If cos(0) = -8/17 and sin(O) is negative, then sin(O) = -15/17 and tan(O) = 15/8.
Given that cos(O) = -8/17 and sin(O) is negative, we can use the Pythagorean identity to find sin(O).
The Pythagorean identity states that sin²(O) + cos²(O) = 1. So, sin²(O) = 1 - cos²(O).
Substituting the given value for cos(O):
sin²(O) = 1 - (-8/17)² = 1 - (64/289)
To find sin(O), we must take the square root of the result, keeping in mind that sin(O) is negative:
sin(O) = -√(289/289 - 64/289) = -√(225/289) = -15/17
Now, we can find tan(O) using the sine and cosine values:
tan(O) = sin(O) / cos(O)
Substituting the values we found:
tan(O) = (-15/17) / (-8/17) = (-15/17) * (17/8)
Simplifying:
tan(O) = 15/8
So, sin(O) = -15/17 and tan(O) = 15/8.
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Help me quick please
Answer:
y = 3x + 2
Step-by-step explanation:
1. Work out the gradient of the line segment: change in y/change in x: -2 - -6/ -8 - 4 = 4/-12 = -1/3
2. Work out the gradient of the perpendicular bisector: the gradient of the line segment and the perpendicular bisector should multiply to get -1. This means that we can do -1 ÷ -1/3 to work out the gradient which is 3
4. Find the midpoint of the line segment: (-8 + 4) ÷ 2 = -2, and (-2 + -6) ÷ 2 = -4, so the midpoint is (-2, -4)
3. The equation will be in the format y = 3x + c and will go through (-2, -4), so we can substitute those values into the equation to find c:
y = 3x + c-4 = 3(-2) + c-4 = -6 + cc = -4 + 6c = 2The equation of the line is y = 3x + 2
Hope this helps!
simplify to radical form the square root of 40 and then divide by 6
The simplified expression of the radical is √10/3
How to evaluate the expressionFrom the question, we have the following parameters that can be used in our computation:
the square root of 40 and then divide by 6
This statement can be mathematically represented as
√40/6
Simplify the numerator
So, we have the following representation
2√10/6
Divide 2 and 6
√10/3
Hence, the solution is √10/3
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How do you write an inequality step by step?
An inequality in mathematics shows how two values are related in an imbalanced algebraic expression.
What is meant by inequality?In mathematics, an inequality displays the connection between two values in an unbalanced algebraic statement. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.
There are four ways to depict an inequality: solution graph, interval notation, set notation, and equation notation.
A comparison of any two values, known as an inequality, demonstrates whether one value is less than, larger than, or equal to the value on the opposite side of the equation. A relationship in a real-world scenario can be demonstrated by writing an inequality.
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ASAP
If f(x)= 3x-4, which of these is the inverse of f(x)?
O A. f-¹(x)=X-4/3
B. f¹(x)=x+4/3
OC. F¹(x) = x/3+4
OD. ¹(x)=x/3-4
Answer:
Step-by-step explanation:
f(x)=−3x−4
f
(x)=−3x−4 as an equation.
y=−3x−4 Interchange the variables.
x=−3y−4 Solve for y
y=−x3−4
3 Replace y with f−1(x) to show the final answer.
f−1(x)=−x3−43 Verify if f−1(x)=−x3−43
is the inverse of (x)=−3x−4.
F−1(x)=−x3−43
There are some nickels, dimes, and quarters in a large piggy bank. For every 2 nicke × there are 3 dimes. For every 2 dimes there are 5 quarters. There are 500 coins total.
a. How many nickels, dimes, and quarters are in the piggy bank?
Answer:120 dimes, 80 nickels, and 300 quarters
Step-by-step explanation: Go step by step multiplying
He tax rate a a percent, r, charged on an item can be determined uing the formula StartFraction c Over p EndFraction minu 1 equal r. – 1 = r, where c i the final cot of the item and p i the price of the item before tax. Louie rewrite the equation to olve for the final cot of the item: c = p(1 ). What i the final cot of a $40 item after an 8% tax i applied?
