Which classification best represents a triangle with side lengths 6 cm, 10 cm, and 12 cm? acute, because 62 + 102 < 122 acute, because 6 + 10 > 12 obtuse, because 62 + 102 < 122 obtuse, because 6 + 10 > 12
Using the Pythagorean theorem, we find that the sum of the squares of the two shorter sides of the triangle (6 cm and 10 cm) is less than the square of the longest side (12 cm). Hence, the triangle is obtuse because 6² + 10² < 12².
Explanation:To classify a triangle whose sides measure 6 cm, 10 cm, and 12 cm, we can use the Pythagorean theorem which relates the lengths of a right triangle's legs (a and b) to its hypotenuse (c), by the formula a² + b² = c². In our case, we need to check if the squares of the two shorter sides add up to the square of the longest side. We calculate:
6² + 10² = 36 + 100 = 13612² = 144Since 136 is less than 144, 62 + 102 < 122 is true, and the triangle is obtuse because the sum of the squares of the lengths of the two shorter sides is less than the square of the length of the longest side.
find the approximate length of the leg of a right triangle with one leg length 8 and hypotenuse length 19
The approximate length of the leg of a right triangle is 17.
Use the concept of a triangle defined as:
A triangle is a three-sided polygon, which has three vertices and three angles which has a sum of 180 degrees.
And the Pythagoras theorem for a right-angled triangle:
(Hypotenuse)²= (Perpendicular)² + (Base)²
Given that,
One leg = 8 say it is the base of a triangle.
Hypotenuse = 19
Applying the Pythagorean theorem,
(19)²= (Perpendicular)² + (8)²
(Perpendicular)² = 297
Taking square root on both sides,
Perpendicular ≈ 17.2
Hence,
The required length of leg is approximately 17.
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From their location in the diagram, what are two possible values for m and n?
Answer:
m= 6/5, n= √2
Step-by-step explanation:
This is just a simple version of the answer.
Find the Area.
Triangle: A= 1/2 bh.
area = 1/2 b*h
1/2 *10 *015 =
1/2 * 150 =75
area = 75 square feet
45/100 in simplest form
This graph looks like a trigonometric function. Which trigonometric function would be best to use for this model: cosine, sine, or tangent? Why?
Type your response here:
a. It’s time to start making your model fit the path of the mass. Start with amplitude. What is the amplitude of the weight’s motion? How can you modify the base trigonometric function you identified in part b to fit this amplitude? Do this now.
Type your response here:
b. What is the period of the weight’s motion? How can you modify the trigonometric function you identified in part c to fit this period? Do this now.
Type your response here:
c. Check how your model looks compared with the mass by graphing your model with the Edmentum Graphing Tool. Looking at the graph, what is different between your model and the graph of the mass? What needs to change to make your model more accurate? Make this change to your model, and type in the new equation for your model.
Type your response here:
[tex]\displaystyle \boxed{y = \frac{6}{25}cos\:(1\frac{1}{2}\pi{x} - \frac{\pi}{2})} \\ \\ y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{\frac{1}{3}} \hookrightarrow \frac{\frac{\pi}{2}}{1\frac{1}{2}\pi} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{1\frac{1}{3}} \hookrightarrow \frac{2}{1\frac{1}{2}\pi}\pi \\ Amplitude \hookrightarrow \frac{6}{25}[/tex]
OR
[tex]\displaystyle \boxed{y = \frac{6}{25}sin\:1\frac{1}{2}\pi{x}} \\ \\ y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{1\frac{1}{3}} \hookrightarrow \frac{2}{1\frac{1}{2}\pi}\pi \\ Amplitude \hookrightarrow \frac{6}{25}[/tex]
You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the sine graph, if you plan on writing your equation as a function of cosine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = \frac{6}{25}cos\:1\frac{1}{2}\pi{x},[/tex] in which you need to replase "sine" with "cosine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the sine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the cosine graph [photograph on the right] is approximately shifted [tex]\displaystyle \frac{1}{3}\:unit[/tex]to the left, which means that in order to match the sine graph [photograph on the left], we need to shift the graph FORWARD [tex]\displaystyle \frac{1}{3}\:unit,[/tex]which means the C-term will be positive, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{\frac{1}{3}} = \frac{\frac{\pi}{2}}{1\frac{1}{2}\pi}.[/tex]So, the cosine graph of the sine graph, accourding to the horisontal shift, is [tex]\displaystyle y = \frac{6}{25}cos\:(1\frac{1}{2}\pi{x} - \frac{\pi}{2}).[/tex]Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph hits [tex]\displaystyle [-2\frac{2}{3}, 0],[/tex]from there to [tex]\displaystyle [-1\frac{1}{3}, 0],[/tex]they are obviously [tex]\displaystyle 1\frac{1}{3}\:unit[/tex]apart, telling you that the period of the graph is [tex]\displaystyle 1\frac{1}{3}.[/tex]Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = 0,[/tex]in which each crest is extended six-twenty-fifths unit beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.
