Find the slope of the line through each pair of points. (0,0) and (2,6)

Yes, the given set of numbers can be the measures of the sides of a triangle. The triangle is acute.

By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side.

16 + 18 > 26

18 + 26 > 16

26 + 16 > 18

Hence, these set of numbers can be the measures of the sides of a triangle.

According to the Pythagorean Inequality Theorem, a triangle whose sides measure a, b, and c where c is the largest, the triangle can be characterized as:

acute if [tex]a^{2} + b^{2} < c^{2}[/tex]

obtuse if  [tex]a^{2} + b^{2} > c^{2}[/tex]

right if  [tex]a^{2} + b^{2} = c^{2}[/tex]

∴The longest side is 26.

Hence, a = 16, b = 18 and c = 26;

Consider [tex]a^{2} + b^{2[/tex]  :

= [tex]16^{2} + 18^{2}[/tex]

= 580.

Now consider [tex]c^{2}[/tex] :

= [tex]26^{2}[/tex]

= 676.

Thus, [tex]a^{2} + b^{2} < c^{2}[/tex].

Hence, the triangle is acute.

To learn more about the Pythagorean Theorem, refer to this link:

brainly.com/question/14930619

#SPJ4

Answer:

P(17.4 < X < 22.6) = P((X-20)/2.6 < (22.6-20)/2.6) = P(Z < 1.38)

From a standard normal table, we find that P(Z < 1.38) = 0.9128

Step-by-step explanation:

Give me Brainliest if that helped! :)

Answer: god please help the world

Step-by-step explanation: we are struggling

Answer: -6/7p+1/7

Step-by-step explanation: thank god I'm smart lol... I'm a big brain!!!

Option D) is correct option that is the function ,  (f + g)(x) = x – 7

Note that if we have been given two functions which are f(x) and g(x) then their addition will be given as

            (f + g)(x) = f(x) + g(x)             (1)

We have been given the equation as

f(x) = -3x - 5     and g(x) = 4x – 2

putting the required value in equation (1) we get

            (f + g)(x) = (-3x-5) + (4x-2)

            (f + g)(x) = -3x – 5 + 4x – 2

            (f + g)(x) = x – 7

Thus option D) is the correct option that is the function,  (f + g)(x) = x – 7

Learn more about function here : https://brainly.com/question/20384115

#SPJ9

Solution of polynomial 4/2a = 5/a +6 is , [tex]a=-\frac{1}{2}[/tex]

In mathematics, polynomial function can be defined as the equation which consist of coefficient, variables and exponents. A polynomial equation has positive numbers as their exponent which is also known as its degree. All the equations such as monomials, quadratic equation, cubic equation, linear equation of one degree, two degree and more  which has non  negative number as their powers all are part of polynomial equation and can be taken as types of the polynomial equations.

Some examples of polynomial equation are :

According to question,

[tex]\frac{4}{2a} = \frac{5}{a} +6\\\\= > \frac{2}{a} = \frac{5}{a} +6\\\\= > 5 + 6a =2\\ \\= > 6a = -3\\\\= > a = -\frac{3}{6} =-\frac{1}{2}[/tex]

Thus a = -1/2

To know more about polynomial functions, visit:

brainly.com/question/17822016

#SPJ4

The domain of the function is {x | 2 ≤ x ≤ 9}

The domain of the function is the set of input values of the graph

The given parameters are

A linear function begins with closed circle at (2,0) and ends with a closed circle at (9,7)

This is represented as

(x, y) = Closed (2, 0)

(x, y) = Closed (9, 7)

Remove the y values to determine the domain

x = Closed 2

x = Closed 9

The closed statement represents the inequality ≤

So, we have

2 ≤ x ≤ 9

Hence, the domain of the function is {x | 2 ≤ x ≤ 9}

Read more about domain at:

https://brainly.com/question/2264373

#SPJ1

Answer:

B. {x | 2 ≤ x ≤ 9}

Step-by-step explanation:

Answer:

x=8

Step-by-step explanation:

multiply both sides of the equation by 8

combine like terms

divide both sides of the equation by -5

Hence , the diameter of the trunk of the tree is 2.54 × 10⁻¹ m which is option (B) .

Let the diameter of stem of a flower be " x"  and diameter of the trunk of a tree be " y " .

According to the question  "The diameter of the trunk of a tree is 40 times greater than the stem of the flower " which can be represented by

y = 40 x       .....(1)

It is given that stem of a flower has a diameter of 6.35 × 10⁻³ meters.

