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3 years ago

If the price of gold went from $460an ounce to $483 an ounce in one week. What was the percent change in the price of gold?

1 answer:

3 0

It was a 5 percent change because if you subtract 460 form 483 you will get 23, then you need to divide 23 by 460. You will get 0.05. You need to multiply that answer by 100 to get 5

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When truckers are on long-haul drives, their driving logs must reflect their average speed. Average speed is the total distance

bekas [8.4K]

a) $v=\frac{d_{tot}}{t_{tot}}=\frac{(3 h)(60 mph)+20 mi}{3 h +t_2}$

The average speed is equal to the ratio between the total distance ( $d_{tot}$ and the total time taken ( $t_{tot}$ ):

$v=\frac{d_{tot}}{t_{tot}}$

the distance travelled by the trucker in the first 3 hour can be written as the time multiplied by the velocity:

$d_1 = (3 h)(60 mph)=180 mi$

So the total distance is

$d_{tot}=d_1 +d_2 = 180 mi+20 mi=200 mi$

The total time is equal to the first 3 hours + the time taken to cover the following 20 miles in the city:

$t_{tot}=3 h +t_2$

So, the equation can be rewritten as:

$v=\frac{d_{tot}}{t_{tot}}=\frac{(3 h)(60 mph)+20 mi}{3 h +t_2}$

b) 0.50 h (half a hour)

Since we know the value of the average speed, $v=57.14 mph$ , we can substitute it into the previous equation to find the value of $t_2$ , the time the trucker drove in the city:

$v=\frac{200 mi}{3h +t_2}\\3h+t_2 = \frac{200 mi}{v}\\t_2 = \frac{200 mi}{v}-3h=\frac{200 mi}{57.14 mph}-3 h=0.50 h$

3 0

3 years ago

La respuesta del ejercicio numero 7

andriy [413]

In a math book??? Need more explanation

8 0

3 years ago

Examine this system of equations. Which numbers can be multiplied by each equation so that when the two equations are added toge

WARRIOR [948]

You can use the fact that when coefficient of x variable are of equal magnitude but opposite sign, then adding them will make the coefficient 0, thus, making the x variable eliminated.

The numbers that can be multiplied by each equation so that when the two equations are added together, the x term is eliminated is given by

Option A: –10 times the first equation and 3 times the second equation

<h3>How does elimination works?</h3>

This method is actually called method of elimination to solve a system of linear equations.

We make one specific variable's coefficients of equal magnitude so that we can subtract or add the equations and eliminate that variable to make it easy to get the value of the other variable which will then help in getting the value of the first variable (if working in dual variable system).

If we have equations:

$a_1x + b_1y = c_1\\a_2x + b_2y = c_2$

then, if we want to eliminate variable x, then we have to multiply equation 1 with

$- \dfrac{a_2}{a_1}$

which will make coefficient of x in first equation as

$a_1 \times - \dfrac{a_2}{a_1} = -a_1$

Then adding both equation will eliminate the variable x.

We could've skipped that -ve sign and at then end, instead of adding, we could've subtracted the equations.

<h3>What is magnitude and sign?</h3>

5 has 5 as magnitude, and sign isn't present which means its of positive (+) sign.

-5 has 5 as magnitude and sign is negative(-).

For this case, we're multiplying both the equations but the core concept or aim is same, ie, making the coefficients of equal magnitude but with opposite sign.

<h3>Using the above facts to get the numbers to multiply the equations of the given system</h3>

The given system of equations is

$\dfrac{1}{5}x + \dfrac{3}{4}y = 9\\\\\dfrac{2}{3}x - \dfrac{5}{6}y = 8$

Let two numbers be p,and q who multiply equation first and second respectively to make coefficient of x of equal magnitude but opposite sign.

We have

$\text{Coefficient of x in first equation}= a_1 = \dfrac{1}{5}\\\\\text{Coefficient of x in second equation} = a_2 = \dfrac{2}{3}$

Multiplying with p and q will give us

$p\times a_1 = \dfrac{p}{5}\\\\q \times a_2 = \dfrac{2q}{3}$

We need both resultant coefficient to add up to 0, or

$p/5 + 2q/3 = 0\\p = -10q/3\\q = -3p/10$

Now in options, we see first equation is either getting multiplied with -10, 10, or -3,3

If we put q = 3, we get p = -10q/3= -10

If we put q = -3, we get p = 10

If we put q = 5, we get p = -50/3

Thus only first choice is matching the correct pairs.

Thus,

The numbers that can be multiplied by each equation so that when the two equations are added together, the x term is eliminated is given by

Option A: –10 times the first equation and 3 times the second equation

Learn more about method of elimination here:

brainly.com/question/20385690

7 0

2 years ago

Read 2 more answers

Car A is currently traveling 8 miles per hour slower than Car B. If Car A is currently traveling at a speed of 58 mile per hour,

garri49 [273]

58 + 8 = 66 miles per hour

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3 years ago

A sphere and cylinder have the same radius and height. The volume of the cylinder is 30m^3. What is the volume of the sphere?