A $40 item will ultimately cost $43.2 when an 8% tax is included.
The formula Lousie used is:
c = p(1 + r)
We will solve this problem with the help of percentages.
A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.
We are given that the price of the item is $40
r = 8% .
Therefore,
c = 40(1 + 8%)
c = 40 (1 + 8/100)
c = 40 ((100+8)/100)
c = 40 (108/100)
c = 40 * 1.08 = 43.2
Final cost = $43.2
Therefore the final cost of the $40 item after an 8% tax is applied will be $43.2.
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6. Keith's charge account uses the unpaid-balance method to compute the finance charge
at a monthly periodic rate of 1.5%. His previous balance was $200. During the month,
he charged $178.62, made a $200 payment.
a. What is Kieth's unpaid balance?
b. What is Kieth's finance charge?
c. What is Kieth's new balance?
Keith's unpaid balance is $178.62, finance charge is $2.6795 and new balance is $181.2995
Kieth's unpaid balanceTo find Keith's unpaid balance, we need to find the difference between the previous balance and the payments made during the month.
Keith's previous balance was $200.
During the month, he charged $178.62, made a $200 payment.
So, Keith's unpaid balance is:
$200 (previous balance) - $200 (payment) + $178.62 (charges) = $178.62
Finance chargeTo find Keith's finance charge, we need to multiply the unpaid balance by the monthly periodic rate (1.5% in this case).
Keith's finance charge is:
$178.62 (unpaid balance) * 0.015 (monthly periodic rate) = $2.6795
New balanceTo find Keith's new balance, we need to add the finance charge to the unpaid balance.
Keith's new balance is:
$178.62 (unpaid balance) + $2.6795 (finance charge) = $181.2995
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What is the value of x? round to the nearest tenth, if necessary. responses x = 6 x, = 6 x = 11 x, = 11 x = 11.5 x, = 11.5 x = 13.6
Round to the nearest tenth , if necessary the value of x is 11.5.
What is right triangle ?
A right triangle is a type of triangle in which one angle is equal to 90 degrees. The side opposite this 90-degree angle is known as the hypotenuse, and the other two sides are known as the legs. The Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs, applies to all right triangles.
Triangle ABC is a right angle triangle,
We can apply the Pythagorean Theorem to get,
[tex]x^{2} +8^{2} = 14^{2} \\x^{2} = 14^{2}-8^{2} \\x^{2} = 196-64\\x^{2} =132[/tex]
x ≈ 11.5
So , Round to the nearest tenth , if necessary the value of x is 11.5.
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The endpoints of directed line segment DC are C(-10,6) and D(-2,18).
The coordinate of the point that partitions the line segment is; (-4, 15)
How to partition line segment?
We are given the line DC with coordinates as;
C(-10, 6) and D(-2, 18)
Now the formula to find the coordinates of a partitioned line segment in the ratio a:b is;
(x, y) = (bx₁ + ax₂)/(a + b), (by₁ + ay₂)/(a + b)
From the ratio given to us, we can say that a = 1 and b = 3. Thus;
(x, y) = ((3*-2) + (1*-10))/(1 + 3), ((3*18) + (1*6))/(1 + 3)
(x, y) = (-16/4), (60/4)
(x, y) = (-4, 15)
This is the coordinate of the point that partitions the line segment.
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It is a property of exponents that if ax = ay and a is not 0 or 1, then x = y. You used this property to solve the equation in Question 1. Now use this same property to solve the equation 3x = 729 by rewriting to get a common base number
Using the property of exponents, the value of x for the formula 3x=729 is 6.
What is exponents?The number of times a number is multiplied by itself is referred to as its exponent. For instance, 2 to the third (written as 23) means: 2 x 2 x 2 = 8. 2 x 3 = 6 does not equal 23. Keep in mind that a number raised to the power of one is itself. Exponentiation is the process of expressing huge numbers in terms of powers. That is, exponent refers to the number of times a number has been multiplied by itself. For example, 6 is multiplied by itself four times, yielding 6 6 6 6. This is written as 64. The exponent is 4 and the base is 6.
