1. Squares with side lengths 6, 8, and 10 meters?2. Squares with areas 64 in?, 100 in?, 144 in2? 3. Two squares with side length 5 feet and a square with area 50 square feet?4. Explain how you know whether three squares will join at their corners to form a right triangle.
Answers
In order to know if 3 squares will form a right triangle,
a. The sum of the length of two of the squares must be greater than the length of the last square.
b. The lengths of the squares (if they are integers) must form a Pythagorean triple.
Pythagorean triples are:
3, 4, 5
5, 12, 13
8, 15, 17
9, 40, 41
there are more triples but we only need these for this question
c. They must conform to the Pythagoras Theorem.
[tex]\begin{gathered} \text{Pythagoras theorem is:} \\ c^2=a^2+b^2 \\ \text{where c is the largest side of the right angled triangle or hypothenus} \\ \text{while a and b are adjacent and opposite of the right angled triangle} \end{gathered}[/tex]Now we can proceed with these points at hand.
1. Squares with side lengths 6, 8, 10 can be written as:
2(3), 2(4), 2(5).
Ignoring the "2", we can see that this follows the Pythagorean triple.
therefore, 6, 8, 10 can form a right-angled triangle
2. 64, 100, 144 can be written as:
4(16), 4(25), 4(36)
Ignoring the "4", we can see that this does not follow the Pythagorean triple.
If we input the values into the Pythagoras theorem, we shall have:
[tex]\begin{gathered} 64^2+100^2\text{ = 4096 + 10000 = 14096} \\ 144^2=\text{ 20736} \\ \text{Therefore, we can s}ee\text{ that:} \\ 64^2+100^2\text{ }\ne\text{ }144^2 \end{gathered}[/tex]Therefore, 64, 100, 144 cannot form a right-angled triangle
3. Two squares with lengths 5 and a Square with an area of 50 square feet:
We need to find the length of the square with an area of 50 square feet.
[tex]\begin{gathered} \text{Area of square = l}^2 \\ \text{where l is the length of the side} \\ 50=l^2 \\ \text{square root both sides} \\ l\text{ = }\sqrt[]{50\text{ }}\text{ = 5}\sqrt[]{2} \end{gathered}[/tex]Now that we know the length of the 3rd and largest side of this triangle, we can now determine whether it is a right-angled triangle.
This case has a non-integer as part of the sides of the triangle, thus, condition b does not apply.
We must check via Pythagoras theorem:
[tex]\begin{gathered} By\text{ pythagoras:} \\ 5^2+5^2=25+25=50 \\ \text{while,} \\ (5\sqrt[]{2})^2=5^2\times(\sqrt[]{2})^2=25\times2=50 \\ \text{Thus we can s}ee\text{ that:} \\ 5,5,5\sqrt[]{2}\text{ can form a right-angled triangle} \end{gathered}[/tex]Therefore, the final answer: 1 and 3 can form a right-angled triangle but 2 cannot
4. I have given the reasons why they form a right-angled triangle above. But let me restate them:
In order to know if 3 squares will form a right triangle,
a. The sum of the length of two of the squares must be greater than the length of the last square.
b. The lengths of the squares (if they are integers) must form a Pythagorean triple.
Pythagorean triples are:
3, 4, 5
5, 12, 13
8, 15, 17
9, 40, 41
there are more triples but we only need these for this question
c. They must conform to the Pythagoras Theorem.
[tex]\begin{gathered} \text{Pythagoras theorem is:} \\ c^2=a^2+b^2 \\ \text{where c is the largest side of the right angled triangle} \\ \text{while a and b are adjacent and opposite of the right angled triangle} \end{gathered}[/tex]
Related Questions
Hey bb I know that it was ur b day and u said u were gonna come out to ur parents as bi. Did u do it and if u did how did it go. Just checking in, ofc u don’t know me so u don’t even have to tell me anything if you want.
Answers
An event can be said to be a set of possible outcomes which results from an experiment.
An individual can be said to create a theory after he observes events.
A theory is said to be a set of ideas that explains the results from an experiment.
Therefore, an individual creates a theory after he observes an event.
ANSWER:
Theory
what percent of 29 is 13?
