MATHEMATICS HIGH SCHOOL

Given a>0 and b>0, which inequality shows the result of solving -ax/b >/ (c-d) for x?

a)x </ ad-ac/b

b)x </ bd-bc/a

c)x >/ bc-bd/a

d)x >/ bd-bc/a

Answers

Answer 1
Answer:

We will see that the solution of the given inequality is:

( -(c - d)*b)/(a) \ge x

How to solve the inequality?

Here we have the inequality:

-(ax)/(b) \ge c - d

To solve it, we need to isolate x on one side of the inequality.

First, we can multiply both sides for b:

-ax \ge (c - d)*b

Now we divide both sides by -a, because we are operating with a negative number, we need to change the direction of the greater than or equal to sign, so we will get:

( -(c - d)*b)/(a) \ge x

That is the solution to the given inequality.

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Answer 2
Answer: -(ax)/(b)\geq c-d\n-ax\geq bc-bd\nx\leq-(bc-bd)/(a)\nx\leq(bd-bc)/(a)

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Write the equation of a line through the points (2,3) and (-1,-9)

Answers

Answer:

with the points (2,3) and (-1,-9) the answer is y=4x+10

Step-by-step explanation:

you have to do (x1,y1) (x2,y2) thats for each point

the equation to get the slope is y2-y1 divided by x2,x1

to get the y-intercept to plug in one of the points to the slope-intercept equation

y=4x+5

I picked the points (2,3) but you should get the same answer with the other points

3=4(2)=5

3=8+5

3=13

-3+-3

=10 thats your y intercept.

If line segment is 100 feet, and line segment is 80 feet, what is the length of line segment ?

Answers

which, in theory, would be the third side of the triangle formed by these three lines, would be 60 feet.

Doors for the small cabinets or 19.5 inches long. Doors for the large cabinets are 3.9 times as long as the doors for the small candidates. How many large doors can be cut from a board that is 11 feet long.

Answers

Answer: 1 large door.

Step-by-step explanation:

You know that the lenght of each door for the small cabinets is:

lenght_((small))=19.5\ in

Since the lenght of the doors for the large cabinets are 3.9 times as long as the doors for the small candidates, the lenght of any of these doors is:

lenght_((large))=3.9(19.5\ in)=76.05\ in

The lenght of the board is 11 feet, so you need to convert it to inches:

(11\ ft)((12\ in)/(1\ ft))=132\ in

Then, the number of large doors that can be cut from that board is:

(132\ in)/(76.05\ in)=1.73

So, 1 large door can be cut from that board.

Use the definition of exponential notation to demonstrate why 2^3*4^3=2^9

Answers

exponential notation allows the representation of numbers in shorter form.
(2 x 2 x 2)(4x4x4) = 2x2x2x2x2x2x2x2x2
2^3*4^3=2^9 

8*4^3=2^9 

8*64=2^9 

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Infinitely Many Solutions

Solve x2 + 20x + 100 = 36 for x.a. x = –16 or x = –4
b. x = –10
c. x = –8
d.x = 4 or x = 16

Answers

x² + 20x + 100 = 36⇒ x² + 20x + 100 - 36 = 0⇒ x² + 20x + 64 =0

Δ = b²-4ac = 20² -4·1·64 = 400-256 = 144

x₁= (-b+√Δ)/2a = (-20+√144)/2·1 = (-20+12)/2 = -8/2 = -4
x₂= (-b-√Δ)/2a = (-20-√144)/2·1 = (-20-12)/2 = -32/2 = -16

x=-4 or x=-16

The solution to the quadratic equation x² + 20x + 100 = 36 is x = 4 or x = -16 option (a) is correct.

What is a quadratic equation?

Any equation of the form \rm ax^2+bx+c=0  where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

As we know, the formula for the roots of the quadratic equation is given by:

\rm x = (-b \pm√(b^2-4ac))/(2a)

We have an quadratic equation:

x² + 20x + 100 = 36

\rm x^2+20x+64=0

a = 1, b = 20, and c = 64

\rm x_(1,\:2)=(-20\pm √(20^2-4\cdot \:1\cdot \:64))/(2\cdot \:1)

After solving:

x = 4 or x = -16

Thus, the solution to the quadratic equation x² + 20x + 100 = 36 is x = 4 or x = -16 option (a) is correct.

Learn more about quadratic equations here:

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Circle R has a radius of 6, and QP is tangent to circle R at point Q. Also, QP = 8. (a) What is the measure of ∠RQP ? Explain your answer. (b) What is the length of RP ? Explain your answer. (c) What is the length of RS ? Explain your answer. (d) What is the length of SP ? Explain your answer.

Answers

RQ = 6; RS = 6 ; these are radius

The triangle formed is right triangle. ∠RQP = 90°

QP = 8 ; this is the long leg.
RQ = 6; this is the short leg
RP = ? is the hypotenuse

a² + b² = c²
8² + 6² = c²
64 + 36 = c²
100 = c²
10 = c

The hypotenuse is 10, but RS is part of the hypotenuse, it has a measure of 6.

6 + x = 10
x = 10 - 6
x = 4   length of SP
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