MATHEMATICS HIGH SCHOOL

Solve 2cos^2x + cosx − 1 = 0 for x over the interval [0, 2 π ).a.π and π/3
b.π, π/3, and 5π/3
c.1 and 2π/3
d.1, 2π/3, and 4π/3
e.1, π/3, and 5π/3

Answers

Answer 1
Answer: Let cos x = a, then
2a^2 + a - 1 = 0,
solving the quadratic equation, we have:
a = 0.5 or -1.

i.e. cos x = 0.5 or cos x = -1
for cos x = 0.5,
x = pi/3, 2pi - pi/3 = pi/3, 5pi/3

for cos x = -1,
x = pi

therefore, x = pi, pi/3, 5pi/3
Answer: B
Answer 2
Answer:

Answer:

Option B is correct for plato

Step-by-step explanation:

\pi ,(\pi )/(3), and (5\pi )/(3)

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Henrietta has $120 to buy a new bicycle. She finds the bike that she wants to buy on sale for 20% off the regular price of $150. If there is 6% sales tax, which of the following best describes the amount of money Henrietta has with regards to buying the bike. a. Henrietta has enough before the tax, but not enough after the tax. b. Henrietta has enough money even after the tax. c. Henrietta does not have enough money even before the tax. d. There is not enough information given.

Answers

Given:
Henrietta budget: 120
Original Price of the bike : 150
discount: 20%
sales tax: 6%

150 * 20% = 30
150 - 30 = 120 discounted price

120 * 6% = 7.2 sales tax
120 + 7.2 = 127.20 total cost of the bike

Since Henrietta only has 120, A.) Henrietta has enough before the tax, but not enough after the tax.

Answer:

A. Henrietta has enough before the tax, but not enough after the tax.

Step-by-step explanation:

Solve the following linear inequality: 

3(x + 4) ≥ 5x – 123

Answers

3(x+4)\geq5x-123\n3\cdot x+3\cdot4\geq5x-123\n3x+12\geq5x-123\ \ \ \ /-12\n3x\geq5x-135\ \ \ \ /-5x\n-2x\geq-135\ \ \ /:(-2) < 0\ then\
3(x + 4) \geq 5x - 123 \n 3x+12\geq5x-123\n 2x\leq135\n x\leq(135)/(2)

Suppose ∠A and ∠B are complementary angles, m∠A = (3x + 5)°, andm∠B = (2x – 15)°. Solve for x and then find m∠A and m∠B.

Answers

         m∠A + m∠B = 90
(3x + 5) + (2x - 15) = 90
(3x + 2x) + (5 - 15) = 90
                  5x - 10 = 90
                      + 10  + 10
                         5x = 100
                          5      5
                           x = 20

m∠A = 3x + 5
m∠A = 3(20) + 5
m∠A = 60 + 5
m∠A = 65

m∠B = 2x - 15
m∠B = 2(20) - 15
m∠B = 40 - 15
m∠B = 25
m∠A + m∠B = 90

(3x + 5) + (2x - 15) = 90

(3x + 2x) + (5 - 15) = 90

5x - 10 = 90

5x - 10 +10 = 90+10

5x = 100

5x/5 = 100/5      Divide \ both \ sides \ by \ 5

x = 20                 Solutions

m∠A = 3x + 5     (x=20)

m∠A = 3(20) + 5          Substitute \ x \ for \ 20

m∠A = 60 + 5               Simplify

m∠A = 65


m∠B = 2x - 15

m∠B = 2(20) - 15

m∠B = 40 - 15

m∠B = 25

A toddler crawled 3 yards, stopped, then continued to crawl 11 more feet. How many feet did he travel in total?

Answers

So how many Feet right? A yard has 3 feet in it so 3*3=9, nine feet there. So 9+11= 20. The toddler traveled 20 feet total.
add them up
wait, convert yards to feet
3 feet in 1 yard
times 3
9 feet in  3 yard

9 feet first, then 11 feet
add
9+11=20 feet

This one just scares me how do i even figure this out?

Answers

Because the middle point is in the center of the square, the triangle containing angle 2 is isosceles and right (since two sides are equal to half the square's side length), so angle 2 measures (180-90)/2=45 degrees.

Answer:

this is c

Step-by-step explanation:

Luisianna

Calculate the average speed of a gazelle that runs 140 meters in 5.0 seconds.

Answers

Answer:

Average speed(S) is given by:

S =(D)/(t)              ....[1]

where,

D is the total distance and t is the time.

As per the statement:

A gazelle that runs 140 meters in 5.0 seconds.

⇒D = 140 meters and t = 5 seconds

Substitute in [1] we have;

S =(140)/(5)

Simplify:

⇒S = 28 m/sec

Therefore, average speed of a gazelle is, 28 m/sec
You would multiply to find the average meters/minute.
140 x 5.0 = 700.
But, if you're looking for average m/s you would divide.
140/5 = 28.
If you want meters/hour, you have to multiply the average meters/minute by 60.
140 x 5 x 60 = 4,200.

I'm not sure which one you're looking for but I hope something I wrote helps!
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