Select the equation for the line in point-slope form.

Answer: Hi this would be the arrow that goes to the left and the dot on the right, so something like ← and dot. Hope this helps, I know this is confusing but try your best.

Step-by-step explanation:

Answer:

After solving the inequality, we get:

[tex]x\leq -10[/tex]

With the plotted inequality given.

Step-by-step explanation:

Step 1: Manipulate and solve the inequality

The inequality is given as:

[tex]\frac{1}{2}x+8\leq 3[/tex]

Make [tex]x[/tex] the subject of the inequality to solve it:

[tex]\frac{1}{2}x+8\leq 3\\\\\text{Subtract 8 from both sides of the equation:}\\\frac{1}{2}x+8-8\leq 3-8\\\\\text{Simplify:}\\\frac{1}{2}x\leq -5\\\\\text{Multiply by 2 on both sides of the inequality:}\\2\times \frac{1}{2}x\leq -5\times 2\\\\\text{Simplify:}\\x\leq-10[/tex]

Step 2: Plot the inequality

After solving the inequality, we get:

[tex]x\leq -10[/tex]

Which means that [tex]x[/tex] consists of all values that are equal to and less than [tex]-10[/tex].

On a number line, when the inequality includes the value, it is denoted by a closed circle.

With all this information, let's plot the number line:

On a hot summer day, 606 people used the public swimming pool; daily admission prices are $1.75 for children and $2.50 for adults; admission receipts totaled $1357.50; 396 adults and 210 children swam at the public pool that day.

Therefore,

1.75C + 2.50A = 1357.50

C + A = 606

C = 606-A

1.75(606 - A) + 2.50A = 1357.5

1060.5 - 1.75A + 2.50A = 1357.5

1060.5 + 0.75 A = 1357.5

0.75 A = 297

A = 297/0.75

A = 396

No of adults = 396

Therefore children = 606-396

No of children = 210

396 adults and 210 children swam at the public pool that day

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The angle between the ladder and the ground changes when the bottom of the ladder is 8 ft from the wall is -1/12 radians per second.

Denoting the distance in feet between the wall and the base of the ladder by x and the angle in radians between the ladder and the ground by y, it is noted;

cos(y) = x/10

which implies;

y = arccos(x/10)

Denoting time in seconds by t, it is further noted that;

[tex]\frac{dx}{dy} = \frac{dy}{dx} \frac{dx}{dt}[/tex]  (chain rule)

Noting (using a standard table of derivatives for convenience)

[tex]\frac{dy}{dx}= -\frac{1}{\sqrt{1-(0.1x)^2} }(0.1)[/tex] (also by chain rule)

The above equation changes as;

[tex]\frac{dy}{dx}= -\frac{0.1}{\sqrt{1-0.1x^2} }[/tex]

It is noted from the question that in this particular system;

[tex]\frac{dx}{dt} = 0.5[/tex]  feet per second

So (denoting the derivative as a function of x)

[tex]\frac{dy}{dt}(x)=\frac{dy}{dx} \frac{dx}{dt} = - \frac{0.05}{\sqrt{1-0.01x^2} }[/tex]

At last;

[tex]\frac{dy}{dt}(8)=\frac{dy}{dx} \frac{dx}{dt} = - \frac{0.05}{\sqrt{1-0.01(64)} }[/tex]

         = [tex]\frac{0.05}{\sqrt{1-0.64} }[/tex]

         = [tex]\frac{-0.05}{\sqrt{0.36} }[/tex]

         = -5/60

         = -1/12 radians per second

The angle between the ladder and the ground changes when the bottom of the ladder is 8 ft from the wall is -1/12 radians per second.

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Answer: s= -4u/9  +  5t/9

Step-by-step explanation: Hope it helps

Step-by-step explanation:

First of all, we have to take -5t to the other side and after taking it to the other side it will be +5t, then we have to take (only) 9 to the other as it is 9s (multiplication) it will be division if u take it to the other side.

Done

Using proportions, it is found that:

a) The graph for the distance-time journey is given at the end of the answer.

b) The average speed for the whole journey was of 25 miles per hour.

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using basic arithmetic operations such as multiplication or division from the rates of the variables.

Proportions are applied to find the relation between velocity, distance and time, as velocity is distance divided by time, that is:

v = d/t.

Then, applying cross multiplication, the distance is given by:

d = vt.

On the first interval of his trip, for the first 15 minutes = 1/4 of an hour, he traveled at a velocity of 40 mph, hence the distance is:

d = 40 x 1/4 = 10 miles.

During the second interval, of 25 minutes, from 15 minutes to 40 minutes, he stopped, hence his distance remained constant at 10 miles.

