What is the solution to the system of equations shown on the graph?
(-1,-3)
(-3,-1)
(13,-1)
No Solution

Answer:

2, 1/2

Step-by-step explanation:

Arithmetic mean of two numbers is given as

[tex]n=\frac{a+b}{2}[/tex]

Here a=x and b=1/x

[tex]n=\frac{x+1/x}{2}[/tex]

[tex]\frac{5}{4} =\frac{x^{2}+1}{2x}[/tex]

[tex]\frac{5}{2}x=x^{2} +1\\ x^{2}-\frac{5}{2}x+1=0[/tex]

[tex]x=2, \frac{1}{2}[/tex]

Hence the numbers are 1/2 and 2.

If x is any real number, then the reciprocal of this number will be 1/x. For example, the reciprocal of 5 is 1 divided by 8, i.e. 1/5.

Given, one number is reciprocal to another.

So if we choose the first number to be x , the the other number becomes its reciprocal i.e. 1/x.

Now, it is given that the arithmetic mean of these two numbers is 5/4.

So using formula for arithmetic mean ,

Mean = Sum of Observations / No. of observations

[tex]\frac{5}{4} =\frac{x+\frac{1}{x}}{2} \\\frac{5*2}{4}= \frac{x^{2} +1}{x} \\\frac{5}{2} =\frac{x^{2}+1}{x} \\[/tex]

On cross Multiplication and Factorization, we get:

[tex]5x=2x^{2}+2\\2x^{2} -5x+2=0\\2x^{2} -4x-x+2=0\\2x(x-2)-1(x-2)=0\\(2x-1)(x-2)=0\\2x-1=0 , x=1/2\\x-2=0 , x=2[/tex]

So , when x=1/2 , then 1/x=2

and when x=1/2 , then x=2

Hence,  the numbers are 2 and 1/2 .

Learn more about reciprocals at :

https://brainly.com/question/2534506

#SPJ2

Answer:

See description.

Step-by-step explanation:

The first way you could use 60/5 is you could say the 60 students need to be divided into 5 buses. The second way you could use 60/5 is you could do 60 students divided into five groups of areas.

Answer:

The normal price of mixer is $150.

Step-by-step explanation:

Given that:

Normal prices are reduced by 15% in sale.

The normal price of mixer is reduced by $22.50

It means that it is the amount of discount.

Let,

x be the normal price of the mixer.

15% of x = 22.50

[tex]\frac{15}{100}x=22.50\\0.15x=22.50[/tex]

Dividing both sides by 0.15

[tex]\frac{0.15x}{0.15}=\frac{22.50}{0.15}\\x=150[/tex]

Hence,

The normal price of mixer is $150.

The normal price of the mixer is $150.

Given that,

Based on the above information, the calculation is as follows;

Let us assume the normal price be x

15%x = 22.50

0.15x = 22.50

x = $150

Learn more: brainly.com/question/16911495

Answer:

Step-by-step explanation:

in 1rupee, (105/35) envelope can be purchased

then

in 10 rupees, (105*10)/35  envelopes can be purchased

in 10 rupees, 30 envelopes can be purchased

i hope this will help you

Answer: g(x) = 2*x

Step-by-step explanation:

We want to find the formula of g(x) if we know that g(x - 3) = 2*x - 6

Well, the first step is to find the expression (x - 3) = y in the g(x - 3)

Then:

g(x - 3) = 2*x - 6 = 2*x - 2*3

Now we can just take the common factor 2, and write this as:

2*x -2*3 = 2*(x - 3) = 2*y

then:

g( x - 3) = g(y) = 2*y

if we just replace x by y, we get:

g(x) = 2*x

This is the formula of g(x)

The answer is 18 with a remainder of 0.

Answer:

= 18 R 0

= 18

Step-by-step explanation:

YAY SO MANY POINTS

Answer:

Both questions are inaccurate.

Step-by-step explanation:

You cannot have a +- next to each other without a number on the right of it.

Also 2-2=0 not 4.

Answer:

Let's define the East as the x-axis, and the North as the y-axis

Now we can write the speed of the plane as:

(Vx, Vy)

Such that the total velocity of the plane is 350mph

This means that, if the plane flies at an angle of A degrees from the East, then:

Vx = 350mph*cos(A)

Vy = 350mph*sin(A)

We know that the speed of the wind is 65mph at 43° North from East.

This velocity, (Wx, Wy), can be written in components as:

Wx = 65mph*cos(43°) = 47.54 mph

Wy = 65mph*sin(43°) = 44.33 mph

Now, when the plane flies with the wind, the velocity of the plane will be equal to the velocity of the plane plus the velocity of the wind.

