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[tex]\\ \sf\longmapsto \dfrac{x}{y}+\dfrac{y}{x}=2[/tex]

[tex]\\ \sf\longmapsto \dfrac{x^2+y^2}{xy}=2[/tex]

[tex]\\ \sf\longmapsto x^2+y^2=2xy[/tex]

[tex]\\ \sf\longmapsto x^2+y^2-2xy=0[/tex]

[tex]\boxed{\sf (a-b)^2=a^2-2ab+b^2}[/tex]

[tex]\\ \sf\longmapsto (x-y)^2=0[/tex]

[tex]\\ \sf\longmapsto x-y=\sqrt{0}[/tex]

[tex]\\ \sf\longmapsto x-y=0[/tex]

Now

[tex]\\ \sf\longmapsto 4x-4y-4[/tex]

[tex]\\ \sf\longmapsto 4(x-y-4)[/tex]

[tex]\\ \sf\longmapsto 4(0-4)[/tex]

[tex]\\ \sf\longmapsto 4(-4)[/tex]

[tex]\\ \sf\longmapsto -16[/tex]

Answer:

x-√x -12

Step-by-step explanation:

(√x +3)(√x -4)=

x-√x -12

Answer:

the answer is C

Step-by-step explanation:

I used PEMDAS and school knowledge that I learned 2 years ago that I can't explain much, cause I i am bad at math, most of the time

Answer: A. mean: 10, median: 8, mode: none

Step-by-step explanation:

Given : The number of patients treated at Dr. Jason's dentist office each day was recorded for seven days: 3, 8, 11, 22, 17, 5, 4.

First we arrange it order.

3, 4, 5, 8, 11, 17, 22

Mean = (Sum of observations) ÷ (Number of observations)

Number of observations = 7

Sum of observations = 3+4+5+8+11+17+22 =70

Mean = 70 ÷7 = 10

Median = Middle-most value

= 8

Mode = Most repeatted value

= none

Hence, the mean, median, and mode for this sample = A. mean: 10, median: 8, mode: none

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

Explanation:

Compute the simple interest on a deposit of x

The per annum (p.a.) interest rate is r = 0.12 from the 12% value mentioned.

We do so over t = 2 years

i = p*r*t

i = x*0.12*2

i = 0.24x

Let A = 0.24x

Do the same for the compound interest. We'll have n = 1 to reflect annual compounding.

i = p*(1+r/n)^(n*t) - p

i = x*(1+0.12/1)^(1*2) - x

i = 1.2544x - x

i = 0.2544x

Let B = 0.2544x

We're told that "The simple interest on a sum of money in 2 years is Rs 36 less than the compound interest compounded annually"

This means the interest earned in the simple interest (value A) is Rs 36 less than the amount earned with quantity B

So,

A = B-36

0.24x = 0.2544x - 36

0.24x - 0.2544x = -36

-0.0144x = -36

x = -36/(-0.0144)

x = 2500

The amount invested or deposited is Rs 2500

Answer:

70.6x 10-⁵ is answer of first

Answer:

x = -2

Step-by-step explanation:

To solve for x always get x on one side

First add 4 on each side, 4 + 7x - 4 = -18 + 4

Next subtract 18 from 4, making it -14    7x = -14

Now divide 7 on each side, x = -2

Step-by-step explanation:

Since Ca(OH)2 is Basic, we need to find pOH:

pOH = - log [OH-]

pOH = - log(0.0001)

pOH = - ( - 4)

pOH = 4

Since, pH + pOH = 14

Therefore,

pH of 0.0001M sol. of Ca(OH)2 = 10

Step-by-step explanation:

You can solve a system of three equations by multiplying each equation by a number that allows you to add or suvtract the same equation together by eliminating the x or y variable

Answer:

To use elimination to solve a system of three equations with three variables, follow this procedure:

Write all the equations in standard form cleared of decimals or fractions.

Choose a variable to eliminate; then choose any two of the three equations and eliminate the chosen variable.

Select a different set of two equations and eliminate the same variable as in Step 2.

Solve the two equations from steps 2 and 3 for the two variables they contain.

Substitute the answers from Step 4 into any equation involving the remaining variable.

Check the solution with all three original equations.

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

There are 4 individual terms in the polynomial:

3xy

12y

-5x

7w

Answer:

6.8 gallions i believe. im not quite sure

Answer:

A. Zero.

Step-by-step explanation:

Technically, the correct answer is "undefined", as there will be infinite change in the slope amount. However, of all the given choices, Zero should be the best answer. However, if it is wrong, do ask your teacher, and state that undefined should be the answer choice, and that credit should be rewarded for such.

Answer:

50.8%

Step-by-step explanation:

Convert fraction (ratio) 33 / 65 Answer: 50.769230769231%

Answer:

1.) Jill = 11 yrs & Jack = 14 yrs. | 2.) (x + 4)(x + 3)

Step-by-step explanation:

1.)

Let j = Jill's age.