During the third interval, of 20 minutes = 1/3 of an hour, Tim completed the journey at a velocity of 45 mph, hence the complete distance is given by:

d = 10 + 45 x 1/3 = 10 + 15 = 25 miles.

The graph with these three intervals is given at the end of the answer.

He drove a distance of 25 miles in one hour, hence his average speed is given as follows:

v = d/t = 25/1 = 25 miles per hour.

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A unit rate means a rate for one of something.

The number of boxes packed in 18 hours is 216 boxes.

A unit rate means a rate for one of something.

We write this as a ratio with a denominator of one. 

We have,

From the graph, we see that,

In 5 hours, there are 60 boxes packed.

This can be written as:

5 hours = 60 boxes

Similarly,

1 hour = 12 boxes

3 hours = 36 boxes

The number of boxes packed in 18 hours:

1 hour = 12 boxes

Multiply both sides by 18.

18 hours = 18 x 12 boxes

18 hours = 216 boxes

Thus,

The number of boxes packed in 18 hours is 216 boxes.

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ANSWER

y - 3 = -8/5 (x + 5)

EXPLANATION

The point-slope form of the equation of a line, that has a slope m and passes through point (x1, y1) is:

In this problem m = -8/5 and the given point is (-5, 3). The equation is:

Step-by-step explanation:

your teacher gave you the law of sines already.

this was the only "trick" needed to solve this.

now, we just need to use it.

to be considered : a, b, c are always the sides opposite to the angles A, B, C.

so,

sin(28)/11 = sin(x)/22

sin(x) = 22×sin(28)/11 = 2×sin(28) = 0.938943126...

x = 69.87481894...° ≈ 69.9°

Answer:

1.265 x 10-10

Step-by-step explanation:

⇒The line passes through the points (3,0) and (1,-3) I will use them to find the gradient of the line. Note this information is from the graph.

⇒[tex]m=\frac{y_{2}-y_{1} }{x_{2} -x_{1} } \\m=\frac{-3-0}{1-3} \\m=\frac{3}{-2} \\m=-\frac{3}{2}[/tex]

Answer:

x=8

Step-by-step explanation:

83+(12x+1)=180

It equal to 180 because the line measures to 180.

Then write out the equation and solve.

Answer:

3/4

Step-by-step explanation:

Probability

8 red marbles, 3 blue marbles, and 1 green marble = 12 total marbles

8 red marbles+ 1 green marble = 9 not blue marbles

P ( not blue ) = not blue marbles / total marbles

                     = 9/12 = 3/4

Answer:

9

Step-by-step explanation:

8+3+1=12

12-3=9

umm ok i think i got it wrong or overcomplicated it lol

hope this helped

Should be B.

There is a nested function structure. Let's first look at the limit of the interior (f(0)). The point we need to pay attention here is to look at the limits from the right and left. If both values are equal, we can say that it has a limit at that point.

If we express it algebraically;

The left limit and the right limit of [tex]f(0)[/tex] are equal and equal to [tex]2.[/tex]

The left limit and the right limit of f(2) are equal and equal to 3.

As I have drawn with colored arrows in the graph below, we approach from the left and from the right, and if they both point to the same point, we can talk about the existence of the limit at that point. Otherwise, this function does not have a limit at that point.

Answer:

6cm by 1.5cm

18cm by 4.5cm

80cm by 20cm

Step-by-step explanation:

Answer:

Solve for x by simplifying both sides of the equation, then isolating the variable.

x=17

Step-by-step explanation:

The value of the function f(0) = 1, obtained from the graph.

For the given question;

The graph for the function is given.

For finding the value of function f(0), simply see the value of y with respect to x = 0.

f(0) = 1, taken from graph.

Thus, the value of function f(0) is found as 1.

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Answer:

20002

Step-by-step explanation:

100*20=2000

2000*10=20000

20000+2=20002

28% is the correct answer because it is the closest to true value sine people are sensitive about information like this.

The density of the material of mass 200 g and volume 10.4 ml is 19.2 g/ml.

According to the question,

We have the following information:

Density is defined as the mass per unit volume.

So, we have the formula of density:

Density = Mass/volume

Mass of the metal object = 200 g

Volume of the metal object = 10.4 ml

Density = 200/10.4 g/ml

Density = 19.231 g/ml

Now, we will round it off to nearest 1 decimal point.

We know that when the digit is greater than 5 then the number is increased by 1 and when the digit is less than 5 then the number remains same.

So, we have:

Density = 19.2 g/ml

Hence, the density of the metal object is 19.2 g/ml.

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a) 10 percent people arrive before 7 am.

b) 64 percent of the people arrive after 7:59 am.

