Consider the proof.
Given: In △ABC, BD ⊥ AC
Prove: the formula for the law of cosines, a2 = b2 + c2 – 2bccos(A)
Statement
Reason
1. In △ABC, BD ⊥ AC 1. given
2. In △ADB, c2 = x2 + h2 2. Pythagorean thm.
3. In △BDC, a2 = (b – x)2 + h2 3. Pythagorean thm.
4. a2 = b2 – 2bx + x2 + h2 4. prop. of multiplication
5. a2 = b2 – 2bx + c2 5. substitution
6. In △ADB, cos(A) = 6. def. cosine
7. ccos(A) = x 7. mult. prop. of equality
8. a2 = b2 – 2bccos(A) + c2 8. ?
9. a2 = b2 + c2 – 2bccos(A) 9. commutative property
What is the missing reason in Step 8?
a. Pythagorean theorem
b. definition of cosine
c. substitution
d. properties of multiplication
Answers
substituting 2bx for 2bccos(a)
The Law of Cosines is used to find the remaining parts of a triangle when the triangle is not a right triangle and when either the lengths of two sides and the measure of the included angle is known (SAS) or the lengths of the three sides (SSS) are known.
The law of cosine states if a,b,c are the three sides of any triangle then [tex] a^{2} =b^{2} +c^{2} -2bccosA [/tex]
In the above proof in statement 8 the x in statement 5 is replaced by c cos A from statement 6.
Among the given options ,option C holds true as the reason for statement 8.
Related Questions
Please help.
What are the dimensions of the matrix?
⎡1 0 9⎤
⎢-2 3 5⎢
⎢5 4 -6⎢
⎣11 5 7⎦
Enter your answers in the boxes.
The matrix is a [_] × [_] matrix.
Answers
Count the rows: 4
Count the columns: 3
The matrix is a 4 x 3 matrix
The size of a matrix is defined by the number of rows and columns that it contains.
The dimensions of a matrix are the number of rows by the number of columns.
The number of rows and columns of a matrix, written in the form rows×columns.
The given Matrix has four rows and three columns,
The rows go side to side; the columns go up and down. "Row" and "column" are technical terms, and are not interchangeable.
Matrix dimensions are always given with the number of rows first, followed by the number of columns.
The matrix is a [4_] × [3_] matrix.
Help me solve this math problem
Answers
If you want the graph of f(x), perhaps it looks like this one.
6.3% of 41 is?
a. 2.6
b. 6.5
c. 258.3
d. 650.8
Answers
a✓
Carbon-14 has a half-life of 5,730 years. If the age of an object older than 50,000 years cannot be determined by radiocarbon dating, then
* carbon-14 levels in a sample are undetectable after approximately ten half-lives.
* carbon-14 levels in a sample are undetectable after approximately nine half-lives.
* the half-life of carbon-14 is too long to accurately date the object.
* a radioisotope with a shorter half-life should be used to date the object.
Answers
Nine half-lives pf carbon 14 is 51,570 years.
Source:
https://en.wikipedia.org/wiki/Radiocarbon_dating
A large bag of marbles contains an equal amount of red, orange, yellow, blue, and green marbles. Brody randomly selects 1 marble from the bag. Which of the following represents the probability of selecting a red, blue, yellow, or green marble
A) 0.8
B) 0.7
C) 0.9
D) 0.6
Answers
[tex] \frac{4}{5} = 0.8[/tex]
hope this helps
Answer: The correct option is (A) 0.8.
Step-by-step explanation: Given that a large bag of marbles contains an equal amount of red, orange, yellow, blue, and green marbles. Brody randomly selects 1 marble from the bag.
We are to find the probability of selecting a red, blue, yellow or green marble.
Let n be the number of each color of marbles in the bag.
That is, the number of red, orange, yellow, blue, and green marbles, each equals n.
Let S denote the sample space of selecting a marble from the bag and A denote the event of selecting a red, blue, yellow or green marble.
Then, we have
n(S) = n + n + n + n + n = 5n,
n(A) = n + n + n + n = 4n.