Answers
Answer:
45%
Step-by-step explanation:
x * 29 = 13
x = 13/29
x = 0.448
45%
4
A TV that usually sells for $167.77 is on sale for 15% off. If sales tax on the TV is 6%, what is the price of the TV, including tax?
OA. $201.49
OB. $152.59
OC. $151.16
OD.
$149.73
Answers
The price including tax is $151.16
What is tax?
A tax is a mandatory financial charge or other type of levy imposed by a governmental organization on a taxpayer (an individual or legal entity) in order to fund government spending and various public expenditures (regional, local, or national), and tax compliance refers to policy actions and individual behavior aimed at ensuring that taxpayers pay the correct amount of tax at the correct time and receive the correct tax allowances and tax reliefs. The earliest known taxes occurred in Ancient Egypt between 3000 and 2800 BC. Failure to pay on time (non-compliance), as well as avoidance or resistance to taxation, is illegal and punished by law. Taxes can be paid in cash or in labor equivalents and can be direct or indirect.
Selling price of TV = $167.77x0.85 (15% discount)
= $142.6025
Price of TV (including tax) = $142.6025x1.06 (6% tax)
= $151.16
Hence, the price including tax is option (c) $151.16
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Though 70% of women with children younger than 18 years participate in the labor force, society still upholds the stay-at-home mother as the traditional model. Some believe that employment distracts mothers from their parenting role, affecting the well-being of children. In the GSS 2014, respondents were asked to indicate their level of agreement to the statement, “A working mother hurts children.” Of the 435 male respondents who answered the question, 18% strongly agreed that a working mother does not hurt children.
Answers
Using the z-distribution, the 95% confidence interval for the proportion of male respondents that agree that a working mother does not hurt children is:
(0.1439, 0.2161).
What is a confidence interval of proportions?The bounds of a confidence interval of proportions is given according to the following rule:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the parameters are described as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
The values of the other parameters are given as follows:
[tex]\pi = 0.18, n = 435[/tex]
Hence the lower end of the interval is calculated as follows:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.18 - 1.96\sqrt{\frac{0.18(0.82)}{435}} = 0.1439[/tex]
The upper end of the interval is calculated as follows:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.18 + 1.96\sqrt{\frac{0.18(0.82)}{435}} = 0.2161[/tex]
Missing informationThe problem asks for the 95% confidence interval for the proportion of male respondents that agree that a working mother does not hurt children is:
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» Solve the equation 2y+6=y-7
Answers
Answer:
y = -13
Step-by-step explanation:
a) Subtract y from both sides.
2y + 6 − y = y − 7 − y
y + 6 = −7
b) Subtract 6 from both sides.
y + 6 − 6 = −7 − 6
y = -13
Help, please, it's urgent
Answers
∠10 and ∠16 are Alternate exterior angles, ∠4 and ∠12 are Consecutive exterior angles, ∠12 and ∠13 are Consecutive Interior angles and ∠3 and ∠9 are Alternate Interior angles.
1. If two lines which are in the same plane are intersected by another line at two different lines, eight angles are formed, and that another line is called the transversal.
In the provided figure,
In the angles,
∠10 and ∠16, q is the transversal and these are Alternate exterior angles.
∠4 and ∠12, n is the transversal and these are Consecutive exterior angles.
∠12 and ∠13, q is the transversal and these are Consecutive Interior angles.
∠3 and ∠9, n is the transversal and these are Alternate Interior angles.
2. Referring tot the cube ABCDHGFE,
a. All planes that are parallel to the plane DEH are CBF and FGC.
b. All segments that are parallel to AB are EF, HG and DC.
c. All segments that intersect GH are EH, HG, FG and CG.
d. All segments that are skew to CD are AB, EF and HG.
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Solve for x. Enter the solutions from least to greatest.2x^2 - 24x + 54 = 0lesser x =greater x =
Answers
To solve the equation
[tex]2x^2-24x+54=0[/tex]we are going to use the general formula for quadratic equations:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]In our case a=2, b=-24 and c=54. Then
[tex]\begin{gathered} x=\frac{-(-24)\pm\sqrt[]{(-24)^2-4(2)(54)}}{2(2)} \\ =\frac{24\pm\sqrt[]{576-432}}{4} \\ =\frac{24\pm\sqrt[]{144}}{4} \\ =\frac{24\pm12}{4} \end{gathered}[/tex]Then x is:
[tex]\begin{gathered} x=\frac{24-12}{4}=\frac{12}{4}=3 \\ or \\ x=\frac{24+12}{4}=\frac{36}{4}=9 \end{gathered}[/tex]A camera has a listed price of $788.99 before tax. If the sales tax rate is 7.75%, find the total cost of the camera with sales tax included. Round your answer to the nearest cent, as necessary.
