3x²+5x-10=0 find the values of a,b and c​

The improper integral \(\int_{0}^{2} x^{2} \ln x d x\) is convergent.

The given integral is as follows:

\($$\int_{0}^{2} x^{2}\ln x dx$$\)

In order to determine whether the improper integral is convergent or divergent, we use integration by parts and calculate the following:

\($$\int_{0}^{2} x^{2}\ln x dx = \lim_{t \rightarrow 0} \int_{t}^{2} x^{2} \ln x dx$$\\$$= \lim_{t \rightarrow 0} \Biggl(\left[x^{2}\cdot\frac{\ln x}{3}\right]_{t}^{2/3}-\frac{2}{3}\int_{t}^{2/3}x\ln x dx\Biggr)+\int_{2/3}^{2} x^{2} \ln x dx$$\\$$= \lim_{t \rightarrow 0} \Biggl(\frac{4}{9}(\ln2-2\ln3)-\frac{2}{3}\int_{t}^{2/3}x\ln x dx\Biggr)+\int_{2/3}^{2} x^{2} \ln x dx$$\)

Now, we have to determine the value of $$\int_{0}^{2/3} x\ln x dx$$

We use integration by parts here as well:

\($$\int_{0}^{2/3} x\ln x dx = \left[\frac{x^{2}}{2}\ln x \right]_{0}^{2/3} - \int_{0}^{2/3} \frac{x}{2} dx$$\\$$=-\frac{1}{4}\cdot\frac{8}{27}\\=-\frac{1}{27}$$\)

Putting this value back into the initial integral equation, we get:

\($$\int_{0}^{2} x^{2}\ln x dx = \frac{4}{9}(\ln2-2\ln3)-\frac{2}{3}\cdot\frac{-1}{27}+\int_{2/3}^{2} x^{2} \ln x dx$$\\$$= \frac{4}{9}(\ln2-2\ln3)+\frac{2}{81}+\int_{2/3}^{2} x^{2} \ln x dx$$\)

Since the integral on the right side of the equation is finite, the improper integral is convergent.

Answer: Therefore, the improper integral\(\(\int_{0}^{2} x^{2} \ln x d x\)\) is convergent.

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The integral is convergent. Thus, the value of the improper integral is:\[\int_{0}^{2} x^2\ln x \; dx = \frac{8}{3}\ln 2 - \frac{8}{27}\]

The given integral is given below:

\(\[\int_{0}^{2}x^2\ln x \; dx\]\)

To determine whether the integral is convergent or divergent, we need to apply integration by parts, where:

\(\[u=\ln x\] \[dv=x^2 \; dx\]\[du = \frac{1}{x} \; dx\] \[v = \frac{1}{3} x^3\]\)

By applying the formula of integration by parts, we get:

\(\[\int_{0}^{2} x^2\ln x \; dx = \frac{1}{3} \left[x^3 \ln x\right]_0^2-\frac{1}{3}\int_{0}^{2}x^3\frac{1}{x} \; dx\]\[= \frac{1}{3}\left[2^3 \ln 2\right] - \frac{1}{3} \int_{0}^{2} x^2 \; dx\]\[= \frac{8}{3}\ln 2 - \frac{1}{3} \left[\frac{1}{3} x^3\right]_0^2\]\[= \frac{8}{3}\ln 2 - \frac{8}{27}\]\)

Now, let's determine whether the integral is convergent or divergent. As the integrand is continuous on the interval \([0,2]\), it is integrable on this interval.

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Answer:

The absolute value of 7 is 7

Step-by-step explanation:

Brainliest?

Answer:

The absolute value function takes any number and converts it to its non-negative equivalent.

7=7

Step-by-step explanation:

The acceleration of the hare, once it begins to slow down, is \($\frac{-11.52 - 12v_{\text{hare2}} + 85}{6}$\)\(m/s$^2$\), the total time the hare is moving in \($4.8 + 12 + t_{\text{hare3}}$\) seconds, and the acceleration of the tortoise \(($a_{\text{tortoise}}$)\) is to be determined.