Therefore, the probability of event A is given by
[tex]P(A)=\dfrac{n(A)}{n(S)}=\dfrac{4n}{5n}=\dfrac{4}{5}=0.8.[/tex]
Thus the required probability selecting a red, blue, yellow or green marble is 0.8.
Option (A) is CORRECT.
99pts WILL GIVE BRAINLIEST Use the diagram and given information to answer the questions and prove the statement. Given: X Z
Prove: [see image] Re-draw the diagram of the overlapping triangles so that the two triangles are separated.
What additional information would be necessary to prove that the two triangles, XBY and ZAY, are congruent?
What congruency theorem would be applied?
Prove using a list/flow chart proof.
Answers
Statements [Reasons]
1. Angle X is congruent to Angle Z [Given]
2. Line XY is congruent to Line YZ [Given]
3. Angle Y is congruent to Angle Y [Congruence is reflexive]
4. Triangle XBY is congruent to Triangle ZAY [ASA]
ANSWER: The ASA (Angle Side Angle) Congruency Theorem could be applied.
A sphere has a radius of 2x + 5. Which polynomial in standard form best describes the total surface area of the sphere? Use the formula S = 4pir2 for surface area of a sphere.
Answers
[tex] S = 4 \pi r^2 [/tex]
Now substitute 2x + 5 in for r, the radius.
Then simplify the expression and write it in standard form.
[tex] S = 4 \pi (2x + 5)^2 [/tex]
[tex] S = 4 \pi (4x^2 + 20x + 25) [/tex]
[tex] S = 16 \pi x^2 + 80 \pi x + 100 \pi [/tex]
The sales tax on a $250 computer is 17.50. find the sales tax rate.
Answers
[tex]\bf \begin{array}{ccll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 250&100\\ 17.50&t \end{array}\implies \cfrac{250}{17.50}=\cfrac{100}{t}\implies t=\cfrac{17.50\cdot 100}{250}[/tex]
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answers
we are given
[tex]\frac{3x^6-19x^4-4x^3-24x^2+2x+178}{-2x^2-6}[/tex]
we can use long division method to divide it
so, we get
[tex]Quotient=-\frac{3x^4}{2}+14x^2+2x-30[/tex]
[tex]Remainder=14x-2[/tex]...........Answer
Abby walked miles on Monday, miles on Tuesday, and miles on Wednesday. What is the total distance Abby walked in the three days?
a. miles
b. miles
c. miles
d. miles
Answers
Answer:WE Cant se the numbers
Step-by-step explanation:the ancwer would be 7 and 7/12
Simplify the expression. w5(w2)–4
Answers
By simplifying this expression, we would first have to (find the roots which would be polynomial).
We would have to find the the polynomial root of [tex] \boxed{F(w) = w7-4}[/tex]
After resolving this, we would then have to find the leading coefficient and also the trailing constant.
[tex]LC \Longrightarrow[/tex] = (1)
_________
[tex]TC \Longrightarrow[/tex] = (1,2,4)
This would be the result of the simplification of this expression listed above.
Therefore, your correct answer would be [tex]\boxed{w^7-4}[/tex]
I hope this helps you!
Answer:
[tex]\frac{1}{w^{3} }[/tex]
A freight carrier charges $0.57 for a package weighing up to one ounce plus and additional $0.32 for each additional ounce or fraction of an ounce. A company is shipping a package weighing 224 grams. What is the weight of the package in ounces?
