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belka [17]
3 years ago
7

Suppose that a rectangular picture is surrounded by a frame of uniform width of x

Mathematics
1 answer:
user100 [1]3 years ago
3 0

Answer:

Ok so the area of the frame is 18*12 = 216cm^2

Let’s suppose the width of the frame is x

The total area (painting and frame) is (2x+18)(2x+12) and this is equal to 432

4x^2 + 60x + 216 = 432

4x^2 + 60x - 216 = 0

x^2 + 15x - 54 = 0

(x+18)(x-3) = 0

Therefore x = {-18,3}

Since width of the frame has to be positive, the width has to be 3cm Step-

i hope i helped!

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12. Find three consecutive even integers such that
borishaifa [10]

Answer:

10, 11, 12

Step-by-step explanation:

Hi there!

Let <em>x</em> be equal to the smallest integer.

Let <em>x</em>+1 and <em>x</em>+2 be equal to the consecutive integers.

We're given that:

⇒ smallest integer + 2 × middle integer = 20 + largest integer

Construct an equation:

(x)+2(x+1)=20+(x+2)

Combine like terms:

(x)+2(x+1)=20+(x+2)\\x+2x+2=20+x+2\\3x+2=22+x\\2x=20\\x=10

Therefore, the smallest integer is 10.

This makes the consecutive integers 11 and 12.

I hope this helps!

6 0
3 years ago
7x. <br> 5x+18 <br> find the size of the smallest angle
expeople1 [14]

where are the anglessssssssss

3 0
3 years ago
Two gears in a machine are aligned by a mark drawn from the center of one gear to the center of the other. If the first gear has
Aleksandr [31]

Answer:

5

Step-by-step explanation:

for the first gear

revolutions/teeth

1 / 24

2 / 48

3 / 72

4 / 96

5 / 120

6 / 144

for the second gear

revolutions/teeth

1 / 40

2 / 80

3 / 120

4 / 160

<em>the two marks will meet after 120 teeth, 5 revolutions of the first gear and 3 revolutions of the second.</em>

the way to get that amount of teeth is

24 = 2 \times 2 \times 2 \times 3 =  {2}^{3}  \times 3

40 = 2 \times 2 \times 2 \times 5 =   {2}^{3}  \times 5

the Least Common Multiple equals the product of all factors, but those factors who are repeted for both numbers should be only once.

{2}^{3} \times 5 \times 3 = 120

120 teeth are 5 revolutions for gear1 and 3 por gear2

8 0
3 years ago
She didn't see him either. (into affirmative)​
Scilla [17]

Answer:

i Don't know this but other's can help you.

3 0
3 years ago
Help as soon as possible please
marta [7]

(3x + 5)° + (10x - 7)° = 180°

13x + (-2) = 180

13x = 180 + 2

13x = 182

x = 14

∠QRT = 3 * 14 + 5 = 42 + 5 = 47°

∠TRS = 10 * 14 - 7 = 140 - 7 = 133°

6 0
4 years ago
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