Answer:
lhs = (5+2√3)/(7+4√3)
= [(5+2√3)(7-4√3)]/[(7-4√3)(7+4√3)]
=[35-20√3+14√3-24]/[7²-(4√3)²]
=[11-6√3]/[49-48]
=11-6√3
therefore
11-6√3 = a+b√3
compare both sides
a= 11, b= -6
Step-by-step explanation:
Hope this answer helps you :)
Have a great day
Mark brainliest
Answer:
a = 11, b = 6
Step-by-step explanation:
Given
[tex]\frac{5+2\sqrt{3} }{7+4\sqrt{3} }[/tex]
Rationalise the denominator by multiplying numerator/ denominator by the conjugate of the denominator.
The conjugate of 7 + 4[tex]\sqrt{3}[/tex] is 7 - 4[tex]\sqrt{3}[/tex]
= [tex]\frac{(5+2\sqrt{3})(7-4\sqrt{3}) }{(7+4\sqrt{3})(7-4\sqrt{3} }[/tex] ← expand numerator/ denominator using FOIL
= [tex]\frac{35-20\sqrt{3}+14\sqrt{3}-24 }{49-28\sqrt{3}+28\sqrt{3}-48 }[/tex]
= [tex]\frac{11-6\sqrt{3} }{1}[/tex]
= 11 - 6[tex]\sqrt{3}[/tex]
with a = 11 and b = 6
Help pls it easy for everyone, i need it before 20 mins plss
A 25-degree angle is an __ angle. which angle
A. obtuse
B. triangle
C. acute
D. straight
Please show the steps. and the answer
Answer:
$321562.50
Step-by-step explanation:
Exponential growth can be modeled by the formula [tex]y = a(1+r)^{x}[/tex] , with y representing the final value, a being the starting value, r being the growth rate, and x being the number of time intervals passed.
To figure out the rate, we must use the values given from the months we have data of. Our starting value is 60,000 , ending value is 105,000 , and given that monthly sales are given, we can assume that sales grew exponentially each month. There were 4 years, or 48 months, that the store had to grow. Our formula is thus
[tex]105000 = 60000(1+r)^{48}\\[/tex]
To solve for r, we can first divide both sides by 60,000 , then put each side to the power of 1/48, resulting in
[tex]105000/60000 = (1+r)^{48}\\1.75 = (1+r)^{48}\\\\1.75^{1/48} = 1+r[/tex]
Since we know our rate, and there are 8 years/96 months between January 2005 and January 2013, we can make our starting value 105,000 , plug (1.75)^(1/48) for r and 96 for x in [tex]y = a(1+r)^{x}[/tex], and go from there.
Our final value is then
[tex]y = 105000(1.75^{1/48})^{96}\\y = 105000(1.75^{2})\\y = 321562.5[/tex]. We were able to turn 1.75^(1/48)^(96) into 1.75² using the exponent rule stating that x^y^z = x^(y*z)
Use the discriminant to determine how many and what
kind of solutions the quadratic equation x2 - x = 1/4
has.
Answer:
Step-by-step explanation:
x²-x-1/4=0
or 4x²-4x-1=0
disc.=(-4)²-4(4)(-1)=16+16=32>0 ,not a perfect square.
Roots are real,different and irrational.
It has 2 roots or 2 solutions.
Answer:
Step-by-step explanation:
x² - x = 1/4
[tex]x^{2}-x -\frac{1}{4}=0\\\\a = 1 \\\\b = -1\\\\c = \frac{-1}{4}\\\\D = b^{2}-4ac\\\\ = (-1)^{2}-4*1*\frac{-1}{4}\\\\= 1 + 1\\= 2[/tex]
D = 2 > 0
So, this equation has real roots
find the area D (1,3) F (-4,-3) E (4, -3)
Answer:
Step-by-step explanation:
FE=4+4=8
Altitude=3+3=6
area=1/2×FE×6=1/2×8×6=24 sq. units.
or
area=1/2×
I 1 3|
|-4 -3|
| 4 -3|
| 1 3|
=1/2[(-3+12)+(12+12)+(12+3)]
=1/2[9+24+15]
=1/2[48]
=24 sq. units
Find the values of x and y. State with postulate/theorem you used.
