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Soloha48 [4]
3 years ago
14

Consider the expressions below

Mathematics
1 answer:
Pachacha [2.7K]3 years ago
5 0
Before we begin, remember the following:
-ve * -ve = +ve
-ve * +ve = -ve
+ve * -ve = -ve
+ve * +ve = +ve

Now, for each of the given expression, we will expand the brackets, combine like terms and then compare the final output with the given expressions.

First expression:
(x² + 15x + 65) + (2x - 5)(3x + 8)
x² + 15x + 65 + (2x*3x + 2x*8 - 5*3x - 5*8)
x² + 15x + 65 + (6x² + 16x - 15x - 40)
x² + 15x + 65 + 6x² + 16x - 15x - 40
x²(1+6) + x(15+16-15) + 65-40
7x² + 16x + 25
This expression corresponds to letter B

Second expression:
(4x + 1)(3x - 4) - (5x² - 10x - 12)
4x(3x) + 4x(-4) + 1(3x) + 1(-4) - (5x² - 10x - 12)
12x² - 16x + 3x - 4 - 5x² + 10x + 12
x²(12-5) + x(-16+3+10) - 4+12
7x² - 3x + 8
This expression corresponds to letter D

Third expression:
(8x² + 19x + 4) + (3x + 2)(x - 5)
8x² + 19x + 4 + (3x*x + 3x*(-5) + 2*x + 2*(-5))
8x² + 19x + 4 + (3x² - 15x + 2x - 10)
8x² + 19x + 4 + 3x² - 15x + 2x - 10
x²(8+3) + x(19-15+2) + 4-10
11x² + 6x - 6
This is equivalent to letter A

Fourth expression:
(6x + 1)(3x - 7) - (7x² - 34x - 20)
6x(3x) + 6x(-7) + 1(3x) + 1(-7) - (7x² - 34x - 20)
18x² - 42x + 3x - 7 - 7x² + 34x + 20
x²(18-7) + x(-42+3+34) - 7+20
11x² - 5x + 13
This is equivalent to letter C

Hope this helps :)
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Just solve the question :)
VashaNatasha [74]

Answer:

775

Step-by-step explanation:

Hello :3

750 + 25 = 775.

8 0
3 years ago
In ΔBCD, the measure of ∠D=90°, the measure of ∠C=77°, and CD = 41 feet. Find the length of BC to the nearest foot.
OLga [1]

Answer:

182 ft

Step-by-step explanation:

When you are not given a diagram, always draw one for yourself (see diagram).

When you have a right triangle (triangle with 90° angle), you can use the trigonometry ratios, You can remember them using SohCahToa. It is read like this:

<u>s</u>inθ = <u>o</u>pposite/<u>h</u>ypotenuse           Soh

<u>c</u>osθ = <u>a</u>djacent/<u>h</u>ypotenuse          Cah

<u>t</u>anθ = <u>o</u>pposite/<u>a</u>djacent                Toa

"θ" means the angle of reference (the angle you are talking about).

We are looking for the length of BC, which is the <u>hypotenuse</u>. I labelled it "d" (lowercase D) because it is opposite to ∠D.

We know ∠C = 77°. This will be our angle of reference (replace θ).

The side we know is DC, also known as "b" (lowercase B) because it's opposite to ∠B. "b" is the <u>adjacent</u> side when θ = C because "b" is touching ∠C.

Take the general trig. formula that has <u>hypotenuse</u> and <u>adjacent</u>: (cosine ratio)

cosθ = adjacent/hypotenuse

Substitute the variables specific for this problem.

cosC = b/d

Substitute the values you know.

cos77° = (41 ft) / d

Isolate "d" to the left side

dcos77° = d*\frac{41ft}{d}     Multiply both sides by "d"

dcos77° = 41 ft                          

dcos77° / cos77° = 41 ft / cos77°        Divide both sides by cos77°

d = 41 ft / cos77°                      Input into calculator

d = 182.261874....... ft           Unrounded answer

d ≈ 182 ft                       Rounded to nearest foot (whole number)

Remember d = BC. It's often easier to use one letter for calculations.

Therefore the length of BC is about 182 feet.

8 0
3 years ago
The quotient of a number and 4 is at most 5
gladu [14]
N/4 less than or equal to 5
5 0
3 years ago
Heather brought $7.14 to school. She then spent $1.08 to buy lunch. How much money does she have left?
Wewaii [24]

Answer:

6.06

Step-by-step explanation:

Simple subtraction.

5 0
3 years ago
Read 2 more answers
A dragon likes to eat red peppers and green peppers because they help him breathe fire. If the dragon eats 2 red peppers, he can
N76 [4]

it's 45

Step-by-step explanation:

Okay, so if 2 peppers is 25 meters long, you just divide 25 by 2 to get how many peppers the dragon breathes as  1 pepper. So then you get 12.5, And if you do that with the green peppers, you get 1.5. So, the dragon ate 3 green peppers, so it's 12.5 x 3 , aka. 12.5+12.5+12.5. That's  37.5, and if you do 1.5x5 for the green peppers, it's 7.5, And now you add 37.5+7.5, and you get 45.

4 0
2 years ago
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