Find an equation of the line passing through the given points. Use function notation to write the equation,
(-1,6) and (-2,11)
f(x) =

The area of a triangle whose vertices are r(3, 4), s(6, 2), and t(7, 10) is calculated to be 9.5 units²

Given that,

Vertices are  r(3, 4), s(6, 2), and t(7, 10) which means ,

(x₁,y₁) = (3,4)

(x₂,y₂) = (6,2)

(x₃,y₃) = (7,10)

From formula,

The triangle area

A= 1/2 (|x₁(y₂ -y₃) + x₂(y₂ - y₁) + x₃(y₁ -y₂))

A=1/2(3(2 - 10) + 6(2-4) + 7(4-2))

A = 1/2 (3* -7 + 6* -2 +7* 2 )

A = 1/2 |(-21-12+14)|

A = 1/2 (19)

A = 9.5 units²

area of triangle is 9.5 units² with the given vertices.

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The following equation, y − 8 = 15 (x + 5) is in the slope-intercept form and will be y=15x+83.

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

A linear equation has the form y = mx + b in the slope-intercept format. X and Y are the variables in the equation. The values m and b represent the line's slope (m) and the value of y when x is 0.

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

It is given that the equation is,

y − 8 = 15 (x + 5)

y=15(x+5)+8

y=15x+75+8

y=15x+83

A linear equation has the form y = mx + b in the slope-intercept format.

Thus, the following equation, y − 8 = 15 (x + 5) is in the slope-intercept form and will be y=15x+83.

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The pattern isn't linear as the difference in values is different from 30.

From the information, jezabel had 1,452 subscribers last week and now she had 1,483 subcribers.

The difference will be:

= 1483 - 1452

= 31

It was further stated that every video she posts gains her about 30 new subscribers.

This shows that it isn't linear.

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The value of variable in first figure will be;

⇒ x = 5

The value of variable in second figure will be;

⇒ y = 4

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

There are two figures is shown in figure.

Now,

In first figure;

By using definition of proportional as;

⇒ 4 / 2 = 6 / (x - 2)

Solve for x as;

⇒ 2 (x - 2) = 6

⇒ x - 2 = 3

⇒ x = 3 + 2

⇒ x = 5

Thus, The value of variable in first figure will be;

⇒ x = 5

In second figure;

By using definition of proportional as;

⇒ y / 6 = 12 / 9

Solve for y as;

⇒ y / 6 = 4 / 3

⇒ y = 4 x 6 / 3

⇒ y = 24 / 6

⇒ y = 4

Thus, The value of variable in second figure will be;

⇒ y = 4

Therefore, The value of variable in first figure will be;

⇒ x = 5

The value of variable in second figure will be;

⇒ y = 4

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Answer:

0.18

Step-by-step explanation:

1005 - 82% = 18%  Divide by 100 to get the decimal answer of 0.18

The volume of the block after cutting the smaller cubes is:

volume = 56/125 [tex]cm^{3}[/tex]

What is volume?

Volume is a mathematical term that describes how much three-dimensional space an object or closed surface occupies.

The formula to calculate the volume of the cube is given by:

Volume = [tex]a^{3}[/tex], where a is the length of its sides or edges

Length of solid wooden cube= [tex]\frac{4}{5} cm[/tex]

Length of smaller wooden cube= [tex]\frac{1}{3} cm[/tex]

Volume of the large cube = [tex](\frac{4}{3} )^{3}[/tex]

Volume of the large cube = [tex]\frac{64}{125} cm^{3}[/tex]

Volume of the small cube = [tex]\frac{1}{5} cm^{3}[/tex]

Volume of the small cube = [tex]\frac{1}{125} cm^{3}[/tex]

Volume of block after cutting out the smaller cubes is

                = [tex]\frac{64}{125} -\frac{(8)(1)}{125}[/tex]

                = [tex]\frac{64-8}{125}[/tex]

                =[tex]\frac{56}{125}[/tex][tex]cm^{3}[/tex]

Hence, the volume of the block after cutting the smaller cubes is:

volume = 56/125 [tex]cm^{3}[/tex]

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Step-by-step explanation:

mia went shopping. she had $20.00. she bought 1 shirt for $7.50 and a new bracelet for $5.25. how much money does mia have left?​

20 - 7.5 - 5.25 = $7.25 left

[assuming no sales tax]

Answer:

she has 7.25

Step-by-step explanation:

So, Mia has twenty dollars then purchases a shirt which is 7.25 and a bracelet for the price of 5.25

20.00 - 7.50= 12.50-5.25=7.25

Answer:

Line A and C

Step-by-step explanation:

The perpendicular slope of another line is the negative reciprocal of the other slope.