Answers
Answer:
$850.14
Step-by-step explanation:
7.75% as decimal: 0.0775
788.99 x 0.0775 = 61.146725
788.99 + 61.146725 = 850.136725
850.136725 rounded to nearest cent is 850.14
So the total price of the camera with sales tax included is $850.14
The common factors of 36, 240, and 504
Answers
Answer: 1, 2, 3, 4,6 12
Step-by-step explanation:
every single number can be divided by the answer numbes
The new strain of covid is spreading at the rate of 12% a week. Currently, there are 100,000 people infected with the virus. How long will it take before the virus has infected 800,000 people?
Answers
The covid strain will take 17.33 weeks to infect 800,000 people.
To solve the given problem, we only need to utilize the exponential function formula, which is stated as
[tex]A = Pe^{rt}[/tex]
Where A is the final value,
P denotes the starting value
The rate is r and time is given by t.
Given:
The rate of spread of the new strain of covid = 12% a week
Currently the number of people infected with the virus = 100,000
To determine how long will it take before the virus has infected 800,000 people, substitute the values in the formula
[tex]A = Pe^{rt}[/tex]
[tex]800000 = 100000e^{0.12*t}[/tex]
[tex]8 = e^{0.12*t}[/tex]
[tex]ln 8 = {0.12*t}[/tex]
[tex]t = ln 8/0.12[/tex]
[tex]t = 17.33 weeks[/tex]
Therefore, the covid strain will take 17.33 weeks to infect 800,000 people.
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Find the missing angle:
?=
134⁰
Answers
Answer: 46
Step-by-step explanation:
180 - 134 = 46
Abdul drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 8 hours. When Abdul drove home, there was no traffic and the trip only took 6 hours. If his average rate was 16 miles per hour faster on the trip home, how far away does Abdul live from the mountains? Please show work because it doesn’t make sense any other way!
Answers
Average speed there = x / 8 mph
Average speed back = x / 6 mph
x / 6 = x / 8 + 16
Multiply both sides by 24 (lowest common multiple of 6 and 8)
24x / 6 = 24x / 8 + 16x24
4x = 3x + 384
x = 384 miles
katie placed $2500 in a savings account compounded annually at 1.75%. what is the value of her account after 4 years?
Answers
We can solve this question using the formula for compound interest:
[tex]F=P\cdot(1+i)^n[/tex]F = ?
P = $2500
i = 1.75
n = 4
Then, we have:
[tex]F=2500\cdot(1+\frac{1.75}{100})^4\Rightarrow F=2679.6475\Rightarrow F=2679.65[/tex]The value of her account after 4 years is about $2679.65.
Find the savings plan balance after 15 months with an APR of 6% and monthly payments of $200.
Answers
The savings plan balance after 15 months with an APR of 6% and monthly payments of $200 is $3,123.
Saving plan balanceGiven data :
The APR = 6% coincides with a .06/12 = .005 monthly interest rate
Now let determine or find the total after 15 months
Total after 15 month :
Total after 15 month = 200 [ (1 +.005^ 16) - (1 + .005] /(.005)
Total after 15 month = 200 [( 1.005 ^ 16 - 1.005] /(.005)
Total after 15 month = 200 (15.614)
Total after 15 month = $3,122.8
Total after 15 month = $3,123 (Approximately)
Therefore we can conclude that the total sum is the amount of $3,123.
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Write the numbers in increasing order with a comma separating eachnumber: 1.99, -3.45, 2.01, -3.42, 0.99
Answers
To write the numbers in increasing order, we start from the most negative to the most positive:
[tex]-3.45,-3.42,0.99,1.99,2.01.[/tex]Answer
-3.45, -3.42, 0.99, 1.99, 2.01
Mr. Jones and Mr. Evansbee both have gardens shaped as squares. The length of each side of Mr. Jones’ garden is 6 yd. The length of each side of Mr. Evansbee’s garden is 10 yd.
