Answers
Answer:
[tex]\frac{10\sqrt{6} }{3}[/tex] and [tex]\frac{11\sqrt{3} }{3}[/tex]
Step-by-step explanation:
(a)
A = [tex]\frac{1}{2}[/tex] × 4[tex]\sqrt{2}[/tex] × [tex]\frac{5}{\sqrt{3} }[/tex]
= 2[tex]\sqrt{2}[/tex] × [tex]\frac{5}{\sqrt{3} }[/tex]
= [tex]\frac{10\sqrt{2} }{\sqrt{3} }[/tex] × [tex]\frac{\sqrt{3} }{\sqrt{3} }[/tex] ← rationalise the denominator
= [tex]\frac{10\sqrt{6} }{3}[/tex] units²
(b)
Using Pythagoras' identity in the right triangle
let hypotenuse be h , then
h² = (4[tex]\sqrt{2}[/tex] )² + ([tex]\frac{5}{\sqrt{3} }[/tex] )²
= 32 + [tex]\frac{25}{3}[/tex]
= [tex]\frac{96}{3}[/tex] + [tex]\frac{25}{3}[/tex]
= [tex]\frac{121}{3}[/tex] ( take the square root of both sides )
h = [tex]\sqrt{\frac{121}{3} }[/tex] = [tex]\frac{11}{\sqrt{3} }[/tex] × [tex]\frac{\sqrt{3} }{\sqrt{3} }[/tex] ← rationalise the denominator
h = [tex]\frac{11\sqrt{3} }{3}[/tex]
Related Questions
PLEASE HELP
The graph of y = f(x) is shown below. What are all of the real solutions of
f(x) = o?
Answers
Answer:
The real solutions are : -6, -3 and 2
Step-by-step explanation:
The solutions of a functions are the input values at an output zero
Graphical wise, this can be represented by the order pairs (x, 0)
In other words, these are the points that lie on the x-axis
Examining the given graph, we can see that the points lying on the x-axis are:
(-6, 0), (-3, 0) and (2, 0)
This means that:
The real solutions of the function are:
-6, -3 and 2
Hope this helps :)
Please, if anyone knows help me, I need a lot of help in this activity.
Answers
Answer:
Step-by-step explanation:
Perimeter of the given polygon = n + 2 + 3 + 4 + n + 2 + 3 + 4
= 2(n + 2 + 3 + 4)
= 2(n + 9) units
Area of the composite figure = Area of rectangle A + Area of rectangle B + Area of rectangle C
= (3 × 4) + (n ×2) + (2 × 3)
= 12 + 2n + 6
= 2n + 18
= 2(n + 9) units²
Therefore, perimeter of the given figure = Area of the figure
Jessie spent a total of 14.00 to purchase a gift and have it gift-wrapped and mailed. The cost for the postage was $2.25, and she knows the gift itself cost $9.50.
Answers
Answer:
she spent 11.75$ total
Step-by-step explanation:
9.50+2.25=11.75
Help pls for brainlest and extra points i need done soon
Answers
Answer:
5/6= 10/12
12/100<10/12
There are two mystery numbers. The sum of 2 times the first number and 5 times the second number is -5. The sum of 3 times the first number and 10 times the second number is -5. What are the two numbers?
Answers
Answer:
the two numbers are -5 and 1
Step-by-step explanation:
Let x and y be the first number and second number respectively.
According to the question, we can find 2 equations:
2x + 5y = -5
3x + 10y = -5
On solving,
x = -5
y = 1
Answer:
X=-5,Y=1
Step-by-step explanation:
First equation: 2X+5Y=-5
Second equation:3X+10Y=-5
If we subtract the first from the second equation
(3X+10Y)-(2X+5Y)= 0 so, X+5Y= 0
So X= -5Y .then substitute in the second equation
So ,3(-5Y)+10Y= -5 , therefore -15Y + 10Y=-5 so, -5Y=-5 which means that Y=1
Then substitute with that in the first equation so 2X+5= -5
2X= -10 therefore X=-5
Anna put $500 into a savings account and made no more deposits or withdrawals. The account earns 2% simple interest per year. How much money will be in the account after 5 years?
