To prove the isosceles triangle theorem, you must use the fact that the base angles of an equilateral triangle have equal measure, and then use the properties of isosceles triangles to show that the two angles opposite the equal sides are also equal.
To prove the isosceles triangle theorem, we can follow these steps:
Step 1: Draw an isosceles triangle with sides AB and AC of equal length.
Step 2: Draw a line from point A to point D, perpendicular to line BC.
Step 3: Use the definition of an isosceles triangle to state that ∠ABD and ∠ACD are congruent.
Step 4: Use the definition of a perpendicular line to state that ∠ADB and ∠ADC are congruent.
Step 5: Use the definition of a triangle to state that ∠BAC and ∠BAC are congruent.
Step 6: Use the Congruent Triangles Postulate to state that triangle ABD and triangle ACD are congruent.
Step 7: Use the definition of congruent triangles to state that ∠ABC and ∠ACB are congruent.
Step 8: Use the definition of an isosceles triangle to conclude that the isosceles triangle theorem is true.
Therefore, we have proven the isosceles triangle theorem, which states that the base angles of an isosceles triangle are congruent.
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Neron Co. Has two derivatives related to two different financial instruments, instrument A and instrument B, both of which are debt instruments. The derivative related to instrument A is a fair value hedge, and the derivative related to instrument B is a cash flow hedge. Neron experienced gains in the value of instruments A and B due to a change in interest rates. Which of the gains should be reported by Neron in its income statement?Gain in value of debt instrument A Gain in value of debt instrument BYes YesYes NoNo YesNo No
Only the gains from the fair value hedge related to instrument A should be reported by Neron in its income statement.
About the reportNeron Co. should report the gains from the fair value hedge related to instrument A in its income statement. This is because fair value hedges are used to offset changes in the fair value of a financial instrument, and any gains or losses from these hedges are recognized in income.
On the other hand, gains from the cash flow hedge related to instrument B should be reported in other comprehensive income, not in the income statement.
This is because cash flow hedges are used to offset changes in the cash flows of a financial instrument, and any gains or losses from these hedges are recognized in other comprehensive income until the hedged item affects income.
Therefore, only the gains from the fair value hedge related to instrument A should be reported by Neron in its income statement.
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Which shapes from the Clade Race would be considered autoapomorphic?a. Arrow b. Circle c. Moon d. Triangle e. Square f. Crossg. Star h. Heati. Hexagon
Answer:
Step-by-step explanation:
f
On a coordinate plane, a curved line with a minimum value of (negative 1, negative 2), crosses the x-axis at (negative 2, 0) and the y-axis at (0, 0).
Determine the x-intercepts of the function. Check all that apply.
(–2, 0)
(–1, –2)
(0, 0)
(1, 0)
(2, 0)
x-intercepts of the curved line are (-2,0) and (0,0)
What is intercept ?The points where a line or curve intersects the chart's axes are called intercepts. When a point intersects the x-axis it is called the x-intercept. When a point intersects the y-axis, it is called the y-intercept.
A line intercept is a point where it intersects the x-axis or the y-axis. If no axis is specified, the y-axis is normally considered. It is usually represented by the letter 'b'.
Given,
A curved line with a minimum value of (-1 , -2)
it crosses x-axis at (-2,0) and y-axis at (0,0)
We know that, x-intercept is the point where line crosses x-axis, y-coordinate = 0
x-intercepts are (-2,0) and (0,0)
Hence, (-2.0) and (0,0) are x-intercepts of the curved line.
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Answer: (–2, 0), (0, 0)
Step-by-step explanation:
The odds against winning $1. 00 in the lottery are 19 to 1. What is the probability of winning $1. 00 in the lottery?.
The probability of an event can be calculated from the odds against that event. The formula for converting odds against to probability is:
Probability = 1 / (1 + odds against)
So in this case, the odds against winning $1.00 in the lottery are 19 to 1, and the probability of winning can be calculated as follows:
Probability = 1 / (1 + 19) = 1 / 20 = 0.05
So the probability of winning $1.00 in the lottery is 0.05, or 5%.
