MATHEMATICS COLLEGE

Find the perimeter and total area of the composite shape shown below. All measurements are given in inches. Use pi = 3.14 in any formulas used.

Answers

Answer 1

Answer:

The perimeter and area of the composite shape is:

B. Perimeter = 19.42 inches; Area = 26.13 square inches

Recall:

Area of a circle = πr²

Perimeter of circle = 2πr

Area of triangle = 1/2(bh)

The composite shape given is composed of a triangle and a semicircle.

Perimeter of the composite shape = Perimeter of semicircle + the length of the two sides of the triangle

Perimeter = 1/2(2 × 3.14 × 3) + 2(5) = 19.42 inches

Area of the composite shape = area of semicircle + area of triangle

Area = 1/2(3.14 × 3²) + 1/2(6 × 4)

Are = 14.13 + 12

Area of the composite shape = 26.13 square inches.

Therefore, the perimeter and area of the composite shape is:

B. Perimeter = 19.42 inches; Area = 26.13 square inches

Learn more about area and perimeter of composite shapes on:

brainly.com/question/6317134

Answer 2

Answer:

Step-by-step explanation:

The composite shape consists of a semi circle and a triangle. The formula for determining the perimeter of a semicircle is expressed as

Perimeter = 1/2 × 2πr = πr

Since radius, r = 3, then

Perimeter of semi circle = 3 × 3.14 = 9.42 inches

Perimeter of composite shape = 9.42 + 5 + 5 = 19.42 inches

Area of semi circle = 1/2 × πr²

Area of semicircle = 1/2 × 3.14 × 3² = 14.13 inches²

Area of triangle = 1/2 × base × height

Area of triangle = 1/2 × 6 × 4 = 12 inches²

Area of composite shape = 14.13 + 12 = 26.13 inches²

Related Questions

i will mark brainliest !!!! Which method of solving quadratic equations do you prefer: factoring, completing the square, or quadratic formula? Why? Your response should be 3-5 sentences long and show that you’ve thought about the topic/question at hand. Please be aware we are looking for YOUR PERSONAL OPINION and there is not a single “correct answer.”
Please help me with this word problem!Suppose you lay exactly 160 feet of fencing around a rectangular garden. If the length of the garden is 3 times its width, find the dimensions of the garden. Length: __ feet Width: __ feet
Find the next three terms in the geometric sequence. 2,-16,128,-1024,...
Determine the slope and the y intercept . 4x+y=3 please help
What is 6 minutes 30 seconds converted to minutes?

What is an equation of the line that passes through the points (3,4) and (5,8)

Answers

Answer:

i think 5

Step-by-step explanation:

In the equation y=mx+b, 'm' is the slope of the line and 'b' is the y-intercept.

First, you should find the slope of the line. To do this, use the equation M=y2-y1/x2-x1. Using the two given points (3,6) and (8,4), you can solve for M.

M=4-6/8-3

M=-2/5 (-0.4 in decimal form)

Now, your equation is y=-0.4x+b

Next you must solve for b to find the y-intercept. You can do this by subbing one of the given points in for x and y.

Using the point (3,6):

y=-0.4x+b

6=-0.4(3)+b

6=-1.2+b

Isolate b:

6+1.2=b

b=7.2

And now you have the equation of the line!

y=-0.4x+7.2 (IN FRACTION FORM: y=-2/5x+36/5)

What is the equation of the line passing through the points (2, -1) and (5.-10) in slope-intercept formO y=-3x-5
O y=-3x+5
Oy - 3x-5
O y=3x+5

Answers

Final answer:

The slope of the line through points (2, -1) and (5,-10) is -3. With y-intercept +5, the line's equation in slope-intercept form is y = -3x + 5.

Explanation:

The subject of your question is in the field of Mathematics, specifically algebra.

You are looking for the equation of the line in slope-intercept form, which is y = mx + b where m is the slope and b is the y -intercept. We first calculate the slope using the formula (y2 - y1) / (x2 - x1). Plugging in the values we get, m = (-10 - (-1)) / (5 - 2) = -9 / 3 = -3. Thus, m = -3. Then, to find the y-intercept, we use the point-slope form of a line equation y - y1 = m(x - x1), and plug in one of the points (2, -1) and the slope value, and then solve for b. The equation in slope-intercept form will be y = -3x + 5.

