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2 years ago

The line x +ky=18 has a gradient of - 1/6 (a) Find the value of k.

Mathematics

2 answers:

Phoenix [80]2 years ago

7 0

Answer:

$k =6$

Step-by-step explanation:

$~~~~~~~x+ky = 18\\\\\implies ky = -x +18\\\\\implies y = -\dfrac 1k x+ \dfrac{18}k\\\\\text{It is now in the slope intercept form (y=mx +c), where m is the slope.}\\\\\text{Given that,}\\\\~~~~~m = -\dfrac 16\\\\\implies -\dfrac 1k = -\dfrac 16\\\\\implies \dfrac 1k = \dfrac 16\\\\\implies k =6$

Sophie [7]2 years ago

3 0

Answer:

k = 6

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope(gradient) and c the y- intercept )

given

x + ky = 18 ( subtract x from both sides )

ky = - x + 18 ( divide through by k )

y = - $\frac{1}{k}$ x + $\frac{18}{k}$ ← in slope- intercept form

with slope m = - $\frac{1}{k}$

given m = - $\frac{1}{6}$ , then equating

- $\frac{1}{k}$ = - $\frac{1}{6}$ ⇒ k = 6

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shutvik [7]

Answer a is correct

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3 years ago

A playground is shaped like a quaderaleteral with all sides 27 feet long, with two angles measures of 65 degrees and two angles

Ksivusya [100]

Answer:

Rhombus

Step-by-step explanation:

Shape of a playground is a quadrilateral

It is given that all sides of a quadrilateral are= 27 feet

Since all the sides of a quadrilateral are equal that it can be either a rhombus or it can be a square

Two angle are 65° each

And other two angers are 115° each

65°+ 115°= 180°

It forms a co-interior angle

Hence the quadrilateral is a parallelogram

Since all the four sides of parallelogram are equal, than the given figure must be rhombus

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7 0

3 years ago

Suppose that you were not given the sample mean and sample standard deviation and instead you were given a list of data for the

Troyanec [42]

Answer:

So, the sample mean is 31.3.

So, the sample standard deviation is 6.98.

Step-by-step explanation:

We have a list of data for the speeds (in miles per hour) of the 20 vehicles. So, N=20.

We calculate the sample mean :

$\mu=\frac{19 +19 +22 +24 +25 +27 +28+ 37 +35 +30+ 37+ 36+ 39+ 40+ 43+ 30+ 31+ 36+ 33+ 35}{20}\\\\\mu=\frac{626}{20}\\\\\mu=31.3$

So, the sample mean is 31.3.

We use the formula for a sample standard deviation:

$\sigma=\sqrt{\frac{1}{N-1}\sum_{i=1}^{N}(x_i-\mu)^2}$

Now, we calculate the sum

$\sum_{i=1}^{20}(x_i-31.3)^2=(19-31.3)^2+(19-31.3)^2+(22-31.3)^2+(24-31.3)^2+(25-31.3)^2+(27-31.3)^2+(28-31.3)^2+(37-31.3)^2+(35-31.3)^2+(30-31.3)^2+(37-31.3)^2+(36-31.3)^2+(39-31.3)^2+(40-31.3)^2+(43-31.3)^2+(30-31.3)^2+(31-31.3)^2+(36-31.3)^2+(33-31.3)^2+(35-31.3)^2\\\\\sum_{i=1}^{20}(x_i-31.3})^2=926.2\\$