Please help me with this question.

Using the definition of slope, the triangle with vertices (3 , 5), (-2 , 6), and (1 , 3) is a right triangle.

The slope, m, determines the steepness of a line. It can be measured by the vertical distance from one point to another divided by the horizontal distance of the same points.

m = (y2 - y1)/(x2 - x1)

To prove that the triangle with vertices (3 , 5), (-2 , 6), and (1 , 3) is a right triangle, there should be a pair of adjacent lines perpendicular with each other(forms 90 degree angle). The slope of this pair of adjacent lines must be negative reciprocal of one another.

let A = (3 , 5)

B = (-2 , 6)

C = (1 , 3)

Determine the slope of each line of the triangle: AB, BC, AC.

AB : m = (6 - 5)/(-2 - 3) = 1/-5 = -1/5

BC : m = (3 - 6)/(1 - -2) = -3/3 = -1

AC : m = (3 - 5)/(1 - 3) = -2/-2 = 1

-1 is the negative reciprocal of 1. The slope of BC is the negative reciprocal of the slope of AC, hence, side BC is perpendicular with each other.

Therefore, the triangle with vertices (3 , 5), (-2 , 6), and (1 , 3) is a right triangle.

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The expression for h in the information illustrated will be h = 2r.

It should be noted that the expression is given as:

2πr³ = πr²h

In this situation, the information is that we should make h the subject of the formula.

This will be:

2πr³ = πr²h

Divide both side by πr²

2πr³/πr² = πr²h/πr²

2r = h

Therefore h = 2r

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An equation that models the balance y after x​ months is; y = -130x + 1900

From the given parameters, we can form a table of values as;

Month    Balance

0              1900

3              1510

5              1250

Now, the formula for slope between two coordinates is;

m = (y2 - y1)/(x2 - x1)

At first coordinate, we have;

m = (1510 - 1900)/(3 - 0)

m = -390/3 = -130

At second coordinate;

m = (1250 - 1510)/(5 - 3)

m = -260/2

m = -130

Now, the formula for equation in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

Thus, equation is;

y = -130x + 1900

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Complete question is;

Zachary purchased a computer for ​$1,900 on a payment plan. 3 months after he purchased the​ computer, his balance was ​$1,510. 5 months after he purchased the​ computer, his balance was ​$1,250 What is an equation that models the balance y after x​ months?

The total change in the stock market from the beginning of the day to the end of the day is 89.75 points.

Here, we are given that the stock market goes down 30 1/2 points at the beginning of the day.

30 1/2 can be written as-

{(30*2) + 1}/2 = 61/2

Further it is given that the stock market goes up by 120 1/4 points at the end of the day.

120 1/4 can be written as-

{(120*4) + 1}/4 = 481/4

Thus, the total change in the stock market will be-

481/4 - 61/2

= 481/4 - 122/4

= 359/4

or 89.75

Thus, the total change in the stock market from the beginning of the day to the end of the day is 89.75 points.

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In Jared's experiment, we can conclude that; No, cause-and-effect relationships can be established only by collecting observations from

nature, not from a controlled experiment.

The correlation coefficient is simply the specific measure that quantifies the strength of the linear relationship between two variables in a correlation analysis. It varies from -1 to 1.

Now, we are told that the correlation coefficient is 0.93. This means that it is close to 1. Now, we know that when the correlation coefficient is near 1 or −1, the linear relationship is strong; when it is near 0, the linear relationship is weak.

We also know that correlational studies allow researchers to detect the presence and strength of a relationship between variables, while experimental studies allow researchers to look for cause and effect relationships.

Thus, in Jared's experiment, we can conclude that; No, sunlight doesn't cause pea plant growth because  cause-and-effect relationships can be established only by collecting observations from

nature, not from a controlled experiment.

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Distance between the points D and E is [tex]5\sqrt{3}[/tex] and the mid point of the line segment joining D and E is (1/2,5/2,7/2) .

Distance Formula is used to calculate distance between two given points.

the distance between points A(a,b,c) and B(x,y,z) is given by [tex]\sqrt{(x-a)^{2}+(y-b)^{2}+(z-c)^{2} }[/tex]

Mid point formula the mid point M(m₁,m₂,m₃) between the points  A(a,b,c) and B(x,y,z) is given by M(m₁=[tex]\frac{a+x}{2}[/tex],m₂=[tex]\frac{b+y}{2}[/tex],m₃=[tex]\frac{c+z}{2}[/tex])

To calculate the distance between the points D(0,0,0) and E(1,5,7) we will use distance formula.

