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3 years ago

F(x)=3x^5+7x^3-8x^2-x+23

1 answer:

7 0

Simplifying
f(x) = x2 + 8x + -3

Multiply f * x
fx = x2 + 8x + -3

Reorder the terms:
fx = -3 + 8x + x2

Solving
fx = -3 + 8x + x2

Solving for variable 'f'.

Move all terms containing f to the left, all other terms to the right.

Divide each side by 'x'.
f = -3x-1 + 8 + x

Simplifying
f = -3x-1 + 8 + x

Reorder the terms:
f = 8 + -3x-1 + x

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Complete the table below.

Nana76 [90]

Angle 1 is 122 degrees bc of vertical angle
Angle 2 is 87 degrees bc of alt ext angle converse
Angle 3 93 degrees
Angle 4 is 58 degrees

7 0

2 years ago

Kyle took a total of 9 pages of notes during a 3hr class. How many hours of class will it take for Kyle to take 12 pages of ntoe

Vladimir [108]

Answer:

4 hours

Step-by-step explanation:

9÷3=1

1 hour for 3 pages

12÷3= 4

4 hours

5 0

1 year ago

All the boxes in a certain warehouse were arranged in stacks of 12 boxes each, with no boxes left over. After 60 additional boxe

AveGali [126]

Answer:

(1) There were fewer than 110 boxes in the warehouse before the 60 additional boxes arrived. (2) There were fewer than 120 boxes in the warehouse after the 60 additional boxes arrived.

Step-by-step explanation:

Given that all the boxes in a certain warehouse were arranged in stacks of 12 boxes each, with no boxes left over.

This implies that boxes are in multiples of 12

i.e. 12, or 24, or 36 or....

Let us say this as 12m for m an integer

Now additional boxes arrived =60

Total number of boxes now = $12m+60$

This when arranged in stacks of 14,nothing left out

Or this is multiple of 14

$12m+60 = 14n$ for some positive integer n.

By trial and error we find that if 60 is to be divided by 14, 24 should be added and 24 is a multiple of 12.

So we say originally 24 boxes were there now 84 boxes there.

Hence both options are right.

(1) There were fewer than 110 boxes in the warehouse before the 60 additional boxes arrived. (2) There were fewer than 120 boxes in the warehouse after the 60 additional boxes arrived.

3 0

3 years ago

Questions 16-17 | Math 1 - 0 points Solve the graph Help needed !!

iris [78.8K]

Answer:

16) The area of the circle is 25.1 units²

17) JKLM is a parallelogram but not a rectangle

Step-by-step explanation:

16) Lets talk about the area of the circle

- To find the area of the circle you must find the length of the radius

- In the problem you have the center of the circle and a point on

the circle, so you can find the length of the radius by using the

distance rule

* Lets solve the problem

∵ The center of the circle is (1 , 3)

∵ The point on the circle is (3 , 5)

- Using the rule of the distance between two points

* Lets revise it

- The distance between the two points (x1 , y1) and (x2 , y2) is:

Distance = √[(x2 - x1)² + (y2 - y1)²]

∴ r = √[(3 - 1)² + (5 - 3)²] = √[4 + 4] = √8 = 2√2 units

∵ The area of the circle = πr²

∴ The area of the circle = π (2√2)² = 8π = 25.1 units²

* The area of the circle is 25.1 units²

17) To prove a quadrilateral is a parallelogram, prove that every

to sides are parallel or equal or the two diagonal bisect

each other

* The parallelogram can be rectangle if two adjacent sides are

perpendicular to each other (measure of angle between them is 90°)

or its diagonals are equal in length

- The parallel lines have equal slopes, then to prove the

quadrilateral is a parallelogram, we will find the slopes of

each opposite sides

* Lets find from the graph the vertices of the quadrilateral

∵ J = (0 ,2) , K (2 , 5) , L (5 , 0) , M (3 , -3)

- The opposite sides are JK , ML and JM , KL

- The slope of any line passing through point (x1 , y1) and (x2 , y2) is

m = (y2 - y1)/(x2 - x1)

∵ The slop of JK = (5 - 2)/(2 - 0) = 3/2 ⇒ (1)

∵ The slope of LM = (-3 - 0)/(3 - 5)= -3/-2 = 3/2 ⇒ (2)

- From (1) and (2)

∴ JK // LM

∵ The slope of KL = (0 - 5)/(5 - 2) = -5/3 ⇒ (3)

∵ The slope of JM = (-3 - 2)/(3 - 0)= -5/3 ⇒ (4)

- From (3) and (4)

∴ KL // JM

∵ Each two opposite sides are parallel in the quadrilateral JKLM

∴ It is a parallelogram

- The product of the slopes of the perpendicular line is -1

* lets check the slopes of two adjacent sides in the JKLM

∵ The slope of JK = 3/2 and the slope of KL = -5/3

∵ 3/2 × -5/3 = -5/2 ≠ -1

∴ JKLM is a parallelogram but not a rectangle

4 0

3 years ago

If 2500 amounted to 3500 in 4 years as simple interest .find the rates at wish the interest was charged

Bad White [126]

Answer:

The interest rate per year is 0.1

Step-by-step explanation:

The equation is A = P(1+rt)

Substitute the numbers

3500 = 2500 (1+4r)

solve for r:

$3500/2500 = 1+4r$

$1.4-1 = 4r$

$0.4 /4 = r$

$r = 0.1$

6 0

2 years ago