So the answer to your question is y = -3x + 5.

Learn more about Equation of a line here:

brainly.com/question/33578579

#SPJ2

Answer:

y = -3x + 5

Step-by-step explanation:

Usually by drawing a simple graph, you can tell what the equation is, even if the graph isn't 100% accurate. From the points alone, you can tell that the slope is negative, since as you increase in x you decrease in y (which is a negative relationship). You can tell that it's +5 rather than -5 because the graph sketched shows that the line goes above 0 (indicating a positive number), rather than below (a negative number).

how can you determine that the polynomial function does not have any zeros with even Multiplicity? Explain.

Answers

Answer:

See Below.

Step-by-step explanation:

Remember multiplicity rules:

If a factor has an odd multiplicity (e.g. 1, 3, 5...), then the graph will cross the x-axis at that point.

If a factor has an even multiplicity (e.g. 2, 4, 6...), then the graph will bounce off the x-axis at that point.

From the graph, we can see that at our zeros, the graph always passes through the x-axis.

Hence, we do not have any zeros with even multiplicity since the graph does not "bounce" at any of the zeros.

Final answer:

To determine if a polynomial function has zeros with even multiplicity, examine the graph or the exponents of the factors in the function. If there are no real zeros or all the factors are raised to odd powers, there won't be any even multiplicity zeros.

Explanation:

In order to determine if a polynomial function has zeros with even multiplicity, we can examine the function's graph. If a polynomial function does not have any real zeros, then it does not have any zeros with even multiplicity. This is because even multiplicity zeros occur when a factor appears multiple times in the function. However, if all the factors are raised to odd powers, then there won't be any even multiplicity zeros. On the other hand, if the function does have real zeros, we can look at the graph of the function to check if any zeros occur with even multiplicity.

Learn more about Determining zeros of polynomial functions here:

brainly.com/question/11284559

#SPJ11

Find the measure of <8

Answers

I’m pretty sure it’d be 72 degrees because they are alternate exterior angles

A certain test preparation course is designed to help students improve their scores on the MCAT exam. A mock exam is given at the beginning and end of the course to determine the effectiveness of the course. The following measurements are the net change in 6 students' scores on the exam after completing the course: 19, 15, 9, 17, 7, 16. Using these data, construct a 95% confidence interval for the average net change in a students's score after completing the course. Assume the population is approx. normal.Step 1. calculate the sample mean for the given sample data (round answer to 1 decimal place)Step 2. Calculate the sample standard deviation for the given sample data ( round answer to 1 decimal place)Step 3. Find the critical value that should be used in constructing the confidence interval. ( round answer to 3 decimal placed)Step 4. construct the 95% confidence interval (round answer to 1 decimal place)

Answers

Answer:

1) $\bar X =(\sum_(i=1)^n X_i)/(n)=13.8$

2) $s=\sqrt{(\sum_(i=1)^n (X_i -\bar X)^2)/(n-1)}=4.8$

3) $t_(\alpha/2)=2.571$

4) The 95% confidence interval would be given by (8.8;18.8)

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

We can calculate the sample mean and sample deviation with the following formulas:

Step 1. calculate the sample mean for the given sample data (round answer to 1 decimal place)

$\bar X =(\sum_(i=1)^n X_i)/(n)=13.8$

Step 2. Calculate the sample standard deviation for the given sample data ( round answer to 1 decimal place)

$s=\sqrt{(\sum_(i=1)^n (X_i -\bar X)^2)/(n-1)}=4.8$

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n=6 represent the sample size

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_(\alpha/2)(s)/(√(n))$ (1)

Step 3. Find the critical value that should be used in constructing the confidence interval. ( round answer to 3 decimal places)

In order to calculate the critical value $t_(\alpha/2)$ we need to find first the degrees of freedom, given by:

$df=n-1=6-1=5$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,5)".And we see that $t_(\alpha/2)=2.571$