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3 years ago

Which of the following inequalities matches the graph?

Mathematics

2 answers:

Monica [59]3 years ago

8 0

Answer:

x>-7

Step-by-step explanation:

Natalka [10]3 years ago

4 0

The answer to this question is 7

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Find the radius or diameter of each circle with the given dimensions. d=18 in.

Dovator [93]

Answer

If d equals diameter the radius is 9

Step-by-step explanation:

5 0

2 years ago

Allison is working two summer jobs, making $12 per hour lifeguarding and $8 per hour washing cars. Last week Allison worked 3 mo

timama [110]

Answer:

Allison worked 6 hours lifeguarding and 3 hours washing cars.

Step-by-step explanation:

Let

Number of hours Allison worked lifeguarding last week = x

Number of hours Allison worked washing cars last week = y

1. Last week Allison worked 3 more hours lifeguarding than hours washing cars hours, then

$x-y=3$

<u>Lifeguarding:</u>

$12 per hour

$12x in x hours.

<u>Washing cars:</u>

$8 pere hour

$8y in y hours.

2. Allison earned a total of $96, hence

$12x+8y=96$

You get the system of two equations:

$\left\{\begin{array}{l}x-y=3\\ \\12x+8y=96\end{array}\right.$

Plot the graphs of these two equations (see attached diagram). These line intersect at point (6,3), so Allison worked 6 hours lifeguarding and 3 hours washing cars.

3 0

3 years ago

Rationalise the denominator of:<br>1/(√3 + √5 - √2)

Paul [167]

Step-by-step explanation:

$\large\underline{\sf{Solution-}}$

Given expression is

$\rm :\longmapsto\:\dfrac{1}{ \sqrt{3} + \sqrt{5} - \sqrt{2} }$

can be re-arranged as

$\rm :\longmapsto\:\dfrac{1}{ \sqrt{3} - \sqrt{2} + \sqrt{5} }$

$\rm \: = \: \dfrac{1}{( \sqrt{3} - \sqrt{2} ) + \sqrt{5} }$

On rationalizing the denominator, we get

$\rm \: = \: \dfrac{1}{( \sqrt{3} - \sqrt{2} ) + \sqrt{5} } \times \dfrac{( \sqrt{3} - \sqrt{2} ) - \sqrt{5} }{( \sqrt{3} - \sqrt{2} ) - \sqrt{5} }$

We know,

$\rm :\longmapsto\:\boxed{\tt{ (x + y)(x - y) = {x}^{2} - {y}^{2} \: }}$

So, using this, we get

$\rm \: = \: \dfrac{ \sqrt{3} - \sqrt{2} - \sqrt{5} }{ {( \sqrt{3} - \sqrt{2} )}^{2} - {( \sqrt{5}) }^{2} }$

$\rm \: = \: \dfrac{ \sqrt{3} - \sqrt{2} - \sqrt{5} }{3 + 2 - 2 \sqrt{6} - 5}$

$\rm \: = \: \dfrac{ \sqrt{3} - \sqrt{2} - \sqrt{5} }{5 - 2 \sqrt{6} - 5}$

$\rm \: = \: \dfrac{ \sqrt{3} - \sqrt{2} - \sqrt{5} }{ - 2 \sqrt{6}}$

$\rm \: = \: \dfrac{ - ( - \sqrt{3} + \sqrt{2} + \sqrt{5}) }{ - 2 \sqrt{6}}$

$\rm \: = \: \dfrac{- \sqrt{3} + \sqrt{2} + \sqrt{5}}{2 \sqrt{6}}$

On rationalizing the denominator, we get

$\rm \: = \: \dfrac{- \sqrt{3} + \sqrt{2} + \sqrt{5}}{2 \sqrt{6}} \times \dfrac{ \sqrt{6} }{ \sqrt{6} }$

$\rm \: = \: \dfrac{- \sqrt{18} + \sqrt{12} + \sqrt{30}}{2 \times 6}$

$\rm \: = \: \dfrac{- \sqrt{3 \times 3 \times 2} + \sqrt{2 \times 2 \times 3} + \sqrt{30}}{12}$

$\rm \: = \: \dfrac{- 3\sqrt{2} + 2 \sqrt{3} + \sqrt{30}}{12}$

Hence,

$\boxed{\tt{ \rm \dfrac{1}{ \sqrt{3} + \sqrt{5} - \sqrt{2} } =\dfrac{- \sqrt{3 \times 3 \times 2} + \sqrt{2 \times 2 \times 3} + \sqrt{30}}{12}}}$

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<h3><u>More Identities to </u><u>know:</u></h3>

$\purple{\boxed{\tt{ {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2}}}}$

$\purple{\boxed{\tt{ {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2}}}}$

$\purple{\boxed{\tt{ {(x + y)}^{3} = {x}^{3} + 3xy(x + y) + {y}^{3}}}}$

$\purple{\boxed{\tt{ {(x - y)}^{3} = {x}^{3} - 3xy(x - y) - {y}^{3}}}}$

$\pink{\boxed{\tt{ {(x + y)}^{2} + {(x - y)}^{2} = 2( {x}^{2} + {y}^{2})}}}$

$\pink{\boxed{\tt{ {(x + y)}^{2} - {(x - y)}^{2} = 4xy}}}$

6 0

3 years ago

If (2⁶)×=1, what is the value of x?

marissa [1.9K]

Answer:

Step-by-step explanation:

(2⁶)ˣ = 1

2⁶ˣ = 1

6x = 0

x = 0

3 0

3 years ago

What operation is being done to the variable in the equation -5m = -40?

yaroslaw [1]

Answer:

m=8

Step-by-step explanation:

-5m=-40

divide both side by -5

-5m=-40

-5=-5 answer is m=8

6 0

1 year ago