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2 years ago

The figure shows a rhombus ABCD. The diagonal DB is produced to E such that BC = BE and CDE = 46°.

Mathematics

1 answer:

natita [175]2 years ago

6 0

Answer:

(i) 88°

(ii) 23°

Step-by-step explanation:

See the picture below.

The numbers added in red are the angle measures. The numbers added in black are the order in which each angle measure was written.

ABCD is a rhombus, so all sides are congruent.

Triangle BCD is isosceles with sides DC and BC congruent, so <DBC is congruent to <BDC. From the sum of the measures of the angles of a triangle, we get m<DCB. Opposite angles of a rhombus are congruent, so m<A = m<DCB. From the sum of the measures of the angles of a triangle and from isosceles triangle ADB we get m<ADB and m<ABD. From m<DBC and supplementary angles, we get m<CBE. From isosceles triangle BCE, we get m<BCE.

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erik [133]

$2.=c.\\\\2\sin4x\cos4x=2\sin(2\cdot4x)=2\sin8x\\\\Used:\\\sin2\alpha=2\sin\alpha\cos\alpha$

$1.=b.\\\\\csc x-\sin x=\dfrac{1}{\sin x}-\dfrac{\sin^2x}{\sin x}=\dfrac{1-\sin^2x}{\sin x}=\dfrac{\cos^2x}{\sin x}\\\\=\dfrac{\cos x\cos x}{\sin x}=\cos x\cdot\dfrac{\cos x}{\sin x}=\cos x\cot x\\\\Used:\\\csc x=\dfrac{1}{\sin x}\\\\\sin^2x+\cos^2x=1\to\cos^2x=1-\sin^2x\\\\\cot x=\dfrac{\cos x}{\sin x}$

$3.=a.\\\\\dfrac{\sin x-1}{\sin x+1}=\dfrac{\sin x-1}{\sin x+1}\cdot\dfrac{\sin x+1}{\sin x+1}=\dfrac{\sin^2x-1^2}{(\sin x+1)^2}=\dfrac{\sin^2x-1}{(\sin x+1)^2}\\\\=\dfrac{-(1-\sin^2x)}{(\sin x+1)^2}=\dfrac{-\cos^2x}{(\sin x+1)^2}\\\\Used:\\(a-b)(a+b)=a^2-b^2\\\\\sin^2x+\cos^2x=1\to \cos^2x=1-\sin^2x$

8 0

3 years ago

In a fractional-reserve banking system with no excess reserves and no currency holdings, if the central bank buys $100 million w

loris [4]

Answer:

reserves increase by $100 million and the money supply increases by more than $100 million.

Step-by-step explanation:

Consider the provided information.

It is given that central bank buys $100 million worth of bonds, that means an amount of $100 million in the deposits account of the account holders.

Therefore the reserves increase by $100 million.

It is also given that there are no excess reserves, it means banks can lend the reserves and that will increase the money supply by more than $100 million.

Hence, reserves increase by $100 million and the money supply increases by more than $100 million.

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3 years ago

Simplify (2x-3)(5x⁴-7x³+6x²-9)

alexdok [17]

The answer to this question is....

6 0

3 years ago

Naruto drew a right triangle on the ground. While he doesnt know the measures of the other two angles he does know that one is a

tiny-mole [99]

Answer:

30°, 60°

Step-by-step explanation:

Let x represent the measure of the smaller angle in degrees. Then the larger unknown angle is 2x, and the sum of the angles in the triangle is 180°:

x + 2x + 90° = 180° . . . the sum of the angles in the triangle

3x = 90° . . . . . . . . . . . . subtract 90°, collect terms

x = 30° . . . . . . . . . . . . . divide by 3; this is the smaller angle

2x = 60° . . . . . . . . . . . .this is the larger angle

The two angles that are not the right angle are 30° and 60°.

7 0

4 years ago

Read 2 more answers

Use the Quadratic Formula to solve x2 + 20x + 98 = 0

Lubov Fominskaja [6]

$ax^2+bx+c=0\\\\\Delta=b^2-4ac\\\\if\ \Delta \ \textless \ 0\ then\ no\ solution\\\\if\ \Delta =0\ then\ one\ solution\ x_0=\dfrac{-b}{2a}\\\\if\ \Delta \ \textgreater \ 0\ then\ two\ solutions\ x_1=\dfrac{-b-\sqrt\Delta}{2a}\ and\ x_2=\dfrac{-b+\sqrt\Delta}{2a}\\-----------------------------$

$x^2+20x+98=0\\a=1;\ b=20;\ c=98\\\\\Delta=20^2-4\cdot1\cdot98=400-392=8 \ \textgreater \ 0\\\sqrt\Delta=\sqrt8=\sqrt{4\cdot2}=\sqrt4\cdot\sqrt2=2\sqrt2\\\\x_1=\dfrac{-20-2\sqrt2}{2\cdot1}=\dfrac{-20-2\sqrt2}{2}=-10-\sqrt2\\\\x_2=\dfrac{-20+2\sqrt2}{2\cdot1}=\dfrac{-20+2\sqrt2}{2}=-10+\sqrt2$

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4 years ago