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2 years ago

Which is the solution for 3 (10x+4) = 8(3x + 6)

Mathematics

2 answers:

hammer [34]2 years ago

7 0

Answer:

3(10x+4)=8(3x+6)

Step 1: Simplify both sides of the equation.

3(10x+4)=8(3x+6)

(3)(10x)+(3)(4)=(8)(3x)+(8)(6)(Distribute)

30x+12=24x+48

Step 2: Subtract 24x from both sides.

30x+12−24x=24x+48−24x

6x+12=48

Step 3: Subtract 12 from both sides.

6x+12−12=48−12

6x=36

Step 4: Divide both sides by 6.

6x = 36

Answer:

x=6

Zarrin [17]2 years ago

3 0

Answer:

x=6

Step-by-step explanation:

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Solve the equation: <br> - 5 = 5x + 7

HACTEHA [7]

Subtract 5x from both sides

-5x - 5 = 7
add 5 to both sides

-5x = 12

divide both sides by -5

ANSWER:
x = -2.4

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2 years ago

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U.S census bureau data shows that the number of families in the United States (in millions) in year x is given by h(x)= 51.42 +

Katena32 [7]

Answer:

C. 72 million

Step-by-step explanation:

Put the appropriate value of x into the correct formula and do the arithmetic.

... For the year 2002, x = 2002 -1980 = 22.

Then the population estimate is ...

... h(22) = 51.42 +15.473·log(22)

... = 51.42 +15.473·1.3424

... = 51.42 +20.77

... = 72.19 ≈ 72 . . . . million . . . . . matches choice C.

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2 years ago

Carpet costs $21.95 per square yard and the padding to put under it costs $2.55 per square yard. Felix plans to install padding

marusya05 [52]

Answer:

$1679.175 or $1679.18

Step-by-step explanation:

split the carpet into rectangles to make it easier to look at

one rectangle is 2 yards in height and 9 yards in width (5 yards plus 4 yards)

area of a rectangle = (w)(h), so 9 x 2 = 18 yards in area.

second triangle is 4 yards in width, and 3 yards in height.

area of a rectangle = (w)(h), so 4 x 3 = 12 yards in area.

Total area = 30 yards

30(21.95)(2.55) = $1679.175 or $1679.18

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2 years ago

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On an alien planet with no atmosphere, acceleration due to gravity is given by g = 12m/s^2. A cannonball is launched from the or

almond37 [142]

Answer:

a) $\vec r (t) = \left[(90\cdot \cos \theta)\cdot t \right]\cdot i + \left[(90\cdot \sin \theta)\cdot t -6\cdot t^{2} \right]\cdot j$ , b) $\theta = \frac{\pi}{4}$ , c) $y_{max} = 84.375\,m$ , $t = 3.75\,s$ .

Step-by-step explanation:

a) The function in terms of time and the inital angle measured from the horizontal is:

$\vec r (t) = [(v_{o}\cdot \cos \theta)\cdot t]\cdot i + \left[(v_{o}\cdot \sin \theta)\cdot t -\frac{1}{2}\cdot g \cdot t^{2} \right]\cdot j$

The particular expression for the cannonball is:

$\vec r (t) = \left[(90\cdot \cos \theta)\cdot t \right]\cdot i + \left[(90\cdot \sin \theta)\cdot t -6\cdot t^{2} \right]\cdot j$

b) The components of the position of the cannonball before hitting the ground is:

$x = (90\cdot \cos \theta)\cdot t$

$0 = 90\cdot \sin \theta - 6\cdot t$

After a quick substitution and some algebraic and trigonometric handling, the following expression is found:

$0 = 90\cdot \sin \theta - 6\cdot \left(\frac{x}{90\cdot \cos \theta} \right)$

$0 = 8100\cdot \sin \theta \cdot \cos \theta - 6\cdot x$

$0 = 4050\cdot \sin 2\theta - 6\cdot x$

$6\cdot x = 4050\cdot \sin 2\theta$

$x = 675\cdot \sin 2\theta$

The angle for a maximum horizontal distance is determined by deriving the function, equalizing the resulting formula to zero and finding the angle:

$\frac{dx}{d\theta} = 1350\cdot \cos 2\theta$

$1350\cdot \cos 2\theta = 0$

$\cos 2\theta = 0$

$2\theta = \frac{\pi}{2}$

$\theta = \frac{\pi}{4}$

Now, it is required to demonstrate that critical point leads to a maximum. The second derivative is:

$\frac{d^{2}x}{d\theta^{2}} = -2700\cdot \sin 2\theta$

$\frac{d^{2}x}{d\theta^{2}} = -2700$

Which demonstrates the existence of the maximum associated with the critical point found before.

c) The equation for the vertical component of position is:

$y = 45\cdot t - 6\cdot t^{2}$

The maximum height can be found by deriving the previous expression, which is equalized to zero and critical values are found afterwards:

$\frac{dy}{dt} = 45 - 12\cdot t$

$45-12\cdot t = 0$

$t = \frac{45}{12}$

$t = 3.75\,s$

Now, the second derivative is used to check if such solution leads to a maximum:

$\frac{d^{2}y}{dt^{2}} = -12$

Which demonstrates the assumption.

The maximum height reached by the cannonball is:

$y_{max} = 45\cdot (3.75\,s)-6\cdot (3.75\,s)^{2}$

$y_{max} = 84.375\,m$

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2 years ago

HELP ME I NEED SOMEHELP<br> PLZ<br> PLZ<br> PLZ

otez555 [7]

Step-by-step explanation:

2/7

2×2 = 4

___

7×2 = 14

2×3 = 6

___

7×3 = 21

2×4 = 8

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7×4 = 12

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2 years ago