Answer:
The values of [tex]a[/tex] and [tex]b[/tex] are [tex]33[/tex] and [tex]\frac{20\sqrt{3}}{3}[/tex], respectively.
Step-by-step explanation:
The statement is equivalent to the following mathematic expression:
[tex]\left(5 + 2\sqrt{2})^{2} = a + b\cdot \sqrt{6}[/tex] (1)
By definition of the perfect square trinomial:
[tex]25 + 20\cdot \sqrt{2} + 8 = a + b\cdot \sqrt{6}[/tex]
[tex]33 + 20\sqrt{2} = a + b\cdot \sqrt{6}[/tex]
And by direct comparison we have the following system:
[tex]a = 33[/tex] (2)
[tex]b\cdot \sqrt{6} = 20\sqrt{2}[/tex] (3)
By (3), we solve for [tex]b[/tex]:
[tex]b = \frac{20}{\sqrt{3}}[/tex]
[tex]b = \frac{20\sqrt{3}}{3}[/tex]
The values of [tex]a[/tex] and [tex]b[/tex] are [tex]33[/tex] and [tex]\frac{20\sqrt{3}}{3}[/tex], respectively.
Help needed to solve this
Given:
The expression is:
[tex]\dfrac{1}{a+b}+\dfrac{2a}{a^2+b^2}+\dfrac{4a^7+4a^3b^4}{b^8-a^8}[/tex]
To find:
The simplified form of the given expression
Solution:
Formula used:
[tex]x^2-y^2=(x-y)(x+y)[/tex]
We have,
[tex]\dfrac{1}{a+b}+\dfrac{2a}{a^2+b^2}+\dfrac{4a^7+4a^3b^4}{b^8-a^8}[/tex]
It can be written as:
[tex]=\dfrac{1}{a+b}+\dfrac{2a}{a^2+b^2}+\dfrac{4a^3(a^4+b^4)}{(b^4)^2-(a^4)^2}[/tex]
[tex]=\dfrac{1}{a+b}+\dfrac{2a}{a^2+b^2}+\dfrac{4a^3(a^4+b^4)}{(b^4-a^4)(b^4+a^4)}[/tex]
[tex]=\dfrac{1}{a+b}+\dfrac{2a}{a^2+b^2}+\dfrac{4a^3}{(b^2-a^2)(b^2+a^2)}[/tex]
[tex]=\dfrac{1}{a+b}+\dfrac{2a}{a^2+b^2}+\dfrac{4a^3}{(b-a)(b+a)(b^2+a^2)}[/tex]
Taking LCM, we get
[tex]=\dfrac{1(b-a)(b^2+a^2)+2a(b-a)(b+a)+4a^3}{(b-a)(b+a)(b^2+a^2)}[/tex]
[tex]=\dfrac{b^3+a^2b-ab^2-a^3+2a(b^2-a^2)+4a^3}{(b-a)(b+a)(b^2+a^2)}[/tex]
[tex]=\dfrac{b^3+a^2b-ab^2-a^3+2ab^2-2a^3+4a^3}{(b-a)(b+a)(b^2+a^2)}[/tex]
[tex]=\dfrac{b^3+a^2b+ab^2+a^3}{(b-a)(b+a)(b^2+a^2)}[/tex]
Using the grouping method factories the numerator.
[tex]=\dfrac{b(b^2+a^2)+a(b^2+a^2)}{(b-a)(b+a)(b^2+a^2)}[/tex]
[tex]=\dfrac{(b+a)(b^2+a^2)}{(b-a)(b+a)(b^2+a^2)}[/tex]
Cancel out the common factors.
[tex]=\dfrac{1}{b-a}[/tex]
Therefore, the value of the given expression is [tex]\dfrac{1}{b-a}[/tex].
1 tàu hỏa đi từ A đến B với quãng đường là 40km . Khi đi đến B , tàu dừng lại 20 phút rồi đi tiếp 30km đến C với vận tốc lớn hơn vận tốc khi đi từ A đến B là 5km/h . Tính vận tốc của tàu khi đi trên quãng đường AB . Biết thời gian kể từ khi tài xuất phát từ A đến khi tới C hết tất cả 2gio
Answer:
The speed from A to B is 40 km/h.
Step-by-step explanation:
Distance from A to B = 40 km
Distance from B to C = 30 km
Speed from A to B is v km/h
Speed fro B to C is v + 5 .
total time, t = 2 hours
Stopping time at B = 20 minutes
Let the time from A to B is t'.
[tex]t'=\frac{40}{v}[/tex]
Let the time from B to C is t''.
