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2 years ago

Graph the line y = kx +1 if it is known that the point M belongs to it: M(1,3)

Mathematics

1 answer:

tigry1 [53]2 years ago

3 0

Answer:

$M(x,y) = (1,3)$ belongs to the line $y = 2\cdot x +1$ . Please see attachment below to know the graph of the line.

Step-by-step explanation:

From Analytical Geometry we know that a line is represented by this formula:

$y=k\cdot x + b$

Where:

$x$ - Independent variable, dimensionless.

$y$ - Dependent variable, dimensionless.

$k$ - Slope, dimensionless.

$b$ - y-Intercept, dimensionless.

If we know that $b = 1$ , $x = 1$ and $y = 3$ , then we clear slope and solve the resulting expression:

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

$k = \frac{3-1}{1}$

$k = 2$

Then, we conclude that point $M(x,y) = (1,3)$ belongs to the line $y = 2\cdot x +1$ , whose graph is presented below.

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Jeremy opens a chocolate shop in the city. He pays $1,500 a month for rent and maintenance of the shop. The price of raw materia

KATRIN_1 [288]

Amount of money paid by Jeremy as rent and maintenance of shop per month = $1500
Cost of raw materials and manufacturing per month = $6000
Total cost that Jeremy has to spend per month = (1500 + 6000) dollars
      = 7500 dollars
Number of individual chocolates sold = 2400
Number of chocolates sold in boxes = 50 boxes
   = (12 * 50) chocolates
   = 600 chocolates
Then
Total number of chocolates sold by Jeremy = 2400 + 600
   = 3000
Now
Price of each chocolate = 7500/3000 dollars
   = 75/30 dollars
   = 5/2 dollars
   = 2.5 dollars
Price of 600 chocolates = 600 * (5/2) dollars
   = 300 * 5 dollars
   = 1500 dollars
Price of 12 chocolates = (1500/600) * 12
   = 15 * 2
   = 30 dollars
Then
We can say that each box of chocolate should be sold at $30. All the loose chocolates should be sold at $2.5 each.

8 0

2 years ago

The team first experiments with changing the position of the curved pit. In the computer program, the

Tju [1.3M]

Answer:

1). Shifted 2 units right.

2). Shifted 2 units left.

3). Shifted 2 units up.

4). Shifted 2 units down.

Step-by-step explanation:

Parent quadratic function is,

y = x²

1). When curved pit of the parent function is shifted 2 units right,

Translated function will be,

y = (x - 2)²

2). The curved pit is shifted 2 units left,

y = (x + 2)²

3). The curved pit is shifted 2 units up,

y = x² + 2

4). The curved pit is shifted 2 units down,

y = x² - 2

6 0

2 years ago

A treasure map says that a treasure is buried so that it partitions the distance between a rock and a tree in a 5:9 ratio. Marin

djyliett [7]

Answer:

A) (7.6, 8.8)

which are the coordinates of the treasure.

Missing Problem Statement:

Given Options:

A) (11.4, 14.2)

B) (7.6, 8.8)

C) (5.7, 7.5)

D) (10.2, 12.6)

I have added the picture showing the traced map onto a coordinate plane to find exact location of treasure.

The coordinates of Tree are (16,21)

Coordinates of rock are (3,2)

Step-by-step explanation:

Let,

Coordinates of treasure be (a,b)

$d_{1}$ = distance from tree to treasure

$d_{2}$ =distance from rock to treasure

$d_{1}=\sqrt{(16-x)^2 + (21-y)^2}$

$d_{2}=\sqrt{x\2 + (y-2)^2}$

Given ratio between rock and tree, $\frac{d_{2}}{ d_{1}}=\frac{5}{9}$ = 0.55_______(Equation.1)

which will be used to locate the treasure.

Now we just need to cross check by putting the coordinates given in the options one by one to find out value of $d_{1}$ , $d_{2}$ and checking if it satisfies the Equation 1.

Check (A) (11.4, 14.2)

$d_{2}$ = 14.8, $d_{1}$ = 8.2,

$\frac{d_{2}}{ d_{1}}$ = 1.8