Mathematics College

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?

Answers

Answer 1

Solution: The missing reason in Step 8 is substitution of [tex]x=c\cos (A)[/tex].

Explanation:

The given steps are used to prove the formula for law of cosines.

From step 5 it is noticed that our equation is

[tex]a^2=b^2-2bx+c^2[/tex]      ..... (1)

From step 7 it is noticed that the value of [tex]x[/tex] is [tex]c\cos (A)[/tex].

So by substituting [tex]c\cos (A)[/tex] for [tex]x[/tex] in equation (1) we get the equation of step 8, i.e.,

[tex]a^2=b^2-2bc\cos (A)+c^2[/tex]

Hence, the missing reason in Step 8 is substitution of [tex]x=c\cos (A)[/tex].



Answer 2
Final answer:

The missing reason in Step 8 of the proof for the Law of Cosines is substitution, where x is replaced with cc cos(A) in the expression.

Explanation:

The missing reason in Step 8 of the proof that shows how the Law of Cosines is derived, a2 = b2 + c2 – 2bc cos(A), is the substitution property. In Step 7, we established that c cos(A) is equal to x. Thus, for Step 8, when we replace x with cc cos(A) in the expression b2 – 2bx + c2, we effectively utilize substitution to arrive at the expression a2 = b2 – 2bccos(A) + c2.

Related Questions

Matt has $550 in his savings account. He is eager to know how much interest the bank will pay him for the whole year. He knows that the bank pays a 3 percent interest rate. He sits down with a pen, paper, and calculator to find out the simple interest. Let’s help him out. Matt has already jotted down the formula he needs to use: I = P × r × t First, help him substitute the correct values in this formula. Write down the appropriate numbers for principal, rate of interest, and time

Answers

From Matt's formula:
I=P×r×t
P=principle amount (amount invested)
r=rate
t=time
From the information given:
P=$550
r=0.03
t=1
therefore
I=550*0.03*1
I=$16.5

Answer:I = 550 × 0.03 × 1

Step-by-step explanation: from plato

5 3/4 in a improper fraction?

Answers

5 and 3/4 as an improper fraction would be 23/4. Hope it helps! :)
the improper fraction would be 23/4 because you need to multiply 5 by 4 and get 20 and add 3 which gets you 23. You will keep the denominator so the answer in an improper fraction is 23/4

The chemical formula for lithium phosphide is Li3P. Which best describes this ionic compound?

Answers

Lithium ions have 1 positive charge, and phosphorus ions have 3 negative charges.

When lithium and phosphorus combine to form lithium phosphide, three lithium cations (Li+) combine with one phosphide anion (P₃-) to balance the charges and form a neutral compound, Li₃P.

What is Ionic compound?

an ionic compound is a chemical compound composed of ions held together by electrostatic forces termed ionic bonding.

The correct description of the ionic compound lithium phosphide, with the chemical formula Li3P, is "Lithium ions have 1 positive charge, and phosphorus ions have 3 negative charges."

This is because lithium is a Group 1A element, which means it has one valence electron that it tends to lose in chemical reactions to form a cation with a charge of +1.

Phosphorus, on the other hand, is a Group 5A element, which means it has five valence electrons and tends to gain three electrons to form an anion with a charge of -3.

Thus, When lithium and phosphorus combine to form lithium phosphide, three lithium cations (Li+) combine with one phosphide anion (P₃-) to balance the charges and form a neutral compound, Li₃P.

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A company paid $48 for 2 cases of printer paper. Each case contains 12 packages of paper. Next month the company’s office manager needs to order 180 packages of the same paper. If the price per package does not change, what would be the total cost of next month’s order?

Answers

48/24 = $2.00 per package

PLEASE HELP!!!!

Which of the following functions is graphed below?!?

Answers

The given graph is for a piecewise function consisting of two intervals:

(1) x ≤ 1 ⇒⇒⇒ the graph in this interval like a cubic function.

(2) x > 1 ⇒⇒⇒ the graph in this interval like a quadratic function

By comparing to the given options

The answer is option c.

Answer:

Option C is correct.

Explanation:

A piece-wise function is a function which is defined by multiple sub-functions, each sub-function applying to a certain interval of the main function's domain.

From the graph we can see that the function is made up of 2 pieces.

Solid dot means- Including

Open-dot means - not- including.

As we can see that the boundary lines are at x=1.

We have to look each line separately to determine each equation:

when [tex]x>1[/tex], it gives the function [tex]y=x^2+4[/tex] and

when [tex]x\leq 1[/tex], it gives the function [tex]y =x^3-2[/tex].

