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2 years ago

Four times the sum of twice a number and -3 is less than times that same number

Mathematics

1 answer:

MakcuM [25]2 years ago

3 0

Four times the sun of twice a number and -3

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You are building a shelf that fits in a corner. In the figure, the entire shelf is △XYZ. Each unit in the coordinate plane repre

natima [27]

Complete Question: You are building a shelf that fits in a corner in the figure the entire shelf is XYZ each unit in the coordinate plane represents one inch find the area of the shelf.

Answer:

112.5 units²

Step-by-step explanation:

Area of the shelf = ½*base*height.

The base is the distance between Z(0, 5) and Y(15, 5)

The height is the distance between X(15, 20) and Y(15, 5).

Therefore area of the shelf = ½*ZY*XY

Use the distance formula to find ZY and XY.

Distance between Z(0, 5) and Y(15, 5):

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

Let,

$Z(0, 5) = (x_1, y_1)$

$Y(15, 5) = (x_2, y_2)$

$ZY = \sqrt{(15 - 0)^2 + (5 - 5)^2}$

$AB = \sqrt{(15)^2 + (0)^2}$

$AB = \sqrt{225 + 0} = \sqrt{225}$

$AB = 15$

Distance between X(15, 20) and Y(15, 5):

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

Let,

$X(15, 20) = (x_1, y_1)$

$Y(15, 5) = (x_2, y_2)$

$XY = \sqrt{(15 - 15)^2 + (5 - 20)^2}$

$XY = \sqrt{(0)^2 + (-15)^2}$

$XY = \sqrt{0 + 225} = \sqrt{225}$

$XY = 15$

Area of shelf = ½*15*15 = ½*225 = 112.5 units²

4 0

3 years ago

Solve this equation 3+5/2x=1/2x-8

guajiro [1.7K]

Answer:

Step-by-step explanation:

3 0

3 years ago

Find the value of x. Express your answer in simplest radical form

klemol [59]

Since x=x, this is an isosceles right triangle. By the Pythagorean Theorem:

h^2=a^2+b^2 (the hypotenuse squared is equal to the sum of the squared sides)

5^2=x^2+x^2

25=2x^2

2x^2=25

x^2=25/2

x=√(25/2)

x=5/√2 now if we rationalize the denominator...

x=(5√2)/(√2√2)

x=(5√2)/2

7 0

3 years ago

Wich is the first step in simplifying the expression 2(x+3)+5

34kurt

Mult 2 by x you'll get 2x then 2 by 3 you'll get 6 and add 6 to 5, after that you'll get 11 it should look like this 2x+11.

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3 years ago

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Simplify the expression 4|-4|

Naddik [55]

An absolute value means something distance from 0, so |8| = 8 because the distance of 8 from 0 is 8. However the |-8| still equals 8 because the distance from -8 to 0 is 8

So with that in mind, we know that |-4| is 4 because the distance -4 is from 0 is 4

So we have 4*4 = 16

3 0

3 years ago

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