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2 years ago

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Bert and Ernie are looking at their paper clip collections. Bert has 5 paper clips for every 3 paper clips that Ernie has. If Be

rt gives Ernie 12 paper clips, they will have the same number of paper clips. How many paper clips did Bert have before he gave away any to Ernie?.

1 answer:

iVinArrow [24]2 years ago

4 0

Answer:

He has 60 paper clips before giving some away.

Step-by-step explanation:

Before : 5x : 3x

After: 5x - 12 = 3x + 12

5x - 12 = 3x + 12

First, we need to take away the smallest value of x from the largest.

-3x

2x - 12 = 12

Then, we need to add +12 to get rid of -12 on the lefthand side.

2x = 24

Divide by 2 to get x on its own.

x = 12

Bert had 5x so we need to multiply x (what we found as 12) by 5. 12 x 5 = 60. Bert had 60 paper clips before he gave some away.

We can prove this answer as correct, too.

5 x 12 = 60

3 x 12 = 36

60 - 12 = 36 + 12

48 = 48

Hope this helps, have a good day. :D

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Write the converse of the conditional statement. Determine whether the converse is true or false. If it is false, find a counter

Bumek [7]

Answer:

a. is True.

Step-by-step explanation:

Collinear points are on the same line.

The converse is:

If the points are on the same line the the points are collinear. This is True.

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3 years ago

Select all number combinations that COULD make a triangle

tester [92]

Answer:

2 cm, 9 cm, 10 cm

Step-by-step explanation:

To know if a combination is a triangle all you have to do is see if the combinations add up to 180

(2)(9)(10)=180 therefore it is a triangle.

All the other angles do not add up to 180 so they can't be triangles!!

(4)(10)(3) =120

(5)(6)(11) =330

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3 years ago

Helppp!! I NEED HELP PLEASE

Elodia [21]

Given:

The table of values for the function f(x).

To find:

The values $f^{-1}(f(3.14))$ and $f(f(-7))$ .

Solution:

From the given table, it is clear that the function f(x) is defined as:

$f(x)=\{(-14,11),(-7,-12),(-12,-5),(9,1),(10,-2),(-2,13)\}$

We know that if (a,b) is in the function f(x), then (b,a) must be in the function $f^{-1}(x)$ . So, the inverse function is defined as:

$f^{-1}(x)=\{(11,-14),(-12,-7),(-5,-12),(1,9),(-2,10),(13,-2)\}$

And,

$f^{-1}(f(a))=f^{1}(b)$

$f^{-1}(f(a))=a$ ...(i)

Using (i), we get

$f^{-1}(f(3.14))=3.14$

Now,

$f(f(-7))=f(-12)$

$f(f(-7))=5$

Therefore, the required values are $f^{-1}(f(3.14))=3.14$ and $f(f(-7))=5$ .

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3 years ago

What are the factors of 2x + 3x - 54? Select two options

tiny-mole [99]

Answer:

The answer: The factors are (2x-9) and (x+6).

The Problem:

Factor $2x^2+3x-54$

Step-by-step explanation:

So I'm going to do trial factors using the choices to aid me.

Factored form for this problem if it exist will be in the form:

$(mx+n)(kx+p)$ .

In general this is what it would look like if we factored any quadratic in terms of $x$ (given the quadratic is not prime but technically you could factor even over the complex numbers).

Let's look at:

$(mx+n)(kx+p)$

We want to choose $k \text{ and } m$ such that when you multiply them you get 2. Well those would have to be 2 and 1.

$(2x+n)(x+p)$

we want to choose $n \text{ and } p$ such that when you multiply them you get -54. Based on the choices we want to get with -9 and 6, or 9 and -6. We don't know the order we want to choose it in either.

For example which of these would work:

$(2x-6)(x+9)$

$(2x+6)(x-9)$

$(2x-9)(x+6)$

$(2x+9)(x-6)$

We are going to consider only the outer and inner of FOIL since we already know the first times the first is $2x^2$ and the last times the last is $-54$ .

Let's test the first one:

$(2x-6)(x+9)$

Outer: 2x(9)=18x

Inner: -6(x)=-6x

------------------------ADD!

18x-6x=12x

The first choice did not give us the middle term 3x.

Trying the second one would give us the opposite since they are in the same form as previous just the + and - are switched.

Let's look at the third one:

$(2x-9)(x+6)$

Outer: 2x(6)=12x

Inner: -9(x)=-9x

--------------------------ADD!

12x-9x=3x

This is the winner.

The answer: The factors are (2x-9) and (x+6).

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3 years ago

Read 2 more answers

A carpenter cut out a small trapezoid as a wooden support for the front step. it has an altitude of 4 inches. One base of the tr

docker41 [41]

Area of wooden support is 36 square inches

<em><u>Solution:</u></em>

Given that, carpenter cut out a small trapezoid as a wooden support for the front step

<em><u>The area of trapezoid is given as:</u></em>

$area = \frac{a+b}{2} \times h$

Where, "h" is the height

"a" and 'b" are the length of base

Here given that,

Height = h = 4 inches

a = 6 inches

b = 12 inches

Substituting the values we get,

$area = \frac{6+12}{2} \times 4\\\\area = 18 \times 2\\\\area = 36$

Thus area of wooden support is 36 square inches

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4 years ago