Putting x = 6.35 × 10⁻³ in equation (1) , we get

 y = 40 × 6.35 × 10⁻³

 y = 254 × 10⁻³

 y = 2.54 × 10⁻¹ m

Learn more about linear equation here :

https://brainly.com/question/2030026

#SPJ1

Answer:

-2

Step-by-step explanation:

Slope = rise/run

[tex]\mathrm{Slope} = \frac{y_2-y_1}{x_2-x_1}\\m=\frac{1-5}{4-2}\\1 - 5 = -4\\4 - 2 = 2\\=\frac{-4}{2}\\ =-2[/tex]

Using Pythagorean theorem, the student walked 53.58 meters more compared to the total displacement from the starting point.

If a student walks 100 meters north, then 100 meters west, then the path he travels resembles the sides of a right triangle (see attached photo).

Using Pythagorean theorem, we can solve for the total displacement from the starting point to the end point.

c^2 = a^2 + b^2

where c is the total displacement from the starting point to the end point

a is the distance he walks up north

b is the distance he walks to the west

c^2 = 100^2 + 100^2

c^2 = 10,000 + 10,000

c^2 = 20,000

c = 141.42 meters

Comparing the total distance the student walked and the total displacement from the starting point to the end point by subtraction.

100 meters + 100 meters - 141.42 meters = 53.58 meters

Learn more about Pythagorean Theorem here: brainly.com/question/343682

#SPJ4

The solution to the system of equations is (2.5, -2)

The system of equations is given as:

2x + y = 3

2x - 5y = 15

Subtract the equations to eliminate the variable x

This is represented as

2x - 2x + y - -5y = 3 - 15

Evaluate the like terms in the above equation

So, we have

y + 5y = 3 - 15

Evaluate the like terms in the above equation

So, we have

6y = -12

Divide both sides of the above equation by 6

So, we have

y = -2

Substitute y = -2 in 2x + y = 3

2x - 2 = 3

This gives

2x = 5

Divide by 2

x = 2.5

Hence, the solution to the system of equations is (2.5, -2)

Read more about system of equations at

https://brainly.com/question/13729904

#SPJ1

Answer:

2.5, -2

Step-by-step explanation:

Mr. Shaw can use 70 shelves with 2 books each.

or

Mr. Shaw can use 35 shelves with 4 books each.

or

Mr. Shaw can use 28 shelves with 5 books each.

or

Mr. Shaw can use 20 shelves with 7 books each.

or

Mr. Shaw can use 14 shelves with 10 books each.

Mr. Shaw has 140 books in his library.

Divisibility rule of 2:

A number is always entirely divisible by 2 if it is even or has an even last digits, such as 2,4,6,8, or 0.

The last digit of 140 is 0 which is an even number. So, 140 is divisible by 2.

Therefore,

Number of shelves = 140/2 = 70

Divisibility rule of 4:

An integer is divisible by 4 if its last two digits are also divisible by 4. A number is divisible by 4 if its last two digits are zeros since 4 divides 100.

The last two digits of 140 are 4 and 0.

Now, 40/ 2 = 20. Hence, 140 is divisible by 4.

Therefore,

Number of shelves = 140/4 = 35

Divisibility rule of 5:

If the last digit of a given integer is either 5 or 0, then the number is divisible by 5 according to the divisibility rule of five.

Since the last digit of the number 140 is 0. Hence 140 is divisible by 5.

Therefore,

Shelves = 140 / 5 = 28

Now,

Divisibility rule of 7:

According to the divisibility rule of 7, if a number is divisible by seven, then "the difference between twice the unit digit of the provided number and the remaining part of the given number should be a multiple of seven or it should be equal to zero."

140 = 14 - 2 × 0 = 14

Since 14 is divisible by 7. Hence 140 is divisible by 7.

Therefore,

Number of shelves = 140 / 7 = 20

Similarly,

Divisibility rule of 10:

The divisibility rule for 10 states that any number whose last digit is 0, is divisible by 10.

As the last digit of 140 is 0, hence 140 is divisible by 10.

Therefore,

Number of shelves = 140/10 = 14

Learn more about the divisibility rule here:

https://brainly.com/question/11330156

#SPJ9

The image of the point (3,4)(3,4) after a rotation of 90^{\circ}90 ∘ counterclockwise about the origin is (-3,4).

A point's reflection

The mirror's "reflection" of the specified point P causes it to appear at an equal distance away on the other side of the line. To view this, move the point P. According to tradition, the "image" of point P is the reflection of point P across the line, which is designated by the term P' (pronounced "P prime").

As the rotation is counterclockwise around the origin,

the coordinates of the image will be - (-3,4)

The graph is attached at the end of the solution.

To learn more about image of the points from given link

https://brainly.com/question/2288668

#SPJ9

Answer:

-4, 3

Step-by-step explanation:

The length of the fence around the triangular land is equal to 180 meters.

The perimeter of a figure is the sum of the side lengths of the figure. Triangles have three sides and we need to determine the perimeter of the triangular land. If we know that l₁ = 55 meters, l₂ = 60 meters and l₃ = 65 meters, then the perimeter of the figure is:

p = l₁ + l₂ + l₃

p = 55 m + 60 m + 65 m

p = 180 m

The length of the fence around the triangular land is equal to 180 meters.

To learn more on perimeters: https://brainly.com/question/6465134

#SPJ1

The properties in each step is:

Step 1 and 2: distributive property

Step 3: addition property of equality

Step 4: division property of equality

Given the equation, x + 0.06x - 1.50 = 3.80, we can solve for x using the steps with the following appropriate properties shown below:

Step 1:

(1 + 0.06)x - 1.50 = 3.80 (distributive property)

Step 2:

1.06x - 1.50 = 3.80 (distributive property)

Step 3: Add 1.50 to both sides of the equation

1.06x = 5.30 (addition property of equality)

Step 4: Divide both sides by 1.06

x = 5.00 (division property of equality)

Learn more about the properties of equality on:

https://brainly.com/question/13260378

#SPJ1

Answer:

3

Step-by-step explanation:

Parenthesis

Exponents

Multiplication

Division

Addition

Subtraction

5-2*3+4   First multiply.

5-6+4 Now do addition or subtraction what comes first, from left to right.

-1+4 =

3

Answer:

Inverse Property of Addition

Step-by-step explanation:

The length of BD is 4.29

BF is the radius of circle and CE is the chord. BF perpendicularly bisects the chord into two equal halves. Thus, we can say that -

CD = 1/2CE

Keep the values in equation to find the value of CD

CD = 1/2×13.5

CD = 6.75

Now, taking BCD as right angled triangle, we can say -

BC is hypotenuse, CD is base and BD is perpendicular. Using Pythagoras theorem to find the length of BD.

BC² = CD² + BD²

8² = 6.75²  + BD²

BD² = 64 - 45.5625

BD² = 18.4375

BD = √ 18.4375

BD = 4.29

Hence, the length of BD is 4.29

Learn more about  chord -

https://brainly.com/question/1869643

#SPJ4

The complete question is attached in the image below.

Answer: C

Step-by-step explanation:

180° = 96° + 8y + 12

180° = angles on a straight line

180 - 96 - 12 = 8y

8y = 180 - 96 - 12

8y = 72

y = 72 / 8

y = 9

The total amount raised is the same for both Roxy and Randy if they sell 50 Plates.

Let the number of plate = 'p'

Roxy :

Selling price of plates = $5.00

Raised = $175

Total plates sold = 5.00p

Total amount raised = 5.00p + 175  ...eq.(1)

Randy :

Selling price of plates = $3.50

Raised = $250

Total plates sold = 3.50p

Total amount raised = 3.50p + 250  ...eq.(2)

Now we will equate the eq.(1) and eq.(2) to find the same amount raised by both Roxy and Randy ,

5.00p + 175 = 3.50p + 250

5.00p - 3.50p =250 - 175

              1.5p = 75

                   p = 75/1.5

                   p = 50

To learn more about this Patterned Question visit :

https://brainly.com/question/13028628

#SPJ9

The simplified expression for (6-5 / 4-2) is 1/2 .

The given expression is,

6-5 / 4-2

First we need to solve the numerator which is (6-5) and on simplifying the numerator we can write,

Numerator = ( 6 - 5 ) = 1                         equation 1

Similarly, now we can proceed to solve the denominator which is (4 - 2) and on simplifying the denominator we write,

Denominator  = (4 - 2) =2                       equation 2

Now we can substitute the value of numerator and the denominator from equation 1 and equation 2 in the given expression (6-5 / 4-2) as,

(Numerator / Denominator) = (6-5 / 4-2) = 1/2

The simplified expression for (6-5 / 4-2) is 1/2 .

To know more about Simplifying Expressions refer to the link:

https://brainly.com/question/1280754

#SPJ4

Answer:

  D

Step-by-step explanation:

You want to find the number line that shows the solution to -4 -(-6).

The first number in the "sum" is -4, so the first arrow on the number line should go from 0 to -4. (All choices show that.)

The second number is -6. Addition of -6 would create an arrow from -4 going 6 units to the left. Subtraction works in the opposite direction, so the subtraction of -6 will show as an arrow from -4 extending 6 units to the right. Only answer choice D shows this.

__

Additional comment

You know the solution is -4 -(-6) = -4 +6 = +2, so the graph showing the solution will have an arrow ending at +2. This eliminates all answer choices except the correct one.

