Two angles of a triangle have the same measure and the third one is 60 degrees greater than the measure of each of the other two. Find the measure of the LARGEST angle in the triangle.
Answers
The measure of the largest angle will be 100°.
What is Parallelogram? What is triangle?In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -
∠x + ∠y + ∠z = 180°
There are different types of triangles such as -
equilateral triangle , scalene triangle , isosceles triangle etc.
Given is a triangle such that two angles of a triangle have the same measure and the third one is 60 degrees greater than the measure of each of the other two.
We can write -
[x] + [x] + [x + 60] = 180
3x + 60 = 180
3x = 120
x = 40
Largest angle = [x + 60] = 40 + 60 = 100°
Therefore, the measure of the largest angle will be 100°.
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Related Questions
Need help on this asap
Answers
The Total surface area of a pyramid formula = ½ pl + B, Where 'p' is the perimeter of the base and 'l' is the slant height of the pyramid and B is the area of the base.
What is the formula for volume of pyramids?A pyramid's volume can be calculated by multiplying the base area by the height, then dividing the result by three. The formula V=13Bh, where B is the area of the pyramid's base and h is its height, is used to express this product.
A triangular pyramid, for instance, has a base area of 20 cm2 and a height of 9 cm. The formula V = (1/3) Bh, where "B" stands for the base area and "h" for the height of the pyramid, is used to calculate the volume of a pyramid.
We can use the formulas for the area of polygons to calculate "B" because we know that the base of a pyramid can be any polygon. A pyramid with a triangle base is referred to as a triangular pyramid.
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The value of x is 2, when the volume of pyramid is 125 cm³ which is equal to \(\mathrm{5^{\tfrac{x}{6}} }\).
What is the formula for volume of pyramids?A pyramid's volume can be calculated by multiplying the base area by the height, then dividing the result by three. The formula V=1/3Bh, where B is the area of the pyramid's base and h is its height, is used to express this product.
We know that pyramid's volume is
\(\mathrm{{\textstyle V={\tfrac {1}{3}}Bh}}\)
B = base area = \(25^{1/4} \times25^{1/4}\)
= \(\sqrt[4]{25} \times \sqrt[4]{25}\)
= \(\sqrt[4]{25}^2\)
= \(\sqrt[2]{25}\)
= 5 cm²
and
h = 75 cm
\($\mathrm{{\textstyle V={\dfrac {1}{3}} \times5 \times 75}}\)
V = 125 cm³
Now it is given that \(\mathrm{5^{\tfrac{x}{6}} = 125 }\)
So,
\(\mathrm{5^{\tfrac{x}{6}} = 125 }\)
\(\mathrm{5^{\tfrac{x}{6}} = \sqrt[3]{5} }\)
\(\mathrm{5^{\tfrac{x}{6}} = 5^{\tfrac{1}{3}} }\)
\(\dfrac{x}{6} = \dfrac{1}{3}\)
3x = 6
x = 6/3
x = 2
Thus, the value of x is 2, when the volume of pyramid is 125 cm³ which is equal to \(\mathrm{5^{\tfrac{x}{6}} }\).
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For the following equation, find three ordered pair solutions by completing the table. Then use the ordered pairs to graph the equation.
y = - 4x + 8
Answers
The graph of the linear equation can be seen in the image below.
How to complete the table?
Here we have the linear equation:
y = -4x + 8
And we want to find 3 ordered pairs, to do so, we need to evaluate x in different values.
if x = 0 then:
y = -4*0 + 8 = 8
So we have the ordered pair (0, 8).
if x = 1 then:
y = -4*1 + 8 = 4
Then we have the ordered pair (1, 4)
If x = 2 then:
y = -4*2 + 8 = 0
Then we have the ordered pair (2, 0).
Now that we have these 3 ordered pairs, we can graph them in a coordinate axis and then connect them with a line, we will get something like the graph below.
That is the graph of our linear equation:
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When a grizzly bear hibernates, its heart rate drops to 10 beats per minute, which is 20% of its normal
value.
Answers
Answer:
Its normal value would be 50 beats per minute.
Step-by-step explanation:
20% = 10bpm
40% = 20bpm
60% = 30bpm
80% = 40bpm
100% = 50bpm
Please turn the sentence into an expression
3. twelve more than the sum of ten and a
number
Answers
Answer:
Do U-Turn
Step-by-step explanation:
Step-by-step explanation:
12+(10+x)
I hope this helps
The marketing manager of a firm that produces laundry products decides to test market a new laundry product in each of the firm's two sales regions. He wants to determine whether there will be a difference in mean sales per market per month between the two regions. A random sample of 12 supermarkets from Region 1 had mean sales of 79.8 with a standard deviation of 8.8. A random sample of 17 supermarkets from Region 2 had a mean sales of 85.2 with a standard deviation of 8.3. Does the test marketing reveal a difference in potential meal sales per market in Region 2? Use a signifiance level of a = 0.02 for the test. State the null and alternative hypotheses for the test and find the test statistic.
