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3 years ago

The measures of three angles are (2x)°, (3x)° , and (x+60)°. what is the value of x?

Mathematics

2 answers:

VLD [36.1K]3 years ago

7 0

2x+3x+x+60=180
6x=180-60=120
x=20
(Assume that those are the measure of triangle)

ratelena [41]3 years ago

6 0

Well combine:
2x + 3x + x + 60 = 180
combine like terms:
6x + 60 =180
then move the 60:
6x = -120
now divide both sides by 6:
x= -20
i hope this helped! :)

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A town's recreation department is updating its parks. The parks must have slides and swings.

Fittoniya [83]

Number of swings = x
Number of slides = y

First condition:
number of slides must be more than 3 times number of swings
This means that: y > 3x

Second condition:
each swing cost 275$ and each slide costs 168$. They cannot spend more than 1250$. This means that the sum of costs of swings and slides should not exceed 1250$ (should be less than or equal to 1250$)
This means that: 275x+168y ≤ 1250

Based on this:
The correct choices are: b and d

5 0

3 years ago

Read 2 more answers

A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard devia

Butoxors [25]

Answer:

Probability that their mean is above 215 is 0.0287.

Step-by-step explanation:

We are given that a bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50.

For this, 40 different applicants are randomly selected.

Let X = ratings for credit

So, X ~ N( $\mu=200,\sigma^{2}=50^{2}$ )

Now, the z score probability distribution for sample mean is given by;

Z = $\frac{X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\mu$ = population mean = 200

$\sigma$ = standard deviation = 50

$\bar X$ = sample mean

n = sample of applicants = 40

So, probability that their mean is above 215 is given by = P( $\bar X$ > 215)

P( $\bar X$ > 215) = P( $\frac{X-\mu}{\frac{\sigma}{\sqrt{n} } }$ > $\frac{215-200}{\frac{50}{\sqrt{40} } }$ ) = P(Z > 1.897) = 1 - P(Z $\leq$ 1.897)

= 1 - 0.97108 = 0.0287

Therefore, probability that their mean is above 215 is 0.0287.

5 0

3 years ago

write the equation of a line in point-slope form that has a slope of 2/3 and passes through the point (2, -7).

Lelechka [254]

The core answer is Y+7= (2/3)(X-2)

4 0

4 years ago

Which set of line segments can be used to construct a triangle?

Darina [25.2K]

Answer:

Option B

Step-by-step explanation:

Option A

In order to make a triangle: a + b > c and b + c > a and c + a > b

2 is a, 6 is b, and 1 is c

a + b > c

2 + 6 > 1

8 > 1 -> TRUE

b + c > a

6 + 1 > 2

7 > 2 -> TRUE

c + a > b

1 + 2 > 6

3 > 6 -> FALSE

Option B

In order to make a triangle: a + b > c and b + c > a and c + a > b

3 is a, 3 is b, 2 is c

a + b > c

3 + 3 > 2

6 > 2 -> TRUE

b + c > a

3 + 2 > 3

5 > 3 -> TRUE

c + a > b

2 + 3 > 3

5 > 3 -> TRUE

OPTION B IS A TRIANGLE

Option C and D are automatically incorrect because Option B is incorrect. But, the same process would go to the end.

Answer: Option B

4 0

4 years ago

Can the sides of a triangle have lengths 2.8, 3.6, and 7.1? yes or no

tekilochka [14]

No, it's not possible for the sides of a triangle to have those lengths.

According to the triangle inequality theorem, the sum of any two sides of the triangle has to be bigger than the last side. Let's test this.

$2.8+7.1\ \textgreater \ 3.6$

This inequality satisfies the triangle inequality theorem.

$3.6+7.1\ \textgreater \ 2.8$

This also satisfies the theorem.

$2.8+3.6\ \textless \ 7.1$

Uh oh. This does not satisfy the triangle inequality theorem. Thus, it is not possible for a triangle to have these side lengths.

6 0

3 years ago