Example 4 PH00F Write a two-column proof of Theorem 4.3 .
Answers
The proof of Theorem 4.3 with an example is shown.
What is theorem 4.3?Third Angles Theorem: If two angles of one triangle are congruent with two angles of another triangle, then the third angles must be congruent as well.To prove Theorem 4.3:
Let,s take two triangles, that is △ABC and △ADC.
In which AC⊥BD so ∠ACB ≅∠ACD.As, AC bisects ∠A so, ∠BAC ≅ ∠DAC.Since two pairs of angles are congruent, then the △ABC≅△ADC is under AA condition.
Then, ∠B≅∠D under CPCT condition (corresponding parts of congruent triangles).Therefore, the proof of Theorem 4.3 with an example is shown.
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Related Questions
a. If T U=14 feet, what is the radius of ®Q ?
Answers
If TU = 14 feet, then the radius of the circle is 7 feet.
What is meant by radius?
The radius of a circle is the distance between the circle's center and any point on its circumference. It is usually represented by the letters 'R' or 'r'.
A radius of a circle or sphere is any of the line segments from its center to its perimeter in classical geometry, and in more modern usage, it is also their length.
Simply dividing the circle's diameter in half yields the radius formula. If we connect the points on the circle's circumference to the exact center.
Let the radius of the circle be TU = 14 feet
Radius of the circle = c/2
Where, c = 14 then substitute the value in the above equation, then
r = 14/2
r = 7 feet
Therefore, the radius of the circle is 7 feet.
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Two similar cylinders have heights of 35 meters and 25 meters. What is the ratio of the volume of the large cylinder to the volume of the small cylinder?
Answers
The ratio of the volumes of two similar cylinders with heights of 35 meters and 25 meters, respectively, is 2.744.
Solids of the same type that have proportional corresponding linear
measures are similar solids. In the case of similar cylinders:
height of A/ height of B = radius of A/radius of B
If two solids are similar, then the ratio of their volumes is equal to the cube of the ratio of their corresponding linear measures.
volume of A/ volume of B = (height of A/ height of B)^3 = (radius of A/radius of B)^3
If two similar cylinders have heights of 35 meters and 25 meters, then the ratio of the volume of the large cylinder to the volume of the small cylinder is:
height of larger cylinder / height of smaller cylinder = 35 meters / 25 meters = 7/5
volume of larger cylinder/ volume of smaller cylinder = (height of larger cylinder / height of smaller cylinder)^3 = (7/5)^3 = 2.744
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Given ABCD, solve for x.
Answers
Answer:
D. 1
Step-by-step explanation:
16+2x = 10+8x
6 = 6x
x = 1
BC and AD parallel and congruent (=) to each other
Solve each equation. Check your answers. 0.2(x+8)-3.4=2.4
Answers
The solution to given equation 0.2(x + 8) - 3.4 = 2.4 is x = 21
In this question, we have been given an equation 0.2(x+8)-3.4=2.4
We need to solve given equation.
0.2(x + 8) - 3.4 = 2.4
0.2x + 1.6 - 3.4 = 2.4
0.2x - 1.8 = 2.4
0.2x = 2.4 + 1.8
0.2x = 4.2
x = 21
We need to check above solution.
Substitute x = 21 in LHS of given equation.
LHS
= 0.2(21 + 8) - 3.4
= 0.2(29) - 3.4
= 5.8 - 3.4
= 2.4
= RHS
Therefore, the solution to given equation 0.2(x + 8) - 3.4 = 2.4 is x = 21
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Solve the word problems
1) There are 45 red balloons, 85 blue balloons and
120 yellow balloons. How many red and blue
balloons are there altogether?
(Show your work)
Answers
Answer:
add the red and the blue balloons
45+85=130
simplify 11 root square 8
11) √8
Answers
Answer: 2.82842712 or 2[tex]\sqrt{2}[/tex]
Step-by-step explanation:
solve for u and simplify your answer. using reciprocals
-23 = -3/2 u
Answers
U = 3/46 is reciprocal of the solution of equation .
What is reciprocal in math?
The definition of reciprocal in mathematics is the inverse of a value or a number. If n is a real number, then 1/n will be n's reciprocal. Therefore, we must change the number to its upside-down form. For instance, 1 divided by 9 is the reciprocal of 9, or 1/9.Making up or coming from paired crosses where the sort that provides the female parent for the first cross also provides the male parent for the second cross, and vice versa.-23 = -3/2 u
-1/23 = -2/3u
cross multiply
-3 = -46 u
u = -3/-46
u = 3/46
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Find the diameter and radius of a circle with the given circumference. Round to the nearest hundredth.