Answers
Answer:
The null hypothesis is \(H_o: \mu_1 = \mu_2\)
The alternative hypothesis is \(H_1 : \mu_1 \ne \mu_2\)
The test statistics is \(t = -1.667\)
Step-by-step explanation:
From the question we are told that
The first sample size is \(n_1 = 12\)
The first sample mean is \(\= x_1 = 79.8\)
The first standard deviation is \(\sigma _1 = 8.8\)
The second sample size is \(n_2 = 17\)
The second sample mean is \(\= x_2 = 85.2\)
The second standard deviation is \(\sigma _2 = 8.3\)
The null hypothesis is \(H_o: \mu_1 = \mu_2\)
The alternative hypothesis is \(H_1 : \mu_1 \ne \mu_2\)
Generally the test statistics is mathematically represented as
\(t = \frac{\= x_ 1 - \= x_2 }{ \sqrt{ \frac{\sigma_1^2 }{n_1 } +\frac{\sigma_2^2 }{n_2} } }\)
=> \(t = \frac{ 79.8 - 85.2 }{ \sqrt{ \frac{8.8^2 }{12} +\frac{ 8.3^2 }{17} } }\)
=> \(t = -1.667\)
8x = x² +4
The answer?
Answers
Answer: =4±23√
Step-by-step explanation:
Costs of Attendance
Category Dollar Amount
Annual Tuition and Fees $21,195.00
Annual Room and Board $4,250.00
Annual Cost of Books and Supplies $1,125.00
Annual Scholarship and Grants 35% of tuition & books
Using the information from the table, determine the total cost of attendance for one year. (4 points)
$7,254.00
$9,575.88
$18,758.00
$26,570.00
Answers
Answer:
$18,758.00 (choice #3)
Step-by-step explanation:
Total costs =
$21,195.00 + $4,250.00 + $1,125.00 = $26,570
However this amount is reduced by scholarships and grants of 35% of tuition and books
Cost of tuition and books = $21,195.00 + $1,125.00 = $22,320
35% of $22,320 = $22,320 x 35/100 = $7,812
Therefore net attendance cost
= $26,570 - $7,812
= $ 18,758
convert 1 4/5 into an improper fraction
Answers
Answer:
9/5
Step-by-step explanation:
I hope this helps im pretty sure its correct
An employee was hired at a wage of $12 per hour. After a raise, she now earns $13.17 per hour.
Answers
Answer:
ok keep going more questions cause ido t get it what u trying to ask
f(x)=3x+2
g(x)=-2x²-3x+5
Find g(f(x))
Answers
Answer: g(f(x)) is equal to -18x² - 27x - 13.
Step-by-step explanation:
To find g(f(x)), we need to substitute f(x) into the expression for g(x).
First, we need to find f(x), which is given by:
f(x) = 3x + 2
Next, we can substitute f(x) into the expression for g(x), which is given by:
g(x) = -2x² - 3x + 5
So we replace x in g(x) with f(x), which gives:
g(f(x)) = -2f(x)² - 3f(x) + 5
= -2(3x + 2)² - 3(3x + 2) + 5 (Substituting f(x) = 3x + 2)
= -2(9x² + 12x + 4) - 9x - 1
= -18x² - 27x - 13
Therefore, g(f(x)) is equal to -18x² - 27x - 13.
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which of the following best describes the bases of a cylinder? A. Congruent B. Polygons C. Parallel D. Discs (Check All That Apply)
Answers
Answer:
A. Congruent and D. Discs
Step-by-step explanation:
You won't see a cylinder that doesn't have congruent bases
Look at the shape of the bases and look at a disc compare their shape
We can describe the bases of a cylinder as congruent.
What is the volume of cylinder?The volume of cylinder is given by -
V = πR²h
Given is to describe the bases of a cylinder.
The cylinders are uniform in cross - section. Therefore, the bases of the cylinder will have the same area. So, we can conclude that the given bases are congruent.
Therefore, we can describe the bases of a cylinder as congruent.
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37= -3+5(x + 6) slove for x
Answers
37
=
−
3
+
5
(
x
+
6
)
37
=
−
3
+
(
5
)
(
x
)
+
(
5
)
(
6
)
(Distribute)
37
=
−
3
+
5
x
+
30
37
=
(
5
x
)
+
(
−
3
+
30
)
(Combine Like Terms)
37
=
5
x
+
27
37
=
5
x
+
27
Step 2: Flip the equation.
