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Keith_Richards [23]

3 years ago

14

Triangle abc is similar to triangle xyz, and the hypotenuses of both triangles lie on line m. the slope of line m between (-6,-8

) and (-2,-5) is . what is the slope of line m between (2,-2) and (10,4)?

1 answer:

olchik [2.2K]3 years ago

4 0

Slope of (-6,-8) and (-2,5) is -1.625
Slope of (2,2) and (10,4) is 0.75

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The sum of three consecutive natural numbers is 1146, find the numbers.

-BARSIC- [3]

$\text{Let the 3 consecutive numbers be}~ x,~x+1~ \text{and} ~x+2.\\\\\text{According to the condition,}\\\\x+x+1+x+2 = 1146\\\\\implies 3x +3 = 1146\\\\\implies 3(x+1) = 1146\\\\\implies x+1 = \dfrac{1146}3 = 382\\\\\implies x= 382-1 = 381\\\\\text{Now, the numbers are}~ 381,~382~\text{and}~383$

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2 years ago

katovenus [111]

Answer:

x = $\frac{7+\sqrt{47}\times i }{4}$

Step-by-step explanation:

<u>To solve quadratic systems,we always substitute one variable in terms if the other and then solve the equation.</u>

x + 2y = 6 ---------------(1)

y - 5 = $(x-2)^{2}$ ---------------(2)

y = $(x-2)^{2}$ + 5 ---------------(3)

Substitute (3) in (1) ,

x + 2( $(x-2)^{2}$ + 5 ) = 6

$(a + b)^{2}$ = $a^{2} + 2ab + b^{2}$

x + 2( $x^{2} - 4x + 4$ + 5 ) = 6

$2x^{2} - 7x + 12=0$ --------------(4)

The roots of the quadratic equation $ax^{2} +bx+c$ is

x = $\frac{(-b) + \sqrt{(-b)^{2}-4 \times ac } }{2 \times a}$ -----------(5)

According to equation (5),solution of (4) is

x = $\frac{7 + \sqrt{(-7)^{2}-4 \times 24 } }{2 \times 2}$

x = $\frac{7+\sqrt{49-96}}{4}$

x = $\frac{7+\sqrt{47}\times i }{4}$

4 0

3 years ago

How many solutions does this linear system have y= 1/2x+4 <br> x+2y=-8

lara [203]

Answer:

1 solution

Step-by-step explanation:

y = 1/2x + 4

x + 2y = -8

Solve the second equation for y.

2y = -x - 8

y = -1/2x - 4

The two equations in slope-intercept form are:

y = 1/2x + 4

y = -1/2x - 4

The system consists of two lines with different slopes, so they intercept at a single point which is the solution.

Answer: 1 solution

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Digiron [165]

Answer:

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Step-by-step explanation:

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2 years ago