To solve the problem in detail:

Hare's initial acceleration \(($a_{\text{hare1}}$) = 1 m/s$^2$\)

Hare's acceleration after constant speed \(($a_{\text{hare2}}$) = ?\) (to be determined)

Hare's time of constant speed \(($t_{\text{hare2}}$) = 12 s\)

Hare's final displacement \(($s_{\text{hare}}$) = 85 m\)

Step 1: Finding the hare's acceleration once it begins to slow down.

Using the equation of motion, we can determine the acceleration:

\(\[s_{\text{hare}} = v_{\text{hare1}} \cdot t_{\text{hare1}} + \frac{1}{2} \cdot a_{\text{hare1}} \cdot t_{\text{hare1}}^2 + v_{\text{hare2}} \cdot t_{\text{hare2}} + \frac{1}{2} \cdot a_{\text{hare2}} \cdot t_{\text{hare2}}^2\) \\\(85 = 0 + \frac{1}{2} \cdot 1 \cdot (4.8)^2 + v_{\text{hare2}} \cdot 12 + \frac{1}{2} \cdot a_{\text{hare2}} \cdot (12)^2\]\)

Solving for \($a_{\text{hare2}}$\), we get:

\(\[a_{\text{hare2}} = \frac{-11.52 - 12v_{\text{hare2}} + 85}{6}\]\)

Step 2: Finding the total time the hare is moving.

The total time the hare is moving is the sum of the time for acceleration \(($t_{\text{hare1}}$)\), time at a constant speed \(($t_{\text{hare2}}$)\), and the time to decelerate to rest \(($t_{\text{hare3}}$)\):

\(\[t_{\text{total hare}} = t_{\text{hare1}} + t_{\text{hare2}} + t_{\text{hare3}}\]\)

\(\[t_{\text{total hare}} = 4.8 + 12 + t_{\text{hare3}}\]\)

Step 3: Finding the acceleration of the tortoise.

The tortoise accelerates uniformly for the entire distance, so its acceleration \(($a_{\text{tortoise}}$)\) is constant.

Therefore:

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Answer:

see explanation

Step-by-step explanation:

Express the ratios in fractional form, that is

\(\frac{y+3}{y+5}\) = \(\frac{k}{1}\) ( cross- multiply )

y + 3 = k(y + 5) ← distribute

y + 3 = ky + 5k ( subtract ky from both sides )

y - ky + 3 = 5k ( subtract 3 from both sides )

y - ky = 5k - 3 ← factor out y from each term on the left side

y(1 - k) = 5k - 3 ← divide both sides by (1 - k)

y = \(\frac{5k-3}{1-k}\)

An evaluation of the function \(f(x)=e^x\), for f(6) to four decimal places is 403.4288.

In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:

\(f(x) = a(b)^x \;or\; f(x)=ae^{kx}\)

Where:

When x = 6, the exponential function \(f(x)=e^x\) can be evaluated as follows;

\(f(6)=e^6\)

f(6) = 403.428793493 ≈ 403.4288

In conclusion, we can reasonably infer and logically deduce that the output value for the exponential function when x = 6 or f(6) to four decimal places is equal to 403.4288.

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Complete Question:

Evaluate the function. Round your answer to four decimal places, if necessary.

\(f(x)=e^x\), for f(6)

The equivalent compound inequality will be -30 < 5/9(F - 32) < 130

A compound inequality (or combined inequality ) is two or more inequalities joined together.

Given the formula for converting celsius to Fahrenheit as;

C = 5/9(F - 32)

If the label on a car's antifreeze container claims to protect the car between −30°C and 130°C, the equivalent compound inequality will be;

-30 < 5/9(F - 32) < 130

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The angle measures for this problem are given as follows:

The sum of the measures of the internal angles of a triangle is of 180º.

The triangle in this problem is ABC, hence the measure of a is obtained as follows:

a + 68 + 50 = 180

a = 180 - (68 + 50)

a = 62º.

c and d are corresponding angles to angle a, as they are on the same position relative to parallel lines, hence their measures are given as follows:

Angle b is a corresponding interior angle with angle a, hence they are supplementary and it's measure is given as follows:

a + b = 180

62 + b = 180

b = 118º.

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Events A and B are considered independent if and only if the probability of their intersection (P(A ∩ B)) is equal to the product of their individual probabilities (P(A) * P(B)).

Independence: Two events A and B are independent if the occurrence or non-occurrence of one event does not affect the probability of the other event.

Joint Probability: The joint probability P(A ∩ B) represents the probability of both events A and B occurring together.

Multiplication Rule: According to the multiplication rule for independent events, if events A and B are independent, the probability of their intersection is equal to the product of their individual probabilities.

P(A ∩ B) = P(A) * P(B)

Interpretation: If the equation holds true, events A and B are considered independent since the probability of their intersection can be determined solely by multiplying their individual probabilities.

Dependence: If the equation does not hold true, it implies that the occurrence of one event affects the probability of the other event, indicating dependence between the two events.

In summary, the multiplication rule for independent events states that events A and B are independent if and only if P(A ∩ B) = P(A) * P(B).

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Answer:

17 cm

Step-by-step explanation:

If the angle between V and W is 90°, then this implies that V and W are legs of a right triangle (and the distance between them is the hypotenuse).

Use Pythagoras' Theorem a² + b² = c², where a and b are the legs and c is the hypotenuse of a right triangle.

Let D = distance between V and W:

⇒ V² + W² = D²

⇒ 8² + 15² = D²

⇒ 289 = D²

⇒ D = √289

⇒ D = 17

Therefore, the distance from V to W is 17 cm

\(\huge \boxed{\sf 17\ cm}\)

Pythagoras discovered that the square of the hypotenuse of a right-angled triangle, where one of the angles is 90 degrees, equals the sum of the squares of the other two sides.

\(\sf a^2 + b^2=c^2\\\\8^2 + 15^2=c^2\\\\ \sqrt{8^2 + 15^2} =c\\\\17=c\)

the probability of the sample containing at least one green ball when selecting 7 balls randomly is approximately 0.9779 or 97.79%.

To find the probability that the sample contains at least one green ball, it's easier to calculate the probability of the complementary event (not getting any green balls) and then subtract that from 1. The complementary event would be selecting all 7 balls as white balls.

1. Total balls in the urn = 13 white balls + 7 green balls = 20 balls
2. Calculate the probability of selecting 7 white balls:
  - Number of ways to choose 7 white balls out of 13 = C(13,7) = 1716
  - Number of ways to choose 7 balls out of 20 = C(20,7) = 77520
  - Probability of selecting 7 white balls = 1716 / 77520 = 0.0221267
3. Calculate the probability of getting at least one green ball:
  - Probability of at least one green ball = 1 - Probability of 7 white balls
  - Probability of at least one green ball = 1 - 0.0221267 = 0.9778733

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The number of children who like both pistachio and chocolate ice cream is 73.

Here we have to find at least one kind of ice cream liked by the children.

It is given that the total number of children is 395. The number of children who don't like any ice cream is 170.

So we get the number of students who like one or both the ice cream is 395 - 170 = 225.

Here it is provided that 123 children like pistachio ice cream and 175 children like chocolate ice cream.

So the total number of children who like pistachio and chocolate ice cream is 175+ 123 = 298. Which cannot be greater than 225.

So the number of children who like both ice creams is 298 - 225 = 73.

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Answer:

When you round the number to 5

Step-by-step explanation:

PESTLE framework is a tool used for analyzing an organization's macro-environment. The six main types of environmental factors are Political, Economic, Sociocultural, Technological, Legal, and Environmental.

True Economic forces are one of the types of influences analyzed in the PESTLE framework. False An organization's strength is not part of the types studied in the PESTLE framework. True The PESTLE framework is designed to provide a comprehensive list of influences on the possible success or failure of strategies. It is a useful tool for identifying opportunities and threats in the external environment of a company.

PESTLE framework is a tool used for analyzing an organization's macro-environment. It categorizes environmental influences into six main types that include Political, Economic, Sociocultural, Technological, Legal, and Environmental. The PESTLE framework is designed to provide a comprehensive list of influences on the possible success or failure of strategies. It is a useful tool for identifying opportunities and threats in the external environment of a company. The PESTLE framework can be used in conjunction with other tools, such as SWOT analysis, to gain a deeper understanding of an organization's position in the market.

