MATHEMATICS HIGH SCHOOL

Parallel lines never intersect, therefore, do not have a solution.
a. True
b. False

Answers

Answer 1
Answer: If the lines are parallel to each other, it won't intersect. It means that we can't get any intersect point by solving equations. There is no coordinate which satisfy both lines.

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Evaluate if x=13.2 and y=4.3 -x-2y
1. The main show tank has a radius of 70 feet and forms a quarter sphere where the bottom of the pool is spherical and the top of the pool is flat. (Imagine cutting a sphere in half vertically and then cutting it in half horizontally.) What is the volume of the quarter-sphere shaped tank? Round your answer to the nearest whole number. You must explain your answer using words, and you must show all work and calculations to receive credit.2. The holding tanks are congruent. Each is in the shape of a cylinder that has been cut in half vertically. The bottom of each tank is a curved surface and the top of the pool is a flat surface. What is the volume of both tanks if the radius of tank #1 is 35 feet and the height of tank #2 is 120 feet? You must explain your answer using words, and you must show all work and calculations to receive credit.3. The company is building a scale model of the theater’s main show tank for an investor's presentation. Each dimension will be made one sixth of the original dimension to accommodate the mock-up in the presentation room. What is the volume of the smaller mock-up tank?Using the information from #3, answer the following question by filling in the blank: The volume of the original main show tank is ____% of the mock-up of the tank.

Find the roots of the equation by completing the square: 3x^2-6x-2=0. Prove your answer by solving by the quadratic formula.

Answers

Calculating delta: 
Δ=b²-4ac
a=3
b=-6
c=-2
Δ=36-4*3*(-2)=36+24=60
√Δ=√60
Delta is positive so there are two roots:
x1=\frac{ -b+ \sqrt[2]{delta} }{2a}
x1=(6+ √(delta) )/(2*3)=(3+ √(15) )/(3)
x2=(3- √(15) )/(3)
3x^2-6x-2=0\n\n(\sqrt3\ x)^2-2\cdot\sqrt3\ x\cdot\sqrt3+(\sqrt3)^2-(\sqrt3)^2-2=0\n\n(\sqrt3\ x-\sqrt3)^2-3-2=0\n\n(\sqrt3\ x-\sqrt3)^2=5\iff\sqrt3\ x-\sqrt3=-\sqrt5\ \vee\ \sqrt3\ x-\sqrt3=\sqrt5\n\n\sqrt3\ x=\sqrt3-\sqrt5\ \vee\ \sqrt3\ x=\sqrt3+\sqrt5\ \ \ \ \ |multiply\ both\ sides\ by\ \sqrt3\n\n3x=3-√(15)\ \vee\ 3x=3+√(15)\ \ \ \ \ \ \ |divide\ both\ sides\ by\ 3\n\nx=(3-√(15))/(3)\ \vee\ x=(3+√(15))/(3)



Prove:\n\n3x^2-6x-2=0\na=3;\ b=-6;\ c=-2\n\Delta=b^2-4ac\to\Delta=(-6)^2-4\cdot3\cdot(-2)=36+24=60\n\nx_1=(-b-\sqrt\Delta)/(2a);\ x_2=(-b+\sqrt\Delta)/(2a)\n\n\sqrt\Delta=√(60)=√(4\cdot15)=\sqrt4\cdot√(15)=2√(15)\n\nx_1=(6-2√(15))/(2\cdot3)=(3-√(15))/(3)\ \vee\ x_2=(6+2√(15))/(2\cdot3)=(3+√(15))/(3)

Factor 2x(squared)-9x-18?

Answers

Here: =(2x+3)(x-6) =2x²-12x+3x-18 =2x²-9x-18 So the answer is (2x+3)(x-6)

FUTA tax is paid A. only weekly. B. by an employee. C. by the employer. D. by both the employee and the employer.

Answers

Answer:

C. by the employer.

Step-by-step explanation:

The Federal Unemployment Tax Act or FUTA is a payroll tax, paid by the employers on employee wages.

These are paid annually or quarterly to fund for the unemployment benefits that are helpful for employees who lose their jobs.

Hence, the answer is : FUTA tax is paid by the employer.
The only one that pays the FUTA (Federal Unemployment Tax Act) is the employer.

A frog is at the bottom of a 78 meter well. Each day he leaps 4 meters up the well. At night, while he is asleep, he slips 2 meters backwards.How many days does it take him to escape from the well?

Answers

78 divided by 4 = 19.5 so 19 and a half days to climb up the well. 

Teresa recorded the number of drinks of each type that she sold on Monday and Tuesday. She sold 300 drinks each day.Which drink represents of the sales for the day?

Two two-column tables titled Drinks Sold on Monday and Drinks Sold on Tuesday. In the Monday table, data are Orange juice 150, Grape juice 34, Water 100, Apple juice 16. In the Tuesday table, data are Orange juice 50, Grape juice 65, Water 85, Apple juice 100.













A.

Orange juice sold on Monday






B.

Orange juice sold on Tuesday






C.

Water sold on Monday






D.

Grape juice sold on Tuesday

Answers

water sold on Monday

Answer:

the other guy was WRONG, its OJ sold on Tuesday.

I got a 60% thansk to him -_-

Please help!!!!!!!!!!!!!!!!!!!!

Answers

\left \{ {{6a+11b=36} \atop {4a-2b=-32}} \right. \n \left \{ {{6a+11b=36} \atop { (-(3)/(2)) *(4a-2b=-32)}} \right.
(6a+11b=36)+ (-6a+3b=48)= 6a-6a+11b+3b=36+48 \n 14b=84 \n b=6
4a-2(6)=-32 \n 4a=-32+12=-20 \n a=-5
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