When is the estimation of products a useful tool?

Answers

Answer 1
Answer: The estimation of products are usefull so with you real answer, you can check back and fourth if you answer is reasonable

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The area of a square piece of cardboard is 81 square inches. What is the length of the cardboard?A. 8 inches
B. 9 inches
C. 20.25 inches
D. 10 inches

Answers

Answer:

Step-by-step explanation:

The area of a square is found in the formula

A=s^2

We have the Area value so we will plug it in:

81=s^2

Take the square root of both sides to undo the square on the s to get that

s = 9

The quadratic equation (3k-2)x^2 +12x+3(k+1) =0 has equal roots. Find the two possible values of k.

Answers

x_1=x_2 \Rightarrow \Delta=0\n\Delta=12^2-4\cdot(3k-2)\cdot3(k+1)\n\Delta=144-(36k-24)(k+1)\n\Delta=144-36k^2-36k+24k+24\n\Delta=-36k^2-12k+168\n-36k^2-12k+168=0\n-3k^2-k+14=0\n-3k^2+6k-7k+14=0\n-3k(k-2)-7(k-2)=0\n-(3k+7)(k-2)=0\nk=-(7)/(3) \vee k=2

Factor this radical expression. 50a^2-10ab/20a^3b^3

Answers

remembe
(ax)/(bx)=(a/b)(x/x)=(a/b)1
find ones aka common factors and use distributive

top
50a^2-10ab
common facotrs is 10a
undistribute (ab+ac=a(b+c))
10a(5a-b)

bottom
20a^3b^3
see if 10a is also a common factor and undistribute that to cancel and make ones
10a(2a^2b^2)

now we have
(10a(5a-b))/(10a(2a^(2)b^(3))=(10a)/(10a)(5a-b)/(2a^(2)b^(3))
1)split into two fractions 
(50a^(2) )/(20a ^(3) b ^(3) )(10ab )/(20a ^(3) b ^(3) )

2) cancel what you can on both sides
(5)/(2ab ^(3) )(1)/(2a ^(2)b ^(2) )

3) Make the denominators the same by cross multiplying and then put together as 1 fraction again
(5a-b)/(2a ^(2)b ^(2) )

What is the vertex of the quadratic function f(x) = (x – 8)(x – 2)?

(
,
)

Answers

Answer:

( 5, -9 ) is the answer

Answer:

⅞2781x 3862

Step-by-step explanation:

i don't know but that is my answer ok kayat taposin Mona ang module mo

Max was solving the equation below and isn’t sure if his answer is correct. Explain to Max how he can check his answer and then help him identify any errors he made. Provide the correct solution in your How can he check his answer?



Show the correct solution:

Answers

HOW CAN HE CHECK HIS ANSWER:
  HE CAN CHECK HIS ANSWER BY PLUGGING IN HIS X VALUE, AFTER HE GETS THE CORRECT ANSWER. 
SHOW THE CORRECT ANSWER: 
 3(3x+6) = 4(7x-1)
 9x+18 = 28x-4
 18 = 19x-4
 22 = 19x
 22/19 = x

CHECK:
3(22/19+6)/8 = 7(22/19-1)/6
45/38 = 45/38 ( Is true)


hope this helps!!

Well, first of all, the bottom 2 lines are cut off of the bottom of Max's solution,
and his final answer doesn't even appear there.

Here . . . let me complete it for you:
Under the part printed on the page should be:

             19  =  19x

               x  =  1

=========================================

Now that Max has an answer, he can check it by writing it into the
original equation wherever there's an 'x' there.

The original:                                (3x-6) / 8  =  (7x-1) / 6

With Max's answer written in:    (3·1 - 6) / 8  =  (7·1-1) / 6

Simplify the left side:                   (3 - 6) / 8  =  (7·1-1) / 6
                                                          -3/8  =  (7·1-1) / 6

Simplify the right side:                       -3/8  =  (7-1) / 6
                                                          -3/8  =   6 / 6
                                                          -3/8  =  1
This result is not a true statement,
so 'x' can't be ' 1 '.

We have to go back, look through Max's work, and find his mistake.
(Actually, Max won't learn anything that way ... MAX should be looking through
his work to find his mistake. But life is not always fair.)

The third line of Max's solution is      3 (3x + 6)  =  4 (7x - 1)

Then he goes on to clear the
parentheses, and the next line is:        9x + 18  =  28x - 1

That's where his mistake is.  The left side is correct,
but on the right side, Max distributed the '4' incorrectly.
Shame on Max. 
This line should be                              9x + 18  =  28x - 4 .


4 An alloy is a mixture of metals. Most of the gold used in jewellery is an alloy of pure gold and other metals which are added to make the gold harder. Pure gold is 24 carats (ct), so 18 carat parts pure gold 18 gold is an alloy of gold and other metals in the ratio 18:6. In other words, 18/24 parts pure gold and 6/24 other metals. a. A jeweller makes an 18 ct gold alloy using three grams of pure gold. What mass of other metals does she add?
b . An 18 ct gold chain contains four grams of pure gold. How much other metal does it contain? c. What is the ratio of gold to other metals in 14 ct gold?
d. What is the ratio of gold to other metals in 9 ct gold? ​

Answers

To calculate the mass of other metals in each scenario, we need to use the given ratios.

Given:

- Pure gold is 24 carats (ct).

- 18 carat gold is an alloy of gold and other metals in the ratio 18:6 (18/24 parts pure gold and 6/24 other metals).

a. A jeweller makes an 18 ct gold alloy using three grams of pure gold. What mass of other metals does she add?

First, let's find the mass of other metals in the 18 ct gold alloy.

18 ct gold contains 18/24 parts pure gold and 6/24 parts other metals. So, if the jeweller uses 3 grams of pure gold, the amount of other metals in the alloy can be calculated as follows:

Mass of other metals = (6/24) * 3 grams

Mass of other metals = (1/4) * 3 grams

Mass of other metals = 3/4 grams

b. An 18 ct gold chain contains four grams of pure gold. How much other metal does it contain?

Similarly, for the 18 ct gold chain containing 4 grams of pure gold:

Mass of other metals = (6/24) * 4 grams

Mass of other metals = (1/4) * 4 grams

Mass of other metals = 4/4 grams

Mass of other metals = 1 gram

c. What is the ratio of gold to other metals in 14 ct gold?

For 14 ct gold, the ratio of gold to other metals is 14:10 (since 14 + 10 = 24, and gold is 14 out of 24 parts, while other metals are 10 out of 24 parts).

d. What is the ratio of gold to other metals in 9 ct gold?

For 9 ct gold, the ratio of gold to other metals is 9:15 (since 9 + 15 = 24, and gold is 9 out of 24 parts, while other metals are 15 out of 24 parts).