(a) Write an expression with exponents for the area of Mr. Jones’ garden. Then, find the area of the garden.
(b) Write an expression with exponents for the area of Mr. Evansbee’s garden. Then, find the area of the garden. Each plant takes up 2 yd(squared) of space in both gardens.
(c) How many plants can Mr. Jones place in his garden? How many plants can Mr. Evansbee place in his garden? Explain your reasoning.
(d) For each garden, the cost per plant is $4.99. Using your answers from part (c), how much will each gentleman spend on plants for his garden?
Answers need to be step-by-step please
Answers
Answer:
(a) expression: (6 yd)²; area: 36 yd²
(b) expression: (10 yd)²; area: 100 yd²
(c) Jones: 18; Evansbee: 50
(d) Jones: $89.82; Evansbee: $249.50
Step-by-step explanation:
You want the area, number of plants that can be placed, and the cost of plantings for gardens that are 6 yards square and 10 yards square. Each plant takes 2 square yards and costs $4.99.
Area of a squareThe formula for the area of a square of side length s is ...
A = s²
(a) Jones' gardenThe area of a square garden with a side length of 6 yards is ...
A = (6 yd)² . . . . . expression for the area
A = 36 yd² . . . . . the area of the garden
(b) Evansbee's gardenThe area of a square garden with a side length of 10 yards is ...
A = (10 yd)² . . . . . expression for the area
A = 100 yd² . . . . . the area of the garden
(c) Number of plants
The area used by the plants is the product of their number and the area taken by each.
For Jones' garden, the number of plants that can be placed is ...
n(2 yd²/plant) = 36 yd²
n = (36 yd²)/(2 yd²/plant) = 18 plants
Mr. Jones can place 18 plants in his garden.
For Evansbee's garden, the number of plants that can be placed is ...
n(2 yd²/plant) = 100 yd²
n = (100 yd²)/(2 yd²/plant) = 50 plants
Mr. Evansbee can place 50 plants in his garden.
(d) Cost of plantsAt $4.99 each, the cost of plantings will be $4.99 times the number of plants.
Plants for Jones' garden cost 18($4.99) = $89.82.
Pants for Evansbee's garden cost 50($4.99) = $249.50.
Please help with both ?s I’ll mark you brainly
Answers
Answer:
1) CW 270° or CCW 90°
Step-by-step explanation:
In each case, you want to identify two transformations that will map the preimage to the image.
1)We note the transformation maps ...
A(-7, 0) ⇒ A'(0, -7) . . . . . . CCW 90° or CW 270°
B(-4, -1) ⇒ B'(1, -4)
C(-7, 3) ⇒ C'(-3, -7)
These can be described by ...
(x, y) ⇒ (-y, x)
This transformation is equivalent to either of the two transformations ...
rotation CW 270° about the originrotation CCW 90° about the origin2)As above, rotation about the origin by 90° in one direction is the same as rotation 270° about the origin in the other direction. The attached graph shows the result either way. The two equivalent transformations are ...
rotation CW 90° about the originrotation CCW 270° about the originThe coordinate transformation is ...
(x, y) ⇒ (y, -x)
I need help with this question but no one is helping me! Can someone please help me
Answers
Answer:
13 + 13 = 26
13/26 * 12/25 = 6/25 = 0.24
Find missing side length
Answers
Answer:
7
Step-by-step explanation:
42 divided by 3 = 14 = total of triangle XYZ
14 divided by 2 = 7
line X/Y = 7
Match the area formula with the correct polygon. A = 1/2bh parallelogram A = bh triangle A = 1/2 (b1 + b ) + trapezoid
Answers
The area of a parallelogram can be determined by multiplying its base and height, the formula is
[tex]A=bh[/tex]The area of a triangle is equal to half the product between the base and the height, following the formula:
[tex]A=\frac{1}{2}(bh)[/tex]The area of a trapezoid is equal to the product of half the sum of its bases and its height following the formula:
[tex]A=\frac{1}{2}(b_1+b_2)h[/tex]
On a number line, a number, b, is located the same distance from 0 as another number, a, but in the opposite direction.
The number b varies directly with the number a. Forexample b = 22 when a = -23. Which equation represents this
direct variation between a and b?
