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3 years ago

Rewrite as a simplified fraction. 3.5 = ?

Mathematics

1 answer:

Allushta [10]3 years ago

7 0

Answer: 3 1/2 ( mixed number)

Step-by-step explanation:

First you have to put 3.5 into na fraction

In a fraction it is 35/10
as a mixed number, it would be: 3 5/10 ( a mixed number )
Bur we still have to simplify so simplified would be: 3 1/2 ( mixed number)

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The diagonals of rhombus ABCD intersect at E. Given that m∠CAD=20° and CE=4, find the m∠CDA.

V125BC [204]

Answer:

< CDA = 140 degrees

Step-by-step explanation:

For a rhombus, the sum of the interior angles is 360 degrees and also the opposite angles are equal i.e <ABC = <CDA and <BAD = <BCD

Given

<CAD = 20 degrees

<BCE = 20 degrees (based on geometry)

<BAD = <CAD + <BCE

<BAD = 20 + 20

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Since <BAD = <BCD, then <BCD = 40 degrees

Get <CDA

<CDA + <ABC + <BAD + <BCD = 360

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3 years ago

Use the completing the square method to find the roots of 2x^2+3x-15=13 include the steps, it would be greatly appreciated thank

ValentinkaMS [17]

Answer:

The roots are

$x1= \frac{-3+\sqrt{233}}{4}$

$x2= \frac{-3-\sqrt{233}}{4}$

Step-by-step explanation:

we have

$2x^{2}+3x-15=13$

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$2x^{2}+3x=13+15$

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Factor the leading coefficient

$2(x^{2}+(3/2)x)=28$

Complete the square. Remember to balance the equation by adding the same constants to each side

$2(x^{2}+(3/2)x+(9/16))=28+(9/8)$

$2(x^{2}+(3/2)x+(9/16))=233/8$

$(x^{2}+(3/2)x+(9/16))=233/16$

Rewrite as perfect squares

$(x+(3/4))^{2}=233/16$

square root both sides

$(x+\frac{3}{4})=(+/-)\sqrt{\frac{233}{16}}\\ \\(x+\frac{3}{4})=(+/-)\frac{\sqrt{233}}{4}\\ \\x= -\frac{3}{4}(+/-)\frac{\sqrt{233}}{4}$

$x1= -\frac{3}{4}(+)\frac{\sqrt{233}}{4}=\frac{-3+\sqrt{233}}{4}$

$x2= -\frac{3}{4}(-)\frac{\sqrt{233}}{4}=\frac{-3-\sqrt{233}}{4}$

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