Answers
Answer:
50
Step-by-step explanation:
What I did was 2 divided by 100 = 0.02 Then multiply 0.02 times 500 and you should get 10 then multiply by how many years of interest and you get 50
hope this helped!solve for x
x- 5/3=1
Answers
Answer:
x = 8/3 or 2 2/3
Step-by-step explanation:
x - 5/3 = 1
x - 5/3 + 5/3 = x
1 + 5/3 = 8/3 or 2 2/3
x = 8/3 or 2 2/3
Answer:
x = [tex]\frac{8}{3}[/tex]
Step-by-step explanation:
Given
x - [tex]\frac{5}{3}[/tex] = 1 ( multiply through by 3 to clear the fraction )
3x - 5 = 3 ( add 5 to both sides )
3x = 8 ( divide both sides by 3 )
x = [tex]\frac{8}{3}[/tex]
First three terms of n^2+40
How many terms in the sequence are less than 100?
Answers
Answer:
7.
Step-by-step explanation:
If N= 1, 2, 3, 4, 5, 6, or 7, the equation is still less than 100.
Apple juice and cranberry juice have been mixed in the ratio of 4:5. If the price of apple juice is 45 cents per pint and the price of cranberry juice is $0.8 per pint, what should the price of one pint of the mixture be?
Answers
Answer:
$0.24
Step-by-step explanation:
The computation of the price of the one pint of the mixture is shown below:
Since the ratio of apple juice and cranberry juice is 4:5
And, the price of apple juice is 45 cents i.e. = 0.45 × 4 ÷ 9 = 0.2
Also the price of cranberry juice is $0.8 = $0.08 × 5 ÷ 9 = 0.04
SO, the price of one pint of the mixture is
= 0.2 + 0.04
= $0.24
Answer:
$0.24444
Step-by-step explanation:
Pls solve this i need help quick
Answers
Answer:
13 is the answer
Step-by-step explanation:
m = 13
(8+5)
A designer decides to create a larger scale model of a smart phone so that his team can work more easily on the design. The length of the screen of his model is 60 centimeters, which is 2.5 times longer than it is wide. The designer asked his team to build the screen of the actual phone with a width of 6 centimeters. What is the scale factor of the model phone to the actual phone?
Answers
Answer:
The length of the model is 250% of the width and is 60 centimeters, and the width of the actual phone is 6 so it has a scale factor of 4:1.
Hope this helps!
Evaluate 11.3v + 10.7w when v=7 and w=8
Answers
Answer:
11.3(7)+10.7(8)=79.1+85.6
=164.7
Solve: please, THANKS
Answers
Answer:
20/21
Step-by-step explanation:
have a nice day or evening
HELLLLLP MEEEE IDENTIFY THE HEIGHT
Answers
Answer:
11
Step-by-step explanation:
The height is 11 inches.
I Need help ASAP.(please )
Answers
The rest are wrong, if you need a reason why please tell me
Hope this helps!
The area of a rhombus is 60 cm one diagonal is 10cm other dignonl is
Answers
Answer: 12 cm
Explanation: The other diagonal is 12 cm as I calculated.
subtract 8xy+3 from 15xy +9
Answers
Answer:
7xy + 6
Step-by-step explanation:
=> here's your solution
=>. we need to subtract (8xy + 3) from
( 15xy +9 )
=> (15xy + 9) - ( 8xy + 3)
=>. 15xy + 9 - 8xy - 3
=> 15xy - 8xy + 9 - 3
=>. 7xy + 6
hope it helps
A fitness trainer sets the incline on a
treadmill to 7º. The walking surface is 5
feet (60 inches) long. Approximately how
many inches did the trainer raise the
end of the treadmill from the floor?
Answers
Answer:
Step-by-step explanation:
sin Ф equal the opposite leg of the triangle dividend by the hypotenuse
sin Ф = opp / hyp
the problem gave you the Ф (the angle 7°)
and the length of the hypotenuse (the walking surface 60 inches)
You want to use the inches since the question wants to know how many inches off the floor is the end of the walking surface
sin 7 = opp / 60 solve for opp
60 × sin(7) = opp use your calculator, I don't have one handy
What is the best measure of center for this data?