Here,
3ˣ=729
3ˣ=3⁶
x=6
The value of x for expression 3ˣ=729 is 6 using property of exponents.
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What is the equation of this line in slope intercept form?
y = mx + b
m = slope
b = y-intercept
The equation of the line in slope intercept form is y = -4x + 1.
What is Slope?Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.
Intercept of a line is the point where the line touches with one of the axis.
The general equation of a line in slope intercept form is,
y = mx + d, where m is the slope and d is the y intercept.
y intercept point touches the y axis.
Take any two points from the line.
Let it be (0, 1) and (-1, 5).
Slope = (5 - 1) / (-1 - 0) = 4 / (-1) = -4
m = -4
We have the point (0, 1), where the line touches the Y axis.
y intercept, d = 1.
Equation of the line is,
y = -4x + 1
Hence the equation of the line is y = -4x + 1, when slope is -4 and y intercept is 1.
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If mary had 456 apple, and her iter had half of mary apple, and they both give half of their apple to their mom, nhow many apple doe the girl till have?
Answer:
Mary:228
iter:114
Step-by-step explanation:
Mary's "iter" would have 228 apples (half of what mary has) and would be left with 114 after giving half to her mother.
Mary would be left with 228 apples because 456/2=228.
What are the lines of longitude also called as Class 6?
Longitudes: The vertical lines running north-south, join the two poles. They are called the meridians of longitude. They are spaced farthest apart at the equator and converge at a point at each pole.
Horizontal lines called latitudes are used to measure distances north or south of the equator. Vertical lines known as longitudes are used to determine the west or east of the meridian in Greenwich, England. Latitude and longitude work together to help cartographers, geographers, and others find specific locations on the globe.
What is the uses of latitude?
Any location's distance from the equator may be determined using its latitude, which is based on its degree. We can locate any point on Earth using longitude and latitude. The GPS or Global Positioning System uses these coordinates.
The grid system that enables us to locate absolute or precise places on the surface of the Earth is made up of latitude and longitude. Latitude and longitude can be used to pinpoint certain locations. Landmark identification also benefits from knowledge of latitude and longitude.
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The total charge on 4 particles is −36 units. All the particles have the same charge. What is the charge on each particle? (3 points) a −9 units b −8 units c 8 units d 9 units
Use the origin as the center of dilation and the given scale factor to find the coordinates of the vertices of the image of the polygon.
k = 2
The coordinates of the points after dilation is P'(6,10), Q'(8,0), and R'(2,2).
What is dilation?Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size.
Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size.
Given that the scale factor is 2. The coordinates of the points after dilation is,
P(3,5) = P'(6,10)
Q(4,0) = Q'(8,0)
R(1,1) = R'(2,2)
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24. Mr. Karbon is 35 years old and his heart beats on average 62 beats per minute.
How many times has his heart been beating during his life? (assume there are no leap
years)
Mr. Karbon 1,14,05,52,000 times has his heart been beating during his life.
Adults typically have a resting heart rate between 60 and 100 beats per minute. A lower resting heart rate typically indicates improved cardiovascular fitness and more effective cardiac function. A well-trained athlete, for instance, might have a typical resting heart rate that is closer to 40 beats per minute.
Based on your age, you may calculate your maximum heart rate. Subtract your age from 220 to get a ballpark idea of your maximal age-related heart rate. For instance, the predicted maximum age-related heart rate for a 50-year-old person would be computed as 220 - 50 years = 170 beats per minute (bpm).
There are total 60 minutes in an hour,
1440 minutes in a day,
There are 365 days in a year,
and Mr. Karbon has lived for 35 years.
his heart beats on average 62 beats per minute.
His heart has beaten for 35 × 365 × 1440 × 62
1,14,05,52,000 times has his heart been beating during his life.
