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3 years ago

The line y =3x-5 meet x-axis at the point M.

Mathematics

1 answer:

dusya [7]3 years ago

3 0

y = 3x - 5 meets the x-axis at the x-intercept, and that happens when y = 0

$\bf \stackrel{y}{0}=3x-5\implies 5=3x\implies \cfrac{5}{3}=x~\hspace{5em}\stackrel{M}{\left( \frac{5}{3},0 \right)}$

3y + 2x = 2, meets the y-axis when x = 0, and that'd be the y-intercept

$\bf 3y+2(\stackrel{x}{0})=2\implies 3y=2\implies y=\cfrac{2}{3}~\hspace{5em}\stackrel{N}{\left( 0,\frac{2}{3} \right)}$

so let's find the equation of the line with points M and N in standard form, bearing in mind that

standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

$\bf M(\stackrel{x_1}{\frac{5}{3}}~,~\stackrel{y_1}{0})\qquad N(\stackrel{x_2}{0}~,~\stackrel{y_2}{\frac{2}{3}}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{~~\frac{2}{3}-0~~}{0-\frac{5}{3}}\implies \cfrac{2}{3}\cdot -\cfrac{3}{5}\implies -\cfrac{2}{5}$

$\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-0=-\cfrac{2}{5}\left( x-\cfrac{5}{3} \right)\implies y=-\cfrac{2}{5}x+\cfrac{2}{3} \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{15}}{15y=-6x+10}\implies \stackrel{\textit{standard form}}{6x+15y=10}\implies 6x+15y-10=0$

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Diameter of the smaller spherical ball = 5 inches

Radius of the smaller spherical ball = 5/2 = 2.5 inches

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Volume of the smaller spherical ball ≈ 65.5 in.³

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Volume of the larger spherical ball ≈ 1,150.3 in.³

The amount of space (volume) that is in the larger spherical ball than the smaller = 1,150.3 - 65.5

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1 year ago

If x10=235 find x <br> Answer needed ASAP please

nikdorinn [45]

Answer:

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Step-by-step explanation:

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Answer:

The generalisation she can make from her work is that the other two angles of the quadrilateral are supplementary i.e their sum is 180°

Step-by-step explanation:

We are given the following from what she knows

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m∠2+m∠3=360 ... 3

From what is given, we can substitute equation 1 and 2 into equation 3 as shown:

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m∠2+m∠3=360

Substituting 1 and 2 we will have:

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