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2 years ago

Write an equation of the line that passes through (1, 2) and is perpendicular to the line y = -5x + 4

Mathematics

1 answer:

stira [4]2 years ago

6 0

Answer:

y = -1/5 + 7

Step-by-step explanation:

Substitute the point (1,2) for the x and the y in the equation, set the 4 to b since we are solving for b.

2 = -5(1) + b now solve for b

2 = -5 + b

+5 +5

7 = b

we know that the slope must be the reciprocal for it to be perpendicular

y = -1/5 + 7 add b (7) to the equation and change the reciprocal

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8 by the power of -5

Paha777 [63]

Answer:

In significant figure is

$3.051757813 \times 1 {0}^{ - 05}$

You can turn it into normal decimal number.

In decimal number:

$0.0000305175713$

Hope this will help :))

8 0

3 years ago

Question 7 (3 points) This scatter plot shows the number of trees planted and the amount of time that has passed (in hours). Bas

Alexandra [31]

Answer:

According to the scatter plot given, and studying that, we get that the most likely number of trees planted in 12 hours will be 13 trees.

Hope my answer helps :)

7 0

2 years ago

The production planner for Fine Coffees, Inc. Produces two coffee blends: American (A) and British (B). He can only get 300 poun

VladimirAG [237]

Answer:

P=2A+B where:

A= # of pounds of American blend and

B= # of pounds of British blend

Step-by-step explanation:

This is a linear programming problem. In order to solve it we need to determine how we are going to use the provided data and we need to keep in mind what we need to maximize (or minimize depending on the problem)

So, the problem states that "The goal of Fine Coffees, Inc. Is to maximize profits." This last sentence will tell us what the objective function will be. The objective function must model the desired value we want to maximize. So the objective function should represent the profits of selling the two tipes of cofee blends.

So this is the data the problem gives us:

"He can only get 300 pounts of Colombian beans per week and 200 pounts of Dominican beans per week." This part or the problem is talking about the amount of coffee beans he can get depending on its type. This will help us find the restrictions for our linear programming problem, so they are not necessary to state the objective function. Next it states:

"Each pount of American blend cofee requires 12 oz of Colombian beans and 4 oz. of Dominican beans, while a pound of British blend coffee uses 8 oz of each type of bean." Again, this data will help us find the restrictions for our linear programming problem, since they will tell us how much coffe we can manufacture, so they are not needed to find the objective function.

The next part states: "Profits for the American blend are $2.00 per pound, and profits for the British blend are $1.00 per pound." Now, we are interested in this part since it's talking about profits, which is what we need to maximize.

We set A to be the number of pounds of American blend and B to be the number of pounds of British blend. So the profit for American blend is found by using the following equation:

$P_{American}=$2.00*A$

And the profit for the British blend is found by using the following equation:

$P_{British}=$1.00*B$

so the total profit is found by adding the two given profits, so we get:

$P_{total}=P_{American}+P_{British}$

$P_{total}=$2.00A+$1.00B$

which can be simplified to:

P=2A+B

which is our objective function.

6 0

2 years ago

Write an equation of a line with the given slope and y intercept m =1/4,b=-3/4

leva [86]

Answer: y=1/4x-3/4

Step-by-step explanation:

We have our equation of a line formula y=mx+b

Then we substitute the given and get y=1/4x-3/4

3 0

2 years ago

A telephone pole has a wire to its top that is anchored to the ground. The distance from the bottom of the pole to the anchor po

Bumek [7]

Answer:

The height of the pole is 105ft,

Step-by-step explanation:

Let us call $h$ the height of the pole, then we know that the distance from the bottom of the pole to the anchor point is 49, or it is $h - 49$ .

The wire length $d$ is 14 ft longer than height $h$ , hence

$d= h+14$ .

Thus we get a right triangle with hypotenuse $d= y+14$ , perpendicular $h$ , and base $h-49$ ; therefore, the Pythagorean theorem gives

$(h-49)^2+h^2 = (h+14)^2$

which upon expanding we get:

$h^2-98h+2401 = h^2+28h+196$

further simplification gives

$h^2-126h+2205=0$ ,

which is a quadratic equation with solutions

$h =21ft\\h = 105ft.$

Since the first solution $h =21ft$ will give the triangle base length of $21ft-49ft = -28ft$ which is negative; therefore, we disregard it and pick the solution $h = 105ft$ .

Hence, the height of the pole is 105ft.

3 0

2 years ago