For example, we have line [tex]x_{1}[/tex].

y = x

The line that is perpendicular to it is:

y= [tex]-\frac{1}{x}[/tex]

Lets tranform all of these equation to slope intercept form:

y = mx+b

M is the slope or how much the y value increases every time the x value increases by one. b is the y-intercept or when x=0.

Divide 2 on both sides to simplify line a into slope intercept form.

[tex]\frac{2y}{2} = \frac{8x+10}{2}[/tex]

Simplify.

y = 4x + 5

Now it is in slope-intercept form. Slope of 4 and y-intercept of 5.

Line B

Isolate y on both sides by subtracting 3x on both sides.

6y + 3x - 3x = 12 - 3x

6y = 12 - 3x

Divide 6 on both sides.

[tex]\frac{6y}{6} = \frac{-3x+12}{6}[/tex]

Simplify.

y = -1/2x + 2

Now it is in slope-intercept form. Slope of -1/2 and y-intercept of 2.

Line C

Divide both sides by 8.

[tex]\frac{8y}{8} = \frac{-2x-16}{8}[/tex]

Simplify.

y = -1/4x - 2

Line A has a slope of 4. Line C has a slope of -1/4x. Line C is the negative reciprocal of Line A as multiplying Line A by -1 and flipping the fraction simple gets you Line C. (and vice versa).

Answer:

The y-intercept represents the number of mammals when they were originally counted.

The line y = 0 is an asymptote of the graph.

The y-intercept is 120.

The asymptote indicates that as years pass, the number of mammals will approach 0.

Step-by-step explanation:

Took the test

Answer:

The y-intercept represents the number of mammals when they were originally counted.

The line y = 0 is an asymptote of the graph.

The y-intercept is 120.

The asymptote indicates that as years pass, the number of mammals will approach 0.

Answer:

Step-by-step explanation:

Half of the 80 people are women, so divide 80 by 2.

[tex]80/2=40[/tex]

One quarter of that is men.

[tex]40/4=10[/tex]

The rest are children, so:

[tex]40+10=50\\80-50=30[/tex]

There are 30 children, 40 women, and 10 men.

The number of children to men is n:1.

There are 30 children to 10 men, and after simplifying that by dividing by 10, so the value of n is 3, and the ratio is 3:1.

Answer:

3:1

Step-by-step explanation:

Half of the 80 people are women. 80 divided by 2 is 40.

One-quarter of the 40 women are men. 40 divided by 4 is 10.

The total number of men and women is 50, and the rest are children. 50 subtracted from 80 is 30.

There are 40 women, 30 children, and 10 men.

The ratio of children to men is 30:10, which simplifies to 3:1.

The dimensions of the dumpster that will minimize its surface area are Length = 4.43 yds ,Width  = 2.215 yds and Height  = 2.956 yds

since l = 2w.

Now, the formula for a cube's surface area is;

S = 2lw + 2lh + 2wh.

Changing 2w to l yields;

S = 4wh + 4w² + 2wh.

S = 4w² + 6wh

in the meantime, the formula for a cube's volume is;

V = lwh

add 2w for l to receive;

V = 2w²h

h = V/2w²

In the SA equation, substitute V/2w² for h to get;

SA = 4w² + 6w(V/2w²)

SA = 4w² + 3V/w

V is stated to equal 29 yd3.

Thus;

S = 4w² + 87/w

Let's find the first derivative of S as we want to reduce the surface area;

S' = 8w - 87/w²

At S' = 0;

8w - 87/w² = 0

8w = 87/w²

w³ = 87/8

w = ∛(87/8)

w = 2.215 yds

L = 2 x 2.215= 4.43

since, l = 2w.

l = 4.43 yds

h = V/2w²;

h = 29/(2 × 2.215²)

h = 2.956 yds

Hence, The dimensions of the dumpster that will minimize its surface area is l = 4.43 yds, w = 2.215 yds and h = 2.956 yds

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According to the Pythagoras theorem, the value of x is 13.8

Pythagoras theorem:

Pythagoras theorem describes that the square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.

Given,

Here we have the two right angled triangles with the side values.

Here we have to find the value of x.

In order to find the value of x, we have to find the value of the bisector KM,

So, for that we have to use the concept of Pythagoras theorem,

We can written this one the following type of equation,

=> (12.3)² = (5.4)² + KM²

=> 151.29 = 29.16 + KM²

=> KM² = 122.13

=>  KM = 11.05

Therefore, the value of x is calculated in the same manner,

=> x² = (8.2)² + (11.05)²

=> x² = 67.24 + 122.10

=> x² = 189.34

=> x = √189.34

=> x = 13.76

When we round off this into the nearest tenth the we get the value of x as 13.8.

