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3 years ago

How do I solve (|x-3|+5|x|) ?

Mathematics

1 answer:

11111nata11111 [884]3 years ago

6 0

Answer:

x≤0 ⇒|x-3|+5|x| = -6x + 3

0≤x≤3 ⇒ |x-3|+5|x| = 4x + 3

x≥3 ⇒ |x-3|+5|x| = 6x - 3

Step-by-step explanation:

Check the picture below.

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Parallelogram JKLM has vertices J(-1, 6), K(0, 9), L(6, −3), and M(3, −3). What is the coordinates of the image if the parallelo

Digiron [165]

Answer: $(\dfrac13,-2),\ (0,-3),\ (-2,1),\ (-1,1) .$

Step-by-step explanation:

Transformation rule for dilation:

$(x,y)\to(kx,ky)$ , where k = scale factor

Given : Scale factor = $-\dfrac13$

Parallelogram JKLM has vertices J(-1, 6), K(0, 9), L(6, −3), and M(3, −3)

Vertices after dilation:

$(-1,6)\to(-1\times\dfrac{-1}{3},6\times\dfrac{-1}{3})=(\dfrac13,-2)$

$(0,9)\times(0\times-\dfrac13,9\times-\dfrac13)=(0,-3)$

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$(3,-3)\to (3\times-\dfrac13,\ -3\times-\dfrac13)=(-1,1)$

Hence, the coordinates of the image if the parallelogram = $(\dfrac13,-2),\ (0,-3),\ (-2,1),\ (-1,1) .$

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3 years ago

The sum of two and a number is less than five

Furkat [3]

Answer:

Please check the explanation.

Step-by-step explanation:

Given the English statement

''The sum of two and number is less than five''.

Let us breakdown the statement.

Let 'n' be the number.

The sum of two and number = 2 + n

We know that the less than symbol is denoted by '<' which is used for comparison.

Thus, the statement 'The sum of two and a number is less than five' is algebraically represented as:

2 + n < 5

Let us solve the algebraic expression.

$2+n$

Subtract 2 from both sides

$2+n-2$

Simplify

$n$

Thus, the solution is:

$2+n$

Please also check the attached solution line graph.

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3 years ago

45 of the 80 children in the club or girls what was the ratio of boys to girls in the club?

Oxana [17]

There are 80 children. 45 of them are girls. The amount of boys is equal to:

$80-45 = 35$

That means there are 45 girls and 35 boys.

The ratio of boys to girls is: $35:45$

Simplify:

$35 \div 5 = 7 \\ 45 \div 5 = 9 \\ \\35:45 \rightarrow 7:9$

Your answer is 7:9

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3 years ago