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docker41 [41]
2 years ago
9

Which expression is equivalent to 6x2 – 19x – 55?

Mathematics
2 answers:
seraphim [82]2 years ago
4 0
Answer, (6x + 11) (x - 5)
Vanyuwa [196]2 years ago
3 0

Answer:

Option D. (6x + 11)(x - 5)

Step-by-step explanation:

The given expression is 6x² - 19x - 55

We have to convert it into factored form as given in the various options.

6x² - 19x - 55 = 6x² - 30x + 11x - 55

6x(x - 5) + 11(x - 5)

(6x + 11)(x - 5)

Therefore, option D. (6x + 11)(x - 5) is the correct answer.

You might be interested in
The graph of y=3x^2-3x-1 is shown. Use the graph to find estimates for the solutions of i)3x^2-3x+2=2 ii) 3x^2-3x-1=x+1
AlexFokin [52]

Answer:

i) (0, 2) and (1, 2), ii) (0.333, 1.333) and (1, 2).

Step-by-step explanation:

i) Let be y=3\cdot x^{2}-3\cdot x -1, if 3\cdot x^{2}-3\cdot x +2 = 2, which is equivalent to the following system of equations:

y = 3\cdot x^{2}-3\cdot x +2

y = 2

Now, this system is now represented by means of a graphing tool and whose outcome is attached below. There are two solutions: (0, 2) and (1, 2)

ii) Let be y=3\cdot x^{2}-3\cdot x -1, if 3\cdot x^{2}-3\cdot x +2 = x+1, which is equivalent to the following system of equations:

y = 3\cdot x^{2}-3\cdot x +2

y = x+1

Now, this system is now represented by means of a graphing tool and whose outcome is attached below. There are two solutions: (0.333, 1.333) and (1, 2)

7 0
2 years ago
A member of a student team playing an interactive marketing game received the fol- lowing computer output when studying the rela
nirvana33 [79]

Answer:

p_v = 2*P(t_{n-2} > |t_{calc}|)= 0.91

So on this case for the significance level assumed \alpha=0.05 we see that p_v >\alpha so then we can conclude that the result is NOT significant. And we don't have enough evidence to reject the null hypothesis.

So on this case is not appropiate say that :"the more we spend on advertising this product, the fewer units we sell" since the slope for this case is not significant.

Step-by-step explanation:

Let's suppose that we have the following linear model:

y= \beta_o +\beta_1 X

Where Y is the dependent variable and X the independent variable. \beta_0 represent the intercept and \beta_1 the slope.  

In order to estimate the coefficients \beta_0 ,\beta_1 we can use least squares procedure.  

If we are interested in analyze if we have a significant relationship between the dependent and the independent variable we can use the following system of hypothesis:

Null Hypothesis: \beta_1 = 0

Alternative hypothesis: \beta_1 \neq 0

Or in other words we want to check is our slope is significant (X have an effect in the Y variable )

In order to conduct this test we are assuming the following conditions:

a) We have linear relationship between Y and X

b) We have the same probability distribution for the variable Y with the same deviation for each value of the independent variable

c) We assume that the Y values are independent and the distribution of Y is normal  

The significance level assumed on this case is \alpha=0.05

The standard error for the slope is given by this formula:

SE_{\beta_1}=\frac{\sqrt{\frac{\sum (y_i -\hat y_i)^2}{n-2}}}{\sqrt{\sum (X_i -\bar X)^2}}

Th degrees of freedom for a linear regression is given by df=n-2 since we need to estimate the value for the slope and the intercept.  

In order to test the hypothesis the statistic is given by:

t=\frac{\hat \beta_1}{SE_{\beta_1}}

The p value on this case would be given by:

p_v = 2*P(t_{n-2} > |t_{calc}|)= 0.91

So on this case for the significance level assumed \alpha=0.05 we see that p_v >\alpha so then we can conclude that the result is NOT significant. And we don't have enough evidence to reject the null hypothesis.

So on this case is not appropiate say that :"the more we spend on advertising this product, the fewer units we sell" since the slope for this case is not significant.

3 0
1 year ago
Consider the lengths of stay at a hospital’s emergency department. Hours Count Percent 1 18 3.44 2 55 10.50 3 81 15.46 4 109 20.
Vladimir [108]

Answer:

Probability = 0.502

Step-by-step explanation:

We are given the following data :

 Hours         Count            Percent

  1                    18               3.44

  2                    55              10.50

  3                    81               15.46

  4                    109             20.80

  5                     88              16.79

  6                     66              12.60

  7                     39               7.44

  8                     17                3.24

  9                     17                3.24

  10                   19                3.63

   15                  15                2.86

We need to calculate the probability

P(Length of stay of exactly 1 is less than or equal to 4)

P(Y \leq 4) = P(Y = 1) + P(Y = 2) + P(Y = 3) + P(Y = 4)

P(Y \leq 4) = 0.0344 + 0.1050 + 0.1546 + 0.2080 = 0.502

We convert the percent into probabilities by dividing them with 100. This gave us the required probabilities.

8 0
2 years ago
Name two ways you might see decimals used outside of school.
slega [8]
In money and weighing things 
7 0
1 year ago
Read 2 more answers
The rule for the dilation of quadrilateral QRST to the image Q'R'S'T' is DO,0.5(x, y) → (0.5x, 0.5y).
Harlamova29_29 [7]
Applying the rule for dilation, we will multiply the scale factor to its coordinates. 
Having Q (0,2) and DO 0.5(x.y), the coordinates of Q' will be:

x = (.5)(0) = 0
y = (.5)(2) = 1

Therefore coordinates of Q' is (0,1) 

*Having a scale factor of >1, the figure is said to be reduced. 
8 0
1 year ago
Read 2 more answers
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