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1 year ago

Which point lies on the line described by the equation below? y+4=4(x-3

1 answer:

3 0

$\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies \begin{array}{llll} y+4=4(x-3)\implies y-(\stackrel{y_1}{-4})=\stackrel{m}{4}(x-\stackrel{x_1}{3})\\\\ ~\hfill (\stackrel{x_1}{3}~~,~~\stackrel{y_1}{-4}) \end{array}$

You might be interested in

A cylinder has a height that is twice the length of the diameter. The diameter of the cylinder is 10 centimeters. What is the su

siniylev [52]

Answer:

Step-by-step explanation:

Givens

pi = 3.14

d = 10 cm

h = 2*d

Formula

The top of the cylinder is a solid circle. So the area of the circle is pi r^2
There is both a top and bottom to the circle so the fomula is 2*pi*r^2

The surrounding area of the cylinder is the circumference of the circle times the height. The circumference of the circle is 2*pi*r.
Then you just multiply by the height.
formula = 2*pi * r * h

The combined formula is given below.

SA = 2*pi*r^2 + 2*pi*r * h

Conversions

d = 10 cm

h = 2*10

h = 20 cm

r = d/2

r = 10 / 2

r = 5cm

Solution

SA = 2*pi*r^2 + 2*pi*r * h

SA = 2*3.14*5^2 + 2*3.14*5*20

SA = 157 + 628

SA = 785 cm^2

Answer: The surface area is 785 cm^2

5 0

2 years ago

Express the terms of the following sequence by giving a recursive formula.

emmasim [6.3K]

The recursive formula for given sequence is: $a_n = a_{n-1}-7$

And the terms will be expressed as:

$a_1 = 11\\a_2 = a_{2-1} - 7 \\a_2= a_1 - 7\\a_2 = 11- 7\\a_2 = 4\\a_3 = a_{3-1} - 7 \\a_3= a_2 - 7\\a_3 = 4 - 7\\a_3 = -3\\a_4 = a_{4-1} - 7 \\a_4= a_3 - 7\\ a_4= -3 - 7\\a_4 = -10\\a_5 = a_{5-1} - 7 \\a_5= a_4 - 7\\a_5 = -10 - 7\\a_5 = -17\\$

Step-by-step explanation:

First of all, we have to determine if the given sequence is arithmetic sequence or geometric. For that purpose, we calculate the common difference and common ratio

Given sequence is:

11,4,-3,-10,-17...

Here

$a_1 = 11\\a_2 = 4\\a_3 = -3\\So,\\d = a_2 - a_1 = 4-11 = -7\\d = a_3-a_2 = -3-4 = -7$

As the common difference is same, given sequence is an arithmetic sequence.

A recursive formula is a formula that is used to generate the next term of the sequence using the previous term and common difference

So, the recursive formula for an arithmetic sequence is given by:

$a_n = a_{n-1} +d\\Putting\ d = -7\\a_n = a_{n-1}-7$

Hence,

The recursive formula for given sequence is: $a_n = a_{n-1}-7$

And the terms will be expressed as:

Keywords: arithmetic sequence, common difference

Learn more about arithmetic sequence at:

#LearnwithBrainly

6 0

4 years ago

Ten times the sum of half a number and 6 is 8

nexus9112 [7]

Let the required number is 2x ,

According to the condition,

➡ 10 times the sum of half of 2x and 6 = 8

$= > 10 \times ( \frac{2x}{2} + 6) = 8 \\ \\ \\ = > 10 \times (x + 6) = 8 \\ \\ \\ = > 10x + 60 = 8 \\ \\ \\ = > 10x = 8 - 60 \\ \\ \\ = > 10x = - 52 \\ \\ \\ = > x = - \frac{ 52}{10} \\ \\ \\ = > x = - 5.2$

Therefore the value of x is -5.2

And, required number is -5.2

3 0

3 years ago

Sarah claims that the thickness of the spearmint gum she produces is 7.5 one-hundredths of an inch. A quality control specialist

satela [25.4K]

Answer:

$t=\frac{7.55-7.5}{\frac{0.103}{\sqrt{10}}}=1.539$

$p_v =2*P(t_{(9)}>1.539)=0.158$

If we compare the p value and the significance level assumed $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to fail reject the null hypothesis.

Step-by-step explanation:

Data given and notation

Data: 7.65, 7.60, 7.65, 7.7, 7.55, 7.55, 7.4, 7.4, 7.5, 7.5

We can begin calculating the sample mean given by:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

And the sample deviation given by:

$s=\sart{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

And we got:

$\bar X=7.55$ represent the sample mean

$s=0.103$ represent the sample standard deviation

$n=10$ sample size

$\mu_o =7.5$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is equal to 7.5 or no, the system of hypothesis would be:

Null hypothesis: $\mu = 7.5$

Alternative hypothesis: $\mu \neq 7.5$

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{7.55-7.5}{\frac{0.103}{\sqrt{10}}}=1.539$

P-value

The first step is calculate the degrees of freedom, on this case:

$df=n-1=10-1=9$

Since is a two sided test the p value would be:

$p_v =2*P(t_{(9)}>1.539)=0.158$

Conclusion

If we compare the p value and the significance level assumed $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to fail reject the null hypothesis.

3 0

4 years ago

Evaluate abc² if a= -3, b= 6, and c= -8

Andreas93 [3]

Answer:

-1152

Step-by-step explanation:

abc² the expression can be rewritten using the given values for each letter

(-3)*6*(-8)^2 now we find the second power of (-8) by multiplying it with itself

(-8)*(-8) = 64

(-3)*6*64 = -1152

8 0

3 years ago