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3 years ago

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1. Sally said that when you add or subtract positive or negative decimals, you can change the order of the decimals and still ge

t the same answer. Use these decimals to answer the questions:
-6.2, 5.71, -3.96, 2.84

(a) Is Sally’s statement always true, sometimes true, or always false? Write two pairs of equations using addition and two pairs of equations using subtraction to support your answer.

(b) Write a rule about changing the order of the numbers in adding and in subtracting positive and negative decimals.

(c) Is Sally’s statement true for addition and subtraction of three positive or negative decimals? Write two pairs of equations (one pair for addition, and one pair for subtraction) that support your answer.

1 answer:

gogolik [260]3 years ago

7 0

ally’s answer is sometimes true. -6.2+5.71=-11.91 5.71+-6.2=11.91 5.72-2.84=2.99

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Find the length of the chord made by 3x2 - y2 = 3 and y + x – 5 = 0.

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Answer:

The correct answer is "9√2 units".

Step-by-step explanation:

The given equations are:

⇒ $3x^2-y^2=3$ ...(equation 1)

⇒ $y+x-5=0$ ...(equation 2)

According to the 2nd equation, we get

⇒ $y+x-5=0$

⇒ $y=5-x$

On substituting the value of "y" in the 1st equation, we get

⇒ $3x^2-y^2=3$

$3x^2-(5-x)^2=3$

$3x^2-(25+x^2-10x)=3$

$2x^2+10x-28=0$

On taking common, we get

$x^2+5x-14=0$

On applying factorization, we get

$x^2+7x-2x-14=0$

$x(x+7)-2(x+7)=0$

$(x+7)(x-2)=0$

$x+7=0$

$x=-7$

or,

$x-2=0$

$x=2$

Now,

The points are:

(-7, 12) = (x₁, y₁)

(2, 3) = (x₂, y₂)

By using the distance formula, the length of chord will be:

= $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

On substituting the values in the above formula, we get

= $\sqrt{(2-(-7))^2+(3-12)^2}$

= $\sqrt{(9)^2+(-9)^2}$

= $\sqrt{81+81}$

= $9 \sqrt{2}$ units

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D

This is because the expression can be simplified to get the same result. -1+2log_4((1/4)x)

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