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3 years ago

How do I answer this??

Mathematics

1 answer:

Mandarinka [93]3 years ago

4 0

We know that:
∠ABC=∠BCA=xº
∠BDC=∠BCD=xº

1) we have to find the angle ∠DBC:
∠BDC+∠BCD+∠DBC=180º
xº+xº+∠DBC=180º
2xº+∠DBC=180º
∠DBC=180º-2xº

2) we have to find the angle ∠ABD:
∠ABD=∠ABC-∠DBC
∠ABD=xº-(180º-2x)
∠ABD=xº-180º+2xº
∠ABD=3xº-180º

Answer: ∠ABD=3xº-180º

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Perpendicular lines must have a negative slope. do perpendicular lines have slopes which have opposite signs.

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Yes perpendicular lines are negative reciprocals.

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3 years ago

Assume z = x + iy, then find a complex number z satisfying the given equation. d. 2z8 – 2z4 + 1 = 0

kodGreya [7K]

Answer: complex equations has n number of solutions, been n the equation degree. In this case:

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i11,25°}$

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i101,25°}$

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i191,25°}$

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i281,25°}$

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i78,75°}$

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i168,75°}$

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i258,75°}$

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i348,75°}$

Step-by-step explanation:

I start with a variable substitution:

$Z^{4} = X$

Then:

$2X^{2}-2X+1=0$

Solving the quadratic equation:

$X_{1} =\frac{2+\sqrt{4-4*2*1} }{2*2} \\X_{2} =\frac{2-\sqrt{4-4*2*1} }{2*2}$

$X=\left \{ {{0,5+0,5i} \atop {0,5-0,5i}} \right.$

Replacing for the original variable:

$Z=\sqrt[4]{0,5+0,5i}$

or $Z=\sqrt[4]{0,5-0,5i}$

Remembering that complex numbers can be written as:

$Z=a+ib=|Z|e^{ic}$

Using this:

$Z=\left \{ {{{\frac{\sqrt{2}}{2} e^{i45°} } \atop {{\frac{\sqrt{2}}{2} e^{i-45°} }} \right.$

Solving for the modulus and the angle:

$Z=\left \{ {{\sqrt[4]{\frac{\sqrt{2}}{2} e^{i45}} = \sqrt[4]{\frac{\sqrt{2}}{2} } \sqrt[4]{e^{i45}} } \atop {\sqrt[4]{\frac{\sqrt{2}}{2} e^{i-45}} = \sqrt[4]{\frac{\sqrt{2}}{2} } \sqrt[4]{e^{i-45}} }} \right.$

The possible angle respond to:

$RAng_{12...n} =\frac{Ang +360*(i-1)}{n}$

Been "RAng" the resultant angle, "Ang" the original angle, "n" the degree of the root and "i" a value between 1 and "n"

In this case n=4 with 2 different angles: Ang = 45º and Ang = 315º

Obtaining 8 different angles, therefore 8 different solutions.

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3 years ago

A Delivery service charges $25 per pound for making a delivery. If there is an additional 8% sales tax, what is the cost of deli

mafiozo [28]

The cost of delivering an item that weighs 4/5 of a pound?$21.60.

<h3>How to find the delivery cost?</h3>

Let x = the number of pounds

Thus, we can say that;

Cost = 25x * 1.08

Since we want to find the cost of delivering an item that weighs 4/5 of a pound, the we will put 4/5 for x to get;

Cost = (25 * 4/5) * 1.08

Cost = 20 * 1.08

Cost = 21.6

The delivery cost would be $21.60.

Read more about Delivery Cost at; brainly.com/question/24870596

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2 years ago

The Hudson high school wrestling team just won the state tournament and have been awarded a triangular pennant to hang on the wa

Eduardwww [97]

Answer:

3 feet.

Step-by-step explanation:

Base of the triangular pennant = 1.5 feet long.
Area of the triangular pennant = 2.25 Square feet.

Now, we know that:

Area of a Triangle $=\frac{1}{2}$ X Base X Height$

Substituting the given values, we have:

$2.25=\dfrac{1}{2}$ X 1.5 X Height\\\\2.25=$\dfrac{1.5}{2}$ X Height\\\\Cross multiply\\\\2.25*2=1.5 X Height\\\\Divide both sides by 1.5 to solve for the height\\\\\dfrac{2.25*2}{1.5}=\dfrac{1.5 X Height}{1.5}\\\\$Height of the Triangle =3 feet$

Therefore, the height of the pennant is 3 feet.

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3 years ago

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The answer is $72
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3 years ago

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