The oldest child in a family of four children is twice as old as the yougest. The two middle children are 12 and 16 years old. If the average age of the children is 13.75 , how old is the youngest child?

Answer:

The only function is C.

Step-by-step explanation:

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:

[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

Answer:

$6.45

Step-by-step explanation:

Answer:

5 and 5b: y=-2x+10

5a: y-2=-2(x-6)

Step-by-step explanation:

We can use the mentioned data points to identify the slope. Time will always the x coordinate/axis, so gallons will be the y coordinate/axis. As you probably already know, slope is rise over run, so we can measure the change in y over the change in x, or we can do [tex]\frac{y-y_{1}}{x-x{1}}[/tex]. When we plug in our points, (2,6) and (5,0), we get  [tex]\frac{6-0}{2-5}[/tex], or [tex]\frac{6}{-3}[/tex], or [tex]\frac{2}{-1}[/tex], or simply -2. So our slope is -2.

We can use our y-intercept (which is (0,10), as mentioned in the attached graph and table) to make the equation, in slope-intercept form, [tex]y=-2x+10[/tex] This can answer both question 5 and 5b. Remember that slope-intercept form is written using the format y=mx+b, where x any given x-coordinate, y is the corresponding y-coordinate, m is the slope and b is the y-intercept.

To put this equation in point-slope form, one must first remember that point-slope form is written in the format [tex]y-y_{1} = m(x-x_{1})[/tex], using the coordinates of any given coordinates on the same line, except for the y intercept. m also represents slope in this equation. So for this one, we can easily use (2,6). we can plug in these coordinates to get the equation y-2=-2(x-6).

Hope this helps.

Graph and table were created using Desmos dot com graphing calculator.

Answer:

The value of f(x) - g(x) is:

f(x) - g(x) =  2x² + 6x - 4

Step-by-step explanation:

Given

f(x) = 3x² + x - 3

g(x) = x² - 5x + 1

To determine

f(x) - g(x)

Using the formula

f(x) - g(x) =  3x² + x - 3 - ( x² - 5x + 1)

              = 3x² + x - 3 - x² + 5x - 1

              = 2x² + 6x - 4

Therefore, the value of f(x) - g(x) is:

f(x) - g(x) =  2x² + 6x - 4

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: 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:

anwer is i dont know im sorry

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:

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

Given:

The graph of linear function.

To find:

The rate of change the given linear function.

Solution:

From the given graph it is clear that the line passes through the points (0,1) and (1,-1). So, rate of change is

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\dfrac{-1-1}{1-0}[/tex]

[tex]m=\dfrac{-2}{1}[/tex]

[tex]m=-2[/tex]

Therefore, the rate of change of the given linear function is -2. Hence, the correct option is A.

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:

1/5

Step-by-step explanation:

If you focus on one of the coordinates, for example (10,10) you will notice that 10 divided by 5 equals 2.  If you do that on both X and Y it will give you 2.  The black shape's top right cordinate is (2,2) which explains why its 1/5...

Can I plz have it!

Answer:

2

3

–

3

4

=

– 1

12

Step-by-step explanation: is this the answer?

Step-by-step explanation:

Using Trignometry,

sin60° = BC/10.

=> BC = 10sin60°

= 10 * (√3/2) = 5√3 = 8.7. (1d.p.)

Answer:

[tex] \sin(60°) = \frac{BC}{10} \\ \frac{ \sqrt{3} }{2} = \frac{BC}{10} \\ BC = \frac{10 \sqrt{3} }{2} \\ BC= 5 \sqrt{3}\\\boxed{\red{BC= 8.7}}[/tex]

Step-by-step explanation:

given

g(r)= -1 -7r

g ( 6) = - 1 - 7 * 6

= - 1 - 42

= - 43

Answer:

General solution    x   = log | sec y | + C            

Step-by-step explanation:

Step(i):-

Given

          [tex]e^{x} cosy dx - e^{x} sin y d y = 0[/tex]

         [tex]e^{x} (cosy dx = e^{x} sin y d y[/tex]

           cos y dx = sin y d y

                [tex]dx = tan y d y[/tex]

Step(ii):-

now integrating on both sides , we get

            [tex]\int\limits {1} \, dx = \int\limits {tany} \, dy[/tex]

by using formula

               [tex]\int\limits {tany} \, dy = log | sec y | + C[/tex]

             x   = log | sec y | + C

Final answer:-

General solution    x   = log | sec y | + C

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.

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:

x = {0, π/3, π, 4π/3}

Step-by-step explanation:

4cos⁴(x) - 5cos²(x) + 1 = 0

(u² - 1)(4u² - 1) = 0

u² - 1 = 0

u² = 1

u = ± 1

cos x = ± 1

=> x = 0 or π

4u² - 1 = 0

4u² = 1

u² = 1/4

u = ± 1/2

cos x = ± 1/2

=> x = π/3 or 4π/3

Therefore, x = {0, π/3, π, 4π/3}.

Answer:

20%

Step-by-step explanation:

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:

$14.90

Step-by-step explanation:

357.60 ÷ 24 is 14.9

Answer:

The value of x will be:

[tex]x=22\sqrt{2}[/tex]

or

[tex]x = 31.1[/tex]

Step-by-step explanation:

Given

To determine

hypotenuse x = ?

For a right-angled triangle with sides, a and b the hypotenuse c is defined as

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

substituting a = 22, b = 22 and c = x

[tex]x=\sqrt{22^2+22^2}[/tex]

[tex]x=\sqrt{22^2\cdot \:2}[/tex]

Apply radical rule:  [tex]\sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b},\:\quad \mathrm{\:assuming\:}a\ge 0,\:b\ge 0[/tex]

[tex]x=\sqrt{2}\sqrt{22^2}[/tex]

[tex]x=22\sqrt{2}[/tex]

or

[tex]x = 31.1[/tex]

Therefore, the value of x will be:

[tex]x=22\sqrt{2}[/tex]

or

[tex]x = 31.1[/tex]

Answer:

 -4

Step-by-step explanation:

Answer:

true I think. I rember some, sorry if its wrong