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3 years ago

What is m angle A B E?

Mathematics

1 answer:

sattari [20]3 years ago

6 0

Answer:

∠ABE = 60°
∠DBE = 40°
∠FBA = 47°
y = 2

Step-by-step explanation:

The various markings tell you that ...

GH = GI

5x -10 = 3x

2x = 10

x = 5

and

∠ABD ≅ ∠DBC

10y° = (8y+4)°

2y = 4

y = 2

The markings on GH and GI tell you that ΔGBI ≅ ΔGBH, so ...

∠CBE ≅ ∠DBC ≅ ∠ABD = 10y° = 20°

A) m∠ABE = 60° . . . matches choice D

B) m∠DBE = 40° . . . matches choice C

C) m∠FBA = 7(5) +6(2) = 35 +12 = 47 . . . matches choice C

D) The value of y is 2. . . . matches choice A

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Can someone please help me answer these 2 questions with a full explanation so I can do the rest on my own? will give brainliest

Anton [14]

Answer:

a) ∠ABC = 54°

a) ∠ABC = 43°

Step-by-step explanation:

Trigonometric ratios

$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$

where:

$\theta$ is the angle
O is the side opposite the angle
A is the side adjacent the angle
H is the hypotenuse (the side opposite the right angle)

Part (a)

Use the cos trig ratio to find an expression for the measure of BD:

$\implies \sf \cos (38^{\circ})=\dfrac{BD}{24.3}$

$\implies \sf BD=24.3\cos (38^{\circ})$

Use the cos trig ratio and the found length of BD to find angle ABD:

$\sf \implies \cos(ABD)=\dfrac{BD}{19.9}$

$\sf \implies \angle ABD=\cos^{-1}\left(\dfrac{24.3\cos (38^{\circ})}{19.9}\right)$

$\sf \implies \angle ABD=15.79446612...^{\circ}$

Therefore:

$\sf \implies \angle ABC=\angle ADB + 38^{\circ}$

$\sf \implies \angle ABC=15.79446612...^{\circ}+ 38^{\circ}$

$\sf \implies \angle ABC=54^{\circ}\:\:(nearest\:degree)$

Part (b)

Use the tan trig ratio to find angle CAD:

$\implies \sf \tan(CAD)=\dfrac{4.9}{7.4}$

$\implies \sf \angle CAD=\tan^{-1} \left(\dfrac{4.9}{7.4}\right)$

$\implies \sf \angle CAD=33.5110188...^{\circ}$

Therefore:

$\sf \implies \angle BAD=13^{\circ}+33.5110188...^{\circ}$

$\sf \implies \angle BAD=46.5110188...^{\circ}$

∠ABC = ∠ABD

Interior angles of a triangle sum to 180°

$\sf \implies \angle ABD + \angle BAD + \angle BDA=180^{\circ}$

$\sf \implies \angle ABC + 46.5110188...^{\circ} + 90^{\circ}=180^{\circ}$

$\sf \implies \angle ABC=43^{\circ}\:\:(nearest\:degree)$

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2 years ago

What is the mass of a 350 cm cubed sample of pure silicon with a density of 2.336 g/cm cubed?

olganol [36]

D = m
----
v

2.336 g/cm^3 = m
----
350
(350) 2.336 = m

817.6g = m

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3 years ago

Need help ASAP! Directions and problem in the picture;) Will give brainliest

iren2701 [21]

Answer:

x = 24 , y = 19

Step-by-step explanation:

The opposite sides of a parallelogram are congruent , then

2x - 8 = x + 16 ( subtract x from both sides )

x - 8 = 16 ( add 8 to both sides )

x = 24

and

2y = y + 19 ( subtract y from both sides )

y = 19

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2 years ago

At a local fruit stand, luisa spends 3.96 for 2 pounds of strawberries. How much can she expect to pay for 4 pounds of strawberr

Oliga [24]

2 pounds = $3.96
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--------------------------------------------------------------------
Answer: $7.92
--------------------------------------------------------------------

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3 years ago

What are the solutions to the systems? y=x^2-4x-2 y=x-2

kirill115 [55]

y=x^2-4x-2
y=x-2

$x^2-4x-2=x-2\\\\x^2-4x-2-x+2=0\\\\x^2-5x=0\\\\x(x-5)=0\\\\x=0 \ or \ x-5=0$

x=0 or x=5

y = x - 2
1)
x=0
y = 0 - 2= -2
2)
x=5
y=5-2=3

Answer
x=0 , y=-2
or
x=5 , y=3

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3 years ago