<95141404393>

Based on the table of the number of species in the United States, the probability that a randomly selected endangered species is a bird is 17.1%

The probability that a randomly selected mammal is endangered is 81.4%.

The probability that when an endangered species is selected randomly, it is a bird can be found as:

= Number of endangered birds / Number of endangered species

= 80 / (70 + 80 + 318)

= 17.1%

The probability that should a randomly selected mammal be picked, the mammal is endangered is:
= Number of endangered mammals / Number of mammals

= 70 / (70 + 16)

= 81.4%

Find out more on probability at https://brainly.com/question/27430621

#SPJ1

Answer:

5x - 6y + 126 = 0

Step-by-step explanation:

y-y1=m(x-x1)

y - 6 = 5/6 (x - (-18))

6y - 36 = 5x + 90

5x - 6y + 126 = 0

The 46th term of a Arithmetic Progression (AP) is (a₄₆ = 95.)

The difference between the two numerical orders is a constant value in Arithmetic Progression (AP). Another name for it is Arithmetic Sequence.

We'd end up coming across a few key words in AP, which were denoted as:

The AP can also be defined in terms of common differences, as shown below.

Now, in the question, the given sequence is;  3,5,7, ...........

Assume the first term is'a₁' = 3

Assume 'a₂' = 5 is the second term.

Assume the third term is 'a₃' = 7

Find the common difference;

d = a₂ - a₁  

Substitute the values in the above equation;

d = 5 - 3 = 2

Now, to calculate the value of the 46th term use the formula of nth term.

an = a + (n − 1) × d , n = total number of terms = 46.

Substitute all the values;

a₄₆ = 5 + (46 - 1) × 2

a₄₆ = 5 + 45 × 2

a₄₆ = 5 + 90

a₄₆ = 95

Therefore, the value of the 46th term is estimated as 95.

To know more about the arithmetic progression, here

https://brainly.com/question/6561461

#SPJ4

Answer:

a ) mean = 1.8

b ) new mean = 11.8

c ) new mean = 23.6

hope this helps

The ΔXYZ is an Right Angled triangle.

Pythagoras Theorem states that the sum square of two sides of triangle is equal to the  square of longest side.

Distance Formula is used to calculate distance between two points A(a,b) and B(c,d)

denoted by [tex]d=\sqrt{(c-a)^{2} +(d-b)^{2} }[/tex]

In the given question , first calculate the length of each side of the triangle.

given X(3,1),Y(3,7),Z(11,1)

using distance formula

XY=[tex]\sqrt{(3-3)^{2} +(7-1)^{2} } =\sqrt{36} =6[/tex]

YZ=[tex]\sqrt{(11-3)^{2} +(1-7)^{2} } =\sqrt{8^{2}+(-6)^{2} } =\sqrt{64+36}= \sqrt{100} =10[/tex]

XZ=[tex]\sqrt{(11-3)^{2}+(1-1)^{2} } =\sqrt{8^{2} } =\sqrt{64} =8[/tex]

The longest side is 10 and other two sides are 8,6.

by using Pythagoras Theorem

[tex]hypotnuse^{2} =base^{2} +perpendicular^{2}[/tex]

[tex]YZ^{2} =XY^{2} +XZ^{2} \\ \\ 10^{2} =8^{2} +6^{2} \\ \\ 100=64+36\\ \\ 100=100[/tex]

Since Pythagoras Theorem is satisfied It is a right  angled triangle.

Therefore ,  The ΔXYZ is an Right Angled triangle.

Learn more about Pythagoras Theorem here https://brainly.com/question/23276715

#SPJ4

It should be noted that the distance of

Bellevue from the office be located will be 13.85 miles.

It should be noted that based on the information, the handyman company serves customers from two cities 60 miles apart, Jonesville and Bellevue and the vompany would like to position a new office between the two cities using weighted averages based on the typical number of calls received from each city.

From the information, Jonesville has a weight of 3 and Bellevue has a weight of 5, the distance of

Bellevue from the office be located will be:

= (0 × 5 + 60 × 4) / (5 × 8)

= 180 / 13

= 13.85

The office should be 13.85 miles from Bellevue.

Learn more about weight on:

brainly.com/question/2337612

#SPJ1

Answer:

you should use subtraction to solve this problem

Antonio spent 1/2 hours longer at soccer practice then baseball practice

Step-by-step explanation:

9/10-2/5

9/10-4/10

=

5/10 or 1/2

4 lines of symmetry are there in the pattern.

What are an example and a pattern?

The square's two diagonals are symmetry lines.

Additionally, symmetry lines are formed by connecting the midpoints of the opposing sides. Consequently, there are four lines of symmetry overall.

4 lines of symmetry are there in the pattern.

Learn more about pattern

brainly.com/question/14720576

#SPJ4