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Natasha_Volkova [10]

4 years ago

5

Mauro has 140 ft of rope. He will cut it into two pieces so that the length of the longer piece is 3 times the length of the sho

rter piece. What will the length of the longer piece be? _________ ft

2 answers:

ipn [44]4 years ago

4 0

140= x +3x
140 =4x
140/4= 4x/4
35= x
3x= 105
The length of the longer piece is 105 feet

Studentka2010 [4]4 years ago

4 0

Answer:

The length of the longer piece is 35 feet.

Step-by-step explanation:

Let the length of the longer piece is x

Hence, length of the shorter piece is 3x

Now, the length of the rope is 140 ft. Thus, we have the equation

$x+3x=140$

Add the like terms. $x+3x=4x$

$4x=140$

Divide both sides by 4

$x=35$

Therefore, the length of the longer piece is 35 feet.

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A circle is centered at the point (-3, 2) and passes through the point (1, 5). The radius of the circle is ___ units. The point

mixas84 [53]

Answer:

The radius is 5 units

(-7,-1) and (-7,5) lies on the circle

Step-by-step explanation:

Use the distance formula to find the distance between the center and the given point that gives you the radius.

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

The center is (-3,2) and the point on the circumference is (1,5)

$r=\sqrt{(1--3)^2+(5-2)^2}$

$r=\sqrt{(4)^2+(3)^2}$

$r=\sqrt{16+9}$

$r=\sqrt{25}$

$\therefore r=5$

The radius is 5 units.

The equation of the circle is given by:

$(x--3)^2+(y-2)^2=5^2$

$(x+3)^2+(y-2)^2=25$

When x=-7, we obtain y by substituting into the equation of the circle:

$(-7+3)^2+(y-2)^2=25$

$(-4)^2+(y-2)^2=25$

$16+(y-2)^2=25$

$(y-2)^2=25-16$

$(y-2)^2=9$

$y-2=\pm \sqrt{9}$

$y=2\pm 3$

$y=-1$ or y=5

Therefore (-7,-1) and (-7,5) lies on the circle.

6 0

4 years ago

A rectangle has a perimeter of 80 cm and its length is 1 cm more than twice its width. Find the dimensions of a rectangle given

zimovet [89]

Answer: (a) P = 6W + 2

(b) L = 2W + 1

(c) Width = 13cm

Length = 27cm

Step-by-step explanation:

The formula for perimeter of a rectangle is 2(length + width). Since the length is 1 cm more than twice its width, then the length will be:

L = (2 × W) + 1

(b) L = 2W + 1

Therefore, P = 2(L + W)

P = 2( 2W + 1) + 2W

P = 4W + 2 + 2W

(a) P = 6W + 2

Since perimeter is given as 80cm. Therefore,

P = 6W + 2

6W + 2 = 80

6W = 80 - 2

6W = 78

W = 78/6

W = 13

Width is 13cm

Length = 2W + 1

Length = 2(13) + 1

Length = 27cm

6 0

3 years ago

9x-3x-5=19 solve for x

Natasha_Volkova [10]

Answer: x=4

Step-by-step explanation:

Simplify the left side of 9x-3x-5=19 by combining like terms:

6x-5=19

Add 5 to both sides:

(6x-5)+5=19+5

Simplify:

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Divide both sides by 6:

(6x)/6=24/6

Simplify:

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3 years ago

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Rama09 [41]

The answer will be D

3 0

3 years ago

Read 2 more answers

I don’t understand any of this

AysviL [449]

Answer:

Step-by-step explanation:

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∠B ≅ ∠Y [Given]

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Similarity statement:

Corresponding sides of these similar triangles will be proportional.

$\frac{XZ}{AB}= \frac{ZY}{BC}=\frac{XY}{AC}$

Similarity ratio:

$\frac{XY}{AC}=\frac{24}{16}$

= $\frac{3}{2}$

= 3 : 2

5 0

3 years ago