[tex]j+(j+3)=25\\2j+3=25\\2j=22\\j=11\\\\\\(11)+3=14[/tex]

Therefore, Jill is 11 and Jack is 14.

2.)

[tex]x^2+7x+12\\(x+4)(x+3)[/tex]

Answer:

a) 4⁻³ = 1/64 = 0.015625

b)13⁻² = 1/169 = 0.0059171598

c)(-3)⁻² = 1/-3² = 0.1111111111

Step-by-step explanation:

To solve the question above, when we have an integer ( positive or negative) that is raised to a negative power, this means the reciprocal of that integer raised to the positive power

Example:

a⁻ⁿ = 1/aⁿ

a) 4⁻³ = 1/4³

= 1/(4 × 4 × 4)

= 1/64

= 0.015625

b) 13⁻² = 1/13²

= 1/(13 × 13)

= 1/169

= 0.0059171598

c)(-3)⁻² = 1/-3²

= 1/(-3 × -3)

= 1/9

= 0.1111111111

Answer:

AC = 4.5 units

Step-by-step explanation:

In the given triangle ABC,

Segment AD is the angle bisector of ∠BAC.

m∠CAD = m∠BAD = θ

By applying angle bisector theorem in ΔABC,

An angle bisector of the interior angle in a triangle divides the opposite side into segments that are proportional to the other two sides.

[tex]\frac{\text{AB}}{\text{BD}}=\frac{\text{AC}}{\text{CD}}[/tex]

By substituting measures of the given sides,

[tex]\frac{6.8}{3.8}=\frac{\text{AC}}{2.5}[/tex]

AC = [tex]\frac{6.8\times 2.5}{3.8}[/tex]

AC = 4.473

AC ≈ 4.5 units

Therefore, measure of the missing side AC will be 4.5 units.

Answer:

0.6

Step-by-step explanation:

A probability is the likelihood of an event occurring. A probability function is a function in which at any point, its probability value can be estimated. The integral of the probability function is always ≤ 1

To find the probability that x = 2 or 3, we simply add their respective individual probabilities, therefore:

P(X = 2 or 3) = P(X = 2) + P(X = 3) = P(2) + P(3) = 0.5 + 0.1 = 0.6.

P(X = 2 or 3) = 6

Answer:

7 block s

Step-by-step explanation:

3 from North plus

4 from West

4+3=7

Answer:

r = 6

Step-by-step explanation:

Hello!

-8 - 2(7r + 1) = -94

Add 8 to both sides

-2(7r + 1) = -86

Divide both sides by -2

7r + 1 = 43

Subtract 1 from both sides

7r = 42

Divide both sides by 7

r = 6

Hope this Helps

Answer:

A. EF

Step-by-step explanation:

Answer:

EF

Step-by-step explanation:

The reason is because EF and BC are in the same plane

Answer:

AandB=80miles

Total=240miles

Step-by-step explanation:

Draw the figure first indicating the figures then find the distance each degrees then find the total

The distance ship travels from A to B is 273.2 miles and total distance covered by ship is  707.82 miles.

The law of sines specifies how many sides there are in a triangle and how their individual sine angles are equal. The sine law, sine rule, and sine formula are additional names for the sine law.

The side or unknown angle of an oblique triangle is found using the law of sine. Any triangle that is not a right triangle is referred to as an oblique triangle. At least two angles and their corresponding side measurements should be used at once for the sine law to function.

Given distance from C to A = 100 miles north

From B to A ship travels 60° east of north,

and From B to C 45° west of south,

the figure for problem is attached,

from figure we can  calculate the angles of A, B and C

so ∠A makes supplementary with 60°

∠A + 60° = 180°

∠A = 120°

for ∠B we need to draw an imaginary perpendicular on the line extending from A, we get

∠B + 45° + 30° = 90° (30° is angle of imaginary right triangle)

∠B = 90 - 75 = 15°

and ∠C can be found by,

∠A + ∠B + ∠C = 180°

∠C = 180 - 15 - 120

∠C = 45°

now use sine formula for triangles,

sinA/a = sinB/b = sinC/c

where A, B and C are angles of triangle and a, b and c are length of opposite side of angle A, B and C respectively.

a = BC, b = AC, and c = AB

so

sinA/BC = sinB/AC = sinC/AB

we have AC = 100 miles

substitute the values

sinC/AB = sinB/AC

sin(45)/AB = sin(15)/100

AB = 100/(√2sin(15))

AB = 100/0.3659

AB = 273.298 miles

and sinA/BC = sinB/AC

BC = AC sinA/sinB

BC = 100(sin 120/sin15)

BC = 100(0.866/0.2588)

BC = 100 x 3.3462

BC = 334.62 miles

total distance = AB + BC + AC

total distance = 334.62 + 273.2 + 100

total distance =  707.82 miles

Hence the distance from A to B is 273.2 miles and total distance is 707.82 miles.

Learn more about  laws of sines;

https://brainly.com/question/17289163

#SPJ2

Answer:

She had $2.00 left.

