1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
tatuchka [14]
3 years ago
7

Can I please have help with question 2) a and b

Mathematics
1 answer:
Ulleksa [173]3 years ago
7 0

Answer:

\frac{10\sqrt{6} }{3} and \frac{11\sqrt{3} }{3}

Step-by-step explanation:

(a)

A = \frac{1}{2} × 4\sqrt{2} × \frac{5}{\sqrt{3} }

   = 2\sqrt{2} × \frac{5}{\sqrt{3} }

   = \frac{10\sqrt{2} }{\sqrt{3} } × \frac{\sqrt{3} }{\sqrt{3} } ← rationalise the denominator

= \frac{10\sqrt{6} }{3} units²

(b)

Using Pythagoras' identity in the right triangle

let hypotenuse be h , then

h² = (4\sqrt{2} )² + (\frac{5}{\sqrt{3} } )²

    = 32 + \frac{25}{3}

    = \frac{96}{3} + \frac{25}{3}

    = \frac{121}{3} ( take the square root of both sides )

h = \sqrt{\frac{121}{3} } = \frac{11}{\sqrt{3} } × \frac{\sqrt{3} }{\sqrt{3} } ← rationalise the denominator

h = \frac{11\sqrt{3} }{3}

 

You might be interested in
a triangle has two sides of length 6 and 3. what is the smallest possible whole number length for the third side?
svp [43]
Answer: 3
Explanation:
5 0
3 years ago
Please help ASAP IM IN DESPREATE NEED OF HELP
Advocard [28]

Answer:

See the attached image for the graph of the first system.

Step-by-step explanation:

Here's how to graph the first system.

Start with the inequality -y \le -2x-3.  You can make this easier to work with by multiplying through by -1.  Remember to switch the inequality sign when multiplying by a <u>negative</u> number.  OK, you get the inequality

y \ge 2x+3.

The graph will be a half-plane -- all the points on one side of a line.  The line that is the boundary of the half-plane has an equation:  y=2x+3 -- just use an  =  sign instead of the inequality sign.

Graph the line.

The equation of the line is in slope-intercept form:  y = mx + b, so you can tell the y-intercept is 3 and the slope is 2 (think of it as a fraction 2/1).  Graph the line by going to the point (0, 3) -- the y-intercept -- then use the slope 2/1 interpreted as "rise over run" to go up 2 units and right 1 unit, arriving at the point (1, 5).  Draw the line through those points, (0, 3) and (1, 5).

Now you have to decide which side of the line the inequality y \ge 2x+3 is describing. To do this, pick a point which is not on the line, plug its coordinates into the inequality; if the result is true, shade the side of the line the point you picked is on (if false, shade the <u>other</u> side!)

An easy point to pick in this case is the origin, (0, 0).  Put zeros in for x and y in the inequality, and you'll get the statement 0 \ge 2(0)+3 \, \Rightarrow \, 0 \ge 3.  That's <u>false</u>, so shade the side of the line <u>not</u> containing the origin.  In the image below, the shading is in purple.

All right, now for the other inequality, x+2\le 0.  Subtract 2 from both sides and the inequality becomes x \le -2.  This, too, graphs as a half-plane whose boundary line has equation x=-2.  Graph the line.  A line with an equation that has  x  in it but not  y is a vertical line with all its x-coordinates equal to the number on the right side of the equation.  This line is vertical and goes through points such as (-2, 0).

Pick a point <u>not</u> on the line (the origin works again).  Put the coordinates into the inequality to get 0\le -2 which is <u>false</u>.  Shade the side of the vertical line which does <u>not</u> contain the origin.  In the image below, the shading is in black.

Finally,  YAY!  \o/ ,  the solutions to the system are all the points in the plane that got shaded twice.  In the image, they are the cross-hatched points above the purple line and to left of the black line.

Note: If you get a system with three inequalities, you'll be graphing three half-planes and looking for points that got shaded three times!

Note: One of your questions has the inequalities x \ge 0 and y \ge 0 in it.  These two inequalities say that the x and y coordinates are both positive or zero, confining your attention to Quadrant I in the upper-right part of a graph, above the x-axis <u>and</u> to the right of the y-axis.

7 0
3 years ago
Vera is using her phone.Its battery life is down to 2/5,and it drains another 1/9 every other. How many hours will her battery l
Margarita [4]

Let x be total hours of battery life. We have been given that battery life of Vera's phone is down to 2/5. So remaining battery life,

1-\frac{2}{5}=\frac{5-2}{5}=\frac{3}{5}

We have been also given that it drains another 1/9 every other hour. Now let us substitute our given information into an equation.

\frac{1}{9}\cdot x=\frac{3}{5}

Now we will solve for x.

x=\frac{3\cdot 9}{5}=\frac{27}{5}

x=(5+\frac{2}{5})hours

Let us convert 2/5 into minutes. We know 1 hour has 60 minutes.

60\cdot \frac{2}{5}=24\text{minutes}

Therefore, remaining battery life will be 5 hours and 24 minutes.



3 0
3 years ago
Read 2 more answers
PLZ HELP THIS IS DUE SOON!!!!!!! Divide. Round to the nearest hundredth if necessary.
ivolga24 [154]

Answer:

10

Step-by-step explanation:

when you divide 80.88 by 8.425 you get 9.6

and since youre rounding, you can round up 6 because its higher than 5

and your final answer should be 10.

hoped this helped! :)

4 0
3 years ago
PLS HELP .........................
Otrada [13]

Answer:

I believe the answer is C :)

Step-by-step explanation:

5 0
3 years ago
Other questions:
  • Find each percent of change. round to the nearest whole percent if necessary. state whether the percent of change is an increase
    11·1 answer
  • PLEASE HELP , should be pretty easy though
    8·2 answers
  • Find the sum and product of the zeros 2 X square + X - 5 = 0​
    14·2 answers
  • Use a calculator to find angle theta for which tan theta = 2. Round to the nearest hundredth.
    9·1 answer
  • What is the expression in factored form? <br> 6x^2+4x
    6·1 answer
  • Answers please this is very hard :))
    8·2 answers
  • One question, please help!
    8·1 answer
  • Consider function f, where B is a real number.
    6·2 answers
  • what does it mean if a guy leaves his phone unlocked with you while he goes to the restroom? like he handed me his phone and wal
    5·1 answer
  • Which number is equal to 10 Superscript negative 3? â€"1,000 â€"30 0. 001 0. 3.
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!