Substituting the values in Distance formula we get

d=[tex]\sqrt{(1-0)^{2}+(5-0)^{2}+(7-0)^{2} }[/tex]

=[tex]\sqrt{1^{2} +5^{2} +7^{2} }[/tex]

=[tex]\sqrt{1+25+49}[/tex]

=[tex]=\sqrt{75} \\ 5\sqrt{3}[/tex]

to determine the midpoint M we will use mid point formula.

Substituting the values of the given points in the mid point formula we get

mid point = [tex](\frac{0+1}{2} ,\frac{0+5}{2} ,\frac{0+7}{2} )[/tex]=(1/2,5/2,7/2)

Therefore , Distance between the points D and E is [tex]5\sqrt{3}[/tex] and the mid point of the line segment joining D and E is (1/2,5/2,7/2) .

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Answer: 70,464 people

Step-by-step explanation:

         We will write an equation to help us solve. Note that a percent divided by 100 becomes a decimal and that "of" means multiplication in mathematics. Let x be the number of people who will support the measure.

96% of 73,400 voters will support the local measure.

(0.96)(73,400) = x

70,464 people = x

The slope of the line containing (4,2) and (4,-3) is Infinity.

The slope of a straight line can be written as follows,

m = [tex](y_{2} -y_{1} ) / (x_{2} -x_{1} )[/tex]                  equation1

The line is containing the points  (4,2) and (4,-3). So, we can write

[tex]y_{2}[/tex] = -3 , [tex]y_{1}[/tex] = 2 , [tex]x_{2}[/tex] = 4 , and [tex]x_{1}[/tex] = 4 .

On substituting the values of variables in equation1, we will get

m = ( (-3)-(2) ) / ( (4)-(4) ) = (-6/0) = Infinity

As the slope of a line is Infinity, so we can conclude that the given line is a straight line.

Here:

m = the slope of the line

( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] ) are the first coordinates.

( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )are the second coordinates.

The slope of the line containing (4,2) and (4,-3) is Infinity.

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The perimeter of a circle with an area of 36 square units is 21.29 units.

For a circle with a radius R, the area is given by the formula:

A = pi*R^2

And the perimeter is given by:

P = 2*pi*R

Where pi = 3.14

In this case the area is A = 36 square units, then the radius is given by:

36 = 3.14*R^2

R = √(36/3.14) = 3.39 units.

Replacing that in the perimeter equation we get:

P = 2*3.14*3.39 units = 21.29 units.

The perimeter of a circle with an area of 36 square units is 21.29 units.

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From 125 yards, a marksman hit 55.6 of the targets last year, which is equal to (55.6 × 100)% that is 5560%

A percentage (from Latin: per centum, "by a hundred") is a number or ratio stated as a fraction of 100 in mathematics. The abbreviations "pct.", "pct.", and occasionally "pc" are also used to indicate it, while the percent symbol, "%," is most frequently employed. A percentage is a dimensionless (pure) number; it does not have a unit of measurement.

A percentage is a fraction or a ratio in which the full number is always 100. For example, if Sam received 30% on his arithmetic test, he received 30 points out of a possible 100. It is written as 30/100 in fraction form and 30:100 in ratio form.

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Full question

Rewrite the decimal in the sentence below as a percentage.

From 125 yards away, a marksman hit 55.6 of the targets last year.

Based on the interest rates available to Michael, the option that would allow him to pay the least interest is B. 18-month loan with a 3.50% annual simple interest rate

The interest on the first option is:
= (7.25% x 12,000) x 12/12months in year

= $870

Interest on second loan:

= (3.5% x 12,000) x 18 / 12 months in year

= $630

Interest on third loan:

= (3.75% x 12,000) x 24/12 months in year

= $900

Interest on fourth loan:

= (2.75% x 12,000) x 36/12  months in year

= $990

In conclusion, the 18-month loan with a 3.50% annual simple interest rate gives the lowest rate.

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f (9) =  - 5/2 is the output for the given input .

How can you tell whether a function is linear or not?

f(x)= (2/9)x - (9/2)

Put x = 9    ⇒   (2/9) * 9 - (9/2)

                ⇒   2 - 9/2

                ⇒  -5/2

Therefore f (9) =  - 5/2

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the bacterial cell is 6.25*10 times smaller than the amoeba cell.