This is:

Velocity = (Vx, Vy) + (Wx, Wy) = (Vx + Wx, Vy + Wy)

The plane wants to keep going to the East, then the y-component must vanish (remember that the y-component is the one associated with the North)

Then we must have that:

Vy + Wy = 0

replacing the correspondent values, we have:

 350mph*sin(A) + 44.33 mph = 0

350mph*sin(A) = -44.33 mph

Sin(A) = -44.33 mph/350mph

A = Arcsin(-44.33 mph/350mph) = -7.27°

This means that the plane must fly at -7.27° degrees North of East (Or 7.27° South of East)

That is the direction at which the plane must fly.

Answer:D

Step-by-step explanation:

This is D because your dividing by 5 or each one and thats how you get Your output number

Proportional relationship between x and y is x/y = 5. Only table D shows a proportional relationship between x and y.

A proportional relationship is a relationship between two expressions and where changes in one expression means some constant change in other expression as well. Generally it is represented as x/y = k, where x and y are two expressions and k is constant.

In order to solve this problem, first we’ll have to figure out the proportionality ratio between the x and y.

that is x/y = k (let), it should be constant.

In the table A;

first term, 3/4 = 0.75

second term, 10/6 = 1.667

Since the value of constant is not the same. Therefore the table A does not show the proportional relationship between x and y.

In the table B;

first term, 4/2 = 2

second term, 8/4 = 2

third term, 12/8 = 1.5

Since the value of constant is not the same. Therefore the table B does not show the proportional relationship between x and y.

In the table C;

first term, 12/6 = 2

second term, 14/12 = 1.667

Since the value of constant is not the same. Therefore the table B does not show the proportional relationship between x and y.

In the table D;

first term, 5/1 = 5

second term, 10/2 = 5

third term, 15/3 = 5

Since the value of constant is the same in every term. Therefore the table B shows the proportional relationship between x and y.

Therefore, proportional relationship between x and y is x/y = 5. Only table D shows a proportional relationship between x and y.

To learn more about the proportional relationship;

https://brainly.com/question/28777033

#SPJ2

Answer:

6:36:12

Step-by-step explanation:

1+6+2=9

54÷9=6

1×6=6

6×6=36

2×6=12

and to double-check you can add them up and you should get the total amount

Answer:

$4400

Step-by-step explanation:

Total earnings = $1038

Base salary = $675

What part of the total earnings was from the commission?

$1038 - $675 = $363

She made $363 in commissions.

The commissions are 8.75% of the sales.

Let sales = x.

8.25% of x = $363

0.0825x = 363

Divide both sides by 0.0825

x = 4400

Answer: Her sales were $4400

Answer: 24xy

I'm not sure if I'm right, but if I am and you have any questions about how it was solved, feel free to ask!! :)

Answer:

uhvyfhxesegxt&6&6&#^π¢π¢

The Expression that exactly equivalent to "5a + 3b + 4 + 7a + 9" is

"8a + 11b + 9".

The terms in the brackets can be immediately simplified. Therefore, we can carry out the operations indicated by the brackets in the following order: multiplication, addition, subtraction, and division. Note: The brackets should be shortened in the following order (), {}, []. The rule used for simplifying equations is PEMDAS.

Given, An equation 5a + 3b + 4 + 7a + 9  that we need to simplify.

Thus adding the Constants of the same variable

12a + 4 + 3b + 9

adding the constants

12a +3b +13

Therefore, "8a + 11b + 9" is the exact equivalent expression to "5a + 3b + 4 + 7a + 9."

Learn more about simplification here:

https://brainly.com/question/11589761

#SPJ2

Answer: 1

Step-by-step explanation: divide 3 by 3

wath do you meen point to the mathe matical problem

Step-by-step explanation:

okay

Answer: 742.68

Step-by-step explanation:

Answer:

[tex]g + h > f[/tex] is an example of inequality

Step-by-step explanation:

Given

[tex]g + h > f[/tex]

Required

What does it represent

When a mathematical statement has any of:

[tex]>, <, \le, \ge, \ne[/tex]

Then, the mathematical statement is regarded as an inequality:

Hence:

[tex]g + h > f[/tex] is an example of inequality

The answer is x = 5.

You want me to examine Jack's answer to the equation X + 5 = 10, I take it.

I can outline the broad procedures to solve this problem without knowing Jack's answer:

Add 5 to both sides of the equation to equal 10 and 5: X + 5 - 5 = 10 - 5.

Condense: X = 5.

As a result, X = 5 is the answer to the equation X + 5 = 10.

If you give me Jack's answer, I can assist you determine whether it is accurate or if there are any mistakes.

Therefore, the value of x is 5.

To know more about algebraic expression visit : https://brainly.com/question/20660076

#SPJ1

Answer:

x= y-5/2

Step-by-step explanation:

Swap the numbers to the other side. This makes it a minus. Because its the inverse, y-5 over 2.

Answer:

9.5 < x < 15

Step-by-step explanation:

The possible values of x for the given problem lies in  (-infinity, -1.33) ∪ (9.5, 15).

Linear inequality refers to the relation between a linear algebraic expression to some known value that contains inequality sign.

Unlike a linear equation it can have a range of values inside an interval.

