Really need help on these two math questions ??

Where will her cut be located? Round to the nearest tenth. x = (StartFraction m Over m + n EndFraction) (x 2 minus x 1) + x 1 A

Arte-miy333 [17]

Answer:

The correct answer is 25.2 in.

Step-by-step explanation:

It is given that number line goes from 0 to 60 which can be used to represent a ribbon of length = 60 inches.

2 inches of the ribbon are frayed so actual length = 58 inches

Please refer to the attached image for the ribbon.

A is at 0

C is at 60

B is at 2

P is the point to divide the remaining ribbon in the ratio 2:3.

Part AB of the ribbon is frayed.

BP: PC = 2:3

Let BP = 2 $x$ and PC = 3 $x$

Now, BP + PC = BC = 58 = 2 $x$ + 3 $x$ = 5 $x$

So,

$5x =58\\\Rightarrow x =11.6$

BP = $2\times x = 2 \times 11.6 = 23.2\ inches$

Location of the Cut = 2 + 23.2 = <em>25.2 inches</em>

Alternatively, we can use the formula directly:

$x = \dfrac{m} {m + n } (x_2 - x_1) + x_1$

$x_1 = 2\\x_2 = 60$

m: n is the ratio 2:3

$x = \dfrac{2} {2 +3 } (60- 2) + 2\\\Rightarrow 0.4 (58 )+2\\\Rightarrow 23.2+2 \\\Rightarrow \bold{25.2\ inches}$

5 0

3 years ago

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Write the set of points from −2 to 6 but excluding 3 and 6 as a union of intervals:

KengaRu [80]

Answer:

[-2,6] - {3} - {6} = [-2,3) ∪ (3,6)

Step-by-step explanation:

Union Of Intervals

Let us assume two interval A = (a,b) and C = (c,d).

Their union is written as : A ∪ C = (a,b) ∪ (c,d)

Now, if interval is written in form [a,b] ⇒ a and b are INCLUDED in interval

Also, if interval is written in form (a,b) ⇒ a and b are NOT INCLUDED in interval

Here, the given interval is [-2,6]

excluding 3 and 6 from this will give:

[-2,3) ∪ (3,6)

The first set is [-2.3) where -2 is INCLUDED but 3 is NOT INCLUDED.

The second set is (3,6) where 3 and 6 both are NOT INCLUDED.

Hence, [-2,6] - {3} - {6} = [-2,3) ∪ (3,6)

6 0

3 years ago

TIME REMAINING

Svet_ta [14]

Answer:

12.5h

Step-by-step explanation:

12.5 hr x h $/hr = $12.5h

7 0

3 years ago

Which show’s Cassandra number is rounded to the nearest tenth 2.7, 2.6, 2.65, 2.0 ?

GalinKa [24]

Answer:

2.7

Step-by-step explanation:

if you round 2.65 to the nearest tenth, it is 2.7

5 0

3 years ago

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A rectangular turtle aquarium is 6 ft long by 4 ft wide. The aquarium is enlarged by increasing

My name is Ann [436]

Answer:

8ft x 6ft

Step-by-step explanation:

For this problem, we want to create measurements of length and width that double our current area. First we need to find the current area.

C_Length = 6 ft

C_Width = 4 ft

C_Area = C_Length * C_Width

C_Area = 6 ft * 4 ft = 24 ft^2

Now we want our new area to be double the old area.

N_Area = 2C_Area

N_Area = 2 * 24 ft^2

N_Area = 48 ft^2

Now we simply need to find the increase in width and length, distributed equally, that will create the new area.

N_Area = (C_Length + x) * (C_Width + x)

Where x is the amount that each variable is increased by to create the new area.

Now we simply solve for x.

N_Area = (C_Length + x) * (C_Width + x)

48 = (6 + x) * (4 + x)

48 = 24 + 10x + x^2

0 = -24 + 10x + x^2

Now we can either apply the quadratic formula or attempt to factor using the constant break down method.

(x + 12) (x - 2) = 0

x = -12; x = 2

Note that we will choose x = 2 since the other option would require us to have negative material, which is impossible.

Now we can check to validate our answer by plugging in the value of x.

48 ?= (6 + 2) * (4 + 2)

48 ?= (8) * (6)

48 == 48

Thus, we have found the dimensions of the new aquarium, 8ft x 6ft.

Cheers.

6 0

3 years ago