{101, 2, 108, 104, 102, 107, 109, 102}
Question 5 options:
A. mean or median because there is no outlier
B. median because there is an outlier
C. mean because there is an outlier
D. mode because there is an outlier
Answers
Answer:
The answer is A
Becaise Mode is not a measure of centre, and Mean is dramatically changed with the outli
I think that would be correct, Hope it helps!!!
A store purchased a plasma screen TV for $770 and marked it up 150%. During a sale, the store marked it down 20%. What was the discount price on the plasma screen TV?
Answers
Answer:
1540
Step-by-step explanation:
First find the new price after the markup
The markup is
770 * 150%
770 * 1.5
1155
Add this to the original price
770 + 1155
1925
Now find the discount
1925*20%
1925*.20
385
Subtract this amount from the 1925
1925-385
1540
The final price is 1540
Answer:
Solution given:
cost price [c.p] of TV =$770
MP=c.p+ 150% of c.p=$770+150/100×770=$1925
discount [D]=20%
now
discount amount=D% of MP=20/100×1925=$385 is your answer.
$385 was the discount price on the plasma screen TV.
PLEASEEEEEEEEEEEE HELPOPPBMEEEEE
Answers
Answer:
The answer is 7.14
Step-by-step explanation:
good luck
Are my answers for the conditional statement correct? I would just like to check them and if they're incorrect, could you let me know how to fix them? Thank you.
Statement: If I brush my teeth twice a day, then I will not get cavities.
Inverse: If I don't brush my teeth twice a day, then I will get cavities.
Truth Value: True
Converse: If I don't get cavities, then I am brushing my teeth twice a day.
Truth Value: True
Contrapositive: If I get cavities, then I am not brushing my teeth twice a day.
Truth Value: True
Answers
Statement: If p, then q
Inverse: If q, then p
Converse: If not p, then not q
Contrapositive: If not q, then not p.
We can see from the statement that p = brush teeth twice a day and q = not get cavities.
Thus:
Inverse: If I don't get cavities, then I brush my teeth twice a day. FALSE (for example, I might floss extra well instead. Brushing my teeth twice a day is not the only way to avoid cavities)
Converse: If I don't brush my teeth twice a day, then I get cavities. FALSE (for example, I might not eat a lot of sugar and thus I don't get cavities)
Contrapositive: If I get cavities, then I did not brush my teeth twice a day. TRUE
If this confuses you, try the example of p = cat and q = four legs. (i.e. the statement is If this is a cat, it has four legs). Try making the inverse, converse, and contrapositive, and see the truth of those statements.
It takes Jason 30 minutes to wash the dishes, but it takes 50 minutes for his younger brother. How many minutes will it take to wash the dishes if they work together? Round your answer to the nearest hundredth if necessary.
Answers
Write an equivalent expression to
3² x 15 x 54
Answers
Equivalent Expression: 9x + 15x = 54
Step-by-step explanation:
First, yo would do 3^2 which is 3 times 3 equals 9.
So, it would be 9x + 15x = 54
Then, you combine like terms, 9x + 15x
So 9+15= 24x
Last, would be 54 = 24x
divide by 24 onto both sides and then x will be by itself and then it will give you an answer.
Answer: 2.25
Find the surface area of the regular pyramid.
14 cm
11 cm
Answers
Answer: you on this to
Step-by-step explanation:
GUYS HELP HELP HELP PLEASE HELP
Answers
someone pls help thank you so much if you do!!
Answers
Find the solution to the equation.
7m = 112
Answers
Answer:
m= 16
Step-by-step explanation:
please please help me with number 28 i’ll mark b
Answers
Answer:
both
Step-by-step explanation:
given sss, you will need to use Law of Cosines.
However, one you get one of the angles, the easiest way to solve for the second angle is to just use law of sines.
Find the solution set of the inequality
8x−8≤−72.
Answers
Answer:
x≤-8
Step-by-step explanation:
When solving 8x-8≤-72, first add 8 to both sides of the inequality.
This leaves you with 8x≤-64.
Divide both sides by 8: 8x/8 and -64/8
This leaves you with x≤-8 as your solution.