5
x
+
27
=
37
Step 3: Subtract 27 from both sides.
5
x
+
27
−
27
=
37
−
27
5
x
=
10
Step 4: Divide both sides by 5.
5
x
5
=
10
5
x
=
2
Blank hundreds is the same as 4 thousand
Answers
Kira set a goal to walk 60 miles this month. She walks at a consistent rate of 4 miles per
hour. How long will Kira have to walk in order to reach her goal?
Write and solve an equation to find the answer.
Answers
Answer:
15
Step-by-step explanation:
The equation helpful to find the number of hours it takes to reach her goal is 4x = 60 and it takes 15 hours to reach her goal.
What is an expression?An expression is a combination of some mathematical symbol such that an arithmetic operator and variable such that all are constrained and create an equation.
As per the given,
Goal = 60 miles
Rate of walking = 4 miles per hour
Suppose after x hour she will reach her goal.
After x hour ⇒ 4x = 60 miles
x = 60/4 = 15 miles
Hence "4x = 60 is a useful equation to determine how many hours it will take her to achieve her objective, and it will take her 15 hours".
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Mr. Carson makes $21.50 an hour. He works 8 hours a day and works 5 days a week.
Answers
Answer:
$860
Step-by-step explanation:
21.50 times 8 = 172
172 times 5 = 860
CallmeCarson lol
Answer:
860$
Step-by-step explanation:
In order to find the answer to this question you need to multiply the amount of hours Carson worked to the amount of days he worked and then you need to multiply that by the amount he gets paid per hour.
\(21.50 = ph\)
\(hours=8\)
\(days = 5\)
\(8\times5=40\)
So he worked 40 hours a week
\(40 \times21.50 = 860\)
Therefore Mr.Carson has made 860$ that week.
Hope this helps.
triangle QRS is reflected across the y axis to create triangle Q'R'S' complete the rule that describes the coordinates of triangle Q'R'S' after the reflection has occurred
Answers
To reflect a point or a shape across the y-axis, the x-coordinates of each point must be negated. Therefore, the coordinates of triangle Q'R'S' after the reflection would be (-x, y) for point Q', (-x, y) for point R', and (-x, y) for point S'.
What is the rationale for the above response?When reflecting a point or a shape across the y-axis, each point's x-coordinate is negated, while its y-coordinate remains the same. The y-axis is a vertical line that passes through the origin, which is at (0, 0).
Thus, when reflecting triangle QRS across the y-axis to create Q'R'S', the x-coordinates of each point must be negated. Therefore, the new coordinates of each point will be (-x, y) to reflect it across the y-axis.
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The transformation rule that describes the coordinates of triangle Q'R'S' after the reflection has occurred is: (x, y) → (-x, y)
How to find the transformation rule?The transformation rule for describing the reflection of the given figure QRS is as follows:
If the coordinate of each point of the triangle is (x, y), then, after the reflection across the y-axis the new coordinates will become:
(x, y) → (-x, y)
This means that the rule for reflecting over the y-axis is to negate the value of the x-coordinate of each point, but leave the -value the same
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3. A test consists of 30 true/false questions. To pass the test a student must answer at least 18 questions correctly. If a student guesses on each question, what is the probability that the student will pass the test?
Answers
Answer: the answer would be15%
Step-by-step explanation:
123^3 as a power of 5
Answers
Answer:
5043
Step-by-step explanation:
Describe the y-intercept and end behavior of the following graph:
a
(−2, 0); The graph approaches y = −6 to the right.
b
(0, −5); The graph approaches y = −6 to the right.
c
(−2, 0); The graph decreases to the left.
d
(0, −5); The graph decreases to the left.
Answers
The graph has a y-intercept at the coordinate pair: (0, -5). The graph also approaches the asymptote of y=-6 to the right, meaning as x increases, y gets closer and closer to -6.
Which derivation rule justifies the following argument? If n is a multiple of 8, then n is even. However, n is not even. Therefore, n is not a multiple of 8. O double negation O simplification De Morgan's Laws O modus ponens O modus tollens
Answers
Commutativity justifies the statement, of If n is a multiple of 8, then n is even. However, n is not even. Therefore, n is not a multiple of 8.
Commutativity is used in Maths equations and describes sums that can be moved around and will still give the same answer.
'Commutative' comes from the word 'commute' which means to move and travel around, so equations that are commutative have numbers that can be moved within the equation.
commutative law, in mathematics, is either of two laws relating to number operations of addition and multiplication that are stated symbolically as a + b = b + a and ab = ba.