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A company launches two new products. The market price, in dollars, of the two products after a different number of years, x, is shown in the following table
Based on the data in the table, for which product does the price eventually exceed all others, and why? (1 point)
Product 1, because the function is exponential
Product 2, because the function is exponential
Product 1, because it has a greater start value
Product 2, because it has a greater Year 3 value
Answer:
Product 1, because the function is exponential
Step-by-step explanation:
An exponential function, such as f(x) = 3^x, grows very quickly.
Answer: Product 1, because the function is exponential
I need help with this! L, M belong on line KN
The value of x in the triangle is 38 degrees.
How to find angles in a triangle?A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.
The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.
The exterior angle theorem can be used to find the angle x in the triangle.
Hence,
x + (180 - 84) = 134
x + 96 = 134
subtract 96 from both sides of the equation
x = 134 - 96
Therefore,
x = 38 degrees
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Answer: x=38
Step-by-step explanation:
x=38
Juanita has saved 20% of the money that she needs to buy a new bicycle If she has saved $36 how much money does the bycycle cost
Answer:
$180
Step-by-step explanation:
20*5=100
36*5=180
Answer: the cost of the bicycle is 180$
Step-by-step explanation:
If Juanita has saved 20% of the money she needs to buy a new bicycle and she has saved $36, we can calculate the cost of the bicycle using the following formula:
(100% - 20%) x cost of bicycle = $36
To find the cost of the bicycle, we can divide both sides of the equation by 80% (100% - 20%), like this:
cost of bicycle = $36 / (100% - 20%)
We know that Juanita has saved $36 and the percentage saved is 20% , so the cost of the bicycle is $180
HELPPP AGAIN PLEASEE. What is the equation of the line that passes through the point (-6,5) and has a slope of -3/2?
Answer:
y - y1 = m(x - x1)
y - 5 = -3/2 [x - (-6) ]
2 (y - 5) = 2 × -3/2 [x - (-6) ]
2y - 10 = -3 [x + 6]
2y - 10 = -3x - 18
2y- 10 + 3x + 18 = 0
2y + 3x -10 + 18 = 0
2y + 3x + 8 = 0
Step-by-step explanation:
I stated the formula to find the equation of the line . Then replaced the y1 and x1 with -6 and 5 respectively. I multiplied the whole equation by the LCM, which is 2. Group the whole equation to the left and equate it to 0. Then group like terms and solve. The final answer is the equation of the line
m=-2/3b=-4 Write in slope intercept form, solve, graph
The equation for a slope of -2/3 and an intercept of -4 is 2x+3y+12=0.
What is equation?In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation. Linear equations are classified into three types: point-slope, standard, and slope-intercept.
Here,
y=mx+b
m=-2/3
b=-4
y=-2/3x+(-4)
y=-2x/3-4
3y=-2x-12
2x+3y+12=0
The equation for slope given as -2/3 and intercept as -4 is 2x+3y+12=0.
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one more than the difference between 18 and 7 times a number is -9
eight times a number plus 6 less than twice the number is 34
twelve less than the quotient of a number and 8 is -1
i don't think they're supposed to be fractions as going over the others in class didn't and tried checking over my work
Answer:
The difference between 18 and seven times a number: 18 - 7x
Step-by-step explanation:
(ii) One more than the difference between 18 and seven times a number:
Add 1 to the expression from step (i) and get
1 + (18 - 7x)
(iii) One more than the difference between 18 and seven times a number is -9:
Set expression from step (ii) equal to -9 and get
1 + (18 - 7x) = -9
You can simplify and solve for x.
For what value of k do the equation 3x 8y 0 and 6x Ky =- 16 represent coincident lines?
For what value of k = -48 the equation 3x 8y 0 and 6x Ky =- 16 represent coincident lines.
The equation 3x + 8y = 0 and 6x + Ky = -16 represent coincident lines when the two lines are identical, or when their slope and y-intercept are the same.