To find how many times smaller is the bacterial cell than the amoeba cell, we need to take the quotient between the amoeba cell's length and the  bacterial cell's length

We know that:

bacterial cell's length = 4*10^(-6) m

amoebas cell's length. = 2.5*10^(-4) m

The quotient gives:

Q = ( 2.5*10^(-4) m)/(4*10^(-6) m) = (2.5/4)*(10^(-4)*10^6) = 0.625*10^(-4 + 6)

Q = 0.625*10^2

Now we want this in scientific notation, so we need to have a digit in the left fo the decimal point, so we can rewrite this as:

Q = 0.625*10^2 = 6.25*10^1 = 6.25*10

Then the bacterial cell is 6.25*10 times smaller than the amoeba cell.

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Answer:

One way you could do it is to do a Systematic Sample \textbf{Systematic Sample} Systematic Sample and go to every other house in the neighborhood and ask their opinion.

Step-by-step explanation:

The solution of given rational equation [tex]\frac{2}{n} +\frac{n+2}{n+1}=\frac{-2}{n^2+n}[/tex] is n = -2

In this question,

We have been given a rational equation.

[tex]\frac{2}{n} +\frac{n+2}{n+1}=\frac{-2}{n^2+n}[/tex]

We need to find the solution of given rational equation.

First we simplify the LHS of given equation.

[tex]\frac{2}{n} +\frac{n+2}{n+1}\\\\=\frac{2(n+1)+n(n+2)}{n(n+1)} \\\\=\frac{2n+2+n^2+2n}{n^2+n}\\\\ =\frac{n^2+4n+2}{n^2+n}[/tex]

So, given equation would be,

[tex]\frac{n^2+4n+2}{n^2+n}=\frac{-2}{n^2+n}[/tex]

Here, the denominator is same on the both sides.

⇒ n² + 4n + 2 = -2

⇒ n² + 4n + 4 = 0

⇒ (n + 2)² = 0

⇒ n + 2 = 0

⇒ n = -2

We need to check above solution.

so, substitute n = -2 in LHS of given equation.

[tex]\frac{2}{-2} +\frac{-2+2}{-2+1}\\\\=-1+0\\\\=-1[/tex]

Now, substitute n = -2 in RHS of given equation.

[tex]\frac{-2}{-2^2-2}\\\\=\frac{-2}{4-2}\\\\= \frac{-2}{2} \\\\-1[/tex]

For n = -2, LHS = RHS

Therefore, the solution of given rational equation [tex]\frac{2}{n} +\frac{n+2}{n+1}=\frac{-2}{n^2+n}[/tex] is        n = -2

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Answer:

7x - 35

Step-by-step explanation:

This states the product of (5 less than x) and (7). Five less than x can be written as (x - 5), and 7 is just 7. The product of (x-5) and 7 is 7x - 35.

Hope this helped :)

When two sides are provided without an angle measurement, such as a = 13m and b = 17m , we can create an infinite number of obtuse triangles.

As an example:

How many different obtuse triangles can we make if our side lengths are 13m and 17m, and our angle value ranges from 90 to 360 degrees?

Make a triangle with sides of 13m and 17m metres, a 120 degree angle, and a third side that can be protractored to the length you desire. You've constructed a triangle.

We may create a whole different triangle that is identical to this one by altering the third side's length and angle.

You must always remember to select the side lengths and angles. It's hinted that you could choose another course of action. There are an infinite amount of distinct triangles that can be created by using the same angles.

Thus, we can make an infinite number of triangles by employing a single angle and a single side length.

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Ricky has the number of stamps in the number of 15 stamps.

According to the question, the given parameters can be used to form the expression by using simplification method and the parameters are as follows:

Stamps for Ana: 8

Stamps for Ricky and Ana: 23

Given equation: 23 = r + 8

The equation formed by the simplification method is:  r + a = 23

Solving above two equations, we get a = 8 stamps and r = 15 stamps.

Hence, Ricky has the number of stamps in the number of 15 stamps.

What is simplification?

The word simplification is the procedure in which complicated expression can be written in a simpler form to make the calculation easy. This method is used to calculated the answers for the unknown quantity.

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The equation of the line is: y = 4x + 37

m = 4

b = 37

The equation of the line that is perpendicular to x + 4y = 12, will have a slope that is the negative reciprocal of the its slope.

Rewrite the equation, x + 4y = 12 in slope-intercept form:

4y = -x + 12

y = -x/4 + 3

The slope is -1/4. Therefore, the slope of the perpendicular line would be 4.

Substitute m = 4 and (a, b) = (-8, 5) into y - b = m(x - a)

y - 5 = 4(x - (-8))

y - 5 = 4x + 32

y = 4x + 32 + 5

y = 4x + 37

The equation of the line is: y = 4x + 37

m = 4

b = 37

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Determine whether each infinite geometric series diverges or converges.

The series converges.

If the series converges, state the sum. 4+2+1+ . . .

The sum of the infinite series is 8

What is the sum of the infinite series?

Given:

[tex]a(\text{ the first term})=4\\\\r(\text{ the common ratio})= \frac{a_2}{a_1} = \frac{2}{4}=\frac{1}{2}[/tex]

Since , [tex]\vert r\vert < 1[/tex]  , the  infinite series converges.  

The sum of infinite geometric series is:

[tex]S_\infty=\frac{a}{1-r} ; -1 < r < 1\\\\S_\infty=\frac{4}{1-\frac{1}{2} } =\frac{4}{\frac{1}{2} }=8[/tex]

The sum of the infinite series is 8

What is an infinite geometric series?

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[tex]f(x)=x^2-3x+20\\\\f(5)=(5)^2-3(5)+20\\\\f(5) = 25-15+20\\\\f(5)=\boxed{30}[/tex]

Answer:

32

Step-by-step explanation:

Sorry for not neat explanation but i hope u understand

Answer:

32?

Step-by-step explanation:

when i did it with a Pythagorean theorem calculator i got 32

Answer:

1. 7.8

2. -1/5

3. -16.2

4. -25/8

Step-by-step explanation:

-

Answer:

7.8

-0.2

-16.2

-3.125

I really hope it helps

ps: from ultra instinct Giga Chad

I believe the answer would be Y=125+25(h

Answer: 125 + 25h

Step-by-step explanation:

The total amount of money is the cost of the window plus the amount of hours.

Answer:

Step-by-step explanation:

The volume of the cone as shown in the diagram is 192 cm²

Diameter in the question is given as 16cm

We need to find the radius of the cone to find the volume of cone which is half of the diameter = 16/2 = 8 cm

The height of the cone as given in the question is 3cm

The volume of the cone =1/3  (πr²h)

We are told to use the value of pi as 3 so we are not using 3.14 or 22/7 as the value of pie

Volume = 1/3  ( 3 × 8² × 3)

= 1/3  ( 9× 64)

  = 1/3  (576)

         = 192 cm²

Hence, the volume of the cone as shown in the diagram is 192 cm²

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The distance from the center of a circle to a point in the interior of a circle is always less than radius of the circle.

It is given that there is a point inside the circle.

We have to find that whether its distance from center of circle is sometimes, always, or never less than the radius of the circle.

What is the radius of a circle ?

The distance between the center of a circle and any point on the circle is called the radius of circle.

We know that ;

Radius is the distance between the center of a circle and any point on the circle.

Let's assume three points which are A, B, and C, where A is a point inside circle, B is a point on circle, and C is a point outside circle.

Also ;

O is the center of circle.

So ;

OA = the length of the line from center to point inside the circle.

OB = radius of the circle.

OC = the length of the line from center to the point outside the circle.

So ;

We can conclude that ;

OA<OB<OC.

or

The length of the line from the center of a circle to any point inside the circle will be always less than it's radius.

Thus , the distance from the center of a circle to a point in the interior of a circle is always less than radius of the circle.

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Answer:

[tex]{ \tt{ {x}^{2} + 6x + 2 = 0}} \\ { \tt{ {x}^{2} + 6x = - 2 }}[/tex]

- Add the square of the half of the sum on either sides:

[tex]{ \tt{ {x}^{2} + 6x + ( { \frac{6}{2}) }^{2} = - 2 + {( \frac{6}{2}) }^{2} }} \\ \\ { \tt{ {x}^{2} + 6x + 9 = - 2 + 9}} \\ { \tt{ {(x + 3)}^{2} = 7}} \\ { \tt{x + 3 = \sqrt{7} }} \\ { \tt{x = - 3 \pm2.648}} \\ { \tt{x = ( - 3 \pm \sqrt{7} )}}[/tex]

Since the distribution is symmetric, the mean and the median of the distribution are equal.

When a distribution is symmetric, the mean and the median are equal. From the dot plot in this problem, the distribution is uniform(as all outcomes are equally as likely, that is, they have the same frequency in the dot plot), and symmetric, hence the the mean and the median of the distribution are equal.

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