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3 years ago

A triangle has base 15ft and area 60 ft^2. what is the height?

Mathematics

1 answer:

shepuryov [24]3 years ago

5 0

Answer:

Height = 8ft

Step-by-step explanation:

Area of triangle = 60ft²

base of triangle = 15ft

$area \: of \: triangle \: = \frac{1}{2} (base)(height) \\ \\ 60 = \frac{1}{2} (15)(height) \\ \\ \frac{60 {ft}^{2} \times 2}{15ft} = height \\ \\ 8ft \: = height$

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Trapezoid EFGH is inscribed in a circle, with <img src="https://tex.z-dn.net/?f=EF%20%5Cparallel%20GH" id="TexFormula1" title="E

oksano4ka [1.4K]

Answer:

Arc EPF is 240°

Step-by-step explanation:

Since the quadrilateral, EFGH is a trapezoid and EF is parallel to GH, we have;

∠HGF + ∠GFE = 180°

∠GHE + ∠GFE = 180°

∠HGF + ∠HEF = 180°

∴∠HEF = ∠GFE

In ΔHEF and ΔGFE

∠EHF = ∠EGF (Angles subtending the same segment)

With side EF common to both triangles and ∠HEF = ∠GFE , we have;

ΔHEF ≅ ΔGFE (Angle Angle Side rule)

Hence, side FG = EH

For cyclic trapezoid side FG = EH

The base angles subtended by GH = 70

Arc EH = x² - 2·x

Arc FG = 56 - 3·x

Therefore;

70 + x² - 2·x + 56 - 3·x + arc EPF = 360 .............(1)

Also since the equation of a circle is (x-h)² + (y-k)² = r², where the center of the circle is (h, k), then as EF is a displacement of say z from GH, then arc EH = FG which gives;

x² - 2·x = 56 - 3·x

x² - 2·x - 56 + 3·x = 0

x² + x - 56 = 0

(x - 7)(x + 8) = 0

Therefore, since x > 0 we have x = 7

Plugging in the value of x into the equation (1), we have

70 + 7² - 2·7 + 56 - 3·7 + arc EPF = 360 .............(1)

70 + 70 + arc EPF = 360

arc EPF = 360 - 140 = 240°.

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3 years ago

A scientist invents a car that can travel for many hours without stopping for fuel. The car travels around a track at 51 miles a

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4 0

3 years ago

Read 2 more answers

Question

IgorLugansk [536]

Answer:

the time is 1.57 sec and the distance is 49.32mm

Step-by-step explanation:

Given that,

The angle is 180°

Angular velocity is 2rev/sec

The radius is 10mm

we are to find the time and distance traveled at that time

The formula is

θ = at

where t is the time,

a is the angular velocity

θ is angle in radian

so,

θ = 180° × π/180°

θ = π

= 3.14

Hence ,

θ = at

3.14 = 2t

t = 1.57sec

let the distance be xmm

$\frac{1.57 \times 180^0}{360} = \frac{x}{20 \pi} \\\\0.785 = \frac{x}{20 \pi} \\\\x = 49.32mm$

Therefore , the time is 1.57 sec and the distance is 49.32mm

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3 years ago

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What are the like terms in the expression 8+ x2 - 4x3 + 5x+ 2x2?

Orlov [11]

Answer:

B. $x^2$ and $2x^2$

Step-by-step explanation:

The expression given is:

$8+ x^2 - 4x^3 + 5x+ 2x^2$

Like terms are terms in which their variables and the power of the variables (exponents) are the same.

While it is not necessary that the coefficient of the variables are the same, the power of the variables must be the same.

In that case, the like terms in the expression given are $x^2$ and $2x^2$ .

Note: The question says $8+ x^2 - 4x^3 + 5x+ 2x^2$ but the option has $-4x^2$ .

In case its actually $-4x^2$ instead of $-4x^3$ , then, $-4x^2$ is also a like term and the answer will be D.

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3 years ago

The Factored form of 4a^3 b^5-16a^5 b^2+ 12a^2 b^3

iren [92.7K]

Answer:

Step-by-step explanation:

4a³b⁵ - 16a⁵b² + 12a²b³ = 4a³b⁵ - 4*4*a⁵b² + 4*3*a²b³

= 4a²b² * (ab³ - 4a³ + 3b )

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3 years ago

A triangle has base 15ft and area 60 ft^2. what is the height?​

A triangle has base 15ft and area 60 ft^2. what is the height?