All categories

3 years ago

True or False: When completing the square, the first step is to double the middle term.

Mathematics

1 answer:

andrew11 [14]3 years ago

6 0

Answer:

true?

Step-by-step explanation:

You might be interested in

Geometry:<br> Solve for x.<br> 1)

nlexa [21]

Simplifying
43x + 2 = 45x + -2

Reorder the terms:
2 + 43x = 45x + -2

Reorder the terms:
2 + 43x = -2 + 45x

Solving
2 + 43x = -2 + 45x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-45x' to each side of the equation.
2 + 43x + -45x = -2 + 45x + -45x

Combine like terms: 43x + -45x = -2x
2 + -2x = -2 + 45x + -45x

Combine like terms: 45x + -45x = 0
2 + -2x = -2 + 0
2 + -2x = -2

Add '-2' to each side of the equation.
2 + -2 + -2x = -2 + -2

Combine like terms: 2 + -2 = 0
0 + -2x = -2 + -2
-2x = -2 + -2

Combine like terms: -2 + -2 = -4
-2x = -4

Divide each side by '-2'.
x = 2

Simplifying
x = 2

3 0

3 years ago

Read 2 more answers

Find the coefficient of variation for each of the two sets of data, then compare the variation. Round results to one decimal pla

svp [43]

Here is the correct computation of the question given.

Find the coefficient of variation for each of the two sets of data, then compare the variation. Round results to one decimal place. Listed below are the systolic blood pressures (in mm Hg) for a sample of men aged 20-29 and for a sample of men aged 60-69.

Men aged 20-29: 117 122 129 118 131 123

Men aged 60-69: 130 153 141 125 164 139

Group of answer choices

Men aged 20-29: 4.8%

Men aged 60-69: 10.6%

There is substantially more variation in blood pressures of the men aged 60-69.

Men aged 20-29: 4.4%

Men aged 60-69: 8.3%

There is substantially more variation in blood pressures of the men aged 60-69.

Men aged 20-29: 4.6%

Men aged 60-69: 10.2 %

There is substantially more variation in blood pressures of the men aged 60-69.

Men aged 20-29: 7.6%

Men aged 60-69: 4.7%

There is more variation in blood pressures of the men aged 20-29.

Answer:

(c)

Men aged 20-29: 4.6%

Men aged 60-69: 10.2 %

There is substantially more variation in blood pressures of the men aged 60-69.

Step-by-step explanation:

From the given question:

The coefficient of variation can be determined by the relation:

$coefficient \ of \ variation = \dfrac{standard \ deviation}{mean}*100$

We will need to determine the coefficient of variation both men age 20 - 29 and men age 60 -69

To start with;

The coefficient of men age 20 -29

Let's first find the mean and standard deviation before we can do that ;

SO .

Mean = $\dfrac{\sum \limits^{n}_{i-1}x_i}{n}$

Mean = $\frac{117+122+129+118+131+123}{6}$

Mean = $\dfrac{740}{6}$

Mean = 123.33

Standard deviation $= \sqrt{\dfrac{\sum (x_i- \bar x)^2}{(n-1)} }$

Standard deviation = $\sqrt{\dfrac{(117-123.33)^2+(122-123.33)^2+...+(123-123.33)^2}{(6-1)} }$

Standard deviation = $\sqrt{\dfrac{161.3334}{5}}$

Standard deviation = $\sqrt{32.2667}$

Standard deviation = 5.68

The $coefficient \ of \ variation = \dfrac{standard \ deviation}{mean}*100$

$coefficient \ of \ variation = \dfrac{5.68}{123.33}*100$

Coefficient of variation = 4.6% for men age 20 -29

For men age 60-69 now;

Mean = $\dfrac{\sum \limits^{n}_{i-1}x_i}{n}$

Mean = $\frac{ 130 + 153 + 141 + 125 + 164 + 139}{6}$

Mean = $\dfrac{852}{6}$

Mean = 142

Standard deviation $= \sqrt{\dfrac{\sum (x_i- \bar x)^2}{(n-1)} }$

Standard deviation = $\sqrt{\dfrac{(130-142)^2+(153-142)^2+...+(139-142)^2}{(6-1)} }$

