The simplified form of the expression is [tex]\frac{14+5\sqrt{3}}{11}[/tex]
How to rationalize surd functions?
Given the surd function expressed as:
[tex]\frac{\sqrt{3} +5}{\sqrt{3} - 5 }[/tex]
Multiply by the conjugate of the denominator to have:
[tex]= \frac{\sqrt{3} +5}{\sqrt{3} - 5 } \times \frac{\sqrt{3} +5}{\sqrt{3} + 5 } \\=\frac{\sqrt{9}+5\sqrt{3}+5\sqrt{3}+25 }{3-25}[/tex]
Simplify the resulting expression
[tex]\\=\frac{3+10\sqrt{3}+25 }{-22}\\=\frac{28+10\sqrt{3}}{-22} \\= \frac{14+5\sqrt{3}}{11}[/tex]
Hence the simplified form of the expression is [tex]\frac{14+5\sqrt{3}}{11}[/tex]
Learn more on rationalization here: https://brainly.com/question/14261303
Jaxson bought a pair of sunglasses online for $71. He used a coupon code to get a 20% discount. The website also applied a 5% processing fee to the price after the discount. How much was the discount, in dollars and cents?
Answer:
$17.75
Step-by-step explanation:
$71-($71×20%)
$71-$14.2
=$56.8
after coupon code
$56.8-($56.8×5%)
=$56.8-$2.84
=$53.96 about .
then applied a 5% processing fee online.
Help, what is the area of this figure? (Don’t write a big explanation!!, i really need this quick, a picture or just numbers u used is fine)
Answer:
146 m²
Area of triangle:
1/2 * base * height1/2 * 16 * 756 m²Area of upper rectangle:
Length * Width8 * 972 m²Area of bottom rectangle:
Length * Width6 * 318 m²Total area:
18 m² + 72 m² + 56 m²146 m²Answer:
146 m²
Step-by-step explanation:
Divide the figure into a triangle and 2 rectangles (see attached diagram)
Formulae
Area of a triangle = 1/2 x base x heightArea of a rectangle = width x lengthTriangle 1
⇒ area = 1/2 x 16 x (6 + 9 - 4 - 4)
= 1/2 x 16 x 7
= 56 m²
Rectangle 2
⇒ area = 3 x (6 + 9)
= 3 x 15
= 45 m²
Rectangle 3
⇒ area = 5 x 9
= 45 m²
Total area
⇒ Total area = triangle 1 + rectangle 2 + rectangle 3
= 56 + 45 + 45
= 146 m²
LOTS OF BRAINLY POINTS HELP ASAP PLS TYSM
you are flipping a coin and you flip tails 3 out of 10 times you flipped the coin. what is the experimental probability that you flip a tails. express your answer as a simplified fraction.
Answer:
3/10
Step-by-step explanation:
So, you already have the experimental probability. The theoretical probability is 5/10, but that's not what you're lookig for.
A boat is traveling at 28 knots in a direction of 36 degrees. It encounters wind moving at 10 knots in a direction of 22 degrees. What is the true velocity and direction of the boat? round to the nearest whole #
a) 38knots;58 degrees
b) 32knots;30 degrees
c) 1,427knots;58 degrees
d) 38knots;32 degrees
The magnitude of the total velocity of the boat is 38 knots, and the direction is 32°, so the correct option is d.
How to get the velocity of the boat?
First, we need to write need to find the component of the two given velocities.
