Answer:
Use trig ratios to find unknown sides in right triangles.
Step-by-step explanation:
By apply the distributive property of multiplication, the value of k which makes the statement true is 1.
<h3>What is the
distribution property?</h3>
Mathematically, the distributive property of multiplication is given by tis expression:
x(y + z) = xy + xz.
Next, we would apply the distributive property of multiplication to the given equation by distributing to the left-hand side using xy⁴:
k(2x⁴y⁴ + 7x³y⁸) = 2x⁴y⁴ + 7x³y⁸
Dividing both sides by the common factor, we have:
k = (2x⁴y⁴ + 7x³y⁸)/(2x⁴y⁴ + 7x³y⁸)
k = 1.
In conclusion, the value of k which makes the statement true is 1.
Read more on distributive property here; brainly.com/question/2807928
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<u>Complete Question:</u>
What value of k makes the statement true?
y⁴(2x³ + 7x²y⁴) = 2x⁴y⁴ + 7x³y⁸
Answer:
125 deg
Step-by-step explanation:
Keep these three rules in mind:
1) A central angle (vertex is the center of the circle) has the same measure as the arc it intercepts.
2) The measure of an inscribed angle (vertex is point on circle) is half the measure of the intercepted arc.
3) Opposite angles of a rectangle inscribed in a circle are supplementary.
110 deg is a central angle.
By rule 1), the arc intercepted by the central angle 110 deg also measures 110 deg.
a is an inscribed angle that intercepts an arc of 110 deg.
By rule 2), the measure of an inscribed angle is half the measure of the intercepted arc.
angle a measures 55 deg.
Rule 3) Angles a and b are supplementary.
a + b = 180
55 + b = 180
b = 125
Answer:
Deductive reasoning
Step-by-step explanation:
Here, we want to know the kind of reasoning the statement is.
In this question, the kind of reasoning is deductive
In the deductive reasoning type, we go from general cases to specific cases
It is just like saying the reason why there will be hurricanes in the tropics this fall is because there is an hurricane every fall
So we have gone from a general case to give a specific case
Answer:
(a) 4
(b) 2√3
(c) 60°
(d) 120°
Step-by-step explanation:
(a) The relationship between tangents and secants is ...
CB^2 = CD·CA
Filling in the given values, we find ...
CB^2 = 2·(2+6) = 16
CB = √16 = 4
The length of BC is 4 units.
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(b) Triangle ABC is a right triangle, so the sides of it satisfy the Pythagorean theorem.
CA^2 = CB^2 +AB^2
8^2 = 16 +AB^2
AB = √48 = 4√3
The radius is half the length of AB, so the radius is 2√3.
__
(c) The measure of angle C can be determined from the cosine relation:
cos(C) = CB/CA = 4/8 = 1/2
C = arccos(1/2) = 60°
The measure of angle C is 60°.
__
(d) Arc AD is intercepted by angle ABD, which has the same measure as angle C. Hence the measure of arc AD is twice the measure of angle C.
The measure of arc AD is 120°.
