The simplification of the expression is [tex]\frac{15\sqrt{2} }{4}[/tex]
How to rationalize the denominatorFirst, find the factors of the number that ahs square root
Given,
= [tex]\frac{5}{\sqrt{2} } + \frac{9}{\sqrt{6} } - \frac{2}{\sqrt{50} } + \sqrt{32}[/tex]
Multiply the numerators by the surd of the denominators
= [tex]\frac{5 *\sqrt{2} }{\sqrt{2}*\sqrt{2 } } + \frac{9 *\sqrt{8} }{\sqrt{8}* \sqrt{8} } - \frac{2 *\sqrt{50} }{\sqrt{50 * \sqrt{50} } } + \sqrt{32}[/tex]
Multiply through and find their square root
= [tex]\frac{5\sqrt{2} }{2} + \frac{18\sqrt{2} }{8 } - \frac{10\sqrt{2} }{50} + 16\sqrt{2}[/tex]
To simply, we have
= [tex]\frac{5\sqrt{2} }{2}+ \frac{9\sqrt{2} }{4} + \frac{1\sqrt{2} }{5} + 16\sqrt{2}[/tex]
Find the LCM
= [tex]\frac{10\sqrt{2} + 45\sqrt{2}+ 4\sqrt{2} + 16\sqrt{2} }{20}[/tex]
Add through
= [tex]\frac{75\sqrt{2} }{20}[/tex]
= [tex]\frac{15\sqrt{2} }{4}[/tex]
Thus, the simplification of the expression is [tex]\frac{15\sqrt{2} }{4}[/tex]
Learn more about surds here:
https://brainly.in/question/4594146
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What is the fastest way to solve the following question:
The ratio of boys to girls in Mr. Brown's class is 2:3. If there are 30 students in the class, how many more girls than boys are in the class?
Answer:
There are 6 more girls than boys
Step-by-step explanation:
boys :girls : total
2 3 2+3 = 5
There are 30 total students
30/5 = 6
Multiply each number by 6
boys :girls : total
2*6 3*6 5*6
12 18 30
There are 18 girls and 12 boys
18-12 = 6
There are 6 more girls than boys
Answer:
Answer is 6.
Step-by-step explanation:
I will now explain the fastest way to solve this. First off, the ratio is 2:3 so the first thing I do is combine that for 5, then do 30/5 for an answer of 6. Then, I multiply 6 for the ratio, which comes out as 12:18, 12 boys and 18 girls. 18-12=6, so there are 6 more girls than boys in the class.
A hot air balloon is released into the air. During its straight ascent, the angle of elevation was 15° and, 3 minutes later, the angle of elevation increased 20°. How fast is the balloon traveling, in km/h, if the angle measurements were taken 300m away from the launch site?
Answer:
The speed of balloon is 0.16 m/s.
Step-by-step explanation:
BC = 300 m
AD = x
AB = y
time, t = 3 min = 3 x 60 = 180 s
By the triangle, ADC,
[tex]tan 15 = \frac{AD}{BC}\\\\0.27 \times 300 = x \\\\x = 80.4 m[/tex]
By the triangle, BDC
[tex]tan 20 = \frac{BD}{BC}\\\\0.36 \times 300 = x + y \\\\x + y = 109.2 m[/tex]
So, y = 109.2 - 80.4 = 28.8 m
Speed of balloon = 28.8/180 = 0.16 m/s
HELPPP
Solve: r = -5 + 19. r =____?
-24
14
-14
24
Answer:
14
Step-by-step explanation:
19 - 5 = 14
A team of 5people to be selected from 7women & 6men. Find the number of different teams that could be selected if there must be more women than men in the team
Answer:i would say 2 differentt teams where there is more then women than men in the team
Step-by-step explanation:
well how i came to this answer is that the team is limited to only 5 people giving the only team where there is more women over men is this first team would be 4 women and 1 men , second team would be 3 women and 2 men anything lower then 3 make its where the team has more men than women so the only options would be 2 team where either they go with 4 women or 3 women and you can't go with more then 4 because then there would be no men in the team which is what the question asks for please go with 2 teams
if this helps please make me brainlist ?!
4(6*9)+90=?
