The triangle with side lengths 6, 9, and 12 is an obtuse triangle. To classify the triangle as acute, right, or obtuse, we need to determine the type of triangle based on the lengths of its sides.
Recall that in a triangle, the sum of the lengths of any two sides must be greater than the length of the third side for it to be a valid triangle.
Let's check if the given triangle with side lengths 6, 9, and 12 satisfies the triangle inequality:
1. Sum of two shorter sides: 6 + 9 = 15 (greater than the length of the longest side, 12). Valid.
2. Sum of the two longer sides: 9 + 12 = 21 (greater than the length of the remaining side, 6). Valid.
3. Sum of the longest side and the shortest side: 6 + 12 = 18 (greater than the length of the remaining side, 9). Valid.
Since all three inequalities are satisfied, the given side lengths form a valid triangle.
Now, to classify the triangle, we can use the Pythagorean theorem. In a right-angled triangle, the square of the length of the longest side is equal to the sum of the squares of the other two sides.
In this case, the side lengths are 6, 9, and 12. To determine if it is a right-angled triangle, we can check if:
[tex]12^2 = 6^2 + 9^2\\144 = 36 + 81\\144 \neq 117[/tex]
Since the Pythagorean theorem is not satisfied, the triangle is not a right-angled triangle.
Now, let's check if it is an acute or obtuse triangle. In an acute triangle, all three angles are less than 90 degrees, while in an obtuse triangle, one angle is greater than 90 degrees.
To determine this, we can use the law of cosines, which states that in any triangle:
[tex]c^2 = a^2 + b^2 - 2ab * cos(C)[/tex]
where c is the longest side (12 in this case), a and b are the other two sides (6 and 9), and C is the angle opposite the longest side.
Calculate the value of cos(C):
[tex]12^2 = 6^2 + 9^2 - 2 * 6 * 9 * cos(C)\\144 = 36 + 81 - 108 * cos(C)\\144 = 117 - 108 * cos(C)\\108 * cos(C) = 117 - 144\\108 * cos(C) = -27\\cos(C) = -27 / 108\\cos(C) = -0.25[/tex]
Since the value of cos(C) is negative, the angle C is obtuse. Therefore, the triangle is an obtuse triangle.
In summary, the triangle with side lengths 6, 9, and 12 is an obtuse triangle.
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A is five times as old as B. after 10 years a will be 3 times as old as B will be then. find their present age
According to given information, A is 50 years old and B is 10 years old.
What is expression ?In mathematics, an expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, and division) that can be evaluated to produce a numerical result or a value.
According to given information :Let's use algebra to solve the problem.
Let A's current age be x, and B's current age be y.
From the problem, we know that:
x = 5y (A is five times as old as B)
x + 10 = 3(y + 10) (After 10 years, A will be 3 times as old as B)
We can use the first equation to substitute x in the second equation:
5y + 10 = 3(y + 10)
Simplifying this equation gives:
5y + 10 = 3y + 30
2y = 20
y = 10
So B is currently 10 years old. We can use the first equation to find A's current age:
x =5y = 5(10) = 50
So A is currently 50 years old.
Therefore, according to given information, A is 50 years old and B is 10 years old.
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Solve For The Radius:
a. r = 9.7 m
b. r = 7 m
c. r = 123.5 m
d. r = 19.4 m
Answer:
a) r = 9.7 m
Step-by-step explanation:
CD = CE + ED
= 9 + r +r
= 9 + 2r
If a tangent and a secant are drawn from a common point outside the circle, then
CE * CD = CB *CB
9 * ( 9 + 2r) = 16 * 16 {Distributive property}
9*9 + 9*2r = 256
81 + 18r = 256
Subtract 81 from both sides,
18r = 256 - 81
18r = 175
Divide both sides by 18,
r = 175÷ 18
[tex]\boxed{\bf r = 9.7 \ m }[/tex]
The difference between two numbers is 2. When each number is rounded to nearest hundred, the difference between them is 100. What could the numbers be?
