Find the equation of a line that passes through the points (1,-3) and (3,-1). Leave your answer in the form y = m x + c

[tex]\begin{cases} x = -4\implies &x+4=0\\ x=-5\implies &x+5=0\\ x = 0\implies &x=0\\ x=\frac{1}{3}\implies &x -\frac{1}{3}=0\\ &3\left( x -\frac{1}{3} \right)=3(0)\\ &3x-1=0 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ (x+4)(x+5)(x)(3x-1)=\stackrel{\textit{original equation}}{0} \\\\\\ (x^2+9x+20)(x)(3x-1)=y\implies (x^3+9x^2+20x)(3x-1)=y \\\\\\ (3x^4+27x^3+60x^2)+(-x^3-9x^2-20x)=y[/tex]

[tex]3x^4+27x^3+60x^2-x^3-9x^2-20x=y \\\\[-0.35em] ~\dotfill\\\\ ~\hfill 3x^4+26x^3+51x^2-20x=y~\hfill[/tex]

Answer:

True.

Step-by-step explanation:

If a relation forms a vertical line, then that means a given input has multiple outputs. Because of this, it is not a function.

Answer:

Step-by-step explanation:

A = πr²/2 = 3.142(11²)/2 = 190.091 cm²

Answer: 1.8

Step-by-step explanation: Divide 9/5

[tex] \sf \longmapsto1 \frac{1}{3 } \div 1\frac{3}{4} [/tex]

[tex]\sf \longmapsto \frac{4}{3} \div \frac{7}{4} [/tex]

[tex]\sf \longmapsto \frac{4}{3} \times \frac{4}{7} [/tex]

[tex]\sf \longmapsto \frac{4 \times 4}{3 \times 7} [/tex]

[tex]\sf \longmapsto \frac{16}{21} [/tex]

Therefore, the answer is :

[tex]\sf \frac{16}{21} [/tex]

Answer:

Step-by-step explanation:

as the chart is broken into steps with the same precision we're looking for. Just choose the one where height is closest to zero or 0.6 s

To do it mathematically

The equation is

h = 2 - ½gt²

to find g, plug in a time and height

0.236 = 2 - ½g(0.6²)

g = 9.8 m/s

check another one just to be sure

1.559 = 2 - ½(9.8)0.3²

1.559 = 1.559

now plug in zero elevation with an unknown time

0 = 2 - ½(9.8)(t²)

-2 = - ½(9.8)(t²)

t² = 4/9.8

t = 0.6388765...

t = 0.6 s

The time it takes for the penny to hit the ground is about 0.6 seconds.

Option B is the correct answer.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

To determine the time it takes for the penny to hit the ground, we need to find the point where the height of the penny is equal to zero.

Looking at the table,

We can see that the height of the penny is negative when t = 0.7 and becomes more negative for larger values of t.

So the penny must hit the ground between t = 0.6 and t = 0.7 seconds.

Now,

We can use linear interpolation to estimate the time at which the height of the penny is zero by finding the equation of the line that passes through the two points closest to zero on the table, namely (0.6, 0.775) and (0.7, -0.401).

So,

The slope of the line passing through these points.

= (change in height) / (change in time)

= (-0.401 - 0.775) / (0.7 - 0.6)

= -1.176

The equation of the line passing through these points.

y - 0.775 = -1.176(x - 0.6)

Simplifying

y = -1.176x + 1.438

Setting y to zero and solving for x.

0 = -1.176x + 1.438

x = 1.438 / 1.176

x ≈ 1.22

Therefore,

To the nearest tenth of a second, the time it takes for the penny to hit the ground is about 0.6 seconds.

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5 bombas deben trabajar durante 4 dias para llenar la piscina.

Cada bomba trabaja a un rate (razon de trabajo) R.

Sabemos que 3 bombas, trabajando 5 horas diarias por 10 días (un total de 50 horas), llena una piscina, entonces:

(3R)*50 horas= 1 piscina.

R = (1 piscina)/(150 horas).

Es decir, una sola bomba tarda 150 horas en llenar una piscina.

En el caso de que 5 bombas trabajen, tenemos que para llenar una piscina tienen que trabajar un tiempo T.

5*((1 piscina)/(150 horas))*T = 1 piscina.

(1 piscina)/(30 horas)

Resolviendo para T, obtenemos:

T = 1 piscina*(30 horas)/(1 piscina) = 30 horas.

Y sabemos que trabajan 8 horas diarias, es decir, las bombas deben trabajar durante:

30/8 = 3.75 ≈ 4 días.

5 bombas deben trabajar durante 4 dias para llenar la piscina.

Sí quieres aprender más sobre razones de trabajo.

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Answer:

a trapezoid:ll and a dented triangle:l

Answer:

x>3

Step-by-step explanation:

Work:

2x^2-x>15

Subtract 15 on both sides:

2x&2-x-15>0

Factor the left side of equation to cancel out the ^2.

(2x+5)(x−3)>0

2x+5=0 or x−3>0

Then to make it easier we will do the x-3>0 one, add 3 to both sides = x>3

Answer: 18

Step-by-step explanation:

The question is asked to know 30% of 60, we get

60 x 30% = 60 x 0.3 = 18

Answer:

18

Step-by-step explanation:

We know that 30% means 30/100

30/100 multiplied by 60

hence, the answer is 18

Answer:

Jeremy's team won more games

Step-by-step explanation:

Let's transform these fractions into ratios:

[tex]\frac{7}{10} =7:10\\\\\frac{2}{5} =7:10[/tex]

Then, simplify:

[tex]7:10[/tex] ≈ [tex]1:1.4[/tex]

[tex]2:5=1:2.5[/tex]

Finally, compare:

[tex]1:1.4\neq 1:2.5[/tex]

Result:

Jeremy's team won more games since [tex]1:2.5>1:1.4[/tex]

Note:

The way I simplify the ratios may be confusing so here is a quick explanation;

Make the smaller of the two numbers in the ratio into one then divide the larger number by the smaller number for the other part of the ratio

Example:

5:10

5 turns into 1

10 divided by 5 equals 2

Simplified Ratio: 1:2

Jeremy won more games than Howard.

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

Given:

Howard Team won = 7/10

Jeremy team won = 2/5

Now, taking LCM (5, 10)= 10

So, Jeremy team won = 2/5

                                     = 4/10

So, Jeremy won more games than Howard.

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The confidence interval can be calculated from the margin of error, and vice versa,

The margin of error of the confidence interval is 2.156

The confidence interval is given as:

[tex]\mathbf{CI = 3.2 \pm 1.96 \cdot 1.1}[/tex]

The formula of confidence interval is:

[tex]\mathbf{CI = \bar x\pm E}[/tex]

Where E represents the margin of error.

So, by comparison:

[tex]\mathbf{E = 1.96 \cdot 1.1}[/tex]

Multiply

[tex]\mathbf{E = 2.156}[/tex]

Hence, the margin of error of the confidence interval is 2.156

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Step-by-step explanation:

mean of 20 lb and a standard deviation of 9. If 9 fish are randomly selected,

what is the probability that the mean weight will be between 17.6 and 23.6

Ib? Write your answer as a decimal rounded to 4 places

Answer:

You can't draw a diagram for a improper

fraction

Answer:

(x+1)(x+8)

Step-by-step explanation:

I just got multiples of 8 that when added equal to 9. In this case, it was 1 and 8 which when you multiply is 8 and when you add, it's 9.

Answer:

5/8

Step-by-step explanation:

there is 8 total and 5 of them are basketballs

Answer:

No

Step-by-step explanation:

Considering domain and range of a function, we first have to create the function based off the given points.

So this would mean first having to find the slope of the equation, which would be using the slop/point formula of [tex]\frac{y_{1} -y_{2} }{x_{1} -x_{2} }[/tex]

Taking the first 2 points, it would make the equation as follows:

[tex]\frac{y_{1} -y_{2} }{x_{1} -x_{2} } = \frac{6-3}{8-5} = \frac{3}{3} = 1[/tex]

To be sure, we take the 2nd pair of points (point 2 and point 3) and make the equation with those as well.

[tex]\frac{y_{1} -y_{2} }{x_{1} -x_{2} } = \frac{11-6}{10-8} = \frac{5}{2} = 2.5[/tex]

Since these 2 slopes do not match, this set of relations cannot be a function, and therefore a domain/range cannot be found.

Answer:

1.4

Step-by-step explanation:

Use the distance formula

d= √(x2-x1)² +(y2-y1)² , where x1, x2, y1, y2 are the coordinates of the points

A(x1 = −1, y1 =  5) and B(x2 = 0, y2 = 4)

d= √(0 - -1 )² +(4 - 5)²

d= √(1)² +(-1)²

d= √2

d= 1.414213562, round to the nearest tenth

d≈ 1.4

Answer:

Step-by-step explanation:

Use the half angle formulas

sin(θ/2) = ±√((1 - cosθ)/2)

sin(θ/2) = ±√((1 - (3/5))/2)

sin(θ/2) = ±√((2/5)/2)

sin(θ/2) = ±√(1/5)

knowing θ is in the 4th quadrant, θ/2 will be in the second quadrant where sines are positive.

sin(θ/2) = +√(1/5) = √0.2

Step-by-step explanation:

1 hour - $8.50

21.5 hours (one week) - $8.50 × 21.5 = $182.75

One week = $183

Answer:

4(2x raise to power 2-4-7x)

Answer:

y = -1/2

Step-by-step explanation:

   (3x + 4y = 4)

+

   (2x - 4y = 6)

______________

   5x = 10

   x = 2

plug in x for any of the two equations ....

2(2) - 4y = 6

4 - 4y = 6

-4y = 2

y = -1/2

Based on the investment ratio and the amount invested, the amount that Zach invested is $102,857.14.

First thing to do is to add up the numbers in the ratio:

= 1 + 2 + 0.5

= 3.5

The amount that Zach invested is:

= Zach's ration/ Sum of ratio x Amount invested

= 1 / 3.5 x 360,000

= $102,857.14

In conclusion, Zach invested $102,857.14.

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Answer:

1 11/12 cups of water

Inequalities are used to represent unequal expressions.

The inequality is [tex]24 + 8R \ge 100[/tex]

The given parameters are:

[tex]Paid = 24[/tex]

[tex]Rolls = 12[/tex]

[tex]Cost = 8[/tex] --- the unit cost per roll.

Assume the number of additional roll is R.

So, the total number of sushi is:

[tex]Total=Paid + Cost \times R[/tex]

This gives

[tex]Total=24 + 8\times R[/tex]

Multiply 8 and R

[tex]Total=24 + 8R[/tex]

The sushi needed is at least 100.

This implies that:

[tex]Total \ge 100[/tex]

So, we have:

[tex]24 + 8R \ge 100[/tex]

Hence, the inequality is [tex]24 + 8R \ge 100[/tex]

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Answer:

$11,480

Step-by-step explanation:

Answer:

Here you go :)

Step-by-step explanation: