MATHEMATICS HIGH SCHOOL

Which of the following is the product of (3x − 5) and (3x + 5)?A. 9x2 − 25
B. 9x2 − 30x − 25
C. 9x − 10
D. 9x2 + 25

Answers

Answer 1

Answer:

Answer:

Step-by-step explanation:

These binomials make up the difference of squares.

3x * 3x = 9x^2

3x * 5 = 15x

-5 * 3x = - 15x

-5 * 5 = - 25

Notice the 2nd and 3rd terms. They are equal except that one is plus and the other minus. That means they cancel. You are left with

9x^2 - 25

D ) None of the above.

a chemist has two alloys, one of which is 10% gold and 15% lead and the other of which is 30% gold and 40% lead. how many grams of each of the two alloys should be used to make an alloy that contains 60 grams of gold and 88 grams of lead

Answers

Let the weight of the first alloy will be x grams.
Weight of gold will be 0.1x grams, weight of lead will be 0.15x grams.
Let the weight of the second alloy will be y grams.
Weight of gold will be 0.3y grams, weight of lead will be 0.4y grams.
Summarizing:
0.1x+0.3y=60 - gold
0.15x+0.4y=88 - lead

0.1x+0.3y=60 * 10
0.15x+0.4y=88 * 100

x+3y=600 * 15
15x+40y=8800

15x+45y=9000
15x+40y=8800

15x+45y=9000 /15
45y-40y=9000-8800

x+3y=600
5y=200

x+3y=600
y=40

y=40
x=600-3*40=480

y=40
x=480

↑The answers.

Find the area of a regular pentagon with radius 9mm

Answers

The required area of pentagon is 212.36 mm².

What is area of a shape?

Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. The area of a plane figure is the area that its perimeter encloses. The quantity of unit squares that cover a closed figure's surface is its area.

Given that,

radius of pentagon = 9 mm

Since in pentagons there are 5 sides.

Therefore,

Area is = (5/4)x s² x tan(π/5)

Where s is the pentagon's length along one side.

Use the pentagon's radius to get s using the following calculation

since we already know,

S = 2x radius x sin(π/5)

When we enter the values ,

we obtain: s = 2 x 9 x sin(π/5)

= 14.56 mm.

We can now enter this value of s into the area formula as follows:

Area = (5/4) x s² x tan(π/5)

= 212.36mm².

Consequently, the regular pentagon's area with a 9 mm radius is roughly 212.36 mm²

To learn more about area visit:

brainly.com/question/23948404

#SPJ2

The area is calculated by using the formula A=(r^2)*n*sin(360/n)/2 where n is the number of sides which is 5 for pentagon and r is the radius which is 9 mm. So, using the formula, the answer is 51.4 mm^2.

What are the coordinates of the vertex for f(x) = x2 + 4x + 10? (1 point) (−2, 2) (2, 2) (−2, 6) (2, 6)

Answers

You have to complete the square to get it into vertex form. Do this by setting the function equal to zero and at the same time moving the constant over to the other side of the equals sign so you have this: . Now we can complete the square on the polynomial by taking half the linear term, squaring it, and adding it to both sides. Our linear term is 4. Half of 4 is 2, and 2 squared is 4, so we add 4 to both sides: and simplify to get . In this process we have created a perfect square binomial on the left, which happens to be . Now move the -6 back over by addition to get . The vertex is found at (-2, 6), the third choice down.

Answer:

A or C

Step-by-step explanation:

x = x2 + 4x + 10

x = 6x + 10

-5x = 10

x = -2

A taut string of length 10 inches is plucked at the center. The vibration travels along the string at a constant rate of c inches per millisecond in both directions. If x represents the position on the string from the left-most end, so that 0≤x≤10, which of the following equations can be used to find the location x of the vibration after 0.3 milliseconds? A. | x -5 | =0. 3 B. ∣cx−5∣=0.3 C. | x -0.3 | = 5 D. | x - 10 | =0.3c

Answers

Answer:

The correct option is

$A. \ (1)/(c) * \left | x - 5 \right | = 0.3$

Step-by-step explanation:

The parameters given are;

The length of the string = 10 inches

The speed or rate of travel of the wave = c inches per millisecond

The position on the string from the left-most end = x

The time duration of motion of the vibration to reach x= 0.3 milliseconds

The distance covered = Speed × Time = c×0.3

Given that the string is plucked at the middle, with the vibration travelling in both directions, the point after 0.3 millisecond is x where we have;

The location on the string where it is plucked = center of the string = 10/2 = 5 inches

Distance from point of the string being plucked (the center of the string) to the left-most end = 5 inches

Therefore, on the left side of the center of the string we have;

The distance from the location of the vibration x (measured from the left most end) to the center of the string = 5 - x = -(x -5)

On the right side of the center, the distance from x is -(5 - x) = x - 5

Therefore, the the equation that can be used to find the location of the vibration after 0.3 milliseconds is $(1)/(c) * \left | x - 5 \right | = 0.3$ or $\left | x - 5 \right | = 0.3 * c$ which gives the correct option as A

Christiana works at Texas Road House and makes $50 each night in tips plus $7.50 per hour. Write a function rule in function notation where M is the total money she makes and h is the number of hours she works in one night.