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3 years ago

Solve the following system of equations using the substitution method.

1 answer:

7 0

X=2y
2x+5y=9

substitute the x=2y into the second equation
2(2y)+5y=9
multiple the 2y by 2. 4y+5y=9
combine like terms. 9y=9
divide the 9 out from both sides. y=1
plug the y back into the first equation
x=2(1)
multiply. x=2

your answer is: x=2
y=1

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Determine whether each equation is True or False. In case you find a "False" equation, explain why is False.

elixir [45]

Answer:

(1) TRUE.

(2) FALSE.

(3) FALSE.

(4) TRUE.

(5) FALSE.

Step-by-step explanation:

(1) $\sqrt{32} = 2^{\frac{5}{2} }$

$2^{\frac{5}{2} } = (\sqrt{2} )^5 = (\sqrt{2} \ \times \ \sqrt{2} \ \times \ \sqrt{2} \ \times \ \sqrt{2} \ \times \ \sqrt{2}) = 4\sqrt{2}\\\\\sqrt{32} = \sqrt{16 \ \times \ 2}\ = \ \sqrt{16} \ \times \ \sqrt{2} \ = \ 4\sqrt{2}$

Thus, the equation is TRUE.

(2) $16^{\frac{3}{8} } = 8^2$

$16^{\frac{3}{8} } =(2^4)^{\frac{3}{8} } = 2^\frac{3}{2} }= (\sqrt{2} )^3 = (\sqrt{2} \ \times \ \sqrt{2} \ \times \ \sqrt{2}) = 2\sqrt{2} \\\\8^2 = 64$

Thus, the equation is FALSE.

(3) $4^{\frac{1}{2} } = \sqrt[4]{64}$

$4^{\frac{1}{2} }= \sqrt{4} = 2\\\\\sqrt[4]{64} = (64)^{\frac{1}{4} } = (2^6)^{\frac{1}{4} }= 2^{\frac{6}{4} } = 2^{\frac{3}{2} }=(\sqrt{2} )^3 = (\sqrt{2} \times \sqrt{2} \times \sqrt{2} ) = 2\sqrt{2}$

Thus, the equation is FALSE.

(4) $2^8 = (\sqrt[3]{16} )^6$

$2^8 = 256\\\\ (\sqrt[3]{16} )^6 = (16)^{\frac{6}{3} } = (2^4)^{\frac{6}{3} } = (2)^{\frac{24}{3} } = 2^8 = 256$

Thus, the equation is TRUE.

(5) $(\sqrt{64} )^{\frac{1}{3} } = 8^{\frac{1}{6} }\\\\$

$8^{\frac{1}{6} } = (2^3)^{\frac{1}{6} } = 2^{\frac{3}{6} } = 2^{\frac{1}{2} } = \sqrt{2} \\\\(\sqrt{64} )^{\frac{1}{3} } = (2^6)^{\frac{1}{3} } = 2^{\frac{6}{3} } = 2^2 = 4$

Thus, the equation is FALSE.

4 0

3 years ago

Does anyone know how to like graph it for me like just tell me where they go please and thank you!

emmainna [20.7K]

Answer:(0,4), (-1,0), (-4,-2)

Step-by-step explanation:

5 0

3 years ago

Dovator [93]

12^2=144

144 is divided by b which also is an odd interger, there only 2 numbers : 1 and 3

if b=3, a^2=48, then there will be no a available

if b=1 , a^2=144, then a is 12 and 12 can not be divided by 9

The answer is D

3 0

3 years ago

How to write an equation and use The Distributive Property .

Airida [17]

<h2>Answer</h2>

Distributive Property

The distributive property states that when a factor is multiplied by the sum of two numbers, you can multiply each of the two numbers by that factor and then add them.

<h2>Example</h2><h3>Equation </h3>

10(x + 2) = 45

Apply the distributive property to the left side of the equation by multiplying

two numbers inside the parentheses by 10

10(x) + 10(2) = 45

Now add them

10x + 20 = 45

Rearrange the like terms

10x = 45 -20

10x = 25

x = 25/10

x = 2.5

7 0

3 years ago

Sketch the graph of y (x +3)2-4 and identify the axis of symmetry.

masya89 [10]

The axis of symmetry is at x = -3.

This can be found by looking at the basic form of vertex form:

y = (x - h)^2 + k

In this basic form the vertex is (h, k). By looking at what is plugged into the equation, it is clear that h = -3 and k = -4. This means the vertex is at (-3, -4).

It is a fact that the axis of symmetry is a vertical line of x = (vertex value of x). So we can determine that the axis of symmetry is at x = -3

6 0

3 years ago