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3 years ago

Which biconditional is NOT a good definition ?

Mathematics

1 answer:

alexgriva [62]3 years ago

6 0

Answer:

Step-by-step explanation:

An angle is straight if and only if its measure is 180

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What values of x and y satisfy the system of equations {3x+2y=14x=4y−2? infinitely many solutions (5011,1811) (1811,5011) no sol

irinina [24]

3x+2y=14x=4y-2

(x,y)=(1/4,11/8)

8 0

3 years ago

Write the equation of the line in slope-intercept form using y=mx+b

adelina 88 [10]

Answer:

y = 1/2x+2

Step-by-step explanation:

5 0

3 years ago

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Looking at the top of tower A and base of tower B from points C and D, we find that ∠ACD = 60°, ∠ADC = 75° and ∠ADB = 30°. Let t

katrin2010 [14]

Answer:

$\text{Exact: }AB=25\sqrt{6},\\\text{Rounded: }AB\approx 61.24$

Step-by-step explanation:

We can use the Law of Sines to find segment AD, which happens to be a leg of $\triangle ACD$ and the hypotenuse of $\triangle ADB$ .

The Law of Sines states that the ratio of any angle of a triangle and its opposite side is maintained through the triangle:

$\frac{a}{\sin \alpha}=\frac{b}{\sin \beta}=\frac{c}{\sin \gamma}$

Since we're given the length of CD, we want to find the measure of the angle opposite to CD, which is $\angle CAD$ . The sum of the interior angles in a triangle is equal to 180 degrees. Thus, we have:

$\angle CAD+\angle ACD+\angle CDA=180^{\circ},\\\angle CAD+60^{\circ}+75^{\circ}=180^{\circ},\\\angle CAD=180^{\circ}-75^{\circ}-60^{\circ},\\\angle CAD=45^{\circ}$

Now use this value in the Law of Sines to find AD:

$\frac{AD}{\sin 60^{\circ}}=\frac{100}{\sin 45^{\circ}},\\\\AD=\sin 60^{\circ}\cdot \frac{100}{\sin 45^{\circ}}$

Recall that $\sin 45^{\circ}=\frac{\sqrt{2}}{2}$ and $\sin 60^{\circ}=\frac{\sqrt{3}}{2}$ :

$AD=\frac{\frac{\sqrt{3}}{2}\cdot 100}{\frac{\sqrt{2}}{2}},\\\\AD=\frac{50\sqrt{3}}{\frac{\sqrt{2}}{2}},\\\\AD=50\sqrt{3}\cdot \frac{2}{\sqrt{2}},\\\\AD=\frac{100\sqrt{3}}{\sqrt{2}}\cdot\frac{ \sqrt{2}}{\sqrt{2}}=\frac{100\sqrt{6}}{2}={50\sqrt{6}}$

Now that we have the length of AD, we can find the length of AB. The right triangle $\triangle ADB$ is a 30-60-90 triangle. In all 30-60-90 triangles, the side lengths are in the ratio $x:x\sqrt{3}:2x$ , where $x$ is the side opposite to the 30 degree angle and $2x$ is the length of the hypotenuse.

Since AD is the hypotenuse, it must represent $2x$ in this ratio and since AB is the side opposite to the 30 degree angle, it must represent $x$ in this ratio (Derive from basic trig for a right triangle and $\sin 30^{\circ}=\frac{1}{2}$ ).

Therefore, AB must be exactly half of AD:

$AB=\frac{1}{2}AD,\\AB=\frac{1}{2}\cdot 50\sqrt{6},\\AB=\frac{50\sqrt{6}}{2}=\boxed{25\sqrt{6}}\approx 61.24$

3 0

3 years ago

Read 2 more answers

X + 3/2= 2 1/4 whats the answer

kicyunya [14]

Move all terms not containing x to the right side of the equation.

Exact Form:

x=15/4

Decimal Form:

x=3.75

Mixed Number Form:

x=3 3/4

hope this helps

5 0

2 years ago

Can anybody help me solve this? You must solve for X first.

gogolik [260]

Answer:

45 degrees

Step-by-step explanation:

angle QRS is same as (2x + 3) because it is an isosceles triangle

so, 90 + (2x+3) + (2x+3) =180 degrees

2x+3 +2x+3=180-90

2x+2x +3+3=90

4x+6=90

4x=90-6

4x=84

x=84/4

x=21

substitute x=21 in (2x+3)

2*21+3=45

6 0

3 years ago