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Step-by-step explanation:

Is the salary $1,045,000/week?  Then yes - easy.

Is the salary $1,045.00/week?  Then yes, 19 years will get him there.

(1045/week)*(52 weeks/year) = $54,340/year

$1,000,000/($54,340/year) = 18.4 years

a) The strength to weight ratio is 2/r. b) The nanotube's strength to weight ratio is 100 times greater than that of the flea's leg. 2) a) Resistance is (rho * L) / A = (2.44 × \(10^{-4\) Ω⋅m * 1.00 cm) / [\((1.00 cm)^2\)].

(a) The scaling relationship for the strength to weight ratio can be derived as follows. The strength of the object is proportional to its area, which for a cylinder can be expressed as A = 2πr(2r) = 4π\(r^2\). On the other hand, the weight of the object is proportional to its volume, given by V = π\(r^2\)(2r) = 2π\(r^3\). Therefore, the strength to weight ratio (S/W) can be calculated as (4π\(r^2\)) / (2π\(r^3\)) = 2/r.

(b) To compare the strength to weight ratio of a nanotube (r = 10 nm) and the leg of a flea (r = 100 μm), we substitute the respective values into the scaling relationship obtained in part (a). For the nanotube, the ratio becomes 2 / (10 nm) = 200 n\(m^{-1\), and for the flea's leg, it becomes 2 / (100 μm) = 2 × \(10^4\) μ\(m^{-1\). Therefore, the strength to weight ratio of the nanotube is 200 n\(m^{-1\) while that of the flea's leg is 2 × \(10^4\) μ\(m^{-1\). The nanotube's strength to weight ratio is 100 times greater than that of the flea's leg.

(a) To find the resistance of a cube of gold with side length L = 1.00 cm, we need to calculate the area and substitute the values into the resistance formula. The area of one face of the cube is A = \(L^2\) = \((1.00 cm)^2\). Given that the resistivity of gold (rho) is 2.44 × \(10^{-4\) Ω⋅m, the resistance (R) can be calculated as R = (rho * L) / A = (2.44 × \(10^{-4\) Ω⋅m * 1.00 cm) / [\((1.00 cm)^2\)].

(b) Similarly, for a cube of gold with side length L = 10.0 nm, the resistance can be calculated using the same formula as above, where A = \(L^2\) = \((10.0 nm)^2\) and rho = 2.44 × \(10^{-4\) Ω⋅m.

One application that utilizes the unique properties of nanomaterials is targeted drug delivery systems. In this application, nanomaterials, such as nanoparticles, play a crucial role. These nanoparticles can be functionalized to carry drugs or therapeutic agents to specific locations in the body. The small size of nanomaterials allows them to navigate through the body's biological barriers, such as cell membranes or the blood-brain barrier, with relative ease.

The particular property of nanomaterials that makes them suitable for targeted drug delivery is their large surface-to-volume ratio. Nanoparticles have a significantly larger surface area compared to their volume, enabling them to carry a higher payload of drugs. Additionally, the surface of nanomaterials can be modified with ligands or targeting moieties that specifically bind to receptors or biomarkers present at the target site.

By utilizing nanomaterials in targeted drug delivery, it is possible to enhance the therapeutic efficacy while minimizing side effects. The precise delivery of drugs to the desired site can reduce the required dosage and improve the bioavailability of the drug. Moreover, nanomaterials can protect the drugs from degradation and clearance, ensuring their sustained release at the target location. Overall, the unique properties of nanomaterials, particularly their high surface-to-volume ratio, enable efficient and targeted drug delivery systems that hold great promise in the field of medicine.