C = 375.3 cm
Answers
A circle is a curve sketched out by a point moving in a plane. The radius and the diameter of the circle are 59.73 cm and 119.46 cm, respectively.
What is a circle?A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the center.
Given that circumference of the circle as 375.3 cm. Therefore, the radius and the diameter of the circle can be written as,
Circumference of circle = 2 × π × (Radius of the circle)
375.3 cm = 2 × π × (Radius of the circle)
(Radius of the circle) = 375.3cm/ (2 × π)
The radius of the circle = 59.73 cm
Diameter of circle = 2 × (Radius of the circle)
= 2 × 59.73 cm
= 119.46 cm
Hence, the radius and the diameter of the circle are 59.73 cm and 119.46 cm, respectively.
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David has 10 cent pieces in one pocket and 25 cent pieces in the other pocket. if he has the same amount of money in each , what is the least amount he can have in each pocket
Answers
25 is not divisible by 10
The length of the rectangle is three times its width. If the perimeter of the rectangle is one hundred and sixty meters, find the length and width of the rectangle. Enter two integers
Answers
Answer:
Please give brainliest if it applies!
w = 20m
l = 60m
Step-by-step explanation:
P = 2l + 2w
We know the perimeter = 160 and we know that l = 3w, so write what we know and solve for w.
P = 2l x 2w
160 = 2(3w) + 2w
160 = 6w + 2w
160 = 8w
Divide both sides by 8
20 = w
Now we can figure out the length, which is 3(w) or 3 x 20 = 60
Write an equation of each line.slope =5 ; through (0,2)
Answers
The equation of the line, with slope equal to 5 and passing through the point located at (0 , 2), is 5x - y = -2.
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).
Using the point slope form, plug in the values to set up the equation.
(y - y1) = m(x - x1)
where m = 5 and (x1 , y1) = (0 , 2)
(y - 2) = 5(x - 0)
y - 2 = 5x
In slope-intercept form, the equation of the line is:
y - 2 = 5x
y = 5x + 2
In standard form, the equation of the line is:
y = 5x + 2
5x - y = -2
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Find m/_1 and m/_2. Justify each answer
Answers
angle 1 is 50° and angle 2 is 130°
for the second one;
angle 1 is 79° and angle 2 is 101°
I need this answered please
Answers
12g - 8
We get 12g from multiplication rules because when a coefficient is present, we always have to multiply the number and variable by each other.
The phrase “eight less than” is written as “[insert value] - 8” because we are subtracting 8 from the value.
The representation of the phrase in algebraic form is:
12g - 8 or (12g) - 8
Solve the following inequality algebraically.
x^2-3x-70< 0
Answers
Answer:
-7<x<10
Step-by-step explanation:
trust :)
which value of x makes lines r and s parellel
Answers
Answer:
75
Step-by-step explanation:
If two lines and a transversal form same-side interior angles that are supplementary, then the two lines are parallel
x + 25 + 80 = 180
x = 180 - 80 - 25
x = 75
Suppose you have an outdoor pool measuring 25 ft by 10ft . You want to add a cement walkway around the pool. If the walkway will be 1 ft thick and you have 304 ft³ of cement, how wide should the walkway be?
Answers
The area covered by the pool and the cement walkway is 304 square feet. The width of the walkway would be 5 feet
What is the area of the rectangle?The area of the rectangle is the product of the length and width of a given rectangle.
The area of the rectangle = length × Width
Let x be represent the width of the walkway.
The pool measures 25 ft by 10ft . If the walkway must have a uniform width around the entire pool, then the total length of the pool and the walkway = 25+ x + x = 25 + 2x
The total width of the pool and the walkway = 10 + x + x = 10 + 2x
The area covered by the pool and the cement walkway is 304 square feet. This means that;
(25 + 2x)(10 + 2x) = 304
250 + 50x + 20x + 4x^2 = 304
4x^2 + 70x + 250 - 304 = 0
4x^2 + 70x - 54 = 0
x(x + 20) - 5(x + 20) = 0
(x - 5)(x + 20) = 0
x = 5 or x = - 20
Thus The width cannot be negative.
Therefore, the width of the walkway is 5 feet.
