Answers
With the Pythagorean theorem: a^2 + b^2 = c^2 is used with the numbers accordingly- 5 and S are legs and can be either a or b while √50 being the hypotenuse can only be c
(5)^2 + (s)^2 =(√50)^2
25 + (s)^2 = 50
√ ((s)^2) = √ (50 - 25)
s = 5
The special Triangles rule actually states that a shortcut can be applied to the corresponding sides (look at picture). S is directly across from a 45 degree angle (and so is 5!)
If a = 5, than s must also = 5.
5
Step-by-step explanation:
You can use Tan(45)=S/5 to solve for S. Tan basically means Opposite/Adjacent. So the opposite side is S and the adjacent side is S. You plug tan(45) into your calc and then multiply it by 5.
Proportion Below
Tan(45)/1 = S/5
You cross multiply to get Tan(45)*5=S
S would be 5
To check you can use the Pythagorean theorem a^2+b^2=c^2
5^2+5^2=
[tex] {5}^{2} + {5}^{2} = \sqrt{50} [/tex]
25+25=50
Related Questions
Using the number 3,5,and 8 can you right nine proper fractions and nine improper fractions
Answers
Answer with step-by-step explanation:
We are to write nine proper fractions (where the numerator is smaller than the denominator) and nine improper fractions (where the denominator is bigger than the numerator) using the number 3, 5 and 8.
Proper fractions:
[tex] \frac { 3 } { 5 },\frac { 3 } { 8 } \frac { 5 } { 8 }, \frac { 3 }{ 5 . 8 },\frac{5}{3.8}, \frac{8}{5.3},\frac{3}{5+8},\frac{5}{3+8}, \frac{5-3}{8} \imples\frac{3}{5},\frac{3}{8} \frac{5}{8},\frac{3}{40},\frac{5}{24}, \frac{8}{15},\frac{3}{13},\frac{5}{11}, \frac{1}{4}[/tex]
Improper fractions:
[tex]\frac{5}{3},\frac{8}{3} \frac{8}{5},\frac{40}{3},\frac{24}{5}, \frac{15}{8},\frac{13}{3},\frac{11}{5}, \frac{19}{3}[/tex]
Answer: Yes, you can write nine Proper Fractions and nine Improper Fractions using the numbers 3,5,and 8.
Step-by-step explanation:
You need to remember that a fraction is Proper when the numerator is less than the denominator and it is Improper fraction when the numerator is greater than the denominator.
Knowing this, you can write the following nine Proper Fractions and nine Improper Fractions, using the numbers 3,5 and 8:
Proper Fractions:
[tex]\frac{3}{5},\frac{3}{8},\frac{3}{5+8},\frac{3}{8*5},\frac{5}{8},\frac{5}{3+8},\frac{5}{8*3},\frac{5-3}{8},\frac{8}{5*3}\\\\\\\frac{3}{5},\frac{3}{8},\frac{3}{13},\frac{3}{40},\frac{5}{8},\frac{5}{11},\frac{5}{24},\frac{1}{4},\frac{8}{15}[/tex]
Improper Fractions:
[tex]\frac{5}{3},\frac{8}{5},\frac{8}{3},\frac{8+3}{8},\frac{5+8}{3},\frac{3*5}{8},\frac{8*5}{3},\frac{3+8}{5},\frac{8*3}{5}\\\\\\\frac{5}{3},\frac{8}{5},\frac{8}{3},\frac{11}{8},\frac{13}{3},\frac{15}{8},\frac{40}{3},\frac{11}{5},\frac{24}{5}[/tex]
Suppose 46% of American singers are Grammy award winners.
If a random sample of size 622 is selected, what is the probability that the proportion of Grammy award winners will be less than 47%? Round your answer to four decimal places.
Answers
Answer:
The probability that the proportion of Grammy award winners will be less than 47% is 0.6915
Step-by-step explanation:
* Lets explain how to solve the problem
- Suppose 46% of American singers are Grammy award winners.