PLS CAN SOMEONE HELP ME
Answer:
306
Step-by-step explanation:
6*9=54
54*4=216
216+90=306
find the trigonometric ratio tan m multiple choice
Answer:
a/b
Step-by-step explanation:
Tan = Opposite/Adjacent
Therefore, Tan M = a/b.
what is a power according to mathematics
Answer:
A power is the product of multiplying a number by itself. Usually, a power is represented with a base number and an exponent. The base number tells what number is being multiplied. The exponent, a small number written above and to the right of the base number, tells how many times the base number is being multiplied
Answer:
United States: Retail sales rebound in June
Step-by-step explanation:
United States: Retail sales rebound in June: Retail sales increased 0.6% month-on-month in seasonally-adjusted terms in June (May: -1.7% mom). The figure was largely due to a strong increase in gasoline sales in June, while sales at electronic and appliances, health and personal care, and general merchandise stores all rebounded robustly over the previous month. #accelerationism
Two standard dice are rolled together. What is the probability of rolling a sum less than 7 or a sum divisible by 5?
Answer:
Sum less than: 7 (1,1), (1,2), (1,3), (1,4), (1,5), (2,1), (2,2), (2,3), (2,4), (2,5), (3,1), (3,2), (3,3), (3,4), (3,5), (,4,1), (4,2), & (5,1)
Sum divisible by 5 (1,4), (2,3), (3,2), (4,1)
What is the percent of change from 45to56
Answer:
24.44%
Step-by-step explanation:
initial value :45
final value:56
change in value= 56-45=11
percentage change= 11
[tex] \frac{11}{45} \times \frac{100}{1} [/tex]
[tex] \frac{1100}{45} [/tex]
=24.44%
Answer:
24.44%
Step-by-step explanation:
Çhange =56-45
=11
Percentage change =change/previous change ×100%
Percentage change=11/45 ×100%
=0.2444444×100%
=24.4444%
determine the condition under which job Shane should collect and explain
Answer:
By the 4th hour of working, both jobs pay 80, but Job B will pay less by the 5th hour, and continues to pay less as time progresses after that.
Draw the graph of Job b on the same graph as A and you'll see exactly when A passes B.
He'll make more at job A if he works more than 4-5 hours, but more at job B if he works less than 4-5 hours (again, don't know at exactly what time A passes B, wouldn't recommend putting "4-5" on a paper)
Step-by-step explanation:
hour job A pay job B pay
----------------------------------------------------------
0 $0 $30
1 $ 20 $42.50
2 $40 $55
3 $60 $67.50
4 $ 80 $80
5 $100 $ 92.50
Hope this helps!
Can someone help I don't understand
Answer:
Step-by-step explanation:
The quotient of five less than a number and six, is -4
Answer:
(a-5) / 6 = -4
or
-19
Step-by-step explanation:
(a-5) / 6 = -4
multiply by 6
a - 5 = -24
+5 +5
a = -19
What is the distance in units between the points (4, -7) and (1, -7)?
Step-by-step explanation:
To evaluate such, the following formula is required:
Distance Formula: d(P, Q) = √ (x2 − x1)^2 + (y2 − y1)^2
Denote the following points as the following,
(4, -7). (1, -7)
X1 Y1. X2. Y2
D(P, Q) = √(1 - 4)^2 + (-7 + 7)^2. <== Since there is a double negative, such will be considered addition.
√(-3)^2 + (0)^2
√9 = 3
Thus, the agglomerate distance of such points on the Cartesian plane is disclosed as 3 units.
The yearly income of a family was Rs. 5,00,000. Tax was exempted upto Rs. 1,50,000. If the tax for the first Rs 20,00,000 was 10 % and for the rest was 15%, find how much amount of income tax will be paid in a year?
Answer: Rs. 35,000
Step-by-step explanation:
The taxable income is:
= Yearly income - Tax exemption
= 500,000 - 150,000
= Rs. 350,000
The tax on the first Rs. 2,000,000 is 10% which means that tax is:
= 350,000 * 10%
= Rs. 35,000
an expression that equals to 6/5
Answer:
(3+3) / (2+3) = 6/5
:)))
..........
The graph of which functions has an axis of symmetry at x = -1/4?
