Expand the following: 6(x-4y)

I don't understand what I'm supposed to do here. I have a test on this tomorrow so if you explain how to do it that would be gre

VladimirAG [237]

Here is a little tip for this: The unit above cancels the unit below. So in this problem you are asked to convert pounds to ounce. So your equation will look like this.

ounce = 2.93 pounds $( \frac{16 ounces}{1 pounds} ) = 46.88$
Your ratio should involve the conversion factor. So 16 and 1 is involved canceling A and D. Then, Notice that you started with poubls. Then the ratio must have pounds at the bottom to cancel the units leaving ounces.

7 0

3 years ago

Heidi wants to make some biscuits using this recipe.

Andre45 [30]

The most cookies Heidy can make is 36 cookies.

<h3>How to calculate how many cookies can Heidy make?</h3>

To know how many cookies Heidy can make, you have to take into account the following information:

12 cookies need the following ingredients:

125g butter
200g flour
50g sugar

In the case in which Heidy has more ingredients, we must carry out the following operations:

Divide the quantities, in the reference quantity we have:

500g of butter ÷ 125g of butter = 4
700g flour ÷ 200g flour = 3.5
250g of sugar ÷ 50g of sugar = 5

According to the above, we must take into account the lowest value of all because if that ingredient is enough, we can infer that the rest of the ingredients also.

So the number of cookies Heidy can make are:

12 × 3.5 = 42

Learn more about ingredients in: brainly.com/question/26532763

7 0

3 years ago

A) The perimeter of a rectangle is the sum of the lengths of its four sides. Write an expression for the perimeter of the rectan

goblinko [34]

Answer:

Below

Step-by-step explanation:

The length of this triangle is 3x+1 and the width is x.

The perimeter P is:

P= 2(3x+1)+2*x

P= 6x+2+2x

P= 8x+2

Let's evaluate it when x=1/2

●1/2 =0.5

P= 8*0.5+2 =4+2= 6 ft

●●●●●●●●●●●●●●●●●●●●●●●●

The area A is:

A = (3x+1)*x

A= 3x^2 +x

Let's evaluate it when x=0.5 feet

A= 3*0.5^2 +0.5

A= 3*0.25+0.5

A= 0.75 +0.5

A= 1.25 ft^2

6 0

3 years ago

How can you use number patterns to find the least common factor

Aleks04 [339]

Answer:

The correct answer is: 360.

Explanation:

First we can express 120 as follows:

2 * 2 * 2 * 3 * 5 = 120

You can get the above multiples as follows:

120/2 = 60

60/2 =30

30/2 = 15

15/3 = 5 (Since 15 cannot be divisible by 2, so we move to the next number)

5/5 = 1

Take all the terms in the denominator for 120, you would get: 2 * 2 * 2 * 3 * 5 --- (1)

Second we can express 360 as follows:

360/2 = 180

180/2 = 90

90/2 =45

45/3 = 15 (Since 45 cannot be divisible by 2, so we move to the next number)

15/3 = 5

5/5 = 1

Take all the terms in the denominator for 360, you would get: 2 * 2 * 2 * 3 * 3 * 5 --- (2)

Now in (1) and (2) consider the common terms once and multiple that with the remaining:

2*2*2*3*5 = Common between the two

3 = Remaining

Hence (2*2*2*3*5) * (3) = 360 = LCM (answer)

5 0

3 years ago

Solve for x 0=3x^2+3x+7

Aloiza [94]

Answer:

x =(3-√-75)/-6=1/-2+5i/6√ 3 = -0.5000-1.4434i

x =(3+√-75)/-6=1/-2-5i/6√ 3 = -0.5000+1.4434i

Step-by-step explanation:

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

0-(3*x^2+3*x+7)=0

Step by step solution:

Step 1:

Equation at the end of step 1 :

0 - (( $-3x^{2}$ + 3x) + 7) = 0

Pulling out like terms:

2.1 Pull out like factors:

$-3x^{2}$ - 3x - 7 = -1 • ( $3x^{2}$ + 3x + 7)

Trying to factor by splitting the middle term

2.2 Factoring $3x^{2}$ + 3x + 7

The first term is, $3x^{2}$ its coefficient is 3 .

The middle term is, +3x its coefficient is 3 .

The last term, "the constant", is +7

Step-1 : Multiply the coefficient of the first term by the constant 3 • 7 = 21

Step-2 : Find two factors of 21 whose sum equals the coefficient of the middle term, which is 3 .

-21 + -1 = -22

-7 + -3 = -10

-3 + -7 = -10

-1 + -21 = -22

1 + 21 = 22

3 + 7 = 10

7 + 3 = 10

21 + 1 = 22

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Equation at the end of step 3 :

$-3x^{2}$ - 3x - 7 = 0

Parabola, Finding the Vertex:

3.1 Find the Vertex of y = $-3x^{2}$ -3x-7

For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is -0.5000

Plugging into the parabola formula -0.5000 for x we can calculate the y -coordinate :

y = -3.0 * -0.50 * -0.50 - 3.0 * -0.50 - 7.0

or y = -6.250

Parabola, Graphing Vertex and X-Intercepts :

Root plot for : y = $-3x^{2}$ -3x-7

Axis of Symmetry (dashed) {x}={-0.50}

Vertex at {x,y} = {-0.50,-6.25}

Function has no real roots

Solve Quadratic Equation by Completing The Square

3.2 Solving $-3x^{2}$ -3x-7 = 0 by Completing The Square .

Multiply both sides of the equation by (-1) to obtain positive coefficient for the first term:

$3x^{2}$ +3x+7 = 0 Divide both sides of the equation by 3 to have 1 as the coefficient of the first term :

$x^{2}$ +x+(7/3) = 0

Subtract 7/3 from both side of the equation :

$x^{2}$ +x = -7/3

Now the clever bit: Take the coefficient of x , which is 1 , divide by two, giving 1/2 , and finally square it giving 1/4

Add 1/4 to both sides of the equation :

On the right hand side we have :

-7/3 + 1/4 The common denominator of the two fractions is 12 Adding (-28/12)+(3/12) gives -25/12

So adding to both sides we finally get :

$x^{2}$ +x+(1/4) = -25/12

Adding 1/4 has completed the left hand side into a perfect square :

$x^{2}$ +x+(1/4) =

(x+(1/2)) • (x+(1/2)) =

(x+(1/2))2

Things which are equal to the same thing are also equal to one another. Since

$x^{2}$ +x+(1/4) = -25/12 and

$x^{2}$ +x+(1/4) = (x+(1/2))2

then, according to the law of transitivity,

(x+(1/2))2 = -25/12

We'll refer to this Equation as Eq. #3.2.1

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of

(x+(1/2))2 is

(x+(1/2))2/2 =

(x+(1/2))1 =

x+(1/2)

Now, applying the Square Root Principle to Eq. #4.2.1 we get:

x+(1/2) = √ -25/12

Subtract 1/2 from both sides to obtain:

x = -1/2 + √ -25/12

√ 3 , rounded to 4 decimal digits, is 1.7321

So now we are looking at:

x = ( 3 ± 5 • 1.732 i ) / -6

Two imaginary solutions :

x =(3+√-75)/-6=1/-2-5i/6√ 3 = -0.5000+1.4434i

or:

x =(3-√-75)/-6=1/-2+5i/6√ 3 = -0.5000-1.4434i

6 0

3 years ago