MATHEMATICS HIGH SCHOOL

By looking at linear equations we can tell how they will interact in the coordinate plane. What are possible if two linear equations are graphed?. . a.They could be parallel to each other..
b.They could intersect at two points..
c.They could be perpendicular to each other..
d.They could be skew lines..
e.They could be the same line.

Answers

Answer 1

Answer:

The correct answers are options:

a. They could be parallel to each other.

c. They could be perpendicular to each other

e. They could be the same line.

Explanation:

Two lines are parallel if they do no intersect each other any point. Such lines have same slopes and the cross the y axis at different points.

Two lines can intersect either at one point or they intersect at infinite number of points. Second case occurs when both equations represent the same line so we say that the two equations have infinite number of solutions as each point will satisfy both the equations.

Two line can be perpendicular if they are at right angle to each other. This means a right angle is formed at their point of intersection. The slope of such lines is negative reciprocal of each other.

Skew lines can occur only in 3D. Two lines are skew lines if they are neither parallel nor they intersect each other at any point. Such condition can not be achieved when two linear equations are graphed on the coordinate axis.

Two equations can represent the same line when one equation is obtained by multiplying the second equation by a constant number. In this case the two equations have infinite number of solutions.

Answer 2

Answer: Answer:
A ) they could be parallel to each other
C ) they could be perpendicular to each other
E ) they could be the same line.
Two lines could intersect at one point and skew lines are not in the same plane.

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One yardstick for measuring how steadily—if slowly—athletic performance has improved is the mile run. In 1958, the local record for the running of a certain distance was 3 minutes, 59.3 seconds, or 239.3 seconds. In the half-century since then, the record has decreased by 0.5 seconds per year.

Answers

Answer:

They will hit 180 seconds in 118.6 year

Step-by-step explanation:

Let M be the record for the mile (in seconds)

Let x be the year after 1958

So, x=(year)-19548

We are given that In the half-century since then, the record has decreased by 0.5 seconds per year

So, slope = m = 0.5

Now we will use point slope form

y = mx+c

So, we can express M as,

$M=239.3-0.5 * x$

Now we are supposed to find when they will hit 180 seconds

Substitute M = 180 in equation

180=239.3-0.5x

x=118.6

So, they will hit 180 seconds in 118.6 year

Final answer:

You can model the decreasing record time with the linear equation y=239.3-0.5x, where x is years since 1958 and y is the run time in seconds. By using this model, you can find the record time for any given year.

Explanation:

The subject of this question is Mathematics, specifically linear equations. The question mentions an initial record of 239.3 seconds for a run which decreases by 0.5 seconds every year. We are tasked to find the running time after a certain number of years.

Let's let x represent the number of years since 1958 and y represent the number of seconds to run the race. Based on the information provided:

The starting time (y-intercept) in 1958 was 239.3 seconds.
The rate of decrease (slope) is 0.5 seconds per year.

Therefore, the relationship between x and y can be expressed by the linear equation: y=239.3-0.5x

To find a certain year's running time, we substitute the number of years passed since 1958 into x in the equation above and solve for y. For example, to find the running time in 50 years after 1958 (2008), we replace x with 50: y = 239.3 - 0.5(50) = 214.3 seconds.

Learn more about Linear Equations here:

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Solve the equation A = 2LW + 2LH + 2WH for H.a) H = A - 2LW/2L + 2W
b) H = A + 2LW/2L + 2W
c) H = A - 2LW/4LW
d) H = A/2L + 2W - 2LW

Answers

H = A - 2LW / 2 (L+W)

What is the product of -9 and -15?
135
-135
-24
24

Answers

-9 * (-15) = 135
it's positive 135 because when you have negative time a negative it's always positive.

Answer:

Please mark me brainliest and I hope this helped!

135

Step-by-step explanation:

The product of something is what the outcome is when you multiply the numbers together. Since 9 and 15 are both negatives, they cancel each other out and become positives. Then we just multiply 9 and 15. That gives us 135.

Evaluate m0 - n2 for m = 2 and n = -1.

Answers

Given:

m = 2 & n = -1

so, m0 - n2

= 2*0 - (-1)*2

= 0 - (-2)

= 0 + 2

= 2

What is algebra?

Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols. In elementary algebra, those symbols (today written as Latin and Greek letters) represent quantities without fixed values, known as variables.

What is variable?

A variable is a symbolic name for (or reference to) information. The variable's name represents what information the variable contains. They are called variables because the represented information can change but the operations on the variable remain the same.

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this is simply a plug n' chug method. you plug in the values and solve

m=2
n= -1

(2)0 - (-1)2 (Plug)
0 - (-2) (solve)
0+2 (simplify)
2 (answer)

Bob and mark talk about their families. Bob says he has 3 kids, the product of their ages is 72. He gives another clue: the sum of the ages of his children. Mark points out there is still not enough information to accurately guess. Finally, Bob says" my youngest child called justice". Mark can then correctly determine the ages of bob's children. What are the ages?

Answers

I can only give possible combinations of the ages. This is because only the product is given. Had the sum of all ages been given, possible combinations would boil down into 1 combination.

3 kids with a youngest. This means that the ages are not the same.
We do prime factorization to get the age combination.

72 ÷ 2 = 36
36 ÷ 2 = 18
18 ÷ 2 =   9
9 ÷ 3 =   3
3 ÷ 3 =   1

1 x 2 x 2 x 2 x 3 x 3 = 72

Possible combination with no repeating number.

1 x 8 x 9 = 72
2 x 4 x 9 = 72
4 x 6 x 3 = 72
1 x 6 x 12 = 72

Solve for x : 2x^2+4x-16=0

Answers

$2x^2+4x-16=0\ \ \ /:2\n\nx^2+2x-8=0\n\n\underbrace{x^2+2x\cdot1+1^2}_((*))-1^2-8=0\n\n(x+1)^2-1-8=0\n\n(x+1)^2-9=0\n\n(x+1)^2=9\iff x+1=-3\ or\ x+1=3\n\nx=-3-1\ or\ x=3-1\n\nx=-4\ or\ x=2\n\n\n(*)\ (a+b)^2=a^2+2ab+b^2$

$2x^2+4x-16=0\ \ \ /:2\n\nx^2+2x-8=0\n\na=1;\ b=2;\ c=-8\n\n\Delta=b^2-4ac\ if\ \Delta > 0\ then\ x_1=(-b-\sqrt\Delta)/(2a)\ and\ x_2=(-b+\sqrt\Delta)/(2a)\n\n\Delta=2^2-4\cdot1\cdot(-8)=4+32=36;\ \sqrt\Delta=√(36)=6\n\nx_1=(-2-6)/(2\cdot1)=(-8)/(2)=-4;\ x_2=(-2+6)/(2\cdot1)=(4)/(2)=2$

in order to solve it, we need find the zero of the polynomial.

we find the zero of the polynomial by splitting the middle term method

2x2 -+ 4x - 16

= 2x2 + 8x - 4x -16

= 2x( x + 4)- 4(x + 4)
= (2x-)(x+4)

we find the zeroes of the factors

experimentally we find two values, 2 and -4.

Thus, values of x are 2 and -4

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