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3 years ago

5

Three candidates were competing for a new job. One of them got half the vote. Another got two fifths of the vote. What fraction

does the third candidate get?

1 answer:

blagie [28]3 years ago

4 0

Answer:

1/10

Step-by-step explanation:

2/5+1/2

=9/10

1/1-9/10

=1/10

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Evaluate the expression without using a calculator.<br> In1/e^7

Sati [7]

Answer:

-7

Step-by-step explanation:

$ln(\frac{1}{e^7})\\=ln(e^{-7})\\ =-7ln(e)\\=-7$

8 0

3 years ago

All three sides of a triangle are initially 4 m in length. One of the triangle's sides is oriented horizontally. The triangle is

Arlecino [84]

Answer:

the new height of the triangle = 2.449

Step-by-step explanation:

Given that:

the sides of the triangle are 4m in length i.e they are equal. It shows that the triangle is known to be an equilateral triangle.

Let say the triangle is a triangle IJK

Let the length of the side to be i = 4

Definitely

IJ = JK = IK = i = 4

If a midline is drawn and cuts the equilateral triangle in two equal halves of a right-angle triangle. Then, suppose the midline is L

Then ;

$JL = \dfrac{1}{2} JK$

$JL = \dfrac{1}{2} i$

Let consider triangle IJL

(IL)² = (IJ)² - (JL)²

$(IL)^2 = i^2 - \dfrac{i^2}{4}$

$(IL)^2 = \dfrac{3i^2}{4}$

$(IL) =\sqrt{ \dfrac{3i^2}{4}}$

$IL =\sqrt{3} \dfrac{i}{2}$

Area of triangle IJK can be expressed as:

$Area = \dfrac{1}{2}\times Base \times Height$

$Area = \dfrac{1}{2}\times i \times \sqrt{3}\dfrac{i}{2}$

$Area = \sqrt{3}\dfrac{i^2}{4}$

where, i = 4

Then:

$Area = \sqrt{3}\dfrac{4^2}{4}$

$Area = \sqrt{3} \dfrac{16}{4}$

$Area =4 \sqrt{3}$

when the area is exactly half of the original triangle's area, the new height is :

$A = \dfrac{1}{2} \times Area$

$\sqrt{3} \dfrac{i^2}{4} = \dfrac{1}{2} \times 4\sqrt{3}$

$\dfrac{i^2}{4} = \dfrac{1}{2} \times 4$

$\dfrac{i^2}{4} =2$

$i^2 = 8$

$i= \sqrt{8}$

$i= \sqrt{4 \times 2}$

$i= 2 \sqrt{2}$

Finally, the new height of the new triangle is:

$IL =\sqrt{3} \dfrac{i}{2}$

$IL =\sqrt{3} \dfrac{2 \sqrt{2}}{2}$

$IL =\sqrt{3 \times 2}$

$IL =\sqrt{6}$

IL = 2.449 m

6 0

4 years ago

How do you get the answer for .0003 is 1/10 of?

Hitman42 [59]

0.0003 would be 1/10 of 0.00003. If you divided 0.00003 by 10 you would get 0.0003. In fraction form it is 3/10,000

Hoped this helped.

5 0

3 years ago

Combine and simplify the following radical expression.

guajiro [1.7K]

Answer:

<h2> $24 \sqrt{5}$ </h2>

Step-by-step explanation:

$2 \sqrt{20} + 8 \sqrt{45} - \sqrt{80}$

$= 2 \sqrt{2 \times 2 \times 5} + 8 \sqrt{3 \times 3 \times 5} - \sqrt{2 \times 2 \times 2 \times 2 \times 5}$

$= 2(2 \sqrt{5} ) + 8(3 \sqrt{5} ) - (4 \sqrt{5} )$

$= 4 \sqrt{5} + 24 \sqrt{5} - 4 \sqrt{5}$

$= 24 \sqrt{5} (ans)$

3 0

3 years ago

Read 2 more answers

Please help ASAP THIS IS MY FINAL QUESTION!!!! 20 points!!!!

givi [52]

Answer:

y= 1/2x-3

Step-by-step explanation:

2y - x = 8

First find the slope

2y = x+8

Divide by 2

2y/2 = x/2 +8/2

y = 1/2 x +4

The slope is 1/2 ( y=mx+b where m is the slope and b is the y intercept)

When lines are parallel they have the same slope)

Using y = mx+b

y =1/2x+b

Substituting the point (4,-1) into the equation

-1 =1/2(4)+b

-1 = 2+b

-3 =b

The equation of the line is

y= 1/2x-3

4 0

3 years ago