O b=-a
O-b=-a
Ob-a=0
Ob(-a)=0
Answers
The equation b=-a is the correct equation.
What is an equation?
An equation is a statement in maths that demonstrates the equivalence of two factors by linking them with the equivalent symbol =. Equations are used to define geometric patterns in Euclidean geometry. Because the equations beneath consideration, such as implicitly equations or descriptive equations, contain an unlimited variety of solutions, the goal has started to shift: instead of directly stating the alternatives or collecting them, which again is unattainable, one utilizes equations to analyze the features of figures. This is the fundamental concept of elementary algebra, a significant mathematics discipline. Differential equations is equations in which 1 or more polynomials and its implications are involved. They are addressed by locating a functional expression that doesn't employ derivatives. Differential equations are utilized to analyze rate-related phenomena.
The equation b=-a is the correct equation.
Hence, option (a) b=-a is correct.
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You deposit $300 each month into an account earning 6% interest compounded monthly. a) How much will you have in the account in 30 years? $ b) How much total money will you put into the account? $ c) How much total interest will you earn?
Answers
Using the future value formula, it is found that:
a) You will have $301,355 in the account after 30 years.
b) You will have put $108,000 in the account.
c) You will have earned $193,355 in interest.
What is the future value formula?The future value formula is given by:
[tex]V(n) = P\left[\frac{(1 + r)^n - 1}{r}\right][/tex]
In which the parameters are described as follows:
P is the payment.n is the number of payments.r is the interest rate.Considering the $300 deposits, the interest rate of 6% and the monthly compoundings for 30 years, the values of the parameters are given as follows:
P = 300, r = 0.06/12 = 0.005, n = 12 x 30 = 360.
Hence the balance of the account after 30 years will be given by:
[tex]V(30) = 300\left[\frac{(1.005)^{360} - 1}{0.005}\right][/tex]
V(30) = $301,355.
The amount placed into the account is given by:
360 x 300 = $108,000.
The remaining amount is earned in interest, hence:
301355 - 108000 = $193,355.
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Trish's resting heart rate is 50 beats per minute. For every
minute she exercises, her heart rate increases 5 beats per
minute. How long will it take her to reach a heart rate of
120 beats per minute?
A 5 minutes
B 14 minutes
C 34 minutes
D 70 minutes
Answers
Answer:
B
Step-by-step explanation:
(120 - 50 b/m) / 5 b / m^2 = 14 minutes
Sean is hiking the Appalachian Trail from Georgia to Maine. The distance of his hike is 2200 miles. It
took Sean 134 days to complete the hike. The data below represent the distance, D, he had hiked t
days after the start of his trip.
t
D(0)
0
0
19
308
In
34
578
67
1070
1. Determine the linear regression equation for this data.
Linear Regression Equation: D =
Round to the nearest tenth as needed.
2. Interpret the meaning of the slope of this regression model.
Sean hiked at a rate of approximately
91
1715
miles.
112
1902
Select an answer
3. Use your linear regression equation to estimate the total number of miles Sean had hiked in 52
days. Round your answer to the nearest mile.
In 52 days, Sean had hiked
4. Use your linear regression equation to estimate the total number of days it took for Sean to hike
377 miles. Round your answer to the nearest day.
days, Sean had hiked 377 miles.
134
2200
Answers
From the given table, it is found that:
1. The linear regression equation is: y = 16.96x + 3.
2. The meaning of the slope is that he hiked an average of 16.96 miles a day.
3. In 52 days, Sean had hiked 885 miles.
4. In 22 days, Sean had hiked 377 miles.
How to find the equation of linear regression?To find the regression equation, also called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator. These points are given on a table or in a scatter plot in the problem.
In the context of this problem, the points are given as follows:
(0,0), (19,308), (34, 578), (67, 1070), (91, 1715), (112, 1902), (134, 2200).
Using a calculator, the equation is given as follows:
y = 16.96x + 3.
The input of the function and the output of the function are given as follows:
Input: number of days.Output: number of miles hiked.The slope is the rate of change, that is, change in the output divided by change in the input. Hence the slope of 16.96 means that he hiked an average of 16.96 miles a day.
In 52 days, the number of miles hiked is:
y = 16.96(52) + 3 = 885 miles.
The number of days is took to hike 377 miles is found as follows:
377 = 16.96x + 3
x = 374/16.96
x = 22 days.
