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3 years ago

What is the distance between points (1, 4) and (9, 16)? round to the nearest tenth.

Mathematics

1 answer:

11Alexandr11 [23.1K]3 years ago

6 0

Answer:

14.4 to nearest tenth.

Step-by-step explanation:

By the Pythagoras theorem:-

Distance = √ [ (y2-y1)^2 + (x2-x1)^2 ] where the 2 points are (x1,y1) and (x2,y2)

= √ [ (16-4)^2 + (9-1)^2]

= √ 208

= 14.4

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By using the table in the handbook, the present value of $12,000 for six years compounded at 6 percent semiannually is

denis23 [38]

Take a look at the attachment to see the solution.
A = future value
P = principal (P = 12,000)
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6 0

3 years ago

Just need help on #7 thru 8(a), b and c

Stella [2.4K]

a. The slope of the line passing through the points R(3, 5) and H(-1,2) is -3/4

b. The distance between two points (x₁, y₁) and (x₂,y₂) is 5 units

c. The midpoint of the R(3, 5) and H(-1,2) is (2, 4)

a. The transformation rule is (x,y) → (x + 1, y - 1)

The x-coordinate is shifted 1 unit to the left and

The y - coordinate is shifted 1 unit downwards.

c. The image of B' the pre-image of B(5, 6) is (6, 5)

<h3 /><h3>7 a. How to find the slope of the line?</h3>

The slope of a line passing through the points (x₁, y₁) and (x₂,y₂) is m = (y₂ - y₁)/(x₂ - x₁)

Given that

(x₁, y₁) = (3, 5) and
(x₂,y₂) = (-1, 2)

So, m = (y₂ - y₁)/(x₂ - x₁)

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

m = -3/-4

m = -3/4

So, the slope of the line passing through the points R(3, 5) and H(-1,2) is -3/4

<h3>b. The distance between the points</h3>

The distance between two points (x₁, y₁) and (x₂,y₂) is d = √[(y₂ - y₁)² + (x₂ - x₁)²]

Given that

(x₁, y₁) = (3, 5) and
(x₂,y₂) = (-1, 2)

d = √[(y₂ - y₁)² + (x₂ - x₁)²]

d = √[(2 - 5)² + (-1 - 3)²]

d = √[(-3)² + (-4)²]

d = √[9 + 16]

d = √25

d = 5 units

So, the distance between two points (x₁, y₁) and (x₂,y₂) is 5 units

<h3>7 c How to find the midpoint of the R(3, 5) and H(-1,2) </h3>

The midpoint of the the points (x₁, y₁) and (x₂,y₂) is (x, y) = [(x₁ + x₂)/2, (y₁ + y₂)/2]

Given that

(x₁, y₁) = (3, 5) and
(x₂,y₂) = (-1, 2)

So, the midpoint (x, y) = [(x₁ + x₂)/2, (y₁ + y₂)/2]

(x, y) = [(3 + (-1))/2, (5 + 3)/2]

(x, y) = [(3 - 1)/2, (5 + 3)/2]

(x, y) = [4/2, 8/2]

(x, y) = (2, 4)

So, the midpoint of the R(3, 5) and H(-1,2) is (2, 4)

<h3>8. a The rule for the transformation of point A(1, 4) to point B(2, 3)</h3>

Given that point A(1, 4) and point B(2, 3) we see that point B(1 + 1, 4 - 1).

Let pont A be (x,y).

So, point B = (x + 1, y - 1)

So, the transformation rule is (x,y) → (x + 1, y - 1)

<h3>b. Describe the transformation</h3>

Since the transformation rule is (x,y) → (x + 1, y - 1), we see that

the x-coordinate is shifted 1 unit to the left and
the y - coordinate is shifted 1 unit downwards.

<h3>c. The image of B' the pre-image of B(5, 6)</h3>

Since the transformation rule is (x,y) → (x + 1, y - 1) and point B is (5, 6), thus the image of B' is

(x,y) → (x + 1, y - 1)

(5,6) → (5 + 1, 6 - 1)

(5,6) → (6, 5)

So, the image of B' the pre-image of B(5, 6) is (6, 5)

Learn more about slope of a line here:

brainly.com/question/1617757

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3 0

1 year ago

In preperation for an easter egg hunt, 4 blue eggs are filled for every 7 green. How many green eggs will be filled if 100 blue

ivann1987 [24]

Answer:

1. Typed question: 175 green eggs

2. Attached: 22 tables

Step-by-step explanation:

For the question you typed down, it is a ratio and proportion problem. You need to solve for the ratio proportional to the first ratio given.

4 blue eggs are filled for every 7 green. This means that the ratio between blue eggs and green eggs is 4:7.

Now yo need to figure out a ratio proportional to 4:7 if 100 blue eggs were filled. Below is how this is set up:

$\dfrac{4\;blue\;eggs}{7\;green\;eggs} = \dfrac{100\;blue\;eggs}{x\;green\;eggs}$

Now let's solve for x:

$\dfrac{4\;blue\;eggs}{7\;green\;eggs} = \dfrac{100\;blue\;eggs}{x\;green\;eggs}\\\\or\\\\\dfrac{4}{7}=\dfrac{100}{x}\\\\Cross-multiply\\\\4x = (7)(100)\\\\4x = 700\\\\Divide\;both\;sides\;by\;4\\\\\dfrac{4x}{4}=\dfrac{700}{4}\\\\x=175$

For your attached problem:

You have a total of 175 people, you need to figure out how many round tables you need if here are 8 chairs for each table You just need to divide the number of people by the number of chairs per table.

175 ÷ 8 = 21.9 tables

Now since you cannot have half a table, you round up to the nearest whole number. (we round up because you need to make sure that all of them are seated)

21.9 ≅ 22 tables.

8 0

3 years ago

The gas mileage of Car A is 21 miles per gallon. The gas mileage of Car B is 30 miles per gallon. Which of the following graphs

Anna [14]

Answer:

c for plato users;)

Step-by-step explanation:

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3 years ago

Choose a number between 55 and 101 That is multiple of 6,9, and 18

kirza4 [7]

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5 0

3 years ago