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3 years ago

LMNP is a rectangle. Find the value of x and the length of each diagonal. LN=2x+25 and MP=6x−7

Mathematics

2 answers:

kenny6666 [7]3 years ago

7 0

Answer: The value of x is 8.

Length of LN = 2(8)+25 = 16+25 = 41 units.

Length of MP = 6(8)-7 = 48-7 = 41 units.

Step-by-step explanation:

As we know that

Diagonals of rectangle is equal to each other.

LN = 2x+ 25

MP = 6x - 7.

According to above statement, we have that

LN = MP

$2x+25=6x-7\\\\25+7=6x-2x\\\\32=4x\\\\x=\dfrac{32}{4}=8$

Hence, the value of x is 8.

Length of LN = 2(8)+25 = 16+25 = 41 units.

Length of MP = 6(8)-7 = 48-7 = 41 units.

Nana76 [90]3 years ago

3 0

2x+25=6x-7
4x=32
x = 8
LN = 41
MP = 41

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3 years ago

The point P(1,1/2) lies on the curve y=x/(1+x). (a) If Q is the point (x,x/(1+x)), find the slope of the secant line PQ correct

lukranit [14]

Answer:

See explanation

Step-by-step explanation:

You are given the equation of the curve

$y=\dfrac{x}{1+x}$

Point $P\left(1,\dfrac{1}{2}\right)$ lies on the curve.

Point $Q\left(x,\dfrac{x}{1+x}\right)$ is an arbitrary point on the curve.

The slope of the secant line PQ is

$\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{\frac{x}{1+x}-\frac{1}{2}}{x-1}=\dfrac{\frac{2x-(1+x)}{2(x+1)}}{x-1}=\dfrac{\frac{2x-1-x}{2(x+1)}}{x-1}=\\ \\=\dfrac{\frac{x-1}{2(x+1)}}{x-1}=\dfrac{x-1}{2(x+1)}\cdot \dfrac{1}{x-1}=\dfrac{1}{2(x+1)}\ [\text{When}\ x\neq 1]$

1. If x=0.5, then the slope is

$\dfrac{1}{2(0.5+1)}=\dfrac{1}{3}\approx 0.3333$

2. If x=0.9, then the slope is

$\dfrac{1}{2(0.9+1)}=\dfrac{1}{3.8}\approx 0.2632$

3. If x=0.99, then the slope is

$\dfrac{1}{2(0.99+1)}=\dfrac{1}{3.98}\approx 0.2513$

4. If x=0.999, then the slope is

$\dfrac{1}{2(0.999+1)}=\dfrac{1}{3.998}\approx 0.2501$

5. If x=1.5, then the slope is

$\dfrac{1}{2(1.5+1)}=\dfrac{1}{5}\approx 0.2$

6. If x=1.1, then the slope is

$\dfrac{1}{2(1.1+1)}=\dfrac{1}{4.2}\approx 0.2381$

7. If x=1.01, then the slope is

$\dfrac{1}{2(1.01+1)}=\dfrac{1}{4.02}\approx 0.2488$

8. If x=1.001, then the slope is

$\dfrac{1}{2(1.001+1)}=\dfrac{1}{4.002}\approx 0.2499$

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3 years ago

An athlete runs 8 miles in 50 minutes on a treadmill. At this rate how long will it take the athlete to run 9 miles? Your answer

zvonat [6]

56.25 minutes

Explanation: to find how long it takes to run one mile, divide 50 minutes by 8 miles.
50/8 = 6.25
Then you can multiply 6.25 by 9 to find the answer.
9 x 6.25 = 56.25 minutes

4 0

3 years ago

What is the width of this shape

77julia77 [94]

We see that the area is 159 3/8 and the length is 18 3/4.

Because the area is the length*width, to find the width, we must divide the area by the length.

Think of it this way:
$A = l*w$

Divide l on both sides:
$\frac{A}{l} = w$

And w is what we're looking for.
So, divide 159 3/8 by 18 3/4.

You should get that the width is 8.5 feet :)

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3 years ago

Pls help me ill give brainliest and no links ty!<3:)

Neko [114]

T is the midpoint of PQ

PT=TQ

5x+7 = 7x-7

2x= 14

x= 14/2

x= 7

PT = 5(7)+7 = 42

5 0

3 years ago