Need help on question 9

Answers

Answer 1

Answer:

Answer: Choice A) The figure and its image are similar, but not congruent, and the image has been translated 1 unit up.

The jump from (x,y) to (2x,2y) means we dilated by a scale factor of 2. The image is twice as large as its original. There is no way the two figures are congruent (the larger image has longer side lengths). Despite congruence not being preserved, the two figures are the same shape, so they are similar figures. After the dilation is done, the "+1" tacked onto the "2y" means we shifted every point up 1 unit.

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if (ax+2)(bx+7) = 15xsquared + cx +14 for all values of x, and a+b =8, what are the two possible values for c?

Answers

The two possible values for c are 31 and 41

Step-by-step explanation:

Given Expression:

$(a x+2)(b x+7)=15 x^(2)+c x+14$

a + b = 8

To expand,

Multiply a x with (b x + 7) = $a b x^(2)+7 a x$

Multiply 2 with (b x + 7) = 2 b x +14

Now, combining the above, we get

$a b x^(2)+7 a x+2 b x+14=15 x^(2)+c x+14$

$a b x^(2)+x(7 a+2 b)+14=a b x^(2)$

When comparing both sides, we get

a b = 15, 7 a + 2 b = c

$a=(15)/(b) \text { or } b=(a)/(15)$

Now, substitute above value in a + b = 8. So,

$(15)/(b)+b=8$

$15+b^(2)=8 b$

$b^(2)-8 b+15=0$

Factorising above, we get the equation as

$b^(2)-3 b-5 b+15=0$

(b - 3) (b - 5) = 0

b = 3 and 5

If b = 3, then

$a=(15)/(b)=(15)/(3)=5$

If b = 5, then

$a=(15)/(5)=3$

If a = 3, b = 5

c =7 a + 2 b = 7 (3) + 2 (5) = 21 + 10 = 31

If a = 5, b = 3

c =7 (5) +2 (3) = 35 + 6 = 41

Therefore, the values of ‘c’ are 31 and 41.

Mark has some nickels, dimes, and quarters in his pocket. He has three times as many quarters as nickels. He has five more dimes than nickels. The total amount he has in his pocket is $5. How many of each coin does he have

Answers

15 quarters
10 dimes
5 nickels

five more dimes than nickels means we know there is at least 5 dimes, or 50 cents
if we subtract this from $5, we have $4.50.
With those 5 dimes gone, the number of dimes equals the number of nickels. If there are 3 times as many quarters as nickels, there are also 3 times as many quarters as dimes. So for every 3 quarters (0.75), there is one dime (0.10) and one nickel (0.05).
0.75 + 0.10 + 0.05 = 0.90
you find the number of remaining coins by dividing the total minus the 5 dimes (4.50) by 0.90.
4.50 ÷ 0.90 = 5
this is how many times 3 quarters, one dime, and one nickel go into 4.50
so, the answer to how many of each coin is:
3 quarters × 5 = 15 quarters
one dime × 5 = 5 plus the original 5 we took out = 10 dimes
one nickel × 5 = 5 nickels

to check answer:
5.00 = 15(0.25) + 10(0.10) + 5(0.05)
5.00 = 3.75 + 1.00 + 0.25
5.00 = 5.00 ✔

Arthur earned $136 in three weeks. he goes back to school in one more week. he needs at least $189 to buy the new coat that he wants for school. how much must arthur earn in the next week?write an inequality to represent this siutation.