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3 years ago

The perimeter of a rectangular concrete patio is 34 meters. the area is 70 square meters. what are the dimensions of the patio?

Mathematics

1 answer:

Ad libitum [116K]3 years ago

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A triangle with two vertices located at (5, −8) and (5, 4) has an area of 48 square units. Determine one possible location of th

RoseWind [281]

Answer:x=1.5

Step-by-step explanation:

Given

Two points co-ordinates are given

A=(5,-8)

B=(5,4)

let other point be C =(x,y)

Area of triangle is given by

$A=\begin{vmatrix}5& -8&1\\5& 4&1\\x& y&1\end{vmatrix}$

$A=5\left ( 4-y\right )+8\left ( 5-x\right )+1\left ( 5y-4x\right )$

A=20-5y+40-8x+5y-4x

A=60-8x

and A=48 square unit

48=60-8x

x=1.5

As area is independent of y therefore at x=1.5 any value of y will give area of 48 square unit

7 0

3 years ago

Solve the proportion

mario62 [17]

Answer:

$\boxed{\sf x = 5}$

Step-by-step explanation:

$\sf Solve \: for \: x \: over \: the \: real \: numbers: \\ \sf \implies \frac{2}{x - 3} = \frac{5}{x} \\ \\ \sf Take \: the \: reciprocal \: of \: both \: sides: \\ \sf \implies \frac{x - 3}{2} = \frac{x}{5} \\ \\ \sf Expand \: out \: terms \: of \: the \: left \: hand \: side: \\ \\ \sf \implies \frac{x}{2} - \frac{3}{2} = \frac{x}{5} \\ \\ \sf Subtract \: \frac{x}{5} - \frac{3}{2} \: from \: both \: sides: \\ \sf \implies \frac{x}{2} - \frac{3}{2} - ( \frac{x}{5} - \frac{3}{2} ) = \frac{x}{5} - ( \frac{x}{5} - \frac{3}{2} ) \\ \\ \sf \implies \frac{x}{2} - \frac{3}{2} - \frac{x}{5} + \frac{3}{2} = \frac{x}{5} - \frac{x}{5} + \frac{3}{2} \\ \\ \sf \frac{x}{5} - \frac{x}{5} = 0 : \\ \sf \implies \frac{x}{2} - \frac{x}{5} - \frac{3}{2} + \frac{3}{2} = \frac{3}{2} \\ \\ \sf \frac{3}{2} - \frac{3}{2} = 0: \\ \sf \implies \frac{x}{2} - \frac{x}{5} = \frac{3}{2} \\ \\ \sf \frac{x}{2} - \frac{x}{5} = \frac{5x - 2x}{10} = \frac{3x}{10} : \\ \sf \implies \frac{3x}{10} = \frac{3}{2} \\ \\ \sf Multiply \: both \: sides \: by \: \frac{10}{3} : \\ \sf \implies \frac{3x}{10} \times \frac{10}{3} = \frac{3}{2 } \times \frac{10}{3} \\ \\ \sf \frac{3x}{10} \times \frac{10}{3} = \cancel{\frac{3}{10} } \times( x) \times \cancel{ \frac{10}{3} } = x : \\ \sf \implies x = \frac{3}{2} \times \frac{10}{3} \\ \\ \sf \frac{3}{2} \times \frac{10}{3} = \cancel{ \frac{3}{2} } \times \cancel{ \frac{3}{2} } \times 5 : \\ \sf \implies x = 5$

8 0

3 years ago

What is the name of a shape with two parallel sides and four right angles

Sonja [21]

A square has two parallel sides and four right angles.

6 0

2 years ago

Read 2 more answers

A ramp is to be built beside the steps to the campus library. Find the angle of elevation of the 23-foot ramp, to the nearest

Usimov [2.4K]

Answer:

the angle of elevation is 12.56°

Step-by-step explanation:

the height of the ramp represents the opposite side and the length of the ramp the hypotenuse

we see that it has (angle, hypotenuse, opposite)

well to start we have to know the relationship between angles, legs and the hypotenuse

a: adjacent

o: opposite

h: hypotenuse

sin α = o/h

cos α= a/h

tan α = o/a

we choose the one with opposite and hypotenuse

sin α = o/h

sin α = 5ft / 23ft

sin α = 5/23

α = sin^-1 ( 5/23)

α = 12.56°

the angle of elevation is 12.56°

3 0

3 years ago

What is the result of adding these two equations?<br> 6x + 2y = -2<br> 3x – 2y = -5

Artemon [7]

Answer:

x=-7/9

y = 12/9

Step-by-step explanation:

6x + 2y = -2

3x - 2y = -5

9x = -7 (-2y and +2y eliminated)

x = -7/9

if 3x -2y = -5 then

3 ×(-7/9) -2y =-5➡

-21/9 -2y = -5➡

-2y = -5 + 21/9

-2y = -24/9

8 0

3 years ago

Read 2 more answers