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How do you bisect an angle using compass and straightedge moves
Answers
Step-by-step explanation:
Open your compass to any radius r, and construct arc (K, r) intersecting the two sides of angle K at A and B.Open your compass to any radius r, and construct arc (K, r) intersecting the two sides of angle K at A and B.Use any radius s to construct arc (A, s) and arc (B, s) that intersect each other at point Z. Note that you must choose a radius s that's long enough for the two arcs to intersect.Open your compass to any radius r, and construct arc (K, r) intersecting the two sides of angle K at A and B.Use any radius s to construct arc (A, s) and arc (B, s) that intersect each other at point Z. Note that you must choose a radius s that's long enough for the two arcs to intersect.Draw line KZ and you're done.Given p(x)= −2(x−5) 2 + 4, what is the value of p(4)?
Answers
p(4)= 8
because
-2(x-5)2+4
-2(4-5)2+4
-8+10+2+4
2+2+4=8
At a local department store, sweaters are typically priced at $25. Due to a special, the sweaters are reduced to 80% of their original price. How much are the sweaters now? Round your answer to the nearest whole number if necessary.
PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
The sweaters are now $20.
Step-by-step explanation:
$25 × .8 = $20
how to i solve 2/15
Answers
Answer:
2/15 = 2/
15
≅ 0.1333333
Step-by-step explanation:
Rules for expressions with fractions:
Fractions - use a forward slash to divide the numerator by the denominator, i.e., for five-hundredths, enter 5/100. If you use mixed numbers, leave a space between the whole and fraction parts.
Mixed numerals (mixed numbers or fractions) keep one space between the integer and
fraction and use a forward slash to input fractions i.e., 1 2/3 . An example of a negative mixed fraction: -5 1/2.
Because slash is both signs for fraction line and division, use a colon (:) as the operator of division fractions i.e., 1/2 : 1/3.
Answer:
for a decimal its 0.13 for a percent its 13.33%
Step-by-step explanation:
What is the probability of rolling a number less than 3? express your answer as a simplified fraction or a decimal rounded to four decimal places.
Answers
The probability of rolling a number less than or equal to 3 is 0.5.
What is the probability of rolling a number?The likelihood of getting any side of the dice is 1/6 because there are six possible results. Rolling a 1 has a 1/6 chance of happening, a 2 has a 1/6 chance, and so on.The sum of the three probabilities equals 1/36, or the likelihood that all three will occur.A dice has only 6 sides, and only 1 of those sides is 6, meaning there are 16 chances to roll a 6.63 + 216 = total number of outcomes. When a die is rolled, there is a 1/6 chance of rolling a 4.What is the probability of rolling a number less than 3?
Event: The collection or the set of outcomes in an experiment is called as an event.
Outcomes: The possible results of a trail in an experiment are called as outcome.
Probability:
The ratio of the number of favorable outcomes to certain event and the total number of possible outcomes is called as the probability of an event.
The probability of rolling a number less than or equal to 3 is obtained by taking the ratio of the number of favorable outcomes by the total number of outcomes. It is expected about 50% of times that rolling a number less than or equal to 3.
The probability of rolling a number less than or equal to 3 is 0.5.
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Write the specified type of proof.
flow proof
Given: K || LM, JL || KM
Prove: ΔJ M L≅ ΔM J K
Answers
We can state that ΔJML ≅ ΔMJK under SSS condition.
What specifically do we mean by a triangle's congruency?Two triangles are said to be congruent if their three corresponding sides are equal and their three corresponding angles are equal in size.These triangles can be moved, rotated, flipped, and turned to appear identical.If they are repositioned, they will coincide.Two triangles are congruent if they satisfy all five congruence conditions.They are side-side-side (SSS), side-angle-side (SAS), angle-side-angle (ASA), angle-angle-side (AAS), and right angle-hypotenuse-side (RHS).
So,
Given: KJ || LM, JL || KM
To Prove: ΔJML ≅ ΔMJK
KJ = ML = (Given: equal)JL = KM = (Given: equal)JM = JM = (Common)So, ΔJML ≅ ΔMJK under SSS condition.
Therefore, ΔJML ≅ ΔMJK.
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Factor by grouping (sometimes called the ac-method).
10x²-3x-4
First, choose a form with appropriate signs.
Then, fill in the blanks with numbers to be used for grouping.
Finally, show the factorization.
Form:
O
O
10x + 0x + 0*-4
2
10x +
0*- 0*-4
2
10x
10x²
O 10x
x +
- 0*- 0x-4
Factorization:
0
X
Answers
The factorization of the polynomial 10x² - 3x - 4 by grouping is (2x + 1)(5x - 4)
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A polynomial is an expression involving addition, subtraction and multiplication of variables. A quadratic equation is a polynomial of degree two.
