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I am Lyosha [343]
3 years ago
7

Substitution method for 7x-2y=1 & x-2y=1

Mathematics
1 answer:
RUDIKE [14]3 years ago
6 0
We want to use the Substitution method to solve
7x - 2y = 1          (1)
x - 2y = 1           (2)

From equation (1), obtain
2y = 7x - 1          (3)

Substitute (3) into (2).
x - (7x - 1) = 1
-6x + 1 = 1
-6x = 0
x = 0

From (3), obtain
2y = 7*0 - 1 = -1
y = -1/2

Answer: (0, -1/2)  or x=0, y= -1/2.

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Y_Kistochka [10]
X = price of the ingredients

so based on the proportion , we can write that :
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peanut needed   =  2x   = 2x * $ 8     =  $ 16x
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Equation = 
12x + 16x + 18x  ≤  $ 23

46x                  =     $23

x    =  $ 0.5

The pound of mix he can made :

0.5 * 1 pound of almond  + 0.5 x  * 2 pound of peanuts + 0.5 * 3 pound of raisins

= 3 Pound of mix

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3 years ago
Straight line depreciation. A car has an initial value of 29,564 and depreciates 532 a year . V represents value of car after t
LenaWriter [7]
V=29,564-532t would be the equation for that scenario
5 0
3 years ago
hello. I hope your day was fine and have some difficulties in the three question I just took a picture of please help me ​
goblinko [34]
What do you wanna find in these questions?
3 0
3 years ago
Can someone help me
Lemur [1.5K]
Multiplying fractions is just multiplying the numerators together and the denominators together.

\sf\dfrac{4}{7}\times\dfrac{1}{4}\rightarrow\dfrac{4\times 1}{7\times 4}\rightarrow\dfrac{4}{28}\rightarrow\dfrac{1}{7}

\sf\dfrac{4}{7}\times\dfrac{1}{6}\rightarrow\dfrac{4\times 1}{7\times 6}\rightarrow\dfrac{4}{42}\rightarrow\dfrac{2}{21}

To find out which one is bigger, we need a common denominator. The LCM of 7 and 21 is 21, so convert the first fraction into a denominator of 21. 7 goes into 21 three times, multiply this to the numerator and denominator:

\sf\dfrac{1}{7}\rightarrow\dfrac{1\times 3}{7 \times 3}\rightarrow\dfrac{3}{21}

Now just compare the numerators to see which one is bigger.

\sf\dfrac{3}{21}>\dfrac{2}{21} therefore, \sf\dfrac{4}{7}\times\dfrac{1}{4}>\dfrac{4}{7}\times\dfrac{1}{6}
5 0
3 years ago
Simplify this please​
Ugo [173]

Answer:

\frac{12q^{\frac{7}{3}}}{p^{3}}

Step-by-step explanation:

Here are some rules you need to simplify this expression:

Distribute exponents: When you raise an exponent to another exponent, you multiply the exponents together. This includes exponents that are fractions. (a^{x})^{n} = a^{xn}

Negative exponent rule: When an exponent is negative, you can make it positive by making the base a fraction. When the number is apart of a bigger fraction, you can move it to the other side (top/bottom). a^{-x} = \frac{1}{a^{x}}, and to help with this question: \frac{a^{-x}b}{1} = \frac{b}{a^{x}}.

Multiplying exponents with same base: When exponential numbers have the same base, you can combine them by adding their exponents together. (a^{x})(a^{y}) = a^{x+y}

Dividing exponents with same base: When exponential numbers have the same base, you can combine them by subtracting the exponents. \frac{a^{x}}{a^{y}} = a^{x-y}

Fractional exponents as a radical: When a number has an exponent that is a fraction, the numerator can remain the exponent, and the denominator becomes the index (example, index here ∛ is 3). a^{\frac{m}{n}} = \sqrt[n]{a^{m}} = (\sqrt[n]{a})^{m}

\frac{(8p^{-6} q^{3})^{2/3}}{(27p^{3}q)^{-1/3}}        Distribute exponent

=\frac{8^{(2/3)}p^{(-6*2/3)}q^{(3*2/3)}}{27^{(-1/3)}p^{(3*-1/3)}q^{(-1/3)}}        Simplify each exponent by multiplying

=\frac{8^{(2/3)}p^{(-4)}q^{(2)}}{27^{(-1/3)}p^{(-1)}q^{(-1/3)}}        Negative exponent rule

=\frac{8^{(2/3)}q^{(2)}27^{(1/3)}p^{(1)}q^{(1/3)}}{p^{(4)}}        Combine the like terms in the numerator with the base "q"

=\frac{8^{(2/3)}27^{(1/3)}p^{(1)}q^{(2)}q^{(1/3)}}{p^{(4)}}        Rearranged for you to see the like terms

=\frac{8^{(2/3)}27^{(1/3)}p^{(1)}q^{(2)+(1/3)}}{p^{(4)}}        Multiplying exponents with same base

=\frac{8^{(2/3)}27^{(1/3)}p^{(1)}q^{(7/3)}}{p^{(4)}}        2 + 1/3 = 7/3

=\frac{\sqrt[3]{8^{2}}\sqrt[3]{27}p\sqrt[3]{q^{7}}}{p^{4}}        Fractional exponents as radical form

=\frac{(\sqrt[3]{64})(3)(p)(q^{\frac{7}{3}})}{p^{4}}        Simplified cubes. Wrote brackets to lessen confusion. Notice the radical of a variable can't be simplified.

=\frac{(4)(3)(p)(q^{\frac{7}{3}})}{p^{4}}        Multiply 4 and 3

=\frac{12pq^{\frac{7}{3}}}{p^{4}}        Dividing exponents with same base

=12p^{(1-4)}q^{\frac{7}{3}}        Subtract the exponent of 'p'

=12p^{(-3)}q^{\frac{7}{3}}        Negative exponent rule

=\frac{12q^{\frac{7}{3}}}{p^{3}}        Final answer

Here is a version in pen if the steps are hard to see.

5 0
3 years ago
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