So, the piece-wise function is:

[tex]y=\left \{ {{x^3-2}, x\leq1 \atop {x^2+4}, x>1} \right.[/tex]

An electronics shop offers a small ic chip for $1.50 per unit and $4.00 for large ic chip. on a certain day, 2200 chips were sold and $5050 is collected. how many small ic chips and how many large ic chips were sold?

Answers

Let s and l represent the numbers of small and large ICs sold that day. The problem statement gives rise to two equations.
.. s + l = 2200
.. 1.50s +4.00l = 5050

Solving these by your favorite method gives
.. s = 1500
.. l = 700

1500 small ICs and 700 large ICs were sold.

To determine the number of small and large IC chips sold, we set up a system of linear equations with the given total number of chips (2200) and total earnings ($5050). Solving the system, we found that 1500 small IC chips and 700 large IC chips were sold.

To solve the problem, we can set up a system of linear equations to represent the sales for small and large IC chips. We have two unknowns: the number of small IC chips (let's call it x) and the number of large IC chips (let's call it y). We have two pieces of information to create our equations:

The total number of chips sold is 2200, so x + y = 2200.

The total amount collected is $5050, so 1.50x + 4.00y = 5050.

Solving this system of equations, we multiply the first equation by 1.50 to align it with the second equation:

1.50x + 1.50y = 3300 (Multiply the first equation)

1.50x + 4.00y = 5050 (Second equation)

Subtracting the first new equation from the second gives us:

2.50y = 1750

Dividing both sides by 2.50 to find y gives us y = 700. That means 700 large IC chips were sold. Now, we can substitute y in the first equation to find x:

x + 700 = 2200

x = 2200 - 700

x = 1500

Hence, 1500 small IC chips and 700 large IC chips were sold.

Here is the histogram of a data distribution. What is the shape of this distribution?

Answers

This histogram is unimodal skewed. There are two parts to this answer. The first part has to do with the number of modes. This would be the item that is occurring the most frequently. In this case the mode is only 4. It is occurring more than any other.
The second part of this has to do with the distribution of the data as it is displayed on the histogram. There are 4 pieces of data that are only occurimg one time on the right of the histogram. We call this skewing the data. When both sides looks almost the same we say it is symmetric.

There are approximately 2.2 million births in a country each year. Find the births per minute.

Answers

1. you divide by 365 to get per day,
2. you divide by 24 to get per hour,
3. and then divide by 60 to get per minute.

(1. days in a year, 2. hours in a day, 3. minutes in an hour)

In a​ region, there is a 0.95 probability chance that a randomly selected person of the population has brown eyes. Assume 13 people are randomly selected. Find the probability that the number of selected people that have brown eyes is 11 or more.

Answers

is there more to this question?

Experts/ace/geniuses

Answers

the answer would be D. 3/15
The answer is D. I hope this helped

If two fair dice are​ rolled, find the probability that the sum of the dice is 77​, given that the sum is greater than 33.

Answers

The probability is 3/7

tossing a number cube numbered from 1 to 6 and getting an even number that is greater than or equal to 2

Answers

3 because you take away the other numbers and leave the 1, 3 and 5 but I am not in college so.....Good luck

The expression 4i gives the perimeter of a square with a side lengh of i units .
what is the perimeter of a square with a side lenth of 5/7 units ?

Answers

we know that

[perimeter of a square]=4*i

for i=5/7 units
so

[perimeter of a square]=4*(5/7)----------> 20/7 units


the answer is
20/7 units

Given that Rectangle MNOP ~ rectangle STUV, what is the length of TU?

Answers

The measure of TU is 15.

We set up a proportion to solve this.  Using the similarity statement, we know that MN is proportional to ST, NO is proportional to TU, OP is proportional to UV, and PM is proportional to VS.

NO/TU = OP/UV
10/x = 4/6

Cross multiply to solve it:
10*6 = x*4
60 = 4x

Divide both sides by 4:
60/4 = 4x/4
15=x

Answer:

The measure of TU is 15.

Step-by-step explanation:

What information is found in the left column of a two column proof?

Answers

The left column is for statements and the right column is for reasons which justify the corresponding statement. 

Answer: C) Statements

A statement is simply a sentence with words and/or math expression. For example, one statement could be "Segment AB is parallel to segment CD". That same statement can be translated to "AB || CD". The two vertical lines indicate "parallel". 

Which is the measure of the reference angle for 227 degrees

Answers

47 degrees

hope this helps<3
Geometrically, the reference angle is the smallest angle between the terminal ray and the x-axis.

Algebraically, the reference angle for X is the smaller of (X mod 180°) and (-X mod 180°).

