Given that (in picture)...

Find the values of a and b

Please help- confused on rationalising denominator but not sure

Given That (in Picture)...Find The Values Of A And BPlease Help- Confused On Rationalising Denominator

Answers

Answer 1
Answer:  a = -3 and b = 5

=================================================

Work Shown:

Multiply top and bottom by [tex]\sqrt{2}[/tex] to rationalize the denominator

[tex]\frac{10-\sqrt{18}}{\sqrt{2}}\\\\\frac{\sqrt{2}(10-\sqrt{18})}{\sqrt{2}*\sqrt{2}}\\\\\frac{\sqrt{2}*10-\sqrt{2}*\sqrt{18}}{\sqrt{2*2}}\\\\\frac{\sqrt{2}*10-\sqrt{2*18}}{\sqrt{4}}\\\\\frac{10\sqrt{2}-\sqrt{36}}{2}\\\\\frac{10\sqrt{2}-6}{2}\\\\\frac{-6+10\sqrt{2}}{2}\\\\\frac{2(-3+5\sqrt{2})}{2}\\\\-3+5\sqrt{2}\\\\[/tex]

We end up with something in the form [tex]a+b\sqrt{2}[/tex] where a = -3 and b = 5


Related Questions

What is 100 ÷ 5 × 4 + 43
A. 69
B. 144
C. 0.3
D. 1.2

Answers

123 - Use PEMDAS but since you have both division and multiplication you can just go from left to right

Answer:

123

Step-by-step explanation:

100 ÷ 5 x 4 + 43

20 x 4 + 43

80 + 43

123

in which graph does the slope of the line l lequal zero

Answers

Answer:

wait can you make the same question with a picture or you don't have any pictures that comes with the problem?

Which expression is equivalent to (x^4/3 x^2/3)^1/3
?

x^2/9
x^2/3
x^8/27
x^7/3

Answers

Answer:

X^2/3

Step-by-step explanation:

If sin θ +cosec θ = 2 then sin2θ+ cosec2θ is equal to

a) 1 b) 4

c) 2 c) 9

Answers

Answer:

C

Step-by-step explanation:

We are given that:

[tex]\sin \theta +\csc \theta = 2[/tex]

And we want to find the value of:

[tex]\sin^2\theta + \csc^2\theta[/tex]

From the first equation, we can square both sides:

[tex](\sin \theta + \csc \theta)^2=(2)^2[/tex]

Square:

[tex]\sin ^2\theta +2\sin\theta\csc\theta +\csc^2\theta =4[/tex]

Let csc(θ) = 1 / sin(θ):

[tex]\displaystyle \sin ^2\theta +2\sin\theta\left(\frac{1}{\sin \theta}\right) +\csc^2\theta =4[/tex]

Simplify:

[tex]\displaystyle \sin ^2\theta +2(1) +\csc^2\theta =4[/tex]

Therefore:

[tex]\sin ^2\theta + \csc^2\theta =2[/tex]

Our answer is C.

B) 4 is the answer I believe

The area of a square is 81 cm squared find its perimeter​

Answers

Answer:

the answer is 36

Step-by-step explanation:

25 POINTS Find the slope of the line khan academy

Answers

Answer:

-8/5

Step-by-step explanation:

Using the points given ( -1,4) and (4,-4)

We can use the slope formula

m = ( y2-y1)/(x2-x1)

    = ( -4 -4)/(4- -1)

    = (-4 -4)/(4+1)

    = -8/5

Cylinder A has a radius of 12 inches and a height of 6 inches. Cylinder B has a volume of 648π. What is the percent change in volume between cylinders A and B? (5 points)



Question 6 options:

1)

Cylinder B is 50% smaller than cylinder A.


2)

Cylinder B is 25% smaller than cylinder A.


3)

Cylinder B is 150% bigger than cylinder A.


4)

Cylinder B is 200% bigger than cylinder A.

Answers

Answer: 2) Cylinder B is 25% smaller than cylinder

The equation of a line is 5x + 10y = 15

Answers

Answer:

c

Step-by-step explanation:

I don't think I understand this one try graphs n diagram

Which expression is equal to 2sin(pi/10)cos(pi/10)?

Answers

Answer:

sin pi/5,

Step-by-step explanation:

which of the following is equivalent to (i+3)+i(2i-4)

a. -5i + 1
b. -3i + 1
c. i-3
d. -i + 3

Answers

Answer:

answer is b

Step-by-step explanation:

i+3 -2 -4i = 1-3i

The expression that is equivalent to (i+3)+i(2i-4) is -3i  +  1

Option B is correct

The given expression is:

(i+3)+i(2i-4)

Open the parenthesis by expanding the expression using the distributive rule

i  +  3  +  2i²  -  4i

Note that i²  =  -1

The expression, therefore, becomes:

i  +  3  +  2(-1)  -  4i

i  +  3  -  2  -  4i

Collect like terms by bring the real parts together and the imaginary parts together

i  -  4i   +  3  -  2

Simplify to get the final expression

-3i  +  1

Therefore, the expression that is equivalent to (i+3)+i(2i-4) is -3i  +  1

Learn more here: https://brainly.com/question/12375854

If Kiri has 17 part-time members this month, how many full-time members does she need according to your equation?