Given that,

The sides of the triangle are as follows,

CD = x - 4,  DE = 3x + 21 and  CE = 6x - 13.

There can be three cases for the given problem.

Case 1,

The longest side of the triangle is CE = 6x - 13.

Since the sum of the two sides of a triangle is always greater than the longest one, the following inequality can be written for the given triangle,

6x - 13 < x - 4 + 3x + 21

=> 6x - 13 < 4x + 17

=> 6x - 4x < 17 + 13

=> 2x < 30

=> x < 15

Case 2,

The longest side of the triangle is DE = 3x + 21.

Since the sum of the two sides of a triangle is always greater than the longest one, the following inequality can be written for the given triangle,

3x + 21 < 6x - 13 + x - 4

=> 3x + 21 < 7x - 17

=> 7x - 3x > 21 + 17

=> x > 38/4

=> x > 9.5

Case 3,

The longest side of the triangle is CD = x - 4.

Since the sum of the two sides of a triangle is always greater than the longest one, the following inequality can be written for the given triangle,

x - 4 < 3x + 21 + 6x - 13

=>  x - 4 < 9x + 8

=> x - 9x > 8 + 4

=> x < -1.33

Thus, the range of the values of x is intersection of x < 15, x > 9.5 and  x < -1.33, which is equivalent to (-infinity, -1.33) ∪ (9.5, 15).

Hence, the range of possible values of x lies in the interval (-infinity, -1.33) ∪ (9.5, 15).

To know more about linear inequality click on,

https://brainly.com/question/11897796

#SPJ2

Answer:

The binomial is a factor

Step-by-step explanation:

In order to show that x+3 is a factor of the polynomial, then;

f(a) = 0

Get a by equating x+3 to zero

x+3 = 0

x = -3

Get f(-3)

f(-3) =  (-3)^4 + 8(-3)^3 + 11(-3)^2 -11(-3) + 3

f(-3) = 81 - 216 + 99 + 33 + 3

f(-3) = 216-216

f(-3)  = 0

Since the remainder of the polynomial when divided by x+3 is zero, this shows that x+3 is a factor of the given polynomial

Answer:

$42,000

Step-by-step explanation:

280,000*0.15=42,000

Answer:

They would have $42,000 saved.

Step-by-step explanation: You take the money the home is valued at, which is $280,000, and you multiply it by 15%, or 0.15 and you can put this in a calculator for a faster and definite answer. Hope this helps ^-^.

Answer:

c. The car travels different distances per unit of time because the portion shows a nonlinear, increasing function.

Step-by-step explanation:

We are given the graph of a function of the distance in function of the time.

We want to study the graph during the part of the graph labeled K, which is non-linear, meaning that the accelaration is not constant. This means that the car travels different distances per unit of time, and the correct answer is:

c. The car travels different distances per unit of time because the portion shows a nonlinear, increasing function.

Answer:

Large avocados should cost $ 1.83 or less to be a good deal.

Step-by-step explanation:

Since there are two types of avocado in the store, some small at $ 0.92 and others larger, to determine at what price large avocados would be a good deal, an equivalence must be established in this regard:

Thus, if two small avocados are equal to one large, buying two small avocados at $ 0.92 the total price would be $ 1.84. Therefore, any large avocado that sells for less than $ 1.84 would be a good deal. Thus, large avocados should cost $ 1.83 or less to be a good deal.

The answer is 6800 = 80m

Answer:

The domain of the function should be:

'x greater than or equal to negative -5'.

Hence, option A is true.

Step-by-step explanation:

Given the expression

[tex]2\sqrt{x-5}[/tex]

The domain of a function is the set of input or arguments for which the function is real and defined

We know that the value, inside the radicand, is the number found inside a radical symbol which must be greater than 0, otherwise, it would make the function undefined,

i.e.

x-5 ≥ 0

x ≥ 5

In other words, the domain of the function should be:

'x greater than or equal to negative -5'.

Therefore, the domain of the function:

x ≥ 5

[tex]\mathrm{Domain\:of\:}\:2\sqrt{x-5}\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\ge \:5\:\\ \:\mathrm{Interval\:Notation:}&\:[5,\:\infty \:)\end{bmatrix}[/tex]

Hence, option A is true.

The domain of the function y = 2√(x - 5) will be x greater-than-or-equal-to 5. Then the correct option is C.

The domain means all the possible values of x and the range means all the possible values of y.

The function is given below.

y = 2√(x - 5)

Then the domain of the function will be

We know that the value inside the square root should be greater than or equal to zero. Then the domain will be

x - 5 ≥ 0

Simplify the inequality, then the domain of the function will be

x - 5 ≥ 0

x ≥ 5

The domain of the function y = 2√(x - 5) will be x greater-than-or-equal-to 5.

Then the correct option is C.

More about the domain and range link is given below.

https://brainly.com/question/12208715

#SPJ6

Answer:V(t) = C·(0.5)t

Step-by-step explanation:

V(t) = computer's value at year t = 600

C = initial cost = 2100

t = years