12. Write the equation of the graphed line.

Afina-wow [57]

We are asked in the problem to determine the value of x in the equation 4x² + 2x = 7 using completing the square method. in this case,

4x² + 2x = 7
x2 + 0.5 = 1.75
(x + 0.25)^2 - 0.0625 = 1.75
(x + 0.25)^2 = 1.8125
x+0.25=1.3462
x1 =1.0963
x2 =-1.5962

3 0

2 years ago

Consider the two data sets below:

alina1380 [7]

Answer:

Option c) The data sets will have the same values of their interquartile range.

Explanation:

1. The values are in order: they are in increasing oder, from lowest to highest value.

2. Calculate the interquartile range.

Interquartile range, IQR, is the third quartile, Q3, less the first quartile Q1:

IQR = Q3 - Q1

To find the first and the third quartile, first find the median:

Data Set 1: 19, 25, 35, 38, 41, 49, 50, 52, 59

[19, 25, 35, 38], 41, [49, 50, 52, 59]

↑

median = 41

Data Set 2: 19, 25, 35, 38, 41, 49, 50, 52, 99

[19, 25, 35, 38] , 41, [49, 50, 52, 99]

↑

median = 41

Now find the median of each subset: the values below the median and the values above the median.

Data set 1: First quartile

[19, 25, 35, 38],

↑

Q1 = [25 + 35] / 2 = 30

Third quartile

[49, 50, 52, 59]

↑

Q3 = [50 + 52] / 2 = 51

IQR = Q3 - Q1 = 51 - 30 = 21

Data set 2: First quartile

[19, 25, 35, 38]

↑

Q1 = [25 + 35] / 2= 30

Third quartile

[49, 50, 52, 99]

↑

Q3 = [52 + 50]/2 = 51

IQR = 51 - 30 = 21

Thus, it is shown that the data sets have will have the same values for the interquartile range: IQR = 21. (option c)

This happens because replacing one extreme value (in this case the maximum value) by other extreme value does not affect the median.

An outlier will change the range because the range is the maximum value less the minimum value.

5 0

2 years ago

Need help with solving both of these questions for geometry homework.

faltersainse [42]

Answer:

m<R = m<T = 80.5 deg

Step-by-step explanation:

3)

Since WXYZ is a square, <WXZ is formed with a diagonal of the square and has measure 45 deg.

m<WXZ = 8x - 19 = 45

8x - 19 = 45

8x = 64

x = 8

4)

Draw the kite. Make sure that segments QR and RS are not congruent. Fill in the given angle measures. Angles R and T are congruent opposite angles.

The sum of the measures of the interior angles of a convex, n-sided polygon is

180(n 2).

A kite is a quadrilateral, so n = 4.

180(4 - 2) = 180(2) = 360

The sum of the measures of the interior angles of a kite is 360 deg.

m<Q + m<R + m<S + m<T = 360

75 + m<R + 124 + m<T = 360

m<R + m<T + 199 = 360

m<R + m<T = 161

m<R = m<T, so we substitute m<T with m<R.

m<R + m<R = 161

2m<R = 161

m<R = 80.5

m<R = m<T = 80.5 deg

8 0

2 years ago

If the population of a country increases at a rate of 1.5% annually and its current population is 430,000, how many years will i

Sphinxa [80]

Answer:

That is 74 years.

Step-by-step explanation:

1.5% = 0.015.

The equation for the rate of growth is P = 430,000(1.015)^n where n is the number of years.

Triple the population is 430,000 * 3 = 1,290,000, so:

1,290,000 = 430,000(1.015)^n

(1.015)^n = 1290,000 / 430,000 = 3

Taking logs of both sides:

n log 1.015 = log 3

n = log 3 / log 1.015 = 73.8 years

5 0

2 years ago

Read 2 more answers

Please solve this linear equation will mark brainliest for correct answer

Ierofanga [76]

Answer:

x=-1/2

Step-by-step explanation:

$\frac{5x-2}{3x+1}=9\\\\\frac{5x-2}{3x+1}*(3x+1)=9*(3x+1)\\\\5x-2=9(3x+1)\\\\5x-2=9(3x)+9(1)\\\\5x-2=27x+9\\\\5x-2-9=27x+9-9\\\\5x-11=27x\\\\5x-5x-11=27x-5x\\\\0-11=22x\\\\-11=22x\\\\-11=11(2x)\\\\-11*(\frac{1}{11})=\frac{11(2x)}{11}\\\\-1=2x\\\\x=-\frac{1}{2}$

and now we check

$\frac{5(-\frac{1}{2})-2}{3(-\frac{1}{2})+1}=9\\\\\frac{-2.5-2}{-1.5+1}=9\\\\\frac{-4.5}{-0.5}=9\\\\\frac{4.5}{0.5}=9\\\\\frac{\frac{9}{2}}{\frac{1}{2}}=9\\\\\frac{9*2}{1*2}=9\\\\\frac{9}{1}=9\\\\9=9$

so the answer is -1/2

7 0

2 years ago