Answers

Answer:

5050 = 225f + 125p

If p = 17 this month, then, f = 13

Step-by-step explanation:

Kiri owns a coworking space that has two primary types of memberships, full time and part-time. In order to pay her bills each month (rent on the building, electricity, internet, and so on) she needs to make $5050. Full-time memberships (f) cost $225 per month, and part-time memberships (p) cost $125 per month.

If Kiri has 17 part-time members this month, how many full-time members does she need according to your equation?

Total cost = $5050

cost of full-time memberships = $225

number of full time members = f

cost of part-time memberships = $125

number of part-time members = p

Total cost = cost of full-time memberships * number of full time members + cost of part-time memberships * number of part-time members

5050 = 225f + 125p

If p = 17 this month,

5050 = 225f + 125p

5050 = 225f + 125(17)

5050 = 225f + 2,125

5050 - 2,125 = 225f

2,925 = 225f

f = 2,925/225

f = 13

number of full time members = f = 13

If p = 17 this month, then, f = 13

Erica took out a loan to buy her new motorcycle. The purchase price of the motorcycle was $11349.00 plus 5% GST and 7% PST. She pays $409.00 per month on her loan, which has a term of 3 years. How much more is she paying than the purchase price? a. $2415.74 b. $1610.50 c. $2254.69 d. $2013.12

Answers

Answer:

The correct answer is D. $2,013.12.

Step-by-step explanation:

Since Erica took out a loan to buy her new motorcycle, and the purchase price of the motorcycle was $ 11349.00 plus 5% GST and 7% PST, and she pays $ 409.00 per month on her loan, which has a term of 3 years, for To determine how much more is she paying than the purchase price, the following calculation must be performed:

11,349 + (11349 x 0.12) = X

11,349 + 1,361.88 = X

12,710.88 = X

409 x 12 x 3 = X

4,908 x 3 = X

14.724 = X

14,724 - 12,710.88 = X

2,013.12 = X

Therefore, Erica is paying $ 2,013.12 more than the purchase price.

(HELP) A glass jar contains 5 red, 7 green, 9 blue and 11 yellow marbles. If a single marble is picked at random from the jar, what is the probability of it being a blue marble? *

1/11
5/18
9/32
5/12

Answers

Answer:

Find the volume of this prism.

Tony sold t-shirts and hats at the festival. He made a $4 profit for each t-shirt he sold. He also made a profit of $34 from selling hats. If he made a total profit of $106, how many t-shirts did he sell?

Answers

Answer:

18 T-shirts

Step-by-step explanation:

$4×18= $72 $72+$34=$106

18 t shirts

106 - 34 = 72
72 / 4 = 18

Oof, I'm to tired to remember how to do this T-T
Can anyone help asap? This is timed. Brainliest for best answer!!

Answers

Answer:

D

Step-by-step explanation:

Equation of the line

y - y1 = m(x - x1)

y - (-4) = 1/3 (x - 3)

y + 4 = 1/3x - 1

y = 1/3 x - 5

the graph that intercept y axis in -5 is the graph D

Answer:

i can't remember how to do this rn because its like 2:30am

C seems like most accurate answer, if this is wrong im really sorry :C

Step-by-step explanation:

A line's y-intercept is 1, and its slope is -5. What is its equation in
slope-intercept form?
help please

Answers

y=-5x+1

Slope intercept form is y=mx+b

m is slope and b is the y-intercept
y= -5x+1
As general equation of y-intercept is y=mx +b

Hope it helps!

In the system of equations , x represents .... ( please answer 12a and 12b )

Answers

Answer:

x = cost of each t-shirt

y = cost of each sweatshirt

Step-by-step explanation:

Given equation:

2x + 2y = 26 (1)

x + 3y = 33 (2)

From (2)

x = 33 - 3y

Substitute x = 33 - 3y into (1)

2x + 2y = 26 (1)

2(33 - 3y) + 2y = 26

66 - 6y + 2y = 26

- 6y + 2y = 26 - 66

-4y = -40

y = -40/-4

y = 10

Substitute y = 10 into (2)

x + 3y = 33 (2)

x + 3(10) = 33

x + 30 = 33

x = 33 - 30

x = 3

Where,

x = cost of each t-shirt = $3

y = cost of each sweatshirt = $10

pls help me answer this question and plsss do not send link

QUESTION:
The angled of a triangle are (x-40), (x-20), (1/2- 10), find x

Answers

Answer:

x=124.75

Step-by-step explanation:

Sum of angles of a triangle=180°

(x-40)+(x-20)+(1/2- 10)=180°

(x-40)+(x-20)+(−9.5)=180°

x-40+x-20−9.5=180°

x+x-40-20-9.5=180°

2x−69.5=180°

2x=180°+69.5

2x=249.5

2x/2=249.5/2

x=124.75

HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP ASAP

Answers

They are alternate Exteror angles and internet but as for the question they would be corresponding angles

Determine whether the parallelogram is a rhombus, rectangle, square, or none. Explain.
Q(1,5), R(3,8), S(5,5), T(3,2)
Help ASAP

Answers

QRST is a rhombus

Let’s look at the diagonals
Length QS = sr(4^2 + 0) = 4
Length RT = sr(0 + 6^2) = 6
This means it cannot be a square or rectangle as they both have equal length diagonals.

