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spin [16.1K]
3 years ago
8

The length of a rectangle is 4x+1 and the width is 2x+5. Write an expression and simplify it in terms of x: whats the perimeter

of the rectangle and whats the area of the rectangle
Mathematics
1 answer:
enot [183]3 years ago
5 0

Answer: ( P - 10 )/12, (2x + 5)(4x + 1)

Step-by-step explanation:

The length of the rectangle = 4x + 1,

The breadth = 2x + 5

Formula for finding perimeter of a rectangle, = 2( L + B )

Now, substitute for L and B in the formula, open the formula and simplify,

= 2(4x + 1 + 2x + 5 )

= 2(6x + 5 )

= 12x + 10

Therefore, the perimeter (p)of the rectangle, = 12x + 10.

If P = 12x + 10

12x = P - 10

x = ( P - 10 )/12

Area of a rectangle = L x B

=( 4x + 1 )( 2x + 5)

We therefore open the brackets

(4x + 1)(2x + 5)= 4x X 2x + 4x X 5+ 1 X 2x + 1 X 5

= 8x² + 20x + 2x + 5

A = 8x² + 22x + 5

A = (2x + 5)(4x + 1)

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The table shows how the number of cars, c, depends on the number people, t. How would you write this as an equation?
Nataly [62]

Answer:

t = 3c - 5

Step-by-step explanation:

The relation between c and t is linear as the increase of the value of t is uniform for each unit increase in the value of c.

Now, any two points on the graph of the t = f(c) equation are sufficient to determine the equation.

Let the points are (2,1) and (3,4).

So, using two points formula of straight line we get the equation is  

\frac{t - 4}{4 - 1} = \frac{c - 3}{3 - 2}

⇒ t - 4 = 3(c - 3)

⇒ t - 4 = 3c - 9

⇒ t = 3c - 5 (Answer)

6 0
3 years ago
Find the area A of polygon CDEFGH with the given vertices. C(0,5), D(2,5), E(2,3), F(3,2), G(-1,2), H(0,3)
enot [183]

Answer:

<em>The area of the polygon CDEFGH is 7</em>

Step-by-step explanation:

<u>Area of a Polygon</u>

The area of a polygon is generally calculated as the sum of the smaller areas that form its full shape, give each partial area has a known shape, like a square, rectangle, triangle, circle, etc.

The six points given in the question are plotted in the image below. They form a polygon whose area can be divided into two smaller shapes:

The area CDHE is a square of length side 2. Area of a square:

A1=L^2

The area HEFG is a trapezoid with bases lengths 4 and 2,  and height 1. Area of a trapezoid:

\displaystyle A2=\frac{b1+b2}{2}h

Calculate both areas:

A1=2^2=4

\displaystyle A2=\frac{2+4}{2}\cdot 1=3

Total Area=4+3=7

The area of the polygon CDEFGH is 7

8 0
3 years ago
What is the radius of a circle with a circumference measuring 24 pie cm?
Tpy6a [65]
By the way, it's pi, not pie. just wanted you to know as you may lose marks in tests for spelling (but i may be wrong)

we know circumference is pi multiplied by the diameter.
the diameter is 2x the radius
we can re-arrange the first fact to get:
diameter (or 2x radius) = circumference divided by pi.
since the circumference is 24pi we can cancel off pi from the circumference (24pi) and pi.
now we have the diameter = 24
since the diameter is 2x the radius you divide both sides by 2 and get:
radius=12cm
5 0
2 years ago
PLEASE HELP 10 POINTS
julsineya [31]

If she makes $9 per hour and the amount of hours is h, her amount of pay p is equal to 9h, so p = 9h

I hope this helps!

8 0
3 years ago
Find the value of each measure.
zloy xaker [14]

The two congruent base angles tell us that this is an isosceles triangle, meaning the triangle has two congruent sides. Therefore, we can set these two expressions equal to each other and solve from there.

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7 = 8x - 17

8x = 24

x = 3

Side = 15(3) + 7 = 45 + 7 = 52

Hope this helps!

4 0
3 years ago
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