MATHEMATICS HIGH SCHOOL

Y+7=-2/3(x+6) as a linear function

Answers

Answer 1
Answer: Go to your graph , and make a straight line . A linear function is basically a line , so make a line to those numbers in the graph .

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Find the area of the triangle. A.54B.18C.36D.27
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Find all solution of the equation.
y=-x
y=xlnx

Answers

\left\{\begin{array}{ccc}y=-x\ny=xlnx\end{array}\right;\ \ \ D:x\in\mathbb{R^+}\n\nxlnx=-x\n\nxlnx+x=0\n\nx(lnx+1)=0\iff x=0\notin D\ or\ lnx+1=0\n\nlnx=-1\iff x=e^(-1)\to x=(1)/(e)\in D\n\nAnswer:x=(1)/(e)\ and\ y=-(1)/(e)

Which value of x makes the following equation true?4(x - 1) = -4x + 60

A. 8
B. 12
C. 11
D. 9

Answers

The easiest way is to just solve the equation.
4x - 4 = -4x + 60
4x + 4x = 4 + 60
8x = 64
x = 8

A slower way to do this is to plug each of the numbers into the equation to see which makes the equation is true.
So for A.
4(8 - 1) = -4(8) + 60
4(7) = -32 + 60
28 = 28
Fortunately, this is true, so A is the answer and you don't have to try the other options.
It would be A because if you plug in 8 for x on each side you get 28 which makes the equation true

A group of 18 people ordered soup and sandwiches for lunch. Each person in the group had either one soup or one sandwich. The sandwiches cost $7.75 each and the soups cost $4.50 each. If the total cost of all 18 lunches was $113.50, how many sandwiches were ordered? A. 7
B. 8
C. 9
D. 10

Answers

Let a be the number of soups ordered and b be the number of sandwiches ordered. We know that, a + b = 18, so a = 18 - b. Now we form an equation for the total cost, which is: 4.5a + 7.75b = 113.5. Now, we substitute the value of a into the cost equation to form a single equation in terms of b, number of sandwiches, only. 4.5(18 - b) + 7.75b = 113.5. Solving for b, we get b = 10. Therefore, the answer is D.

FIND MAGNITUDE AND DIRECTIONS OF TRANSLATIONS APPLIED ON A TRIANGLE. Question Linked below.

Answers

The three translations applied on the triangle, where the first element of each vector represents the magnitude of the translation, and the second element represents the direction of the translation.

To find the magnitude and direction of the translations applied on a triangle, we need to know the coordinates of the vertices of the original triangle and the coordinates of the vertices of the transformed triangle.

Let's say the coordinates of the original triangle are (x1, y1), (x2, y2), and (x3, y3), and the coordinates of the transformed triangle are (x1', y1'), (x2', y2'), and (x3', y3').

The magnitude of the translation can be found by calculating the distance between the corresponding vertices of the original and transformed triangles using the distance formula. For example, the magnitude of the translation from (x1, y1) to (x1', y1') is given by:

sqrt((x1' - x1)^2 + (y1' - y1)^2)

Similarly, we can find the magnitudes of the other two translations.

The direction of the translation can be found by calculating the angle between the line connecting the corresponding vertices of the original and transformed triangles and the x-axis. We can use the arctangent function to find this angle. For example, the direction of the translation from (x1, y1) to (x1', y1') is given by:

tan^-1((y1' - y1)/(x1' - x1))

Similarly, we can find the directions of the other two translations.

Once we have the magnitudes and directions of the translations, we can describe the transformation using vector notation. The vector of the translation is given by:

< magnitude1, direction1 >

< magnitude2, direction2 >

< magnitude3, direction3 >

This represents the three translations applied on the triangle, where the first element of each vector represents the magnitude of the translation, and the second element represents the direction of the translation.

Learn more about translations here

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A father is four times as old as his daughter. In 18 years he will be two times as old as she. How old is the daughter now?

Answers

Let's say x to the daughter's age, since the father's age is four times the daughter's age, his age will be 4x. 18 years later, the daughter's age will be x+18 and the father's will be 4x+18. And we know that 18 years later the father's age will be twice the daughter' so , 4x+18 = 2(x+18) and 4x+18=2x+36 then, 4x-2x=36-18,
2x=18 then divide both sides by 2, x = 9. The daughter's age was x, so she is 9 years old.

3m - 3(m+8) > 3m(Teacher didn't go over this hopefully I can get an explanation)

Answers

Alrighty!

*Note the ">" sign is similar to the "=" sign.

3m - 3(3m + 8) > 3m
3m - 6m + 24 > 3m (distribute)
-3m + 24 > 3m (combine like terms)
24 > 6m (Compute/simplify)
8 > m

Makes sense?
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