For the boat, the magnitude is 28 knots and the angle is 36°, then the components are:
x-component = (28 knots)*cos(36°) = 22.65 knotsy-component = (28 knots)*sin(36°) = 16.46 knotsFor the wind, the components are:
x-component = (10 knots)*cos(22°) = 9.27 knotsy-component = (10 knots)*sin(22°) = 3.75 knotsAdding these, the total components of the boat's velocity are:
x-comp = 22.65 knots+ 9.27 knots = 31.92 knotsy-comp = 16.46 knots + 3.75 knots = 20.21 knotsThen the magnitude of the velocity is:
|V| = √( (31.92 knots)^2 + (20.21 knots)^2) =37.78 knots
That can be rounded to 38 knots
To get the angle, we take the arctangent of the quotient between the y-component and the x-component:
a = Atan(20.21 knots/31.92 knots) = 32.34°
Then the correct option is d) 38 knots and 32°
If you want to learn more about velocity, you can read:
https://brainly.com/question/4931057
Answer:
It is 38 knots; 32 degrees
Step-by-step explanation:
The answer below is right
I took the test
What is the square root of 546 divided by 67 (100 points!)
Round answer to 2 decimal points
Answer: the answer is 0.35 because
Square root of 546 is 23.3666428911
23.3666428911 divided by 67 is 0.34875586404
0.34875586404 rounded to 2 decimal points is 0.34875586404
the answer I had is 0.3487. first of all you have to find the square root of 546 which is 23.366 then you divide it by 67 which will give you 0.3487
Find the lateral surface area of the triangular prism. refer to your staar 8th grade math reference sheet for the appropriate formula. question 8 options: 90 in2 110 in2 120 in2 130 in2
The lateral surface area of the triangular prism is 130 in sq. So, option D is the correct answer.
What is the lateral surface area of the triangular prism?The lateral surface area of the triangular prism is the product of the perimeter of the base and length.
L = perimeter of the base × length.
The side of the base is given as 7in, 3in, and 3in
and the length is 10in
The lateral surface area of the triangular prism = perimeter of the base × length.
L = (7in + 3in + 3in) 10
L = 13 × 10
L = 130 in sq.
Hence, The lateral surface area of the triangular prism is 130 in sq. So, option D is the correct answer.
Learn more about prism;
https://brainly.com/question/1601740
Answer:
130 ig
Step-by-step explanation:
The graph of this system of equations is which of the following?
2x + y = 6
6x + 3y = 18
Overlapping lines
Parallel lines
Intersecting lines
A curve intersecting with a line
Answer:
They are the same line. It means that they are overlapping line.
Answer:
Overlapping
Step-by-step explanation:
Divide every term of the second equation, it would be 2x + y = 6, which is the same as the first equation.
Consider the quadratic equation x2+7x+8=0. Which of the following is the correct form after substituting a, b, and c into the Quadratic Formula?
x=7 ±(7)2−4(1)(8)√2(1)
x=(7)2−4(1)(8)√2(1)
x=−7 ±(7)2−(1)(8)√2(1)
x=−7 ±(7)2−4(1)(8)√2(1)
Answer:
x=−7 ±(7)2−4(1)(8)√2(1)
Step-by-step explanation:
I risked it all and got it right
Please need help this question
Answer:
b they are perpendicular
Step-by-step explanation:
they intersect each other at point D
work out the next term of this quadratic sequence
6 9 15 24 _
Answer:
36
Step-by-step explanation:
Every next term is added by a multiple of 3
6 + 3 = 9
9 + ( 3 × 2 ) = 15
15 + ( 3 × 3 ) = 24
24 + ( 3 × 4 ) = 36
Answer:
36.
Step-by-step explanation:
The differenes in the terms are 3, 6, 9 so the next difference is 12.
24 + 12 = 36.
ANSWER QUESTION BELOW CORRECTLY FOR BRAINLIEST
One day, a person went to a horse racing area. Instead of counting the number of humans and horses, he counted 74 heads and 196 legs. How many humans and horses were there?
A. 37 humans and 98 horses
B. 24 horses and 50 humans
C. 31 horses and 74 humans
D. 24 humans and 50 horses
Answer:
the answer is a
Step-by-step explanation:
Answer:
B. 24 horses and 50 humans
Step-by-step explanation:
74 x 2 = 148
196 - 148 = 48
48/2 = 24 (number of horses)
74 heads - 24 horses = 50 humans
Which fraction does this line plot represent?
