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Nitella [24]
2 years ago
10

write a system of linear equations that has only one solution. solve the system of equations in two ways.

Mathematics
1 answer:
Iteru [2.4K]2 years ago
7 0
X + 5y = 1 . . . . (1)
8x - 2y = 3 . . . .(2)
Solution 1.
From (1), x = 1 - 5y
substituting for x in (2), we have:
8(1 - 5y) - 2y = 3
8 - 40y - 2y = 3
8 - 42y = 3
42y = 5
y = 5/42
x = 1 - 5(5/42) = 1 - 25/42 = 17/42.

Solution 2.
Multiply (1) by 8, to get:
8x + 40y = 8 . . . . . (3)
(3) - (2) = 40y - (-2y) = 8 - 3
42y = 5
y = 5/42
substitute for y into (3), to get:
8x + 40(5/42) = 8
8x + 100/21 = 8
8x = 8 - 100/21 = 68/21
x = (68/21)/8 = 17/42
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Divide using synthetic division, and write a summary statement in fraction form. 2x^4-x^3-15x^2+3x/x+3
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So... first off, we sort the dividend, the numerator, in descending order... so, looking at the exponents in this one, is already sorted in descending order, from 4 down to 1, so that's done.

then the divisor, we have x+3, that means x + 3 = 0, x = -3,
so, we'll be using -3 for the synthetic division then.

\bf \cfrac{2x^4-x^3-15x^2+3x}{x+3}\\\\
-------------------------------\\\\

\begin{array}{r|rrrrrrrrrl}
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--&&-&--&--&--\\
&&2&-7&6&\boxed{-15}&\leftarrow remainder
\end{array}

and now, we'll use those coefficients, dropping the exponents of the polynomial by one, and the remainder, remains as a fraction with the divisior of x+3.

\bf 2x^3-7x^2+6x-\frac{15}{x+3}
6 0
3 years ago
Write a multiplication equation using one whole number and one fraction that have a product of 18/8.
DedPeter [7]
18 x 1/8
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3 0
3 years ago
Read 2 more answers
In a sample of 1000 randomly selected consumers who had opportunities to send in a rebate claim form after purchasing a product,
Vadim26 [7]

Answer: 0.2872

Step-by-step explanation:

Given : In a sample of 1000 randomly selected consumers who had opportunities to send in a rebate claim form after purchasing a product, 260 of these people said they never did so.

i.e. n= 1000 and x= 260

⇒ Sample proportion : \hat{p}=\dfrac{260}{1000}=0.26

z-value for 95% confidence interval : z_c=1.960

Now, an upper confidence bound at the 95% confidence level for the true proportion of such consumers who never apply for a rebate. :-

\hat{p}+ z_c\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}

=0.26+ (1.96)\sqrt{\dfrac{0.26(1-0.26)}{1000}}

=0.26+ (1.96)(0.01387)=0.26+0.0271852=0.2871852\approx0.2872

∴ An upper confidence bound at the 95% confidence level for the true proportion of such consumers who never apply for a rebate : 0.2872

7 0
3 years ago
How many 3 digit numbers can you make using these numbers: 4,2,9 (numbers can be reapeated)
bogdanovich [222]

Answer:

You can make 27 different 3 digit numbers

Step-by-step explanation:

Since we can use 3 different numbers this means that each of the 3 digits can be one of the 3 numbers (4,2,9). This means that there are 3 different values for the first digit, 3 different values for the second digit, and 3 different values for the third digit, which mean that we can make 3 x 3 x 3 different 3 digit numbers (we took the number of possible values for each digit and multiplied them together.

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3 years ago
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vodka [1.7K]

Answer:

7/20

Step-by-step explanation:

7/10 ÷ 2/1 is the same as 7/10 * 1/2 which is 7/20

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