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ivanzaharov [21]
3 years ago
9

If angle adc=134 and adb=5x+4 and bdc=7x-2 what does angle bdc measure

Mathematics
1 answer:
ruslelena [56]3 years ago
8 0
As I've shown on picture that I attached:
∠ADC=∠ADB+∠BDC⇒134=5x+4+7x-2
12x+2=134
12x=132⇒x=132/12
x=11
Angle BDC measure 7x-2=7*11-2⇒∠BDC=75.

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3x+2 if x less than 5
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Anwer:

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Step-by-step explanation:

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3 years ago
If the sum of the even integers between 1 and k, inclusive, is equal to 2k, what is the value of k?
Alisiya [41]
If k is odd, then

\displaystyle\sum_{n=1}^{\lfloor k/2\rfloor}2n=2\dfrac{\left\lfloor\frac k2\right\rfloor\left(\left\lfloor\frac k2\right\rfloor+1\right)}2=\left\lfloor\dfrac k2\right\rfloor^2+\left\lfloor\dfrac k2\right\rfloor

while if k is even, then the sum would be

\displaystyle\sum_{n=1}^{k/2}2n=2\dfrac{\frac k2\left(\frac k2+1\right)}2=\dfrac{k^2+2k}4

The latter case is easier to solve:

\dfrac{k^2+2k}4=2k\implies k^2-6k=k(k-6)=0

which means k=6.

In the odd case, instead of considering the above equation we can consider the partial sums. If k is odd, then the sum of the even integers between 1 and k would be

S=2+4+6+\cdots+(k-5)+(k-3)+(k-1)

Now consider the partial sum up to the second-to-last term,

S^*=2+4+6+\cdots+(k-5)+(k-3)

Subtracting this from the previous partial sum, we have

S-S^*=k-1

We're given that the sums must add to 2k, which means

S=2k
S^*=2(k-2)

But taking the differences now yields

S-S^*=2k-2(k-2)=4

and there is only one k for which k-1=4; namely, k=5. However, the sum of the even integers between 1 and 5 is 2+4=6, whereas 2k=10\neq6. So there are no solutions to this over the odd integers.
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Artyom0805 [142]

Answer:

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Step-by-step explanation:

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Read 2 more answers
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stiv31 [10]

ANSWER

a=-2, b=3

EXPLANATION

The given equation is

(a {x}^{2})( - 6 {x}^{b}  ) = 12 {x}^{5}

Recall that:

{a}^{m}  \times  {a}^{n}  =  {a}^{m + n}

We simplify the left hand side to get:

- 6a {x}^{2 + b}  = 12 {x}^{5}

For this equation to be true, we must have:

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This implies that,

a=-2 and b=3

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=========================================================

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