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Aleonysh [2.5K]
3 years ago
12

24 times 21 using the area model

Mathematics
1 answer:
AlladinOne [14]3 years ago
4 0
20. × 20

4. × 1
you also multiply 20×1 and 20×4 twice science both numbers are 20
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the triangle are equilateral

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Which ordered pair is a solution to the system of linear equations One-half x minus three-fourths y = StartFraction 11 Over 60 E
s344n2d4d5 [400]

Answer:

\left(\dfrac{2}{3},\dfrac{1}{5}\right)

Step-by-step explanation:

Given the system of two equations:

\left\{\begin{array}{l}\dfrac{1}{2}x-\dfrac{3}{4}y=\dfrac{11}{60}\\ \\\dfrac{2}{5}x+\dfrac{1}{6}y=\dfrac{3}{10}\end{array}\right.

Multiply the first equation and the second equation by 60 to get rid of fractions:

\left\{\begin{array}{l}30x-45y=11\\ \\24x+10y=18\end{array}\right.

Now multiply the first equation by 4 and the second equation by 5:

\left\{\begin{array}{l}120x-180y=44\\ \\120x+50y=90\end{array}\right.

Subtract them:

(120x-180y)-(120x+50y)=44-90\\ \\120x-180y-120x-50y=-46\\ \\-230y=-46\\ \\y=\dfrac{46}{230}=\dfrac{1}{5}

Substitute it into the first equation:

30x-45\cdot \dfrac{1}{5}=11\\ \\30x-9=11\\ \\30x=11+9\\ \\30x=20\\ \\x=\dfrac{2}{3}

The solution is \left(\dfrac{2}{3},\dfrac{1}{5}\right)

4 0
3 years ago
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The coordinates of the vertices of a rectangle are (−3, 4) , (7, 2) , (6, −3) , and (−4, −1) . What is the perimeter of the rect
ki77a [65]

Answrer

Find out the what is the perimeter of the rectangle .

To prove

Now as shown in the figure.

Name the coordinates as.

A(−3, 4) ,B (7, 2) , C(6, −3) , and D(−4, −1) .

In rectangle opposite sides are equal.

Thus

AB = DC

AD = BC

Formula

Disatnce\ formula = \sqrt{(x_{2} - x_{1})^{2} +(y_{2} - y_{1})^{2}}

Now the points  A(−3, 4) and  B(7, 2)

AB = \sqrt{(7- (-3))^{2} +(2- 4)^{2}}

AB = \sqrt{(10)^{2} +(-2)^{2}}

AB = \sqrt{100+4}

AB = \sqrt{104}

AB = 2\sqrt{26}\units

Thus

CD= 2\sqrt{26}\units

Now the points

A (−3, 4) , D (−4, −1)

AD = \sqrt{(-4 - (-3))^{2} +(-1- 4)^{2}}

AD = \sqrt{(-1)^{2} +(-5)^{2}}

AD = \sqrt{1 + 25}

AD = \sqrt{26}\units

Thus

BC = \sqrt{26}\units  

Formula

Perimeter of rectangle = 2 (Length + Breadth)

Here

Length = 2\sqrt{26}\ units

Breadth = \sqrt{26}\ units  

Perimeter\ of\ rectangle = 2(2\sqrt{26} +\sqrt{26})

Perimeter\ of\ rectangle = 2(3\sqrt{26})

Perimeter\ of\ rectangle = 6\sqrt{26}

\sqrt{26} = 5.1 (Approx)

Perimeter\ of\ rectangle = 6\times 5.1

Perimeter of a rectangle = 30.6 units.

Therefore the perimeter of a rectangle is 30.6 units.

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3 years ago
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B. Reflect the graph about the y-axis and translate one unit up
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