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4 years ago

Half of G Multiplied by t squared is equal to its area A divided by its width w

Mathematics

1 answer:

natima [27]4 years ago

4 0

Half of G Multiplied by t squared is equal to its area A divided by its width w is written as

$\frac{1}{2} G \times {t}^{2} = \frac{A}{W}$

$\frac{1}{2} G {t}^{2} = \frac{A}{W}$

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The first quartile of a data set is 52, and the third is 72. what is the outlier ?

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To cover his rectangular backyard, Will needs at least 170.5 square feet of sod.The length of Will’s yard is 15.5 feet.What are

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3 years ago

X + 1 > -5( 7-2x) I need help please.

Ede4ka [16]

Answer:

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Step-by-step explanation:

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3 years ago

The graph of which function has an axis of symmetry at x =-1/4 ?

Phoenix [80]

we know that

The equation of the vertical parabola in vertex form is equal to

$y=a(x-h)^{2}+k$

where

(h,k) is the vertex

The axis of symmetry is equal to the x-coordinate of the vertex

$x=h$ ------> axis of symmetry of a vertical parabola

we will determine in each case the axis of symmetry to determine the solution

case A) $f(x)=2x^{2}+x-1$

Convert to vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$f(x)+1=2x^{2}+x$

Factor the leading coefficient

$f(x)+1=2(x^{2}+0.5x)$

Complete the square. Remember to balance the equation by adding the same constants to each side

$f(x)+1+0.125=2(x^{2}+0.5x+0.0625)$

$f(x)+1.125=2(x^{2}+0.5x+0.0625)$

Rewrite as perfect squares

$f(x)+1.125=2(x+0.25)^{2}$

$f(x)=2(x+0.25)^{2}-1.125$

the vertex is the point $(-0.25,-1.125)$

the axis of symmetry is

$x=-0.25=-\frac{1}{4}$

therefore

the function $f(x)=2x^{2}+x-1$ has an axis of symmetry at $x=-\frac{1}{4}$

case B) $f(x)=2x^{2}-x+1$

Convert to vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$f(x)-1=2x^{2}-x$

Factor the leading coefficient

$f(x)-1=2(x^{2}-0.5x)$

Complete the square. Remember to balance the equation by adding the same constants to each side

$f(x)-1+0.125=2(x^{2}-0.5x+0.0625)$

$f(x)-0.875=2(x^{2}-0.5x+0.0625)$

Rewrite as perfect squares

$f(x)-0.875=2(x-0.25)^{2}$

$f(x)=2(x-0.25)^{2}+0.875$

the vertex is the point $(0.25,0.875)$

the axis of symmetry is

$x=0.25=\frac{1}{4}$

therefore

the function $f(x)=2x^{2}-x+1$ does not have a symmetry axis in $x=-\frac{1}{4}$

case C) $f(x)=x^{2}+2x-1$

Convert to vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$f(x)+1=x^{2}+2x$

Complete the square. Remember to balance the equation by adding the same constants to each side

$f(x)+1+1=x^{2}+2x+1$

$f(x)+2=x^{2}+2x+1$

Rewrite as perfect squares

$f(x)+2=(x+1)^{2}$

$f(x)=(x+1)^{2}-2$

the vertex is the point $(-1,-2)$

the axis of symmetry is

$x=-1$

therefore

the function $f(x)=x^{2}+2x-1$ does not have a symmetry axis in $x=-\frac{1}{4}$

case D) $f(x)=x^{2}-2x+1$

Convert to vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$f(x)-1=x^{2}-2x$

Complete the square. Remember to balance the equation by adding the same constants to each side

$f(x)-1+1=x^{2}-2x+1$

$f(x)=x^{2}-2x+1$

Rewrite as perfect squares

$f(x)=(x-1)^{2}$

the vertex is the point $(1,0)$

the axis of symmetry is

$x=1$

therefore

the function $f(x)=x^{2}-2x+1$ does not have a symmetry axis in $x=-\frac{1}{4}$

the answer is

$f(x)=2x^{2}+x-1$

7 0

4 years ago

Read 2 more answers

Line w and line v are perpendicular to each other. Line w passes through the points ( -4,8 ) and ( 12,-2 ). What is the slope of

erik [133]

The slope of line "v" is $\frac{8}{5}$

<h3>Solution:</h3>

Given that Line w and line v are perpendicular to each other

Also given that line w passes through the points ( -4, 8 ) and ( 12, -2 )

To find: slope of line v

Since line w and line v are perpendicular to each other, product of slopes of line w and line v are equal to -1

$\text {slope of line } w \times \text { slope of line } v=-1$ ---- eqn 1

Let us first find slope of line w

The slope "m" of a line is given as:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$\text {Here } x_{1}=-4 \text { and } x_{2}=12 \text { and } y_{1}=8 \text { and } y_{2}=-2$

$m=\frac{-2-8}{12-(-4)}=\frac{-10}{16}=\frac{-5}{8}$

Thus the slope of line "w" is $\frac{-5}{8}$

Substituting the slope of w in eqn 1 we get,

$\begin{array}{l}{\frac{-5}{8} \times \text { slope of line } v=-1} \\\\ {\text { slope of line } v=\frac{8}{-5} \times-1=\frac{8}{5}}\end{array}$

Thus the slope of line "v" is $\frac{8}{5}$

5 0

3 years ago