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yarga [219]
3 years ago
14

For what value of x does (x + 3)^2-5=0

Mathematics
1 answer:
ArbitrLikvidat [17]3 years ago
7 0

Answer:

x = -3±sqrt( 5)

Step-by-step explanation:

(x + 3)^2-5=0

Add 5 to each side

(x + 3)^2-5+5=0+5

(x + 3)^2 = 5

Take the square root of each side

sqrt((x + 3)^2 )=±sqrt( 5)

x+3 = ±sqrt( 5)

Subtract 3 from each side

x+3-3 = -3±sqrt( 5)

x = -3±sqrt( 5)

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True or false: a. ln56/ln7 = ln8 b. ln(x+y)-ln(x+y)=0
Nonamiya [84]

a) FALSE (would be TRUE if it said LN(56)-LN(7)=LN(8))

b) TRUE (because LN(x+y)-LN(x+y)=LN[(x+y)/(x+y)]=LN(1)=0)

7 0
3 years ago
Day care centers expose children to a wider variety of germs than the children would be exposed to if they stayed at home more o
Ostrovityanka [42]

Answer:

a) The study is an observational study

b) The proportion of children with significant social activity in children with acute lymphoblastic leukemia is approximately 0.802

The proportion of children with significant social activity in children without acute lymphoblastic leukemia is approximately 0.8565

c) The odds ratio is approximately 0.6780

d) The 95% CI is approximately 0.523 < OR < 0.833

e) i) Yes

ii) Children with more social activity have a higher occurrence of acute lymphoblastic leukemia

Step-by-step explanation:

a) An experimental study is a study in which the researcher adds inputs to the study and then monitors the outcomes

An observational study is one in which the researcher observes risk factors and does not intervene in the process

Therefore, the study is an observational study

b) The proportion of children with significant social activity in children with acute lymphoblastic leukemia is \hat p_1 = 1020/1272 = 85/106 = 0.8\overline {0188679245283} ≈ 0.802

The proportion of children with significant social activity in children without acute lymphoblastic leukemia is \hat p_2 = 5343/6238 ≈ 0.8565

c) We have the following two way table;

\begin{array}{ccc}Lymphoblastic \ Leukemia &With \ Social \ Activity & Without \ Social \ Activity\\With&1020 \ (a)&252 \ (b)\\Without&5343 \ (c)&895 \ (d) \end{array}

The \ odds \ ratio = \dfrac{1,020 \times 895}{5,343 \times 252} \approx 0.6780

The odds ratio ≈ 0.6780

d) The 95% confidence interval for the odds ratio is given as follows;

95 \% \ CI = OR \ \pm \ 1.96 \times \sqrt{\dfrac{1}{a} +\dfrac{1}{b}+\dfrac{1}{c}+\dfrac{1}{d}}

Where;

a = 1020, b = 252, c = 5343, d = 895

Therefore;

95 \% \ CI \approx  0.6780 \ \pm \ 1.96 \times \sqrt{\dfrac{1}{1,020} +\dfrac{1}{252}+\dfrac{1}{5,343}+\dfrac{1}{895}} \approx 0.678 \pm0.155

The 95% CI ≈ 0.523 < OR < 0.833

e) i) Given that the observed Odds Ratio is within the Confidence Interval, therefore, there is an indication that the amount of social activity is associated with acute lymphoblastic leukemia

ii) Based on the proportion of the study findings, children with more social activity have a higher occurrence of acute lymphoblastic leukemia

6 0
2 years ago
The system of linear equations 5x+2y = 3 and x+y = -1 is graphed below.What is the solution to the system of equations?
Kazeer [188]

Answer:

<h2>C. (3, -4)</h2>

Step-by-step explanation:

If the system of linear equations is graphed, then the solution is the intersection of lines.

Read it from the graph (look at the picture).

7 0
3 years ago
Writey=1/8 x+7 in standard form using integers.
sineoko [7]

Answer:

x - 8y = - 56

Step-by-step explanation:

The equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

Given

y = \frac{1}{8} x + 7

Multiply through by 8 to clear the fraction

8y = x + 56 ( subtract 8y from both sides )

0 = x - 8y + 56 ( subtract 56 from both sides )

- 56 = x - 8y, that is

x - 8y = - 56 ← in standard form

5 0
3 years ago
In the graph shown, suppose that f(x) = 3.5x and h(x) = 1.5x. Choose the statement that COULD be true.
faust18 [17]

Answer: D

Step-by-step explanation:

The given functions are

Now these are exponential curves and the bases for the functions are 3.5 & 1.5

Also the graph of g(x) is between f(x) & h(x)

Hence the value of base called the scale factor must be between 3.5 & 1.5.

4 & 5 are more than 3.5

0.9 is smaller than 1.5

But π = 3.14 lies between 3.5 & 1.5.

Hence the only option which can represent the graph of g(x) is

Option D) is the right answer

3 0
3 years ago
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