Standard deviation = $\sqrt{\dfrac{1048}{5}}$

Standard deviation = $\sqrt{209.6}$

Standard deviation = 14.48

The $coefficient \ of \ variation = \dfrac{standard \ deviation}{mean}*100$

$coefficient \ of \ variation = \dfrac{14.48}{142}*100$

Coefficient of variation = 10.2% for men age 60 - 69

Thus; Option C is correct.

Men aged 20-29: 4.6%

Men aged 60-69: 10.2 %

There is substantially more variation in blood pressures of the men aged 60-69.

4 0

3 years ago

Please help! what is an equation of a parabola with x-intercepts at (2,0) and (-7,0) and which passes through the point (1,32)?

Vika [28.1K]

Answer:

Step-by-step explanation:

f(x) = a(x - x₁)(x - x₂) - factored form of the equation of the parabola with zeros x₁ and x₂

x-intercepts at (2,0) and (-7,0) means zeros: x₁=2 and x₂=-7

So:

f(x) = a(x - 2)(x + 7) - factored form of the equation of the parabola with x-intercepts at (2,0) and (-7,0)

The parabola passing through point (1, 32) means if x=1 then f(x)=32

Then:

32 = a(1 - 2)(1 + 7)

32 = a(-1)(8)

32 = - 8a

a = - 4

Therefore the equation of a parabola with x-intercepts at (2,0) and (-7,0) and which passes through the point (1,32):

Expanding to standard form:

f(x) = -4(x - 2)(x + 7)

f(x) = -4(x² + 7x - 2x - 14)

8 0

3 years ago

For the pair of points find the distance between them and the midpoint of the line segment joining them.(720,50), (125,18)The di

Lana71 [14]

Given two points

$(x_1,y_1)$

and

$(x_2,y_2)$

The distance between them is >>>

$D=\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2}$

The points given are (Sqrt(20), Sqrt(50)) and (Sqrt(125), Sqrt(8)), so their distance is >>>

$\begin{gathered} D=\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2} \\ D=\sqrt[]{(\sqrt[]{8}-\sqrt[]{50})^2+(\sqrt[]{125}-\sqrt[]{20})^2} \\ D=\sqrt[]{(\sqrt8)^2-2(\sqrt[]{8})(\sqrt[]{50})+(\sqrt[]{50})^2^{}+(\sqrt[]{125})^2-2(\sqrt[]{125})(\sqrt[]{20})+(\sqrt[]{20})^2} \\ D=\sqrt[]{8-2(2\sqrt[]{2})(5\sqrt[]{2})+50+125-2(5\sqrt[]{5})(2\sqrt[]{5})+20} \\ D=\sqrt[]{8-40+50+125-100+20} \\ D=\sqrt[]{63} \\ D=3\sqrt[]{7} \end{gathered}$

----------------------------------------------------------------------------------------------------------

The midpoint formula is >>>

$M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

Plugging in the points, we have >>>

$\begin{gathered} M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}) \\ M=(\frac{\sqrt[]{20}+\sqrt[]{125}}{2},\frac{\sqrt[]{50}+\sqrt[]{8}}{2}) \\ M=(\frac{2\sqrt5+5\sqrt[]{5}}{2},\frac{5\sqrt[]{2}+2\sqrt[]{2}}{2}) \\ M=(\frac{7\sqrt[]{5}}{2},\frac{7\sqrt[]{2}}{2}) \end{gathered}$

3 0

2 years ago

I need help ASAP.........

aliina [53]

Answer:

it will take 20 minutes for her to weed all of her garden

Step-by-step explanation:

8 minutes=40% 16 minutes= 80% 20 minutes=100%

plz mark brainliest

7 0

3 years ago

Read 2 more answers