I'M FROM THE PHILIPPINES;)
help please asap just the answers
Answer:
"2"
(9-2-3)/2
4/2
2
Step-by-step explanation:
Tami spins a spinner with 7 sections. The sections are numbered 1 through 7 and all sections are the same size
Answer:
1 / 7
Step-by-step explanation:
Number of sections on spinner = 7
Section is numbered 1 to 7
Since the probability of landing on each section is the same:
Probability that spinner lands on 4 :
Probability, p = Required outcome / Total possible outcomes
Required outcome = landing on 4 = 1
Total possible outcomes = (1 to 7) = 7
P(landing on 4) = 1 /7
Find the missing side of the triangle and leave the answer in simplest radical form.
Answer:
x = [tex]\sqrt5[/tex]
Step-by-step explanation:
Using Pythagoras theorem,
Square of longer side = Sum of square of other sides .
Therefore,
[tex](\sqrt{11})^2 = x^2 + (\sqrt{6})^2\\\\11 = x^2 + 6\\\\11 - 6 = x^2\\\\5 = x^2\\\\x = \sqrt 5[/tex]
Answer:
x = √5.
Step-by-step explanation:
By Pythagoras:
x^2 = (√11)^2 - (√6)^2
x^2 = 11 - 6 = 5
x = √5.
Which of the following is the best definition of the domain of a relation?
A. The set of all allowable input values, or values
B. The set of all allowable output values, or y-values
c. The set of all allowable input values, or x-values
D. The set of all allowable output values or values
Answer:
C. The set of all allowable input values, or x-values
Step-by-step explanation:
The domain is the input values, x, and the range is the output values, y, in a relation or function.
Find sin X, sin Z, cos X, and cos Z. Write each answer as a simplified fraction.
Answer:
Find the answers below
Step-by-step explanation:
Using m<X as the reference angle
Opposite YZ = 7
Adjacent XY = 10
Hypotenuse XZ = √149
Using the SOH CAH TOA identity
sinX = opp/hyp
sinX =YZ/XZ
sinX = 7/√149
For cos X
cos X = adj/hyp
cos X =10/√149
Using m<Z as reference angle;
Opposite XY = 10
Adjacent YZ = 7
Hypotenuse XZ = √149
Using the SOH CAH TOA identity
sinZ = opp/hyp
sinZ =10/√149
sinZ = 7/√149
For cos Z
cosZ = 7/√149
There are 2 mystery books, 2 romance books, 2 poetry books to be randomly placed on a shelf. What is the
probability that the mystery books are next to each other, the romance books are next to each other, and the
poetry books are next to each other? (For example, MMRRPP).
Answer:
there would be a 2 out of 6 chance i think
Step-by-step explanation:
7. A gym is offering a deal to members. Customers can sign up by paying a
registration fee of $100 and $28 per month. The function that models this
situation is c(m) = 28m + 100, where m is the number of months and c(m) is
the cost of becoming a member.
Answer:
I dont know
Step-by-step explanation:
Last question math please help
Help please I would really appreciate it thank you so much
Answer:
12 in the first blank
20 in the second one
Step-by-step explanation:
12 because it is 8+4
20 because it is 60/3
Plz help, its due soon!! Ill give brainliest
Express it in slope-intercept form.
Answer:
y = 1/2x -1
The slope is increasing by 2/4, which can be reduced to 1/2. You can find this by doing rise over run.
The y intercept is -1
minus 15 over minus 4
Answer:
3.75
Step-by-step explanation:
Hey guys I need help again please.. it’s question number 5
Simplify the expression 2* = 210.
Answer:
1/64
Step-by-step explanation:
When dividing numbers with exponential values (that have the same base), you subtract the exponential values. 4 - 10 is -6, so the answer would be 2^-6. However, that is not simplified yet. If the exponent is negative, the expression turns into a fraction. 1/2^6 can also be written as 1/64, which is the final answer.
