find the value of a and b if [tex]5+√3/7+2√3=a-b√3[/tex]

Answers

Answer 1

Answer:

The values of [tex]a[/tex] and [tex]b[/tex] are [tex]5[/tex] and [tex]-\frac{15}{7}[/tex], respectively.

Step-by-step explanation:

There are mistakes in the statement, correct form is presented below:

[tex]5+\frac{\sqrt{3}}{7} + 2\sqrt{3} = a - b\cdot \sqrt{3}[/tex].

By direct comparison we have the following system of equations:

[tex]a = 5[/tex] (1)

[tex]\frac{\sqrt{3}}{7}+2\sqrt{3} = -b\cdot \sqrt{3}[/tex] (2)

In (2) we solve for [tex]b[/tex]:

[tex]\left(\frac{1}{7}+2 \right)\cdot \sqrt{3} = -b\cdot \sqrt{3}[/tex]

[tex]b = -\frac{15}{7}[/tex]

The values of [tex]a[/tex] and [tex]b[/tex] are [tex]5[/tex] and [tex]-\frac{15}{7}[/tex], respectively.


Related Questions

a particle P moves in a straight line such that, t s after leaving a point O, its velocity v ms^-1 is given by v=36t - 3t^2 for t>_ 0
1) find the value of t when the velocity of P stops increasing
2)find the value of t when P comes to instaneous rest
3) find the distance of P from O when P is at instaneous rest
4) find the speed of P when P is again at O​

Answers

Answer:

jajjskslslskjsjxjj k k

Do the activity please it's trigonometry ​

Answers

Answer:

SinA=k/g

cotA=k/j

secA=g/j

cosecB=g/k

tanB=l/k

cosB=k/g

The perimeter of a rectangular park is 300 feet. The length of the park is 10 feet longer than the width.
Find the length of the park.
What is the length of the park?
feet=?​

Answers

Answer:

80 ft

Step-by-step explanation:

width = w

length = w+10

Perimeter of a rectangle

P = 2(l+w)

300 = 2(w+10+w)

300 = 2(2w+10)

Divide by 2

300/2 = 2/2(2w+10)

150 = 2w+10

Subtract 10

150-10 = 2w+10-10

140 = 2w

Divide by 2

140/2 = 2w/2

70 = w

l = w+10

l = 70+10

w = 80

rule. L1
b)
I
R = (24, 28)
S = (4, 20)
Q = (28, 12)
P = 8,4)
R' = (36, 4)
S = (16,-4)
*Q' = (40, -12)
P' = (20, -20)
Determine the transformation rule for the translation
from PQRS to P'QʻR'S'

Answers

Answer:

(x+12, y-24)

Step-by-step explanation:

The rule is (x, y) -> (x+12, y-24)

what is (-5x-3y) - (-x-3z)

Answers

Answer:

-4x-3y+3z

Step-by-step explanation:

(-5x-3y)-(-x-3z)

-5x+x-3y+3z

-4x-3y+3z

Choose the graph below that represents the following system of inequalities: y is greater than and equal -3x + 1 and y is greater than and equal 1/2x + 3

Answers

Answer:

Step-by-step explanation:

Choose the graph below that represents the following system of inequalities: y is greater than and equal -3x + 1 and y is greater than and equal 1/2x + 3

O 131 If cos 23°=P, express without the use of a calculator the following in terms of p.
Cos203°​

Answers

Answer:

cos203° = - p

Step-by-step explanation:

Using the addition formula for cosine

cos(a + b) = cosacosb - sinasinb

cos203°

= cos(180 + 23)

= cos180°cos23° - sin180°sin23°

= cos180°. p - 0

= - 1 . p

= - p

The figure below is a square. Find the length of side x in simplest radical form with a rational denominator.

Answers

9514 1404 393

Answer:

  x = (√2)/2

Step-by-step explanation:

The diagonal is √2 times the side length (x), so ...

  1 = x√2

  √2 = 2x . . . . . multiply by √2

  (√2)/2 = x . . . . divide by 2

The side length x is (√2)/2.