Here, we are given the following data-

Time                                No. of people

before 7 am                           15

7am to 7:59 am                     39

8am to 8:59 am                    75

9am to 9:59 am                    21

a) the number of people who arrive at the office before 7am = 15

The total number of people in the office = 150

Thus, the percentage of people surveyed who arrived before 7 am = (15/150)*100

= (1/10)*100

= 10

Thus, 10% people arrive before 7 am.

b) The number of people who arrive after 7:59 am = 75 + 21

= 96

Thus, the percentage of people surveyed who arrived after 7:59 am =

(96/150)*100

= (0.64)*100

= 64

Thus, 64 percent of the people arrive after 7:59 am.

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A zero function is a constant function for which, regardless of the inputs, the output value is always zero.A zero function's input can be any real number, but its output is always zero, hence it can take any value from the real numbers

Solve the problem ?

The function f (x) = x - 8  has zeros.

To make f (x) = x  -  8 = 0,   find x.

Start by factoring f (x),

then f(x) =(x-8)=0

f (8 )  =    0

x =  8

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Answer:

y = 3x - 1

Step-by-step explanation:

In order for lines to be parallel, they must have the same slope.

The slope of y = 3x - 8 is 3.

Now, we can solve it using point-slope form. Remember that m = 3, x₁ = -2 and y₁ = -7:

y − y₁ = m(x − x₁)

y - (-7) = 3(x - (-2))

y + 7 = 3(x + 2)

Distribute 3 and isolate y:

y + 7 = 3x + 6

y = 3x - 1

given that

consider the chances,

therefore x lies between -6 and 2

The error interval for the area will be expressed as 64.2< a < 63.93

Error intervals may be defined as the limits of accuracy when a number has been rounded or truncated. They are the range of possible values that a number could have been before it was rounded or truncated. According to the question, Area of circle = 78.1 cm² and Area of square = 21.4 cm². If we round the area to one decimal point, we get the Area of circle = 78.1 + 0.05   and = 78.1 - 0.05 that is 78.15 and 78.05. Also, the Area of square = 21.4 - 0.05 and = 21.4 + 0.05 we get 21.35 and 21.45. Now, Area of shaded region in the form m < a < n. So, n = 78.15 - 21.35

=> n= 56.8 and

m = 78.05 - 21.45

=> m = 56.6

Area of shaded region is 56.6< a < 56.8.

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The value of m = -10, which we get by solving the given equation

The given equation is

0.61m - 1.51m = 9

⇒-0.9m = 9                  (we get the minus sign because 0.61  is smaller than 1.51)

⇒-0.9m/(-0.9) = 9/(-0.9)       (dividing both sides of the equation by -0.9)

⇒m = -90/9

⇒m = -10

Thus on solving the given equation we get the value of m as -10

That is m=-10

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A multi step equation with an answer of -8 can be expressed as: 2x + 20 = 4.

x = -8 when solved.

A multi step equation can be an equation that has variables or/and terms on both sides, of which we can solve for the variable in the equation by isolating the variable to one side of the equation using inverse operations.

For example, a multi step equation can be expressed as 2x + 20 = 4.

Solve for x in the equation:

2x + 20 - 20 = 4 - 20 [subtraction property of equality]

2x = -16

2x/2 = -16/2 [division property of equality]

x = -8

Thus, 2x + 20 = 4 is a multi step equation that has a solution of -8.

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The amount that Georgina has invested in savings account and CD are $ 2500 each.

Given that:-

Total amount invested in savings account and CD = $ 5000.

APY in savings account = 0.6 %

APY in CD = 0.9 %

Total interest earned = $ 37.5

Let the amount invested in savings account be x.

Hence, according to the data given in the question, we can write,

Amount invested in CD = 5000 - x

Interest in savings account in a year = x*(0.6)*1/100 = 0.006x

Interest in CD in a year = (5000-x)*(0.9)*1/100 = (0.009)(5000-x) = 45 - 0.009x

Hence,

0.006x + 45 - 0.009x = 37.5

45 - 37.5 = 0.009x-0.006x

7.5 = 0.003x

x = 7.5/(0.003)

x = 7500/3 = 2500

Hence, Georgina has invested $2500 in each savings account and CD.

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In the year 1998, movie tickets will be greater than $5.50 as determined by solving the equation y=4.25[(1.035)^x].

What is an equation?

A movie ticket cost $4.25 in 1990.

The inflation rate is about 3.5%

Rate increased ,r=100%+3.5%=103.5%=1.035

equation generated is,

y=4.25[(1.035)^x]

Solving the equation for each year, we get the following data:

Tabulating the data

Year         cost

1990         4.25

1991          ....

....              ....

1998          5.5964~ 5.6

In the year 1998, the will be greater than $5.50.

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Answer: 28

Step-by-step explanation: 28