Let f(x)=x* + 14x and g(x) = 6 - X. Find the domain off f + g. Determine the domain of f + g. ​

Answer:

5/12

Step-by-step explanation:

1/4 and 1/6 are fractions.

As we directly can't add fractions whenever denominators are different, so we will have to find out the Least common multiple of 4 and 6.

The LCM Of 4&6 will be 12, so we will write 12 instead of 4&6.

Now, 4*3=12, that is why we will have to multiply the numerator and denominator with 3.

1*3/4*3 = 3/12

Same thing applies to 1/6. In order to get 12 in the denominator we need to multiply 2 with numerator and denominator both.

1*2/6*2= 2/12

However, we have two new fractions with same denominator now, that is 3/12 and 2/12

We can directly add the numerators now, as we have the same denominator. So 3+2/12= 5/12 would be my final answer. (addition of like fractions)

5/12

Probabilities are used to determine the chances of events.

The given parameters:

[tex]n = 5[/tex] ---- the number of candy bars

[tex]p = 40\%[/tex] ---- the probability of selling a candy bar

(a) Name distributions

The distribution of X is represented as:

[tex]X \sim(r,p)[/tex]

Where:

[tex]r = 5[/tex]

[tex]p= \frac{5\times 40\%}{10}[/tex]

[tex]p= 0.2[/tex]

So, the name distribution of X is [tex]X \sim(r= 5,p = 0.2)[/tex]

(b) The probability that the last candy is sold at the 11th house

This means that:

[tex]n = 10[/tex] --- the number of previous houses

[tex]r = 4[/tex] --- the previous number of candies

[tex]p = 0.4[/tex] --- the given probability of selling a candy

The probability is calculated using:

[tex]P(x = n+1) = ^{n}C_r \times p^{r +1} \times (1 - p)^{n-r}[/tex]

This gives

[tex]P(x = 10+1) = ^{10}C_4 \times 0.4^{4 +1} \times (1 - 0.4)^{10-4}[/tex]

[tex]P(x = 11) = ^{10}C_4 \times 0.4^{5} \times (0.6)^6[/tex]

[tex]P(x = 11) = 210 \times 0.4^5 \times 0.6^6[/tex]

[tex]P(x = 11) = 0.1003290624[/tex]

Approximate

[tex]P(x = 11) = 0.1003[/tex]

Hence, the probability that the last candy is sold at the 11th house is 0.1003

(b) The probability he sells the candies on or before the 8th house

The probability is calculated using:

[tex]P(x \le 8) = P(5 \le x \le 8)[/tex]

This gives

[tex]P(x \le 8) = ^{10}C_5 \times 0.4^{6} \times (0.6)^5 + ^{10}C_6 \times 0.4^{7} \times (0.6)^4 + ^{10}C_7 \times 0.4^{8} \times (0.6)^3 +^{10}C_8 \times 0.4^{9} \times (0.6)^2[/tex]

[tex]P(x = 11) = 0.1737[/tex] ---- approximated

Hence, the probability he sells the candies on or before the 8th house is 0.1737

Read more about probabilities at:

https://brainly.com/question/251701

[tex]\text{Given that,}\\\\(x_1,y_1) = (-1,-2)~~ \text{and}~~ (x_2,y_2) = (-2,2)\\\\\text{Slope, m =} \dfrac{y_2-y_1}{x_2 -x_1} = \dfrac{2 -(-2)}{-2-(-1)} = \dfrac{2+2}{-2+1} = \dfrac{4}{-1} = -4[/tex]

Answer:

7.79

Step-by-step explanation:

in 30, 60, 90 triangle, hypotenuse is equal to "2x", shortest length is equal to "x" and second longest is equal to "x × square root of 3". hope this helps

The slope is the number in front of the x. And the y-intercept is the number after the x.

A negative y-intercept would be subtracted from the equation.

Answer is B. Y = 7.5x - 2

Answer:

B

Step-by-step explanation:

y = 7.5x - 2

The slope is 7.5

y- intercept is -2

Answer:

syuare root 270 to get 16.4 then subtract 6 to get 10.4

Answer:

y=log_2 (x)

Step-by-step explanation:

We see that the graph passes though the point (2,1). So we can write:

log_a (2) = 1  => a = 2

So it's a log in base 2.

Answer:

D

Step-by-step explanation:

The definition of a quadratic spline is that;

A Quadratic Spline is the creation of a set of polynomial functions that are quadratic and follow the format f(x) = ax² + bx + c.

A Quadratic Spline is simply defined as the creation of a set of polynomial functions that are quadratic, or relatively simple to comprehend and must follow the quadratic function format which is;

f(x) = ax² + bx + c

where;

a, b and c are the values gotten in the process of doing the Splines to create the desired functions.

Read more about quadratic functions at; https://brainly.com/question/1214333

Answer:

y = - [tex]\frac{10}{3}[/tex] x - 23

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 9, 7 ) and (x₂, y₂ ) = (- 6, - 3 )

m = [tex]\frac{-3-7}{-6-(-9)}[/tex] = [tex]\frac{-10}{-6+9}[/tex] = [tex]\frac{-10}{3}[/tex] = - [tex]\frac{10}{3}[/tex] , then

y = - [tex]\frac{10}{3}[/tex] x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (- 6, - 3 ) , then

- 3 = 20 + c ⇒ c = - 3 - 20 = - 23

y = - [tex]\frac{10}{3}[/tex] x - 23 ← equation of line

Answer:

y= -10x/3 + 1

Step-by-step explanation:

gradient of a line= (Y2-Y1)/(X2-X1)

= (-3-7)/[-6-(-9)]

=-10/3

equation of a line

(Y-Y1)/(X-X1)= gradient

(Y-7)/(X+9)= -10/3

3(Y-7)= -1d0(X+9)

3y-21= -10x -19

3y= -10x + 3

dividing both sides by 3

y= -10x/3 + 1

See picture for solution.