10. A moving van company charges a fee of 35.00 dollars for the truck rental and 25 cents for every mile the truck travels from the loading location. Let y be the cost in dollars for using the truck for x miles. Write the slope-intercept form of the equation.

Answers

Answer:

y=0.25x+35

Step-by-step explanation:

if the truck doesn't have to travel at all, it costs $35 for the loading fee, so the y-intercept is (0, 35). As x increases by 1, y increases by 0.25, so the slope is 0.25. Therefore, the equation is y=0.25x+35

Answer:

y = .25 x + 35

Step-by-step explanation:

Total cost = cost per mile * number of miles * flat fee

y be the cost in dollars

x = miles

y = .25 x + 35

Slope intercept form is y = mx+b where m is the slope and b is the y intercept

Kevin says that lines p and m will eventually intersect. Lines A and B intersect. Plane A contains lines p, m, and n. Line n is horizontal on the plane. Lines p and m are both going in the same direction and are identical. Plane B contains vertical line l which forms a right angle with line n. Is Kevin correct?

Answers

Answer:

No, because they are parallel.

Step-by-step explanation:

The lines [tex]p[/tex] and [tex]m[/tex] will not intersect, so Kevin is not correct.

It is given that planes A and B intersects. The plane A contains the line p, m and n on its plane. The lines p and m are parallel to each other. They are identical and move in the same direction.

Since the line p and m are parallel, they will not meet each other at any point because parallel lines does not intersect or meet at a point, they run parallelly along each other.

So, line p and m will not intersect.

Thus the answer is " No, because they are parallel."

Answer:

Step-by-step explanation:

no, because they are parrallel.

9. The ticket at right has a perimeter of 42 cm.
a) Calculate the unknown side length.
A = 42 - 11 x 2 = 20 / 4 = 5
b) Olivia wishes to decorate the ticket by placing a
gold line along the slanted sides. How long is the line on each ticket?
A =
c) A bottle of gold ink will supply enough ink to draw 20 m of line. How many bottles of ink should be purchased if 200 tickets are to be decorated?
A =

Answers

Perimeter simply represents the sum of all side lengths of a shape. The length of the missing side of the ticket is 5 cm; the length of gold line on each ticket is 20 cm, and 2 bottles of gold ink are required to draw gold lines on 200 tickets.

I've added the image of the ticket as an attachment.

(a) The missing side length

From the attachment, the 4 unknown side lengths are equal. Represent this side length with L.

So, we have:

[tex]Perimeter =2\times 11 + 4 \times L[/tex]

This gives

[tex]2\times11 + 4 \times L = 42[/tex]

[tex]22 + 4 \times L = 42[/tex]

Collect like terms

[tex]4 \times L = 42-22[/tex]

[tex]4 \times L = 20[/tex]

Divide both sides by 4

[tex]L =5cm[/tex]

(b) The length of the gold lines

There are 4 slant lines and the length of one of the slant lines is 5 cm (as calculated above).

So, the length of the gold line is:

[tex]Gold = 4 \times L[/tex]

[tex]Gold = 4 \times 5cm[/tex]

[tex]Gold = 20cm[/tex]

(c) The number of gold ink bottles.

[tex]n = 200[/tex] --- number of tickets

The length of all gold line in the 200 tickets is:

[tex]Length = 200 \times Gold[/tex]

[tex]Length = 200 \times 20cm[/tex]

[tex]Length = 4000 cm[/tex]

[tex]Length = 4000 \times 0.01m[/tex] ---- convert to meters

[tex]Length = 40m[/tex]

Given that:

[tex]Bottle = 20m[/tex] --- 1 bottle for 20 m

The number of bottles (n) is:

[tex]n = \frac{Length}{Bottles}[/tex]

[tex]n = \frac{40m}{20m}[/tex]

[tex]n = 2[/tex]

Hence, 2 bottles of gold ink are enough.