Given the polynomial:
10x² - 3x - 4
= 10x² - 8x + 5x - 4
= 2x(5x - 4) + 1(5x - 4)
= (2x + 1)(5x - 4)
The factorization of the polynomial 10x² - 3x - 4 by grouping is (2x + 1)(5x - 4)
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Consider the expression (x+7), do the following.
(a) Use the distributive property twice to show that
this expression is equivalent to x² +14x+49.
(b) Test the equivalency by finding the value
(x+7) and x² +14x+49 when x= 3.
(x+7)²
x² +14x+49
Answers
1 ton makes 90 cars
there are 280 million cars needed
1 ton = 500,000 gallons of water
figure out how much water is needed for 280 million cars.
What I have so far
500,000*280 million= 1.4*[tex]10^{14}[/tex]
Do i divide by 90 and am i even doing this correct?
Answers
The number of gallons required for 280 million cars is 1,555,556 gallons.
Given that, 1 ton makes 90 cars, there are 280 million cars needed
and 1 ton = 500,000 gallons of water.
What are proportions?Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. The proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.
Let the number of gallons of water needed for 280 million cars be x.
Now, 90 : 500,000 :: 280 : x
⇒ 90x=500,000 × 280
⇒ x = 14,00,00,000/90
⇒ x = 1,555,555.555≈1,555,556 gallons
Therefore, the number of gallons required for 280 million cars is 1,555,556 gallons.
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Compare and contrast the perpendicular bisectors, medians, and altitudes of a triangle.
Answers
The perpendicular bisector of a segment is a line that passes through the midpoint of a segment and is perpendicular to the segment.
What is the difference between perpendicular bisectors, medians, and altitudes of a triangle?
A perpendicular bisector is a line that intersects and passes through the midpoint of a given segment at a 90° angle.
A triangle's median is a line segment that connects a vertex to the opposing side's midpoint. Every triangle has three medians, one from each vertex, and they all cross at the triangle's centroid.
A triangle's altitude is a line segment that passes through a vertex and is perpendicular to the baseline.
Median: A median is a segment that connects a vertex to the midpoint of the opposite side.Altitude: Altitude is defined as the perpendicular distance from a vertex to the opposite side.Perpendicular Bisector: The perpendicular bisector of a segment is a line that passes through the midpoint of a segment and is perpendicular to the segment.To learn more about perpendicular bisector refer to:
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What is the product of 48.65(6.2)?
Answers
Answer:
48.65x6.2=301.63
Step-by-step explanation:
Answer:
down below
Step-by-step explanation:
301.63
It's a bit difficult to type this in a mobile so I won't put it. If you would like the explanation, I can always go back and edit my answer
Hope this helps! :)
In this diagram, which equation could you prove to be true in order to conclude that the lines are parallel?
Responses
c−a/b=−d/e
c−a/b*d/e=−1
c−a/b*−d/e=−1
c−a/b=d/e
Answers
The equation that could be used to prove the lines are parallel is: D. (c - a)/b = d/e
What are Parallel Lines?Parallel lines are lines that do not converge at any point and have the same slope.
Slope (m) = change in y / change in x
Slope of the first line = (c - a)/0 - b
Slope of the first line = (c - a)/b
Slope of the second line = (0 - (-d))/(e - 0)
Slope of the second line = d/e
Thus, if both line are parallel, then (c - a)/b = d/e. This is because parallel lines have the same slope.
The equation is: D. (c - a)/b = d/e
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Points D and E are aligned with a ruler. Point D is at the mark of 4.5 cm, and the distance between points D and E is 3.4 cm. At which, two marks on the ruler could point E be located?
Answers
Answer:
E could be located at 7.9cm.
Phoebe is reading a novel for her monthly book club. the novel is 368 pages long. so far, she has read 53 pages. phoebe plans to read 35 pages a day. write an equation that represented, the number of days it will take phoebe to finish the novel
Answers
The equation that represent the number of days it will take phoebe to finish the novel is: x= number of pages left to be read / pages to be read per day
Information about the problem:
novel’s pages = 368read pages = 53pages to be read per day = 35 pages/daynumber of days it will take phoebe to finish the novel = x ?To solve this problem, we have to write the equation in order to calculate (x) the number of days it will take phoebe to finish the novel with the given information:
number of pages left to be read = novel’s pages - read pages
number of pages left to be read = 368 – 53
number of pages left to be read = 315 pages
Knowing the number of pages left to be read we can write the following equation:
x = number of pages left to be read / pages to be read per day
x = 315 pages /35 pages/day
x = 9 days
What is an equation?An equation is the equality between two algebraic expressions, which have at least one unknown or variable.
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