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3 years ago

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The graph of the function f(x) = ax2 + bx +c (where a, b, and c are real and nonzero) has two x-intercepts. Explain how to find

the other x-intercept if one x-intercept is at (-b/a2 +3,0)

2 answers:

sveticcg [70]3 years ago

8 0

Recorded response:

The axis of symmetry is -b/2a

The x-intercept shown is 3 units away from the axis of symmetry.

The other x-intercept also must be 3 units away from the axis of symmetry but on the opposite side.

Subtract 3 from the axis of symmetry.

The other x-intercept is (-b/2a-3,0)

Olin [163]3 years ago

7 0

-b/2a is the formula to find the vertex of a parabola. If one of the intercepts is at (-b/2a + 3, 0), the other one must be at (-b/2a - 3, 0), since the two x-intercepts have to be the same distance from the vertex.

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What is the gcf of 14 and 22

Phantasy [73]

The multiples of 14 are 1,2,7,14
the multiples of 22 are 1,2,11,22
Therefore 2 is the GCF

7 0

3 years ago

Bob needs to wash the windows on his house. He has a 25-foot ladder and places the base of the ladder 10 feet from the wall on t

Andrei [34K]

Answer:

22.9 ft

Step-by-step explanation:

the height of the wall that reached by the ladder = √ (25²-10²)

=√(625-100)

=√525

= 22.9 ft

7 0

2 years ago

Eddi Din [679]

Answer:

a) $y=\dfrac{5}{2}x$

b) yes the two lines are perpendicular

c) $y=\dfrac{5}{4}x+6$

Step-by-step explanation:

a) All this is asking if to find a line that is perpendicular to 2x + 5y = 7 AND passes through the origin.

so first we'll find the gradient(or slope) of 2x + 5y = 7, this can be done by simply rearranging this equation to the form $y = mx + c$

$5y = 7 - 2x$

$y = \dfrac{7 - 2x}{5}$

$y = \dfrac{7}{5} - \dfrac{2}{5}x$

$y = -\dfrac{2}{5}x+\dfrac{7}{5}$

this is changed into the $y = mx + c$ , and we easily see that -2/5 is in the place of m, hence $m = \frac{-2}{5}$ is the slope of the line 2x + 5y = 7.

Now, we need to find the slope of its perpendicular. We'll use:

$m_1m_2=-1$ .

here both slopes $m_1$ and $m_2$ are slopes that are perpendicular to each other, so by plugging the value -2/5 we'll find its perpendicular!

$\dfrac{-2}{5}m_2=-1$ .

$m_2=\dfrac{5}{2}$ .

Finally, we can find the equation of the line of the perpendicular using:

$(y-y_1)=m(x-x_1)$

we know that the line passes through origin(0,0) and its slope is 5/2

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

$y=\dfrac{5}{2}x$ is the equation of the the line!

b) For this we need to find the slopes of both lines and see whether their product equals -1?

mathematically, we need to see whether $m_1m_2=-1$ ?

the slopes can be easily found through rearranging both equations to $y=mx+c$

Line:1

$2x + 3y =6$

$y =\dfrac{-2x+6}{3}$

$y =\dfrac{-2}{3}x+2$

Line:2

$y = \dfrac{3}{2}x + 4$

this equation is already in the form we need.

the slopes of both equations are

$m_1 = \dfrac{-2}{3}$ and $m_2 = \dfrac{3}{2}$

using

$m_1m_2=-1$

$\dfrac{-2}{3} \times \dfrac{3}{2}=-1$

$-1=-1$

since the product does equal -1, the two lines are indeed perpendicular!

c)if two perpendicular lines have the same intercept, that also means that the two lines meet at that intercept.

we can easily find the slope of the given line, y = − 4 / 5 x + 6 to be $m=\dfrac{-4}{5}$ and the y-intercept is $c=6$ the coordinate at the y-intercept will be (0,6) since this point only lies in the y-axis.

we'll first find the slope of the perpendicular using:

$m_1m_2=-1$

$\dfrac{-4}{5}m_2=-1$

$m_2=\dfrac{5}{4}$

we have all the ingredients to find the equation of the line now. i.e (0,6) and m

$(y-y_1)=m(x-x_1)$

$(y-6)=\dfrac{5}{4}(x-0)$

$y=\dfrac{5}{4}x+6$

this is the equation of the second line.

side note:

this could also have been done by simply replacing the slope(m1) of the y = − 4 / 5 x + 6 by the slope of the perpendicular(m2): y = 5 / 4 x + 6

8 0

3 years ago

Jordan spent 22% of his time doing math homework. If hw spent 11 minutes on his math homework. How many minutes did he spend on

Angelina_Jolie [31]

Jordan spends 50 minutes on his homework.

Step-by-step explanation:

Given,

Time spent on Maths homework = 11 minutes

This represents the 22% time of his total homework.

Let,

x be the total time spent on homework.

22% of x = 11

$\frac{22}{100}*x=11\\0.22x=11$

Dividing both sides by 0.22

$\frac{0.22x}{0.22}=\frac{11}{0.22}\\x=50$

Jordan spends 50 minutes on his homework.

Keywords: percentage, division

Learn more about percentages at:

#LearnwithBrainly

8 0

3 years ago

Emilio and friends are in a submarine 500 feet below sea level. They continue to dive 35 feet each hour for 7 hours.

katovenus [111]

You would write the equation out as x=35x+500

You substitute x for 7 so it’s x= 35(7)+500

So the answer will be 745 dollars

4 0

2 years ago