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Alex
2 years ago
8

Use the result (a+b)²=a²+2ab+b² to find the value of 49²+98+1

Mathematics
1 answer:
Leto [7]2 years ago
5 0

Answer:

2500

Step-by-step explanation:

a² + 2ab + b²

49² + 98 + 1

Comparing terms

a²= 49²

a= 49

2ab = 98

2× 49 × b = 98

98b = 98

b= 98/98

b = 1

or

b²= 1

b=√1

b= 1

a=49 and b= 1

Hence (a+b)²= (49+1)²

50²= 2500

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Alia has a AED 20 gift card for an online music store. All songs at the store have the same price. After Alia buys 3 songs, the
sladkih [1.3K]

Answer:

Remaining balance = AED 13.75

Step-by-step explanation:

Given that:

Amount of gift card = AED 20

Amount left after buying 3 songs = AED 16.25

Cost of 3 songs = 20 - 16.25 = AED 3.75

Cost per song = \frac{3.75}{3}

Cost per song = AED 1.25

Cost of 5 songs = 5(1.25) = AED 6.25

Remaining balance = 20 - 6.25 = AED 13.75

Hence,

Remaining balance = AED 13.75

5 0
3 years ago
The United States is about the only country that still uses the units feet, miles, and gallons. However, you might see some car
Black_prince [1.1K]

Answer: 4.5 \text{ miles per gallon}

Step-by-step explanation:

Given :  The fuel efficiency of car = 7.6 km per kilogram

We also given that

1 mile = 1.609 km

Then, \text{1 km}=\dfrac{1}{0.609}\text{ mile}

1 gallon = 3.785 liters

\text{1 liter}=\dfrac{1}{3.785}\text{ gallon}

1 liter of gasoline = 0.729 kg

Then, \text{1 kg}=\dfrac{1}{0.729}\text{ liter}

\Rightarrow\ \text{1 kg}=\dfrac{1}{0.729}\times\dfrac{1}{3.785}\text{gallon}

Now, the fuel efficiency of car will be :

7.6\times\dfrac{1}{0.729}\times\dfrac{1}{3.785}\times\dfrac{1}{0.609}\\\\=4.52275317827\approx4.5 \text{ miles per gallon}

Hence,  the car’s fuel efficiency in miles per gallon= 4.5

3 0
3 years ago
Based on the graphs of f (x) and g(x), what must the domain of (f ⋅ g)(x) be?
bekas [8.4K]

Using the concept of domain, the domain of (f.g)(x) is given by:

{x ∈ ℝ | x ≠ 3}

---------------------

  • The domain of a function is given by all possible input values, that is, <u>on a graph, all values that the x-axis assumes.</u>
  • In the graph, <u>function f assumes all real values.</u>
  • Function g is not defined for x = 3, thus, it's domain is all real values except 3.
  • Thus, the multiplication, as fg(x) = f(x) \times g(x), will also not be defined at x = 3, and the domain of the multiplication is:

{x ∈ ℝ | x ≠ 3}

A similar problem is given at brainly.com/question/4175434

4 0
3 years ago
Regis leans a 10-foot ladder against a wall. The base of the ladder makes a 65 angle with the ground.
hammer [34]

The distance, In feet, from the base of the ladder to the base of the wall is 4.2 ft.

He needs to move the ladder 0.1 ft closer to the base of the building.

The situation forms a right angle triangle.

<h3>Right angle triangle</h3>

Right angle triangle has one of its angles as 90 degrees. The sides and angle can be found using trigonometric ratios.

The length of the ladder is the hypotenuse of the triangle formed. Therefore, the distance, In feet, from the base of the ladder to the base of the wall can be calculated as follows;

cos 65° = adjacent / hypotenuse

cos 65° = d / 10

d = 10 × 0.42261826174

d = 4.22618261741

d = 4.2 ft

She needs to move the ladder so it reached a window 9.6 feet above the ground. Therefore, the distance from the base of the ladder and the wall is as follows;

cos 65 = d / 9.6

d = 9.6 × 0.42261826174

d = 4.05696

d = 4.1

Therefore, he needs to move the ladder 0.1 ft closer to the building.

learn more on right angle triangle here: brainly.com/question/14988069

8 0
2 years ago
1. What is the solution set for -4x - 10 ≤ 2 ?
tresset_1 [31]

Answer:

x≥−3

Step-by-step explanation:

−4x−10≤2

Step 1: Add 10 to both sides.

−4x−10+10≤2+10

−4x≤12

Step 2: Divide both sides by -4.

−4x−4≤12

−4

x≥−3

5 0
3 years ago
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