[tex]t''= \frac{30}{v+5}[/tex]
The total time is
[tex]\frac{40}{v}+\frac{30}{v+5}+\frac{20}{60}=2\\\\\frac{40 v + 200 + 30 v}{v^2 + 5 v}=\frac{10}{6}\\\\420 v + 1200 = 10 v^2 + 50 v\\\\10 v^2 -370 v - 1200 = 0 \\\\v^2 - 37v - 120 = 0 \\\\v^2 - 40 v + 3 v - 120 = 0 \\\\v(v - 40) + 3 (v - 40) = 0\\\\(v - 4)(v + 3) = 0\\\\v = 40 km/h or - 3 km/h[/tex]
Speed cannot be negative so the speed from A to B is 450 km/h.
The figure shows ∆ABC with m∠ABC = 90°.
The first 10 steps to prove that AB2 + BC2 = AC2 are given in the table. Match the remaining steps to their correct sequence in the proof.
Statement Reason
1. Draw . construction
2. ∠ABC ≅ ∠BDC Angles with the same measure are congruent.
4. ∠BCA ≅ ∠DCB Reflexive Property of Congruence
4. AA criterion for similarity
5. Corresponding sides of similar triangles are proportional.
6. BC2 = AC × DC cross multiplication
7. ∠ABC ≅ ∠ADB Angles with the same measure are congruent.
8. ∠BAC ≅ ∠DAB Reflexive Property of Congruence
9. AA criterion for similarity
10. Corresponding sides of similar triangles are proportional.
11.
12.
13.
14.
15.
AB2 + BC2 = AC2
Reason: multiplication
AB2 + BC2 = AC × AC
Reason: segment addition
AB2 = AC × AD
Reason: cross multiplication
AB2 + BC2 = AC(AD + DC)
Reason: Distributive Property
AB2 + BC2 = AC × AD + AC × DC
Reason: addition
11
arrowBoth
12
arrowBoth
13
arrowBoth
14
arrowBoth
15
arrowBoth
Answer:
Hello,
Please, see the attached file.
Thanks.
Step-by-step explanation:
The remaining steps can be ∆ABC ∼ ∆DBA AA criterion for similarity Corresponding sides of similar triangles are proportional, AB/AC = AD/AB, and AB2 = AC × AD.
What is triangle?Triangles are closed two-dimensional geometric figures with three straight sides and three angles. The sum of the three angles in any triangle is always 180 degrees.
The first 10 steps to prove that AB2 + BC2 = AC2 are given in the table. The remaining steps to their correct sequence in the proof are:
Draw . construction∠ABC ≅ ∠BDC Angles with the same measure are congruent.∠BCA ≅ ∠DCB Reflexive Property of CongruenceAA criterion for similarityCorresponding sides of similar triangles are proportional.BC2 = AC × DC cross multiplication∠ABC ≅ ∠ADB Angles with the same measure are congruent.∠BAC ≅ ∠DAB Reflexive Property of CongruenceAA criterion for similarityCorresponding sides of similar triangles are proportional.∆ABC ∼ ∆DBA AA criterion for similarityCorresponding sides of similar triangles are proportional.AB/AC = AD/AB Reason: corresponding sides of similar triangles are proportionalAB2 = AC × AD Reason: cross multiplicationThese steps follow logically from the previous statements in the proof. In step 11, the Pythagorean Theorem is applied to the right triangle ADB.
Thus, this can be the match for the given scenario.
For more details regarding triangles, visit:
https://brainly.com/question/2773823
#SPJ7
lisa had wood that was 12 1/2 feet long. she cut it into 5 pieces that are equal in leangth.how long is each piece of wood?
Answer:
2 1/2
Step-by-step explanation:
divide in 5 then divide half in 5 also
Answer:
2,5
Step-by-step explanation:
The length of a piece of wood is:
12 ½ : 5 = 5/2 = 2,5
1. A square is lengthened by 6 units in one direction and by 5 units in the other
direction to make a rectangle, as shown in the diagram. The length of the side
of the original square is x units. What is the area of the whole new rectangle?
Answer:
a = x² + 11x + 30
Step-by-step explanation:
a = (x + 5)(x + 6)
multiply each term in the first set of parenthesis by each term in the second
a = x(x + 6) + 5(x + 6)
a = (x² + 6x) + (5x + 30)
combine like terms
a = x² + 11x + 30
MARKING BRAINLIEST HELP
Answer:
i think A
Step-by-step explanation:
sorry if im wrong
A squirrel moved 200 meters in 7,200 seconds. What was the speed of the squirrel in meters per hour? *
Answer:
100 meters per hour.
