Shown below are parallel lines n and p which are cut by transversals r and s which are perpendicular to each
other. Which of the following is the measure of 21?
(1) 51
(2) 64
(3) 72
(4) 102
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Given the diagram given where lines n and p are parallel, and transversals r and s are perpendicular, the measure of angle 1 is: [tex]\mathbf{1) 51^{\circ}}[/tex]
The angle measure where two perpendicular lines intersect each other equals 90 degrees.
Therefore, the angle formed as shown in the figure attached, where transversals r and s meet = 90 degrees.
Since lines n and p are parallel lines, therefore:
[tex]m \angle 1 + 90 = 141[/tex] (alternate interior angles are equal)
Subtract 90 from each side[tex]m \angle 1 = 141 - 90\\\\\mathbf{m \angle 1 = 51^{\circ}}[/tex]
Therefore, given the diagram given where lines n and p are parallel, and transversals r and s are perpendicular, the measure of angle 1 is: [tex]\mathbf{1) 51^{\circ}}[/tex]
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[tex] ( { \frac{3}{4} })^{3} = \frac{ {3}^{3} }{ {4}^{3} } = \frac{27}{64} \\ [/tex]
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a and d are parallel
Step-by-step explanation:
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Find a polynomial function with leading coefficient 1 that has the given zeros, multiplicities, and degree. Zero: 2, multiplicity: 3 Zero: 0, multiplicity: 2 Degree: 5
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Given:
Zero: 2, multiplicity: 3
Zero: 0, multiplicity: 2
Degree: 5
Leading coefficient = 1
To find:
The polynomial function.
Solution:
The general form of a polynomial is
[tex]P(x)=a(x-c_1)^{m_1}(x-c_2)^{m_2}...(x-c_n)^{m_n}[/tex]
where, a is a constant, [tex]c_1,c_2,...,c_n[/tex] are zeroes with multiplicity [tex]m_1,m_2,...,m_n[/tex].
Using the given information and the general form of a polynomial, we get
[tex]P(x)=a(x-2)^{3}(x-0)^{2}[/tex]
[tex]P(x)=ax^2(x^3-6x^2+12x-8)[/tex]
[tex]P(x)=a(x^5-6x^4+12x^3-8x^2)[/tex]
Leading coefficient is 1, so the value of a is also 1.
[tex]P(x)=1(x^5-6x^4+12x^3-8x^2)[/tex]
[tex]P(x)=x^5-6x^4+12x^3-8x^2[/tex]
Therefore, the required polynomial is [tex]P(x)=x^5-6x^4+12x^3-8x^2[/tex].
The polynomial for the conditions with leading coefficient 1 that has the given zeros, multiplicities, and degree. Zero: 2, multiplicity: 3 Zero: 0, multiplicity: 2 Degree: 5 is given as
[tex]\rm\bold{ y(x) = 1\times (x-2)^3(x-0)^2 }[/tex]
According to the given condition
The given conditions to write the polynomial equations are as follows
Zero 2 and Multiplicity 3
Zero 0 and Multiplicity 2
Degree of polynomial expression = 5
Leading coefficient of polynomial expression = 1
Let us consider the polynomial equation has only one variable and hence in general form we can write the equation of polynomial as follows
[tex]\rm y (x) = a(x-\alpha)^m (x-\beta)^n........(1)\\Where \\a = Leading \; coefficient\; of\; polynomial\; expression \\\alpha ,\beta = Roots \; of \; the\; polynomial\; expression\\m\; and \; n \; are \; multiplicities \; of \; the \; roots \; \alpha,\beta \; respectively\\Degree = m+n[/tex]
From the general form of polynomial expression as shown in equation (1) we can write
Polynomial expression for the given conditions is formulated in equation (2)
[tex]\rm y(x) = 1\times (x-2)^3(x-0)^2 .......(2)[/tex]
So the polynomial for the conditions given in question is expressed as
[tex]\rm\bold{ y(x) = 1\times (x-2)^3(x-0)^2 }[/tex]
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Marissa knits caps that she supplies to several baby stores. She purchases five bundles of yarn for $62.50. Select the
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ОА. .
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Step-by-step explanation: