Please help with this problem

HELPPPP JUST 2 QUESTIONS BASED ON PYTHAGOREAN THEOREM AND IM CONFUSED HELPPPP

Anna007 [38]

9514 1404 393

Answer:

3. no; does not have the correct ratio to other sides

4. (1; right), (2; obtuse), (3; right)

Step-by-step explanation:

3. There are a couple of ways you can go at this.

a) the ratio of sides of a 30°-60°-90° right triangle (half an equilateral triangle) is 1 : √3 : 2. Here, the ratio of sides is ...

(√30/2) : √15 : √30 = 1 : √2 : 2 . . . . MQ is not the height

b) the height is perpendicular to the base, so if MQ were the height, the sides of the triangle would satisfy the Pythagorean theorem:

LQ² +MQ² = LM²

(√30/2)² +(√15)² = (√30)²

30/4 +15 = 30

22.5 = 30 . . . . NOT TRUE

The length MQ cannot be the height of ∆LMN. (It is too short.)

__

4. To see if these lengths form a right triangle, you can test them in the Pythagorean theorem relation. In the attached we have reformulated the equation so it gives a value of 0 if the triangle is a right triangle:

c² = a² +b² . . . . . Pythagorean theorem

c² -a² -b² = 0 . . . . rewritten

If the value of c² -a² -b² is not zero, then the side lengths do not form a right triangle. The attached shows this math performed by a graphing calculator. The results are ...

right triangle
not a right triangle — long side is too long, so the triangle is obtuse
right triangle

_____

Additional comment

The attached table demonstrates an artifact of computer arithmetic. Not all numbers can be represented exactly in a computer, so a difference that is expected to be zero using exact arithmetic may be slightly different from zero when computed by a computer or calculator. Here, we see a difference of about 6×10^-14 when zero is expected. On most calculators (with 10, or 12 displayed digits), this would be displayed as 0.

The same calculation done "by hand" gives ...

(√425)² -5² -20² = 425 -25 -400 = 0 . . . Triangle 1 is a right triangle

4 0

3 years ago

The options are 40 80 120 140

Nataly [62]

According to given figure,

$\qquad \sf \dashrightarrow \: \angle ABC + 60° = 180°$

$\qquad \sf \dashrightarrow \: \angle ABC = 180 \degree - 60 \degree$

[ By linear pair ]

$\qquad \sf \dashrightarrow \: \angle ABC = 120 \degree$

now, we can see that :

$\qquad \sf \dashrightarrow \: \angle ABC + \angle BAC = \angle 1$

[ By Exterior angle property of Triangle ]

$\qquad \sf \dashrightarrow \: \angle 1 = 20 \degree + 120 \degree$

$\qquad \sf \dashrightarrow \: \angle 1 = 140 \degree$

4 0

2 years ago

Evaluate 5(x - 1) - 2 when x = 3. ОА. 12 ОВ. -4 Ос. о. O D. 8

Harlamova29_29 [7]

Answer:

8

Step-by-step explanation:

5(3-1)-2

5(2)-2

10-2

8

7 0

3 years ago

Read 2 more answers

Witch of these has a slope of -3/4 and a y intercept of 3/2

Arada [10]

Answer:

See explanation. (Also you can write an equation several different ways so without the choices I cannot tell you which)

Step-by-step explanation:

Slope-intercept form is y=mx+b

So one way to write the equation is y=-3/4 x +3/2

There are more ways to write it.

Every line about to write is a way to write it.

Multiply both sides by 4: 4y=-3x+6

Add 3x on both sides: 3x+4y=6

Subtract 6 on both sides: 3x+4y-6=0

There are a lot of ways to write an equation like this.

To better assist you I would need to see options.

5 0

3 years ago

A grinding wheel manufacturer designed a new grinding wheel. Repeated tests were conducted on wheels of approximately the same w

sergejj [24]

Answer:

a) $a=225 +0.674*16.5=236.121$

So the value of height that separates the bottom 75% of data from the top 25% is 236.121.

b) $P(X \geq 3) = 1-P(X$

c) $P(\bar X \geq 225)=1- P(\bar X$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

2) Part a

Let X the random variable that represent the cuts of a population, and for this case we know the distribution for X is given by:

$X \sim N(225,16.5)$

Where $\mu=225$ and $\sigma=16.5$

For this part we want to find a value a, such that we satisfy this condition:

$P(X>a)=0.25$ (a)

$P(X$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.75 of the area on the left and 0.25 of the area on the right it's z=0.674. On this case P(Z<0.674)=0.75 and P(z>0.674)=0.25

If we use condition (b) from previous we have this:

$P(X$

$P(z$

But we know which value of z satisfy the previous equation so then we can do this:

$z=0.674=\frac{a-225}{16.5}$

And if we solve for a we got

$a=225 +0.674*16.5=236.121$

So the value of height that separates the bottom 75% of data from the top 25% is 236.121.

Part b

For this case we know that the individual probability of select one wheel with a cutting rate higher than the calculated value in part a is 0.25, and we select n =10 so then we can use the binomial distribution for this case:

$X\sim Bin(n=10, p=0.25)$