[tex]101 - 99 = 2[/tex]
each number is rounded to nearest hundred101 → 200
99 → 100
the difference between them is 100:[tex]200 - 100 = 100[/tex]
⇒ the numbers could be: 99 and 101
other pairs of numbers: (199,201), (299,301) ...
Q. 1 Solve the following In equality 7(x – 2) + x > – 4(5 – x) – 12
Answ
Step-by-step explanation:
x is equal to -9/2
What is the x and the y Intercept?
For the given function the intercepts are:
x-intercept: x = -4
y-intercept: y = 12.
How to find the intercepts for the given function?Here we have a table that defines a function, and we want to find the intercepts of said function.
We can assume it is linear, then the slope of the function will be given by:
a = (9 - 3)/(-1 + 3) = 6/2 = 3
The linear function is like:
y = 3x + b
To find the value of b we can replace the values of the last point on the table, x = 2 and y = 18.
18 = 3*2 + b
18 = 6 + b
18 - 6 = b = 12
The linear function is:
y = 3x + 12
The x-intercept is the value of x when y = 0
0 = 3*x + 12
-12 = 3x
-12/3 = x = -4
And the y-intercept is the value of y when x = 0.
y = 3*0 + 12
y = 12
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Which net represents this solid figure?
________________________________
(reporting wrong/spam answers)
(giving brainliest to the correct answer)
_________________________________
The net that represents this solid figure is diagram D.
What is a solid figure?A solid figure is a three-dimensional geometric shape that has length, width, and height. It is also called a three-dimensional or 3D figure. Some examples of solid figures include cubes, spheres, cylinders, cones, and pyramids.
Solid figures are different from two-dimensional shapes, which only have length and width. In contrast, solid figures have depth or thickness, making them more complex and interesting.
Solid figures can be classified based on their properties, such as the number of faces, vertices, and edges they have. For example, a cube has six faces, eight vertices, and 12 edges, while a sphere has no faces, vertices, or edges.
In this case, it has 2 squares and 4 rectangles. The appropriate diagram is D
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Juan is hiking a trail that is 2 miles long. He hikes 14 miles before resting.
How much farther does he have to hike?
Answer:
I think the answer is D.) 7/8 mile
Step-by-step explanation:
If you make the mixed numbers improper fractions. 2 and 1/8 is 17/8, 1 and 1/4 (2/8) is 10/8, then you subtract the numerators and keep the denomitators the same to get 7/8 mile (sorry if I spelt something wrong)
In track and field, the 440-yd. race was replaced with the 400-m race when Canada changed from the imperial system to the SI system. Which race is longer and by how much? Use the exact conversion: 1 yd. = 0.9144 m
Answer:
The 440-yd race is longer than the 400-m race by 2.336 meters.
Step-by-step explanation:
We can convert the distance of the 440-yd race to meters using the conversion factor 1 yd = 0.9144 m:
440 yd = 440 x 0.9144 m/yd = 402.336 m
Therefore, the 440-yd race is 402.336 meters long.
On the other hand, the 400-m race is already in meters.
Comparing the two distances, we can see that the 440-yd race is longer than the 400-m race.
To find out by how much longer, we can subtract the length of the 400-m race from the length of the 440-yd race:
402.336 m - 400 m = 2.336 m
Therefore, the 440-yd race is longer than the 400-m race by 2.336 meters.
Please help meee this is due Friday!!! A fully loaded and fueled spacecraft can weigh close to 5.1 million pounds. What is this weight converted to tons?
Answer:
A fully loaded and fueled spacecraft weighing 5.1 million pounds is equivalent to 2550 US tons
Step-by-step explanation:
Pls help simplify liner expressions
The answers to the questions are in the picture
Which of the following statements is MOST LIKELY TRUE?
A-The lower half of Sample A's data is closer to the value 5 than the lower half of Sample B's data.
B-Both of the data sets range from 1 to 10 on the number line.
CThe upper half of Sample A's data is closer to the value 10 than the upper half of Sample B's data.