To find the value of k for which this is true, we can set the two equations equal to each other and solve for k.
3x + 8y = 0
6x + Ky = -16
The equation 3x + 8y = 0 represents the slope-intercept form of a line, where the slope is -3/8 and the y-intercept is 0.
The equation 6x + Ky = -16 represents the general form of a line, where the slope is -K/6 and the y-intercept is -16/K.
To find the value of k for which the two lines are identical, we need to make the slopes and y-intercepts equal.
-3/8 = -K/6
0 = -16/K
Solving for K, we get:
K = -48
So the lines are coincident when K = -48
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What is dilating by a scale factor?
The dilation transformation is determined by the scale factor and the centre of dilation. The image stretches when the scaling factor exceeds 1. When the scale factor is between 0 and 1, the image gets smaller.
What is scale factor of dilation?Ratio of scale (Dilation) How much larger or smaller the image will be depends on the scale factor in a mathematical object's dilatation (compared to the original object). When the scaling factor's absolute value exceeds 1, an expansion takes place.The x and y values of each point will be multiplied by 2 to enlarge the graphic by a factor of 2. To identify the new triangle, I plotted each new point. The x-value of each point will be multiplied by 2 to enlarge the image by a factor of two.A scale factor is defined as the ratio of an original object's scale to that of a new, smaller version of the original object.To learn more about dilation refer to:
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The dilation transformation is determined by the scale factor and the center of dilation. The image stretches when the scaling factor exceeds 1. When the scale factor is between 0 and 1, the image gets smaller.
What is scale factor of dilation?Ratio of scale (Dilation) How much larger or smaller the image will be depends on the scale factor in a mathematical object's dilatation (compared to the original object). When the scaling factor's absolute value exceeds 1, an expansion takes place.
The x and y values of each point will be multiplied by 2 to enlarge the graphic by a factor of 2. To identify the new triangle, I plotted each new point. The x-value of each point will be multiplied by 2 to enlarge the image by a factor of two.
A scale factor is defined as the ratio of an original object's scale to that of a new, smaller version of the original object.
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Why 5 Is it possible to construct a triangle with lengths of its sides as 4 cm 3 cm and 7 cm give reason for your answer?
It is not possible to construct a triangle with the given lengths (4,3,7).
A triangle is a polygon. It has three sides and three vertices. It is one of the famous shapes in geometry. A triangle has three vertices A, B, and C, and is denoted ΔABC.
Triangle Inequality Theorem :
The summation of the lengths of any two sides of a triangle is greater than the length of the third side.
Given three sides are 4,3,7cm
We know that the summation of two sides of a triangle is greater than the third side.
But given sides, 4+3=7 ( using addition)
Hence, it is not likely to construct a triangle with lengths of sides 4cm, 3cm, and 7cm.
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The triangles are similar. What is the value of x? enter your answer in the box. X = two right triangles. The larger right triangle is labeled x on the longer leg, 12 on the shorter leg and 20 on the hypotenuse. The smaller triangle is labeled 4 on the longer leg, 3 on the shorter leg, and 5 on the hypotenuse.
The value of x is 16 units.
The triangles which are alike have the same shape and the measure of the three angles are also the same. The only thing which varies is their edges. However, the ratio of the sides of one triangle is equivalent to the ratio of the sides of another triangle, that is called the scale factor.we know that
If two triangles are similar, then the ratio of their corresponding sides is equal and is called the scale factor.
According to the question,
The larger right triangle of the longer leg is x units.
so,
[tex]\frac{12}{3} = \frac{x}{4}[/tex]
⇒ [tex]x = \frac{12 * 4}{3}[/tex]
∴x = 16
Therefore, the value of x is 16 units.
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What is the accepted ratio * 1 point of an enlarged scale drawing?
Scale is represented as a ratio, such as 1:100. A drawing with a scale of 1:100 indicates that the thing is 100 times smaller than it would be in real life. You may also remark that one unit in the illustration equals one hundred units in real life.
