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1 year ago

Determine whether the following has one solution, no solution, or many solutions.3(3 - x) + 5x = 2(x + 2)

Mathematics

1 answer:

Vilka [71]1 year ago

5 0

Given the equation :

$3(3-x)+5x=2(x+2)$

Solve for x:

$\begin{gathered} 3\cdot3-3x+5x=2x+2\cdot2 \\ 9+2x=2x+4 \\ 9-4=2x-2x \\ 5=0 \end{gathered}$

The last result means that the given equation has no solution

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Write the point-slope form of the line that passes through (6, 1) and is parallel to a line with a slope of -3.

pochemuha

Point-slope form : y-y₁=m(x-x₁)

Passes through (6, 1) and parallel to a line with slope of -3.

Simply plug everything in.

*m =slope

y - y₁=m(x-x₁)

y - 1 = -3(x - 6)

Simplify.

y - 1 = -3x + 18

Add 1 to both sides.

y = -3x + 19

~Hope I helped!~

7 0

3 years ago

School is making digital backups of old reels of film in its library archives the table shown approximate run Times of the films

Gemiola [76]

One technique that you can apply when solving such a problem is trial and error. We try to use each equation to prove that a given value of x on the table given will correspond to the value of y on the table.

a) Let's try to put x = 3 for the first equation and we must get an answer equal to 2.25.

$y=7.72(3)-29.02=-5.86_{}$

Since the value of y is not equal to 2.25 and the deviation is too large. this equation is not a good model,

b) We put x = 3 on the second equation and solve for y

$y=-7.52(3)^2+0.19(3)+3.26=-63.85$

Since the value of y is not equal to 2.25 and the deviation is too large. this equation is not a good model,

c) We put x = 3 on the third equation and solve for y,

$y=0.4(3)^2+0.79(3)-4.93=1.04$

Again, the value that we get is not equal to 2.25, hence, this equation is not a good model. But since its value is close to 2.25, we try to other values of x. If x = 5, we get

$y=0.4(5)^2+0.79(5)-4.93=9.02$

which has a slight deviation on the given value of y on the table for x = 5. let's try for x = 7. We have

$y=0.4(7)^2+0.79(7)-4.93=20.2$

and the answer has a small deviation compared to the actual value given. The other values of x can again be put on the equation and check their corresponding value of y, and the resulting values are as follows

$\begin{gathered} y=0.4(8)^2+0.79(8)-4.93=26.99 \\ y=0.4(12)^2+0.79(12)-4.93=62.15 \\ y=0.4(14)^2+0.79(14)-4.93=84.53 \end{gathered}$

And as you can see, the deviation of values from the table to calculated becomes smaller. Hence, this is the best model.

d) We put x = 3 on the third equation and solve for y,

$y=4.19(1.02)^3=4.45_{}_{}$

Again, the value that we get is not equal to 2.25, hence, this equation is not a good model. But since its value is close to 2.25, we try to other values of x. If x = 5, we get

$y=4.19(1.02)^5=4.63$

where the answer's deviation is too large compared to the value of y if x = 5 on the table given.

Based on the calculations used above, the best equation that can be a good model is equation 3.

5 0

1 year ago

A sports writer wished to see if a football filled with helium travels farther, on average, than a football filled with air. To

kondor19780726 [428]

Answer: According to recentest research no well actually it'd float away

Step-by-step explanation:

6 0

3 years ago

Please list how long it takes for each person to pack a shelf alone

vaieri [72.5K]

It takes Jay, Elle and Kay to work individually for 70 minutes, 105 minutes and 52.5 minutes respectively

<h3>What is Rate and Ratio ?</h3>

A ratio can sometimes be regarded as fraction. While rate has something to do with time.

Given that Jay and Kay can pack the shelves in one aisle of the supermarket in 30 minutes. Kay and Elle take 35 minutes to do the same job. When Jay and Elle work together, the job takes 42 minutes.

Let

J = Jay

K = Kay

E = Elle

The interpretation of the question go thus;

1/J + 1/K = 1/30 ........ (1)

1/K + 1/E = 1/35 .........(2)

1/J + 1/E = 1/42 .........(3)

Make 1/J and 1/E the subject of formula in equation 1 and 2 respectively and substitute them in equation 3

1/J = 1/30 - 1/K ........ (4)

1/E = 1/35 - 1/K .........(5)

1/30 - 1/K + 1/35 - 1/K = 1/42

Collect the like terms

- 1/K - 1/K = 1/42 - 1/30 - 1/35

-2/K = (35 - 49 - 42)/1470

-2/K = -56/1470

1/K = 28/1470

Reciprocate both sides

K = 1470/28

K = 52.5 minutes.

Substitute K in both equation 4 and 5

1/J = 1/30 - 28/1470

1/J = (49 - 28)/1470

1/J = 21/1470

Reciprocate both sides

J = 1470/21

J = 70 minutes

1/E = 1/35 - 28/1470

1/E = (42 - 28)/1470

1/E = 14/1470

Reciprocate both sides

E = 1470/14

E = 105 minutes

Therefore, it takes Jay, Elle and Kay to work individually for 70 minutes, 105 minutes and 52.5 minutes respectively

Learn more about Rate here: brainly.com/question/8728504

#SPJ1

7 0

2 years ago

the perimeter of a rectangle can be found by using the formula P=21+2w. What is the width of the rectangle if the perimeter is 1

mixas84 [53]

$\begin{gathered} P=2l+2w \\ \text{If l=50 and P=100, then:} \\ 100=2(50)+2w\Rightarrow0=2w\text{ !!!!} \end{gathered}$

Since this can't happen, let's suppose that P=150, then:

$\begin{gathered} P=2l+2w \\ \Rightarrow150=2(50)+2w \\ \Rightarrow150=100+2w \end{gathered}$

Now we have to move the 100 to the other side of the equation with a negative sign to get this:

$\begin{gathered} 150=100+2w \\ \Rightarrow150-100=2w \\ \Rightarrow50=2w \end{gathered}$

Finally, to get w, we move the 2 that's multiplying to the other side dividing the 50:

$\begin{gathered} 50=2w \\ \Rightarrow\frac{50}{2}=w \\ \Rightarrow w=25 \end{gathered}$

Therefore, the width of the rectangle would be 25 ft if the perimeter is 150ft, and we can see how the rectangle would look:

6 0

2 years ago