MATHEMATICS HIGH SCHOOL

Look at the linear equation below.2x - 3y = -13

Which pair of numbers is a solution to the equation?
Select one:
(-5, 1)
(5, 1)
(5, -1)
(-5, -1)

Answers

Answer 1
Answer: The answer is (-5,1) because 2(-5)-3(1)=-13 :)

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A. A survey of 110 teachers showed that 28 of them have a second job. B. A survey of 90 teachers showed that 27 of them have a second job.
C. A survey of 70 teachers showed that 21 of them have a second job.
D. A survey of 80 teachers showed that 32 of them have a second job.
In math class, 4 students complete individual surveys to determine the percentage of high school teachers that have a second job. Which two surveys show proportional results?
A) A and B
B) B and D
C) A and D
D) B and C

Answers

Answer:

Correct option is:

D) B and C

Step-by-step explanation:

A. A survey of 110 teachers showed that 28 of them have a second job.  

B. A survey of 90 teachers showed that 27 of them have a second job.  

C. A survey of 70 teachers showed that 21 of them have a second job.  

D. A survey of 80 teachers showed that 32 of them have a second job.

Percentage of teachers having second job is calculated by the formula:

      (Teachers having second job)/(Total number of teachers)* 100

So, percentage of second job teachers of survey A,B,C and D is:

                      A                  B          C           D

Percentage    25.45%       30%      30%      40%

Hence, two surveys that are proportional are

B and C

Hence, Correct option is:

D) B and C
The answer is D. B and C are proportional.

15. (a) Work out the value of 25-3

Answers

25 - 3 = 22

This is because subtraction is the operation of finding the difference between two numbers. To subtract 3 from 25, we start from 25 and count backwards 3 units.

Okay so I have having a little problem with slope- intercept form when you have two points. Help?

Answers

To find the slope of the line you have to do change in y over the change in x. I will be using the example (3,6) and (1,4). So if you find the change in y over the change in x you have 2/2. The slope would be 1. and if you have slope intercept form (y=mx+b) you get y=1x+b. Now all you have to find is b. Substitute in any of the points given and you have 4=1+b. Therefore b = 3. So your full equation is: y=x+3

Estimating Sums of Single Digit NumbersWhich of the following represents the most accurate estimation of 4 + 8? is the answer 5, 10, 20 or 25

Answers

10
We can round 4 down to 0 since it is less than 5 and round 8 up to 10 since it is greater than 5. Giving:
0 + 10 = 10

1. Points A and B are to be mapped onto a number line according to two equations. The solution to the equation is the coordinate of point A. The solution to the equation is the coordinate of point B. (a) Solve the first equation to find the coordinate of point A. need help quick

Answers

I still need that number line.....
the number line dont come with the assighnment right?

The graph of which function has an axis of symmetry at x =-1/4 ?f(x) = 2x2 + x – 1

f(x) = 2x2 – x + 1

f(x) = x2 + 2x – 1

f(x) = x2 – 2x + 1

Answers

we know that

The equation of the vertical parabola in vertex form is equal to

y=a(x-h)^(2)+k

where

(h,k) is the vertex

The axis of symmetry is equal to the x-coordinate of the vertex

so

x=h ------> axis of symmetry of a vertical parabola

we will determine in each case the axis of symmetry to determine the solution

case A)f(x)=2x^(2)+x-1

Convert to vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

f(x)+1=2x^(2)+x

Factor the leading coefficient

f(x)+1=2(x^(2)+0.5x)

Complete the square. Remember to balance the equation by adding the same constants to each side

f(x)+1+0.125=2(x^(2)+0.5x+0.0625)

f(x)+1.125=2(x^(2)+0.5x+0.0625)

Rewrite as perfect squares

f(x)+1.125=2(x+0.25)^(2)

f(x)=2(x+0.25)^(2)-1.125

the vertex is the point (-0.25,-1.125)

the axis of symmetry is

x=-0.25=-(1)/(4)

therefore

the function f(x)=2x^(2)+x-1 has an axis of symmetry at x=-(1)/(4)

case B)f(x)=2x^(2)-x+1

Convert to vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

f(x)-1=2x^(2)-x

Factor the leading coefficient

f(x)-1=2(x^(2)-0.5x)

Complete the square. Remember to balance the equation by adding the same constants to each side

f(x)-1+0.125=2(x^(2)-0.5x+0.0625)

f(x)-0.875=2(x^(2)-0.5x+0.0625)

Rewrite as perfect squares

f(x)-0.875=2(x-0.25)^(2)

f(x)=2(x-0.25)^(2)+0.875

the vertex is the point (0.25,0.875)  

the axis of symmetry is

x=0.25=(1)/(4)

therefore

the function f(x)=2x^(2)-x+1 does not have a symmetry axis in x=-(1)/(4)

case C)f(x)=x^(2)+2x-1

Convert to vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

f(x)+1=x^(2)+2x

Complete the square. Remember to balance the equation by adding the same constants to each side

f(x)+1+1=x^(2)+2x+1

f(x)+2=x^(2)+2x+1

Rewrite as perfect squares

f(x)+2=(x+1)^(2)

f(x)=(x+1)^(2)-2

the vertex is the point (-1,-2)  

the axis of symmetry is

x=-1

therefore

the function  f(x)=x^(2)+2x-1 does not have a symmetry axis in x=-(1)/(4)  

case D)f(x)=x^(2)-2x+1

Convert to vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

f(x)-1=x^(2)-2x

Complete the square. Remember to balance the equation by adding the same constants to each side

f(x)-1+1=x^(2)-2x+1

f(x)=x^(2)-2x+1

Rewrite as perfect squares

f(x)=(x-1)^(2)

the vertex is the point (1,0)  

the axis of symmetry is

x=1

therefore

the function  f(x)=x^(2)-2x+1 does not have a symmetry axis in x=-(1)/(4)

the answer is

f(x)=2x^(2)+x-1
axis of symmetry is the x value of the vertex

for
y=ax^2+bx+c
x value of vertex=-b/2a

first one
-1/2(2)=-1/4
wow, that is right

answer is first one
f(x)=2x^2+x-1
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