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3 years ago

The area of a square garden is 50m^2. How long is the diagonal?

Mathematics

1 answer:

abruzzese [7]3 years ago

3 0

Answer:

Adjacent length = √(50) m

Pythagorean theorem:

a^2 + b^2 = c^2

a = √(50) m

b = √(50) m

c^2 = √(50)^2 + √(50)^2

c^2 = 50 + 50

c^2 = 100

c = 10 m

Diagonal = 10 m

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write an equation for the line that passes through the given point and has the given slope m (4,-5);m= -1/4

EastWind [94]

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Answer: $\textsf{y = -1/4x - 4}$

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Given: $\textsf{Slope = -1/4, Point through = (4, -5)}$

Find: $\textsf{Equation for the line that passes through the given point}$

Solution: In order to get the equation, we need to first use the point-slope form to help us sort out our information and then we solve for y.

Plug in the values

$\textsf{y - y}_1\textsf{ = m(x - x}_1\textsf{)}$

$\textsf{y - (-5) = -1/4(x - 4)}$

Simplify and solve for y

$\textsf{y + 5 = -1/4(x - 4)}$

$\textsf{y + 5 = -1/4x + 1}$

$\textsf{y + 5 - 5 = -1/4x + 1 - 5}$

$\textsf{y = -1/4x - 4}$

Therefore, the final answer would be that the equation that has a slope of -1/4 and passes through (4, -5) is y = -1/4x - 4.

5 0

2 years ago

#11 i

Paraphin [41]

The area of a shape is the amount of space a shape can occupy, while the perimeter is the sum of its lengths.

The perimeter is $18 + 3\sqrt 5 + 3\sqrt 2$ units
The area of the sanctuary is 27 square units

We have:

$A = (5,7)\\B=(8, 7)\\C=(8, 1)\\D=( 1, 1)\\E=( 1, 4)\\F= ( 5,4)$

Perimeter

See attachment for the layout of the sanctuary

$BC = \sqrt{(8 - 8)^2 + (7 - 1)^2} = 6$

$EF = \sqrt{(1 - 5)^2 + (4 - 4)^2} = 4$

$FA = \sqrt{(5 - 5)^2 + (4 - 7)^2} = 3$

From the attachment, the sides are

AB, BF, FC, CD, DE and EA

Start by calculating the length of each side using the following distance formula:

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

So, we have:

$AB = \sqrt{(5 - 8)^2 + (7 - 7)^2} = 3$

$BF = \sqrt{(8 - 5)^2 + (7 -1)^2} = \sqrt{45} = 3\sqrt 5$

$FC = \sqrt{(8 - 5)^2 + (1 -4)^2} = \sqrt{18} = 3\sqrt 2$

$CD = \sqrt{(8 - 1)^2 + (1 - 1)^2} = 7$

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

$EA = \sqrt{(1 - 5)^2 + (4 -7)^2} = 5$

So, the perimeter (P) is:

$P = AB + BF + FC + CD + DE + EA$

$P = 3 + 3\sqrt 5 + 3\sqrt 2 + 7 + 3 + 5$

$P = 18 + 3\sqrt 5 + 3\sqrt 2$

Hence, the perimeter is $18 + 3\sqrt 5 + 3\sqrt 2$ units

Area

To calculate the area, we need to divide the sanctuary into three.

Triangle ABF
Triangle EFA
Trapezium CDEF

The area of ABF is:

$Area = \frac 12 \times AB \times FA$

Where:

$AB = 3$

$FA = \sqrt{(5 - 5)^2 + (4 - 7)^2} = 3$

$Area = \frac 12 \times 3 \times 3$

$Area = \frac 92$

The area of EFA is:

$Area = \frac 12 \times EF \times FA$

Where:

$FA = 3$

$EF = \sqrt{(1 - 5)^2 + (4 - 4)^2} = 4$

So:

$Area = \frac 12 \times 4 \times 3$

$Area = 6$

The area of CDEF is:

$Area = \frac 12(CD + EF) \times DE$

Where

$CD = 7$

$EF = 4$

$DE = 3$

So, we have:

$Area = \frac 12 (7 + 4) \times 3$

$Area = \frac 12 \times 11 \times 3$

$Area = \frac {33}2$

So, the area of the sanctuary is:

$Area = \frac 92 + 6 + \frac {33}2$

$Area = \frac {9 +12 + 33}2$

$Area = \frac {54}2$

$Area = 27$

Hence, the area of the sanctuary is 27 square units

Read more about areas and perimeters at:

brainly.com/question/11957651

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3 years ago

Find a slope-intercept form equation for the line through the points (-10,7) and (5,4).

Naddika [18.5K]

Answer:

Step-by-step explanation:

(4 - 7)/(5 + 10) = -3/15 = -1/5

y - 4 = -1/5(x - 5)

y - 4 = -1/5x + 1

y = -1/5x + 5

8 0

3 years ago

Explain why the functions with the given graphs can't be solutions of the differential equation dy dt = et(y − 1)2.

Brut [27]

Please see attached document for the graphs:

The functions with the given graphs can't be solutions of the differential equation dy dt = et(y − 1)2.

(a) won’t work, since it has negative slope on portions of its solutions. The slope, e t (y − 1)2 , is a nonnegative function.

(b) won’t work, since it has positive slope at y = 1, where the slope must be flat.

3 0

3 years ago

Pls help I don't wanna get a bad grade

galina1969 [7]

Answer:

its B

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers