A rate in which the second quantity in the comparison is one unit

Answers

Answer 1

Answer: I'm thinking the answer is unit rate.

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Is the GCF (Greatest Common Factor) of a pair of numbers ever greater than both numbers? Explain with an example.

Answers

The GCF can be the smaller one of the two numbers,
or else it can be a number smaller than either of them.
It can never be more than the smaller of the two numbers.

-- The GCF of 10 and 100 is 10 .

-- The GCF of 9 and 102 is 3 .

-- The GCF of 10 and any number more than 10
an never be bigger than 10 .

Basically, what I would say is that the Greatest Common Factor is no larger than smallest. Keep in mind that Greatest means biggest, but don't let it trick you.

Solve -r/4 < 8 A.r<-32
B. r. >-32
C.r < -2

D.r>-2

Answers

$(-r)/(4) <8\ /\cdot4\n\n-r<32\ /\cdot(-1)\n\nr>-32\ \ \ \Leftrightarrow\ \ \ x\ \in\ (-32;\ +\infty)$

$Ans.\ B$

Jill got an 85% on a math test if there were 40 questions in total,how many did she get wrong?

Answers

You can solve this by setting up a proportion. You can put the number of items correct over the total number. and substitute the unknown number with x.

$(85)/(100)$ = $(x)/(40)$ Cross-multiply
3400 = 100x Divide both sides by 100
34 = x

40 - 34 = 6

So, Jill got 6 questions wrong.

yeah she got 6 questions wrong

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.

What two numbers multiply to -84 and add to 5

Answers

12 & -7

multiplied = -84
added 12 + -7 = 5

From the top of your head you know 12 * 7 = 84.

But let's rearrange it to suit.

12 * - 7 = -84

12 + (-7) = 12 - 7 = 5.

So the two numbers are 12 and -7.

If Julie needs 3 1/4 cups of oat meal how many 1/4 cups of oatmeal will she use ?

Answers

Basically, you divide 3 1/4 by 1/4. To do that, you have to change the mixed number into an improper fraction. 3 1/4 as an improper fraction is 13/4. I was able to find that since you simply just multiply the denominator by the whole number, 4 x 3, which is 12, then add 12 to the numerator, 1, which is 13. Finally, the improper fraction is 13/4 (the denominator stays the same). Now, we can divide the fractions. One rule about fractions: dividing them is the same as multiplying them with the reciprocal of the other. Like say for example, the reciprocal of 1/5 is 5/1.

Let's solve:

13/4 divided by 1/4 =
13/4 x 4/1 = At this point, you just multiply them straight across.
52/4 = It's not simplified since both can still be divided. So, you simplify by finding the greatest common multiple of 52 and 4, which is 4. 52 divided by 4 = 13; 4 divided by 4 = 1.
52/4 = 13/1 = 13 (any numerator with the denominator of one is a whole number when simplified)

So if Julie needs 3 1/4 cups of oatmeal, she will use 13 of 1/4 cups of oatmeal. Answer's 13. :) I really hope I helped!

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