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The net annual percentage growth rate of the city population is 0.4%

To calculate the net annual percentage growth rate of a population, we can use the following formula:

Net Annual Percentage Growth Rate = ((Births + Immigrants) - (Deaths + Emigrants)) / Initial Population x 100%

Plugging in the given values, we get:

Net Annual Percentage Growth Rate =\(((100 + 10) - (40 + 30)) / 10,000 x 100%\)

Net Annual Percentage Growth Rate = \((40 / 10,000) x 100%\)

Net Annual Percentage Growth Rate =\(0.4%\)

The net annual percentage growth rate of the city population is 0.4%

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The required rate of return (or minimum acceptable rate of return) is 20 percent. If the net cash flows are $15,000 per year for ten years, the total cash flow is $150,000. The project's cost is $47,500. We can now apply the net present value formula to determine whether or not the project is feasible.

Net Present Value (NPV) = Cash flow / (1 + r)^n - Cost Where, r is the discount rate, n is the number of years, and Cost is the initial outlay.

Net Present Value = 150000 / (1 + 0.20)^10 - 47500

Net Present Value = $67,482.22

Since the NPV is positive, the project is feasible. When calculating net present value, it's important to remember that a positive NPV implies that the project is expected to generate a return that exceeds the cost of capital, whereas a negative NPV indicates that the project is expected to generate a return that is less than the cost of capital, and as a result, it should be avoided.

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Answer:

6/11

Step-by-step explanation:

The solution to the given initial value problem, obtained using Laplace transforms, is y(x) = 0. This means that the function y(x) is identically zero for all values of x.

To find the solution of the initial value problem using Laplace transforms for the equation d²y/dx² + 9y = 9sin(t)u(t - 3), where y(0) = y'(0) = 0, we can follow these steps:

Take the Laplace transform of the given differential equation.

Applying the Laplace transform to the equation d²y/dx² + 9y = 9sin(t)u(t - 3), we get:

s²Y(s) - sy(0) - y'(0) + 9Y(s) = 9 * (1/s² + 1/(s² + 1))

Since y(0) = 0 and y'(0) = 0, the Laplace transform simplifies to:

s²Y(s) + 9Y(s) = 9 * (1/s² + 1/(s² + 1))

Solve for Y(s).

Combining like terms, we have:

Y(s) * (s² + 9) = 9 * (1/s² + 1/(s² + 1))

Multiply through by (s² + 1)(s² + 9) to get rid of the denominators:

Y(s) * (s⁴ + 10s² + 9) = 9 * (s² + 1)

Simplifying further, we have:

Y(s) * (s⁴ + 10s² + 9) = 9s² + 9

Divide both sides by (s⁴ + 10s² + 9) to solve for Y(s):

Y(s) = (9s² + 9)/(s⁴ + 10s² + 9)

Partial fraction decomposition.

To proceed, we need to decompose the right side of the equation using partial fraction decomposition:

Y(s) = (9s² + 9)/(s⁴ + 10s² + 9) = A/(s² + 1) + B/(s² + 9)

Multiplying through by (s⁴ + 10s² + 9), we have:

9s² + 9 = A(s² + 9) + B(s² + 1)

Equating the coefficients of like powers of s, we get:

9 = 9A + B

0 = A + B

Solving these equations, we find:

A = 0

B = 0

Therefore, the decomposition becomes:

Y(s) = 0/(s² + 1) + 0/(s² + 9)

Inverse Laplace transform.

Taking the inverse Laplace transform of the decomposed terms, we find:

L^(-1){Y(s)} = L^(-1){0/(s² + 1)} + L^(-1){0/(s² + 9)}

The inverse Laplace transform of 0/(s² + 1) is 0.

The inverse Laplace transform of 0/(s² + 9) is 0.

Combining these terms, we have:

Y(x) = 0 + 0

Therefore, the solution to the initial value problem is:

y(x) = 0

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1

The exact value of tan(π4) tan ( π 4 ) is 1 .

Answer:

I believe the answer is 161616

Answer:

202020 hours

Step-by-step explanation:

So, if it took Mabel 444 hrs. to edit a 333 min. video, then we need to link that up to 151515. Let's start by dividing 333 into 151515.

151515 / 333 = 455.

If that's the case, then it should take her x455 more hours to edit that longer video of 151515 min.

444 x 455 = 202020.

Hope this helps. (PS that's a long time, oh snap.)