Answers
Answer:
its is 8 oz 224 grams is = to 7.901
Step-by-step explanation:
Can someone please help me solve for x and y? Thank you
Answers
Choice D) x*y = -10
============================================
Explanation:
Multiply both sides of the first equation by 10 to clear out the fractions (10 is the LCD)
3x/5 + y/2 = 13/10
10*(3x/5 + y/2) = 10*(13/10)
6x + 5y = 13
Multiply both sides of the second equation by 100 to get each decimal value to turn into a whole number (move the decimal point over 2 spots to the right)
0.5y + 0.04x = 2.42
50y + 4x = 242
4x + 50y = 242
So we have this new system of equations which is equivalent to the original system
6x + 5y = 13
4x + 50y = 242
Multiply both sides of the top equation by 10 so that the 5y turns into 50y
6x + 5y = 13
10*(6x + 5y) = 10*13
60x + 50y = 130
Now we have this system of equations
60x + 50y = 130
4x + 50y = 242
If we subtract straight down then we have
60x-4x = 56x
50y-50y = 0y = 0 ... notice how the y terms go away effectively
130-242 = -112
The y terms go away leaving us with this simplified equation
56x = -112
Which solves to
x = -2
when we divide both sides by 56
Now use that x value to find y
6x + 5y = 13
6(-2) + 5y = 13 ... replace x with -2
-12 + 5y = 13
-12+5y+12 = 13+12 ... adding 12 to both sides
5y = 25
5y/5 = 25/5 .... dividing both sides by 5
y = 5
In summary we have x = -2 and y = 5. Therefore, x*y = -2*5 = -10 is the answer
A teacher gave his class two quizzes; 80% of the class passed the first quiz, but only 60% of the class passed both quizzes. What percent of those who passed the first quiz also passed the second quiz?
Answers
the answer to the question is 75%
Answer:
75
Step-by-step explanation:
P(2ndquiz|1st quiz)=P(passed both quizzes)/P(1st )=0.06/0.08=0.75 that means 75%
Let g(x) = 2x and h(x) = x2 + 4. Evaluate (h ∘ g)(1). 2 8 10 4
Answers
You can solve this by plugging 1 into [tex] g(x) [/tex] and plugging the result into [tex] h(x)[/tex].
[tex]g(x) = 2x[/tex]
[tex]g(1) = 2(1)[/tex]
[tex]g(1) = 2[/tex]
[tex]h(x) = 2x + 4[/tex]
[tex]h(g(1)) = 2(2) + 4[/tex]
[tex]h(g(1)) = 4 + 4[/tex]
[tex]h(g(1)) = 8[/tex]
Answer:
(h ∘ g)(1) = 8
The engine of a car has a displacement of 305 cubic inches. what is the displacement in cubic feet? round your answer to 2 decimal places.
Answers
1 inch = 2.54 centimeters
Therefore, to convert to cubic measurements
(1 in)³ = (2.54 cm)³
Thus;
1 in³ = 16.387 cm³
Hence 305 cubic inches will be equivalent to
305 × 16.387
= 4998.035 cm³
Answer:
0.18 cubic feet (in 2 decimal places)
Step-by-step explanation:
The relationship between the unit of measurement inches and the unit of measurement feet may be expressed mathematically as
12 Inches = 1 feet
finding the cube of both sides i.e both sides to the power of 3,
1728 cubic inches = 1 cubic feet
therefore,
305 cubic inches
= 305/1728 cubic feet
= 0.1765 cubic feet
The table shows the snack preferences of 50 shoppers at the mall. What is the probability that one shopper, selected at random from the 50 surveyed, preferred the potato chips or pretzels? Fruitsnacks/9 shoppers, Potatochips 12 shoppers, Apple 3 shoppers, pretzels 14 shoppers, Water 12 shoppers ---> are the answers for the question---> A. one over five B. thirteen over twenty-five C. one over ten D. eighteen over twenty five
Answers
Please help thank you!
Answers
answer is B
A slice is made parallel to the base of a triangular pyramid. What is the shape of the resulting two-dimensional cross-section? Drag and drop the word to correctly complete the sentence. The cross-section is in the shape of a . rectangletriangletrapezoid
Answers
Thank you for posting your answer at Brainly! Feel free to ask some more questions!
Your answer is Triangle
This is your answer becuase if you split a pyramid in half you will get two Identical triangle shapes.
Hope this has helped :)
John and Matt are going to fill a pool with 2 different sized hoses. John can fill the pool in 5 hours, while Matt can complete it in 10 hours. Explain each step in solving this equation.
