MATHEMATICS
HIGH SCHOOL

Answer: It's 63, all the others are prime numbers.

MIDDLE SCHOOL

10) Carlos wants to mix granola and cranberries together to make trail mix. Granola costs $3 per pound and cranberries cost $5.50 per pound. Carlos is willing to spend $29 and wants to make 8 pounds of trail mix. Which system of equations could Carlos use to figure out how many pounds of granola (g) and cranberries (c) she should buy?

Answer:

6 pounds of granola, 2 pounds of cranberries.

Step-by-step explanation:

3g + 5.5c = 29

g + c = 8

g = 8 - c

3 * (8 - c) + 5.5c = 29

24 - 3c + 5.5c = 29

2.5c = 5

c = 2

g = 8 - c

g = 8 - 2

g = 6

MIDDLE SCHOOL

Describe how to transform the graph of g(x)= ln x into the graph of f(x)= ln (3-x) -2.

Answer:

The graph of g(x) = ㏑x translated 3 units to the right and then reflected

about the y-axis and then translated 2 units down to form the graph of

f(x) = ㏑(3 - x) - 2

Step-by-step explanation:

* Lets talk about the transformation

- If the function f(x) reflected across the x-axis, then the new

function g(x) = - f(x)

- If the function f(x) reflected across the y-axis, then the new

function g(x) = f(-x)

- If the function f(x) translated horizontally to the right

by h units, then the new function g(x) = f(x - h)

- If the function f(x) translated horizontally to the left

by h units, then the new function g(x) = f(x + h)

- If the function f(x) translated vertically up

by k units, then the new function g(x) = f(x) + k

- If the function f(x) translated vertically down

by k units, then the new function g(x) = f(x) – k

* lets solve the problem

∵ Graph of g(x) = ㏑x is transformed into graph of f(x) = ㏑(3 - x) - 2

- ㏑x becomes ㏑(3 - x)

∵ ㏑(3 - x) = ㏑(-x + 3)

- Take (-) as a common factor

∴ ㏑(-x + 3) = ㏑[-(x - 3)]

∵ x changed to x - 3

∴ The function g(x) translated 3 units to the right

∵ There is (-) out the bracket (x - 3) that means we change the sign

of x then we will reflect the function about the y-axis

∴ g(x) translated 3 units to the right and then reflected about the

y-axis

∵ g(x) changed to f(x) = ㏑(3 - x) - 2

∵ We subtract 2 from g(x) after horizontal translation and reflection

about y-axis

∴ We translate g(x) 2 units down

∴ g(x) translated 3 units to the right and then reflected about the

y-axis and then translated 2 units down

* The graph of g(x) = ㏑x translated 3 units to the right and then

reflected about the y-axis and then translated 2 units down to

form the graph of f(x) = ㏑(3 - x) - 2

Answer:

c edge

Step-by-step explanation:

COLLEGE

Solve the equation 4x squared =121

A 2.75,-2.75

B 5.5,-5.5

C 11,-11

D 30.25,-30.25

Answer:B

Step-by-step explanation:

4x2 =121

4x2-121=0

using the general formula

[-b( +/-) √b2-4ac]/2a

a=4, b= 0, c=-121

x= [0 ( +/-)√02-(4*4*-121)]/2.4

= ( +/-)√1936)/8 = ( +/-)5.5

x =5.5

x = -5.5

COLLEGE

The primary goal of using correlational research is to

The Primary goal of using correlation research is to determine the nature and strength of the association between two measured variables.

Here you must know the terms correlation and variable. The term Correlation is simply defined as the relation between two variables. variables are factors that are liable to vary or change.

Here you must know the terms correlation and variable. The term Correlation is simply defined as the relation between two variables. variables are factors that are liable to vary or change.