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Answer:

hello as midpoint is (4,-3)

and an ending point is (8,-5)

there are 4x and 2y among them

so you need to subtract 4x and 2y from the midpoint

which the answer is going to be (0,-1)

i.e. C option

good luck

We will get the solution of the equation g(x) = f(x) by finding the rule for the linear equation g(x) and solving the linear equation, the solution is x = 2.

Here we have two functions, one graphed, which is g(x), and the other defined by a rule:

f(x) = -x + 1

For g(x) we can use the graph to find the rule, notice that this is a linear equation so we can write:

g(x) = m*x + b

Where m is the slope and b is the y-intercept.

On the graph we can see that the y-intercept is y = -3, then:

g(x) = m*x - 3

To find the value of m we can use another point on the graph, for example, (3, 0)

Replacing that we get:

g(3) = 0 = m*3 - 3

3 = m*3

3/3 = m

1 = m

Then g(x) = x - 3

Now we can solve:

g(x) = f(x)

Replacing the functions we get:

x - 3 = -x + 1

Now we can solve this linear equation for x:

x - 3 = -x + 1

x + x = 3 + 1

2x = 4

x = 4/2

x = 2

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The strategy for different scenarios are;

a) Voluntary response

b) Poor sampling

c) Stratified sampling

d) Stratified sampling with follow-up

Given Information;

The school board is debating whether to implement a new rule that would require primary pupils to pass a test in order to advance to the next grade in a large city school system with 20 elementary schools. The pta is interested in learning whether parents support this strategy. Here are a few of the suggestions made for data collection. Indicate the type of sampling technique being used for each and any potential biases that might arise.

a) If they put a big ad in the newspaper asking people to log their opinions on the PTA Web site what kind of bias might they encounter?

→ Only those who volunteer to answer will participate so, bias is due to the use of a voluntary response sample.

b) If they randomly select one of the elementary schools and contact every parent by phone, what kind of bias is there?

→ If we choose just one school, then the answers may not be independent, so under-coverage bias due to a poor sampling frame.

c) Suppose they randomly select 20 parents from each elementary school. Send them a survey, and follow up with a phone call if they do not return the survey within a week. What kind of sampling was done?

→ As there are natural groups, and we get a sample from each group, then it is stratified sampling.

d) randomly select 20 parents from each elementary school. send them a survey, and follow up with a phone call if they do not return the survey within a week.

→ Stratified sampling with follow-up, should be unbiased.

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No the octopus can not differentiate between circles and rectangle and the probability of picking circle is 0.295.

In the give question we have to find the octopus can tell the difference between circles and rectangles or not.

From the question;

Circles: 13

Rectangles: 31

Null hypothesis: proportion of circles found = 0.5

Alternate hypothesis: Proportion of circles found > 0.5

Total number of trials is 31+13=44

Since 13 times circle is choosen.

So the probability that octopus chooses circle is

P(C) = Total number of circle/Total number of trials

P(C)=13/44

P(C)=0.295

As probability is 0.295<0.50

So, no the octopus can not differentiate between circles and rectangle and the probability of picking circle is 0.295.

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The car B was 10 miles east of Car A.

A function is a formula, rule, or law that specifies how one variable (the independent variable) and another variable are related. The linear equation is of the form Ax+By+C=0.

Where A and B are the coefficient and C is the constant.

Speed of car A = 45 miles per hour and the direction of car A is East.

The distance of car B from Johnstown after 2 hours is 100 miles, east

The distance of car B from Johnstown is given on the graph.

So , the initial distance of car A from Johnstown will be,

= 100 - 2 × 45

=100 - 90

= 10 miles

As seen from the graph, the initial distance, east, of car B from Johnstown is 20 miles.

So, the difference between the cars will be 20-10= 10 miles that means car B was 10 miles east of Car A.

Therefore, the car B was 10 miles east of Car A.

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The length of time till the value of the car is at $9, 600, given the depreciation rate of the car per year is 7.98 years.

The car started off with a value of $17, 500, which was its purchase price. The length of time till the car is is $9, 600 can be found by using the NPER function on spreadsheet. This function shows the length of time till a value becomes another value.

The figures going into the formula are:
Rate = -7.25%

PV = $17, 500

FV = $9, 600

The number of years for the car to depreciate would be 7.98 years.

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The combined score for Jodi and Joe is 9-i

Two complex numbers, z₁ = a + bi and z₂ =c +di, can be added by adding the corresponding real and imaginary parts. That is:

z₁+z₂ = (a+c) + (b+d)i

Given: Jodi's score = 5−3i and Joe's score = 4 + 2i

Combined score = 5−3i + 4 + 2i

                           = (5+4) + (-3+2)i

                           = 9-i

Therefore, the combined score is 9-i

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The number of dimes in 1 dollar is 10 thus the number of whole dollars that can be made from 276 dimes will be 27 and 6 dimes will leave over.