- In a random sample of size 622 is selected
- We want to find the probability that the proportion of Grammy award
winners will be less than 47%
* At first we must to calculate z
∵ [tex]z=\frac{P^{'}-P}{\sqrt{\frac{P(1-P)}{n}}}[/tex], where
# P' is the sample proportion
# n is the sample size
# P is probability of success
∵ The sample proportion is 47% = 47/100 = 0.47
∴ P' = 0.47
∵ The sample size is 622
∴ n = 622
∵ The probability of success is 46% = 46/100 = 0.46
∴ P = 0.46
∴ [tex]z=\frac{0.47-0.46}{\sqrt{\frac{0.46(1-0.46)}{622}}}=0.5004[/tex]
- P(P' < 0.47) = P(z < 0.5004)
∵ P(z < 0.5004) = 0.6915
∴ P(P' < 0.47) = 0.6915
* The probability that the proportion of Grammy award winners will
be less than 47% is 0.6915
one pump can fill a swimming pool in 8 hours and another pump can fill it in 10 hours if both pumps are open at the same time how many hours will it take to fill the pool
Answers
Answer:
4.44 hours
Step-by-step explanation:
One pump can fill a swimming pool in 8 hours.
In 1 hour pump can fill the pool = [tex]\frac{1}{8}[/tex]
another pump can fill the swimming pool in 10 hours.
in 1 hour another pump can fill the pool = [tex]\frac{1}{10}[/tex]
Let the total time will it take together to fill the pool = x
[tex]\frac{1}{8}[/tex] + [tex]\frac{1}{10}[/tex] = [tex]\frac{1}{x}[/tex]
[tex]\frac{5+4}{40}[/tex] = [tex]\frac{1}{x}[/tex]
[tex]\frac{9}{40}[/tex] = [tex]\frac{1}{x}[/tex]
9x = 40
x = [tex]\frac{40}{9}[/tex]
x = 4.44 hours
It will take 4.44 hours to fill the pool if both pumps are open.
what is 1/3 to the power of -4
Answers
First, to get applied by the fraction rule: [tex]\displaystyle\frac{3^4}{1}[/tex], then, the applied rule [tex]\displaystyle\frac{a}{1}=a[/tex]. Finally, simplify to find the answer. [tex]\displaystyle3^4=3*3*3*3=81[/tex], the correct answer is 81. I hope this will help you. Have a wonderful day!
[tex]\left(\dfrac{1}{3}\right)^{-4}=3^4=81[/tex]
(x+2) is one of the factors of the polynomial x³+13x²+32x+20. Find its remaining factors.
A little help....
Answers
Answer:
x^2+11x+10
or
(x+1)(x+10) since you can factor x^2+11x+10
Step-by-step explanation:
Let's do synthetic division.
We are dividing by x+2, so -2 will be on the outside. Like this:
-2 | 1 13 32 20
| -2 -22 -20
|___________________________
1 11 10 0
The remainder is 0, so (x+2) is indeed a factor of x^3+13x^2+32x+20.
The other factor we found by doing this is (x^2+11x+10).
You can find more factors by factoring x^2+11x+10.
Two numbers that multiply to be 10 and add to be 11 is 10 and 1 so the factored form of x^2+11x+10 is (x+10)(x+1).
is 5 a soluation to the equation? 3x(+1)=7(×-2)-3
Answers
Answer:
x=5
Step-by-step explanation:
If the equation is:
3(x+1)=7(x-2) -3
Solution:
Multiply (x+1) by 3 and (x-2) by 7
3x+3 = 7x-14 -3
3x+3 = 7x -17
Now combine the like terms:
3+17 = 7x-3x
20 = 4x
Now divide both the terms by 4
20/4 = 4x/4
5 = x
You can write it as x=5
Thus the value of x is 5 ....
