a regular 16-gon:

Sum of internal angles equals (n - 2)180°, where n is the number of sides.

=> With n = 16, we obtain:

=> Interior angle total = (16 - 2) 180 = 2520 degrees.

Because of this, it is accurate to say that

=> 2520 degrees, not 28800, make up the interior angle measure of a regular 16-gon.

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Answer:

see below

Step-by-step explanation:

d = t^2

t =0

 d = 0^2 = 0

t =3

 d = 3^2 = 9

t =5

 d = 5^2 = 25

Answer:

Step-by-step explanation:

If you are using

t =0

d = 0

t =3

d = 3^2 = 9

t =5

d = 5^2 = 25

Answer:

y = 4.

Step-by-step explanation:

I suppose that this question relates to the image that can be seen below.

In the image, the green line represents the exponential function and the blue line represents the linear function.

The y-value after which the exponential function will always be greater than the linear function is the y-value where bot graphs intersect, such that after that point, the blue line starts increasing fast, and is always above the green line.

In this case, this point is the second intersection, and we can see that this intersection happens in the point (2, 4)

Remember that the usual notation for points is (x, y).

Then the y-value after which the exponential function will always be greater than the linear function is y = 4.

To find the divisor (div) and the remainder (mod):

a) To find div and mod, we use the formula: a = m x div + mod.
For a=228 and m=119:
- div = floor(a/m) = floor(1.9244) = 1
- mod = a - m x div = 228 - 119 x 1 = 109
Therefore, div = 1 and mod = 109.

b) For a=9009 and m=223:
- div = floor(a/m) = floor(40.4469) = 40
- mod = a - m x div = 9009 - 223 x 40 = 49
Therefore, div = 40 and mod = 49.

c) For a=-10101 and m=333:
- div = floor(a/m) = floor(-30.3903) = -31
- mod = a - m x div = -10101 - 333 x (-31) = -18
Therefore, div = -31 and mod = -18.

d) For a=-765432 and m=38271:
- div = floor(a/m) = floor(-19.9885) = -20
- mod = a - m x div = -765432 - 38271 x (-20) = -2932
Therefore, div = -20 and mod = -2932.

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The length is 12 cm and width is 9 cm.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Area = 108 cm²

and, The length of a rectangle is 3 cm greater than its width.

let the width of rectangle be x.

so, length = x+ 3

So, Area of Rectangle = l x w

108 = x(x+ 3)

x² + 3x -108 = 0

x² + 12x - 9x  -108 = 0

x( x+ 12) -9 ( x+ 12)= 0

(x + 12)(x- 9)=0

x= -12, +9

So, length is 12 cm and width is 9 cm.

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According to the Conjugate Roots Theorem, the complex zeroes of a polynomial always occur in pairs with its conjugate. This means that is a+ib is the root of the equation then its conjugate a-ib must also be a root of the same polynomial.

Given that x=2+2i is a root, then x=2-2i will also be a root of the given cubic polynomial.

Note that since the degree of polynomial is 3, there can be maximum 3 zeroes. Two of these are known complex zeroes, there is only one zero remaining i.e. not occurring in pair. So it must be a real number.

Let the third root be 'a', this means (x-a) ia a factor of the polynomial.

Apply the Long Division,

It is found that,

Thus, the third root of the given cubic polynomial is 4.

Answer:

x = \(\frac{17}{3}\)

Step-by-step explanation:

\(\frac{10}{x-4}=6\\\\\)

10 = 6*(x -4)

10 = 6*x - 6*4

10 = 6x - 24

Add 24 to both sides

10 + 24 = 6x - 24 + 24

34 = 6x

6x = 34

Divide both sides  by 6

6x/6 = 34/6

x = \(\frac{17}{3}\)

Answer:

b = 2

Step-by-step explanation:

using the tangent ratio in the right triangle and the exact value

tan30° = \(\frac{1}{\sqrt{3} }\) , then

tan30° = \(\frac{opposite}{adjacent}\) = \(\frac{b}{a}\) = \(\frac{b}{2\sqrt{3} }\) = \(\frac{1}{\sqrt{3} }\) ( cross- multiply )

b × \(\sqrt{3}\) = 2\(\sqrt{3}\) ( divide both sides by \(\sqrt{3}\) )

b = 2

Answer:

Given that a = 2√3.

Let's find value of b...

The baker can get approximately 6.28 "perfect" slices out of one pie. By using the central angle of 1 radian as a basis, we can calculate the number of "perfect" slices that can be obtained from a pie.

Dividing the total angle around the center of the pie (360 degrees or 2π radians) by the central angle of 1 radian gives us the number of slices.

In this case, the baker can get approximately 6.28 "perfect" slices out of one pie. It is important to note that this calculation assumes the pie is a perfect circle and that the slices are of equal size and shape.

The central angle of 1 radian represents the angle formed at the center of a circle by an arc whose length is equal to the radius of the circle. In the case of the baker's pie, assuming the pie is a perfect circle, we can use the central angle of 1 radian to calculate the number of "perfect" slices.

To find the number of slices, we need to divide the total angle around the center of the pie (360 degrees or 2π radians) by the central angle of 1 radian.

Number of Slices = Total Angle / Central Angle

Number of Slices = 2π radians / 1 radian

Number of Slices ≈ 6.28

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Answer:

20%

Step-by-step explanation:

Answer:

20%

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

Given

A = \(\frac{1}{2}\) bh ( multiply both sides by 2 to clear the fraction )

2A = bh ( divide both sides by b )

\(\frac{2A}{b}\) = h

Answer:

x = 6

Step-by-step explanation:

.16x + 2 * .02 = (x + 2) * .17
.16x + .4 = .17x + .34
.06 = .01x
6 = x

Answer:

\(t1 {15y08 \frac{18 \gamma \gamma }{?} }^{2} \)