Simplify this expression: 2(10)+2(x-4)

What is the area of ABC?

notsponge [240]

Let D be the Intersection of Height of the Triangle and Base of the Triangle BC

From the Figure, We can notice that Triangle ADB is a Right angled Triangle.

We know that, In a Right angled Triangle :

$\bigstar$ (Hypotenuse)² = (First Leg)² + (Second leg)²

In Triangle, ADB : AB is the Hypotenuse, AD is the First leg and BD is the Second leg

Given : AB = 15 and BD = 9

Substituting the values, We get :

$:\implies$ (15)² = (AD)² + (9)²

$:\implies$ 225 = (AD)² + 81

$:\implies$ (AD)² = 225 - 81

$:\implies$ (AD)² = 144

$:\implies$ (AD)² = (12)²

$:\implies$ AD = 12

We know that, In a Right angled Triangle :

$\bigstar\;\;\boxed{\mathsf{Tan\theta = \dfrac{Opposite\;Side}{Adjacent\;Side}}}$

Now, Consider Triangle ADC : With respect to 45° Angle, AD is the Opposite Side and DC is the Adjacent Side

$:\implies \mathsf{In\;Triangle\;ADC,\;Tan45^{\circ} = \dfrac{AD}{DC}}$

$\mathsf{:\implies 1 = \dfrac{12}{DC}}$

$:\implies$ DC = 12

$:\implies$ Total Length of the Base (BC) = BD + DC

$:\implies$ Total Length of the Base (BC) = 9 + 12

$:\implies$ Total Length of the Base (BC) = 21

We know that, Area of the Triangle is given by :

$\bigstar\;\;\boxed{\mathsf{Area = \dfrac{1}{2} \times Base \times Height}}$

In Triangle, ABC : AD is the Height and BC is the Base

$:\implies \mathsf{Area\;of\;the\;Triangle\;ABC = \dfrac{1}{2} \times BC \times AD}$

$:\implies \mathsf{Area\;of\;the\;Triangle\;ABC = \dfrac{1}{2} \times 21 \times 12}$

$:\implies \mathsf{Area\;of\;the\;Triangle\;ABC = (21 \times 6)}$

$:\implies \mathsf{Area\;of\;the\;Triangle\;ABC = 126}$

7 0

4 years ago

A museum groundskeeper is creating a semicircular statuary garden with a diameter of 29 feet. There will be a fence around the g

azamat

Answer:

The fencing will cost $330.09

Step-by-step explanation:

First we have to calculate the perimeter of the semicircle for that we use the following formula:

d = diameter = 29ft

s = semicircle

π = 3.14

s = d * 1/2 * π

we replace the values that we know

s = 29ft * 1/2 * 3.14

s = 45.53ft

Now we multiply the number of feet by the price of what comes out 1 foot of fence

45.53 * $7.25 = 330.0925

Round to the nearest hundredth

$330.0925 = $330.09

4 0

3 years ago

Half of an orange juice mixture is orange concentrate. Explain why the ratio of orange concentrate to

Sergeu [11.5K]

The ratio of orange concentrate to water is 1 : 1

• Ratio in maths is defines as an ordered pair of numbers p and q, written p/q where value of q is not equal to 0. A proportion in maths is an equation In which two ratios are made equal to each other.

• For example, if there are 3 oranges and 5 lemons in a bowl of fruit, then the ratio of oranges to lemons is 3 :5

According to the question

Let the orange juice mixture be x ml

We are given that half of it is orange concentrate = 0.5x

And the other half is water = x – 0.5x =0.5x

We need to find ratio of orange concentrate to water

Orange concentrate = 0.5x

Water = 0.5x

Ratio = 0.5x/0.5x

= 1/1

= 1 : 1

Hence Proved, the ratio of orange concentrate to water is 1 : 1

Learn more about ratio here

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6 0

2 years ago

Shun is going to flip a fair coin 450450450 times.

Maru [420]

Answer:

c

exactly 225225225 times

5 0

3 years ago

Read 2 more answers

Susan's cat weighs 3 pounds. Susan's dog weighs 3 1/4 times as much as her cat. How much does Susan's dog weigh?

Marina CMI [18]

Answer:

Susan's dog weighs 9.75 pounds

Step-by-step explanation:

Given

The weight of Susan's cat = 3 pounds

Susan's dog weighs 3 1/4 or 13/4 times as much as her cat.

To determine

The weight of Susan's dog = ?

As the weight of Susan's cat = 3 pounds

Given that Susan's dog weighs 3 1/4 or 13/4 times as much as her cat. so

The weight of Susan's dog = 13/4 of 3

= 13/4 × 3

= 39/4

= 9.75 pounds

Therefore, Susan's dog weighs 9.75 pounds

3 0

3 years ago