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3 years ago

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Which statement explains how you could use coordinate geometry to prove that quadrilateral ABCD is a parallelogram? A. Prove tha

t all sides are congruent and have slopes that are opposite reciprocals. B. Prove that segments AD and AB are congruent and parallel. C. Prove that opposite sides are congruent and have equal slopes. D. Prove that segments BC and CD are congruent and parallel.

1 answer:

Yuri [45]3 years ago

8 0

Answer:

C) Prove that opposite sides are congruent and have equal slopes.

Step-by-step explanation:

Reasons:

1) In a parallelogram opposite side are equal and parallel

2) Parallel lines have same slope

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It takes 5 minutes for 7 people to drink 25 pints of water.At this rate,how long would it take 15 people to drink 160 pints of w

EastWind [94]

Answer:

14.9 min

Step-by-step explanation:

r=rate

r25=5*7

r25=35

r=35/25

r=1.4

substitution

r160=t*15

t=time

r=1.4

1.4*160=t*15

224=t*15/15

224/15=t

14.9 min

4 0

3 years ago

andreev551 [17]

Answer:

$\textsf{A)} \quad x=-2, \:\:x=\dfrac{5}{2}$

$\textsf{B)} \quad \left(\dfrac{1}{4},-\dfrac{81}{8}\right)=(0.25,-10.125)$

C) See attachment.

Step-by-step explanation:

Given function:

$f(x)=2x^2-x-10$

<h3><u>Part A</u></h3>

To factor a <u>quadratic</u> in the form $ax^2+bx+c$ <em> , </em>find two numbers that multiply to $ac$ and sum to $b$ :

$\implies ac=2 \cdot -10=-20$

$\implies b=-1$

Therefore, the two numbers are -5 and 4.

Rewrite $b$ as the sum of these two numbers:

$\implies f(x)=2x^2-5x+4x-10$

Factor the first two terms and the last two terms separately:

$\implies f(x)=x(2x-5)+2(2x-5)$

Factor out the common term (2x - 5):

$\implies f(x)=(x+2)(2x-5)$

The x-intercepts are when the curve crosses the x-axis, so when y = 0:

$\implies (x+2)(2x-5)=0$

Therefore:

$\implies (x+2)=0 \implies x=-2$

$\implies (2x-5)=0 \implies x=\dfrac{5}{2}$

So the x-intercepts are:

$x=-2, \:\:x=\dfrac{5}{2}$

<h3><u>Part B</u></h3>

The x-value of the vertex is:

$\implies x=\dfrac{-b}{2a}$

Therefore, the x-value of the vertex of the given function is:

$\implies x=\dfrac{-(-1)}{2(2)}=\dfrac{1}{4}$

To find the y-value of the vertex, substitute the found value of x into the function:

$\implies f\left(\dfrac{1}{4}\right)=2\left(\dfrac{1}{4}\right)^2-\left(\dfrac{1}{4}\right)-10=-\dfrac{81}{8}$

Therefore, the vertex of the function is:

$\left(\dfrac{1}{4},-\dfrac{81}{8}\right)=(0.25,-10.125)$

<h3><u>Part C</u></h3>

Plot the x-intercepts found in Part A.

Plot the vertex found in Part B.

As the <u>leading coefficient</u> of the function is positive, the parabola will open upwards. This is confirmed as the vertex is a minimum point.

The axis of symmetry is the <u>x-value</u> of the <u>vertex</u>. Draw a line at x = ¹/₄ and use this to ensure the drawing of the parabola is <u>symmetrical</u>.

Draw a upwards opening parabola that has a minimum point at the vertex and that passes through the x-intercepts (see attachment).

5 0

2 years ago

Write 3 equivalent expressions for 12x-36

morpeh [17]

Answer:

1) 24x-72; 2) 6x-18; 3) 2x-9

Step-by-step explanation:

You can divide it or multiply it by whatever number it is to make it a whole number, not a decimal. Or else it will be even more difficult.

4 0

3 years ago

Six and forty-two ten-thousandths as a decimal

sergey [27]

Answer:

6.0042

Step-by-step explanation:

6 and forty-two ten-thousandths as a decimal.

mixed number : $6\frac{42}{10,000}$

decimal : 6.0042

7 0

3 years ago

Write the equation of the line in slope-intercept that has passes through the points (2,-5) and (8, 13).

const2013 [10]

Answer:

The equation of the straight line in Slope- intercept form

y = 3 x - 11

Step-by-step explanation:

<u><em>Explanation:-</em></u>

Given points are (2,-5) and (8, 13)

The Slope of the line

$m = \frac{y_{2} -y_{1} }{x_{2} -x_{1} } = \frac{13-(-5)}{8-2} = \frac{18}{6} =3$

Equation of the line having slope 'm' and given point

$y - y_{1} = m (x - x_{1} )$

(x₁ , y₁) = ( 2, -5 )

$y - (-5) = 3 (x - 2 )$

y + 5 = 3x - 6

The equation of the straight line in slope intercept form

y = m x + c

y = 3 x - 6-5

y = 3 x - 11

<u><em>Final answer:</em></u>-

The equation of the straight line in Slope- intercept form

y = 3 x - 11

8 0

3 years ago