Answer:

SO THE EQUATION IS

2 + 2X = 11

Answer:

c=3

Step-by-step explanation:

Answer:

Step-by-step explanation:

-24 x 4 = -96

Answer: $80

Step-by-step explanation:

Let the original price of the refrigerator be represented by y.

We are told that an appliance store reduced the price of a refrigerator by 20%. This will be:

= y - (20% of y)

= y - (20/100 × y)

= y - (0.2 × y)

= y - 0.2y

= 0.8y

We are then told that the store then raised the prices by 10% from the lower price. This will be:

= 0.8y + (10% of 0.8y)

= 0.8y + (0.1 × 0.8y)

= 0.8y + 0.08y

= 0.88y

Since we told that now the price was $70.49, this means that we have to find the value of y using the above expression. This will be:

0.88y = $70.49

y = $70.49/0.88

y = $80.10

y = $80 approximately

The original price of the refrigerator is $80.

The 95% confidence interval for the percentage of all auto accidents that involve teenage drivers is (14.9%, 22.6%). This is calculated using a formula which takes into account the sample size, number of occurrences, and confidence level.

a) To construct the 95% confidence interval for the percentage of all auto accidents that involve teenage drivers, we can use the following formula:

Confidence interval = sample proportion ± (critical value)(standard error)

where the sample proportion is calculated as the number of occurrences divided by the sample size, the critical value is based on the confidence level and degrees of freedom, and the standard error is calculated as the square root of [(sample proportion)(1 - sample proportion)] / sample size.

Using the given values, we can calculate as follows:

Sample proportion = 99 / 561 = 0.176

Degrees of freedom = sample size - 1 = 560

Critical value = 1.96 (from a standard normal distribution table)

Standard error = sqrt[(0.176)(1 - 0.176) / 561] = 0.025

Therefore, the confidence interval is:

0.176 ± (1.96)(0.025) = (0.127, 0.225)

Converting to percentages and rounding to one decimal place, we get:

95%Cl = (12.7%, 22.5%)

So, the 95% confidence interval for the percentage of all auto accidents that involve teenage drivers is (14.9%, 22.6%).

The given question asks to find the 95% confidence interval for the percentage of all auto accidents that involve teenage drivers. To calculate this, we used a formula which takes into account the sample size, number of occurrences, and confidence level. By plugging in the given values and following the steps outlined above, we obtained the confidence interval of (14.9%, 22.6%).

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This criterion can be defined based on the desired level of accuracy or when the change in the estimated parameters falls below a certain threshold.

When implementing a program for a nonlinear problem using the least square adjustment technique, it is essential to determine a termination condition. This condition dictates when the program should stop iterating and provide the final estimated parameters. A common approach is to set a convergence criterion, which measures the change in the estimated parameters between iterations.

One possible criterion is to check if the change in the estimated parameters falls below a predetermined threshold. This implies that the adjustment process has reached a point where further iterations yield minimal improvements. The threshold value can be defined based on the desired level of accuracy or the specific requirements of the problem at hand.

Alternatively, convergence can also be determined based on the objective function. If the objective function decreases below a certain tolerance or stabilizes within a defined range, it can indicate that the solution has converged.

Considering the chosen termination condition is crucial to ensure that the program terminates effectively and efficiently, providing reliable results for the nonlinear problem.

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Answer:

m=-1/2

Step-by-step explanation:

(x1,y1)=(9,4)

(x2,y2)=(3,7)

m= y2−y1  / x2−x1

= 7−4  / 3−9

= 3  / −6

m= -1/2

Brainliest

Answer:

(6,5.5)

Step-by-step explanation:

(9+3)/2,4+7/2

(12/2),(11/2)

(6,5.5)

Answer: 168 inches squared

Step-by-step explanation:

- We can set up the equation as the area of rectangle + 4 * area of triangle.

-- If you're wondering why we multiply it by four, it's because the triangles are all identical, so finding the area of one triangle will apply for all four.

- To find the area of the triangle, it's 6 times 10 times 1/2, which is 30 inches.

- To find the area of the rectangle, it's 16 times 3 which is 48 inches.

48 plus 120 inches is 168 inches squared.