Answer:
2x^2 + x - 1
If I did anything you didn't understand let me know so I can explain.
Step-by-step explanation:
All of them are quadratics so let's use that.
The first one is 2x^2 + x - 1. To find the axis of symmetry the strategy is usually to find the two zeroes of a quadratic and pick the number between them. Something to notice though is that 2x^2 + x - 1 is just 2x^2 + x sshifted down 1, so they both have the same axis of symmetry. So I am going to ignore the constant, because then finding the zeroes is much much simpler. I am going to do this with all opions.
So 2x^2 + x - 1 I am just going to use 2x^2 + x. If you factor out an x you get x(2x + 1) So now we have it in factored form and we know the zeroes are 0 and -1/2. The number directly in between these is -1/4, so the axis of symmetry is x = -1/4. I don't know if there is only one with that axis of symmetry so i am going to check the rest.
2x^2 - x + 1 means we are only going to look at 2x^2 - x. factoring we get x(2x - 1) so the zeroes are 0 and 1/2, so the axis of symmetry is at 1/4.
x^2 + 2x - 1 we only use x^2 + 2x. Factored form is x(x+2) so zeroes are 0 and -2 whichh means axis of symmetry is -1
x^2 - 2x + 1 has the same axis of symmetry as x^2 - 2x, which has zeros at 0 and 2 so the axis of symmetry is at 1.
So yep, it was just the first one.
9514 1404 393
Answer:
(a) f(x) = 2x^2 +x -1
Step-by-step explanation:
For ax^2 +bx +c, the axis of symmetry is x = -b/(2a). For the offered answer choices, the axes of symmetry are ...
a) x = -1/(2·2) = -1/4 . . . . . . the function we're looking for
b) x = -(-1)/(2·2) = 1/4
c) x = -2/(2·1) = -1
d) x = -(-2)/(2·1) = 1
The function with axis of symmetry x = -1/4 is f(x) = 2x^2 +x -1.
If f(x) = 3x2 + 1 and g(x) = 1 - x, what is the value of (f-9)(2)?
Answer:
14
Step-by-step explanation:
The plot below shows the amount of time Mira spent on maths questions. If Mira had spent the same total amount of time, but spent an equal amount of time on each problem, how many minutes would each problem have taken?
Answer:
See explanation
Step-by-step explanation:
Given
[tex]n = 5[/tex] --- number of questions
Required
The time spent on each question
The question has missing details, as the required plot to calculate the total time is not given.
However, the formula to use is as follows
[tex]Each = \frac{Total}{n}[/tex]
Substitute 5 for n
[tex]Each = \frac{Total}{5}[/tex]
Assume the calculated total time is 60 minutes; The equation becomes
[tex]Each = \frac{60}{5}[/tex]
[tex]Each = 12\ mins[/tex]
Answer:
9 minutes
Step-by-step explanation:
I got it wrong from the other guy so i put get help and that's the Awnser LOL
write the factors of the following numbers 8
the factors of 8 are as follow:
1,2,4,8
Answer:
Factors of 8 are 1, 2, 4, and 8.
Step-by-step explanation:
hope it is helpful to you ☆☆
1)2x(3x^2-2x+1)
2)4x(1-x-3x)
Answer:
1. 3x^3 - 2x^2 - x
2. -4x^2 + x
Step-by-step explanation:
(x − 5)∙ 3 = 2∙ 10 + 8
Answer:
x=17
Step-by-step explanation:
3x-15=20+16
3x-15=36
3x=36+15
3x=51
x=17
Mark rolls a fair dice 36 times. How many times would Mark expect to roll a number greater than 5?
Answer:
Let X be the number of times a Dice rolls 4.
Expected value is 96/6 = 16.
Step-by-step explanation:
Answer:
6
Step-by-step explanation:
In a dice, there are 6 faces, there's {1, 2, 3, 4, 5, 6}.
