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Note that angle CEA = angle DCA + angle DAC and angle BDE = angle DCE + angle EDC, so angle DCA = angle CEA - angle DAC and angle DCE = angle EDC - angle CED.

Also, angle BDE = angle ABD + angle ADB = angle AEC + angle DAC, so angle DCE + angle DCA = (angle EDC - angle CED) + angle DCA.

Therefore, angle ACE = angle ACD + angle DCE = angle CEA, which implies that triangle ACE is isosceles.

b. p = (3/8, -2/8, 1/4).

Andy is correct.  Good work. 

Here's the calculation your teacher wants to see. 

A candy bar and a piece of bubble gum together cost 1.50.  

The candy bar costs a dollar more than the bubble gum.  

How much does the piece of bubble gum cost, in cents?  

Call the cost of a candy bar "C"  

Call the cost of a bubble gum "B"  

                                                                      C + B  =  1.50  

                                                                      C – B  =  1.00  

Just subtract the second from the first               2B  =  0.50  

                                                                            B  =  0.25  =  25¢  

_.

-3/7 I guess

Each person will get 1 favor and there will be 3 favors left ok(This is simple, why am I answering)

It is a little tricky, but the bubble gum is 25 cents, that is because 25 cents plus 1 dollar 25 cents is 1.50. So you have it \(25\)

The sum of the angles in a triangle is 180∘, so we have p+2q+6p−5q+11p+3q=180. Simplifying, we get 20p=180, so p=9​.

The given expression can be rewritten as follows:

1 + 4 + 2 + 8 + 3 + 12 + 4 + 16 + ... + 24 + 96 + 25 + 100 = (1 + 2 + 3 + 4 + ... + 25) + (4 + 8 + 12 + ... + 96 + 100)

The first sum is an arithmetic series with first term 1, last term 25, and common difference 1. The sum of an arithmetic series is given by the following formula:

S_n = \frac{n(a_1 + a_n)}{2}

where n is the number of terms, a1​ is the first term, and an​ is the last term. In this case, n=25, a1​=1, and an​=25, so the sum of the first series is:

S_1 = \frac{25(1 + 25)}{2} = 312.5

The second sum is an arithmetic series with first term 4, last term 100, and common difference 4. The sum of an arithmetic series is given by the following formula:

S_n = \frac{n(a_1 + a_n)}{2}

where n is the number of terms, a1​ is the first term, and an​ is the last term. In this case, n=25, a1​=4, and an​=100, so the sum of the second series is:

S_2 = \frac{25(4 + 100)}{2} = 562.5

Therefore, the value of the given expression is:

1 + 4 + 2 + 8 + 3 + 12 + 4 + 16 + ... + 24 + 96 + 25 + 100 = S_1 + S_2 = 312.5 + 562.5 = 875

One Bagel costs 275 Cents 

t=#of toast 

b=#of bagels

m=#of muffins

2t+b=3.15

b+m=3.5

t+2b+3m=8.15

t=3.15-b                       ( b+m=3.5 which means two more muffins means its an extra 1.5 dollars so one muffin would be .75)

3.15-b+2b+3m=8.15 =  b+3m=5  

b=5-2.25

b=2.25 dollars which equals to 225 cents 

Hi Guest!

I would love to explain this problem to you, but my friend X² already gave a wonderful explanation at https://web2.0calc.com/questions/helpelp#r3.

Thanks,

vockey

Find the ordered triple (p,q,r) that satisfies the following system:  

p - 2q = 3  

q - 2r = -2 + q  

p + r = 9 + p  

We'll identify the three equations as equations 1, 2, and 3.  

p - 2q = 3           (eq 1)  

q - 2r = -2 + q     (eq 2)  

p + r = 9 + p        (eq 3)  

by (eq 3)                                              p + r  =  9 + p  

subtract p from both sides                         r  =  9  

by (eq 2)                                            q – 2r  =  –2 + q  

subtract q from both sides                      –2r  =  –2  

divide both sides by –2                               r  =  1  

If the system is to be true, then  

r cannot be equal to both 9 and 1,  

so there must be something wrong  

with the problem as stated.                   cannot be solved  

_.

There is a mistake in your question. Check it carefully and re-submit it.

a  +  (a*b) ==250,   

a  -  (a*b) == - 240, solve for a, b

Use substitution to get:

a ==5  and  b==49

7 / 12 ==0.58333.......==58.33% percentage of people who are bored by cable news.

280 / (7/12)==280  x  12/7 ==480 - total number of people at the Math Convention.

480  -  280 ==200 people who are NOT bored by the cable news.

1 + 2 + 3 + 4==10 sum of all ratios.

180 / 10 ==18 - this is the constant

18  x  1 ==18 yellow marbles

18  x  2==36 green marbles

18  x  3==54 blue narbles

18  x  4==72 white marbles.

The equation of the plane can be rewritten as z = -\frac{2}{3}x - \frac{1}{3}y. The normal vector to the plane is (2/3, 1/3, -1). The projection of v onto the plane is given by

p = \frac{v \cdot \hat{n}}{\hat{n} \cdot \hat{n}} \hat{n}

where n^ is the unit normal vector to the plane. Plugging in the values, we get

p = \frac{(1,0,1) \cdot (2/3, 1/3, -1)}{(2/3)^2 + (1/3)^2 + (-1)^2} (2/3, 1/3, -1) = \frac{1}{2} (2/3, 1/3, -1) = \boxed{\left(\frac{1}{3},\frac{1}{6},-\frac{1}{2}\right)}

By simple inspection

a = -1 and b = -1 and c = 3
a = -1 and b = 3 and c = -1
a = 3 and b = -1 and c = -1

I could find only 6 such right triangles as follows:

         A     B   H

1  = (16, 12, 20)
2  = (12, 16, 20)
3  = (24, 10, 26)
4  = (10, 24, 26)
5  = (40, 9, 41)
6  = (9, 40, 41)

Their total areas =792

Hello! Here's a solution: https://web2.0calc.com/questions/need-help-with-system_6. Let me know if this is incorrect.

Hello! The answer is simplfy 45-8, which equals 37.

Hello! I'm not sure if me or the other person is correct but I got 5 as my answer. 

20*h= 100

h = 100/20 = 5

To check the answer:

32+8=40/2=20*5=100

Therefore I think the answer is 5.

Can you please post the diagram?

The distance between V and the line is 3*sqrt(5)/2.