How do we do this problem 3(b3-5)

Answers

Answer 1

Answer: Well using the distributive property you get 3b3 - 15

Answer 2

Answer: 3(b3-5)
=3b3-15

hope this helps

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The total number of cookies needed for the bake sale is 812 dozen. Two of your friends will each bake 14 of the cookies. Your sister will bake 18 of the cookies. What fraction of the cookies do you need to bake?

Answers

Answer: $(28)/(51)$

Step-by-step explanation:

1 dozen = 12

Given, Total cookies needed = $8\frac12\ dozen = (17)/(2)\ dozen$

$=(17)/(2)* 12\n\n=102$

2 friends bake 14 cookies each, and your sister will bake 18.

So total cookies already assigned = 2 (14)+18

= 28 + 18 = 46

Remaining cookies you need to bake = 102 - 46 =56

Required Fraction = $\frac{\text{Number of cookies you bake}}{\text{Total}}=(56)/(102)=(28)/(51)$

Hence, fraction of the cookies you need to bake $=(28)/(51)$ .

Exercises
1. The sum of both numbers of a number is 14. On having exchanged the numbers of the tens with that of the units, the number increases in 18. It finds the original number.

2. The sum of two numbers is 21 and his difference is 5. ¿Which are the numbers?

Please I am grateful for them to him very much indeed ...:)

Answers

a)
Note that there are only two numbers that correspond complete wording of question: 59 and 68
It is easy to verify that the number found number is 68:

Look:
6 + 8 = 14 and
86 - 68 = 18

b)
Now you can solve one system:

x + y = 21
x - y = 5

Add both equations:

2x = 26
x = 13

So: y = 8

Prove that 2x^2+x+8>0 for all real values of x.

Answers

$y = 2x^2 + x + 8$ is a polynomial of even degree, with a positive $x^2$ coefficient, meaning that
- it will have exactly one turning point
- that turning point will be a minimum

So, if the y-coordinate of the turning point is positive, then this polynomial will be positive for all real values of x.

At a turning point, the gradient of y will be equal to 0. The gradient of y is given by
$\frac{\mathrm{d}y}{\mathrm{d}x} = 4x + 1$ .

To find the turning point, set this equal to 0 and solve for x:
$4x + 1 = 0 \implies x = -(1)/(4)$ .

Substituting this value into the equation gives
$y = 2(-(1)/(4))^2 + (-(1)/(4)) + 8 = (1)/(4) - (1)/(4) + 8 = 8 \ \textgreater \ 0$ .

Since the minimum point of the equation is greater than 0, the equation will be greater than 0 for all real values of x.

Which is equivalent to (4xy – 3z)2, and what type of special product is it?16x2y2 + 9z2, the difference of squares
16x2y2 + 9z2, a perfect square trinomial
16x2y2 – 24xyz + 9z2, the difference of squares
16x2y2 – 24xyz + 9z2, a perfect square trinomial

Answers

(4xy - 3z)²

(4xy - 3z)(4xy - 3z)
4xy(4xy - 3z) - 3z(4xy - 3z)
16x²y² - 12xyz -12xyz + 9z²

16x²y² - 24xyz + 9z², a perfect square trinomial.

The correct option is $\boxed{{\mathbf{Option D}}}$ .

Further explanation:

The binomial algebraic expression is an algebraic expression that consists two terms and it is separated by plus or minus.

Binomial expression can be mathematically expressed as,

$a + b$

The trinomial algebraic expression is an algebraic expression that consists three terms and it is separated by plus or minus.

Trinomial expression can be mathematically expressed as,

$a + b + c$

Here, $a,b{\text{ and }}c$ are the real numbers.

The square of the binomial $a + b$ can be written as,

${\left( {a + b} \right)^2} = \left( {a + b} \right)\left( {a + b} \right)$

Given:

The given algebraic expression is ${\left( {4xy - 3z} \right)^2}$ .

Step by step explanation:

Step 1:

The square of the binomial $a + b$ can be written as,

${\left( {a + b} \right)^2} = \left( {a + b} \right)\left( {a + b} \right)$

Similarly, the expression ${\left( {4xy - 3z} \right)^2}$ can be written as,

$\begin{aligned}{\left( {4xy - 3z} \right)^2} &= \left( {4xy - 3z} \right)\left( {4xy - 3z} \right) \n&= 4xy\left( {4xy - 3z} \right) - 3z\left( {4xy - 3z} \right) \n\end{aligned}$

Step 2:

The distributive property can be used to solve the square of the binomial.

The distributive property can be expressed as,

$a\left( {b + c} \right) = ab + ac$

Now apply the distributive property to solve the expression ${\left( {4xy - 3z} \right)^2}$ .

$\begin{aligned}{\left( {4xy - 3z} \right)^2} &= 4xy\left( {4xy - 3z} \right) - 3z\left( {4xy - 3z} \right) \n&= 16{x^2}{y^2} - 12xyz - 12xyz + 9{z^2} \n&= 16{x^2}{y^2} - 24xyz + 9{z^2} \n\end{aligned}$

Therefore, the expression $16{x^2}{y^2} - 24xyz + 9{z^2}$ is the perfect square of the binomial $\left( {4xy - 3z} \right)$ .

The expression $16{x^2}{y^2} - 24xyz + 9{z^2}$ is the trinomial.

Thus, option D a perfect square trinomial $16{x^2}{y^2} - 24xyz + 9{z^2}$ is correct.

Learn more:

Learn more about the function is graphed below brainly.com/question/9590016
Learn more about the symmetry for a function brainly.com/question/1286775
Learn more about midpoint of the segment brainly.com/question/3269852

Answer details:

Grade: Middle school

Subject: Mathematics

Chapter: Algebraic expression

Keywords: binomial, polynomial, algebraic expression, difference, product, trinomial, distributive property, equivalent, expression, terms, plus, separated, multiply, minus, addition

45 – 15 – 15 =
A. 15.
B. 0.
C. 1.
D. 30

Answers

The result of the expression 45 - 15 - 15 is 15.

(Option A).

What is the solution of the expression?

The solution of the linear expression is calculated as follows;

The given expression;

45 – 15 – 15 = ?

To solve the expression 45 - 15 - 15, we follow the order of operations, which dictates that we perform the subtraction operations from left to right.

First, we subtract 15 from 45:

45 - 15 = 30

Then, we subtract another 15 from the result of the previous operation:

30 - 15 = 15

Therefore, the result of the expression 45 - 15 - 15 is 15.

Therefore, the correct option is A. 15.

Learn more about expressions here: brainly.com/question/723406

#SPJ6

45 - 15 - 15 = 45 - 30

45 - 30 = (15)

Solve the following system of equations by the substitution method.8x = 2y + 5

3x = y + 7

What is the solution set?

{(-41/2, -9/2)}
{(-9/2, -41/2)}
Ø

Answers

8x = 2y + 5
3x = y + 7

We will use the second equation to substitute in the first one. Here's how to do it:
3x = y + 7
y = 3x - 7 (now substitute this in the first equation)

8x = 2y + 5
8x = 2(3x - 7) + 5
8x = 6x - 14 + 5
8x = 6x - 9
6x - 9 = 8x
6x - 8x = 9
-2x = 9
x = -9/2 (this is the first coordinate, now we need to find y)

We use the second equation again:
3x = y + 7
y + 7 = 3x
y + 7 = 3(-9/2)
y + 7 = -27/2
y = -27/2 - 7
y = -27/2 - 14/2
y = -41/2 (this is the second coordinate)

This means that the solution set is the second option: {(-9/2, -41/2)}

Answer:

{(-9/2, -41/2)}

Step-by-step explanation:

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