Answers
John and Matt are going to fill a pool with 2 different sized hoses. John can fill the pool in 5 hours, while Matt can complete it in 10 hours.How long will it take both to fill the pool? Explain each step in solving this equation.
we know that
John can fill the pool in --------------> 5 hours
therefore
I calculate the amount of pool that John fills in one hour
if John can fill 100% of the pool in----------------> 5 hours
X--------------------------------------> 1 hour
X=1/5=0.20 pool/hour
Matt can fill the pool in --------------> 10 hours
therefore
I calculate the amount of pool that Matt fills in one hour
if Matt can fill 100% of the pool in----------------> 10 hours
X--------------------------------------> 1 hour
X=1/10=0.10 pool/hour
adding both amounts
(0.20+0.10)=0.30 -----------> 30% pool/hour
then
if both can fills 30% of the pool in----------------> 1 hour
100%-------------------------------> X
X=100/30=3.33 hours----------> 3 hours + 19 minutes+ 48 sec
the answer is 3.33 hours (3 hours + 19 minutes+ 48 sec)
The equation to determine the amount of pool filling (y) according to time (t) in hours is given by
y=0.30*t
Please help me answer
Answers
2. transitive prop of equality
3. subtraction property of equality
Use the formula V = s³, where V is the volume and s is the edge length of the cube, to solve this problem.A cube-shaped bin has an edge length of 34 yard.What is the volume of the container? Enter your answer, as a fraction in simplest form, in the box.
Answers
To find the volume, you simply have to use the formula that is given. It is V = s^3. This means you multiply the side by itself 3 times.
S x S x S = V
34 x 34 x 34 = 39304 cubic yards
PLZ HELP ME ON THIS
PLZ EXPLAIN IT TO ME
Answers
80 * 5 = 400
Hope it helps
Factor the common factor out of 8x3 + 12x.
Answers
The factor of this is 4x(2x² + 3)
So the common factor is 4x
I hope this helps~!
As always, it is my pleasure to help students like you.
The area of a right triangle with one leg measuring 5ft and hypotenuse measuring 13ft is
A 30ft to the 2
B 37.5 ft to the 2
C 65ft to the 2
Answers
other leg^2 = 13^2 - 5^2
other leg^2 = 169 -25
other leg^2 = 144
other leg = 12
Area = .5 * 12 *5
Area = 30 sq feet
answer is A
Ben is repacking a 45-pound bag of rice into 8 smaller bags. How much rice is going to be in each smaller bag/11008924/c50ec7f7?utm_source=registration
Answers
1 bag = 45 ÷ 8
1 bag = 5.625 pound
------------------------------------------------------------
Answer: 1 bag = 5.625 pound of rice
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Compare and Contrast: Below are two equations. Solve each equation and compare the two solutions. Choose the statement that is true about each solution. Equation #1 Equation #2 |2x - 4| = 5 |3x - 4| = -12 Equation #1 and Equation #2 have the same number of solutions. Equation #1 has more solutions than equation #2. Equation #1 has fewer solutions than equation #2. None of the statements above describe the number of solutions to equations shown.
Answers
[tex]|2x-4|=5[/tex]
This means:
[tex]2x-4=5[/tex] and [tex]2x-4=-5[/tex]
Simplifying both the equations we get:
x = 4.5 and x = - 0.5
Equation 2:
[tex]|3x-4|=-12[/tex]
There is no solution to this equation, as the modulus or absolute value of any expression can never be negative
Therefore, we can conclude that Equation 1 has more number of solutions that Equation 2.
Find the product of (x + 5)(x − 5). (1 point)
x2 − 10x + 25
x2 + 10x + 25
x2 − 25
x2 + 25
Answers
x^2-5x+5x-25 = x^2-25
Find the absolute maximum and minimum values of the following function on the given interval. If there are multiple points in a single category list the points in increasing order in x value and enter N in any blank that you don't need to use.
f(x)=9x^3−27x+9, [0,3],
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algebra help please?