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Rashid [163]
3 years ago
11

The length of a rectangle is 4 less than 2 times the width. The perimeter is 40 units.

Mathematics
1 answer:
bezimeni [28]3 years ago
8 0

Answer:

Let l be length and w be width.

First equation:

l = 2w-4

Second equation:

perimeter = 40 units

Perimeter of a rectangle: 2(l+w)

2(2w-4+w)=40

2(3w-4)=40

6w-8=40

6w=40+8

6w=48

w=48/6

w=8

Therefore the width=8;

length= 2w-4 = 2(8)-4  = 16-4  = 12

perimeter = 40 units

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Determine whether the point is on the graph of the equation 2x+3y=8.<br> (1,2)
geniusboy [140]

The point (1,2) is on the graph of the equation.

Explanation:

The equation is 2x+3y=8

We need to determine the point (1,2) is on the graph.

To determine the point (1,2) is on the graph, we need to substitute the point in the equation and find whether the LHS is equal to RHS.

Thus, substituting the point (1,2) in the equation 2x+3y=8, we get,

2(1)+3(2)=8

Multiplying the terms within the bracket, we have,

2+6=8

Adding the LHS, we have,

8=8

Thus, both sides of the equation are equal.

Hence, the point (1,2) is on the graph of the equation 2x+3y=8

3 0
3 years ago
3. How many solutions does the system of equations have? 2x=-10y+ 6 and x+5y=3
ozzi

Answer:

<h2>3. Infinitely many</h2>

Step-by-step explanation:

\left\{\begin{array}{ccc}ax+by=c\\dx+ey=f\end{array}\right\\\\(1)\\\text{if}\ a=d,\ b=e,\ c=f,\ \text{then the system of equations has infinitely many solutions}\\Example:\\\left\{\begin{array}{ccc}2x-3y=5\\2x-3y=5\end{array}\right\\(2)\\\text{if}\ a=d,\ b=e,\ c\neq f,\ \text{then the system of equations has no solution}\\Example:\\\left\{\begin{array}{ccc}2x-3y=5\\2x-3y=-5\end{array}\right

(3)\\\text{if}\ a\neq d\ \text{or}\ b\neq e,\ \text{then the system of equations has infinitely many solutions}\\Example:\\\left\{\begin{array}{ccc}x-3y=5\\2x-3y=5\end{array}\right

\text{We have:}\\\\\left\{\begin{array}{ccc}2x=-10y+6&\text{add 10y to both sides}\\x+5y=3\end{array}\right\\\left\{\begin{array}{ccc}2x+10y=6&\text{divide both sides by 2}\\x+5y=3\end{array}\right\\\left\{\begin{array}{ccc}x+5y=3\\x+5y=3\end{array}\right

4 0
4 years ago
Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.
maks197457 [2]
F(g(x)) = [(-7x-8)/(x-1) - 8} / [(-7x - 8)/(x-1) + 7] =

[(-7x - 8 - 8(x-1)) / (x-1)] / [(-7x - 8 + 7(x-1)) / (x-1)] = (-15x) / (-15) = x.

g(f(x)) = [-7*(x-8)/(x+7) - 8] / [(x-8)/(x+7) - 1] =

[(-7x + 56 -8*(x+7)) / (x+7)] / [(x - 8 - (x + 7)) / (x+7)] = (-15x) / (-15) = x.

So since f(g(x)) = g(f(x)) = x we can conclude that f and g are inverses.
5 0
3 years ago
What is the area and perimeter of a polygon with angles that equal 90 and a side the equals 8
IgorC [24]
That is correct, the answer is correct
6 0
3 years ago
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saveliy_v [14]

Answer:

Equivalent ratios

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Both include 60

3 0
3 years ago
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