Which is the most appropriate answer for this problem? Jeremy bought a sandwich for $5.98, a drink for $2.99, and an apple for $1.49. How much change will Jeremy get if he gives the cashier $20? A. exactly $9.54 B. exactly $10.46 C. about $9 D. about $10
W I L L
M A R K
B R A I N L I E S T
Answers
Answer:
A. exactly $9.54
Step-by-step explanation:
First add up how much he bought
Sandwich 5.98
drink 2.99
apple 1.49
---------
10.46
Then subtract this from 20
20.00
-10.46
--------------
9. 54
When you get money back, you get exact change.
He will get this because when you add all the addend you get the sum of $9.54
24. SP6 - M
Jared has a spinner that is divided into four congruent sections (pictured below).
If he spins the spinner 500 times, which statement below is most likely to be true?
a. It will land on an even number exactly 250 times.
b. It will land on 1 approximately 100 times
C. It will land on a 2 or 3 approximately 400 times
d. It will land on 1 about 100 times
Answers
Answer:
No correct answer.
Step-by-step explanation:
C: 2 or 3 is 1/2 the probability. The expectation is that you should get about 250 readings that are either 2 or 3.
A is not correct. It will land on an even number about 250 times. What should happen in theory is far different than what will happen when you try it. Exactly is too confining a word.
B: It will land on 1 about 1 out of every 4 times. 1/4 * 500 = 125. So B is not right.
D: Same as B. There is no answer.
How is the pattern for a perfect square trinomial used to factor the trinomial?
Answers
A perfect square trinomial can be factored using the pattern x²+2ab+b²=(x+a)² or x²-2ab+b²=(x-a)². The term 'a' is the square root of the last term, and 'b' is half of the second term's coefficient.
Explanation:In mathematics, a perfect square trinomial is a type of second-order polynomial or quadratic function with a specific form. It is used in the factorization process, particularly when solving quadratic equations of the form ax² + bx + c.
A perfect square trinomial is a trinomial in the form x²+2ab+b² or x²-2ab+b². To factor such a trinomial, the pattern (x+a)² or (x-a)² is used where 'x' is the variable, 'a' is the square root of the third term, and 'b' is half of the coefficient of the second term. Hence, x²+2ab+b² factors to (x+a)², whereas x²-2ab+b² factors to (x-a)².
Take for example, the trinomial x²+6x+9. Here, 'a' is 3 (as √9=3) and 'b' is 3 (as half of 6 is 3). Both 'a' and 'b' are equal so we know the trinomial is perfect square and it factors to (x+3)².
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The factor a perfect square trinomial, use the pattern [tex](a+b)^2[/tex] = [tex]a^2[/tex] +2ab+ [tex]b ^{2}[/tex] and simplify .
The pattern for a perfect square trinomial is a helpful algebraic expression that represents the square of a binomial.
It takes the form [tex](a+b)^2[/tex] = [tex]a^2[/tex] +2ab+[tex]b ^{2}[/tex]
where a and b are variables. When faced with a trinomial that fits this pattern, you can use it to factor the trinomial efficiently.
To factor a perfect square trinomial, compare it with the pattern. If the trinomial can be expressed in the form [tex](a+b)^2[/tex] =[tex]a^2[/tex]+2ab+ [tex]b ^{2}[/tex] , then it is a perfect square trinomial.
Identify [tex]a^2[/tex] ,2ab and [tex]b ^{2}[/tex] terms in the trinomial.
Once identified, you can write the factored form as [tex](a+b)^2[/tex]. This means the trinomial can be factored as [tex](a+b)^2[/tex] where a is the square root of the first term, and b is the square root of the last term.
This process is essentially reverse-engineering the expansion of the perfect square trinomial pattern.
Factoring using the perfect square trinomial pattern can save time compared to other methods, making it a valuable tool in algebraic manipulations and simplifying expressions.
What is the axis of symmetry for the function shown in the graph?