Given f(x) and g(x) = k-f(x), use the graph to determine the value of k.
f(x)
g(x)
A. -5
B. -1/5
C. 1/5
D. 5
===========================================================
Explanation:
The point (-2,2) is on the red f(x) line. This point is marked in black.
It corresponds to the point (-2,-10) on the g(x) blue line.
The point (-2,2) moves to (-2,-10). The x coordinate stays at x = -2. The y coordinate has gone from y = 2 to y = -10. This is a jump of "times negative 5".
-5*2 = -10
So we see that k = -5
Saying g(x) = k*f(x) is the same as g(x) = -5*f(x)
Recall that y = f(x), so saying -5*f(x) is really saying "whatever the y coordinate is on f(x), multiply it by -5 to get the corresponding y coordinate on g(x)".
Answer:
-5
y = -x + 4 (red)
y=5x -20 (blue)
-5*(-x+4) = 5x-20
Step-by-step explanation:
if f( x )3 X + 4 and g(x)= X + 1 find the value of x given that F - 1g( x) = 2
Answer:
The answer for the question is -1.5
find the area of this figure 15ft 10ft 10ft 5
Answer:
150 feet2 50 feet I hope this helps!
Step-by-step explanation:
HELLPPPPPP PLEASEEE!!!
Answer:
Step-by-step explanation:
The first term is 2
Therefor t₁ = 2
Each aditional term is 5 times the previous term
That's the second choice
What is the circumference of a circle with a diameter of 12 feet? (use 3.14 for pi)
36 ft.
37.68 ft.
36.26 ft.
38 ft.
Answer:
37.68ft
Step-by-step explanation:
Answer:
37.68 ft
Step-by-step explanation:
The circumference of a circle is given by
C = pi *d where d is the diameter
C = 3.14 * 12
C =37.68 ft
323323332222222222222222222
Answer:
Step-by-step explanation:there are 4 spaces between each whole number so each line is 1/4 of a whole.
A is 1 space away from 0 so it is 1/4
B is 2 spaces below 0 so is -1/2
3. Điền tiếp vào dãy số:
a. 0; 1; 4 ;9 ;16 ;25 ;36 ;49 ; …
b. 1; 1; 3; 15; 105; …
c. 0; 100; 6; 94; 12; 88; 18; 82; …….; ……
d. 72496 đối với 1315 62134 đối với 97
85316 đối với 167 28439 đối với ……
Answer:
D hope this kinda helped:)
Step-by-step explanation:
x/3 -6 =y
Solve for x
Answer:
x= 3(y+6) or x = 3y + 18
Step-by-step explanation:
get the "x" by itself.
so first +6 on both sides of the equation to make it x/3=y+6
then multiply both sides by 3 to make it x=(y+6)*3
What is the solution to the equation x/3 = 9 x=
Answer:
x = 27
Step-by-step explanation:
x/3 = 9
Multiply both sides by 3
x/3 * 3 ( the 3's cancel out and we're left with x )
9 * 3 = 27
We're left with x = 27
Answer:
27
Step-by-step explanation:
[tex]\frac{x}{3} =9\\\\\\[/tex]
In order to solve for x, we need to undo the operations. Because x is being divided, we need to multiply both sides by the same number that x is being divided by to find x.
[tex]\frac{x}{3} (3)=9(3)\\x=27[/tex]
How do I solve this? (3^0y)^2x2(xy)^0
Answer:
(y ^2 ) (x ^2)
Step-by-step explanation:
Two of the volleyball team’s coaches and three of the players’ parents would like to
make speeches during the fundraiser. The principal wants the total time for speeches
to be under 30 minutes. Explain how to write an inequality to find the possible average
length of each speech.
Answer:
5x < 30
Step-by-step explanation:
coaches = 2x
parents = 3x
total time = under 30 mins
2x + 3x < 30
5x < 30
x < 6
Answer:
Sample response: Choose a variable to represent the average speech length. If x is the variable, then the inequality would be (2+3)x < 30,="" or="">x < 30. The 2 + 3, or 5, represents the total number of people making speeches. Each one would last an average of x minutes, so we want the product of x and (2+3) to be less than 30, the time limit set by the principal.
For those who wanted the sample response.