MATHEMATICS HIGH SCHOOL

Siti had 135 buttons. 5/9 of the buttons were red and the rest were blue. She used 64 red buttons and bought some more blue buttons. She had 84 buttons left in the end. How many blue buttons did Siti buy?

Answers

Answer 1

Answer:

Answer:

Siti bought 13 blue buttons

Step-by-step explanation:

for not to get confused, we are going to solve the problem step by step

Siti had 135 buttons

5/9 of the buttons were red and the rest were blue

let's calculate how many buttons were red out of 135

135 * 5/9 = 75

if 75 buttons were red and the rest were blue, we can calculate how many were blue

135 - 75 = 60

says she only use 64 red buttons

if we had 75 red buttons and she used 64

75 - 64 = 11

she tells us that she had 84 buttons left, from which we know she had 11 red buttons that had been left over and 60 blue ones that she did not use, so we can calculate how many blue buttons she bought since we have the total number of buttons that she has now

84 - 60 -11 = 13

Siti bought 13 blue buttons

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Find the value of k so that the line through the given points has slope m.(k+1, k-1), (k-k); m=k+1

Answers

Answer:

-3/2

Step-by-step explanation:

formula of slope (y2-y1/x2-x1)

Simplify. your answer should contain only positive exponents y^2x^3y^2

Answers

Answer:

x^2y^4.

Step-by-step explanation:

y^2x^3y^2

= x^2y^2y^2

= x^2y^(2+2)

= x^2y^4.

Find the range of the following piecewise function.[0,11)
(-4,6]
(0,11]
[-4,6)

Answers

Given:

The piecewise function is

$f(x)=\begin{cases}x+4 & \text{ if } -4\leq x<3 \n 2x-1 & \text{ if } 3\leq x<6 \end{cases}$

To find:

The range of given piecewise function.

Solution:

Range is the set of output values.

Both functions $f(x)=x+4$ and $f(x)=2x-1$ as linear functions.

Starting value of $f(x)=x+4$ is at x=-4 and end value is at x=3.

Starting value: $f(-4)=-4+4=0$

End value: $f(3)=3+4=7$

Starting value of $f(x)=2x-1$ is at x=3 and end value is at x=6.

Starting value: $f(3)=2(3)-1=5$

End value: $f(6)=2(6)-1=11$

Least range value is 0 at x=-4 and 0 is included in the range because -4 is included in the domain.

Largest range value is 11 at x=6 and 11 is not included in the range because 6 is not included in the domain.

So, the range of the given piecewise function is [0,11).

Therefore, the correct option is A.

What is the solution to the system of equations?

y=3x+6
3x-y=6

Answers

1st equation: y = 3x + 6
2nd equation: 3x - y = 6

Substitute the y in the 2nd equation by its value in the 1st equation.

y = 3x + 6
3x - y = 6

3x - (3x + 6) = 6
3x - 3x - 6 = 6
-6 = 6 NOT A SOLUTION

3x -y = 6
3x = 6 + y
x = (6 + y)/3

y = 3x + 6
y = 3((6+y)/3) + 6
y = 6 + y + 6
y = 12 + y
y - y = 12
0 = 12 NOT A SOLUTION

Express each as a single power of 2...

2^a X 2^b X 2^c

2^a+b X 2^a-b

Answers

i) $2 ^(a)*2 ^(b)* 2^(c)$
We know that $x^(a) * x^(b) = x^(a+b)$
Therefore,
$2 ^(a)*2 ^(b)* 2^(c)$ = $2 ^(a+b+c)$
ii) $2 ^(a+b) * 2 ^(a-b)= 2^((a+b+a-b))$
$= 2^(2a)$

Simplify {n - 1 - [n - 1 - (n - 1)]}.

Answers

{n-1-[n-1-(n-1)]} | Given
{n-1-[n-1-n+1]} | Distribute most inner negative
{n-1-n+1+n-1]} | Distribute next inner negative
n-1 | Simplify like terms

Answer: the correct answer is n-1

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