D-The data in Sample B is clustered around the center where Sample A is more spread out
Explain
Answer:
Step-by-step explanation:
ntroduction to standard deviation
Standard deviation measures the spread of a data distribution. The more spread out a data distribution is, the greater its standard deviation.
For example, the blue distribution on bottom has a greater standard deviation (SD) than the green distribution on top:
Let f(x)=9x² - 5x - 58 and
g(x) = 7x² + 3x + 6. Identify the solution(s) of
f(x) = g(x).
The solutions of the function as required to be determined is; x = 8 or x = -4.
What is the solution of the equation?As evident in the task content; the given equation are;
f(x)=9x² - 5x - 58 and
g(x) = 7x² + 3x + 6.
The solution of the equation can be determined as follows;
9x² - 5x - 58 = 7x² + 3x + 6.
2x² -8x - 64 = 0
x² - 4x - 32 = 0
(x - 8) (x + 4) = 0
x = 8 Or x = -4.
Ultimately, the solutions of the equation are; x = 8 or x = -4.
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If 25% of a number is 10, find 5% of that number.
Answer:
0.125
Step-by-step explanation:
Answer:
5% of 40 is 2
Step-by-step explanation:
number = x
25% of x is = 10
25% = 25/100, or 1/4
[tex]\frac{1}{4}x = 10[/tex]
multiply each side by 4
[tex]x = 40[/tex]
5% is 5/100, or 1/20
[tex]\frac{1}{20}x = ?[/tex]
plug-in the known value
[tex]\frac{1}{20}*40 = ?\\\frac{40}{20} = ?\\\frac{4}{2} = ?\\\\? = 2[/tex]
a block exerts a force of 7nm on the ground. what is the pressure on the ground in nm2 when its flat on the grounds the area of its base is 0.04m2
The pressure οn the grοund when the blοck exerts a fοrce οf 7 Nm is [tex]175 nm^{-2[/tex].
First, we need tο cοnvert the area οf the blοck's base frοm square meters tο square nanοmeters, since the fοrce is given in newtοn-meters (N m) and we want tο find the pressure in newtοn-meters-squared ([tex]N/m^2[/tex] οr[tex]Nm^{-2[/tex]):
[tex]0.04 m^2 = 0.04 \times 10^18 nm^2 (since 1 m = 10^9 nm)[/tex]
Next, we can use the fοrmula fοr pressure, which is:
pressure = fοrce/area
Substituting the given values, we get:
[tex]pressure = 7 N m / 0.04\times 10^{18} nm^2[/tex]
Simplifying this expressiοn, we get:
[tex]pressure = (7 / 0.04) \times 10^{(-9)} N/nm^2[/tex]
[tex]pressure = 175 \times 10^{(-9)} N/nm{^2[/tex]
[tex]pressure = 175 nm^{-2[/tex]
Therefοre, the pressure οn the grοund when the blοck exerts a fοrce οf 7 Nm is[tex]175 nm^{-2[/tex].
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I need help what is, 8y - 7 - 4y =
show work
Answer:
Step-by-step explanation:
8y-7-4y=
8y-4y= -7
4y=-7
DBS by 4
y=1.75
what has a sum of 147
Answer:
146 and 1
Step-by-step explanation:
146+1=147
Professor Yi, M.A. is an expert on mindfulness meditation, and completed a study on how this practice can reduce stress. In the untreated population of Ionia, stress levels as measured by the HRSI (higher values indicate higher levels of stress) the mean stress level is μ = 30 and σ = 12. Professor Yi obtained a sample of n = 16 students to teach mindfulness meditation to for two months. After the two months of lessons the students show average HRSI stress scores of M = 24. Yi decided in advance he was going to run a two-tailed hypothesis test at an α = .05.
What is the null hypothesis for this study?
The null hypothesis for this study is that there is no significant difference in stress levels between the untreated population and the sample of students who were taught mindfulness meditation.
