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4 years ago

PLZ HELP! please answer both if you can!!

Mathematics

1 answer:

aniked [119]4 years ago

5 0

Answer:

0.324m^2 ; 18 ft

Step-by-step explanation:

Given the triangle :

Base (b) of triangle = 54cm

Height (h) of triangle = 1.2m

Area(A) of a triangle is given by:

0.5 * base * height

Base = 54cm = 54/100 = 0.54 m

Therefore,

A = 0.5 * 0.54m * 1.2m

A = 0.324m^2

2.) Average of the two bases in the trapezoid :

From the trapezium Given :

Base 1 = 15 feets

Base 2 = 7 yards

1 yard = 3 Feets

Therefore, base 2 in Feets = 7 * 3 = 21 Feets

Average of the two bases :

(21 Feets + 15 Feets) / 2

= 36 Feets / 2

= 18 Feets

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A rectangular garden of area 456 square feet is to be surrounded on three sides by a brick wall costing $ 12 per foot and on one

solniwko [45]

Answer:

$l=2\sqrt{114}feet$ $b=2\sqrt{114}feet$ $\left ( l,b \right )=(21.3541,21.3541)$

Step-by-step explanation:

Given,

Area of garden=456 square feet

Brick wall cost three sides $=\$ 12$ per foot

fencing cost of one side $=\$ 7$ per foot

Let length and breadth of rectangular field is (l,b) feet

For minimizing the cost of material perimeter of garden should be minimum and area of garden is more.

Perimeter of garden $=2\left ( l+b \right )=k$

$l+b=k/2$

$l=k/2-b$

A= $l\times b=456$

A= $\left ( k/2-b \right )b=456$

Differentiating the equation to find maximum area

$\frac{d}{db}(\left ( k/2-b \right )b)=\frac{\partial 456}{\partial b}$

$k/2-2b=0$

$k=4b$

$l=4b/2-b$

$l=b$

To find $maxima$ again differentiating

$\frac{\partial A^2 }{\partial b^2}=\frac{\partial \left ( k/2-2b \right )}{\partial b}$

$\frac{\partial A^2 }{\partial b^2}$

The area is maximum when l=b

and perimeter is minimum

$l\times b=456$

$b^{2}=456$

$b=2\sqrt{114}feet$

$l=2\sqrt{114}feet$

Cost material

$=2\sqrt{114}\times 3\times 12+2\sqrt{114}\times 7$

$=72\sqrt{114}+14\sqrt{114}$

$=\$ 86\sqrt{114}$

$=\$ 918.22873$

Dimension of rectangular garden

$\left ( l,b \right )=(21.3541,21.3541)$

4 0

3 years ago

⚠️10 points⚠️

Lostsunrise [7]

Answer:

8.9

Step-by-step explanation:

The distance between each point is 8.9, hope this helps!

7 0

3 years ago

Tyler's father is a used car salesman. He receives 5% commission for every car he sells. How much commission does he earn if he

hoa [83]

Answer:

$23,100

Step-by-step explanation:

First you find 5% of 22,000 which is 1,100. You earn commission so you add 1,100 to 22,000. Therefore getting your answer of $23,100.

4 0

3 years ago

Find the solution of this system of equations -x-4y=-37 -2x-5y=-53

zzz [600]

Answer:

The solution in point form is (9,7) and the equation would be x+9, y=7

Step-by-step explanation:

By using moving the -4y to the right side and by flipping the signs you can turn the equation -x-4y=-37 into x=37-4y.

With this new equation you can use the substitution method and replace the x in -2x-5y=-53 with 37-4y, making it look like this: -2(37-4y)-5y=-53.

Then you solve for y getting y=7.

With the value of y, you can plug that into the equation x=37-4y so it will look like x=37-4(7)

Then you solve for x getting x=9

And with that you get the point (9,7)

7 0

3 years ago

Solve the inequality: -40 < 2(a + 12).

ioda

Answer:

a> -32

Step-by-step explanation:

-40 < 2(a +12)

-40 < 2(a) +2(12) (expand)

-40 < 2a +24

-40 -24 < 2a (bring constant to one side)

-64 < 2a (simplify)

2a > -64

a > -64 ÷2

a > -32

7 0

3 years ago