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3 years ago

A line has a slope of -1/2 and a y-intercept of –2. What is the x-intercept of the line? –4, –1, 1 ,4

1 answer:

5 0

To get the x-intercept, we simply set y = 0 and solve for "x".

now, we have the slope and the y-intercept, well, let's plug those two in the slope-intercept form, reason why is called that anyway,

$\bf y=\stackrel{slope}{-\cfrac{1}{2}}x\stackrel{y-intercept}{-2}\implies 0=-\cfrac{x}{2}-2\implies \cfrac{x}{2}=-2\implies x=-4$

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Which of the following coordinate pairs make the equation x - 9y = 12 true?

Natalka [10]

(12, 0)

12-9(0)=12
12-0=12
12=12

7 0

3 years ago

What is 5.092 rounded to the nearest hundredth?

goblinko [34]

5.09 because 2 is less then 5 so you round down

6 0

3 years ago

Read 2 more answers

Which is bigger 2m or 275cm

aliina [53]

Answer:

275.

Step-by-step explanation:

If you convert 2m into CM you get 200.
If you convert 275 cm into M you get 2.75. So 275cm is bigger.

8 0

2 years ago

Read 2 more answers

at a maximum speed, an airolane travels 1680 miles against the windin 5 hours. Flying with the wind, the plane can travel the sa

Licemer1 [7]

Answer:

Plane Speed (x) = 378 mph

Step-by-step explanation:

Equation

d = r * t

Givens

With the wind

d = 1680 miles
t = 4 hours
r = x + y

Against the wind

d = 1680
t = 5 hours
r = x - y

Equation

The distances are the same, so you can solve for x in terms of y and then deal with the actual distance.

(x + y)*4 = (x - y)*5 Remove the brackets on both sides

Solution

4x + 4y = 5x - 5y Subtract 4x from both sides
4y = -4x + 5x - 5y Combine
4y = x - 5y Add 5y to both sides
5y + 4y = x
x = 9y

Solution part 2

Now take one of the distance formulas and solve for x first then y.

(x - y)*5 = 1680 Substitute 9y for x
(9y - y)*5 = 1680 Subtract on the left
8y * 5 = 1680 Multiply on the left
40y = 1680 Divide by 40
y = 1680/40
y = 42 That's the speed of the wind.

(x - y)*5 = 1680 Substitute the wind speed for y
(x - 42)*5 = 1680 Divide both sides by 5
(x - 42) = 1680 / 5 Do the division on the right
(x - 42) = 336 Add 42 to both sides.
x = 336 + 42
x = 378 mph Plane's speed

7 0

4 years ago

Simplify each expression. Assume that all variables are positive.

kozerog [31]

Q1. The answer is $\frac{8x^{3}y^{6} }{27}$

$( \frac{16 x^{5} y^{10}}{81x y^{2} } )^{ \frac{3}{4} }= ( \frac{16}{81}* \frac{ x^{5} }{x}* \frac{ y^{10} }{y^{2}} )^{ \frac{3}{4} } \\ \\ 
 \frac{ x^{a} }{ x^{b} }= x^{a-b} \\ \\ 
( \frac{16}{81}* \frac{ x^{5} }{x}*\frac{ y^{10} }{y^{2}} )^{ \frac{3}{4} }}=( \frac{16}{81 }* x^{5-1}* y^{10-2})^{ \frac{3}{4} }=( \frac{16}{81 }* x^{4}* y^{8})^{ \frac{3}{4} }= \\ \\ = (\frac{16}{18} )^{ \frac{3}{4} }*(x^{4})^{ \frac{3}{4} }*(y^{8})^{ \frac{3}{4} }=$
$\frac{(16)^{ \frac{3}{4} }}{(18)^{ \frac{3}{4} }}*(x^{4})^{ \frac{3}{4} }*(y^{8})^{ \frac{3}{4} }=\frac{( 2^{4} )^{ \frac{3}{4} }}{( 3^{4} )^{ \frac{3}{4} }}*(x^{4})^{ \frac{3}{4} }*(y^{8})^{ \frac{3}{4} } \\ \\ 
 (x^{a} )^{b} = x^{a*b} \\ \\ 
\frac{( 2^{4} )^{ \frac{3}{4} }}{( 3^{4} )^{ \frac{3}{4} }}*(x^{4})^{ \frac{3}{4} }*(y^{8})^{ \frac{3}{4} } = \frac{ 2^{4* \frac{3}{4} } }{ 3^{4* \frac{3}{4} } } * x^{4* \frac{3}{4} } * y^{8*\frac{3}{4}} = \frac{ 2^{3} }{ 3^{3} } * x^{3} *y^{6} =$
$= \frac{8x^{3}y^{6} }{27}$

Q2. The answer is 1/16

$(-64) ^ \frac{-2}{3} =(-1* 2^{6} ) ^ \frac{-2}{3}=(-1)^ \frac{-2}{3} *(2^{6} ) ^ \frac{-2}{3} \\\\x^{-a} = \frac{1}{ x^{a} } \\\\(-1)^ \frac{-2}{3} *(2^{6} ) ^ \frac{-2}{3} = \frac{1}{(-1)^ \frac{2}{3}} *\frac{1}{(2^{6})^ \frac{2}{3}} \\ \\ (x^{a} )^{b}=x^{a*b} \\\\x^{ \frac{a}{b} = \sqrt[b]{ x^{a} } } \\ \\ 
$
$\frac{1}{(-1)^ \frac{2}{3}} *\frac{1}{2^{6*\frac{2}{3}}} = \frac{1}{ \sqrt[3]{(-1)^{2} } } * \frac{1}{ 2^{4} } = \frac{1}{ \sqrt[3]{1} } * \frac{1}{16} = \frac{1}{1} * \frac{1}{16}= \frac{1}{16}$

Q3. The answer is $a^{ \frac{7}{6} }$

$a^{ \frac{2}{3} } * a^{ \frac{1}{2} } \\ \\ 
 x^{a}* x^{b} =x^{a+b} \\ \\ 
a^{ \frac{2}{3} } * a^{ \frac{1}{2} }= a^{ \frac{2}{3} + \frac{1}{2} } =a^{ \frac{2*2}{3*2} + \frac{1*3}{2*3} }=a^{ \frac{4}{6} + \frac{3}{6} }=a^{ \frac{4+3}{6} }=a^{ \frac{7}{6} }$

7 0

3 years ago