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Irina18 [472]
3 years ago
6

Solve the system of equations. y=3x y=x^2-10

Mathematics
2 answers:
puteri [66]3 years ago
5 0

Answer:

y=3x.........1

y=x^2-10.......2

substituting value of eq 1 to 2

3x=x^2-10

x^2-10-3x=0

x^2-3x-10=0

x^2-5x+2x-10=0

X(x-5)+2(x-5)=0

(x-5)(X+2)=0

then

X=5 or X=-2

again

y=??

when X=5

y=3×5=15

when X=-2

y=-6

Burka [1]3 years ago
5 0

Answer:

(-2, - 6) and (5,15) thats the answer hope that helps

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Say you're making a recipe that needs 2 1/2 cups of water. But you want to make two servings, so you need to know what 2 1/2 + 2 1/2 equals. Or maybe you need a half cup of milk but you don't have enough. You need to know how much left you need so you can buy or borrow the right amount.
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A machine is used to stamp bottle caps. If 150 bottle caps can be stamped in 30 s, the rate is _______ caps per second.
Svetach [21]

Answer:

5 bottle caps each second

Step-by-step explanation:

To find the unit rate, just divide the total number by the total time.

150/30

5

So 5 bottle caps per second

4 0
3 years ago
A student was given the line y=2/3x-1 and the point (-7, 1/2) and asked to find an equation that went through the given point an
Colt1911 [192]

keeping in mind that perpendicular lines have <u>negative reciprocal</u> slopes,  hmmm what's the slope of y=2/3x-1 anyway?


\bf \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}~\hspace{7em}y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{2}{3}}x-1 \\\\[-0.35em] ~\dotfill

\bf \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{\cfrac{2}{3}}\qquad \qquad \qquad \stackrel{reciprocal}{\cfrac{3}{2}}\qquad \stackrel{negative~reciprocal}{-\cfrac{3}{2}}}


so, notice, "one of his mistakes" is that he used 3/2 as the slope, not -3/2.

so, we're really looking for a line whose slope is -3/2 and runs through (-7, 1/2).


\bf (\stackrel{x_1}{-7}~,~\stackrel{y_1}{\frac{1}{2}})~\hspace{10em} slope = m\implies -\cfrac{3}{2} \\\\\\ \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-\cfrac{1}{2}=-\cfrac{3}{2}[x-(-7)]\implies y-\cfrac{1}{2}=-\cfrac{3}{2}(x+7) \\\\\\ y-\cfrac{1}{2}=-\cfrac{3}{2}x-\cfrac{21}{2}\implies y=-\cfrac{3}{2}x-\cfrac{21}{2}+\cfrac{1}{2}\implies y=-\cfrac{3}{2}x-10

3 0
3 years ago
Point V lies between points U and W on Line segment U W. A line has points U, V, W. The length between U V is 2 x minus 4. The l
AlekseyPX

Answer:

UW = 36 units

Step-by-step explanation:

The question is incomplete. Here is the complete question

Point V lies between points U and W on Line segment U W. A line has points U, V, W. The length between U V is 2 x minus 4. The length between V W is 4 x + 10. If UW = 9x – 9, what is UW in units?

If a point V lies between points U and W on line segment UW, then based on vector notation, UV + VW = UW.

Given parameters

The length between U and V i.e UV = 2x-4

The length between V and W i.e VW= 4x + 10.

UW = 9x – 9

Required

The length between U and W in units

Since UW = UV+VW, we will substitute the given functions into the formula as shown;

9x-9 = 2x-4+4x + 10.

9x-9 = 2x+4x-4+10

9x-9 = 6x+6

collect like terms on both sides;

9x-6x = 6+9

3x = 15

x = 15/3

x = 5

Substitute x = 5 into the function UW = 9x-9 to ge the length of UW in units.

UW = 9(5)-9

UW = 45-9

UW = 36 units

<em>Hence the required length between line segment U and W in units is 36units.</em>

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What two numbers give you 343
igor_vitrenko [27]

Answer:171 and 172


Step-by-step explanation;

171+172=343

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