What number should I multiply 1 1/4 by to get 7/12

Answers

Answer 1

Answer: Let's take our given information and transform it into numbers. We will let x equal the "mystery" number we need to find. Here is our equation:
$1 (1)/(4) x= (7)/(12)$
Now, all we need to do is convert the mixed fraction into an improper fraction:
$(5)/(4) x= (7)/(12)$
Now, just multiply the reciprocal of 5/4 with 7/12, giving us:
$x=(4)/(5)* (7)/(12)$
Finally, just straight up multiply to get an answer of x = 28/60, which can be simplified down to x = 7/15. Therefore, the number you have to multiply 1 1/4 to get 7/12 is 7/15. Hope this helped!

Answer 2

Answer: 1 and 1/4 is the same as 5/4 so essentially we are asking what do we multiple 5/4 by to get 7/12. Try to keep things as fractions initially to see if there is a fractional answer with whole numbers.

Let x represent the number:
x . 5/4 = 7/12
i.e. 5x/4 = 7/12
We want to get x on it's own so multiply both sides of equation by 4
5x = 4 . (7/12) = 28/12
now divide both sides by 5 to get x on its own
x = (28/12) / 5
This does not equate to a whole number fraction as 28 and 12 are not divisible by 5. So simply convert to decimal
x = 2.3333 / 5 = 0.46666

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Combine the like terms to create an equivalent expression:
−4p+(−2)+2p+3

Answers

Answer:

-2p+1

Step-by-step explanation:

combine -4p+2p=-2p and -2+3=1 so your answer is -2p+1

Use induction to prove the following formula is true for all integers n where n greaterthanorequalto 1. 1 + 4 + 9 + .. + n^2 = n(n + 1)(2n + 1)/6

Answers

Answer with Step-by-step explanation:

Since we have given that

1+4+9+........................+n² = $(n(n+1)(2n+1))/(6)$

We will show it using induction on n:

Let n = 1

L.H.S. :1 = R.H.S. : $(1* 2* 3)/(6)=(6)/(6)=1$

So, P(n) is true for n = 1

Now, we suppose that P(n) is true for n = k.

$1+4+9+...................+k^2=(k(k+1)(2k+1))/(6)$

Now, we will show that P(n) is true for n = k+1.

So, it L.H.S. becomes,

$1+4+9+......................+(k+1)^2$

and R.H.S. becomes,

$((k+1)(k+2)(2k+3))/(6)$

Consider, L.H.S.,

$1+4+9+..+k^2+(k+1)^2\n\n=(k(k+1)(2k+1))/(6)+(k+1)^2\n\n=k+1[(k(2k+1))/(6)+(k+1)]\n\n=(k+1)[(2k^2+k+6k+6)/(6)]\n\n=(k+1)(2k^2+7k+6)/(6)]\n\n=(k+1)(2k^2+4k+3k+6)/(6)]\n\n=(k+1)[(2k(k+2)+3(k+2))/(6)]\n\n=((k+1)(2k+3)(k+2))/(6)$

So, L.H.S. = R.H.S.

Hence, P(n) is true for all integers n.

A ladder is leaning against the side of a 10 m house. If the base of the ladder is 3 m awayfrom the house, how long is the ladder? Please draw a diagram.

Answers

Answer: It depends on how you round but about 10.44 m.

Step-by-step explanation:

Determine the slope and y-intercept from the following equation

y = (32) x + 3

Answers

y intercept Y=3

I only know the y intercept have a good day

Slope is 32 and the y intercept is 3

What is the sign of the product (-5)(-3)(-8)(-6)? (5 points) Positive, because the products (-5)(-3) and (-8)(-6) are negative, and the product of two negative numbers is positive Positive, because the products (-5)(-3) and (-8)(-6) are positive, and the product of two positive numbers is positive Negative, because the products (-5)(-3) and (-8)(-6) are negative, and the product of two negative numbers is negative Negative, because the products (-5)(-3) and (-8)(-6) are positive, and the product of two positive numbers is negative

Answers

Answer: Choice B

Positive, because the products (-5)(-3) and (-8)(-6) are positive, and the product of two positive numbers is positive

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Explanation:

Recall we have these rules

positive times positive = positive
positive times negative = negative
negative times negative = positive

Here is one example for each rule

8*7 = 56
5*(-9) = -45
-2*(-4) = 8

So based on that, we know that (-5)(-3) is positive. The two negatives cancel each other out so to speak. The same goes for (-8)(-6). Then multiplying any two positive numbers produces another positive outcome.

Given tan(theta)= -2 and pi/2 < theta < pi; find cos theta)