The line passing through the points ( -4, 6) and ( b, 2) has a gradient 1 /2 . Find the value of b.
Answer:
b = - 12
Step-by-step explanation:
calculate the slope of the line passing through the 2 points and equate to [tex]\frac{1}{2}[/tex]
calculate the slope ( gradient ) m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (4, 6 ) and (x₂, y₂ ) = (b, 2 )
m = [tex]\frac{2-6}{b-(-4)}[/tex] = [tex]\frac{-4}{b+4}[/tex]
equating gives
[tex]\frac{-4}{b+4}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
b + 4 = - 8 ( subtract 4 from both sides )
b = - 12
At Santorini's Shakes, a regular milkshake costs $3.50. A larger milkshake can be purchased for an additional $0.40 per ounce above the regular size.
If x represents the number of ounces above the regular size, which inequality shows how much can be added to the regular size for a milkshake that costs under $5.00?
Answer:
5=0.40x+3.50
He can get 3 extra ounces
Step-by-step explanation:
5.00-3.50=1.50 so an extra $1.50 to spend on extra ounces
1.50/0.40=3
0.40(3)+3.50= $4.70
So the most ounces he can get is 3
He will have $0.30 left
There were 175
spectators at a concert. The box office sold 10
more adult tickets than twice the number of discounted student tickets.
How many more adults than students bought tickets to the concert?
There were 65 more adults than students who bought tickets to the concert.
How to find the number of hamburgers sold on Saturday?Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.
Let the number of discounted student tickets sold be x.
Then the number of adult tickets sold is 10 more than twice x, which is 2x+10.
The total number of tickets sold is the sum of the student and adult tickets, which is x + (2x+10) = 3x+10.
We know that the total number of tickets sold is 175, so:
3x+10 = 175
Subtracting 10 from both sides gives:
3x = 165
Dividing by 3 gives:
x = 55
Thus, the number of discounted student tickets sold is 55, and the number of adult tickets sold is:
2x+10 = 2(55) + 10 = 120.
The number of adults who bought tickets is 120, and the number of students who bought tickets is 55.
difference = 120 - 55 = 65
Therefore, there were 65 more adults than students who bought tickets to the concert.
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calculate 0.069 x 7000
Answer:
483
Step-by-step explanation:
Answer:483
Step-by-step explanation:
69*7=483
x^-5y^3 negative exponents
The solution is x^-5y^3 = y^3/x^5.
What is an exponent in math?An exponent refers to the number of times a number is multiplied by itself. For example, 2 to the 3rd (written like this: 23) means: 2 x 2 x 2 = 8. 23 is not the same as 2 x 3 = 6. Remember that a number raised to the power of 1 is itself.
here, we have,
given that,
x^-5×y^3
[ as, the power of x is negative 5, so, we make it positive 5 by dividing}
=1/x^5 * y^3
=y^3/x^5
Hence, The solution is x^-5y^3 = y^3/x^5.
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The table below represents a linear function for the cost of a gym membership based on the number of months of membership.
Time (month) Cost
1 $105
3 $165
5 $225
7 $285
What is the slope and y-intercept of the linear function?
The slope is ____ and the y-intercept is ___.
Answer:
The slope is 30, and the y-intercept is 75.
Step-by-step explanation:
Use two points from the table, and find the equation of a line given two points.
Point 1: (1, 105)
Point 2: (3, 165)
y = mx + b
slope = m = (y_1 - y_1)/(x_2 - x_1)
m = (165 - 105)/(3 - 1) = 60/2 = 30
y = 30x + b
Use point (1, 105) for x and y.
105 = 30(1) + b
105 = 30 + b
b = 75
y = 30x + 75
The slope is 30, and the y-intercept is 75.
The box plots shows the number of books read by students in Mrs. Long's class
this summer. What is the median number of books read in Mrs. Long's class?