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(d) Find the domain of function R. Choose the correct domain below.
Answers
Answer:
d
Step-by-step explanation:
The number of years must be non-negative. This eliminates all of the options except for d.
Complete both transformations below.
Then enter the final coordinates of the figure.
(1,-3)
A
C (2,-5)
B
(5,-1)
A" ([?], [])
B" ([ ], [])
C" ([],[])
1) Reflect across y - axis
2) <4.5>
Answers
Answer:
A''(3, 2), B''(-1, 4), C''(2, 0)
Explanation:
For the first step, negate the y coordinate.
For the second step, add 4 to the x coordinate and 5 to the y coordinate.
[tex]A(1,-3) \longrightarrow A'(-1, -3) \longrightarrow A''(3, 2) \\ \\ B(5,-1) \longrightarrow B'(-5,-1) \longrightarrow B''(-1, 4) \\ \\ C(2, -5) \longrightarrow C'(-2, -5) \longrightarrow C''(2, 0)[/tex]
5 In an experiment, the probability that event B occurs is -, and the probability that event A occurs given 8 5 that event B occurs is – 8 What is the probability that events A and B both occur? Simplify any fractions.
Answers
We have
probability of B occurs is 5/8
probability that event A occurs given B occurs is 5/8
We have the next formula, that is the conditional probability formula
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]where
P(A|B)= probability of A given B
P(B)= probability of B
P(A∩B)=probability of A and B
so we need to isolate the P(A∩B) in order to obtain the probability that events A and B both occur
[tex]P\mleft(A\cap B\mright)=P(A|B)\cdot P(B)=\frac{5}{8}\cdot\frac{5}{8}=\frac{25}{64}[/tex]Find the circumference and area of the circle. Express answers in terms of and then round to the nearest tenth. Part 1. Find the circumference in terms of . C = _ cmPart 2. Find the circumference rounded to the nearest tenth.C = _ cmPart 3. Find the area in terms of A = _ cm2Part 4. Find the area rounded to the nearest tenth. A = _ cm3
Answers
Answer:
1. C = 8π cm
2. C = 25.1 cm
3. A = 16π cm²
4. A = 50.3 cm²
Explanation:
Part 1.
The circumference of a circle can be calculated as
[tex]C=2\pi r[/tex]Where r is the radius. So, replacing r = 4 cm, we get:
C = 2π(4 cm)
C = 8π cm
Part 2.
To round the circumference to the nearest tenth, we need to replace π = 3.14, so
C = 8(3.14) cm
C = 25.1 cm
Part 3.
The area of a circle can be calculated as
A = πr²
Replacing r = 4cm, we get:
A = π(4 cm)²
A = 16π cm²
Part 4.
To round to the nearest tenth, we need to replace π = 3.14, so
A = 16(3.14) cm²
A = 50.3 cm²
Therefore, the answers are
1. C = 8π cm
2. C = 25.1 cm
3. A = 16π cm²
4. A = 50.3 cm²
Describe how to determine the average rate of change between x=3 and x=5 for the function f(x)3x^3+2. Include the average rate of change in your answer.
Answers
Given the function:
[tex]f\mleft(x\mright)=3x^3+2[/tex]3. Do these three points create a right triangle?
A(2,2) B(-2-1) C(-3, 2)
Answers
Answer:
they do NOT create a right-angled triangle
Step-by-step explanation:
to make a right-angled triangle the side lengths must comply with Pythagoras
c² = a² + b²
c being the Hypotenuse (the side opposite of the 90° angle), a and b are the legs.
the side lengths in this ABC triangle are :
AB² = (2 - -2)² + (2 - -1)² = 4² + 3² = 16 + 9 = 25
AB = 5
BC² = (-2 - -3)² + (-1 - 2)² = 1² + (-3)² = 1 + 9 = 10
BC = sqrt(10)
CA² = (-3 - 2)² + (2 - 2)² = (-5)² + 0² = 25
CA = 5
so, this is an isoceles triangle (2 equal legs).
the side lengths 5, 5, sqrt(10) do NOT create a right-angled triangle.
no matter how we combine their squares in the Pythagoras formula, it does not work :
10 = 25 + 25 = 50 no.
25 = 10 + 25 = 35 no.