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3 years ago

Luis computed his taxable income for last

Mathematics

1 answer:

NISA [10]3 years ago

5 0

Answer:

$1,365

Step-by-step explanation:

According to the tax table, he owes 4,296 in taxes but he paid 5,661.

so his refund is 5661-4296 = 1,365

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Find the length of the shorter leg of a right triangle with the longer leg is 9 feet more than the shorter leg the hypotenuse is

Jobisdone [24]

Answer:

Length of Shorter leg = 27 feet

Length of Longer leg = 36 feet

Length of Hypotenuse = 45 feet

Step-by-step explanation:

Given:

Let,

Length of Shorter leg = x,

According to the given condition we have

∴ Length of Longer leg = x + 9 feet

∴ Length of Hypotenuse = 2x - 9 feet

To Find:

Length of Shorter leg = ?

Solution:

Now In Right Angle Triangle, By Pythagoras theorem we have

$(\textrm{Hypotenuse})^{2} = (\textrm{Shorter leg})^{2}+(\textrm{Longer leg})^{2}$

substituting the given values we get

$(2x-9)^{2} = (x)^{2}+(x+9)^{2}\\$

By using Identity (A ± B)² = A² ± 2AB +B² we get

$4x^{2} -36x+81=x^{2} +(x^{2} +18x+81)\\\\4x^{2} -2x^{2} -36x-18x=81-81\\\\2x^{2} -54x=0\\2x(x-27)=0\\2x=0 or x-27=0\\\therefore x\ cannot\ be \ zero\\\therefore x = 27 \feet$

Substituting x=27 we get

∴ Length of Longer leg = x + 9 =27 +9 = 36 feet

∴ Length of Hypotenuse = 2x - 9 = 2×27 -9 = 45 feet

7 0

3 years ago

onyango wishes to fence a rectangular research plot using 100 m of wire .one end of the plot has a wall already erected .calcula

earnstyle [38]

Answer:

1250 m²

Step-by-step explanation:

Let x and y denote the sides of the rectangular research plot.

Thus, area is;

A = xy

Now, we are told that end of the plot already has an erected wall. This means we are left with 3 sides to work with.

Thus, if y is the erected wall, and we are using 100m wire for the remaining sides, it means;

2x + y = 100

Thus, y = 100 - 2x

Since A = xy

We have; A = x(100 - 2x)

A = 100x - 2x²

At maximum area, dA/dx = 0.thus;

dA/dx = 100 - 4x

-4x + 100 = 0

4x = 100

x = 100/4

x = 25

Let's confirm if it is maximum from d²A/dx²

d²A/dx² = -4. This is less than 0 and thus it's maximum.

Let's plug in 25 for x in the area equation;

A_max = 25(100 - 2(25))

A_max = 1250 m²

5 0

3 years ago

Make v the subject of the formula

EleoNora [17]

$T =\dfrac 5{V+1}\\\\\\\implies VT+T = 5\\\\\implies VT = 5-T\\\\\implies V =\dfrac{5-T}T$

7 0

2 years ago

Read 2 more answers

Evaluate the expression when x=3 and y=5 2xy

bija089 [108]

Answer:

Step-by-step explanation:

Substitute for x and y

2 x 3 x 5 = 6 x 5 = 30

I hope this helped and please mark mark me as brainliest!

7 0

2 years ago

Read 2 more answers

Find the area for a trapezoid 9.85 m 15 m 11 m 9 m

igor_vitrenko [27]

Answer:

total area = 99m² + 39.4m²

= 138.4m²

7 0

2 years ago