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3 years ago

Find the requested unknown side of the following triangle

Mathematics

1 answer:

Salsk061 [2.6K]3 years ago

3 0

*Answer* :
5.75
Explanation:
Let the unknown side = X
Cos() = adj/hyp
Cos(44)= X/8
X= 5.75

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Write the following expression. The quantity 81 minus 5k, squared

Stella [2.4K]

Answer:

81-25k²

Step-by-step explanation:

We need to write the expression for "The quantity 81 minus 5k, squared".

Square of any number x is given by x².

Square of 5k is given by : (5k)²= 5²×k²=25k²

Now subtract 25k² from 81.

It means we get : 81-25k². It is required expression.

6 0

3 years ago

Almee is decorating her new house. she found a table at pier one for $425. If the table is 25% off, what will it cost

serious [3.7K]

Answer:

$318.75

Step-by-step explanation:

425*0.25=106.25 425-106.25=318.75

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3 years ago

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Find the mean, median, and mode of the data set? 15, 16, 21, 23, 25, 25, 25, 39

frozen [14]

Answer:

Median: 24

Mode: 25

Mean: 29

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3 years ago

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Find the polynomial of minimum degree, with real coefficients, zeros at

drek231 [11]

Answer:

$\huge\boxed{p(x)=4x^3-20x^2+4x+300}$

Step-by-step explanation:

$\text{If}\ x=4\pm3i\ \text{and}\ x=-3\ \text{are the zeros of a polynomial, then it has a form:}\\\\p(x)=\bigg(x-(4-3i)\bigg)\bigg(x-(4+3i)\bigg)\bigg(x-(-3)\bigg)\bigg(r(x)\bigg)\\\\p(x)=(x-4+3i)(x-4-3i)(x+3)\bigg(r(x)\bigg)\\\\p(x)=\underbrace{\bigg((x-4)+3i\bigg)\bigg((x-4)-3i\bigg)}_{\text{use}\ (a+b)(a-b)=a^2-b^2}(x+3)\bigg(r(x)\bigg)\\\\p(x)=\bigg((x-4)^2-(3i)^2\bigg)(x+3)\bigg(r(x)\bigg)\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2$

$p(x)=(x^2-2(x)(4)+4^2-3^2i^2)(x+3)\bigg(r(x)\bigg)\qquad\text{use}\ i^2=-1\\\\p(x)=(x^2-8x+16-9(-1))(x+3)\bigg(r(x)\bigg)\\\\p(x)=(x^2-8x+16+9)(x+3)\bigg(r(x)\bigg)\\\\p(x)=(x^2-8x+25)(x+3)\bigg(r(x)\bigg)\qquad\text{use FOIL}:\ (a+b)(c+d)=ac+ad+bc+bd\\\\p(x)=\bigg((x^2)(x)+(x^2)(3)+(-8x)(x)+(-8x)(3)+(25)(x)+(25)(3)\bigg)\bigg(r(x)\bigg)\\\\p(x)=(x^3+3x^2-8x^2-24x+25x+75)\bigg(r(x)\bigg)\qquad\text{combine like terms}\\\\p(x)=(x^3-5x^2+x+75)\bigg(r(x)\bigg)$

$\text{The y-intercept is at 300}.\\\\\text{For}\ w(x)=a_nx^n+a_{n-1}x^{n-1}+a_{n-2}x^{n-2}+...+a_1x+a_0\\\\\text{y-intercept is}\ a_0\\\\\text{Therefore for}\ p(x)=(x^3-5x^2+x+75)\bigg(r(x)\bigg)\\\\\text{y-intercet is}\ 75\bigg(r(x)\bigg)\\\\75\bigg(r(x)\bigg)=300\qquad\text{divide both sides by 75}\\\\r(x)=4\\\\\text{Finally:}\\\\p(x)=(x^3-5x^2+x+75)(4)\qquad\text{use the distributive property}\\\\p(x)=(x^3)(4)+(-5x^2)(4)+(x)(4)+(75)(4)\\\\p(x)=4x^3-20x^2+4x+300$

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3 years ago

△MNP≅△QST.<br><br> What is m∠S?<br> Enter your answer in the box.

mezya [45]

Answer: 78

Step by step: congruent side

7 0

3 years ago