(*1,4)
(1,-4)
(1,4)
(-1,3)
Answers
Answer:
x = 1
Step-by-step explanation:
The axis of symmetry for a vertically opening parabola is a vertical line with equation
x = h
where h is the value of the x- coordinate the line passes through.
The axis of symmetry passes through the vertex 1, 4 ) with x- coordinate 1
Hence equation of axis of symmetry is x = 1
Simplify
(4x² – 2x + 8) - (x² + 3x - 2)
Answers
Answer:
3x² – 5x + 10
Step-by-step explanation:
(4x² – 2x + 8) - (x² + 3x - 2) =
Drop the first set of parentheses because it is unnecessary.
= 4x² – 2x + 8 - (x² + 3x - 2)
To get rid of the second set of parentheses, change every sign inside.
= 4x² – 2x + 8 - x² - 3x + 2
Now, combine like terms.
= 3x² – 5x + 10
Answer:
3x^2 -5x +10
Step-by-step explanation:
(4x² – 2x + 8) - (x² + 3x - 2)
Distribute the negative sign
(4x² – 2x + 8) - x² - 3x + 2
I like to line them up vertically
4x² – 2x + 8
-x² - 3x + 2
---------------------
3x^2 -5x +10
HELP ME PLEASE!!! Steps would be helpful :)
Answers
Answer:
i believe the answer is 9.5
Step-by-step explanation:
cos60 = c / 19 = 9.5
A variety of two types of snack packs are delivered to a store. The box plots compare the number of calories in each snack pack of crackers to the number of calories in each snack pack of trail mix. Which statement is true about the box plots? The interquartile range of the trail mix data is greater than the range of the cracker data. The value 70 is an outlier in the trail mix data. The upper quartile of the trail mix data is equal to the maximum value of the cracker data. The number of calories in the packs of trail mix have a greater variation than the number of calories in the packs of crackers.
Answers
Answer:
its D
Step-by-step explanation:
Answer:
D, The number of calories in the packs of trail mix have a greater variation than the number of calories in the packs of crackers.
If g(x) = 3(x + 10), what is the value of the
function when x = -8?
O
-8
-2
24
Answers
Answer:
6 which is none of your answers.
Are you sure your function is right?
Is value to plug in x=-8?
Step-by-step explanation:
To find the value of the function at x=-8, you replace x with -8 in the function.
g(x)=3(x+10)
g(-8)=3(-8+10)
g(-8)=3(2)
g(-8)=6
g(-8) = 6.
The value of g(x) = 3(x + 10) when x = -8 is:
Substituting x = -8 in the function g(x)
g(-8) = 3 (-8+ 10)
Solving the operation in the parenthesis
g(-8) = 3 (-8 + 10)
g(-8) = 3 (2)
Solving the multiplication
g(-8) = 6
Find my number, if it is the smallest four-digit number with all different digits.
Answers
Which expression can be used to determine the slope of the line that passes through the points (-7, 3) and (1,-97
Answers
Answer:
see explanation
Step-by-step explanation:
Calculate the slope m of the line using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 7, 3) and (x₂, y₂ ) = (1, - 97)
m = [tex]\frac{-97-3}{1+7}[/tex] = [tex]\frac{-100}{8}[/tex] = - [tex]\frac{25}{2}[/tex]
a portion of road A climbs steadily for 154 feet over a horizontal distance of 2200 feet. a portion of road B climbs steadily for 153 feet over a horizontal distance of 3400 feet. which road is steeper?
Answers
Answer:
Road A
Step-by-step explanation:
The slope of road A is:
154 / 2200 = 0.07
The slope of road B is:
153 / 3400 = 0.045
Road A has the larger slope, and is therefore steeper.
The steepness of a road is determined by the ratio of the vertical climb to the horizontal distance. By calculating this ratio for both Road A and Road B, we find that Road A, with a ratio of 0.07, is steeper than Road B, which has a ratio of 0.045.