Step-by-step explanation:
7,200 seconds / 60 = 120 minutes
120 minutes / 60 = 2 hours
200 meters / 2 hours = 100 meters
Since the squirrel moved 200 meters in 2 hours, the squirrel moved 100 metres per hour.
Please help me only serious answers ☺️
Answer:
Parallelogram
Result
Area = b × h
= 5.5 × 11
= 60.5 feet260.5 cm²What is 13 divided by 1/4?
Explain how you got your answer.
Answer:
52
Step-by-step explanation:
13 divide 1/4 is the equivilent to 13 x 4
Answer:
52
Step-by-step explanation:
13/(1/4)
when a fraction is in the denominator you inverse the fraction and multiple by the numerator
so it would be 13*(4/1) = 13*4 = 52
Which of the following will form the composite function G(F(x)) shown
below?
G(F(x)) = 7x^4-2x^2-1
Answer:
F(x)=x^2 and G(x)=7x^2-2x-1
Step-by-step explanation:
I have to fill in characters for the step by step explanation so have fun reading the following Junk. KEEp wasting your time Dummy with
HELP PLEASE
Work out the size of angle x.
Answer: its 180 , because it dont matter if its up or side .
Answer:
13°
Step-by-step explanation:
the lines are parallel so
the angle above 85° is also 85° (vertical angles)the other angle in the triangle is 82° (180 - 98)82 + 85 = 167
167 - 180 = 13
x = 13°
Can someone helps mezzzz
PLS ANSWER ASAP. ILL GIVE BRAINLIEST. I don’t understand how to do this and need help. It’s due in 10 minutes.
Triangle 1 is a right triangle with one side length of H inches. Triangle 2 is similar to triangle 1 and has one side length of 18 inches. Sketch a possible example of triangle 1 and triangle 2 and label all side lengths.
Answer:162 might be wrong tho so dont mark as brainlyest
Step-by-step explanation:
Question 15 of 43
A bag of marbles has 12 red, 7 yellow, 5 blue and 1 white. Find the probability
of selecting 4 marbles from the bag where all 4 are red.
9
A.
o
B.
1
C.
75900
o
D.
Answer:
Option A
Step-by-step explanation:
[tex] \frac{12}{25} \times \frac{11}{24} \times \frac{10}{23} \times \frac{9}{22} [/tex]
we start with 12 red marbles out of 25 marbles, that's the probability for the first.
in the second step we have one red marble less, wich also means one marble less overall
and so on
[tex] \frac{12 \times 11 \times 10 \times 9}{25 \times 24 \times 23 \times 22} [/tex]
[tex] = \frac{11880}{303600} [/tex]
can be reduced by 1320 (step by step) to
[tex] \frac{9}{230} [/tex]
A woman is trying to remove holiday decorations from the roof of her house by climbing a ladder. The height of her house is 24 feet, and the distance she has to travel on the ladder is 30 ft. How far away is the ladder from the house?
Answer:
18 ft
Step-by-step explanation:
We are to determine the base given the hypotenuse and length.
The Pythagoras theorem : a² + b² = c²
where a = length
b = base
c = hypotenuse
30² = 24² + b²
900 = 576 + b²
b² = 900 - 576
b² = 324
square root = 18
The graph shown below represents the rate at which water drains from a tank once the drain is opened which statement correctly describes the graph
A. The water is draining at constant rate of 1/2 gallon per minute, and the tank contained exactly 14 gallons when the drain opened
B. The water is draining at a constant rate of 2 gallons per minute,and the tank contained exactly 14 gallons when the drain was opened
C. The water is draining at a constant rate of 5 gallons per minute, and the tank contained exactly 14 gallons when the drain was opened
D.the water is draining at a constant rate of 14 gallons per minute, and the tank contained exactly 1/2 gallon when the drain was opened
Answer:
A
Step-by-step explanation:
The slope is -1/2 and the y-intercept is 14
You want to estimate the number of students in your school who support extra funding for the history club. You survey every ninth student who enters the
school.
Determine whether the sample is based or unbiased
Answer:
unbiased
Step-by-step explanation:
it would be biased if you lets say survey the history club kids
Solve for x.
A. 9
B. 42
C. 10
D. 12
⭐Answer:
✰According to angle property between tangent and secant✰
[tex](4x-8)=1/2(80)[/tex]
[tex]4x-8=40[/tex]
[tex]4x=40+8[/tex]
[tex]4x=48[/tex]
[tex]x=48/4[/tex]
[tex]x=12[/tex]
〖D) 12〗
☁☁☁☁☁☁☁
hope it helps...
The value of x is 12
What is Tangent and Secant Properties of a Circle?Circle is the collection of all points in a plane at a constant distance from a fixed point. The fixed point is known as the centre, and the constant distance is the circle’s radius. A line that intersects a circle in two distinct points is called a secant to the circle.
A line meeting a circle only in one point is called a tangent to the circle at that point. In this article, we will talk about the relative position of the circle and a line in the same plane. We will also examine the existence of tangents to a circle and their properties.
Using angle property between tangent and secant
(4x - 8) = 1/2*80
4x- 8 = 40
4x= 48
x= 12
Learn more about tangent here:
https://brainly.com/question/19064965
#SPJ5
Help me please Help me please Help me please
Answer:
[tex]y = x + 7[/tex]
Step-by-step explanation:
[tex]y = gx + c[/tex]
[tex]gradient = \frac{y}{x} = \frac{1}{1} = 1[/tex]
[tex]where \: the \: line \: meet \: the \: y-axis = 7[/tex]
how to find the constant of proportionality on a graph
Can someone please help me with this I’m stuck on it
Answer:
B and C. if you got them wrong let me know :3
bill changes £450 from his bank to $729 what exchange rate did he get?
Answer:
$1.62
Step-by-step explanation:
Find the measure of the major arc
Answer:
Step-by-step explanation:
If the minor arc is 133, the major arc is going to be
Major arc = 360 - Minor arc
Minor arc = 133
Major arc = 360 - 133
Major arc = 227
Does this make sense? It should. If you put a line from C to A then extend it until it hit the circumference, you would get a diameter which is a 180o angle. The major arc through D is greater than 180. So 227 is a reasonable answer.
PLEASE HELP MEE pleaseee
Answer:
x = 15 and y = 7
Step-by-step explanation:
x = 2y + 1
x + y - 8 = 14
Let's substitute the value of x in the second equation:
(2y + 1) + y - 8 = 14
3y -7 = 14
3y = 14 + 7
3y = 21
y = 21/3
y = 7
And now you substitute the value of y in the first equation:
x = 2•7 + 1
x = 14 + 1
x = 15
Factor the algebraic expression: 28a + 12
Answer:
hope it is helpful to you
Answer:
4(7a+3)
Step-by-step explanation:
28a+12
take common
4 is the common number for both the terms because it divides 28 and 12 exactly.
4(7a+3)
Which is an equation of the inverse of y=3/2x?
Answer:
y
=
3
2
x
Rewrite in slope-intercept form.
Tap for more steps...
y
=
3
2
x
Use the slope-intercept form to find the slope and y-intercept.
Tap for more steps...
Slope:
3
2
y-intercept:
(
0
,
0
)
Any line can be graphed using two points. Select two
x
values, and plug them into the equation to find the corresponding
y
values.
Tap for more steps...
x
y
0
0
2
3
Graph the line using the slope and the y-intercept, or the points.
Slope:
3
2
y-intercept:
(
0
,
0
)
x
y
0
0
2
3
image of graph
Step-by-step explanation:
PLEASE HELP ME!! this is due tonight and i really need help with this so i can do other assignments
explaining your answer = brainliest/ five stars
the area of this square = ___ cm
Answer:
64cm² I think :) if u get it wrong dont blame it on me.
Answer:
64 cm^2
Step-by-step explanation:
The area of a square can be calculated by A = s^2 (Area = side squared aka the side multiplied by itself)
A = s^2
= 8^2 (8 x 8)
= 64 cm^2
True or False: A method of creating a geometric figure that is mathematically precise by using a compass and
straightedge is called drawing or copying.
Answer:
True
Step-by-step explanation:
I have to write more but its true
What is the value of x in the solution to the system of equations shown???
-7
1.6
2.4
4
Answer:
x = 4
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Solving systems of equations using substitution/eliminationStep-by-step explanation:
Step 1: Define Systems
7x + y = 14
-2x - y = 6
Step 2: Solve for x
Elimination
Combine 2 equations: 5x = 20[Division Property of Equality] Divide 5 on both sides: x = 4I NEED HELP WITH THIS PLEASE ITS DUE TONIGHT
==========================================
Work Shown:
(tangent)^2 = (whole secant)*(external secant)
(TU)^2 = (RT)*(ST)
(TU)^2 = (RS+ST)*(ST)
(TU)^2 = (8+4)*(4)
(TU)^2 = 48
TU = sqrt(48)
TU = 6.928203
TU = 6.9
For more info, you can search out "secant tangent chord", or something similar, and you should get to a page that describes the formula of what's going on here. This should match up fairly similarly to what lesson 3.09 is talking about.
Answer: 9.8
TU^2= TS x TR
TU^2= 8 x 12
TU= sqrt(96) = 9.79