Whole number that’s is bigger than 1000 but smaller than 1100

Point A is located at (4, 7). It will be translated 5 units right and 3 units down. Write the rule and give the location of poin

Anarel [89]

Answer:

The rule of translation is $A(x',y') = A(x,y) + (5,-3)$ .

The translated vector is $A(x',y') = (9, 4)$ .

Step-by-step explanation:

Let supposed that translation to the right is in the +x direction and translation downwards in the -y direction.

We procced to translate the operation into mathematic terms. A translation consists in a vectorial sum on a given vector. That is:

$A(x',y') = A(x,y) + U(x,y)$ (Eq. 1)

Where:

$A(x,y)$ - Original vector, dimensionless.

$U(x,y)$ - Translation vector, dimensionless.

$A(x',y')$ - Translated vector, dimensionless.

If we know that $U(x, y) = (5, -3)$ , then the rule of translation is described by:

$A(x',y') = A(x,y) + (5,-3)$ (Eq. 2)

If $A(x, y) = (4,7)$ , then the new location of A is:

$A(x',y') = (4,7)+(5,-3)$

$A(x',y') = (9, 4)$

The translated vector is $A(x',y') = (9, 4)$ .

4 0

4 years ago

a grocery store sells 6 bottles of water for $4 and 18 bottles for $10. is the cost of the water proportional to the number sold

galina1969 [7]

No, because it is more money to buy the 10 for 18 than the 6 for 4.

8 0

4 years ago

Determine whether quantities vary directly or inversely and find the constant of variation. 16 factory workers made 40 pieces in

Andrei [34K]

Answer:

Part A) $8\ workers$

Part B) $10\ workers$

Part C) $40\ workers$

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $k=\frac{y}{x}$ or $y=kx$

Let

x -----> the number of workers

y ----> the number of pieces made

In this problem

The relation between the variables x and y represent a direct variation (proportional variation)

so

For x=16, y=40

Find the value of the constant of proportionality k

$k=\frac{y}{x}$

substitute the values

$k=\frac{y}{x}$

$k=\frac{40}{16}\\k=2.5\ \frac{pieces}{worker}$

The linear equation is equal to

$y=2.5x$

Part A) How many workers are needed to make 20 pieces

For y=20 pieces

substitute in the linear equation

$20=2.5x$

$x=8\ workers$

Part B) How many workers are needed to make 25 pieces

For y=25 pieces

substitute in the linear equation

$25=2.5x$

$x=10\ workers$

Part C) How many workers are needed to make 100 pieces

For y=100 pieces

substitute in the linear equation

$100=2.5x$

$x=40\ workers$

3 0

3 years ago

180 = 16x -5+5х+4+90

k0ka [10]

Answer:

What is your question?

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Tom drank 1 1/4 quarts of water and his sister Jane drank 1.75 quarts of water. Write the amount that Jane drank using a

Andreyy89

Answer:

Jane drank 1 3/4 quarts of water.

Jane drank more water than Tom

Step-by-step explanation:

Tom drank = 1 1/4 quarts of water

Jane drank = 1.75 quarts of water

We have to write the amount of water Jane drank in fraction.

There are some steps to convert decimal into fraction.

Step 1:

Value is 1.75:

Put the 1 aside and just work on 0.75

Write down the decimal value divided by 1

Like, 0.75/1

Step 2:

Now multiply both the numerator and denominator by 100.

We will multiply the numerator and denominator by 100 because 1.75 has two values after the decimal.

0.75 *100/1*100

75/100

Step 3:

Simplify the fraction.

divide the fraction by 5.

=15/20

=3/4

Now bring back the 1: and the fraction will become.

1 3/4

Jane drank 1 3/4 quarts of water.

Now who drank more water?

Jane drank more water than Tom

Reason:

Tom drank 1 1/4 = 5/4

Jane drank 1 3/4 = 7/4

Both the fractions have same denominator, so the value with the greater numerator drank more water than the other.

Therefore Jane drank more water than Tom....

3 0

3 years ago