5/8
6/8
5/9
3/8
Answer:
5/8
Step-by-step explanation:
Just gonna fill up the required space here lol
Solve this on your own and find the unit rate of miles per hour.
look at point C and D on the graph..
What is the distance (in units) between points C and D? Round your answer to the nearest hundredth.
2.24 units
3.16 units
6.40 units
7.07 units
Answer: 7.07
Step-by-step explanation:
Chris invests $5,000 in a savings account that earns 2% interest per year. what would the Eqn be with a(b)^x
Answer:
The equation would be 5000(1.02)^x with x representing the amount of years, as the values keep multiplying.
Help With this Math problem
Answer:
a) c = 11.2
b) c = 2
Step-by-step explanation:
[tex]c^{2} = a^{2} + b^{2}[/tex]
c = line across from the right angle
Given the following unit circle, rotate green dot to the appropriate angle and then find the exact value of the function.
Answer:
you can find the aswer in the question and the in the frist sentes of the question
Step-by-step explanation:
Solve the folllowing question-->2e+3=5
Answer:
[tex]\boxed{\sf{e=1}}[/tex]Step-by-step explanation:
Isolate the term of e from one side of the equation.
2e+3=5First, you subtract by 3 from both sides.
⇒ 2e+3-3=5-3
Solve.
Subtract the numbers from left to right.
⇒ 5-3=2
Rewrite the problem down.
⇒ 2e=2
Divide by 2 from both sides.
⇒ 2e/2=2/2
Solve.
Divide the numbers from left to right.
⇒ 2/2=1
⇒ e=1
Therefore, the correct answer is e=1.I hope this helps you! Let me know if my answer is wrong or not.
Answer:
e = 1
Step-by-step explanation:
Subtract 3 both sides:
⇒ 2e + 3 = 5
⇒ 2e + 3 - 3 = 5 - 3
⇒ 2e = 2
Divide both sides by 2:
⇒ 2e = 2
⇒ 2e/2 = 2/2
⇒ e = 1
Kim brought $39.75 to the art supply store. She bought a brush, a sketchbook, and a paint set. The brush was 1 4 as much as the sketchbook, and the sketchbook cost 2 3 the cost of the paint set. Kim had $4.00 left over after buying these items
Answer:
I can't get past hre, equations are attached tho
Step-by-step explanation:
Equations:
[tex]b + s + p = 35.75[/tex]
[tex]\frac{1}{4} b = s[/tex]
[tex]\frac{2}{3} s = p[/tex]
Now I used Desmos to solve this, im sure theres a way to find it the legit way but i'm too lazy. Here's the image of what the graph is like:
brush =$20.21,. sketchbook =$6.21 , paint set=$9.32
Step-by-step explanation:
let the cost of the brush=x
the cost of the sketchbook=y
the cost of the paint set= z
total money used= $39.75-$4.00
=$35.75
x= 14+y
but y=2/3z
x= 14+2/3z
14+2/3z +2/3z +z =35.75
3×14 +3×2/3z+3×2/3z×3z=3×35.75
42 +2z +2z +3z =107.25
7z=107.25-42
7z=65.25
z=65.25/7
z=$9.32
y=$2/3×9.32
y=$6.21
x=14+y
x=14+6.21
x=$20.21
(HELP!!!)
Identify the variable expression that is “not” a polynomial.
A. x+2
B. XA+7
C. 24
D. y + x
Identify the variable expression that is “not” a polynomial.
Try looking for the one that breaks the rules of it being a polynomial.
please help figure out the range
Answer:
5
Step-by-step explanation:
The range is the highest value number minus the lowest value number. 9 minus 4 is 5.
PLSSSS HELP
Choose ALL answers that describe the polygon.
Answer:
RSTU is a parallelogram, quadrilateral, rectangle, rhombus, and square. NOT trapezoid.