To convert any unit into another is called a unit conversion.

In order to convert units, we need to care about their dimensions their dimension should not be changed.

Another example could be kilo gram to gram.

As per the given,

Number of dimes = 276

1 dollar = 10 dimes.

The number of dollars in 276 dimes, is 276/10 = 27.6

So, 27 dollars and 6 dimes.

Hence "The number of dimes in 1 dollar is 10 thus the number of whole dollars that can be made from 276 dimes will be 27 and 6 dimes will leave over".

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The percentage of people who filed their taxes during the week of tax day is 10%

I can estimate how many people filed their taxes during the week of April 15th using a percentage of 100 is a/b * 100.

A percentage is a portion of a sum divided into 100 equal parts.

Calculate (Number of persons who submitted their taxes during the week of April 15th / total people who filed their taxes that year) times 100 to get the percentage of people who filed during that week.

Let :

a represents the total number of taxpayers during the week of April 15th.

b represents the total number of taxpayers for that year.

The original equation is reduced to

a/b× 100

As an illustration, 100 individuals submitted their taxes the week of April 15th and

Let's say that year, 1000 persons filed their taxes.

= 100/1000 = 10%

Thus, 10% of Americans submitted their taxes during the week of April 15th, or 100 out of 1,000.

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Answer:

A.  See attachment 1.

B.  See attachment 2.

C.  As the number of years of experience increases, so does the hourly wage.

Step-by-step explanation:

When creating a scatter plot with bivariate data:

For the given data, the hourly wage is dependent on the number of years of experience.  Therefore:

Draw the scatter plot

(See attachment 1).

Draw a line of best fit on the scatter plot (see attachment 2).

Correlation measures how closely two variables are linked.

If two variables are correlated, you can draw a line of best fit on the scatter plot.

The line of best fit has a positive slope and is close to the data points.

Therefore, the scatter plot shows a strong positive correlation between the years of experience and the hourly wage.  

This suggests that as the number of years of experience increases, so does the hourly wage.

The formula for T in terms of B and C is T=4B+10C.

How are phrases converted into expressions and equations?

In order to give verbal explanations of mathematical operations:

Find any phrases or key words that denote an operation.

Add the individual processes together to create an expression or equation. Ensure that the sequence of events is maintained.

Let Doughnuts sold in bag be B

Let Doughnuts sold in cartons be C

As given in the question a bag can contain 4 Doughnuts

∴ it is 4B

as cartons can contain 10 Doughnuts

∴ it is 10C

As T is the total number of Doughnuts

∴ the formula is

T=4B+10C

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The required solution to the given expression is 2 - 6y/x which is determined by the distributive property of multiplication.

The product of a number by addition is equal to the total of the products of that number by each of the addends, according to the distribution property of multiplication.

The expression is given in the question

⇒ (y² - 3y³x⁻¹)2m°y⁻²

∵ m° = 1

⇒ (y² - 3y³x⁻¹)2y⁻²

Apply the distributive property of multiplication,

⇒ y² × 2y⁻² - 3y³x⁻¹  × 2y⁻²

⇒ 2y²⁻²- 6y³⁻²x⁻¹

⇒ 2y° - 6y x⁻¹

∵ y° = 1 and x⁻¹ = 1/x

⇒ 2 - 6y/x

Therefore, the required solution to the given expression is 2 - 6y/x.

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According to the given expression, the inequality that can model the given situation can be stated as 520 < 400 + 15x.

Since Dan wants to know how many hours he needs to spend walking dogs, let us assume this to be x:

15x + 400

Dan wants to know how many hours he needs to spend walking dogs to earn more than $520 in a week. So the above expression is greater than 520:

15x + 400 > 520

When400 is subtracted from 520, the result is true:

15x > 120

Thus, the first inequality expression can be rearranged as:

520 < 400 + 15x

Thus, the inequality that can model the given situation can be stated as 520 < 400 + 15x.

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Answer:

good luck

Step-by-step explanation:

Answer:

BANG IT LIKE A CHOLO

Step-by-step explanation:

Orange County's crime rate is predicted to be 83%. This estimate is based on data from the Orange County Sheriff's Office, which showed that the number of crimes reported per 100,000 residents in the county has been steadily declining over the past few years.

A point estimate for the crime rate in Orange County is = 82.7% = 83%

The predicted number of crimes reported per 100,000 residents in Orange County is

= 100,000 X 0.827

= 82,700

The estimate for the crime rate in Orange County is 83%. However, this is just an estimate and the actual rate could be higher or lower. To get a more accurate estimate, we would need to collect more data.

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