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3 years ago

Find the length of side x in simplest radical form with a rational denominator

Mathematics

1 answer:

Luba_88 [7]3 years ago

5 0

It's the triangle 30° - 60° - 90°.

The sides are in proportion 1 : √3 : 2 (look at the picture).

Therefore we have:

$x=\dfrac{\sqrt6\cdot\sqrt3}{2}=\dfrac{\sqrt{(6)(3)}}{2}=\dfrac{\sqrt{18}}{2}=\dfrac{\sqrt{(9)(2)}}{2}\\\\=\dfrac{\sqrt9\cdot\sqrt2}{2}=\boxed{\dfrac{3\sqrt2}{2}}$

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What is the slope of the equation Y=5/4x-7/4?

maksim [4K]

Answer:

Step-by-step explanation:

Compare the equation with y = mx + b where m is slope and b is y intercept

y = (5/4)x - (7/4)

Slope = m = 5/4

4 0

2 years ago

Abigail jogged 10.6 miles in 2.5 hours. What is her jogging speed in miles per hour? A. 4.32 miles/hour B. 4 miles/hour C. 4.24

Lelechka [254]

do miles/hour =

10.6 miles/2.5 hours =

10.6/2.5 =

4.24 miles/hour

5 0

3 years ago

Read 2 more answers

A political polling agency predicts candidate A will win an election with 63% of the votes. Their poll has a margin of error of

scoray [572]

Answer:

56% ≤ p ≤ 70%

Step-by-step explanation:

Given the following :

Predicted % of votes to win for candidate A= 63%

Margin of Error in prediction = ±7%

Which inequality represents the predicted possible percent of votes, x, for candidate A?

Let the interval = p

Hence,

|p - prediction| = margin of error

|p - 63%| = ±7%

Hence,

Upper boundary : p = +7% + 63% = 70%

Lower boundary : p = - 7% + 63% = 56%

Hence,

Lower boundary ≤ p ≤ upper boundary

56% ≤ p ≤ 70%

5 0

3 years ago

What is the length of BC , rounded to the nearest tenth?

Arte-miy333 [17]

Step $1$

In the right triangle ADB

Find the length of the segment AB

Applying the Pythagorean Theorem

$AB^{2} =AD^{2}+BD^{2}$

we have

$AD=5\ units\\BD=12\ units$

substitute the values

$AB^{2}=5^{2}+12^{2}$

$AB^{2}=169$

$AB=13\ units$

Step $2$

In the right triangle ADB

Find the cosine of the angle BAD

we know that

$cos(BAD)=\frac{adjacent\ side }{hypotenuse}=\frac{AD}{AB}=\frac{5}{13}$

Step $3$

In the right triangle ABC

Find the length of the segment AC

we know that

$cos(BAC)=cos (BAD)=\frac{5}{13}$

$cos(BAC)=\frac{adjacent\ side }{hypotenuse}=\frac{AB}{AC}$

$\frac{5}{13}=\frac{AB}{AC}$

$\frac{5}{13}=\frac{13}{AC}$

solve for AC

$AC=(13*13)/5=33.8\ units$

Step $4$

Find the length of the segment DC

we know that

$DC=AC-AD$

we have

$AC=33.8\ units$

$AD=5\ units$

substitute the values

$DC=33.8\ units-5\ units$

$DC=28.8\ units$

Step $5$

Find the length of the segment BC

In the right triangle BDC

Applying the Pythagorean Theorem

$BC^{2} =BD^{2}+DC^{2}$

we have

$BD=12\ units\\DC=28.8\ units$

substitute the values

$BC^{2}=12^{2}+28.8^{2}$

$BC^{2}=973.44$

$BC=31.2\ units$

therefore

the answer is

$BC=31.2\ units$

8 0

3 years ago

Read 2 more answers

How do I find the inverse function of this equation

trapecia [35]

Answer:

y=ln(x/(1-x))

Step-by-step explanation:

y=e^x/(1+e^x)

Cross multiply

y(1+e^x)=e^x

Distribute

y+ye^x=e^x

Put anything with x on with side and everything without x on opposing side:

y=e^x-ye^x

Factor right hand side

y=(1-y)e^x

Divide both sides by (1-y)

y/(1-y)=e^x

Use natural log.

ln(y/(1-y))=x

The inverse is

y=ln(x/(1-x))

4 0

3 years ago