Please help asap :DDD

0=x^2-4x+3 how many roots does this equation have

mars1129 [50]

Answer:

No complex roots; 3 real roots

Step-by-step explanation:

If a third order polynomial has any complex roots, then as a rule it has 1 real root and 2 complex roots. In this particular case, the polynomial has three real roots, as can be determined by graphing the function. The graph crosses the x-axis in 3 places.

5 0

3 years ago

If the area of a rectangle equals 28 square centimeters what is the height?

Slav-nsk [51]

So the length and width would be 7 and 4. hope that helped

3 0

3 years ago

Problem

Sergeu [11.5K]

The lengths of HJ and JK are 50 and 72 respectively.

Given: J is between H and K. the length of HJ=2x+4, JK=3x+3, and HK=22.

The line HJ and JK are collinear then the total length is given as: HJ+JK=HK

substitute values

⇒ (2x+4)+(3x+3)=22

⇒ 5x+7=22

⇒ 5x=22-7

⇒ 5x=15

⇒ x=3

Thus, the length of HJ is (2x+4)=(2*3+4)=10

And the length of JK is (3x+3)=(3*3+3)=12

Learn more about collinear lines here: brainly.com/question/27943430

#SPJ10

8 0

2 years ago

Read 2 more answers

Modern medical practice tells us not to encourage babies to become too fat. Is there a positive correlation between the weight x

Anna11 [10]

Answer:

a) Figure attached

b) $y=1.31 x +98.57$

c) The correlation coefficient would be r =0.47719

d) $y=1.31 x +98.57=1.31*21 + 98.57 =126.08$

Step-by-step explanation:

(a) Draw a scatter diagram for the data.

See the figure attached

(b) Find x, y, b, and the equation of the least-squares line. (Round your answers to three decimal places.) x =__ y =__ b =__ y =__ + __x

$m=\frac{S_{xy}}{S_{xx}}$

Where:

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}$

With these we can find the sums:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=6576-\frac{300^2}{14}=147.429$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i){n}}=38186-\frac{300*1773}{14}=193.143$

And the slope would be:

$m=\frac{193.143}{147.429}=1.31$

Nowe we can find the means for x and y like this:

$\bar x= \frac{\sum x_i}{n}=\frac{300}{14}=21.429$

$\bar y= \frac{\sum y_i}{n}=\frac{1773}{14}=126.643$

And we can find the intercept using this:

$b=\bar y -m \bar x=126.643-(1.31*21.429)=98.571$

So the line would be given by:

$y=1.31 x +98.57$

(c) Find the sample correlation coefficient r and the coefficient of determination r?2. (Round your answers to three decimal places.)

n=14 $\sum x = 300, \sum y = 1773, \sum xy=38186, \sum x^2 =6576, \sum y^2 =225649$

And in order to calculate the correlation coefficient we can use this formula:

$r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}$

$r=\frac{14(38186)-(300)(1773)}{\sqrt{[14(6576) -(300)^2][14(225649) -(1773)^2]}}=0.9534$

So then the correlation coefficient would be r =0.47719

What percentage of variation in y is explained by the least-squares model? (Round your answer to one decimal place.)

The % of variation is given by the determination coefficient given by $r^2$ and on this case $0.47719^2 =0.2277$ , so then the % of variation explaines is 22.8%.

(d) If a female baby weighs 21 pounds at 1 year, what do you predict she will weigh at 30 years of age? (Round your answer to two decimal places.) ___ lb

So we can replace in the linear model like this:

$y=1.31 x +98.57=1.31*21 + 98.57 =126.08$

7 0

2 years ago

A chemistry teacher needs to mix a 20% salt solution with an 80% salt solution to make 20 qt of a 40% salt solution. How many qu

Svetlanka [38]

Answer:

6 2/3 qt 80%
13 1/3 qt 20%

Step-by-step explanation:

It is often convenient to solve a mixture problem by letting a variable represent the quantity of the higher-concentration contributor to the mix.

__

We can let x represent the number of quarts of 80% solution needed. Then (20-x) is the number of quarts of 20% solution needed. The amount of salt in the final mix is ...

0.80x +0.20(20-x) = 0.40(20)

0.60x = 0.20(20) . . . . . . . . subtract 0.20(20) and simplify

x = 20/3 = 6 2/3 . . . . . . . . . divide by 0.60; quarts of 80% solution

(20 -x) = 13 1/3 . . . . . . . . . . amount of 20% solution needed

The teacher should mix 6 2/3 quarts of 80% solution with 13 1/3 quarts of 20% solution.

3 0

2 years ago