QS is horizontal (y values same)
RT is horizontal (x values same)
This means it is a rhombus because diagonals are perpendicular and different lengths.

Squares have perpendicular diagonals of same length
Rectangles have diagonals of same length but not perpendicular

Circle D is shown. Angles F A E, F D E, and F B E intercept arc F E. ∠FAE measures 72°. What other angle must measure 72°? ∠BFD ∠DEA ∠EDF ∠FBE

Answers

Answer:

Option D, ∠FBE

Step-by-step explanation:

The image for the question is attached herewith

Solution

As per the property of arc,  angles subtended by the same arc (chord) on the circumference of a circle have equal measures.

∠FAE is an angle subtended by the arc FE that touches the circle at point 'A'.

∠FBE is also subtended by the arc FE at the point 'B'.

Therefore, we must have

m∠FAE = m∠FBE.

Since, m∠FAE = 72°, so  m∠FBE = 72°.

Hence, option D, ∠FBE

Answer:

Its D

Step-by-step explanation:

Give him brainlest.

There are 120 students in class 7. It is known that
2/3
out of them like Maths, out of which 35
are girls. Also, out of total students,
3/5
are boys. (3)
(a) What is the number of girls in the class?
(b) How many students like Maths?
(c) How many boys like Maths?

Answers

Multiply total students by 2/3 to find how many like math:

Like math = 120 x 2/3 = 240/3 = 80 total students like math

Multiply total students by 3/5 to find number of boys:

120 x 3/5 = 360/5 = 72 boys

A) number of girls = total students - boys = 120 -72 = 48 girls

B) from above 80 students like math

C) number of boys that like math = number of students that like math minus girls that like math: 80- 35 = 35 boys like math

72 boys xjtxkttkftkxktx

The angle of elevation to a nearby tree from a point on the ground is measured to be
31°. How tall is the tree if the point on the ground is 62 feet from the tree? Round
your answer to the nearest tenth of a foot if necessary.

Answers

Answer:

37.3 ft

Step-by-step explanation:

tan A = opp/adj

tan 31° = x/62

x = 62 * tan 31°

x = 37.3 ft

The height of the tree is 37.25 ft if the point on the ground is 62 feet from the tree.

What is the right triangle?

A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.

Trigonometric ratios are used to demonstrate the connection between the sides and angles of a right-angled triangle.

Let h denote the tree if the point on the ground is 62 feet from the tree.

The angle of elevation = 31°. Hence:

tan 31° = h/62

h = 62 × tan 31°

h = 37.25 ft

Thus, the height of the tree is 37.25 ft if the point on the ground is 62 feet from the tree.

Learn more about the right triangle here:

https://brainly.com/question/11899922

#SPJ6

Em uma competição esportiva uma equipe ganhou 80 medalhas sendo que 25% de ouro 35% de prata e o restante de blusa e qual o número de medalhas de bronze que essa equipe ganhou

Answers

Answer:

32 medals

Step-by-step explanation:

Given that

The team wons 80 medals

out of which 25% is gold

35% is silver

and rest is bronze

we need to find out the number of bronze medals that win by the team

The total percentage is 100

So, the remaining percentage is

= 100 - 25 - 35

= 40%

So, the number of bronze medal should be

= 40% of 80 medals

= 32 medals

Solve for all values of x by factoring x² + 6x = 0

Answers

Answer:

Solution given;

x² + 6x = 0

taking x common

x(x+6)=0

either

x=0

or

x+6=0

x=-6

:.x=0 or -6.

Answer:

0 and -6

Step-by-step explanation:

Factor and find the zeros of the equation or graph the line to find the x-intercepts.

What is the solution of the equation x2 − 2x + 4 = 0?

Answers

Answer:

No real solution

Step-by-step explanation:

This leads to a square root of a negative number, which is not possible without imaginary numbers

somebody help me out asap

Answers

Answer:

the first one doesn't represent function

Step-by-step explanation:

in the domain, x can only be once.

Enriques bathroom measures 6 ft. Long by 5 ft. Wide His shower is 3 feet square The title he wants to buy for the floor is sold in square feet. What is the area of the floor that he has to title

Answers

Answer:

Area of the floor is 30 square ft.

Step-by-step explanation:

Length of the floor, L = 6 ft

width of the floor, W = 5 ft  

The floor is in the shape of rectangle.

The area of the rectangle is

A = Length x width

So, the area of the floor is

A = L x W

A = 6 x 5

A = 30 ft^2

What's the surface area of the pyramid?

Answers

The Answer is C    226.8 ft

I remember doing this not to long ago

I think the answer is C

To find the slope of the trend line below Reilly chose the points (1,80) and (2,30). explain whether the points she chose will help her write the correct equation of the line and find the equation of a trend line

Answers

Answer:

We can't see the graph

Step-by-step explanation:

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