Explanation:The steepness of a road is determined by the ratio of the vertical climb to the horizontal distance. This is equivalent to finding the slope in mathematics. We can calculate this for both Road A and Road B:
For Road A, the slope can be calculated as rise over run, or 154 feet over 2200 feet, yielding approximately 0.07. For Road B, applying the same formula gives 153 feet over 3400 feet, resulting in a slope of about 0.045.
Comparing these two results, it is clear that Road A, with a slope of 0.07, is steeper than Road B, which has a slope of 0.045.
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In store A a scarf cost $12, and in store B the same scarf is on sale for $8. How many scarfs can be bought in store B with the amount of money, excluding sales tax, needed to buy 10 scarfs in store A
Answers
Answer:
15 scarfs.
Step-by-step explanation:
The cost of 10 scarfs in Store A = 12 * 10 = $120.
The number of scarfs that can be bought in Store A for $120
= 120 / 8 = 15.
15 scarfs
The cost of 10 scarfs in Store
A = 12 * 10 = $120
The number of scarfs that can be bought in Store A for $120
= 120 / 8 = 15.
How to determine a price for your product?
To do so, you’ve got to be clear on:
The cost of producing your productThe value of your services to your clientsHow much do your customers have and want to spendThe overall running costs of your businessWhat critical costs need to be covered short-term (e.g. loan repayments)How your competitors price their productsLearn more about COST here https://brainly.com/question/20224726
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The ratio of the lengths of corresponding parts in two similar solids is 21.
What is the ratio of their surface areas?
А. 2:1
В. 8:1
D. 4:1
D. 6:1
Answers
Answer:
Option D. 4:1
Step-by-step explanation:
we know that
If two solids are similar, then the ratio of the lengths of corresponding parts is equal to the scale factor and the ratio of its surface areas is equal to the scale factor squared
In this problem
The scale factor is equal to [tex]\frac{2}{1}[/tex] (ratio of corresponding lengths)
therefore
The ratio of their surface areas is equal to
[tex](\frac{2}{1})^{2}=\frac{4}{1}[/tex]
Find the value of a in the picture
Answers
Answer:
= 52°
Step-by-step explanation:
The obtuse angle at O is twice the angle made at the circumference /by the same segment b.
=52×2=104°
The base angles that are made by isosceles triangle that has the apex with angle 104° equal to (180-104)/2=38°
The radii of a circle are equal and meet tangents at right angles.
Angle a= 90-38= 52°
Tangent wz and secant WV intersect at point W. Find the length of YV If necessary, round to the hundredths place.
A 2.67
B5
с.9
D. 10
Answers
Answer:
Option B. [tex]YV=5\ units[/tex]
Step-by-step explanation:
we know that
The Intersecting Secant-Tangent Theorem, states that If a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment
so
In this problem
[tex]WZ^{2}=WV*WY[/tex]
substitute and solve for WV
[tex]6^{2}=WV*4[/tex]
[tex]WV=36/4=9\ units[/tex]
we have that
[tex]WV=WY+YV[/tex]
substitute
[tex]9=4+YV[/tex]
[tex]YV=9-4=5\ units[/tex]
HELP ASAP!!!!
See the figure of ΔABC with auxiliary lines added. If c is the base of ΔABC, the height is _____. sin(A) = ______ . The previous statement is leading to the derivation of which area formula? Area ΔABC = _______
Answers
Answer:
In the given Δ ABC
the height will be CD
sin (A) = [tex]\dfrac{P}{H}[/tex]
sin (A) = [tex]\dfrac{CD}{b}[/tex]................(1)
now to find area of the ΔABC
area of the ΔABC = [tex]\dfrac{1}{2}\times Base \times Height[/tex]
=[tex]\dfrac{1}{2}\times c \times CD[/tex]
from equation (1) we can substitute of the value of CD.
=[tex]\dfrac{1}{2}\times c \times b sin(A)[/tex]
The base of ΔABC is c then the height is CD and the area of triangle is given by: [tex]\rm \dfrac{1}{2}\times c \times b\times sin(A)[/tex]
Given :
AC = b
BC = a
c is the base of triangle ABC.
Solution :
In the given triangle ABC
[tex]\rm sin(A) = \dfrac{Perpendicular}{Hypotenuse}[/tex]
the height will be CD,
[tex]\rm sin (A) = \dfrac{CD}{b}[/tex] ----- (1)
Area of the triangle ABC
[tex]\rm = \dfrac{1}{2}\times base\times height[/tex]
[tex]\rm =\dfrac{1}{2}\times c \times CD[/tex] --- (2)
Now from equation (1) and (2) we get
[tex]\rm Area\;of\;\Delta ABC = \dfrac{1}{2}\times c \times b\times sin(A)[/tex]
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What is the average rate of change for this quadratic function for the interval
from x= 2 to x = 4?
Answers
Answer:
-6
Step-by-step explanation:
The average rate of a function f(x) on the interval from x=a to x=b is [tex]\frac{f(b)-f(a)}{b-a}[/tex].
So in the problem you have from [tex]x=2[/tex] to [tex]x=4[/tex].
The average rate of the function from x=2 to x=4 is
[tex]\frac{f(4)-f(2)}{4-2}=\frac{f(4)-f(2)}{2}[/tex].
Now we need to find f(4) and f(2).
f(4) means what is the y-coordinate that corresponds to x=4 on the curve.
f(4)=-15 since the ordered pair at x=4 is (4,-15).
f(2) means what is the y-coordinate that corresponds to x=2 on the curve.
f(2)=-3 since the ordered pair at x=2 is (2,-3).
So let's plug in those values:
[tex]\frac{f(4)-f(2)}{4-2}=\frac{-15-(-3))}{2}[/tex].
Now we just simplify:
[tex]\frac{-15+3}{2}[/tex]
[tex]\frac{-12}{2}[/tex]
[tex]-6[/tex]
What is 8/2(2+2)
It’s one right?
If it’s not I’ll Be disappointed in humanity
Answers
Answer:
16
Step-by-step explanation:
8 / 2 * (2 + 2)
4 * (2 + 2)
4 * 4
16
Step-by-step explanation:
PEMDAS is ( Thank you google )
" PEMDAS is an acronym for the words parenthesis, exponents, multiplication, division, addition, subtraction. Given two or more operations in a single expression, the order of the letters in PEMDAS tells you what to calculate first, second, third and so on, until the calculation is complete."
First, 2 + 2 = 4
Second, 8 divided by 2 is 4.
Third, 4x4= 16
Therefore, the answer is 16.
Graph the system of equations on graph paper to answer the question.
{y=25x+4
{y=2x+12
What is the solution for this system of equations?
HELP PLS!!
Answers
Answer:
[tex]x = \frac{8}{23} \: \: \: \\ y = \frac{292}{23} [/tex]
Answer:
-5, 2
Step-by-step explanation:
If “u” varies directly with “v,” and u = 6 when v = -7, what’s is “u” when v = 4?
U=__
Answers
In a scenario where 'u' varies directly with 'v', the constant of variation, k is found by: k=u/v. Here, k becomes 6/-7. If we want to know the value for 'u' when v=4, we use the calculated k in our formula, resulting in u=4*(6/-7) which equals -24/7.
Explanation:The question is about the direct variation between two quantities 'u' and 'v'. If 'u' varies directly with 'v', it means that multiplying or dividing one quantity will have the same effect on the other. We use the mathematical formula for direct variation to find the values: 'u' = kv, where k is the constant of variation.
So, we first find 'k' when u = 6 and v = -7. From our formula, k = u/v = 6/-7.
When we know the k, we can find u' when v = 4. Using the formula, 'u' = kv = 4 * (6/-7) = -24/7.
