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3 years ago

Algebra 1 question : Solve for x : 3 - 5x + 6 = 14x - 32 + 10(2-x)

2 answers:

6 0

Hi there!

$3 - 5x + 6 = 14x - 32 + 10(2 - x)$
Work out the parenthesis.

$3 - 5x + 6 = 14x - 32 + 20 - 10x$
Combine like terms.

$9 - 5x = 4x - 12$
Subtract 9 from both sides.

$- 5x = 4x - 21$
Subtract 4x from both sides

$- 9x = - 21$
Divide both sides by -9

$x = \frac{ - 21}{ - 9} = \frac{21}{9} = 2 \frac{3}{9} = 2 \frac{1}{3}$

castortr0y [4]3 years ago

4 0

3 - 5x + 6 = 14x - 32 + 10(2 - x)

Distribute 10 inside the parentheses.

3 - 5x + 6 = 14x - 32 + 20 - 10x

Combine like terms.

9 - 5x = 4x - 12

Add 5x to both sides.

9 = 9x - 12

Add 12 to both sides.

21 = 9x

Divide both sides by 9.

x = 21/9

Simplify 21/9 by dividing both sides by 3: 7/3

Your answer is x = 7/3.

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Can anyone solve part C?

nlexa [21]

Answer:

y - 7 = 4(x - 35)

Step-by-step explanation:

The fundamental theorem of calculus states that:

$\frac{d}{dx}$ $\int\limits^x_a {f(t)} \, dt$ = f(x).

So using the fundamental theorem of calculus, you can find that h'(x) = f(x).

The question tells you that f(x) is periodic with a period of 8, so f(x) repeats itself every 8 units.

Using this, you can find that the slope of h(x) at x = 35 is the same as the slope of h(x) at x = 3, which is 4.

The slope of h(x) at x = 35 is 4.

Now I have to find the value of h(x) when x = 35. It is the area under f(x) from 0 to 35.

The area underneath f(x) from 0 to 35 is 7. When x = 35, h(x) = 7.

Now use the point-slope formula to write the equation of the tangent line.

The answer is <u>y - 7 = 4(x - 35)</u>

3 0

3 years ago

Read 2 more answers

PLS HELP ME ILL MARK BRAINIEST

skad [1K]

Answer:

Question 1- 288.48

Step-by-step explanation:

depending on how they round your answer the number might look different.

V= Bh which means (pi)r^2(h)

3.14 x 1.25^2 x 4.9

V=24.040625 ~ 24.04

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5 0

2 years ago

PLEASE HELP

Sholpan [36]

1) We have that the equation is $x^2=20y$ , hence y=x^2/20. The standard equation of such an equation is y= $\frac{1}{4p} x^2$ . Hence, p=5 in this case. The focus is at (0,5) and the directrix is at y=-5 (a tip is that the directrix is always "opposite" the focus point of a parabola; if the directrix is at x=-7 for example, the focus is at (7,0)).
2) Similarly, we have that the equation is $x=3y^2 \\ \frac{1}{4p} =3$ . Thus, p=1/12. In this case, the parabola opens along the x-axis and the focus is at (1/12, 0). Also, the directrix is at x=-1/12. Hence the correct answer is B.
3) We are given that the parabola has a p of 9. Also, the focus lies along the y-axis, hence the parabola is opening along the y-axis. Finally, the focus is on the positive half, so the parabola is opening upwards. The equation for this case is y= $y=\frac{1}{4p} x^2= \frac{1}{36 } x^2$ .
4) Similarly as above. The directrix is superfluous, we only need the p-value. THe same comments about the parabola apply and if we substitute p=8 in the formula: $y= \frac{1}{4p} x^2$ we get y= $\frac{1}{32} x^2$ .
5) This is somewhat different, even though we do not need the directrix again. The focus lies on the x-axis, thus the parabola opens in this direction. The focus lies on the positive part of the axis, thus the parabola opens to the right. We also are given p=7. Hence, the equation we need is of the form $x= \frac{1}{4p} y^2$ . Substituting p=7, we get $x= \frac{1}{28} y^2$ .
6) The equation of a prabola with a vertex at (0,0) is of the form y=-ax^2. The minus sign is needed since the parabola is downwards. Since we are given anothe point, we can calculate a. We have to take y=-74 and x=14 feet (since left to right is 28, we need to take half). $-a= \frac{y}{x^2} = \frac{-74}{14^2} =-0.378$ . Thus a=0.378. Hence the correct expressions is y=-0.378* $x^2$