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LUCKY_DIMON [66]
3 years ago
8

Choose the number sentence that illustrates the distributive property of multiplication over addition.

Mathematics
1 answer:
Ratling [72]3 years ago
6 0

Answer:

One number sentence shows the distributive property of multiplication over addition. ... (5 + 4) × 3 = (5 × 3) + (4 × 3) is an example of the distributive property. (5 − 4) × 3 = 1 × 3. 1 × 3 is not equal to (1 × 3) − (1 × 3).

Step-by-step explanation:

A

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A decorator has just painted 400 tiles blue and green at a ratio of 5:20.how many were painted green ? how many were painted blu
zheka24 [161]
Blue tiles are 80.
Green tiles are 320
8 0
3 years ago
Item 11
marysya [2.9K]

Answer:

4 ft higher

Step-by-step explanation:

Since the ladder is 10 ft long and its top is 6 feet high(above the ground), we find the distance of its base from the wall since these three (the ladder, wall and ground) form a right angled triangle. Let d be the distance from the wall to the ladder.

So, by Pythagoras' theorem,

10² = 6² + d²  (the length of the ladder is the hypotenuse side)

d² = 10² - 6²

d² = 100 - 36

d² = 64

d = √64

d = 8 ft

Since the ladder is moved so that the base of the ladder travels toward the wall twice the distance that the top of the ladder moves up.

Now, let x be the distance the top of the ladder is moved, the new height of top of the ladder is 6 + x. Since the base moves twice the distance the top of the ladder moves up, the new distance for our base is 8 - 2x(It reduces since it gets closer to the wall).

Now, applying Pythagoras' theorem to the ladder with these new lengths, we have

10² = (6 + x)² + (8 - 2x)²

Expanding the brackets, we have

100 = 36 + 12x + x² + 64 - 32x + 4x²

collecting like terms, we have

100 = 4x² + x² + 12x - 32x + 64 + 36

100 = 5x² - 20x + 100

Subtracting 100 from both sides, we have

100 - 100 = 5x² - 20x + 100 - 100

5x² - 20x = 0

Factorizing, we have

5x(x - 4) = 0

5x = 0 or x - 4 = 0

x = 0 or x = 4

The top of the ladder is thus 4 ft higher

7 0
3 years ago
PROBLEM: Juan hires an electrician. Juan pays a one-time fee of $30. Juan also pays $45 for each hour the electrician works. A.
PolarNik [594]

Answer:

A: C=45h+30

B: C=$322.50

Step-by-step explanation:

A: We'll start with the equation for the total charge. Juan is saying he will pay a one time fee of $30, meaning there is 30 dollars added to what ever the hourly wage is. This can be represented by the +30. Now if "h" represents the variable for which the hourly wage will be calculated, and he pays $45 dollars per hour this will be represented as 45h. <em>As an example if I pay you 2 dollars per hour using the same variable "h", this would be represented as 2h. So if you worked for two hours you would get 4 dollars, this is proven by the fact the 2(2) (remeber im replacing the "h" with the hours you worked) obviously 2 times 2 is 4 proving my point. </em>This information will give you the equation you see above.

B: Onto solving for how much Juan will pay. Now you say youre supposed to have 9 answer but this can't be true. All you need to do is plug the hours given into "h" and solve the equation. It should look something like:

<u>C=45h+30</u>

<u>C=45(6.5)+30</u>

Im using a decimal because it should be clear 1/2=0.5

<u>C= 292.5+30</u>

45x6.5 always go with PEMDAS, we are multiplying first. Then add 292.5 plus 30

This results in the answer of:

<u>C=$322.50</u>

3 0
3 years ago
Find the quotient (25c^4+20c^3) 5c
Black_prince [1.1K]
 Find the quotient: (25c^4 + 20c^3) ÷ 5c5c^3+4c^2.
6 0
3 years ago
Ryan has 9 lollipops and 5 chocolate bars. What is the ratio of lollipops to chocolate bars?
anzhelika [568]

Answer:

9:5

ratios are just putting the numbers next to each other with ':' in the middle

Step-by-step explanation:

4 0
3 years ago
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