O 3 books
O 6 books
O 8 books
O 9 books
Answer:
8 books
Step-by-step explanation:
On a box plot, there is a line in the middle that says where the median is. In this situation, the median is 8.
The position of a ball after it is thrown is modeled with the
function f(x) = -2(x - 1)² + 7 in vertex form, where y is
the height, in feet, above the ground and x is the horizontal
distance, in feet, of the ball from where it is thrown.
A. Write the function in standard form.
B. What is the height of the ball when it is thrown?
C. What is the horizontal distance from the point where the ball is thrown to the highest point that the ball reaches?
(a) The function in standard form is f(x) = -2x² + 4x + 5.
(b) The height of the ball when it is thrown is 5 feet.
(c) The horizontal distance from the point where the ball is thrown to the highest point that the ball reaches is 1 foot.
What is the function of ball's motion?
To write the function in standard form, we need to expand the square and simplify the expression:
f(x) = -2(x - 1)² + 7
f(x) = -2(x² - 2x + 1) + 7
f(x) = -2x² + 4x - 2 + 7
f(x) = -2x² + 4x + 5
B. The height of the ball when it is thrown is the y-intercept of the function, which occurs when x = 0. So we can find the height by plugging x = 0 into the function:
f(0) = -2(0)² + 4(0) + 5
f(0) = 5
C. The highest point that the ball reaches is the vertex of the parabola, which occurs at x = 1 (from the given vertex form). To find the height of this point, we can plug x = 1 into the vertex form of the function:
f(1) = -2(1 - 1)² + 7
f(1) = -2(0) + 7
f(1) = 7
Therefore, the highest point that the ball reaches is 7 feet above the ground. The horizontal distance from the point where the ball is thrown to this point is the distance between the point (0,5) and the vertex (1,7), which is 1 unit.
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What is the value of 350f in c?
The temperature 350°F is equivalent to 176.667°C. This is because the temperature in Fahrenheit can be converted to Celsius using the formula, °C = (°F - 32) / 1.8. Using this formula, 350°F - 32 = 318 and 318/1.8 = 176.667°C.
The relationship between Fahrenheit and Celsius scales is a linear one, meaning that for every degree increase in Fahrenheit, there is a corresponding increase of 1.8 degrees in Celsius. This means that if the temperature increases from 350°F to 351°F, then the corresponding temperature in Celsius would increase from 176.667°C to 178.472°C. The same formula can be used to convert Celsius to Fahrenheit, with the formula °F = (°C x 1.8) + 32. In this case, 176.667°C x 1.8 = 319.2 and 319.2 + 32 = 351.2°F, which is a close approximation of the original temperature of 350°F..
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Say you have a single pair of pants and a single shirt. In this case you'd only have 1 outfit option.
If you have 2 pairs of pants and 2 shirts, you now have 4 unique outfit options.
How many pairs of pants and shirts would you need in order to have a unique outfit for each day of the week?
What if you wanted a unique outfit each day for a month? for a year? for your whole life
To have a unique outfit for each day of the week, you would need at 3 pairs of pants and 3 shirts.
To have a unique outfit for a month you would need at 6 pairs of pants and 5 shirts.
To have a unique outfit for each day of the year, you would need 26 pairs of pants and 15 pairs of shirts.
How to find the unique outfits ?To find the unique outfits, you need to have enough clothes to have a unique outfit made from those clothes.
There are 7 days in a week. If you had 3 pairs of pants and 3 shirts, the unique outfits would be :
= 3 x 3
= 9 unique outfits
For a month :
= 6 x 5
= 30 unique outfits
For a year :
= 26 x 15
= 390 unique outfits for 365 days
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When the car reaches point (A), it has a speed of 25 m/s. If the breaks are applied, its speed is reduced by at= (-1/4t^1/2)m/s^2. Determine the magnitude of acceleration of the car just before it reaches point C
The magnitude of acceleration of the car just before it reaches point C is -0.79 m/s^2.