How to find the null hypothesis ?The null hypothesis states that the mindfulness meditation has no effect on the stress levels of the students.
In terms of the mean stress level (μ), the null hypothesis can be expressed as:
H₀: μ = 30
This means that under the null hypothesis, the mean stress level of the students who were taught mindfulness meditation is equal to the mean stress level of the untreated population (μ = 30).
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PLEASE ANSWER BEFORE 11:59 TONIGHT
1. A factory needs two raw materials. The probability of not having an adequate supply of material A is 0.05, whereas the probability of not having an adequate supply of material B is 0.03. A study determines that the probability of a shortage in both A and B is 0.01. a. Let E be the event "shortage of A" and F be the event "shortage of B". Construct a Venn diagram representing events E and F.
The Venn diagram needed based on the question is given below:
The Venn Diagram__________
/ \
/ A \
/____________\
\ /
\ E ∩ F /
\_________/
B
In the diagram, the set A represents the event of having an adequate supply of material A, and the set B represents the event of having an adequate supply of material B.
The overlap of A and B represents the event of having an adequate supply of both materials.
The set E represents the event of a shortage in material A, and the set F represents the event of a shortage in material B.
The intersection of E and F, denoted by E ∩ F, represents the event of a shortage in both materials.
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What is the probability that a resident is male and in the age group 60-79
Answer:
c. 0.29
Step-by-step explanation:
edge
PLEASE HURRY!!! I WILL GIVE THE BRAINLIEST!!!
Which answer shows the correct steps to solve the equation
a
Subtract 4 from both sides,, multiply by 12 on both sides, subtract 10 from both sides, and divide both sides by 5 to get x=2/5
b
Multiply by 15 on both sides, subtract by 10 on both sides, and divide by 5 on both sides to get x=10
c
Subtract 10 from both sides, multiply by 15 on both sides, and divide by 5 to get x=(-18)
d
Subtract 5x from both sides, subtract 10/15 from both sides, and divide both sides by 5 to get x=10
Answer:
Answer is B
Step-by-step explanation:
Multiply by 15 on both sides, subtract by 10 on both sides, and divide by 5 on both sides to get x=10
Which answer shows shows the equation below written in different forms 9-3=6
The equatiοn 9 -3 = 6 can be written in different fοrms, but the correct one is 9 = 3 + 6.
Are expressiοns cοnsidered equatiοns?Every cοmbinatiοn οf a number, a variables, and οperatiοn symbοls is cοnsidered an expressiοn. An equatiοn is created by cοmbining twο expressiοns and jοining them with the equal sign.
Cοnditiοns οn the parameters are fοund in simple equatiοns. It is clear frοm an equatiοn that the answer οn the left and right are equivalent. The expressiοn tο the left οf the symbοl "=" is the LHS, while the expressiοn tο the right is the RHS. With the fοrm y = "sοme expressiοn invοlving x," a sοlutiοn invοlving x and y can be expressed, such as y = f. ( x). This final statement, which may be interpreted as "y equals f οf x," denοtes that y is a cοefficient οf x.
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Complete question:
Which answer shows the equation 9-3=6 below written in different forms?
6 + 3 = 9, 9 = 3 + 6, 9 - 6 = 3, 3 = 9 - 6Which student found the total surface area of a cylinder with a height that was two times greater than its radius?
The total surface area of a cylinder with a height that was two times greater than its radius is 6πr²
What is the total surface area of a cylinder?The total surface area of a cylinder is the region occupied by the cylinder. It is given by A = 2πr(r + h) where
r = radius of cylinder and h = height of cylinderSince we want to find which student found the total surface area of a cylinder with a height that was two times greater than its radius.
We proceed as follows.
Since we have that the height that was two times greater than its radius. So, for that cylinder, h = 2r
So, to find the surface area, we substitute the values of the variables into the equation for the total surface area.
So, A = 2πr(r + h)
Given that h = 2r, we have that
A = 2πr(r + h)
A = 2πr(r + 2r)
A = 2πr(3r)
A = 6πr²
So, the area is 6πr²
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Please help asap! Need the answer quickly!
