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2 years ago

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What is the solution: (9x+2)(4x^2+35x-9)=0

2 answers:

Dmitrij [34]2 years ago

5 0

$(9x+2)(4x^2+35x-9)=0\\\\9x+2=0\\9x=-2\\x=-\frac29\\or\\4x^2+35x-9=0\\\Delta=1225+144=1369\ \ \sqrt{\Delta}=37\\x_1=\frac{-35-37}{2 \cdot 4}=-9\\\\x_2=\frac{-35+37}{2\cdot 4}=\frac14\\\\x\in\{-9,-\frac29,\frac14\}$

Anni [7]2 years ago

4 0

$(9x+2)(4x^2+35x-9)=0\iff9x+2=0\ or\ 4x^2+35x-9=0\\\\(\#1)\\9x+2=0\ \ \ \ \ \ |subtract\ 2\ from\ both\ sides\\9x=-2\ \ \ \ \ \ \ |divide\ both\ sides\ by\ 9\\\boxed{x=-\frac{2}{9}}\\\\(\#2)\\4x^2+35x-9=0\\4x^2+36x-x-9=0\\4x(x+9)-1(x+9)=0\\(x+9)(4x-1)=0\iff x+9=0\ or\ 4x-1=0\\x=-9\ or\ 4x=1\\\boxed{x=-9}\ or\ \boxed{x=\frac{1}{4}}\\\\Solutions:x=-\frac{2}{9}\ or\ x=-9\ or\ x=\frac{1}{4}.$

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The coordinates of the vertices of a polygon are (-2, 1). (-3, 3), (-1, 5), (2, 4), and (2, 1). What is the perimeter of the pol

kobusy [5.1K]

Answer:

$15.2\ units$

Step-by-step explanation:

step 1

Plot the vertices of the polygon to better understand the problem

we have

$A(-2, 1). B(-3, 3), C(-1, 5), D(2, 4),E(2, 1)$

using a graphing tool

The polygon is a pentagon (the number of sides is 5)

see the attached figure

The perimeter is equal to

$P=AB+BC+CD+DE+AE$

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

step 2

<em>Find the distance AB</em>

$A(-2, 1). B(-3, 3)$

substitute in the formula

$d=\sqrt{(3-1)^{2}+(-3+2)^{2}}$

$d=\sqrt{(2)^{2}+(-1)^{2}}$

$d_A_B=\sqrt{5}=2.24\ units$

step 3

<em>Find the distance BC</em>

$B(-3, 3), C(-1, 5)$

substitute in the formula

$d=\sqrt{(5-3)^{2}+(-1+3)^{2}}$

$d=\sqrt{(2)^{2}+(2)^{2}}$

$d_B_C=\sqrt{8}=2.83\ units$

step 4

<em>Find the distance CD</em>

$C(-1, 5), D(2, 4)$

substitute in the formula

$d=\sqrt{(4-5)^{2}+(2+1)^{2}}$

$d=\sqrt{(-1)^{2}+(3)^{2}}$

$d_C_D=\sqrt{10}=3.16\ units$

step 5

<em>Find the distance DE</em>

$D(2, 4),E(2, 1)$

substitute in the formula

$d=\sqrt{(1-4)^{2}+(2-2)^{2}}$

$d=\sqrt{(-3)^{2}+(0)^{2}}$

$d_D_E=\sqrt{9}\ units$

$d_D_E=3\ units$

step 6

<em>Find the distance AE</em>

$A(-2, 1).E(2, 1)$

substitute in the formula

$d=\sqrt{(1-1)^{2}+(2+2)^{2}}$

$d=\sqrt{(0)^{2}+(4)^{2}}$

$d_A_E=\sqrt{16}\ units$

$d_A_E=4\ units$

step 7

Find the perimeter

$P=AB+BC+CD+DE+AE$

substitute the values

$P=2.24+2.83+3.16+3+4=15.23\ units$

Round to the nearest tenth of a unit

$P=15.2\ units$

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