$\sqrt{3}x^2+10x+7\sqrt{3}=0\\\\\sqrt3(x^2+\dfrac{10x}{\sqrt{3}}+7)=0\\\\x^2+\dfrac{10x}{\sqrt{3}}+7=0\\\\x^2+\dfrac{10x}{\sqrt{3}}+\dfrac{25}{3}-\dfrac{25}{3} +7=0\\\\(x+\dfrac{5}{\sqrt{3}})^2 = \dfrac{4}{3}\\\\|x+\dfrac{5}{\sqrt{3}}| = \dfrac{2}{\sqrt{3}}\\\\x_1 = \dfrac{2}{\sqrt{3}}-\dfrac{5}{\sqrt{3}} = -\dfrac{3}{\sqrt{3}} = -\sqrt{3}\\\\x_2 = -\dfrac{2}{\sqrt{3}}-\dfrac{5}{\sqrt{3}} = \dfrac{-7}{\sqrt{3}} = -\dfrac{-7\sqrt{3}}{3}$

5 0

3 years ago

Write a word problem that you can solve using multiples to estimate the quotient. Include a solution.

Lilit [14]

Answer:

Word problem based that can be solved using multiples to estimate the quotient:

Melissa made 326 cupcakes. She packed four cupcakes into each box. How many boxes of cupcakes did she pack? How many cupcakes were left unpacked?

3 0

3 years ago

Read 2 more answers

Kate just bought a tv that measures 42 inches diagonally, and is 18 inches tall. She wants to place the tv into a 40 inch wide c

VLD [36.1K]

9514 1404 393

Answer:

yes, about 2.05 inches

Step-by-step explanation:

The Pythagorean theorem can be used to find the width of the TV.

w^2 +h^2 = d^2

w = √(d^2 -h^2)

w = √(42^2 -18^2) = √1440 = 12√10

w ≈ 37.95 . . . inches

This dimension is less than 40 inches by a margin of ...

40 -37.95 = 2.05 . . . inches

The TV will fit, with 2.05 inches of space remaining.

3 0

2 years ago