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galben [10]
3 years ago
8

The rectangle below has an area of 14x^4 + 6x^2 square meters. The width of the rectangle (in meters) is equal to the greatest c

ommon monomial factor of 14x^4 and 6x^2. What is the length and width of the rectangle?
Mathematics
1 answer:
Rudik [331]3 years ago
6 0

Answer:

l = (7x² + 3) m; w = 2x² m

Step-by-step explanation:

(1) <em>Monomial factors</em>

Factors of 6: 1, 2, 3, 6

Factors of 14: 1, 2,        7, 14

The highest common factor of 6 and 14 is 2.

Factors of x²: x, x²

Factors of x⁴: x, x², x³, x⁴

The highest common factor of x² and x⁴ is x².

The highest common factor of 6x² and 14x⁴ is 2x².

(2) Solve for length and width

<em>Data:</em>

(1) A = 14x⁴ + 6x²

(2) w = 2x²

<em>Calculations:</em>

   A = lw                                 Divide each side by w

(3) l = A/w                               Insert (1) and (2) into (3)

    l = (14x⁴ + 6x²)/(2x²)          Divide both sides by (2)

   l = (7x² + 3)

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4 coffees and 12 lattes. Costs $61
Gala2k [10]

Answer:

Cost of a coffee is <u>$2.5</u> and cost of a latte is <u>$4.25.</u>

Step-by-step explanation:

Let cost of 1 coffee be 'c' and cost of 1 latte be 'l' dollars.

Given:

4 coffees and 12 lattes cost $61.

12 coffees and 7 lattes cost $59.75.

∵ 1 coffee cost = c

∴ 4 coffees cost = 4c and 12 coffee cost = 12c

∵ 1 latte cost = l

∴ 12 lattes cost = 12l and 7 lattes cost = 7l

Now, as per question:

4c+12l=61-----1\\12c+7l=59.75----2

Now, multiplying equation (1) by -3 and adding the result to equation (2). This gives,

-3(4c+12l)=-3(61)\\\\-12c-36l=-183\\12c+7l=59.75\\+\\----------\\0-29l=-123.25\\\\l=\frac{-123.25}{-29}=\$4.25

Now, plug in the value of 'l' in equation 1 to solve for 'c'. This gives,

4c+12(4.25)=61\\\\4c+51=61\\\\4c=61-51\\\\4c=10\\\\c=\frac{10}{4}=\$2.5

Therefore, cost of a coffee is $2.5 and cost of a latte is $4.25.

4 0
3 years ago
The side of rhombus is 14 in. The obtuse angle is 160º. Find the longer diagonal of the rhombus.
Mandarinka [93]

Answer:

x = 27.57 in to the nearest hundredth.

Step-by-step explanation:

The longer diagonal  is opposite the obtuse angle.

Also as it is a rhombus all sides = 14 in.

Use the Cosine Rule:

x^2 = 14^2 + 14^2 - 2*14^2 cos 160

x^2 =  760.36

x = sqrt 760.36

x = 27.57 in.

3 0
3 years ago
Find the number of real- number solutions of the equation x^2+10=2
Andrew [12]

Answer:

imaginary

Step-by-step explanation:

x {}^{2}  = 2 - 10 \\  {x}^{2}  =  - 8 \\ x =  \sqrt{ - 8}

from the working strp, we know that the number is imaginary

we can't square root the negative number

4 0
2 years ago
A mixture requires 4 cups of water for every 7 cups of flour used. How many cups of water should be used with 28 cups of flour
MAVERICK [17]

Answer:

16 cups of water

5 0
3 years ago
Find the value of x if w is perpendicular to y
Marta_Voda [28]
This relationship again shows that since w and y are perpendicular to each other that the smaller angles will add up to give 90 degrees.

3x + 3 + 15 = 90

3x + 18 = 90

3x = 90 - 18

3x = 72

X =72/3

X = 36 degrees
3 0
3 years ago
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