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1 year ago

A 1st degree polynomial function whose graph intercepts the y-axis at 8.

Mathematics

1 answer:

asambeis [7]1 year ago

4 0

Your answer can be anything in the form y = mx+8 where you replace m with any real number.

You start with y = mx+b, and then replace the b with the y intercept 8.

The y intercept is where the polynomial crosses the y axis.

The value of m does not matter. So you could have y = 2x+8 or y = 3x+8 for instance. Replace m with whatever your favorite number is.

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Nicole bought six pounds of apples at $1.50 per pound. The store had a discount of $2 off her total purchase. Nicole and her fri

Andru [333]

Answer:

Step-by-step explanation:

Total amount of apples that Nicole bought was 6 pounds.

Each pound of apple cost $1.50

This means that the total cost of the 6 pounds of apple that Nicole bought would be

6 × 1.5 = $9

The store had a discount of $2 off her total purchase. This means that the amount that was paid is

9 - 2 = $7

If Nicole and her friend then divided the cost of the purchase evenly, let x represent the amount that each of them would pay. Therefore, the expression that can be used to determine how much Nicole and her friend each paid for the apples would be

x = 7/2

6 0

2 years ago

Li wants to add these items to her suitcase: a hairdryer (1.25 lb), a hand-held video game (0.6 lb), an extra video game (0.25 l

lbvjy [14]

Add some of them or all of them to your sum of 47.75, if either or exceeds the limit then that is what left out.

7 0

2 years ago

Read 2 more answers

A large washer has an outer radius of 10mm and a hole with a diameter of 14mm. What is the area of the top surface of the washer

choli [55]

<h2>Answer:</h2>

The area of the top surface of the washer is: 160.14 square mm.

<h2>Step-by-step explanation:</h2>

The top of the surface is in the shape of a annulus with a outer radius of 10 mm and a inner radius of 7 mm ( since the diameter of the hole is: 14 mm and we know that the radius is half of the diameter)

Now, we know that the area of the annulus region is given by:

$Area=\pi (R^2-r^2)$

where R is the outer radius and r is the inner radius.

Here we have:

$R=10\ mm\\\\and\\\\r=7\ mm$

Hence, we have:

$Area\ of\ top\ surface=\pi (10^2-7^2)\\\\i.e.\\\\Area\ of\ top\ surface=\pi (100-49)\\\\i.e.\\\\Area\ of\ top\ surface=\pi\cdot 51\\\\i.e.\\\\Area\ of\ top\ surface=160.14\ mm^2$

4 0

2 years ago

Read 2 more answers

Find the dimensions of the box with volume 1728 cm3 that has minimal surface area. (Let x, y, and z be the dimensions of the box

Gala2k [10]

Answer:

The dimensions of the box are 12 cm , 12 cm , 12 cm

Step-by-step explanation:

Let x , y and z be the dimensions of box

Volume of box =xyz=1728

$z=\frac{1728}{xy}$

Surface area of box = $2xy+2yz+2xz=2xy+2y(\frac{1728}{xy})+2x(\frac{1728}{xy})$

Let $f(x,y)=2xy+2(\frac{1728}{x})+2(\frac{1728}{y})$

To get minimal surface area

$\frac{\partial f}{\partial x}=0$ and $\frac{\partial f}{\partial y}=0$

$\frac{\partial(2xy+2(\frac{1728}{x})+2(\frac{1728}{y}))}{\partial x}=0$

$2y-2(\frac{1728}{x^2})=0$

$y=\frac{1728}{x^2}$ ----1

$\frac{\partial(2xy+2(\frac{1728}{x})+2(\frac{1728}{y}))}{\partial y}=0$

$2x-2(\frac{1728}{y^2})=0\\x=\frac{1728}{y^2} \\y^2=\frac{1728}{x}$

Using 1

$(\frac{1728}{x^2} )^2=\frac{1728}{x}$

x=0 and $x^3=1728$

Side can never be 0

So, $x^3=1728$

x=12

$y=\frac{1728}{x^2} \\y=\frac{1728}{12^2}$

y=12

$z=\frac{1728}{xy}\\z=\frac{1728}{(12)(12)}$

z=12

The dimensions of the box are 12 cm , 12 cm , 12 cm

5 0

2 years ago

Which system of linear inequalities has the point (2, 1) in its solution set?

AVprozaik [17]

You haven't provided the choices, therefore, I cannot provide an exact answer. However, I will help you with the concept.

For an order pair to be a solution to a system of equations, it has to satisfy BOTH equations. If it satisfies only one equation of the system or satisfy neither of the equations, the, it is not a solutions

Examples:
System 1:
x = y + 1
2x + 3y = 7
Let's check (2,1)
2 = 1 + 1 ........> equation 1 is satisfied
2(2) + 3(1) = 7 ......> equation 2 is satisfied
(2,1) is a solution to this system

System 2:
y = x + 3
y = x - 1
Let's check (2,1):
1 ≠ 2 + 3 ........> equation 1 isn't satisfied
1 = 2 - 1 ..........> equation 2 is satisfied
(2,1) isn't a solution to this system

System 3:
2y = 9 - 3x
3x + 2y = 9
Let's ceck (2,1):
2(1) ≠ 9 - 3(2) ..........> equation 1 isn't satisfied
3(2) + 2(1) ≠ 9 .........> equation 2 isn't satisfied
(2,1) isn't a solution to this system

Based on the above, all you have to do is substitute with (2,1) in the system you have and pick the one where both equations are satisfied

Hope this helps :)

4 0

2 years ago