Geometry help please

Some students are trying to write an expression with fewer terms that is equivalent to 8 - 3(4 - 9x). Noah says, "I worked the p

Irina-Kira [14]

Answer: Yes I agree with Jada. His approach is correct.

Step-by-step explanation: The question requires the student to write an equivalent equation with fewer terms. Nonetheless, this does not prevent applying a mathematically correct approach.

(1) Noah is wrong and the reason is that the initial step is mathematically incorrect. The expression on the right hand side reads 3(4 - 9x), therefore starting with "8 - 3" is very wrong. The right step was to take one side which is 8 and take the other side which is 3(4 - 9x).

(2) Lin is wrong and the reason is that she started inside the parenthesis and this also is mathematically incorrect. The digits inside the parenthesis are "not like terms" and hence calculating 4 - 9x = -5x is very incorrect (the same way you cannot correctly calculate 500 metres minus 200 inches. You must make sure they are both in meters or in inches, that is both must be like terms).

(3) Jada is very correct in using the distributive property and ended up with the only correct solution. The digits on the right hand side of the expression was solved first and that resulted in -12 + 27x. The reason being that the number outside the parenthesis which is -3, multiplied both digits inside the parenthesis. The minus sign had a major effect, and after simplifying the right hand side the expression now becomes;

8 - 12 + 27x

Since the like terms are 8 and 12, you can simplify further to become

- 4 + 27x OR the expression can be rearranged as 27x - 4

(4) Andre is not correct and the reason is that although he used the distributive property, he made a slight mistake while solving for the right side of the expression. What Andre did was

-3(4 - 9x)

-12 - 27x

Remember that when a negative value multiplies another negative value the answer is positive. Therefore -3 times -9x should have been +27x, just like Jada did as shown above.

From that point onward, his answer would be incorrect.

5 0

4 years ago

Find the coordinates of point B along a directed line segment from A(3,4) and

andreev551 [17]

We have been given two points. $A(3,4)$ and $C(3,9)$ . We are asked to find the point B such that it divides line segment AC so that the ratio of AB to BC is 4:1.

We will use segment formula to solve our given problem.

When a point P divides segment any segment internally in the ratio $m:n$ , then coordinates of point P are:

$[\right x=\frac{mx_2+nx_1}{m+n},y=\frac{my_2+ny_1}{m+n}\left]$

$(x_1,y_1)=(3,4)$ and $(x_2,y_2)=(3,9)$ .

$m=4,n=1$

Upon substituting our given information in above formula, we will get:

$[\right x=\frac{4(3)+1(3)}{4+1},y=\frac{4(9)+1(4)}{4+1}\left]$

$[\right x=\frac{12+3}{5},y=\frac{36+4}{5}\left]$

$[\right x=\frac{15}{5},y=\frac{40}{5}\left]$

$[\right x=3,y=8\left]$

Therefore, the coordinates of point B would be $(3,8)$ .

8 0

3 years ago

The list of all factors for 21 is 1, 3, 7, and 21. True or False plz i need help

antiseptic1488 [7]

Answer:

true

Step-by-step explanation:

hope you have a wonderful new year

3 0

3 years ago

Read 2 more answers

Phones-R-Us charges $16.95 per month and $0.05 per text message. Awesome Wireless charges $22.95 per

Dima020 [189]

Answer:

$S \leq 200$

Step-by-step explanation:

Given

Phone R-Us= $16.95 + $0.05 per SMS

Awesome Wireless = $22.95 + $0.02 per SMS

Required

Determine the number of SMS such that Awesome Wireless is greater or equal to Phone R-Us

Represent the SMS with S

For Phone R-Us, we have:

$SMS = 16.95 + 0.05S$

For Awesome Wireless, we have:

$SMS = 22.95 + 0.02S$

For Awesome Wireless is greater or equal to Phone R-Us, we have:

$22.95 + 0.02S \geq 16.95 + 0.05S$

Collect Like Terms

$0.02S - 0.05S \geq 16.95 - 22.95$

$-0.03S \geq -6$

Solve for S

$\frac{-0.03S}{-0.03} \geq \frac{-6}{-0.03}$

$S \leq 200$

Hence: for Awesome Wireless to cost more or equal to Phone R-Us, the number of SMS must not exceed 200

4 0

3 years ago

A company buys pens at the rate of $7.50 per box for the first 10 boxes, $5.50 per box for the next 10 boxes, and $4.50 per box

photoshop1234 [79]

So it is really easy to solve firstly we can see how much does the first 10 boxes make which makes around 75$ obviously. Secondly 55$ for the next 10 boxes.

So for now we can simply calculate that we have spent around 130$ which means 20 boxes. The remaining money left is 18$ so we can buy 18/4.5 = 4 only 4 boxes with that money. Hence a total of 24 boxes.

4 0

3 years ago