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list seven advantages that aluminum parallel-flow plate-and-fin evaporator has over a standard round copper tube plate-and-fin evaporator.
Answers
The aluminum parallel-flow plate-and-fin evaporator has several key advantages over the standard round copper tube plate-and-fin evaporator are Lighter Weight, Improved Heat Transfer Efficiency.
An evaporator is a device used in air conditioning and refrigeration systems to remove heat from the refrigerant, which helps to cool down the air. There are two main types of evaporators: the aluminum parallel-flow plate-and-fin evaporator and the standard round copper tube plate-and-fin evaporator.
The parallel-flow design of the aluminum evaporator provides a larger surface area for heat transfer, which results in more efficient cooling. This means that less energy is required to achieve the same cooling effect.
Reduced Pressure Drop: The parallel-flow design also reduces the pressure drop in the refrigerant, which can improve the overall efficiency of the air conditioning or refrigeration system.
Aluminum is lighter than copper, which makes the aluminum evaporator easier to handle and install. This can be especially important in large air conditioning or refrigeration systems where weight and handling can be a significant concern.
Increased Durability: Aluminum is a more durable material than copper, which means that the aluminum evaporator is less likely to suffer from corrosion or other types of damage over time.
Better Resistance to Leakage: The parallel-flow design of the aluminum evaporator provides a tighter seal, which reduces the risk of refrigerant leakage. This helps to maintain the efficiency of the air conditioning or refrigeration system.
Lower Maintenance Costs: The increased durability and better resistance to leakage of the aluminum evaporator can help to lower maintenance costs over time.
Improved Environmental Performance: The improved efficiency and reduced pressure drop of the aluminum evaporator can help to lower the energy consumption of the air conditioning or refrigeration system. This can result in a reduction in greenhouse gas emissions and other environmental impacts.
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Help plz:))) I’ll mark u Brainliest
Answers
Answer:
C.
Step-by-step explanation:
Anyone please help me pls on how to solve this i really need help
A sample of fish is taken from two different lakes.
Seventy fish are taken from Lake A and the mean length of the
fish is 35 cm.
Thirty fish are taken from Lake B and the mean length of the
fish is 42 cm.
Calculate the mean length of the 100 fish.
Answers
Answer:
So, 100 fish taken from Lake A would have a mean length of 50 cm and 100 fish taken from Lake B would have a mean length of 140 cm
Step-by-step explanation:
1 fish from Lake A would be 0.5 cm long you calculate that by dividing 70 from 35 and you calculate the fish from Lake B by dividing 30 from 42 which would be 1.4 cm, (english is not my first language so I hope you understood everything :D)
step by step explanation to this: A boat leaves a port at 10:15a.m. for another port distance 80km. If the boat's speed is 32km an hour, at what time does it arrive at the other port?
Answers
The boat will arrive at the other port at 12:45 p.m.
To determine the time the boat arrives at the other port, we can use the formula:
Time = Distance / Speed
Given:
Distance = 80 km
Speed = 32 km/h
Calculate the time it takes for the boat to travel the given distance:
Time = Distance / Speed
Time = 80 km / 32 km/h
Time = 2.5 hours
Convert the time to minutes:
Since the time is given in hours, we need to convert it to minutes.
1 hour = 60 minutes
2.5 hours = 2.5 * 60 = 150 minutes
Add the calculated time to the departure time:
The boat leaves the port at 10:15 a.m. We need to add 150 minutes to this time to find the arrival time.
10:15 a.m. + 150 minutes = 12:45 p.m.
Therefore, the boat will arrive at the other port at 12:45 p.m.
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Given g(x) = x2 + 1, find g(x – 2).
Answers
Answer:
g(x)-2g
Step-by-step explanation:
g x(x-2), gx-2g
Which number is irrational?
Answers
Answer:
√11 is the irrational number
Explanation:
Irrational numbers are which numbers that can't be expressed as p/q form that are irrational numbers. root 11 cant be expressed as p/q form so, this is an irrational number.
Can someone please provide a step-by-step explanation for the answer? I would really appreciate it.
Let f(x)= 2(x-1) / x²-2x-3 - 1/ x-3, x ЄR, x > 3.
(a) Show that f(x) = 1/ x+1
(b) Find the inverse function of ƒ (x).
(c) Find the domain of ƒ−¹(x).
(d) Given that g(x) = 2x² – 3, where x Є R. Solve (ƒ o g)(x) = 1/8.