Step-by-step explanation:

PEMDAS

$75 - [(3 x $4) + (2 x $20) + $21 ]

$75 - [ $12 + $40 + $21]

$75 - [ $52 + $21]

$75 - $73

$2

Answer:

Step-by-step explanation:

Since the triangle is a right angled triangle we can use the Pythagoras theorem to find the missing side

Using the Pythagoras theorem

That's

[tex] {a}^{2} = {b}^{2} + {c}^{2} [/tex]

From the question

x is the hypotenuse or the longest side of the triangle

Substituting the values into the above formula we have

[tex] {x}^{2} = {9}^{2} + {7}^{2} [/tex]

[tex] {x}^{2} = 81 + 49[/tex]

[tex] {x}^{2} = 130[/tex]

Find the square root of both sides

We have the final answer as

Hope this helps you

Answer:

B. 4x2 + 9x – 28

Step-by-step explanation:

Multiply out the factors and see what polynomial you end up with.

(4x – 7)(x + 4) = 4x^2 + 16x - 7x - 28 = 4x^2 + 9x - 28

The polynomial with factors of 4x – 7 and x + 4 is 4x² + 9x - 28, Option B is correct.

Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables

To determine which polynomial has factors of 4x – 7 and x + 4, we can use the fact that if a polynomial has a factors.

So, if a polynomial has factors of 4x – 7 and x + 4, then it can be written as:

(4x – 7)(x + 4)

Multiplying these factors together using the distributive property, we get:

4x²+ 16x - 7x - 28

Simplifying, we get:

4x² + 9x - 28

Hence, the polynomial with factors of 4x – 7 and x + 4 is 4x² + 9x - 28, Option B is correct.

To learn more on Polynomials click:

https://brainly.com/question/11536910

#SPJ6

Answer:

Integers include whole numbers. However, whole numbers are the list of positive integers, INCLUDING 0. A whole number cannot be negative.

Step-by-step explanation:

Answer and Step-by-step explanation:

True

Whole Numbers       { 0, 1, 2, 3, 4, . . . }  

Counting Numbers  { 1, 2, 3, 4, . . . }  

Integers                    { . . . −4, −3, −2, −1, 0, 1, 2, 3, 4, . . . }

when its a positive integers, say "positive integers"

(note: zero isn't positive or negative):

Integers are a whole numbers, but they also include negative numbers.

But still no fractions allowed!

Integers = { . . . , −4, −3, −2, −1, 0, 1, 2, 3, 4, . . . }

Negative Integers = { . . . , −4, −3, −2, −1 }

Positive Integers = { 1, 2, 3, 4, . . . }

Non-Negative Integers = { 0, 1, 2, 3, 4, . . . } (it includes zero you see)

hope it helps.

Answer:

8.555.... is a irrationtional number .

Step-by-step explanation:

1. c

2. a

3. c

4. c

5. d

6. b

7. a

8. b

9. c

Answer:

s = 40.2 m

Step-by-step explanation:

It is given that,

Initial speed of the car, u = 0 m/s

Final speed of the car, v = 13.6 m/s

Acceleration of the car, a = 2.3 m/s²

We need to find the distance, s, that it has travelled since stopping at the lights. For this, we will use third equation of motion as :

[tex]v^2-u^2=2as[/tex]

s is distance

[tex]s=\dfrac{v^2-u^2}{2a}\\\\s=\dfrac{(13.6)^2-0}{2\times 2.3}\\\\s=40.2\ m[/tex]

So, the distance covered by the car is 40.2 meters.

Answer:

[tex]t = \frac{ v_{1} - v_{0}}{a} \\[/tex]

Step-by-step explanation:

[tex]a = \frac{v_{1} - v_{0}}{t} \\ a \times t = v_{1} - v_{0} \\ \frac{at}{a} = \frac{ v_{1} - v_{0} }{a} \\ t = \frac{ v_{1} - v_{0}}{a} \\ [/tex]

Answer:

[tex]\huge\boxed{\sf \frac{a^2+b^2}{2(a^2-b^2)}}[/tex]

Step-by-step explanation:

=> [tex]\sf \frac{a}{2(a+b)} + \frac{b}{2(a-b)}[/tex]

LCM = 2(a+b)(a-b)

=> [tex]\sf \frac{a(a-b)+b(a+b)}{2(a+b)(a-b)}[/tex]

Simplifying further

=> [tex]\sf \frac{a^2-ab+ab+b^2}{2(a^2-b^2)}[/tex]

=> [tex]\sf \frac{a^2+b^2}{2(a^2-b^2)}[/tex]

[tex]\dfrac{a}{2(a+b)}+\dfrac{b}{2(a-b)}=\\\\\dfrac{a(a-b)}{2(a+b)(a-b)}+\dfrac{b(a+b)}{2(a+b)(a-b)}=\\\\\dfrac{a^2-ab}{2(a^2-b^2)}+\dfrac{ab+b^2}{2(a^2-b^2)}=\\\\\dfrac{a^2+b^2}{2(a^2-b^2)}[/tex]

Answer:

y=4

Step-by-step explanation:

it has only one solution.