**Now, it really does not matter which function you use because the result will always be the same, but IF the system only wants one function as an answer, then it would be the sine function sinse it intersects the origin. Other than that, it does not matter which one is chosen.
I am delighted to assist you at any time.
Miss Nelson works 154 hours each month he works eight months each year how many hours does Miss
Nelson work each year
A mother bottlenose ate about 278 pounds of food in one week. About how much food did she eat in a day?
how to write 3x2+3y2+12x+18y-15 in general and standard format
5 less than three times a number is 10
3x-5 =10
add 5 to both sides
3x=15
divide both sides by 3
x=5
check:
3(5)-5 = 15-5 = 10
Mrs. Chin paid a 20 percent tip on the bill for lunch. If the tip amount was $2.75, what was the bill for lunch before the tip was added to it?
the three digit number 49x is divisible by 4 with no remainders. if the sum of the digits is divisible by 5 with no remainders, what is the number
Dave is helping his grandmother make trail mix. His grandmother asks him to add cup of fruit for every cup of nuts.
To satisfy his grandmother’s request, Dave must mix cups of fruit for a single cup of nuts.
To satisfy his grandmother's request, Dave needs to mix [tex]\( \frac{1}{5} \)[/tex] cup of fruit for every [tex]\( \frac{1}{3} \)[/tex] cup of nuts.
To find out how many cups of fruit Dave needs to mix for a single cup of nuts, we need to find a common denominator for [tex]\( \frac{1}{5} \)[/tex] and [tex]\( \frac{1}{3} \)[/tex], which is 15.
[tex]\[ \frac{1}{5} \times \frac{3}{3} = \frac{3}{15} \][/tex]
[tex]\[ \frac{1}{3} \times \frac{5}{5} = \frac{5}{15} \][/tex]
So, Dave needs to mix [tex]\( \frac{3}{15} \)[/tex] cup of fruit for every [tex]\( \frac{5}{15} \)[/tex] cup of nuts.
Therefore, to satisfy his grandmother's request, Dave must mix [tex]\( \frac{3}{15} \)[/tex] cup of fruit for a single cup of nuts.
The complete Question is given below:
dave is helping his grandmother make trail mix his grandmother asks him to add 1/5 cup of fruit for every 1/3 cup of nuts. To satisfy his grandmother's request, drave must mix ___ cups of fruit for a single cup of nuts
which expression gives the distance between the points (4,6)and (7,-3)
Answer:
As shown in the image....
Step-by-step explanation:
This equation follows with the distance formula which is (x2-x1)+(y2-y1) squared.
Latoya drove 585 miles in 9 hours.
At the same rate, how many miles would she drive in 5 hours?
585/9 = 65 miles per hour
65 x 5 = 325 miles
she would drive 325 miles in 5 hours
Jeremy created a small garden that measured 5 times 7.5 feet how many 10 feet rolls of fencing will he need to completely surround the garden?
At the party, Aisha and her friends ate 2 1/2 pizzas. After the party, there were 1 1/8 pizzas left. How many pizzas were there at the start of the party?
Answer:
[tex]3\frac{5}{8}[/tex] pizzas were there at the start of the party.
Step-by-step explanation:
At the party let number of pizzas were = x
Aisha and her friends ate [tex]2\frac{1}{2}[/tex] pizzas after which [tex]1\frac{1}{8}[/tex] pizzas were left.
Therefore the equation formed will be
[tex]x-2\frac{1}{2}=1\frac{1}{8}[/tex]
x - (5/2) = 9/8
x = 9/8 + 5/2
x = 29/8 = [tex]3\frac{5}{8}[/tex]
Therefore [tex]3\frac{5}{8}[/tex] pizzas were there at the start of the party.
