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Margarita [4]
3 years ago
7

Factorise (2t-7)²-(5t-4)² with working pls​

Mathematics
1 answer:
sertanlavr [38]3 years ago
5 0

Answer:

33+12t−21t^2

Step-by-step explanation:

(2t-7)²-(5t-4)²

Use binomial theorem (a−b)^2 = a^2−2ab+b^2 to expand (2t-7)².

4t^2−28t+49−(5t-4)²

Use binomial theorem (a−b)^2 = a^2−2ab+b^2 to expand (5t-4)².

4t^2−28t+49−(25t^2−40t+16)

To find the opposite of 25t^2

−40t+16, find the opposite of each term.

4t^2−28t+49−25t^2−40t+16

Combine 4t^2  and −25t^2  to get −21t^2.

−21t^2−28t+49+40t−16

Combine −28t and 40t to get 12t.

−21t^2+12t+49−16

Subtract 16 from 49 to get 33.

−21t^2+12t+33

Swap terms to the left side.

33+12t−21t^2

I hope this helped!

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Answer:

a) slope intercept form: y = -5/14 x + 7/2

b) point slope form: y - 1 = 3/2(x - 4)

Step-by-step explanation:

a) Line A: (4,1) and (0, 7/2)

Slope = (1 - 7/2)/(4 - 0)

Slope = - 5/2 * 1/4

Slope = - 5/14

Equation in slope intercept form:

y = -5/14 x + 7/2

b)

(4,1) and (0, -5)

Slope = (1 + 5)/(4 - 0) = 6/4 = 3/2

Equation in point slope form:

y - 1 = 3/2(x - 4)

4 0
3 years ago
when juggling a ball travels in a complete circle every 2 seconds. how many circles does it make in a minute
andrew11 [14]

Answer: It makes 30 circles in a minute

Step-by-step explanation:

Cirle every 2 seconds

A minute is 60 seconds

So you divide those to get your answer

60 divided by 2= 30

3 0
2 years ago
Read 2 more answers
The length of a rectangle is 5 inches longer than the width. The perimeter of the rectangle is 40 inches. What is the width of t
tangare [24]

Answer: 7.5"

Step-by-step explanation:

First, take away the extra 5" on the longer side lengths

40-5-5=30

Then divide by 4 to get the width

30/4=7.5

This works because if you took the 7.5" and added back the 5 inches, it makes 12.5. Then add all 4 sides together, you get 40.

7.5+7.5+12.5+12.5=

8 0
3 years ago
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hodyreva [135]
1.5 = 1 1/2 = 3/2
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8 0
3 years ago
A basket full of 10 apples costs 23$, another basket full of 15 apples costs 33$. The prices of the baskets are the same. How mu
MArishka [77]

Answer:

Equations:

y + 10x = 23

y + 15x = 33

cost of basket with 25 apples = $53

Step-by-step explanation:

A basket with 10 apples cost $23 and a basket with 15 apples cost $33. Note that these costs also include the cost of the basket, which is same in both case. Let the cost of empty basket with "y" and cost of each apple be "x"

Cost of basket and 10 apples is $23. We can transform this statement into an equation as:

y + 10x = 23                                     Equation 1

Similarly,

Cost of basket and 15 apples is $33. This gives us another equation:

y + 15x = 33                                     Equation 2

Subtracting Equation 1 from Equation 2 , we get:

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Using the value of x in equation 1, we get:

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This means, cost of basket is $3 and cost of each apple is $2.

Now we can calculate the cost of basket with 25 apples, which will be:

Cost of basket + Cost of 25 apples = Total Cost

3 + 25(2) = 3 + 50 = $53

6 0
3 years ago
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