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MAXImum [283]
3 years ago
5

In the circle m∠ACD=2x+14 and m∠ABD=3x+8 what is the value of x

Mathematics
1 answer:
AlekseyPX3 years ago
6 0

Answer:

The value of x = 6

Step-by-step explanation:

The angle subtended on same arc are equal in measure.Here <ACD and <ABD  are on the same arc. therefore these two angle are equal.

it is given that,  m∠ACD=2x+14 and m∠ABD=3x+8

From the figure we get,

m∠ACD = m∠ABD

Therefore we can write,

2x+14 = 3x+8

3x - 2x = 14 - 8

x = 6

Therefor the value of x = 6

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Give the values of a, b, and c needed to write the equation's general form. 2/3(x - 4)(x + 5) = 1
ale4655 [162]

The first step is to write this equation into general form. The general form of an equation is:

ax^2 + bx + c = 0

To make this equation to general form, you have to simplify the equation first.

2/3(x-4) (x+5) = 1

2/3 (x^2 + 5x – 4x – 20) = 1

2/3(x^2 + x -20) = 1

2/3x^2 + 2/3x – 40/3 = 1

2/3x^2 + 2/3x – 40/3 – 1 = 0

2/3x^2 +2/3x – 43/3 = 0

Therefore, a = 2/3 ; b = 2/3 ; c = -43/3   

4 0
3 years ago
Read 2 more answers
The heights of a random sample of 50 college students showed a mean of 174.5 centimeters and a standard deviation of 6.9 centime
Minchanka [31]

Answer:

Step-by-step explanation:

Hello!

For me, the first step to any statistics exercise is to determine what is the variable of interest and it's distribution.

In this example the variable is:

X: height of a college student. (cm)

There is no information about the variable distribution. To estimate the population mean you need a variable with at least a normal distribution since the mean is a parameter of it.

The option you have is to apply the Central Limit Theorem.

The central limit theorem states that if you have a population with probability function f(X;μ,δ²) from which a random sample of size n is selected. Then the distribution of the sample mean tends to the normal distribution with mean μ and variance δ²/n when the sample size tends to infinity.

As a rule, a sample of size greater than or equal to 30 is considered sufficient to apply the theorem and use the approximation.

The sample size in this exercise is n=50 so we can apply the theorem and approximate the distribution of the sample mean to normal:

X[bar]~~N(μ;σ2/n)

Thanks to this approximation you can use an approximation of the standard normal to calculate the confidence interval:

98% CI

1 - α: 0.98

⇒α: 0.02

α/2: 0.01

Z_{1-\alpha /2}= Z_{1-0.01}= Z_{0.99} =2.334

X[bar] ± Z_{1-\alpha /2} * \frac{S}{\sqrt{n} }

174.5 ± 2.334* \frac{6.9}{\sqrt{50} }

[172.22; 176.78]

With a confidence level of 98%, you'd expect that the true average height of college students will be contained in the interval [172.22; 176.78].

I hope it helps!

4 0
3 years ago
In arithmetic sequence the first term is 5 and the common difference is 4. Determine the 6th term of sequence
Harlamova29_29 [7]

Answer:

The 6th term of the sequence is 25

Step-by-step explanation:

first term = a = 5

common difference = d = 4

The nth term of a sequence is

T_n = a + (n - 1)d

Therefore, the 6th term of the sequence is

T_6 = a + (6 - 1)d

T_6 = a + 5d

T_6 = 5 + 5(4)

T_6 = 5 + 20

T_6 = 25

3 0
3 years ago
If the density of a 35.cm3 block of wood is .85 g./ml calculate the woods mass.
Reil [10]
So the equation you're going to be using is mass = density x volume 
So the volume of your block is 35cm^3, and your density is .85g/ml 

so your equation would be 

mass=.85g/ml x 35cm^3 

your final answer is 29.75g/cm^3

Hope this helps :) 
6 0
3 years ago
Find the equation of the line. use exact numbers.
svp [43]

Answer:

y=4x -9

Step-by-step explanation:

y intercept- where the line crosses the y-axis (-9)

Rise over run- 4

6 0
3 years ago
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