Which expression is equivalent to 100 n2 − 1? (10n)2 − (1)2 (10n2)2 − (1)2 (50n)2 − (1)2 (50n2)2 − (1)2
The correct answer is:
(10n)² − (1)²
Explanation:
If we evaluate this expression, we square everything in the first set of parentheses; this means we have 10²n² - 1², or 100n² - 1.
This is the expression we were trying to equal.
100 kg of a fruit contained 90% water one week ago. How many kg of the fruit containing 80% water are there now?
Final answer:
The weight of the solids in the fruit remains constant at 10 kg. When the water content changes to 80%, the total weight of the fruit is 50 kg, since the solids make up 20% of the fruit's weight.
Explanation:
Initially, we have 100 kg of fruit with 90% water content. This means that there are 90 kg of water and 10 kg of solids (since water plus solids equals the total weight of the fruit).
After some time, the fruit dehydrates to where it now contains 80% water. However, the amount of solids in the fruit has not changed; it remains constant at 10 kg. To find the new total weight of the fruit with 80% water, we can set up the equation where 80% of the new weight is equal to the weight of the solids subtracted from the new total weight (since solids comprise the remaining 20% of the weight).
Let's denote the new total weight of the fruit as 'x'. According to the given information, 20% of x is the weight of the solids, which is 10 kg. Therefore, the equation is:
0.20x = 10 kg
Now we solve for 'x':
x = 10 kg / 0.20 x = 50 kg
The result is that there are 50 kg of the fruit with 80% water content now.
If the directrix of a parabola is the horizontal line y = 3, what is true of the parabola?
a)The focus is at (0, 3), and the equation for the parabola is y2 = 12x.
b)The focus is at (0, –3), and the equation for the parabola is x2 = –12y.
c)The focus is at (3, 0), and the equation for the parabola is x2 = 12y.
d)The focus is at (–3, 0), and the equation for the parabola is y2 = –12x.
Answer: on e2020 it’s b
Step-by-step explanation:
Which of the following sets of numbers could be the side lengths of a right triangle?
3, 4, and 7
9, 40, and 42
8, 15, and 16
20, 21, and 29
the answer is 20,21,29 because
20 times 20 is 400
21 times 21 is 441
and 29 times 29 is 841
the formula to ge tthe answer is a^2 + b^2 = c^2
20^2 + 21^2= 29^2
then plug the rest in
400+441= 841
In a circle an arc 60 centimeters lon subtends an angle of 5 radians. What is the radius of the circle?
The cost of three Ice Cream cones is $24.95. If each ice cream cone cost the same amount, what was the price,p, of one ice cream cone?
I have to write and solve an equation. If you can, can you plz just write the equation for me.
What does 5 2/3 - 8 5/6 equal?
5 2/3 = 17/3 = 34/6
8 5/6 = 53/6
34/6 - 53/6 = -19/6 = -3 1/6
Find the missing number
What is the value of the number 7 in 43,782
When measuring board footage for some exotic woods, a carpenter must use 1.25 inches for thickness rather than 1 inch in her calculations. Write 1.25 in expanded form.
Answer: [tex]1.25=1+0.2+0.005[/tex]
Step-by-step explanation:
Given : When measuring board footage for some exotic woods, a carpenter must use 1.25 inches for thickness rather than 1 inch in her calculations.
To write : 1.25 in expanded form.
When we write a decimal number in expanded form, we are showing the place value of each digit.
Now, 1.25 can be written as :
[tex]1.25=1+0.2+0.005[/tex]
Hence, the expanded form of [tex]1.25=1+0.2+0.005[/tex]
Which expression shows the simplified form of (8r^-5) -3 ?
Answer:
[tex]\frac{r^{15}}{512}[/tex]
Step-by-step explanation:
(8r^-5)^ -3
[tex](8r^{-5})^{-3)[/tex]
Apply exponential property
(ab^m) ^n = a^m b^mn
Multiply the outside exponent with the exponents insde
[tex](8r^{-5})^{-3)= 8^{-3}r^{-5*-3}=8^{-3}r^{15}[/tex]
Appy property a^-m = 1/a^m to make the exponent positive
[tex]8^{-3}r^{15}= \frac{r^{15}}{8^3} =\frac{r^{15}}{512}[/tex]
If x = y − 2, simplify the expression x + 6. A. x + 4 B. x − 8 C. y + 4 D. y − 8
The difference between the square roots of a number is 30. What is the number?