MATHEMATICS HIGH SCHOOL

25. Write an expression to represent the area of the shaded region in simplest form.5x + 2
x + 7
3x - 1

Answers

Answer 1
Answer:

Final answer:

The expression to represent the area of the shaded region is (5x + 2)(x + 7) - (3x - 1)(x + 7). Simplifying the expression gives us 2x^2 + 42x + 7.

Explanation:

To find the area of the shaded region, we need to subtract the area of the smaller rectangle from the area of the larger rectangle. The larger rectangle has a length of (5x + 2) and a width of (x + 7), while the smaller rectangle has a length of (3x - 1) and a width of (x + 7). Therefore, the expression to represent the area of the shaded region is:

(5x + 2)(x + 7) - (3x - 1)(x + 7)

To simplify this expression, we can use the distributive property. First, we simplify the expression in the parentheses:

(5x + 2)(x + 7) - (3x - 1)(x + 7)

(5x^2 + 35x + 2x + 14) - (3x^2 - 7x - x + 7)

Next, we distribute the negative sign:

5x^2 + 35x + 2x + 14 - 3x^2 + 7x + x - 7

Finally, we combine like terms:

2x^2 + 42x + 7

Learn more about Simplifying expressions here:

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Answer 2
Answer:

Answer:

Step-by-step explanation:

To determine what the area of the shaded region is, simply find the area of the large rectangle and subtract the product from the smaller one.

Since they are polynomials. Multiply one binomial to the other and first obtain the product, before subtracting the product of the smaller rectangle.

(5x + 2)(3x - 1) - (x)(x + 7)

15x^2 - 5x + 6x - 2 - x^2 - 7

14x^2 + x - 9.

I believe this would be the solution in standard form.

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What is the disadvantages of using a credit card

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Bad credit is a disadvantage especially when you have to pay back the money used from the credit card

An adult elephant drinks about 225 liters of water each day. Is the number of days the water supply lasts proportional to the number of water the elephant drinks

Answers

Answer:

yes

Step-by-step explanation:

Use a calculator to work out
63,789 + 72,983 - 49,367
Give your answer to 2 s.f.

Answers

Answer:

87405

Step-by-step explanation:

Traveling from San Antonio to Dallas, you fist pass through Austin and then Waco before reading Dallas, a total distance of 280 miles. From Austin to Waco is 30 miles faster than from San Antonio to Austin, and also 20 miles farther than from Waco to Dallas. How far is it from Waco to Dallas?

Answers

The answer is 70 miles.

If we express distances as following:
T - total distance
a - distance from San Antonio to Austin
b - distance from Austin to Waco
c - distance from Waco to Dallas
Then:
T = 280 mi
b = a - 30 mi        ⇒ a = b + 30
b = c + 20 mi       ⇒ c = b - 20

T = a + b + c
⇒ a + b + c = 280
⇒ b + 30 + b + b - 20 = 280
⇒ 3b +10 = 280
⇒ 3b = 280 - 10
⇒ 3b = 270
⇒ b = 90 mi.

Distance from Waco to Dallas is c.
c = b - 20
⇒ c = 90 - 20
⇒ c = 70 mi

Therefore, distance from Waco to Dallas is 70 miles.

Of the 75 cars that Lindsay saw pass on the highway, 15% had an out-of-state license plate. How many had an out-of- state license plate?​

Answers

Answer:

it's 11.25 % . I thik it is helpfull right?

Answer:

11.25

Step-by-step explanation:

Factor the expression completely.

4x2 - 12x + 9

Answers

(2x - 3)(2x - 3)
the answer to the question
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