Marty has saved $72. He spent $8 on a video rental. Write a ratio as a fraction in simplest form to represent what portion of his savings he has left.

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]

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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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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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]

Answer: The answer is (A) -5.

Step-by-step explanation:  We are given to find the element [tex]a_{23}[/tex] in the following matrix:

[tex]A=\begin{bmatrix}8 & -4 & -3\\ 3 & -9 & -5\\ -8 & 8 & 8\end{bmatrix}[/tex]

We know that [tex]a_{mn}[/tex] is an element of a matrix present in the m-th row and n-th column.

So, [tex]a_{23}[/tex]  will be the element present in the second row and third column.

Since the element in the second row and third column is - 5, so we have

[tex]a_{23}=-5.[/tex]

Thus, (A) -5 is the correct option.

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)

In the given two column proof two sides and included angles are equal.

Triangles are congruent if any pair of corresponding sides and their included angles are equal in both triangles .In the figure sides BD≅BD , AB≅ BC and <ABD ≅,BDD Therefore triangle ABD and triangle CBD are congruent by SAS property of congruence.

The correct  option for missing statement is D. ΔABD ≅ ΔCBD .

Answer:

ΔABD ≅ ΔCBD

Step-by-step explanation:

Guys this is the right answer,  ΔABD ≅ ΔCBD. I got it right on my test!

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]

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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