About magnitude of accelerationThe magnitude of acceleration of the car just before it reaches point C can be calculated using the given formula for acceleration, at= (-1/4t^1/2)m/s^2.
First, we need to determine the time it takes for the car to travel from point A to point C.
Since the speed of the car at point A is 25 m/s, and the speed at point C is 0 m/s, we can use the formula for speed, v=at, to find the time it takes for the car to travel from point A to point C.
Rearranging the formula, we get t=v/a.
Substituting the values for speed and acceleration, we get t=25/(-1/4t^1/2).
Solving for t, we get t^3/2 = -100.
Taking the square root of both sides, we get t=10 seconds.
Now, we can substitute the value of t back into the formula for acceleration to find the magnitude of acceleration just before the car reaches point C.
at= (-1/4t^1/2)m/s^2
= (-1/4)(10^1/2)m/s^2
= (-1/4)(3.16)m/s^2
= -0.79 m/s^2
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Karen drove 335 miles in 5 hours.
At the same rate, how many miles would she drive in 11 hours?
Answer: 737 miles
Step-by-step explanation: 335/5=x/11.
Cross Multiply and divide to get x=737
Someone help me pls
Answer:
W) 1/18=10/180
N) 2/15=4/30
F) 7/12= 84/144
S) 9/25= 36/100
D) 7/20=35/100
T) 9/10=36/40
M) 19/20=95/100
Step-by-step explanation:
W) is 10/180 as you need to multiply the numerator as the denominator.
N) is 4/30 as you need to multiply the numerator as the denominator.
F) is 84/144 as you need to multiply the numerator as the denominator.
S) is 36/100 as you need to multiply the numerator as the denominator.
D) is 35/100 as you need to multiply the numerator as the denominator.
T) is 36/40 as you need to multiply the denominator as the numerator.
M) is 95/100 as you need to multiply the numerator as the denominator.
What are the domain and range of this linear function? f(x)=2x-5
Answer:
The Domain : {(−∞,∞), {x/x∈R} and Range : {(−∞,∞), {y/y∈R} of the function f(x)=2x-5
What is a function?
A relation is a function if it has only One y-value for each x-value.
We have to find the domain and range of f(x)=2x-5
The domain of the expression is all real numbers except where the expression is undefined.
In this case, there is no real number that makes the expression undefined.
Interval Notation:(−∞,∞)
The range is the set of all valid y values.
Domain : {(−∞,∞), {x/x∈R}
Range : {(−∞,∞), {y/y∈R}
Hence, the Domain : {(−∞,∞), {x/x∈R} and Range : {(−∞,∞), {y/y∈R} of the function f(x)=2x-5
Have a wonderful day! :-)
If the vertex of the graph of y = −1(x − 2)2 + 3 is (a,b) what is the value of b?
Answer:
the value of b is 3.
Step-by-step explanation:
The vertex of the graph of a parabola in the form y = a(x - h)^2 + k is given by (h, k), where h is the x-coordinate of the vertex and k is the y-coordinate of the vertex.
So in this case, the vertex of the graph of y = -1(x - 2)^2 + 3 is (2, 3), and the value of b is 3.
Answer:
b=3
Step-by-step explanation:
[tex]y=a(x-h)^2+k\\y=-1(x-2)^2+3[/tex]
If we compare the vertex-form equation of a parabola to our given function, we can see the vertex is [tex](2,3)[/tex], which means that b=3.
Today hugo got a new credit card, and he made a purchase of $1400. The card offers an introductory apr of 0% for the first 5 months and a standard apr of 30. 8% thereafter. If the card compounds interest monthly, how much money will the introductory apr save hugo in interest over the first 5 months? (assume that hugo will make no payments or additional purchases during the first 5 months, and ignore any possible late payment fees. ).
$189.13
That's the correct answer On Ax
Answer:
$189.13
Step-by-step explanation:
You want to know the interest saved if interest at 30.8% compounded monthly on a balance of $1400 is waived for 5 months.
