13_ ( 9 ) = x a true sentence

Write the equation of a line that is perpendicular to x=3x=3x, equals, 3 and that passes through the point (0,-4)(0,−4)left pare

leva [86]

Answer: $x+3y=12$

Step-by-step explanation:

Slope of two lines that are perpendicular to each other is 1.

If one line is $y=3x$ , then its slope = 3 [by comparing to the linear equation y= mx+c, here m=3]

Let n be the slope of the required line, then

$n\times3=-1\\\\\rightarrow\ n=\dfrac{-1}{3}$

Equation of line with slope n and passers through (a,b) is

$(y-b)=n(x-a)$

Equation of line with slope n= $\dfrac{-1}{3}$ and passes through point ( 0,-4) :

$(y-(-4))=\dfrac{-1}{3}(x-0)\\\\\Rightarrow\ y+4=\dfrac{-1}{3}x\\\\\Rightarrow\ -3(y+4)=x\\\\\Rightarrow-3y-12=x\\\\\Rightarrow x+3y=12$

Hence, Required equation : $x+3y=12$

8 0

3 years ago

1/5 of the shoes in a factory are green. If you pick a shoe, replace it, pick another shoe and replace it, and pick a third shoe

Ne4ueva [31]

Answer:

The probability that none of the three shoes selected are green = 64/125

Step-by-step explanation:

If we have 1/5 of shoes being green, then the number of non-green shoes = 1-1/5 = 4/5

Now, this is a probability with replacement.

probability of the first shoe since it’s not green = 4/5

probability of second shoes since it’s not green = 4/5

probability of third shoe since it’s not green = 4/5

Now, the probability that none of the shoes are green = 4/5 * 4/5 * 4/5 = 64/125

7 0

3 years ago

The altitude of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is increasing at a rate of 2 cm2/m

Mnenie [13.5K]

Answer:

The base is reducing at a rate of 3.4cm per min.

Step-by-step explanation:

Let The Height of the Triangle, h

Area of the triangle = A

Area of a Triangle, $A= \frac{1}{2}bh$

When $A=190 cm^2, h=10cm$

$190= \frac{1}{2}*b*10\\b=38cm$

$\frac{dA}{dt}=\frac{1}{2}h\frac{db}{dt}+ \frac{1}{2}b\frac{dh}{dt}\\\frac{dh}{dt}=1 cm/min, \frac{dA}{dt}=2cm^2/min,$

$2=\frac{1}{2}*10*\frac{db}{dt}+ \frac{1}{2}*38*1\\2=5\frac{db}{dt}+19\\2-19=5\frac{db}{dt}\\-17=5\frac{db}{dt}\\\frac{db}{dt}=-\frac{17}{5} =-3.4 cm/min$

The base is reducing at a rate of 3.4cm per min.

8 0

3 years ago

The data set shows the numbers of hours students study the week before a test. Find and interpret the mean absolute deviation of

patriot [66]

Step-by-step explanation:

3 + 4 + 5 + 6 + 6 + 7 + 8 + 8 + 9 + 9 / total of numbers or 10 = 65 ÷ 10 = 6.5 This is the mean.

3 - 6.5 = 3.5

4 - 6.5 = 2.5

5 - 6.5 = 1.5

6 - 6.5 = 0.5

7 - 6.5 = 0.5

8 - 0.5 = 7.5

9 - 0.5 = 8.5

MAD = 1.7

4 0

3 years ago

CAN SOMEONE PLS HELP ME I WILL MARK U BRAINLIEST

sukhopar [10]

Answer:

$x \geqslant 1$

Step-by-step explanation:

The expression in the square root should be greater than or equal to zero, because square root of a negative number does not give a real number.

$x - 1 \geqslant 0 \\ x \geqslant 1$

6 0

3 years ago

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