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3 years ago

Which value, when placed in the box, would result in a system of equations with infinitely many solutions?

Mathematics

2 answers:

hoa [83]3 years ago

8 0

Answer:

-10

Step-by-step explanation:

ira [324]3 years ago

7 0

For a system of equations to have infinitely many solutions, the equations have to be lineary dependent, (i.e. one of the equations is a multiple of the other equation). For the given equation to have infinitely many solutions, the second equation have to be a multiple of the first equation. The first equation can be rewritten as y - 2x = -5 The second equation is the first equation multiplied by 2, i.e. 2(y - 2x= -5) = 2y - 4x = -10 Therefore, the correct answer is -10 (option a).

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Find parametric equations for the line through point P(-4,5,2) in the direction of the vector (-6,6,-5)

tigry1 [53]

The vector v (-6, 6, -5) points in the direction of itself, so we start there.

We can capture all points on the line through the origin and the point (-6, 6, -5) by scaling v by an arbitrary real number t.

The line through point P and pointing in the same direction as v is parallel to the other line that passes through the origin. Then the line we want can be obtained by translating the line through the origin by a vector p that points to (-4, 5, 2), so the vector equation for this line is

r (t ) = p + t v

r (t ) = (-4, 5, 2) + t (-6, 6, -5)

r (t ) = (-4 - 6t, 5 + 6t, 2 - 5t )

To get the parametric equations, simply take out the components:

x (t ) = -4 - 6t

y (t ) = 5 + 6t

z (t ) = 2 - 5t

4 0

3 years ago

What is the sum of 20x^2-10x-30

ivann1987 [24]

Answer:

The sum of the roots is 0.5

Step-by-step explanation:

The correct question is

What is the sum of the roots of 20x^2-10x-30

we know that

In a quadratic equation of the form

$ax^{2} +bx+c=0$

The sum of the roots is equal to

$-\frac{b} {a}$

in this problem we have

$20x^{2} -10x-30=0$

$a=20\\b=-10\\c=-30$

substitute

$-\frac{(-10)} {20}=0.5$

Verify

Find the roots of the quadratic equation

The formula to solve a quadratic equation is equal to

$x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}$

$a=20\\b=-10\\c=-30$

substitute

$x=\frac{-(-10)\pm\sqrt{-10^{2}-4(20)(-30)}} {2(20)}$

$x=\frac{10\pm\sqrt{2,500}} {40}$

$x=\frac{10\pm50} {40}$

$x=\frac{10+50} {40}=1.5$

$x=\frac{10-50} {40}=-1$

The roots are x=-1 and x=1.5

The sum of the roots are

$-1+1.5=0.5$ ----> is ok

5 0

3 years ago

a rectangle measures 3 yards by 4 feet what is the perimeter of the rectangle in inches show your work please

marissa [1.9K]

Length: 3 yds. 36 in= 1 yd; 108 in.=3 yds
Width: 4 ft. 12 in=1 ft.; 48 in= 4 ft.
Sinve there are two lengths and widths in a rectangle, I like to multiply them both by 2 and add up the results. You also get the same answer when you add everything up twice. My answer is 312 in.

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3 years ago

A car travels 120 miles in 2.5 hours (with a constant speed). What is the car's

kipiarov [429]

Answer:

Step-by-step explanation:

120 divided by 2.5 = 40

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3 years ago

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How many degrees is the angle below?

umka2103 [35]

Answer:

30 degrees

Step-by-step explanation:

the line (not at the 0) is what you measure from. Because the angle is visibly acute, we know that it must be less than 90 degrees, therefore the angle cannot be 150 degrees but 30 degrees (from the lower line)

7 0

3 years ago

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