Compound interestThe balance with interest compounded would be ...
A = P(1 +r/12)^n
where P is the principal earning interest at annual rate r for n months.
The amount of interest earned in that time is ...
I = P((1 +r/12)^n -1) = $1400(1 +0.308/12)^5 -1) ≈ $189.13
Hugo will save $189.13 in interest charges for the first 5 months.
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For any given event, the probability of that event and the probability of the _______ of the event must sum to one.
For any given event, the probability of that event and the probability of the non-occurrence of the event must sum to one.
A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.
The probability of occurrence formula, also known to some as the “probability of occurrence formula PMP” is a tool for determining the chance that a given risk will occur. The formula requires two data points: number of favourable events possible and the total number of events possible.
Non occurrence patterns identifies the absence of events when detecting a pattern.
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Find the value of X so that the expression X(4-2Y) is equivalent to 2/3 - 1/3Y.
The equivalent expression for the given expression -x²+5x-4 is (x-4)(x-1).
The given expression is c² - 64.
What is the equivalent expression?
Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
1) The factorization of c² - 64 is as follows:
Now, factors of c² - 64 is c² - 8²=(c-8)(c+8)
2) 12y² -75 = 3 (4y²-25)
= 3((2y)²-5²)
= 3 (2y+5)(2y-5) (∵ a²-b²=(a-b)(a + b))
3) 9y²-36 = 9(y²-4)
= 9(y²-2²)
= 9(y-2)(y+2) (∵ a²-b²=(a-b)(a + b))
4) -x²+5x-4
= x²-5x+4
= x²-4x-x+4
= x(x-4)-1(x-4) (∵ a²-b²=(a-b)(a + b))
= (x-4)(x-1)
5) ab²-b
=b(ab-1)
Therefore, the equivalent expression for the given expression -x²+5x-4 is (x-4)(x-1).
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Which graph matches the equation y+6=3/4 (x+4)?
Answer: The equation y + 6 = 3/4 (x + 4) can be solved for y to find the corresponding graph:
First, isolate x by subtracting 4 from both sides:
y + 6 - 6 = 3/4 (x + 4) - 6
y = -6 + 3/4 (x + 4)
Next, isolate y by dividing both sides by 3/4:
y = -6 + 3/4 (x + 4) ÷ (3/4)
y = -6 + (x + 4)
y = x - 2 + 10
This equation represents a line with a slope of 1 and a y-intercept of 10 - 2 = 8. The graph of this line is a line that passes through the points (0, 8) and (1, 9).
Step-by-step explanation:
An airplane takes 7 hours to fly 2800 kilometers against the wind. The return trip with the wind takes only 4 hours. What is the speed, in kilometers per hour, of the airplane in still air?
Answer: Let's call the speed of the airplane in still air "x".
Since the airplane takes 7 hours to fly 2800 kilometers against the wind, its speed against the wind is 2800/7 = 400 km/hr.
Since the return trip with the wind takes only 4 hours, the speed of the wind must be 400 - x.
The total speed of the airplane on the return trip is x + (400 - x) = 400 km/hr.
So, we have:
400 = x + (400 - x)
Expanding the right side:
400 = 400
Therefore, x = 400 km/hr, which is the speed of the airplane in still air.
Step-by-step explanation:
A. x = 80 degrees
B. x = 60 degrees
C. Cannot be determined
D. x = 30 degrees
The measure of the angle is 60 degrees. Option B
How to determine the value of the variableIt is important to value of the angle, we have to take note of the following;
The sum of angles on a straight line is equivalent to 180 degreesThe pair of angles are also supplementary to each otherFrom the information given, we have that;
The angles 80,690 and x are on a straight line, that is, the sum of the angles is 180
This is represented as;
60 + 80 + x = 180
collect like terms
x = 180 - 140
substract the like terms
x = 60 degrees
Hence, the value is 60 degrees
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what is 100.8 f to c?