Read more about perimeters at:

https://brainly.com/question/6465134

-2x + 8 = -26
plz help!!!!!!!!!!!!!​

Answers

Answer:

x = 17

Step-by-step explanation:

-2x + 8 = -26

Subtract 8 from each side

-2x + 8-8 = -26-8

-2x = -34

Divide each side by -2

-2x/-2 = -34/-2

x = 17

Answer:

The answer is x=17

Step-by-step explanation:

−2x+8−8=−26−8

−2x=−34

−2x /−2 = −34 /−2

x=17

PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!!
Generally, the ________ the sample, the more accurately it describes the population.
A. closer
B. better
C. smaller
D. larger

Answers

Answer:

The correct answer of this question is( larger)

may this answer is helpful for you

The correct answer is D

- 100
-V4
L.A.1
ints
3. What is the simplest form of
a. -51
b. 25i
c. -251
d. 5i

Answers

Answer:

- 5i

Step-by-step explanation:

sqrt(-100) / -sqrt(4)

We know that  sqrt(a) / sqrt(b) = sqrt(a/b)

- sqrt(-100/4)

- sqrt(-25)

We know that sqrt(ab) = sqrt(a) sqrt(b)

- sqrt(25) sqrt(-1)

We know sqrt(-1) = i

Taking the principle value of sqrt(25)

- 5i

after 2 years the population of a town will be 33620 at the population growth rate of 2.5% pa find the present population of the town.​

Answers

Answer:

Step-by-step explanation:

The standard form of an exponential equation is [tex]y=a(b)^x[/tex] where y is the final count of the population after some time, x, goes by; a is the initial or starting amount of people (our unknown), and b is the growth rate. For us, y is 33620, the time is x = 2 years, and the growth rate is .025; but if we are growing we are expanding on the amount that we started with, so b = 100% + 2.5% = 102.5% and in decimal form, 1.025.

[tex]33620=a(1.025)^2\\33620=1.050625a[/tex] so

a = 32000

The initial population is 32000

While standing outside Carmen's Computer Store,Phyllis noticed that 14 people left the store and 10 people entered the store. Later, 5 more people entered and 13 people left.What was the net increase or decrease in the number of people in Carmen's Computer Store? A. An increase of 12 / B. decrease of 12 C. an increase of 42 / D . decrease of 42

Answers

Answer:

B. decrease of 12

Step-by-step explanation:

Number of people who left the store = 14

Number of people who entered the store = 10

Again,

Number of people who left the store = 13

Number of people who entered the store = 5

Total people who left the store = 14 + 13

= 27 people

Total people who entered the store = 10 + 5

= 15 people

Number of people remaining in the store = Total people who entered the store - Total people who left the store

= 15 - 27

= -12

This means there is a net decrease in the number of people in Carmen's Computer Store

What is the domain of the function shown in the table?
X
-2
-1
0
1
y
0
1
2
3
A. (-2,-1,0,1,2,3)
B. {-2, -1,0,1)
C. {0, 1, 2, 3)
D. (-2, 0),(-1,1),(0, 2), (1,3)

Answers

Answer:

{ -2,-1,0,1}

Step-by-step explanation:

The domain are the values for the input

Domain { -2,-1,0,1}

Round 5,693.251 to
thousands
and
tenths

Answers

Answer:

5693.251 = 5693.251, rounded to thousands (no change)5693.251 = 5693.3 rounded to tenths (rounded up as hundredths digit is 5)

Step-by-step explanation:

Nearest thousandth = 5693.251

Nearest tenths = 5693.3

3x (x - 2) = x^2 - 4

Answers

Answer:

x = 1, x = 2

Step-by-step explanation:

Given

3x(x - 2) = x² - 4 ← distribute parenthesis on left side

3x² - 6x = x² - 4 ( subtract x² - 4 from both sides )

2x² - 6x + 4 = 0 ( divide through by 2

x² - 3x + 2 = 0 ← in standard form

Consider the factors of the constant term (+ 2) which sum to give the coefficient of the x- term (- 3)

The factors are - 1 and - 2 , since

- 1 × - 2 = + 2 and - 1 - 2 = - 3 , then

(x - 1)(x - 2) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 1 = 0 ⇒ x = 1

x - 2 = 0 ⇒ x = 2

13 = 2m + 5

whats m?

Answers

4 is the correct answer

Answer:

M is 4

Step-by-step explanation:

in order to solve, 13=2m+5, you need to subtract 5 from both sides.