Here, that would be
.. min(227 mod 180, -227 mod 180)
.. = min(47, 133)
.. = 47 . . . . degrees

_____
"X mod 180" means you subtract the largest multiple of 180 that is smaller than X.
Then 227 mod 180 = 227 -180 = 47
and -227 mod 180 = -227 -(-360) = 133.

the radius of a quarter circle is 1 mile. What is the quarter circle's perimeter?

Answers

The answer to your question is 6.28mi

Estimate by division ..70/9.24

Answers

the answer is 7.58

hope this helped :)
alisa202

Here we have to divide 70 by 9.24.

we can first covert the decimal 9.24 into fraction, shifting the decimal two units to the right and dividing by 100, we have

9.24 = 924/100

Now let us divide 70 by 924/100

in division of fraction we take reciprocal of second fraction and multiply it with first.

reciprocal of 924/100 is 100/924.

multiplying 70* 100/924, we have

[tex] 70 * \frac{100}{924} [/tex]

[tex] = \frac{7000}{924} [/tex]

converting into decimal we have

[tex] \frac{7000}{924} = 7.5757..... [/tex]

Which of the following functions is graphed below?

Answers

we have that

observing the graph of the problem, it is evident that the solution is option D, since the graph of the parabola presents a domain for x <4 and the line presents a domain for x> = 4 and the only option with these two conditions is option D

using a graph tool
I proceed to verify
see the attached figure

the answer is the option D

The graph consists of two parts: left part (with sign < or ≤) - parabola and right part (with sign > or ≥) - straight line.

Determine signs:

From the diagram you can see that the right endpoint (4,19)  of parabola is not included. This means that x cannot be equal to 4 at this part of graph and the sign should be <.

Also you can see that the left endpoint (4,8)  of line is included. This means that x=4 belongs to the right part and the sign should be ≥.

Using previous conclusions, you can state that correct choice is D.


Which of the following describes the roots of the polynomial function f(x)=(x-3)^4(x-6)^2? –3 with multiplicity 2 and 6 with multiplicity 4 –3 with multiplicity 4 and 6 with multiplicity 2 3 with multiplicity 2 and –6 with multiplicity 4 3 with multiplicity 4 and –6 with multiplicity 2

Answers

In mathematics, the multiplicity of a member of a multi-set is the number of belongings it has in the multi-set.
 For example, this term is used to refer to the number of times a certain polynomial has a root at a certain point.
 For this polynomial we have:
 f (x) = (x-3) ^ 4 (x-6) ^ 2
 3 with multiplicity 4 and 6 with multiplicity 2
 Answer: 
 3 with multiplicity 4 and 6 with multiplicity 2

Answer:

3 with multiplicity 4 and -6 with multiplicity 2

I need help ASAP!!
What is 92 rounded to the nearest yard??

Answers

Here we will tell you what 92 is rounded to the nearest hundred and also show you what rules we used to get to the answer. First, 92 rounded to the nearest hundred is:

100

Remember, we did not necessarily round up or down, but to the hundred that is nearest to 92.

When rounding to the nearest hundred, like we did with 92 above, we use the following rules:

A) We round the number up to the nearest hundred if the last two digits in the number are 50 or above.

B) We round the number down to the nearest hundred if the last two digits in the number are 49 or below.

C) If the last two digits are 00, then we do not have to do any rounding, because it is already to the hundred.

What is the sum of 4.2 × 105 and 5.3 × 10^5?

A.)95 × 10^5

B.)95 × 10^10

C.)9.5 × 10^5

D.)9.5 × 10^10

Answers

(4.2*105)+(5.3*10^5)
441 + 530000
530441

-----------

If your problem is (4.2*10^5)+(5.3*10^5), it would be 
420000 + 530000
950000

Answer:

Option C.

Step-by-step explanation:

The two expressions are [tex]4.2\times 10^{5}[/tex] and [tex]5.3\times 10^{5}[/tex]

We have to find the total of these two terms.

[tex](4.2\times 10^{5}[/tex] + [tex]5.3\times 10^{5})[/tex]

Now we take out [tex]10^{5}[/tex] as a common term.

[tex]10^{5}(4.2+5.3)[/tex]

= [tex]9.5\times 10^{5}[/tex]

Therefore, Option C. will be the answer.

Trigonometric Help Plz?