Answer:

[tex] \frac{1}{8} < \frac{2}{7} [/tex]

1/8 < 2/7

Answer: B

#CarryOnLearning

Answer:

(27000)(27225)

Step-by-step explanation:

Answer:

6/11

Step-by-step explanation:

The kinetic energy of the roller coaster is 2000Joules

Given the formula for expressing the velocity of the roller coaster is given as:

[tex]v = \sqrt{\frac{2k}{1000} }[/tex]

Given the following parameter:

v = 10m/s

Substitute the given parameter into the formula to have:

[tex]10 = \sqrt{\frac{2k}{1000} }[/tex]

Square both sides of the equation:

[tex](10)^2=(\frac{2k}{1000} )^2\\100=\frac{4k^2}{1,000,000} \\4k^2=100,000.000\\k^2=\frac{100,000,000}{4} \\k^2=4,000,000\\k=2000Joules[/tex]

Hence the kinetic energy of the roller coaster is 2000Joules

Learn more on subject of formula here: https://brainly.com/question/657646

Answer:

You need to use √2k/1000 formula.

2000 joule is the correct answer.

Answer:

  10.25

Step-by-step explanation:

The slope of AC is given by the slope formula:

  m = (y2 -y1)/(x2 -x1)

  m = (-4 -1)/(3 -(-1)) = -5/4

Then the slope of CB is the opposite reciprocal, 4/5. The equation of line CB in point-slope form is ...

  y -k = m(x -h) . . . . . . line with slope m through point (h, k)

  y -(-4) = 4/5(x -3) . . . . line CB

When y = 1 (to match the y-value of A), then ...

  1 +4 = 4/5(x -3)

  5(5/4) = (x -3) . . . . . multiply by 5/4

  6.25 +3 = x = 9.25 . . . . add 3

Point B is (9.25, 1).

The length of the hypotenuse is ...

  9.25 -(-1) = 10.25

Answer:

C should be the answer

Answer:

15.4919333848

Step-by-step explanation:

Answer:

Step-by-step explanation:

If you mean length is 2½ times its width not "2½cm times its width"

      2(L + W) = 270

2(2.5W + W) = 270

      2(3.5W) = 270

              7W = 270

                W = 38.5714285714...

                W ≈ 38.57 cm

Answer:

Width = 38. 57 cm

Step-by-step explanation:

The perimeter of a Rectangle = 270 cm

Now,

Let's take x to be the width.

Length = 2½ = 5x/2

According to the formula,

The perimeter of a rectangle = 2 ( l + w )

270 = 2 ( 5x/2 + x )

270 = 5x + 2x

270 = 7x

x = 270/7

x = 38. 57 cm.

• The width of a rectangle is 38.57 cm

Answer:

D is correct

Step-by-step explanation:

Answer:

I imagine you aren't using calculus, so:

A: the leading term is [tex]1>0[/tex], so it opens upwards.

B. First coordinate of the vertex is [tex]-\frac b{2a}=-\frac42=-2[/tex], the second coordinate we'll find by replacing the value: [tex]f(-2)=(-2)^2+4(-2)-12 = 4-8-12=-16[/tex]

C. Quadratic formula or if you stare at the equation long enough you can rewrite the equation as  [tex]f(x) = (x+6)\times(x-2)[/tex]. At this point the x intercepts are the zeroes of the function, or -6 and 2.

D. The y-intercept is the value of the function at 0, or the constant term: -12

E. The graph has a minimum since the curve opens upwards.

Answer:

46 cards

Step-by-step explanation:

We can use a variable to represent the starting amount of cards: (x)

Keith bought 4 new cards: (+4)

His dog ate half of the collection: (x/2)

There are now 25 cards: (=25)

So we can use this expression to find the starting amount: (x+4)/2=25

Start by multiplying both sides by 2 to get rid of the (x/2).

Now subtract 4 from both sides to get rid of the (+4).

Finally, we know x= 46

Thus, Keith started with 46 cards.

Answer:

[tex]\displaystyle m = 3[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Coordinate Planes

Slope Formula: [tex]\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Step-by-step explanation:

Step 1: Define

Identify points.

Point (8, 1)

Point (11, 10)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m.

Answer:

m=3

Step-by-step explanation:

[tex]4(x-3)+3(2x-5)\\\\=4x -12 + 6x -15\\\\=10x - 27[/tex]

Answer : =

Step - by - step explanation :

6 3/6 -- simplest form --> 6 1/2

6 6/12 -- simplest form --> 6 1/2

Answer:

g

is −12

-

1

2

.

−12

-

1

2

·

·

=

=

−1

Answer:

1. a break-even point

Step-by-step explanation:

This is when the two profits are the same between 2 companies / businesses, thus it is when they break even, or have the same amount of money

Answer:

probability = 1/2 or 50%

Step-by-step explanation:

number of red + number of green = 2 + 1 = 3

Probability of landing on a red or green = 3/6 = 1/2

Red

Step-by-step explanation:Red

[tex]\text{Given that,}\\\\f(x) = 3x +12, ~ ~ g(x) = 3x -1\\\\(f \circ g)(x)\\\\=f(g(x))\\\\=f(3x-1)\\\\=3(3x-1) +12\\\\=9x - 3 +12\\\\=9x +9\\\\=9(x+1)[/tex]

Answer:

image attached with answer

Step-by-step explanation: