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3 years ago

What is the equation of a line that has a slope of 2 and passes through the point (4,6) ?

Mathematics

1 answer:

natka813 [3]3 years ago

7 0

Answer:

$y-6=2\,(x-4)$

or in slope y-intercept form :

$y=2x-2$

Step-by-step explanation:

The easiest way of find the answer for this is to use what is called the "point-slope" form of a line, because you are in fact given the value of the slope (m) and also a point $(x_0,y_0)$ it goes through:

$y-y_0=m\,(x-x_0)$

In our case the equation becomes:

$y-y_0=m\,(x-x_0)\\y-6=2\,(x-4)\\$

This can also be written in the slope-intercept form by solving for "y" and operating to remove the parenthesis:

$y-6=2\,(x-4)\\y=2x-8+6\\y=2x-2$

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Mrs smith invests £30,000 (some in a 5% account, some in an 8% account). After the year shes earned £2100. How much did she put

mixer [17]

Answer:

She deposited £10,000 in the 5% yield account and deposited £20,000 in the 8% yield account

Step-by-step explanation:

Let the amount she put in each account be £x and £y respectively

Total amount deposited is ;

x + y = 30,000 ••••••(i)

Now, let’s look at the earnings:

in the £x , amount earned would be;

5/100 * x = 5x/100

For the £y, amount earned would be;

8/100 * y = 8y/100

Adding both gives the total which is £2,1000

5x/100 + 8y/100 = 2,100

Multiply through by 100

5x + 8y = 210,000 ••••••••(ii)

From the first equation, we know that

x = 30,000 -y

Let’s put this into the second

5(30,000-y) + 8y = 210,000

150,000-5y + 8y = 210,000

3y = 210,000 -150,0000

3y = 60,000

y = 60,000/3

y = £20,000

So mathematically;

x = 30,000-y

x = 30,000 -20,000

x = £10,000

7 0

3 years ago

What is the volume of a right circular cylinder with a base diameter of 17.5 ft and a height of 24.5 ft?

Natasha_Volkova [10]

Answer:

The volume of a right circular cylinder with a base diameter of 17.5 ft and a height of 24.5 ft is:

5889.95 ft³

Step-by-step explanation:

We are given a base diameter of a right circular cylinder as :

d = 17.5 ft.

hence radius of cylinder i.e. r =d/2 = 8.75 ft.

height of the cylinder = 24.5 ft.

now we know that volume of cylinder i.e. V is given by :

V = πr²h

putting the value of r and h in the given formula to obtain the volume

V = 3.14×(8.75)²×24.5

= 5889.95 ft³

hence, the volume of a right circular cylinder with a base diameter of 17.5 ft and a height of 24.5 ft is:

5889.95 ft³

3 0

3 years ago

Read 2 more answers

If the radius of a circle is 10 feet, how long is the arc subtended by an angle measuring 81°?

Kaylis [27]

<span>The length of an arc, L = theta/360 * 2 * pie * r Where theta = 81 and r = 10ft = 3.048m So length = 81/360 * 2 * pie * 3.048 L = * 0.225 * 2 * pie * 3.048 L = 1.37 * pie L = pie. Option A</span>

4 0

3 years ago

Lucy will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $53 and costs an add

Alchen [17]

Answer:

The amount driven would be 275, and the cost for both plans will be 77.75$

Step-by-step explanation:

make both equations

y=0.09x+53

y=0.13x+42

set them equal to each other and solve for x to get the distance

take that number and put it in one equation and solve for y to get the price of the plan for that value

6 0

2 years ago

Trianas age is 5 years less than 3 times her brothers age. Trianas age is 11 minus her brothers age. How old is Triana?

erastova [34]

Answer: 7

HOPE THIS HELPS

8 0

3 years ago