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Ede4ka [16]
3 years ago
12

The length plus the width of a rectangle is 10. Let x represent the length. The equation for the area y of the

Mathematics
1 answer:
yuradex [85]3 years ago
8 0

Answer:

length of rectangle = 5

width of rectangle = 5

Area of rectangle = 25

Step-by-step explanation:

Since the length of the rectangle is "x", and the value of the area is given by the product of the length "x" times the width "10-x", indeed, the area "y" of the rectangle is given by the equation:

y=x\,(10-x)=10x-x^2

Now, they tell us that the area of the rectangle is such that coincides with the maximum (vertex) of the parabola this quadratic expression represents. So in order to find the dimensions of the rectangle and therefore its area, we find the x-coordinate for the vertex, and from it, the y-coordinate of the vertex, which is the rectangle's actual area.

Recall that the formula for the x of the vertex of a quadratic of the form :

y=ax^2+bx+c

is given by the formula:

x_{vertex}=-\frac{b}{2\,a}

which in our case gives:

x_{vertex}=-\frac{b}{2\,a}\\x_{vertex}=-\frac{10}{2\,(-1)}\\x_{vertex}=5

Therefore, the length of the rectangle is 5, and its width (10-x) is also 5.

The area of the rectangle is therefore the product of these two values: 5 * 5 = 25

Which should coincide with the value we obtain when we replace x by 5 in the area formula:

y=10x-x^2\\y=50-(5)^2\\y=50-25\\y=25

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△ABC is similar to △XYZ. Also, side AB measures 6 cm, side BC measures 18 cm, and side XY measures 12 cm.
Serggg [28]

Answer:

value of sides YZ is 36 cm

Step-by-step explanation:

Similar triangles states that the length of the corresponding sides are in proportion.

Given that: ΔABC is similar to ΔXYZ

then;

Corresponding sides are in proportion i.e

\frac{AB}{XY}=\frac{BC}{YZ}=\frac{AC}{XZ}    .....[1]

As per the statement:

side AB = 6 cm, side BC =18 cm and side XY = 12 cm.

Substitute these in [1] to solve for side YZ;

\frac{6}{12}= \frac{18}{YZ}

or

\frac{1}{2} = \frac{18}{YZ}

By cross multiply we have;

YZ = 36 cm

Therefore, the value of sides YZ is 36 cm


4 0
3 years ago
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Help me quickly! NO LINKS!!!!
AURORKA [14]

Answer:

180 - 110 = 70

<DBC = 70

4 0
3 years ago
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Jenny used plastic cone shaped cups to serve punch. The cups were 6 inches in diameter and inches tall. What was the volume of e
Volgvan

Answer:

47.14 in³

Step-by-step explanation:

Here is the complete question

Jenny used plastic cone shaped cups to serve punch. The cups were 6 inches in diameter and 5 inches tall. What was the volume of each cup?

Volume of a cone = \frac{1}{3}πr²h

π = 22/7

Radius = diameter / 2 = 6 /2 = 3 inches

(1/3) x (3^2) x (22/7) x 5  = 47.14 in³

5 0
3 years ago
Verdadero o Falso:
crimeas [40]
B is the correct answer
8 0
3 years ago
Please help with areas
Softa [21]

Answer:

Step-by-step explanation:

7) The formula for determining the area of a parallelogram is expressed as

Area = base × height.

Length of base = Area/height

Therefore,

Length of base = 7/2 = 3.5 feet

8) The formula for determining the area of a trapezoid is expressed as

Area = 1/2(a + b)h

Where

a and b are the length of the bases

h is the height. Therefore

21 = 1/2(2 + 4)h

21 = 3h

h = 21/3 = 7 inches

9) Area = base × height.

Height = Area/Length of base

Height = 28/14 = 2 inches

10) a and b are 10 inches each.

Area = 1/2(a + b)h

Therefore,

35 = 1/2(10 + 10)h

35 = 10h

h = 35/10

h = 3 inches

7 0
3 years ago
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