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3 years ago

4. A rectangle with area 1,600 m2 is 4 times as long as it is wide. What is the sum of the diagonals?

Mathematics

1 answer:

Anuta_ua [19.1K]3 years ago

5 0

We need to write out algebraic equations to describe the information we have, then solve them using substitution.

We will define length as a and width as b.

we know that a x b = 1600 cm3 (area = length x width)

and a=4b

So, we can substitute the vaule 4b for a in the first equation:

4b x b = 1600

we can simplify to 4b2 = 1600

divide both sides by 4:

b2 = 400

take the square root of each side:

b = √400

b=20

So we know the width = 20

length = 4 x width = 80

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3 years ago

The dot plots show rainfall totals for several spring storms in highland areas and lowland areas. What is the median rainfall fo

tresset_1 [31]

Answer:

Median highland = 16 mm

Median lowland = 16 mm

Step-by-step explanation:

For the highland area :

The sample size, n = 44

Obtain the median value using :

1/2 * (n + 1)th term

1/2 * (44 +1) th term

1/2 * 45 = 22.5th term.

(22nd + 23rd) term / 2

(16 + 16) / 2 = 16 mm

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3 years ago

Read 2 more answers

Simplify 3 sqrt 5x * 3 sqrt 25x^ 2 completely.

tia_tia [17]

Answer:

=45x√5x

Step-by-step explanation:

The provided expression is: 3√5x×3√25x²

We can simplify 3√25x² because √25x²=5x

3×5x=15x

Combine with the rest of the expression through multiplication.

3√5x×15x

=45x√5x

The expression 3√5x×3√25x² is equivalent to 45x√5x.

The expected simplified answer is 45x√5x

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The area of Kamar’s tabletop is a whole number of square feet. Could the length and width be decimal numbers each with one decim

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3 years ago

Brady made a scale drawing of a rectangular swimming pool on a coordinate grid. The points (-20, 25), (30, 25), (30, -10) and (-

djverab [1.8K]

Answer:

Length = 50 units

width = 35 units

Step-by-step explanation:

Let A, B, C and D be the corner of the pools.

Given:

The points of the corners are.

$A(x_{1}, y_{1}})=(-20, 25)$

$B(x_{2}, y_{2}})=(30, 25)$

$C(x_{3}, y_{3}})=(30, -10)$

$D(x_{4}, y_{4}})=(-20, -10)$

We need to find the dimension of the pools.

Solution:

Using distance formula of the two points.

$d(A,B)=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$ ----------(1)

For point AB

Substitute points A(30, 25) and B(30, 25) in above equation.

$AB=\sqrt{(30-(-20))^{2}+(25-25)^{2}}$

$AB=\sqrt{(30+20)^{2}}$

$AB=\sqrt{(50)^{2}$

AB = 50 units

Similarly for point BC

Substitute points B(-20, 25) and C(30, -10) in equation 1.

$d(B,C)=\sqrt{(x_{3}-x_{2})^{2}+(y_{3}-y_{2})^{2}}$

$BC=\sqrt{(30-30)^{2}+((-10)-25)^{2}}$

$BC=\sqrt{(-35)^{2}}$

BC = 35 units

Similarly for point DC

Substitute points D(-20, -10) and C(30, -10) in equation 1.

$d(D,C)=\sqrt{(x_{3}-x_{4})^{2}+(y_{3}-y_{4})^{2}}$

$DC=\sqrt{(30-(-20))^{2}+(-10-(-10))^{2}}$

$DC=\sqrt{(30+20)^{2}}$

$DC=\sqrt{(50)^{2}}$

DC = 50 units

Similarly for segment AD

Substitute points A(-20, 25) and D(-20, -10) in equation 1.

$d(A,D)=\sqrt{(x_{4}-x_{1})^{2}+(y_{4}-y_{1})^{2}}$

$AD=\sqrt{(-20-(-20))^{2}+(-10-25)^{2}}$

$AD=\sqrt{(-20+20)^{2}+(-35)^{2}}$

$AD=\sqrt{(-35)^{2}}$

AD = 35 units

Therefore, the dimension of the rectangular swimming pool are.

Length = 50 units

width = 35 units

7 0

3 years ago