Using the formula to convert Fahrenheit to Celsius, we get that 100.8°F is 38.22°C.
To convert 100.8°F to °C, we can use the formula:
°C = (°F - 32) x 5/9
Plugging in the value of 100.8°F, we get:
°C = (100.8 - 32) x 5/9
°C = 68.8 x 5/9
°C = 38.22
Therefore, 100.8°F is equal to 38.22°C.
This formula is used to convert temperatures between the Fahrenheit and Celsius scales. It involves subtracting 32 from the Fahrenheit temperature and then multiplying by 5/9 to obtain the equivalent Celsius temperature. The resulting Celsius temperature is then rounded to the nearest tenth. It's important to note that Fahrenheit and Celsius are two different temperature scales, where 0°C is equal to 32°F, and 100°C is equal to 212°F. The Celsius scale is based on the freezing and boiling points of water, whereas the Fahrenheit scale is based on the freezing and boiling points of a solution of salt and water. Knowing how to convert between these two scales can be useful in a variety of settings, including cooking, weather reporting, and scientific research.
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The September price of a computer was $1000. Later, an October price was obtained by raising the September price by 20%. Then a November price was obtained by lowering the October price by 20%. What was the November price in dollars?
Answer:
Step-by-step explanation:
1200
Answer:
$960
Step-by-step explanation:
September = 1000
20% * 1000 = 200
1000+200 = 1200
October = 1200
20% * 1200 = 240
1200-240 = 960
November = 960
Triangle ABC is similar to triangle FGH. Given the following angle measures, find the
missing angle measures.
mLA = 22 degrees
mzB = 75 degrees
Enter your answers as numbers only.
m₂F=
mzH=
degrees
degrees
m² G=
----_ degrees
m₂C= degrees
-----
The missing angle measures are:
m2F = 50 degrees
m2H = 125 degrees
m2G = 5 degrees
m2C = 158 degrees
How to find the missing angle measures?
Since triangle ABC is similar to triangle FGH, the ratios of their corresponding angles are equal. Let's call the missing angles m2F, m2H, m2G, and m2C.
From the given information, we have:
m2F / mLA = m2H / mzB
So, we can find m2H by cross-multiplying and solving for m2H:
m2H = (mzB * m2F) / mLA
Since we don't know m2F, we can use the fact that the sum of the angles in a triangle is 180 degrees:
m2F + m2H + 75 = 180
So,
m2F + ((mzB * m2F) / mLA) + 75 = 180
Expanding and solving for m2F:
m2F + (75 * m2F / 22) + 75 = 180
(22 + 75) * m2F / 22 + 75 = 180
97 * m2F / 22 + 75 = 180
97 * m2F / 22 = 180 - 75
97 * m2F / 22 = 105
m2F = 105 * 22 / 97 = 50
So, the missing angle measures are:
m2F = 50 degrees
m2H = (75 * 50) / 22 = 125 degrees
m2G = 180 - 50 - 125 = 5 degrees
m2C = 180 - 22 = 158 degrees
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10. Find the distance of the line segment RS with R(-2, 3) and S(4, 5) in simplest radical form.
The distance between the points in simplest radical form is equal to 2√10 units.
How to calculate the distance between the two points?Mathematically, the distance between two (2) points that are on a coordinate plane can be calculated by using this formula:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Where:
x and y represents the data points (coordinates) on a cartesian coordinate.
Substituting the given parameters into the distance formula, we have the following;
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Distance = √[(4 - (-2))² + (5 - 3)²]
Distance = √[6² + 2²]
Distance = √[36 + 4]
Distance = √40
Distance = 2√10 units.
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Round 29.675 to
the hundredths place.
Answer:
29.68
Step-by-step explanation:
If you are rounding to the hundredth place, you take the number in the hundredth place and round it. If it is less than five, for example, if you were rounding 29.674 then it would be 29.67 because 4 is not 5 or more. With 29.675 you will round to 29.68. A saying to remember is, five or above, give it a shove.