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Find the distance between the points (0,10) and (-9,1)
Answers
[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{0}~,~\stackrel{y_1}{10})\qquad (\stackrel{x_2}{-9}~,~\stackrel{y_2}{1})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(-9-0)^2+(1-10)^2}\implies d=\sqrt{(-9)^2+(-9)^2} \\\\\\ d=\sqrt{81+81}\implies d=\sqrt{162}\implies d\approx 12.73[/tex]
Multiply 3/sqrt17- sqrt2 by which fraction will produce an equivalent fraction with rational denominator
Answers
Answer:
B.
Step-by-step explanation:
To simplify something that looks like [tex]\frac{\text{whatever}}{\sqrt{a}-\sqrt{b}}[/tex] you would multiply the top and bottom by the conjugate of the bottom. So you multiply the top and bottom for this problem I just made by:
[tex]\sqrt{a}+\sqrt{b}[/tex].
If you had [tex]\frac{\text{whatever}}{\sqrt{a}+\sqrt{b}}[/tex], then you would multiply top and bottom the conjugate of [tex]\sqrt{a}+\sqrt{b}[/tex] which is [tex]\sqrt{a}-\sqrt{b}[/tex].
The conjugate of a+b is a-b.
These have a term for it because when you multiply them something special happens. The middle terms cancel so you only have to really multiply the first terms and the last terms.
Let's see:
(a+b)(a-b)
I'm going to use foil:
First: a(a)=a^2
Outer: a(-b)=-ab
Inner: b(a)=ab
Last: b(-b)=-b^2
--------------------------Adding.
a^2-b^2
See -ab+ab canceled so all you had to do was the "first" and "last" of foil.
This would get rid of square roots if a and b had them because they are being squared.
Anyways the conjugate of [tex]\sqrt{17}-\sqrt{2}[/tex] is
[tex]\sqrt{17}+\sqrt{2}[/tex].
This is the thing we are multiplying and top and bottom.
For this case we have the following expression:
[tex]\frac {3} {\sqrt {17} - \sqrt {2}}[/tex]
We must rationalize the expression, so we multiply by:
[tex]\frac {\sqrt {17} + \sqrt {2}} {\sqrt {17} + \sqrt {2}}[/tex]
So, we have:
[tex]\frac {3} {\sqrt {17} - \sqrt {2}} * \frac {\sqrt {17} + \sqrt {2}} {\sqrt {17} + \sqrt {2}} =\\\frac {3 (\sqrt {17} + \sqrt {2}} {17- \sqrt {17} * \sqrt {2} + \sqrt {17} * \sqrt {2} -2} =\\\frac {3 (\sqrt {17} + \sqrt {2}} {15}[/tex]
Thus, the correct option is option B.
Answer:
OPTION B
Factorise completely 8p-12pq
Answers
Answer:
4p(2-3q)
Step-by-step explanation:
Factor out 4 first:
8p-12pq
4(2p-3pq) Next, factor out p like you would any other number.
4p(2-3q)
Answer:
4p (2-3q)
Step-by-step explanation:
Break each term into its prime factors
8p = 4*2p = 2*2*2p
12pq = 4*3pq = 2*2*3*p*q
The common factors are 2*2*p
That is the greatest common factor. Take that outside the parentheses. Leave what is left inside the parentheses
2*2*p( 2-3q)
4p (2-3q)
Simplify:
a. (-18x2y)/(3x)
Answers
Answer:
Step-by-step explanation: Sorry no time gtg : / (if you really need it I'LL ANSWER TOMMOROW
Answer: The required simplified expression is -6xy.
Step-by-step explanation: We are given to simplify the following rational expression :
[tex]E=-\dfrac{18x^2y}{3x}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We will be using the following property of exponents :
[tex]\dfrac{z^a}{z^b}=z^{a-b}.[/tex]
From expression (i), we get
[tex]E\\\\\\=-\dfrac{18x^2y}{3x}\\\\\\=-\dfrac{18}{3}x^{2-1}y\\\\=-6xy.[/tex]
Thus, the required simplified expression is -6xy.