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3 years ago

PLEASE HELP ME!!! WILL GIVE BRAINLIEST!!!!,find (f+g)(x) for the following functions.

Mathematics

1 answer:

Sphinxa [80]3 years ago

4 0

Answer:

$(f+g)(x)=6x^2+13x+14$

Step-by-step explanation:

(f+g)(x) simply means that you are adding f(x) to g(x) to get a new equation that is the sum of them.

$6x^2+9x+8+4x+6$

simplifies down to, by combining like terms,

$6x^2+13x+14$

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The perimeter of a rectangle is 30.8 km and it’s diagonal length is 11 km. Find it’s length and width

blsea [12.9K]

Answer:

Length of the rectangle is 15.0325 km and width is 0.3765 km.

Explanation:

Given:

Perimeter of a rectangle = 30.8 km

Length of diagonal of rectangle = 11 km

To find:

The length and width of rectangle=?

Solution:

Lets assume length of the rectangle = x km

And assume width of the rectangle = y km

Lets first create equation using given perimeter

perimeter of rectangle = 2 ( length + width )

=> 30.8 km = 2 ( x + y )

=> $x + y = \frac{30.8}{2}$

=> y = 15.4 – x ------(1)

As diagonal and two sides of rectangle forms right angle triangle whose hypoteneus is diagonal ,

=> $length^2 + width^2 = diagonal^2$

=> $x^2 + y^2 = 11^2$

=> $x^2 + y^2 = 121$

On substituting value of y from (1) in above equation we get

=> $x^2 + (15.4-x)^2 = 121$

=> $x^2 + (15.4)^2 + x^2 – 2 x 15.4 \times x = 121$

=> $2x^2-30.8x + 237.16 -121 = 0$

=> $2x^2-30.8x + 116.16 = 0$

Solving above quadratic equation using quadratic formula

General form of quadratic equation is

$ax^2 +bx +c = 0$

And quadratic formula for getting roots of quadratic equation is

$x= \frac{ -b\pm\sqrt{(b^2-4ac)}}{2a}$

As equation is $2x^2-30.8x + 116.16 = 0$ , in our case

a = 2 , b = -30.8 and c = 116.16

Calculating roots of the equation we get

$x=\frac{ -(-30.8)\pm\sqrt{(-30.8)^2-4(2)( 11)} } {(2\times2)}$

$x=\frac{30.8\pm\sqrt{(948.64-88)}}{4}$

$x=\frac{30.8\pm\sqrt{860.64}}{4}$

$x=\frac{(30.8\pm29.33)}4$

$x=\frac{(30.8+29.33)}{4}$

$x=\frac{(30.8-29.33)}{4}$

=> x = 15.0325 or x = 0.3675

As generally length is longer one ,

So x = 1.0325

From equation (1) y = 15.4 – x = 0.3765

Hence length of the rectangle is 15.0325 km and width is 0.3765 km.

6 0

3 years ago

HELPPP 15 POINTS!!

yanalaym [24]

Answer:

Option C, 30

Step-by-step explanation:

<u>Step 1: Identify how many people spent $200</u>

There was only 30 people that spent $200

Answer: Option C, 30

8 0

3 years ago

A certain four-cylinder combination lock has 50 numbers on it. to open it, you turn to a number on the first cylinder, then t

kumpel [21]

A certain four-cylinder combination lock has 50 numbers on it.

It is a four cylinder combination lock

Each cylinder has 50 numbers

So we have to choose 4 numbers for 4 cylinders

_____ , ______ , ______, _____

you turn to a number on the first cylinder

We have 50 numbers so we have 50 combinations

__50___ , ______ , ______, _____

Repetitions are allowed so we do the same for remaining three

50 , 50 , 50 , 50

50 * 50 * 50* 50 = 6250000

There are 6250000 different lock combinations .

7 0

3 years ago

Read 2 more answers

Write an equation in slope-intercept form for the line that passes through the point (-8, 2) and is perpendicular to the line y

tamaranim1 [39]

Answer:

y = -5x/4 - 8

Step-by-step explanation:

Two lines that are perpendicular have slopes that are opposite reciprocals.

Since the slope of the given line is 4/5, the opposite reciprocal of that is -5/4. So the equation has a slope of -5/4.

Since we know the coordinate of a point of the other equation, we can plug that into the point-slope form equation y - y1 = m(x - x1):

y - 2 = -5/4(x-(-8))

Simplify:

y - 2 = -5/4(x+8)

y - 2 = -5x/4 - 10

So the equation in slope-intercept form is:

y = -5x/4 - 8

3 0

3 years ago

2 tables. Table 1 is titled Population data with entries 2, 4, 8, 5, 1, 1, 10, 5, 4, 2, 3, 3. Table 2 is titled Sample data with

alekssr [168]

Answer: //The mean of the population is 4

//The mean of the population is 3.25

//The difference between the mean of the sample and the mean of the population is 0.75

Step-by-step explanation: EGDEUNITY

7 0

3 years ago