MATHEMATICS HIGH SCHOOL

This is due tomorrow, so please help and show step by step

Answers

Answer 1

Answer:

Answer:

slope = 3/2
y-intercept = 3
x-intercept = -2

Step-by-step explanation:

The slope is the coefficient of x when the equation is of the form ...

y = (something).

Here, we can put the equation in that form by subtracting 12x and dividing by the coefficient of y:

12x -8y = -24 . . . . . given

-8y = -12x -24 . . . . .subtract 12x

y = 3/2x +3 . . . . . . . divide by -8

This is the "slope-intercept" form of the equation. Generically, it is written ...

y = mx + b . . . . . . where m is the slope and b is the y-intercept

So, the above equation answers two of your questions:

slope = 3/2

y-intercept = 3

The x-intercept is found fairly easily from the original equation by setting y=0:

12x = -24

x = -24/12 = -2 . . . . . the x-intercept

_____

A graph of the equation can also show you these things. The graph shows a rise of 3 units for a run of 2, so the slope is rise/run = 3/2. The line crosses the axes at x=-2 and y=3, the intercepts.

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Paul travels from Rye to Eston at an average speed of 90km/h. He travels for T hours. Mary makes the same journey at an average speed of 70km/h. She travels for 1 hour long than Paul. Work out the value of T

Answers

Total distance covered;
For Paul;
sxt=distance
90*t= d
For mary;
s*t=d
70*(t+1)=d
70t+70=d

Since they cover same distance;
70t+70=90t
Putting like terms together;
70=90t-70t
70=20t
t=70/20
t= 3 and 1/2 hours

What are the roots of the equation x2 + 4x - 16 = 0?

Answers

see attached picture for answer

What is the intersection of plane STXW and SVUT?A. SV
B. ST
C. YZ
D. TX

Answers

B. ST is the intersection of plane STXW and SVUT.

Answer: B. ST.

Step-by-step explanation: The intersection of two planes, if exists, is a straight line. Since the planes STXW and SVUT have S and T as common points and we can always draw a straight line given any two points in a plane, so ST is the line joining the points S and T, and hence, it is the intersection of the two given planes.

Thus, the correct option is B. ST.

Can you draw an isosceles triangle with only one 80 degree angle. Is this the only possibility or can another triangle be drawn that will meet these conditions?

Answers

Answer:

The correct answer is yes, we can draw an isosceles triangle with only one 80° angle. NO this is not the only possibility.

Step-by-step explanation:

A triangle is a three sided figure. There are three types of triangles: Equilateral, Isosceles and Scalene triangle. The sum of angles in a triangle is 180°.

If all sides have equal length then it is an equilateral triangle. All angles of this triangle are equal.

If two sides are equal then it is an isosceles triangle. Two opposite angles are equal.

If none of the angles and sides are equal then we call it a scalene triangle.

Given one angle of the triangle is 80°.

There exists two possibilities. One, 80° is the equal angle and 80° is not the equal angle.

Required Case : 80° is not the equal angle, i.e. only one 80° angle.

We are to draw an isosceles triangle (say ABC) with one angle say ∠A as 80°.

Other two angles (∠B and ∠C) are 50° each as the other two angles are supposed to be equal. ( $(180-80)/(2)$ °).

Now let us consider side AB and AC be of length say a. These two sides are equal.

Thus now we have successfully constructed an isosceles triangle with only one 80° angle.

We can get infinitely many isosceles triangle by just varying the length of the equal side.

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