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1 year ago

Someone help me with this I will make you brain

Mathematics

1 answer:

vovangra [49]1 year ago

7 0

The third table would be your answer.

I know this because I turned both equations shown into graph form, this allowed me to see what the x-values of 1, 2, and 3 would have for y-values. My graph of both equations is shown in the picture below. (Green is f(x) = x + 4 and purple is g(x) = -2f(x))

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Determine the maximized area of a rectangle that has a perimeter equal to 56m by creating and solving a quadratic equation. What

sveticcg [70]

Answer:

Area of rectangle = $196\,m^2$

Length of rectangle = 14 m

Width of rectangle = 14 m

Step-by-step explanation:

Given:

Perimeter of rectangle is 56 m

To find: the maximized area of a rectangle and the length and width

Solution:

A function $y=f(x)$ has a point of maxima at $x=x_0$ if $f''(x_0)$

Let x, y denotes length and width of the rectangle.

Perimeter of rectangle = 2( length + width )

$=2(x+y)$

Also, perimeter of rectangle is equal to 56 m.

So,

$56=2(x+y)\\x+y=28\\y=28-x$

Let A denotes area of rectangle.

A = length × width

$A=xy\\=x(28-x)\\=28x-x^2$

Differentiate with respect to x

$\frac{dA}{dx}=28-2x$

Put $\frac{dA}{dx}=0$

$28-2x=0\\2x=28\\x=14$

Also,

$\frac{d^2A}{dx^2}=-2$

At x = 14, $\frac{d^2A}{dx^2}=-2$

So, x = 14 is a point of maxima

So,

$y=28-x=28-14=14$

Area of rectangle:

$A=xy=14(14)=196\,m^2$

Length of rectangle = 14 m

Width of rectangle = 14 m

5 0

2 years ago

Devaughn is 5 years younger than Sydney. The sum of their ages is45. What is Sydney's age?

Verizon [17]

Let the age of devaughn be x and Sydney be y.
Then,x+y=45
x+5=y
y=x+5
here,
put y=x+y in x+y=45
then,
x+y=45
x+x+5=45
2x=40
x=20
now,
y=x+5
y=20+5
y=25

5 0

2 years ago

Read 2 more answers

Angelica is currently 13 years old she is 2 years older than her brother. Write an equation to represent the situation.Solve ur

sdas [7]

Answer:

Therefore,

$x+2=13$ .......Equation

Angelica's Brother's age is 11 years old.

Step-by-step explanation:

Given:

Let the current age of Angelica's Brother be 'x' years old

Angelica's current age is 13 years old,

According to given condition,

Therefore the Equation will be,

$x+2=13$

On solving this equation we get

$x=13-2=11\\\\x=11\ years$

Therefore,

Angelica's Brother's age is 11 years old.

Therefore,

$x+2=13$ .......Equation

Angelica's Brother's age is 11 years old.

6 0

2 years ago

Find the interest rate you are borrowing $2,500 for 2 years and you ear $450 in interest

Andrews [41]

Answer:

2500×100/2×450

25/2×450

25/900=

3 0

2 years ago

01:29:

ankoles [38]

Answer:

The length of arc LMN is 14.2cm

Step-by-step explanation:

First of all we have to calculate the circumference of the circle and then extract the portion that corresponds to MN

To solve this exercise we need to use the circumference formula of a circle:

c = circumference

r = radius = 6cm

π = 3.14

c = 2π * r

we replace the known values

c = 2 * 3.14 * 6cm

c = 37.68cm

As we know a circle is represented with 360 ° and they tell us that the angle of the MN part is 75 °, so we have to know the relationship with respect to the total

75° / 360° = 5/24

Now we multiply this number by the circumference and we will obtain the length of the arc MN

MN = 37.68cm * 5/24

MN = 7.85cm

Now we add the values of LM with NM and we will obtain the length of LMN

LMN = 6.3cm + 7.85cm

LMN = 14.15cm

round to the nearest tenth

LMN = 14.15cm = 14.2cm

The length of arc LMN is 14.2cm

8 0

3 years ago