MATHEMATICS HIGH SCHOOL

What is the common difference between successive terms in the sequence?0.36, 0.26, 0.16, 0.06, –0.04, –0.14

Answers

Answer 1
Answer: Depending on the way you look at the numbers, they are increasing/decreasing by 0.1.

0.36- 0.1 =0.26
0.26-0.1=0.16
0.16-0.1=0.06
0.06-0.1=-0.04
-0.04-0.1=-0.14
(Or vice versa by adding 0.1 starting with -0.14)

Make sense?

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What is one half of a number is equal to 14. What is the number?

Answers

Let the number be x
1/2 of x=14
x/2=14
x=14x2
x=28
The number is 28
half=14=> number=14x2=28

or
number  |---n--||---n--|=14+14=28
half        |---n--|=14

Estimated: 253 times 46

Answers

I do believe the answer is 11,638 I did this in my head maybe u should try it.
250 x 45 = 11250

Because you round 253 down to 250 and 46 down to 45

Write a congruence statement for the pair of triangles. Name the postulate or theorem that justifies your statement.

Answers

From the triangles, I think the congruence statement would be that of the ASA theorem. Triangle AWC is congruent to triangle RWC by virtue of the Angle-Side-Angle theorem. Hope this answers the question. Have a nice day.

How do you find the slope

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Remember that the slope of a line never changes, so you can choose whatever 2 points you want and you will always get the same slope. Calculate the rise and run (You can draw it on the graph if it helps). The slope is 2/4, which , of course, you can simplify to ½.

Answer:Use the slope formula, m=y2-y1/x2-x1

Step-by-step explanation:

Which of the following is the graph of f(x) = x2 − 5x + 4?

Answers

Answer:

 refer attachment for the graph.

Step-by-step explanation:

Given: The equation f(x)=x^2-5x+4

We have to draw the the graph for the given equation.

Consider the given equation  f(x)=x^2-5x+4

The vertex of the parabola of the form  f(x)=ax^2+bx+c is given by x=-(b)/(2a)

Here, a = 1 , b = -5 and c = 4

Thus, vertex is

x_v=-(\left(-5\right))/(2\cdot \:1)=(5)/(2)

Also, the y coordinate at x=(5)/(2) is

y_v=\left((5)/(2)\right)^2-5\cdot (5)/(2)+4

Simplify, we get,

y_v=-(9)/(4)

Thus, The vertex of parabola is \left((5)/(2),\:-(9)/(4)\right)

y - intercept is the point where x = 0

Plug x = 0 in given equation f(x)=x^2-5x+4

f(0)=0^2-5(0)+4=4

Thus, y - intercept is (0,4)

Now, we calculate x- intercept

x- intercept is where y is equal to 0.

Put f(x) = 0

We have,

x^2-5x+4=0

Solving the given quadratic equation using quadratic formula ,we have

x_(1,\:2)=(-b\pm √(b^2-4ac))/(2a)

we have a = 1 , b = -5 and c = 4

x_(1,\:2)=(-\left(-5\right)\pm √(\left(-5\right)^2-4\cdot \:1\cdot \:4))/(2\cdot \:1)

Simplify, we have,

x_(1,2)=(5\pm√(9))/(2)

Thus, x_1=4, x_2=1

Thus, The x - intercept are (4,0) and (0,1)

Plot the graph and we obtain as shown below.
I made a graph of the equation hope this helps.

Two points can lie in two different lines

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