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2 years ago

If x is a rational number and y is the opposite of x, why do x and y have the same absolute value

Mathematics

1 answer:

grin007 [14]2 years ago

8 0

Answer:

Absolute value is the distance away from zero, so if x is a rational number and y is opposite, they would both be the same distance away from zero, regardless of their sign.

Step-by-step explanation:

Absolute value is the distance of a number away from zero. For example, if x is equal to the rational number -2, the absolute value of -2 is just 2, given that both 2 and -2 are only a distance of 2 away from the number zero. Think of it as your walk or drive to school. If you live 4 miles from school, you drive a distance of 4 miles there and 4 miles back. That distance is not calculated as a positive 4 miles there and a negative 4 miles back, but rather just 4 miles there and 4 miles back, for a total distance of 8 miles. So, if x=4 and y=(-4), the absolute value of both would be 4.

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Henry is designing a model for a dome shaped glasshouse. He creates the model and records the horizontal distance from the edge

dolphi86 [110]

Answer:

Correct choice is B

Step-by-step explanation:

All given options represent quadratic function. Let the equation of this quadratic function be

$f(x)=ax^2+bx+c.$

Then

1. $f(0)=2=a\cdot 0^2+b\cdot 0+c\Rightarrow c=2;$

2. $f(1)=7.5=a\cdot 1^2+b\cdot 1+c\Rightarrow 7.5=a+b+2;$

3. $f(2)=12=a\cdot 2^2+b\cdot 2+c\Rightarrow 12=4a+2b+2.$

Solve the system of two equations:

$\left\{\begin{array}{l}a+b+2=7.5\\4a+2b+2=12\end{array}\right.\Rightarrow\left\{\begin{array}{l}a=5.5-b\\4(5.5-b)+2b=10\end{array}\right.$

Then

$22-4b+2b=10,\\ \\-2b=-12,\\ \\b=6,\\ \\a=5.5-6=-0.5.$

Thus, the equation of the function is

$f(x)=-\dfrac{1}{2}x^2+6x+2.$

Note that

$f(3)=-\dfrac{1}{2}\cdot 3^2+6\cdot 3+2=-4.5+20=15.5;$

$f(4)=-\dfrac{1}{2}\cdot 4^2+6\cdot 4+2=18.$

8 0

2 years ago

Read 2 more answers

Last month customers at a gift shop bought 40 birthday cards, 19 congratulation cards, 20 holiday cards, 21 thank you cards, sup

Lena [83]

Answer:50 customers would be expected to buy birthday cards next month.

Step-by-step explanation:

Last month customers at a gift shop bought 40 birthday cards, 19 congratulation cards, 20 holiday cards, 21 thank you cards. The total number of greeting cards that the customers bought last month would be

40 + 19 + 20 + 21 = 100

Percentage of customers that bought birthday cards last month would be

40/100 × 100 = 40%

supposed 125 customers by greeting cards next month, the expected number of customers that would buy birthday cards next month would be

40/100 × 125 = 50

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3 years ago

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notsponge [240]

8
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2 years ago