What is the ratio of the larger scale?Enlarging scale indicates that the drawing is made with larger dimensions than the real dimensions of the thing. A representative proportion of 1:0.2 equals 5:1, implying that the depiction is five times larger than the actual thing. As a result, the scale is increasing in size.
On November 28, 2022, it was revised. A ratio scale is a quantitative scale with a real zero and equal gaps between nearby points. In contrast to an interval scale, a zero on a ratio scale indicates that the variable being measured is completely absent. Ratio scales include things like length, area, and population.
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Scale is represented as a ratio, such as 1:100. A drawing with a scale of 1:100 indicates that the thing is 100 times smaller than it would be in real life. You may also remark that one unit in the illustration equals one hundred units in real life.
What is the ratio of the larger scale?Enlarging scale indicates that the drawing is made with larger dimensions than the real dimensions of the thing. A representative proportion of 1:0.2 equals 5:1, implying that the depiction is five times larger than the actual thing. As a result, the scale is increasing in size.
On November 28, 2022, it was revised. A ratio scale is a quantitative scale with a real zero and equal gaps between nearby points. In contrast to an interval scale, a zero on a ratio scale indicates that the variable being measured is completely absent. Ratio scales include things like length, area, and population.
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Calculate the geometric mean return of the following data set: (Negative value should be indicated by a minus sign. Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.)
The geometric mean return of the given data set is 0.02.
The geometric mean return measures the compound rate of return over a period of time. It is calculated by taking the product of all the returns and then taking the nth root of the product, where n is the number of returns.
Formula: GMR = ((1+r1)(1+r2)…(1+rn))^1/n – 1
In this case, the data set is as follows:
r1 = 0.05
r2 = 0.03
r3 = -0.02
Using the formula above, the geometric mean return is calculated as:
GMR = ((1+0.05)(1+0.03)(1-0.02))^1/3 - 1
GMR = ((1.05)(1.03)(0.98))^1/3 - 1
GMR = (1.1394)^1/3 - 1
GMR = 0.0204
Therefore, the geometric mean return of the given data set is 0.02.
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M. Nichol’ cla i having a dicuion about Greek mythology. One tudent ay, "The influence of the godde Demeter can be found throughout Greek hitory and culture. She i the godde of the harvet a well a the cycle of life. " Which would be an appropriate follow-up quetion to ak thi tudent?
an appropriate follow-up quetion to ak thi tudent is the culture
M. Nichol’ cla i having a dicuion about Greek mythology.. She i the godde of the harvet a well a the cycle of life.
What is the follow-up question to be asked?
M. There are four basic theories of myth. Those theories are: the rational myth theory, functional myth theory, structural myth theory, and the psychological myth theory.. Nichol’ cla i having a dicuion about Greek mythology.
What are the 3 biggest Greek gods?
Especially the “big three”. Zeus, Poseidon, and Hades.
an appropriate follow-up quetion to ak thi tudent is the culture
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how to find the acute angle of each angle in a triangle if the given angles are in the form of an equation
To find the acute angle of each angle in a triangle if the given angles are in the form of an equation follow the steps in the main answer part
What is the acute angle?To find the acute angles of a triangle given the angles in the form of an equation, you can use the following steps:
Write down the equation for the triangle's angles, typically in the form of "angle A + angle B + angle C = 180 degrees".Use the equation to solve for one of the angles. For example, if the equation is "angle A + angle B + angle C = 180 degrees", you can solve for angle A by subtracting angle B and angle C from 180 degrees.Repeat step 2 for the other angles.Check if the angles are acute or not. An acute angle is an angle that measures less than 90 degrees.If an angle is not acute, use the property of the triangle that the sum of all the angles is 180° and subtract the angle from 180° to get the acute angle.Example: Let's say you are given an equation,
A+B+C = 180°
If
A = 70°
B = 70° then
C = 40°
C is not acute, so subtract it from 180° to get C= 140°
Now you have A = 70° and C = 140° which are acute angles.
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