MATHEMATICS HIGH SCHOOL

Find the distance between the points (11, 4) and (10, 5). 1 2

Answers

Answer 1

Answer: I hope this helps you

Answer 2

Answer:

Answer:

Hi, I'm on this assignment. :)

√2

Step-by-step explanation:

(x(2) - x(1))^2 + (y(2) - y(1))^2

(10 - 11)^2 + (5 - 4)^2

(-1)^2 + (1)^2

1 + 1

√2

The answer options are

2√2

2 <--

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What are three consecutive integers whose sum is 138? Write and solve an equation with one variable. What are three consecutive integers whose sum is 138? Write and solve an equation with one variable.

Answers

x + (x+1) + (x+2) = 138
combine like terms
3x + 3 = 138
subtract 3
3x = 135
divide by 3
x = 45

so the three numbers are 45, 46, and 47

The quantity n varies jointly with the product of z and the square of the sum of x and y. When n is 18, x = 2, y = 1, and z = 3. What is the constant of variation?

Answers

Answer:

Constant of variation is, $(2)/(3)$

Step-by-step explanation:

Joint Variation states that it is jointly proportional to a set of variables i.e, it means that z is directly proportional to each variable taken one at a time.

Given the statement: The quantity n varies jointly with the product of z and the square of the sum of x and y.

"The square of sum of x and y" means $(x+y)^2$

"Product of z and the square of the sum of x and z" means $z * (x+y)^2$

then; by definition we have;

$n \propto z * (x+y)^2$

our equation will be of the form of:

$n = k \cdot z(x+y)^2$ ......[1] ; where k is constant of Variation.

Given: n =18 , x =2 , y= 1 and z = 3

Solve for k;

Substitute these given values in [1] we have;

$18= k \cdot 3(2+1)^2$

Simplify:

$18= k \cdot 27$

Divide both sides by 27 we get;

$k = (18)/(27) = (2)/(3)$

therefore, the constant of variation is, $(2)/(3)$

Hello,

n=k*z*(x+y)²
with n=18,x=2,y=1 and z=3
==>18=k*3*(2+1)²
==>k=18/27=2/3

What is the equation of the line that passes through the point (-4, 7) and has anundefined slope?

Answers

Answer:

x = -4

Step-by-step explanation:

Since the slope is undefined, the line is a vertical line. All vertical lines have an equation x = k. In your problem k = -4, so the equation of the line is x = -4

HELP PLEASE!!The cross sections shown above are from a rectangular prism.

Cross section A is from a plane that is parallel to the base cutting through the prism. Cross section A has an area of 90 units squared.

Cross section B is from a plane that is perpendicular to the base and parallel to the sides of the prism cutting through the prism. Cross section B has an area of 50 units squared.

Cross section C is from a plane that is perpendicular to the base and parallel to the front of the prism cutting through the prism. Cross section C has an area of 45 units squared.

The prism in which the cross sections were taken has a length of
units, width of
units, and a height of
units.

Answers

The rectangular prism has a length of 9 units, a width of 10 units (since width = 90 / length), and a height of 5 units (since height = (5/9) length).

What is the area of a rectangle?

A rectangle is a quadrilateral with four right angles (90-degree angles) and opposite sides that are parallel and congruent (equal in length). The area of a rectangle is defined as the amount of space that is enclosed by its two-dimensional shape, and it can be calculated by multiplying the length of the rectangle by its width. The formula for the area of a rectangle is:

Based on the given information, we can determine the dimensions of the rectangular prism as follows:

Cross section A has an area of 90 square units, which is equal to the area of the base of the prism. Since the base of the prism is a rectangle, we can use the formula for the area of a rectangle to find its dimensions:

90 = length x width

Cross section B has an area of 50 square units, which is equal to the area of one of the sides of the prism. Since the sides of the prism are also rectangles, we can use the formula for the area of a rectangle to find its dimensions:

50 = height x width

Cross section C has an area of 45 square units, which is equal to the area of the front of the prism. Since the front of the prism is also a rectangle, we can use the formula for the area of a rectangle to find its dimensions:

45 = length x height

We now have three equations with three unknowns, which we can solve for to find the dimensions of the prism:

90 = length x width

50 = height x width

45 = length x height

Solving for width in the first equation gives us:

width = 90 / length

Substituting this into the second equation gives us:

50 = height x (90 / length)

Solving for height gives us:

height = 50 x (length / 90) = (5/9) length

Substituting this into the third equation gives us:

45 = length x (5/9) length = (5/9) length²

Solving for length gives us:

length² = (9/5) x 45 = 81

length = √(81) = 9

Therefore, the rectangular prism has a length of 9 units, a width of 10 units (since width = 90 / length), and a height of 5 units (since height = (5/9) length).

To learn more about the area of a rectangle visit:

brainly.com/question/25292087

#SPJ1

State a conclusion that seems reasonable.Donald is older than Jeanette; Donald is older than Ethel. Donald is older than Allen.

Conclusion: