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Vlad1618 [11]
1 year ago
15

Need step by step detailed answer

Mathematics
1 answer:
kolezko [41]1 year ago
4 0

Answer:

y = -4x - 4

Step-by-step explanation:

If we have two lines in slope intercept form as

y = m_1x + c_1 \text{ and}\\y = m_2x + c_2\\

then the product of the slopes m_1m_2 = -1

In other words, m_2 = -\frac{1}{m_1}

We have the first line as

y = \frac{1}{4}x + 5\\\\

The slope of this line is \frac{1}{4}

The slope of a perpendicular line will be the negative of the reciprocal of this line

Reciprocal of 1/4 is 4

So slope of perpendicular line is -4 which implies

y = -4x + c

We have to determine c

Since the line passes through (-3, 8), plug in these values for x and y in the equation and solve for c

8 = (-4)(-3) + c

8 = 12 + c

c = -4

So the equation of the perpendicular line is y = -4x - 4 (Answer)

It is always a good idea to plot these graphs and see if they fit the data provided

The attached plot shows the two graphs and you can see they are perpendicular to each other and the perpendicular line(the answer) passes through point (-3,8)

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The hour hand on a clock is 4 cm long, and the minute hand is 10 cm long. What is the exact distance between the tips of the han
Allushta [10]

Answer:

2 sqrt(19)

Step-by-step explanation:

We know that the angle between the two hands

360 /12 *2 = 60 degrees

We divide by 12 because there are 12 number and multiply by 2 because there are 2 number between 10 and 12

This is a triangle where we know 2 sides and the angle between them.

We can use the law of cosines to determine the third side

c^2 = a^2 + b^2 -2abcosC

Where C is the angle between sides a and b

a =4 and b = 10  C = 60  and we are looking for side c

c^2 = 4^2 + 10^2 -2*4*10 cos60

c^2 =16+100 - 80cos 60

c^2 = 76

Take the square root of each side

sqrt(c^2) = sqrt(76)

c = sqrt(76)

c =sqrt(4) sqrt(19)

c =2 sqrt(19)


4 0
2 years ago
Write the slope-intercept form of the equation of the line satisfying the given conditions through(3,-3); slope=-4
il63 [147K]

Answer:

y=-4x+9

Step-by-step explanation:

y-y1=m(x-x1)

y-(-3)=-4(x-3)

y+3=-4(x-3)

y=-4x+12-3

y=-4x+9

7 0
3 years ago
What is the surface area of a conical (cone) grain storage tank that has a height of 24 meters and a diameter of 16 meters?
nirvana33 [79]
Surface area of cone is a sum of surface of its base and surface of its mantle.

Surface of its base is a circle which surface we will calculate like this:
Sb = pi*r^2     where r is d/2
Sb = 201m^2

Surface of mantle we calculate by:
Sm = pi*l*r    where l is length of side of cone.

l = \sqrt{r^2 + H^2} = 25.3
Sm = 635.8m^2

Total suface is:
Sb + Sm = 836.8m^2
3 0
2 years ago
What is the range of the function f(x)=(x+4)²+5
hammer [34]

Answer:

Range=\left \{y|y\geq 5\right \}

Step-by-step explanation:

Since given the expression, this represents graphically a parabola with arms pointing up, and a vertical translation of its vertex 5 units up, then the range of the function must be all the y values such that they are greater or equal to 5. This is written as:

Range=\left \{y|y\geq 5\right \}

8 0
3 years ago
5 years ago, my grandfather was five times as old as I was. Three years from now, my grandfather will be three times as old as I
balu736 [363]
<h3>Answer:</h3>

13 years old

<h3>Explanation:</h3>

Let g and m represent grandfather's age now and my age now. The relation 5 years ago was ...

... g -5 = 5(m -5)

The relation in 3 years will be ...

... g +3 = 3(m +3)

Subtracting the first equation from the second, we get ...

... 8 = -2m +34

... 2m = 26 . . . . . add 2m-8

... m = 13

My age now is 13.

4 0
3 years ago
Read 2 more answers
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