Answers
b) The inverse function of ƒ(x) is given by: ƒ⁻¹(x) = (1 - x) / x
c) The domain of ƒ⁻¹(x) is all real numbers except for 1.
d) The solutions for (ƒ o g)(x) = 1/8 are x = √5 and x = -√5.
(a) To show that f(x) = 1 / (x + 1), we need to simplify the expression f(x) and demonstrate that it is equivalent to 1 / (x + 1):
f(x) = [2(x - 1) / (x² - 2x - 3)] - (1 / (x - 3))
f(x) = [2(x - 1) / (x - 3)(x + 1)] - (1 / (x - 3))
f(x) = [2(x - 1) - (x + 1)] / (x - 3)(x + 1)
f(x) = [2x - 2 - x - 1] / (x - 3)(x + 1)
f(x) = (x - 3) / (x - 3)(x + 1)
f(x) = 1 / (x + 1)
Therefore, we have shown that f(x) = 1 / (x + 1).
(b) To find the inverse function of ƒ(x), we interchange the roles of x and y and solve for y:
x = 1 / (y + 1)
xy + x = 1
xy = 1 - x
y = (1 - x) / x
Therefore, the inverse function of ƒ(x) is given by:
ƒ⁻¹(x) = (1 - x) / x
(c) The domain of ƒ⁻¹(x) can be determined by looking at the domain of the original function f(x), which is x > 3.
For ƒ(x), the range is all real numbers except for 1 (since f(x) = 1 / (x + 1)).
Therefore, the domain of ƒ⁻¹(x) is all real numbers except for 1.
(d) Given g(x) = 2x² - 3, we are asked to solve (ƒ o g)(x) = 1/8.
(ƒ o g)(x) means we need to substitute g(x) into ƒ(x):
ƒ(g(x)) = 1 / (g(x) + 1)
Substituting g(x) = 2x² - 3:
ƒ(2x² - 3) = 1 / (2x² - 3 + 1)
ƒ(2x² - 3) = 1 / (2x² - 2)
1 / (2x² - 2) = 1 / 8
8 = 2x² - 2
2x² = 10
x² = 5
x = ±√5
Therefore, the solutions for (ƒ o g)(x) = 1/8 are x = √5 and x = -√5.
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9. Find the quadratic equation whose parabola has vertex (3, –2) and y-intercept (0, 16). Give your answer in vertex form.
Answers
The quadratic equation whose parabola has vertex (3, –2) and y-intercept (0, 16). y = 2(x - 3)² - 2
What is quadratic equation?In algebra, a quadratic equation (from Latin quadratus 'square') is any equation that can be rearranged in standard form as ax²+bx+c=0
Given the quadratic equation with a y-intercept of (0, 16), and has a vertex occurring at point (3, -2):
We can substitute these values into the following vertex form of the quadratic equation:
y = a(x - h)² + k
where:
(h, k) = vertex
a = determines the wideness or narrowness of the graph, and the direction of where the parabola opens.
a > 1: the graph is narrower than the parent function; the parabola also opens upward.
0 < a < 1: the graph is wider than the parent function.
a < 1: the graph opens downward.
Now that we established the definitions for the variables in the vertex form, we can finally substitute the vertex, (3, -2) and y-intercept, (0, 16) into the vertex form and solve for the value of a:
y = a(x - h)² + k
16 = a(0 - 3)² - 2
16 = a(-3)² - 2
16 = 9a - 2
Add 2 to both sides:
16 + 2 = 9a - 2 + 2
18 = 9a
Divide both sides by 9 to solve for a:
18/9 = 9a/9
2 = a
Therefore, the quadratic equation in vertex form is:
y = 2(x - 3)² - 2
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Helpppp I need somthing quick question #4 pls or any of them
Answers
Answer:
4) No, It is not a right triangle
Step-by-step explanation:
12 is the hypotenuse which is the longest side of the triangle
6² + 8² = 12² （Pythagoras Theorem）
36 + 64 ≠ 144
Hence it is not a right triangle
Temperature Change In the United States, temperature is measured on the Fahrenheit temperature scale. On this scale, water boils at 212 degrees and freezes at 32 degrees. To denote a temperature of 32 degrees on the Fahrenheit scale, we write:
32 degrees F, which is read "32 degrees Fahrenheit"
At 10:00 in the morning in White Bear Lake, Minnesota, John notices the temperature outside is 12 degrees below zero Fahrenheit.
A. Write the temperature as a negative number Ans: ———-
degrees Fahrenheit.
B. B.) An hour later it has warmed up by 8 degrees. What is the temperature at 11:00 that morning? Ans: _____degrees Fahrenheit.
Answers
Answer: B
Step-by-step explanation: