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ohaa [14]
3 years ago
6

The sum of t and 2 is equal to 5 less than t

Mathematics
2 answers:
Alex17521 [72]3 years ago
7 0
The sum (addition) of t and 2 is equal to (=) 5 less than (subtraction) t

2 + t = t - 5  
Gala2k [10]3 years ago
4 0
That has no solution. There's no number that ' t ' can be that would make that description work.
You might be interested in
Mr. Lloyd wants to build a dollhouse for a starter this is a proportional to their house he might have to live in this house and
Kaylis [27]

Answer:

12’ x 16’ = 6 in * 8 in

Step-by-step explanation:

Allow me to revise your question for a better understanding.

<em>Mr. avoid wants to build a doll house for his daughter that is proportional to their house you measure the living room of his house and it was 12’ x 16’ what will the dimensions of the doll house living room if every foot of the actual house equals 1/2 inch in the doll house </em>

My answer:

Given:  

The living room of his house  was 12’ x 16’ and this is the actual house

The dimensions of the doll house living room if every foot of the actual house equals 1/2 inch is:

<=> 1 foot = 1/2 inch

=> the dimensions of the doll house living room is:

12’ x 16’ = 6 inch * 8 inch

3 0
3 years ago
In a triangle, the measure of one angle is five more than the first and the third angle is one more than four times the first.
katrin [286]

Answer:

A= 29

B=34

C=117

Step-by-step explanation:

<u>A triangle has three sides and a triangle always adds up to be 180</u>

A + B + C = 180

B = A + 5

C = 4A + 1

Plug in.

A + A + 5 + 4A + 1 = 180

6A + 6 = 180

6A = 174

A = 29

<u>Now since you found A, find the other two by plugging A in!</u>

C = 4(29) + 1

C = 117

<u>Plug in the B equation</u>

B = 29 + 5

B=34

Check your answers

29 + 117 + 34 = 180

4 0
3 years ago
Can someone please help me figure out how to solve for x?​
Anna007 [38]

Answer:

x=30

Step-by-step explanation:

Both triangles in this figure are similar. Therefore, we can set up the following proportion:

\frac{21}{x}=\frac{14}{20}.

Cross-multiply to solve:

14x=21\cdot 20,\\x=\frac{21\cdot20}{14},\\x=\fbox{$30$}.

8 0
3 years ago
Question (c)! How do I know that t^5-10t^3+5t=0?<br> Thanks!
astra-53 [7]
(a) By DeMoivre's theorem, we have

(\cos\theta+i\sin\theta)^5=\cos5\theta+i\sin5\theta

On the LHS, expanding yields

\cos^5\theta+5i\cos^4\theta\sin\theta-10\cos^3\theta\sin^2\theta-10i\cos^2\theta\sin^3\theta+5\cos\theta\sin^4\theta+i\sin^4\theta

Matching up real and imaginary parts, we have for (i) and (ii),


\cos5\theta=\cos^5\theta-10\cos^3\theta\sin^2\theta+5\cos\theta\sin^4\theta
\sin5\theta=5\cos^4\theta\sin\theta-10\cos^2\theta\sin^3\theta+\sin^5\theta

(b) By the definition of the tangent function,

\tan5\theta=\dfrac{\sin5\theta}{\cos5\theta}
=\dfrac{5\cos^4\theta\sin\theta-10\cos^2\theta\sin^3\theta+\sin^5\theta}{\cos^5\theta-10\cos^3\theta\sin^2\theta+5\cos\theta\sin^4\theta}

=\dfrac{5\tan\theta-10\tan^3\theta+\tan^5\theta}{1-10\tan^2\theta+5\tan^4\theta}
=\dfrac{t^5-10t^3+5t}{5t^4-10t^2+1}


(c) Setting \theta=\dfrac\pi5, we have t=\tan\dfrac\pi5 and \tan5\left(\dfrac\pi5\right)=\tan\pi=0. So

0=\dfrac{t^5-10t^3+5t}{5t^4-10t^2+1}

At the given value of t, the denominator is a non-zero number, so only the numerator can contribute to this reducing to 0.


0=t^5-10t^3+5t\implies0=t^4-10t^2+5

Remember, this is saying that

0=\tan^4\dfrac\pi5-10\tan^2\dfrac\pi5+5

If we replace \tan^2\dfrac\pi5 with a variable x, then the above means \tan^2\dfrac\pi5 is a root to the quadratic equation,

x^2-10x+5=0

Also, if \theta=\dfrac{2\pi}5, then t=\tan\dfrac{2\pi}5 and \tan5\left(\dfrac{2\pi}5\right)=\tan2\pi=0. So by a similar argument as above, we deduce that \tan^2\dfrac{2\pi}5 is also a root to the quadratic equation above.

(d) We know both roots to the quadratic above. The fundamental theorem of algebra lets us write

x^2-10x+5=\left(x-\tan^2\dfrac\pi5\right)\left(x-\tan^2\dfrac{2\pi}5\right)

Expand the RHS and match up terms of the same power. In particular, the constant terms satisfy

5=\tan^2\dfrac\pi5\tan^2\dfrac{2\pi}5\implies\tan\dfrac\pi5\tan\dfrac{2\pi}5=\pm\sqrt5

But \tanx>0 for all 0, as is the case for x=\dfrac\pi5 and x=\dfrac{2\pi}5, so we choose the positive root.
3 0
3 years ago
Evaluate the equation. -4x = 14 A.10 B. 7/2 C. -7/2 D. -10
Alex_Xolod [135]

Answer:

c) -7/2

Step-by-step explanation:

14/-4= -3.5

4 0
3 years ago
Read 2 more answers
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