The time needed for the sample size to double is given as follows:
26.3 hours.
How to obtain the time needed for the sample size to double?The exponential function that models the sample size after t hours is given as follows:
y(t) = y(0)e^(0.0264t).
The parameter y(0) represents the initial population, hence when the population is doubled, we have that:
y(t) = 2y(0).
Then we must solve the exponential function for the variable t, applying the natural logarithm, which is the inverse of the exponential, as follows:
2y(0) = y(0)e^(0.0264t).
e^(0.0264t) = 2
0.0264t = ln(2)
t = ln(2)/0.0264
t = 26.3 hours.
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what is the area of the circle below?
The area of the circle shown above is equal to: A. 1,520.5 cm².
How to calculate the area of a circle?Mathematically, the area of a circle can be calculated by using the following mathematical expression:
Area of a circle, A = πr²
Where:
r represents the radius of a circle.
By substituting the radius into the formula for the area of a circle, we have the following;
Area of a circle, A = πr²
Area of a circle, A = 3.14 × 22²
Area of a circle, A = 1,520.5 cm².
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PLEASE HELP FAST!!
Determine the number of solutions to the system of linear equations shown on the graph.
A: No solution
B: Infinitely many solutions
C: One solution at (-3,2)
D:One solution at (2,-3)
Answer:
the answer is D
both lines intersect at (2, -3)
hope this helps <3
Determining Whether a Point Lies on a Circle
10
8
-10 8-6-4-2
6
4
2
-2
-6
8
-10
Y
2
6 8 10
A circle centered at the origin contains the point
(0, -9). Does (8, √17) also lie on the circle? Explain.
O No, the distance from the center to the point
(8, √17) is not the same as the radius.
O No, the radius of 10 units is different from the
distance from the center to the point
(8. √17).
O Yes, the distance from the origin to the point
(8,√17) is 9 units.
Yes, the distance from the point (0, -9) to the point
(8, √17) is 9 units.
The correct statement regarding whether (8, √17) lies on the circle is given as follows:
Yes, the distance from the origin to the point (8,√17) is 9 units.
What is the equation of a circle?The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle, while the diameter of the circle is the distance between two points on the circumference of the circle that pass through the center. Hence, the diameter’s length is twice the radius length.
The parameters for this circle are given as follows:
Center (0,0).Radius 9.Hence the equation is given as follows:
x² + y² = 81.
For point (8, √17), we have that:
8² + (√17)² = 81
64 + 17 = 81
81 = 81.
Hence the point lies on the circle.
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f(x) =
4 if x≤3
-4 if x>3
What is the functions range ?
Answer:
(−∞,∞)
Step-by-step explanation:
Please help me solve these questions that are attached.
The sums, differences, product, and quotient of the functions and their domains are;
f(x) = √(16 - x^2), g(x) = √(x + 3)
f + g = √(16 - x^2) + √(x + 3)
Domain; [-3, 4]
f - g = √(16 - x^2) - √(x + 3)
Domain: [-3, 4]
f × g = √(16 - x^2) × √(x + 3) = √(-x³ - 3·x² + 16·x + 48)
f × g = √(-x³ - 3·x² + 16·x + 48)
Domain; [-3, 4]
f/g = √(16 - x^2)/√(x + 3) = √(16 - x^2)/(x + 3))
f/g = √(16 - x^2)/(x + 3))
Domai; [-3, 4] ∪ [1, 4]
f(x) = √(81 - x^q2), g(x) = √(x² - 16)
f + g = √(81 - x^2) + √(x² - 16)
Domain [-9, -4] ∪ [4, 9]
f - g = √(81 - x^2) - √(x² - 16)
Domain: [-9, -4] ∪ [4, 9]
f × g = √(81 - x^2) × √(x² - 16) = √(-x⁴ + 97·x² - 1296)
f × g = √(-x⁴ + 97·x² - 1296)
Domain: [-9, -4] ∪ [4, 9]
f/g = √(81 - x^2)/√(x² - 16)
Domain: [-9, -4] ∪ [4, 9]
What is the sum of two functions?The sum of two functions is obtained by adding the values of the functions at each point.
The sum of two functions is obtained by adding the values of the functions at each point. The domain of the sum is the intersection of the domains of the two functions, In this case, the domain of f + g is [-3, 4]
The difference of two functions is obtained by subtracting the functions values at each point. The domain of the difference is the intersection of the domains of the two functions. In this case, the domain of f - g is [-3, 4]
The product of two functions is obtained by multiplying the values of the functions at each point. The domain of the product of the functions is the domain of the intersection of the domains of the two functions. The domain of f × g is [-3, 4]
The quotient of two functions is obtained by dividing the values of the functions at each point. The domain of the quotient is the same as the domain of the intersection of two functions, excluding any points where the denominators is zero. The domain of f/g is [-3, -1] ∪ [1, 4].
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What value of n makes the equation true? Show your work.
Answer:6
Step-by-step explanation:
[tex]\frac{a^{b} }{a^{c}} =a^{b-c} \\a^{b} *a^{c} =a^{b+c}\\ \frac{(-4)^{10}}{(-4)^{n}}=(-4)^{2}*(-4)^{2} \\(-4)^{10-n}=(-4)^{4}\\ 10-n=4\\ -n=-6\\n=6[/tex]
Answer:
n = 6
Step-by-step explanation:
[tex]\frac{(-4)^{10}}{(-4)^{n}} =(-4)^{2}*(-4)^{2}\\\\\frac{(-4)^{10}}{(-4)^{n}} =(-4)^{2+2}\\\\\frac{(-4)^{10}}{(-4)^{n}} =(-4)^{4}[/tex]
If they have the same base which is -4 we can either add or subtracting the exponent.
Add the exponenet when multiplying.
Subtract the exponent when dividing.
[tex](-4)^{10-n}=(-4)^4\\\\10-n=4\\10=4+n\\n= 6[/tex]
[tex]\frac{(-4)^{10}}{(-4)^{6}}=(-4)^{10-6}=(-4)^4[/tex]
Pearl earns $34,000 per year, and she is considering buying a $130,000 house by
making a down payment of 10% of the purchase price and taking out a 30-year
fixed-rate mortgage with a 6.3% interest rate. She would pay $1280 annually in
property taxes, and for the first 2 years of the mortgage, she would pay $608.40
annually for PMI. Use this information to answer the following six questions.
1.
How much would Pearl's
mortgage be?
Pearl's mortgage payment would be $678.47 per month.
What is mortgage?A mortgage is a type of loan that is used to finance the purchase of real estate, such as a house or a piece of land. When a person takes out a mortgage, they borrow money from a lender (usually a bank or other financial institution) to buy the property, and they agree to pay back the loan over a set period of time, typically 15 to 30 years.
In the given question,
To calculate Pearl's mortgage, we need to first determine the amount of her down payment.
Down payment = 10% x $130,000
Down payment = $13,000
The amount that Pearl needs to finance with her mortgage is:
$130,000 - $13,000 = $117,000
To calculate the mortgage payment, we can use the formula for a fixed-rate mortgage:
Mortgage Payment = P * r * (1 + r)^n / ((1 + r)^n - 1)
Where:
P = Principal (amount borrowed)
r = Monthly interest rate (annual rate divided by 12)
n = Number of monthly payments (30 years x 12 months per year)
Monthly interest rate = 6.3% / 12 = 0.00525
Number of monthly payments = 30 years x 12 months = 360
Using these values, we can calculate the monthly mortgage payment:
Mortgage Payment = $117,000 * 0.00525 * (1 + 0.00525)^360 / ((1 + 0.00525)^360 - 1)
Mortgage Payment = $678.47 (rounded to the nearest cent)
Therefore, Pearl's mortgage payment would be $678.47 per month.
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