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3 years ago

What's the length of side AB in ∆ABC shown? A. 5 B. √313 C. 6 D. √15

Mathematics

1 answer:

HACTEHA [7]3 years ago

7 0

Answer:

The value of x = 5 units.

Step-by-step explanation:

Given the right-angled triangle ∆ABC with the following dimensions

AC = a = 12

BC = c = hypotenuse = 13

AB = b = x

Pythagorean Theorem

For a right-angled triangle with the sides, a and b the hypotenuse c is defined as:

$c=\sqrt{a^2+b^2}$

Thus, using the Pythagorean Theorem to determine the value 'x',

$b=\sqrt{c^2-a^2}$

as b = x, so

$x=\sqrt{c^2-a^2}$

a = 12

c = 13

$x=\sqrt{13^2-12^2}$

$x=5$

Therefore, the value of x = 5 units.

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Ms. O'Brien makes her own cleaning solution to clean her floors! (yet, she can't clean her measuring cups?) She mixes 8 cups of

Elden [556K]

Answer:

To make a gallons,

Ms. O'Brien needs

12 8/10 cups of water or 12.8 cups of water

3 1/5 cups of water or 3.2 cups of vinegar

Step-by-step explanation:

Ms. O'Brien makes her own cleaning solution to clean her floors! (yet, she can't clean her measuring cups?)

She mixes 8 cups of water with 2 cups of vinegar.

Hence: The total number of cups for the cleaning mixture = 8 cups of water + 2 cups of vinegar = 10 cups

If she wants to make a 1 gallon mixture of her cleaning solution, how much water and how much vinegar should she add?

Note that: There are 16 cups in a gallon

Hence:

For number of cups of water:

10 cups of cleaning mixture = 8 cups of water

16 cups of cleaning mixture = x

Cross Multiply

10x = 16 × 8

x = 16 × 8/10

x = 12 8/10 cups of water or 12.8 cups of water

For the number of cups of vinegar

10 cups of cleaning mixture = 2 cups of water

16 cups of cleaning mixture = x

Cross Multiply

10x = 16 × 2

x = 16 × 2/10

x = 3 1/5 cups of water or 3.2 cups of vinegar

Therefore, to make a gallon

Ms. O'Brien needs

12 8/10 cups of water or 12.8 cups of water

3 1/5 cups of water or 3.2 cups of vinegar

5 0

2 years ago

Max adds 7 to a number the. Múltiples the sum by -4 the result is 3 times the same number write and since an equation to find th

GrogVix [38]

Answer:

The number is -4.

Step-by-step explanation:

Let the number be n.

Given:

Max adds 7 to a number.

hence it is given as n+7

Multiply's the sum by -4 the result is 3 times the same number.

Hence the equation can be written as;

$-4(n+7)=3n$

Now Solving the above equation to find value of n we get;

$-4(n+7)=3n\\-4n-28=3n\\-4n-3n=28\\-7n=28\\n=\frac{28}{7}=-4$

The value of n is -4.

Now when we add 7 to number -4 we get answer as 3.

And when the sum is multiplied by -4 we get answer -12.

Also 3 times of number is equal to 3 multiplied by -4 we get answer as -12.

Hence when the sum is multiplied by -4 it is equal to 3 times of same number.

Hence from above we can say that the number is -4.

7 0

3 years ago

Which ordered pairs in the form (x, y) are solutions to the equation<br><br> 7x−5y=28?

belka [17]

Answer:7x + -5y = -28

(-4, _)

(1, _)

(_, 14)

Step-by-step explanation:

6 0

2 years ago

A pack of 9 toilet rolls costs £4.23

OleMash [197]

a) 9 toilet rolls cost $ 4.23
1 toilet roll costs $ x

9x = 4.23 * 1
x= 4.23 / 9
x = 0.47
So in first case one toilet roll costs $ 0.47.

b) 4 toilet rolls cost $1.96
1 toilet roll costs $ x

4x = 1.96 * 1
x = 1.96 / 4
x = 0.49
So in second case one toilet roll costs $ 0.49.

0.47 < 0.49
The toilet roll in first case is cheaper than the toilet roll in second case.

Hope this heps!

8 0

3 years ago

How to solve this problem ?

jek_recluse [69]

Answer:

bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb

Step-by-step explanation:

8 0

3 years ago

What's the length of side AB in ∆ABC shown? A. 5 B. √313 C. 6 D. √15​

What's the length of side AB in ∆ABC shown? A. 5 B. √313 C. 6 D. √15