Twice the area of a square is 72 square miles. What is the length of each side of the square?

Answers

Answer 1
Answer:

Answer:

6 miles

Step-by-step explanation:

Let's say the length of the sides of the square is x.

The area of a square is denoted by: A = x².

Here, we're given that twice the area of the square is 72, so we can write this is 2 times the area, which is 2 * x². Set this equal to 72 and solve:

2x² = 72

x² = 36

x = 6

Thus the answer is 6 miles.

Answer 2
Answer:

Answer:

6 miles

Step-by-step explanation:

2A = 72

A = 72/2

A = 36

Area = s²

36 = s²

s = 6 miles


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What is the solution of the following quadratic inequality? x2 – 4x – 21 ≤ 0

Answers

Answer:

3, and -7

Step-by-step explanation:

First factor the trinomial

y=x2−4x−21

.

Find 2 numbers knowing sum (-4) and product (c = - 21). They are the numbers in the factor pair (3, -7).

y = (x + 3)(x - 7)

Solving the 2 binomials, we get:

x = -3 and x = 7

We want to solve the given quadratic inequality.

The correct option is the second one, counting from the top.

So we need to solve:

x^2 - 4x - 21  ≤ 0

Because we have the graph, we can avoid all the algebra.

Notice that the equation must be equal to or smaller than zero, then we just need to find the values of x such that the graph intersects the x-axis or is below it.

By looking at the given graph, we can see that the given range goes from -3 to 7

Then the solution is:

-3 ≤ x ≤ 7

This would be represented with a number line going from -8 to 8, two closed circles (because we use the symbols ≤ ≥) at negative 3 and 7, and the region between the circles is shaded.

The correct option is the second one.

If you want to learn more, you can read:

brainly.com/question/11897796

The mass of Box A and Box B is 0.6 kg. The mass of Box A and Box C is 1.3 kg.Box C is 3 times as heavy as Box B. Find the mass of Box A.

Answers

Answer:

A=0.25

B=0.35

C=1.05

Step-by-step explanation:

1. A+B=0.6

2. A+C=1.3

3. C=3B

2 subtract 1:

  • C-B=0.7

3 substituted:

  • 3B-B=0.7
  • B=0.35
  • C=0.7+0.35=1.05
  • A=0.6-0.35=0.25

Multiply. Write your answer in scientific notation. (2 x 10^7) (1 x 10^7)

Answers

2 x 10exponent 14 I think

Hep me on this please

Answers

Answer:

2,240 square meters

Step-by-step explanation:

The shape above is a trapezoid. Therefore, we can use the area formula for a trapezoid:

A=1/2(a+b) *h

where a is the short base, b is the long base is h is the height.

In this trapezoid, the short base is 50 meters , the long base is 90 meters and the height is 32 meters.

a= 50

b=90

h=32

A=1/2(50+90)*32

Add inside the parentheses first.

A=1/2(140)*32

Multiply 1/2 and 140, or divide 140 by 2.

A=70*32

Multiply 70 and 32

A=2240

Add appropriate units. In this case, the units are meters^2

A=2240 meters^2

The area of the playground is 2,240 meters^2

Answer:

The answer is 2240m².

Step-by-step explanation:

Given that the formula of area of trapezium is A = 1/2×(a+b)×h where a and b represents the length and h is height :

area =  (1)/(2)  * (a + b) * h

let \: a = 50 \n let \: b = 90 \n let \: h = 32

area =  (1)/(2)  * (50 + 90) * 32

area =  (1)/(2)  * 140 * 32

area = 70 * 32

area = 2240 \:  {m}^(2)

Determine the maximized area of a rectangle that has a perimeter equal to 56m by creating and solving a quadratic equation. What is the length and width?

Answers

Answer:

Area of rectangle = 196\,m^2

Length of rectangle = 14 m

Width of rectangle = 14 m

Step-by-step explanation:

Given:

Perimeter of rectangle is 56 m

To find: the maximized area of a rectangle and the length and width

Solution:

A function y=f(x) has a point of maxima at x=x_0 if f''(x_0)<0

Let x, y denotes length and width of the rectangle.

Perimeter of rectangle = 2( length + width )

=2(x+y)

Also, perimeter of rectangle is equal to 56 m.

So,

56=2(x+y)\nx+y=28\ny=28-x

Let A denotes area of rectangle.

A = length × width

A=xy\n=x(28-x)\n=28x-x^2

Differentiate with respect to x

(dA)/(dx)=28-2x

Put (dA)/(dx)=0

28-2x=0\n2x=28\nx=14

Also,

(d^2A)/(dx^2)=-2<0

At x = 14, (d^2A)/(dx^2)=-2<0

So, x = 14 is a point of maxima

So,

y=28-x=28-14=14

Area of rectangle:

A=xy=14(14)=196\,m^2

Length of rectangle = 14 m

Width of rectangle = 14 m

Can you guys help me to find the measure of each angle tysm.

Answers

Answer:

∠EBF = 51°

∠DBE = 17°

∠ABF = 141°

∠EBA = 90°

∠DBC = 107°

∠DBF = 68°

Step-by-step explanation:

Hope this helps

Answer:

1.

a. m<EBF = 90 - 39 = 51

b. m<EBA = 90

c. m<DBE = 90 - 73 = 17

d. m<DBC = 90 + 17 = 107

e. m<ABF = 90 + 51 = 141

f. m<DBF = 17 + 51 = 68

2.

<ABD, <DBE, <EBF, <FBC, <DBF

3.

<ABF, <DBC

4.

<ABE, <EBC