So when the question asks a number greater than 5 it means that it wants the "6". The probability to get the "6" is 1/6. So to find the expected value you just times the number of rolls with the probability which means 36 × 1/6 which equals to 6 times
It takes 25 minutes to fry a burger at Jill street, how long will it take to fry 13 burgers
Answer:
325 minutes
Step-by-step explanation:
We can use a ratio to solve
25 minutes x minutes
------------------ = ---------------
1 burger 13 burgers
Using cross products
25*13 = 1x
325 = x
325 minutes
Answer:
325 minutes or 5 hours and 25 minutes
Step-by-step explanation:
If it takes 25 minutes to fry a single burger, assuming only one burger can be made at a time, you must multiply the time per burger by how many burgers are made. So. 25(13) = 325 minutes or 5 hours and 25 minutes.
PLS HELP I'M SOO CONFUSED
Consider the arithmetic senes 336+ 332+328+....+4 Numeric Response 1 The number of terms in the series above is (Record your answer in the numerical-response section below) Your answer DCC Numeric Response 2. The sum of the series above is (Record your answer in the numerical-response section below)
The first term in the series is 336. The second term is obtained by subtracting 4 from the first term; subtract 4 from that to get the third term; and so on. Then the n-th term in the series is
336 - 4 (n - 1)
or
340 - 4n
The last term in this series is 4, so we solve for n :
340 - 4n = 4
336 = 4n
n = 336/4 = 84
The sum of the series is then
[tex]\displaystyle\sum_{n=1}^{84}(340-4n) = 340\sum_{n=1}^{84}1 - 4 \sum_{n=1}^{84}n[/tex]
Recall that
[tex]\displaystyle \sum_{n=1}^{N} 1 = N[/tex]
[tex]\displaystyle \sum_{n=1}^N n = \frac{N(N+1)}2[/tex]
Then the sum we want is
[tex]\displaystyle\sum_{n=1}^{84}(340-4n) = 340\times84 - 4\times\frac{84\times85}2 = \boxed{14,280}[/tex]
find the measure of the indicated angle to the nearest degree
[tex]\boxed{\sf sin\theta=\dfrac{P}{H}}[/tex]
[tex]\\ \sf\longmapsto sin\theta=\dfrac{38}{53}[/tex]
[tex]\\ \sf\longmapsto sin\theta=0.7[/tex]
[tex]\\ \sf\longmapsto sin\theta=\dfrac{1}{1.4}[/tex]
[tex]\\ \sf\longmapsto sin\theta=\dfrac{1}{\sqrt{2}}[/tex]
[tex]\\ \sf\longmapsto sin\theta=sin45°[/tex]
[tex]\\ \sf\longmapsto \theta=45°[/tex]
What are the coefficients for the binomial expansion of (a + b)^3?
Answer:
coefficient of 1st, 2nd, 3rd and 4th term are 1, 3,3,1 respectively. (required coefficient)
Step-by-step explanation:
[tex]\sqrt{x} +\sqrt{5} =\sqrt{12}[/tex]
Make a box-and-whisker plot for the data. What is the lower quartile value?
56 32 48 52 51 53 48 38 35 42 40 46 54 50
Rationalise the denominator and simplify. 5 over root 3
[tex] \frac{5}{ \sqrt{3} } \\ = \frac{5 \times \sqrt{3} }{ \sqrt{3} \times \sqrt{3} } \\ = \frac{5 \sqrt{3} }{ { \sqrt{3} }^{2} } \\ = \frac{5 \sqrt{3} }{3} [/tex]
This is the answer.
If f(x)= sqrt x, which equation describes the graphed function.
Answer:
C. y = -f(x) - 3
Step-by-step explanation:
The given (parent) function is f(x) = √x
The given graph shows a real curve that starts from y = -3, when x = 0 and the y-value increases in magnitude in the negative direction as the x-values increases positively from left to right, by the same amount that the parent function increases from left to right
Therefore;
The graph is real, therefore, the value of x in √x is x ≥ 0, and y ≠ f(-x) + D
Where, D, is the vertical shift
The graph starts at x = 0, y = -3, compared to the parent function, the vertical shift, D = -3
The y-value of the given curve increases in the opposite direction (negatively) as the y-value of the parent function increases in magnitude in the positive direction
Therefore, the equation of the given curve comprises of the reflection of the parent function or -f(x)
The graph shows the reflection of the parent function, across the x-axis, and we have, reflection of the parent function, f(x) which is -f(x)
Therefore, the equation that describes the graphed function is y = -f(x) - 3