Step-by-step explanation:
The shape has four sides, so it's a quadrilateral.
It has four equal sides so its a rhombus.
It has four right angles so its a rectangle.
It has four equal sides AND right angles so its a square.
And if all the sides are parallel (well, two pairs of parallel sides) its a parallelogram.
What is the range? ???????
Answer:
the difference between the highest and lowest values in a set of numbers.
Step-by-step explanation:
Please someone help!!!!
Kristine observes the top of a lookout tower from a point 220 ft from its base.
If the indicated angle of elevation measures 37º, how tall is the tower? Give your answer to the nearest tenth of a foot.
Answer:
height of the tower: 165.8 ft
use tan rule:
[tex]\sf \sf tan(x)= \dfrac{opposite}{adjacent}[/tex]
Here: [ your calculator should be in degree mode [D] ]
x = 37°opposite = height of the toweradjacent = 220Solve:
[tex]\hookrightarrow \sf \sf tan(37)= \dfrac{t}{220}[/tex]
[tex]\hookrightarrow \sf t = \sf tan(37)*220[/tex]
[tex]\hookrightarrow \sf t = 165.8 \ ft[/tex]
A beach volleyball court is 9 meters wide and 18 meters long. The rope used for the boundary line costs $1.67 per meter. How much would it cost to buy a new boundary line for the court?
Answer:
$90.18
Step-by-step explanation:
Since there are two long sides and two wide sides, you would double them. Add them together, and multiply by price
9 + 9 = 18
18 + 18 36
18 + 36 = 54
54 x 1.67 = 90.18
If x=y and y= 2, then 3x=
~Denki Kaminari here~
Answer:
6
Step-by-step explanation:
because x is equal to 1, and y is equal to 2, all we need to do is skip count 3 times by 2 and you get your answer: 6!
hope this helps :D
Answer:
6
Step-by-step explanation:
Given that x = y so that means if y and x are same and have same values. Therefore if y = 2 then x = 2.
So substitute x = 2 in 3x:
3(2) = 6
Therefore, the solution is 6
the quotient of 40 and 5
Answer:
8
Step-by-step explanation:
Taking the quotient of two numbers means you are dividing one by the other. In this case, 40 is the dividend, and 5 is the divisor. This gets you 40/5=8 as the quotient.
If you multiply the quotient with the divisor, you get the dividend, as 8*5=40
Ben has a dog that has a mass of 9 kilograms. What is the mass of the dog in grams?
Answer:
9000 grams
Step-by-step explanation:
Keep in mind the conversion 1 kilogram = 1000 grams, as 1 kilo means 1000.
⇒ 1 kilogram = 1000 grams
⇒ Ben's dog = 9 kilogram = x kilograms = 1000x grams
⇒ x = 9
⇒ Ben's dog = 9 kilogram = 1000x grams
= 1000(9) grams
= 9000 grams
Answer:
Your answer is,
9000 grams
Step-by-step explanation:
Hope this helps you :)
pls mark brainliest <3
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``Tori
Find the length of the third side. If necessary, round to the nearest tenth
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Let's use Pythagoras theorem !
[tex]\qquad \sf \dashrightarrow \:h {}^{2} = p {}^{2} + b {}^{2} [/tex]
where,
h = hypotenuse = unknown b = base = 11 p = perpendicular = 12[tex]\qquad \tt\dashrightarrow \:h {}^{2} = 12{}^{2} + 11 {}^{2} [/tex]
[tex]\qquad \tt\dashrightarrow \:h {}^{2} = 144{}^{} + 121[/tex]
[tex]\qquad \tt\dashrightarrow \:h {}^{2} = 265[/tex]
[tex]\qquad \tt\dashrightarrow \:h {}^{} = \sqrt{265}[/tex]
[tex]\qquad \tt\dashrightarrow \:h {}^{} \approx16.3[/tex]