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vladimir1956 [14]
2 years ago
10

Solve each equation for the given variable: 1) 6a+5a=-11

Mathematics
2 answers:
ivanzaharov [21]2 years ago
4 0
6a+5a=-11 \\
(6+5)a=-11 \\
11a=-11 \\
a=\frac{-11}{11} \\
a=-1
LUCKY_DIMON [66]2 years ago
3 0
6a + 5a=-11. So, 11a=-11 => a =  \frac{-11}{11} , and   a =-1.
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.<br> Evaluate the series 1 + 0.1 + 0.01 + . . .
EastWind [94]

We can employ a simple repeated decimal trick:

x=1.111\ldots

0.1x=0.111\ldots

\implies x-0.1x=1\implies0.9x=1\implies x=\dfrac1{0.9}=\dfrac{10}9

###

Alternatively, we can compute the partial sum of the series.

\displaystyle S_n=\sum_{k=0}^n\dfrac1{10^k}

S_n=1+0.1+0.01+\cdots+\dfrac1{10^n}

0.1S_n=0.1+0.01+0.001+\cdots+\dfrac1{10^{n+1}}

\implies S_n-0.1S_n=0.9S_n=1-\dfrac1{10^{n+1}}

\implies S_n=\dfrac{10}9-\dfrac9{10^n}

As n\to\infty, the second term vanishes and we're left with \dfrac{10}9. Notice that this is really just a more formal version of the earlier trick.

6 0
2 years ago
Read 2 more answers
Rewrite the equation 8x + 6x^2 -7=x^2 in standard form and identify a, b, and c.
Vladimir79 [104]

Answer:

5x^2+8x-7=0\\a=5\\b=8\\c=-7

Step-by-step explanation:

The standard form of a quadratic is ax^2+bx+c=0. You need to subtract the x^2 from the right to set the quadratic equal to 0. Then a,b, and c are equal to the values of the coefficients in front of the terms.

If this helped, a brainliest would be greatly appreciated!

6 0
2 years ago
On Thursday, a local hamburger shop sold a combined total of 378 hamburgers and cheeseburgers. The number of cheeseburgers sold
yuradex [85]

Answer:

252 Cheese Bugers were sold on Thursday

Step-by-step explanation:

378 divided by 3=126

126+126= number of hamburgers

126= number of chese bugers

126+126=252

3 0
2 years ago
A clothing store is selling a shirt for a discounted price of $43.61. If the discount is 11%, what was the original price, in do
svet-max [94.6K]

Answer:

$49

Step-by-step explanation:

Given that the discounted price is $43.61 and this was at an 11% discount

hence the discounted price represents 100% - 11% = 89% of the original price.

if:

89% of original price = $43.61

1% of original price = $(43.61 / 89)

100% of original price = $(43.61 / 89) x 100 = $49

4 0
3 years ago
Read 2 more answers
What does that mean
aivan3 [116]

The question is asking you to find the result when you square root 256.

The symbol of a square root is √

If ² is a square symbol, √ is the one that will convert the number back to it's non-squared form.

You normally can't do this without the calculator.

In this question, √256 = 16

3 0
3 years ago
Read 2 more answers
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