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2 years ago

Can someone please take the time out of they’re day and help me and with this question

Mathematics

1 answer:

Bumek [7]2 years ago

8 0

Answer:

see explanation

Step-by-step explanation:

(a)

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

with (x₁, y₁ ) = (0, 100) and (x₂, y₂ ) = (2, 200) ← 2 points on the line

m = $\frac{200-100}{2-0}$ = $\frac{100}{2}$ = 50

The line crosses the y- axis at (0, 100 ) ⇒ c = 100

y = 50x + 100 ← equation of line

where y is monthly savings and x the time in months

(b)

Slope is the monthly deposit , that is $50 per month

The y- intercept indicates the original amount in her account , that is $100

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|-9c|=8 and solve for c

melisa1 [442]

C = negative 8/9 or 8/9

5 0

3 years ago

The length of a rectangle is 5 meters less than twice the width. If the area of the rectangle is 273 meters, find the dimensions

AleksandrR [38]

The length of the rectangle = 16 meters

The width of the rectangle = 10.5 meters

Step-by-step explanation:

Given that,

The Area of the rectangle is 273.

Step 1 :

Let, the width of the rectangle be 'x'

The length of the rectangle is 2x - 5

Step 2 :

Area of the rectangle = length $\times$ width

273 = (2x - 5) x

273 = 2x^2 - 5x

Step 3 :

The equation formed is 2x^2 - 5x -273 = 0

a= coefficient of x^2 = 2

b= coefficient of x = -5

c = constant = -273

Find the roots of the equation, to find the width.

Step 4 :

Find the roots using factorizing method,

ac = 2 $\times$ -273 = -546 and b= -5

Factorizing -546 as -26 $\times$ 21

The product of -26 $\times$ 21 = -546

The sum of -26 + 21 = -5

Step 5 :

The roots of the equation 2x^2 - 5x -273 = 0 are x= -26/2 and x= 21/2

The values of x are x= -13 and x= 10.5

Since the width cannot be a negative value, neglect x= -13

Step 6 :

Therefore,

The width of the rectangle = 10.5 meters

The length of the rectangle = 2x-5

= 2(10.5) - 5

= 21 - 5

length = 16 meters

5 0

3 years ago

The radius of the cone is 5 in and y = 13 in. What is the volume of the cone in terms of π?

olga nikolaevna [1]

Answer:

The volume of the cone is;

100 π inches^3

Step-by-step explanation:

To calculate the volume, we need the height

We can get the height from the slant height and the radius

Mathematically, we use Pythagoras’ theorem for this as the slant height, the radius and the height forms a right-angled triangle

The right-angled triangle has the slant height as its hypotenuse

By the theorem, the square of the hypotenuse equals the sum of the squares of the two other sides

Let the height be h

Thus;

12^2 = 5^2 + h^2

169= 25 + h^2

h^2 = 169-25

h^2 = 144

h = √1144 inches = 12 inches

The volume of the cone is;

1/3 * π * r^2 * h

= 1/3 * π * 5^2 * 12

= 100 π inches^3

4 0

2 years ago

How to find the area of a triangle with only the radius?

Darya [45]

Divide the bh by 1/2

7 0

3 years ago

Lisa, Juan and isaac equally shared 1/2 of a cake which fraction of the whole cake did each of them recieve

IgorLugansk [536]

Answer:

Each will receive $\frac{1}{6}th$ of the cake.

Step-by-step explanation:

Let the amount of cake = c

Lisa, Juan and Isaac are the persons who are sharing half of a cake equally.

Number of persons = 3

Part of the cake shared = $\frac{c}{2}$

Fraction of the cake shared by each = $\frac{\text{Amount of cake shared}}{\text{Number of persons who shared}}$

= $\frac{\frac{1}{2}c}{3}$

= $\frac{1}{6}c$

Therefore, fraction of total cake shared by each member will be $\frac{1}{6}$ of the total amount of cake.

6 0

2 years ago