Change 46/6 into a whole number

Find the prime factorization of 210.

Xelga [282]

5 x 2 x 7 x 3
Hope it helped! :)

8 0

3 years ago

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2(a-7)=a+4<br> 15 6<br>PLS HELPPPPPPPPPPP

muminat

Answer:

a = 18

Step-by-step explanation:

2(a-7)=a+4

Distribute 2 into left side: 2a -14 = a + 4

subtract a from both sides 2a-a-14 = a+4-a

Simplify: a - 14 = 4

Add 14 to both sides: a - 14 + 14 = 4 +14

Simplify: a = 18

If wanted, plug a into original to double check work:

plug in: 2 (18-7) = 18+4

do parenthesis first: 2 (11) = 18+4

do multiplication : 22 = 18+4

additions: 22 =22

a = 18 is correct.

8 0

2 years ago

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Consider the equation Y=-2x+5 Create a table of five ordered pairs that satisfy the equation. What is the slope of the line repr

Vikentia [17]

Five pairs of points (X,Y) that satisfy the equation Y=-2X+5 may be the following:

For X=0: Y=-2*0+5=5 (0,5)

For X=1: Y=-2*1+5=3 (1,3)

For X=2: Y=-2*2+5=1 (2,1)

For X=3: Y=-2*3+5=-1 (3,-1)

For X=4: Y=-2*4+5=-3 (4,-3)

The slope of the function is m=-2. Correct answer: C

5 0

3 years ago

A cable television compan is laying cable in an area with underground utilities. Two subdivisions are located on opposite sides

Schach [20]

Answer:

Step-by-step explanation:

Given:

Point Q = Q is on the north bank 1200 m east of P $40/m to lay cable underground and $80/m way to lay the cable.

Lets denote T be a point on north bank, therefore, point T is t m east and 100m north of P.

Note that 0 < t < 1200

Distance from P to T using Pythagoras theorem:

PT^2 = PQ^2 + QT^2

PT = √(t²+100²) = √(t²+10,000)

Distance from T to Q:

TQ = 1200 - t

From above, Cable from P to T is underwater, and costs $80/m to lay.

Cable from T to Q is underground, and costs $40/m to lay.

Total cost of the cable:

C(t) = 80√(t²+10,000) + 40(1200 - t)

Cost is at its minimum: when dC/dt = C'(t) = 0 and d^2C/dt^2 = C''(t) > 0

dC/dt = C'(t)

= 80 * 1/2 (t² + 10,000)^(-1/2) × 2t + 40 × (-1)

dC/dt = C'(t)

= 80t/√(t² + 10,000) - 40 = 0

80t/√(t² + 10,000) = 40

80t = 40√(t² + 10,000)

2t = √(t² + 10,000)

square both sides:

4t² = t² + 10,000

3t² = 10,000

t² = 10,000/3

t = 100/√3

≈ 57.735

d^2C/dt^2 =

C''(t) = [80√(t² + 10,000) - 80t × t/√(t²+10,000)] /√(t²+10,000)

C''(t) = [(80(t²+10,000) - 80t²) / √(t²+10,000)] /√(t²+10,000)

C''(t) = 800,000 / (t² + 10,000)^(3/2)

C''(t) > 0 for all t

Therefore C(t) is minimized at t = 100/√3

C(100/√3) = 80√(10,000/3 + 10,000) + 40 × (1200 - 100/√3)

= 80 √(40,000/3) + 48,000 - 4000/√3

= 16000/√3 + 48,000 - 4000/√3

= 48,000 + 12,000/√3

= 48,000 + 4,000√3

= 4000 (12 + √3)

≈ 54,928.20

Minimum cost is $54,928.20

This occurs when cable is laid underwater from point P to point T(57.735 m east and 100m north of P) and then underground from point T to point Q (1200 - 57.735)

= 1142.265 m

5 0

3 years ago

Triangle A″B″C″ is formed using the translation (x + 2, y + 0) and the dilation by a scale factor of one half from the origin. W

Travka [436]

Complete question:

Triangle A″B″C″ is formed using the translation (x + 2, y + 0) and the dilation by a scale factor of one half from the origin. Which equation explains the relationship between segment AB and segment A double prime B double prime?

A) segment a double prime b double prime = segment ab over 2

B) segment ab = segment a double prime b double prime over 2

C) segment ab over segment a double prime b double prime = one half

D) segment a double prime b double prime over segment ab = 2

Answer:

A) segment a double prime b double prime = segment ab over 2.

It can be rewritten as:

$A"B" = \frac{AB}{2}$

Step-by-step explanation:

Here, we are given triangle A″B″C which was formed using the translation (x + 2, y + 0) and the dilation by a scale factor of one half from the origin.

We know segment A"B" equals segment AB multiplied by the scale factor.

A"B" = AB * s.f.

Since we are given a scale factor of ½

Therefore,

$A"B" = AB * \frac{1}{2}$

$A"B" = \frac{AB}{2}$

The equation that explains the relationship between segment AB and segment A"B" is

$A"B" = \frac{AB}{2}$

Option A is correct

5 0

2 years ago