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3 years ago

1/8(8x-5)=-9/8-5/8 Algebra 1 algebraic expressions

Mathematics

2 answers:

ivanzaharov [21]3 years ago

8 0

First, clear out the fractions by ult. all 3 terms by 8:

8x - 5 = - 9 - 5

Then 8x = -9, and x = -9/8 (answer)

Aloiza [94]3 years ago

5 0

Answer:

X=1 &1/8

Step-by-step explanation:

You have to simplify the expression on both sides. So on the left you would subtract. 9/8 minus 5/8 equals 4/8 which simplifies even farther. 4/8 gets simplified into 1/2. on the right you have to distribute in the parentheses. So, 1/8 times 8x is just x because 1 out of 9 is one and the number isn't required at that point.Then you distribute 1/8 to your -5. When you multiply that you get 0.625. But since it was given to you as a fraction you can't leave it as a decimal. Then since you got a decimal it turns into 625/1000. You MUST simplify it down. So you gotta think to yourself what is the biggest number they have in common. 125 goes into them both evenly. SO you have to divide 625/125 and 1000/125 and you get 5/8 as your simplified fraction. Now you have the equation x-5/8=1/2. add the number 5/8 to 1/2. As you know you cant add them just like that so you have to unsimplify so 4/8 plus 5/8 is 9/8. This is equivalent to 1 and 1/8. Your final expression is x=1 adn 1/8

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Find equations of the spheres with center(3, −4, 5) that touch the following planes.a. xy-plane b. yz- plane c. xz-plane

postnew [5]

Answer:

(a) (x - 3)² + (y + 4)² + (z - 5)² = 25

(b) (x - 3)² + (y + 4)² + (z - 5)² = 9

Step-by-step explanation:

The equation of a sphere is given by:

(x - x₀)² + (y - y₀)² + (z - z₀)² = r² ---------------(i)

Where;

(x₀, y₀, z₀) is the center of the sphere

r is the radius of the sphere

Given:

Sphere centered at (3, -4, 5)

=> (x₀, y₀, z₀) = (3, -4, 5)

(a) To get the equation of the sphere when it touches the xy-plane, we do the following:

i. Since the sphere touches the xy-plane, it means the z-component of its centre is 0.

Therefore, we have the sphere now centered at (3, -4, 0).

Using the distance formula, we can get the distance d, between the initial points (3, -4, 5) and the new points (3, -4, 0) as follows;

$d = \sqrt{(3-3)^2+ (-4 - (-4))^2 + (0-5)^2}$

$d = \sqrt{(3-3)^2+ (-4 + 4)^2 + (0-5)^2}$

$d = \sqrt{(0)^2+ (0)^2 + (-5)^2}$

$d = \sqrt{(25)}$

d = 5

This distance is the radius of the sphere at that point. i.e r = 5

Now substitute this value r = 5 into the general equation of a sphere given in equation (i) above as follows;

(x - 3)² + (y - (-4))² + (z - 5)² = 5²

(x - 3)² + (y + 4)² + (z - 5)² = 25

Therefore, the equation of the sphere when it touches the xy plane is:

(x - 3)² + (y + 4)² + (z - 5)² = 25

(b) To get the equation of the sphere when it touches the yz-plane, we do the following:

i. Since the sphere touches the yz-plane, it means the x-component of its centre is 0.

Therefore, we have the sphere now centered at (0, -4, 5).

Using the distance formula, we can get the distance d, between the initial points (3, -4, 5) and the new points (0, -4, 5) as follows;

$d = \sqrt{(0-3)^2+ (-4 - (-4))^2 + (5-5)^2}$

$d = \sqrt{(-3)^2+ (-4 + 4)^2 + (5-5)^2}$

$d = \sqrt{(-3)^2 + (0)^2+ (0)^2}$

$d = \sqrt{(9)}$

d = 3

This distance is the radius of the sphere at that point. i.e r = 3

Now substitute this value r = 3 into the general equation of a sphere given in equation (i) above as follows;

(x - 3)² + (y - (-4))² + (z - 5)² = 3²

(x - 3)² + (y + 4)² + (z - 5)² = 9

Therefore, the equation of the sphere when it touches the yz plane is:

(x - 3)² + (y + 4)² + (z - 5)² = 9

(b) To get the equation of the sphere when it touches the xz-plane, we do the following:

i. Since the sphere touches the xz-plane, it means the y-component of its centre is 0.

Therefore, we have the sphere now centered at (3, 0, 5).

Using the distance formula, we can get the distance d, between the initial points (3, -4, 5) and the new points (3, 0, 5) as follows;

$d = \sqrt{(3-3)^2+ (0 - (-4))^2 + (5-5)^2}$

$d = \sqrt{(3-3)^2+ (0+4)^2 + (5-5)^2}$

$d = \sqrt{(0)^2 + (4)^2+ (0)^2}$

$d = \sqrt{(16)}$

d = 4

This distance is the radius of the sphere at that point. i.e r = 4

Now substitute this value r = 4 into the general equation of a sphere given in equation (i) above as follows;

(x - 3)² + (y - (-4))² + (z - 5)² = 4²

(x - 3)² + (y + 4)² + (z - 5)² = 16

Therefore, the equation of the sphere when it touches the xz plane is:

(x - 3)² + (y + 4)² + (z - 5)² = 16

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A store owner paid $15 for a book. She marked up the price of the book by 40% to determine its selling price. What is the sellin

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Answer:

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aₙ = a₀ + (n -1)*d

So the difference between a term and the nextone is always the same, and in our case the numbers are 5,8,13,21,34,55.

The distance between the numbers is not constant, so this is not a arithmetic sequence.

a geometric sequence is of the form: aₙ = a*rⁿ

So the therms grow exponentially.

here a₀ = a*r⁰ = a = 5.

a₁ = a*r¹ = 5*r = 13, then r = 13/5 = 2.6

a₂ = a*r² = 5*2.6*2.6 = 33.8, so here we can see that this is not our series, so our series isn't geometric.

So the answer for the first part is neither.

Now, the sequence is 5,8,13,21,34,55, ...

you can see that

5 + 8 = 13

13 + 8 = 21,

21 + 34 = 55

So our sequence is of the form: aₙ = aₙ₋₁ + aₙ₋₂.

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Answer:

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length = (7/10)a

width = (3/10)a

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