13=2m+5

-5        -5

Which is,

8=2m, then you divide both sides by 2. That gives you, 4=m. Therefor, m is 4.

what is the predecessor of -36

Answers

Answer:

-35

Step-by-step explanation

A predecessor is something that came before the current version, and -36 is negative so before -36 is -35

Answer:

the correct answer is -34

Step-by-step explanation:

A predecessor is something that came before the current version.

hope it helps you

Which value is the closet approximation of the square root of 27

A 4.5
B 5
C 5.5
D 5.9

Answers

the answer is B 5

the actual answer is 5.1 so round it down and it is 5

Y+y+y+y rewrite in multiplication

Answers

Answer:

4y

Step-by-step explanation:

y+y+y+y

= (1+1+1+1) y

= 4y

Answer:

4y

Step-by-step explanation:

Y+y+y+y

Combine like terms

4y

3. Create and write a real-world situation that could be represented by the equation below:
5x + 15 = 45

Answers

Answer:

You ordered 5 tickets for a show on line...

The cost was $5 a ticket Plus a one time ordering fee of $15.

you total cost was $45 ....

Solving for x will determine the cost of one ticket

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

a taxi charges $5 a mile plus $15 "pull fee" ...

you ride cost a total of $45 ... x is the number of miles that you got driven

Step-by-step explanation:

You rent a car for a down payment of $15 and $5 is charged per mile driven. The total charge is therefore, $45. In essence, x is the no. of miles driven.

According to the question;

We are required to create a real-world problem that could be represented by the equation; 5x + 15 = 45.

In essence, x is the no. of miles driven in this scenario.

By solving for x in 5x + 15 = 45, we may determine the no. of miles driven.

Read more:

https://brainly.com/question/2319353

How do I solve this: 12v + 10v + 14 = 80

Answers

Answer:

v = 3

General Formulas and Concepts:

Pre-Algebra  

Equality Properties

Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of Equality

Algebra I

Terms/Coefficients

Step-by-step explanation:

Step 1: Define

Identify

12v + 10v + 14 = 80

Step 2: Solve for v

Combine like terms:                                                                                         22v + 14 = 80[Subtraction Property of Equality] Subtract 14 on both sides:                       22v = 66[Division Property of Equality] Divide 22 on both sides:                               v = 3

Determine whether each of the following products is rational or irrational.
Expression
Rational
Irrational
77-18
-7,49
5
2
./II

Answers

Answer:

-irrational

-rational

-rational

-irrational

__________________________________________________________quick and easy way is to see if the squares are perfect squares, like square root seven is irrational, so the answer is irrational. square root 9 is 3, which is rational, so its rational.

brainliest is appreciated :)

PLZZZ HELPPPPP, HAVE 10 MORE QUESTIONS AND NEED TO FINISH IN 5 MINS

Answers

Answer:

2 cups

Step-by-step explanation:

It would be 1/2 times 4, which would be 2 cups of lime juice.

for what value of x does 4^x=(1/8)^x+5?

Answers

Use main properties of powers

(a^m)^n=a^{m\cdot n};(am)n=am⋅n;

\dfrac{1}{a^n}=a^{-n}an1=a−n

to simplify given equation.

1.

4^x=(2^2)^x=2^{2x}.4x=(22)x=22x.

2.

\left(\dfrac{1}{8}\right)^{x+5}=\left(\dfrac{1}{2^3}\right)^{x+5}=(2^{-3})^{x+5}=2^{-3x-15}.(81)x+5=(231)x+5=(2−3)x+5=2−3x−15.

3. Then the equation is

2^{2x}=2^{-3x-15}.22x=2−3x−15.

The bases are the same, so equate the powers:

2x=-3x-15,

2x+3x=-15,

5x=-15,

x=-3.

Answer: for x=-3.

30 POINTS

WHERE ARE THE EXPERTS AND ACE!!!!!!! I NEED HELP PLS SHARE YO SMARTNESS!!!!! WILL GIVE BRAINLIEST AND RATE AND VOTE!!! EASY IM JUST NOT SMART

40.
PLEASE GIVE EXPLANATION

Answers

Answer:

3.61%

Step-by-step explanation:

Mathematics, calculator

Answer:

Step-by-step explanation:

If we are looking for the probability that the battery lasts between 7 and 8 years, we find the z-score for the probability that it lasts less than 8 years, and then subtract from it the z-score for the probability that it lasts less than 7 years. This subtraction will give you what's left: the span in between 7 and 8 years. To find the z-score:

[tex]z=\frac{x_i-\mu}{\sigma}[/tex] Therefore,

P(x < 8) has a z-score of

[tex]z=\frac{8-5}{1.2}=1.667[/tex] The p-value that accompanies this z-score is .99379 (which translates to 99.379% of the data falling below 8 years) and

P(x < 7) has a z-score of

[tex]z=\frac{7-5}{1.2}=2.5[/tex] The p-value that accompanies this z-score is .95224 (which translates to 95.224% of the data falling below 7 years).

Subtract the p-value of 2.5 from the p-value of 1.667 to get

.99379 - .95224 = .04155 = 4.16%, choice A.

sin 0= 20/29. Find tan 0.

Answers

Answer: D) 20/21

Explanation:

Recall that sin(theta) = opposite/hypotenuse.

sin(theta) = 20/29 tells us that 20 is the vertical side while 29 is the hypotenuse. Note how the vertical side is opposite the reference angle theta.

Use these two sides to find that the missing side is 21. You'll need the pythagorean theorem a^2+b^2 = c^2.

Once you determine that the adjacent side is 21 units long, we can then say,

tan(theta) = opposite/adjacent = 20/21

Answer:

D. 20/21

Step-by-step explanation:

Other Questions
Karen usually does not spend much time selecting gifts. However, when choosing a fountain pen for her husband's birthday this year, she visited several stores and spent a lot of time asking the sales staff about different features of the pen before making her purchase. This scenario illustrates _______. a. shopping involvement.b. enduring involvement.c. product involvement.d. situational involvement. By appropriately preparing a forecast budget, a company can avoid __________. a net loss inventory shortages insolvency regulation Why was Circuit City so successful as to be fea- tured in Good to Great? What was its strategic position during its successful period? How did it contribute to competitive advantage? please help meIn which way were the American and French revolutions similar?a. The kings of both Britain and France faced financial difficulties and increased taxes.b. Both American and French revolutionary leaders wanted to create a republic.c.The legislative bodies of both Britain and France placed limits on the monarchy.d. Both revolutions resulted in the establishment of a stable, democratic government. What is the range of the data set shown below? A. 36 B. 34 C. 32 D. 30 Describe whether Americans have a greater level of awareness of class divisions or racial and ethnic divisions. Provide examples or illustrations that support your claim Warehouse Sports, a large box store retailer of athletic shoes, orders 200,000 shoes per year from its manufacturer. If w-and spends $10,000 in total annual ordering costs, what is the cost of ordering and delivery per order?O $2,000$50WO $500O There is not enough information to answer this question. Wants something you wanna get off your chest but are too ashamed to? In the United States, the most controversial part of the Treaty of Versailles was What is the theme of "Fighter" by Walter Dean Myers? 3. The vertices of trapezoid WXYZ are W(-2, 4), X(-3, 2), Y(-3, 1), and Z(-2, 1).Which figure shows the image of trapezoid WXYZ for a glide reflection where the translation is (x, y) - (x + 2, y) and the line ofreflection is y = 0? Indica la clase de pronombre que se observa en la siguiente oracin: Deban premiar a los tres ganadores de la competencia, mas no lleg el segundo.a) Posesivob) Numeralc) Exclamativod) Indefinidoe) Relativo Does the VERB agree with the SUBJECT in this sentence?Many people has used this computer.A. YesB. No a program in matchine language is called English grammar please answer on a molecular level why does lifting weights consume energy A bag of rare spice that weighs 2/3 pounds will be split equally among 12 people. How much spice will each person get What is the equation of the line that passes through the point (-1,4)and has a slope of -5? Solve the following system of equations by using the inverse of a matrix.Give your answer as an ordered triple (x , y , z) ASAP!!!!!!!What is the range of the inverse of the given function?[tex]f(x) = \sqrt{x} -2[/tex]a) [2, )b) [-2, )c) (, 2]d) (2, ]