expand and simplify (2t-3)^2

Answer: 1) Pizzeria must sell 78 pizzas for receiving the bonus.

2) The number of pizzas sold is decreased by Approximately 7.69 %.

Step-by-step explanation:

1) The number of pizza sold yesterday = 65,

The target for receiving the bonus = 20% more than the number of pizza sold yesterday

= 20% more than 65,

= 65 + 20% of 65    ( 1% = 0.01 ⇒ 20% = 0.2 )

= 65 + 0.2 × 65

= 65 + 13 = 78.

Hence, they must sell 78 pizzas for receiving the bonus.

2) If the actual number of pizza sold today = 60

⇒ Total reduction in the number of pizza = 65 - 60

= 5

Thus, the percentage decrease in the number of pizza

[tex]=\frac{\text{Total reduction}}{\text{The number of pizza sold yesterday}}\times 100[/tex]

[tex]=\frac{5}{65}\times 100[/tex]

[tex]=\frac{500}{65}=7.69230769\approx 7.69\%[/tex]

The recursive formula that represents the same geometric sequence as [tex]\( a_n = 3 \times 3^{n-1} \)[/tex] is option B: [tex]\( a_n = 3 \times a_{n-1} \).[/tex]

To find the recursive formula that represents the same geometric sequence as [tex]\( a_n = 3 \times 3^{n-1} \)[/tex], we need to find a recursive formula that generates the same sequence.

The formula [tex]\( a_n = 3 \times 3^{n-1} \)[/tex] can be rewritten as:

[tex]\[ a_n = 3 \times 3^{n-1} = 3 \times 3^n \times 3^{-1} = 3 \times \left(3 \times 3^{n-1}\right) \][/tex]

This indicates that each term is 3 times the previous term. So, the recursive formula should involve multiplying the previous term by 3.

Let's examine the options:

A. [tex]\( a_n = 9 \times a_{n-1} \)[/tex] - This represents multiplying the previous term by 9, not 3.

B. [tex]\( a_n = 3 \times a_{n-1} \)[/tex] - This represents multiplying the previous term by 3, which matches the original sequence.

C. [tex]\( a_n = 9 + a_{n-1} \)[/tex] - This represents adding 9 to the previous term, not multiplying it.

D. [tex]\( a_n = 3 + a_{n-1} \)[/tex] - This represents adding 3 to the previous term, not multiplying it.

Therefore, the recursive formula that represents the same geometric sequence as [tex]\( a_n = 3 \times 3^{n-1} \)[/tex] is option B: [tex]\( a_n = 3 \times a_{n-1} \).[/tex]

we have

[tex]x+y=11[/tex]

[tex]x=11-y[/tex] --------> equation A

[tex]4x^{2} -3y^{2}=8[/tex] ----> equation B

Substitute equation A in equation B

[tex]4(11-y)^{2} -3y^{2}=8[/tex]

therefore

the answer is the option B

[tex]4(11-y)^{2} -3y^{2}=8[/tex]

To solve this problem, we have to find the multiples of 3 and then find the probability of selecting them. The probability of having a multiple of 3 is 1/3.

The probability of tossing a six-sided dice and a eight-sided dice.

When we toss them together, the maximum value will be

[tex]6 * 8 = 48[/tex]

The multiplies of 3 will be

Data;

The probability of having a multiple of 3 will be

[tex]P(multiple of 3) = \frac{16}{48} = \frac{1}{3}[/tex]

The probability of having a multiple of 3 is 1/3

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Answer:

-17 - (-8)

Option 3 is correct.

Step-by-step explanation:

Phrase: "the difference between -17 and -8"

Expression: To write the phrase into algebraic form with a variable or constant.

Difference: write two number using subtraction between them.

"the difference between -17 and -8"

First number is -17 and second number is -8

Expression: -17 difference -8

Now using minus sign write as expression.

[tex]\Rightarrow -17-(-8)[/tex]

Hence, The correct expression is -17-(-8)

We are given that the slope is half the y-intercept and their sum is 1. Using these conditions we can solve for b and m (which represent y-intercept and slope) and we find that b=2/3 and m=1/3. Therefore, the equation of the line is y = 1/3x + 2/3.

The question is about finding the equation of a line from given conditions. We know that the equation of a line is typically written in the form y = mx + b, where m is the slope and b is the y-intercept. We are given two conditions: the slope is half the y-intercept, and their sum is 1.

Let's assume that the y-intercept is b and the slope is m. Now we can substitute the value of m from the first equation into the second. This gives us: b + b/2 = 1. Solving this, we get b = 2/3 and therefore, m = 1/3.

So, the equation of the line is y = 1/3x + 2/3.

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Answer:

The required equation is y + 3 = 4(x + 1)

Step-by-step explanation:

Since, the point slope form of a line passes through the point [tex](x_1, y_1)[/tex] having slope m is,

[tex]y-y_1 = m(x-x_1)[/tex]

Here,

[tex]x_1 = -1, y_1 = -3\text{ and }m = 4[/tex]

Hence, the equation of the line,

[tex]y+3 = 4(x+1)[/tex]

Or

[tex]y = 4(x+1) - 3[/tex]

The given expression V-15=-27 gives the value of v = -12.

Using operations like addition, subtraction, multiplication, and division, a mathematical expression is defined as a group of numerical variables and functions.

And we know that a mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The given expression is:

V-15=-27

To solve this equation:

Add 15 on both sides

v - 15 + 15 = - 27 + 15

v = -12

Hence,

The given expression gives the value of v = -12

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The simplified product of 3/7 multiplied by 14 is 6.

To multiply 3/7 by 14, you can follow these steps:

Multiply the numerators: 3 x 14 = 42.

Multiply the denominators: 7 x 1 = 7.

Therefore, the product of 3/7 multiplied by 14 is 42/7.

However, we can simplify this fraction further by dividing both the numerator and denominator by their greatest common divisor, which is 7.

= 42/7

= 6/1

= 6.

So, the simplified product of 3/7 multiplied by 14 is 6.

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