Answers

1)

[tex]\bf sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta) \\\\\\ cos(\theta )=\sqrt{1-sin^2(\theta )}\\\\ -------------------------------\\\\ sin(x)=cos(x)-1\implies sin(x)=\sqrt{1-sin^2(x)}-1[/tex]

[tex]\bf sin(x)+1=\sqrt{1-sin^2(x)}\implies [sin(x)+1]^2=1-sin^2(x) \\\\\\ sin^2(x)+2sin(x)+1=1-sin^2(x)\implies 2sin^2(x)+2sin(x)=0 \\\\\\ 2sin(x)[sin(x)+1]=0\implies \begin{cases} 2sin(x)=0\\ sin(x)=0\\ \measuredangle x=0~,~\pi ~,~2\pi \\ -------\\ sin(x)+1=0\\ sin(x)=-1\\ \measuredangle x=\frac{3\pi }{2} \end{cases}[/tex]



2)

[tex]\bf 3sin(x)+cos^2(x)=2 \\\\\\ 3sin(x)+[1-sin^2(x)]=2 \\\\\\ 3sin(x)-sin^2(x)+1=2 \\\\\\ 3sin(x)-sin^2(x)-1=0 \\\\\\ sin^2(x)-3sin(x)+1=0 \\\\\\ \boxed{[sin(x)-3][sin(x)+1]=0}\impliedby \textit{check closely this }FOIL[/tex]

eva estimates that 475 songs will fit on her mp3 player the actual that fit is 380 findc the percent error

Answers

20% is the percent error
https://studysoup.com/questions/math/100256/eva-estimates-the-475-songs-will-fit-on-mp3-player
20 percent is the percent error. Hope I helped! :)

Does anyone know how to prove that OAC and OBC are Congruent.

Answers

Hello,

The first step is to see that sides OA, OC, OB are all equal because they are the radii of the circle. Knowing that those sides are equal means that we have isosceles triangles. That gives us that the base angles are the same.

In OAC, we can subtract 118 from 180 to give us 62 degrees for the 2 bases angles. This would make each angle 31 degrees.

In OBC, the base angles are already 31, leaving the other angle 118.

There we have all the angles the same and 2 sides the same.

You could use SAS or ASA to prove that the triangles are congruent.

I hope this helps!
Good luck,
MrEquation

Answer:

You could use SAS or ASA to prove that the triangles are congruent.

Step-by-step explanation:

Surface area of right cone radius of 8 and 14 height
A. 896
B. 224
C. 176
D. 167

Answers

[tex]\bf \textit{total surface area of a cone}\\\\ S=\pi r\sqrt{h^2+r^2}+\pi r^2\quad \begin{cases} r=radius\\ h=height\\ -----\\ r=8\\ h=14 \end{cases} \\\\\\ S=\pi (8)\sqrt{14^2+8^2}+\pi (8)^2\implies S=8\pi \sqrt{260}+64\pi \\\\\\ S\approx 405.25+201.06\implies S\approx 606.31[/tex]

The value of Surface area of right cone with radius of 8 and 14 height is,

⇒ SA = 606.31

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

Radius of cone = 8

And, Height = 14

We know that;

Surface area of right cone is,

SA = πr (r + √h² + r²)

SA = 3.14 × 8 (8 + √14² + 8²)

SA = 606.31

Thus, The value of Surface area of right cone with radius of 8 and 14 height is,

⇒ SA = 606.31

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1.
Find the Compound Amount.
Round to the nearest cent.

Amount = $980
Rate = 8%
Compounded = Quarterly
Time (Years) = 5





2.
Find the Interest Earned.
Round to the nearest cent.

Amount = $980
Rate = 8%
Compounded = Quarterly
Time (Years) = 5

Answers

1) 
Principal Amount = P = $980
Interest rate = r = 8% = 0.08
Compounding periods = n = 4
Time = t = 5 years

Formula to be used for finding compounding amount:

[tex]A=P (1+ \frac{r}{n} )^{nt} [/tex]

Using the values in the formula, we get:

[tex]A=980 (1+ \frac{0.08}{4} )^{5*4} =1456.23[/tex]

Therefore, the amount compounded over a period of 5 years will be $1456.23

2)
Principal Amount = $980
Compounded Amount = $1456.23
Interest Earned = Compounded Amount - Principal Amount
Interest Earned = 1456.23 - 980 = $ 476.23

Therefore, $476.23 interest will be earned over a period of 5 years.

0.698 to the bestest hundreth

Answers

I.7
Is the answer ok.
0.698
The 9 is in the hundredths place
Since 9 is greater than 5 we will round up.
0.70 is your answer

Experts/ace/geniuses

Answers

An irrational number for a radical is one that will not have a perfect answer like [tex] \sqrt{49} [/tex] or [tex] \sqrt{16} [/tex]  that means the only one is [tex] \sqrt{84} [/tex]

part of the proceeds from a garage sale was $510 worth of $10 and $20 bills. if there were only 6 more $10 bills than $20, find the number for each denomination

Answers

There are 15 $20 bills and 26 $10 bills.
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