Between what pair of numbers is the product of 289 and 7

The Morgan family just bought 6 crates of eggs, and each crate had 12 eggs. The family already had 9 eggs in their refrigerator.

MariettaO [177]

Answer:

81

Explanation:

Morgan's family bought 6 cartons of eggs, each having 12 eggs in them. So, 6*12=72

Then, you would add 9 the answer you just got: 72+9=81

Making 81

3 0

3 years ago

Point A is located at (4, 7). It will be translated 5 units right and 3 units down. Write the rule and give the location of poin

Anarel [89]

Answer:

The rule of translation is $A(x',y') = A(x,y) + (5,-3)$ .

The translated vector is $A(x',y') = (9, 4)$ .

Step-by-step explanation:

Let supposed that translation to the right is in the +x direction and translation downwards in the -y direction.

We procced to translate the operation into mathematic terms. A translation consists in a vectorial sum on a given vector. That is:

$A(x',y') = A(x,y) + U(x,y)$ (Eq. 1)

Where:

$A(x,y)$ - Original vector, dimensionless.

$U(x,y)$ - Translation vector, dimensionless.

$A(x',y')$ - Translated vector, dimensionless.

If we know that $U(x, y) = (5, -3)$ , then the rule of translation is described by:

$A(x',y') = A(x,y) + (5,-3)$ (Eq. 2)

If $A(x, y) = (4,7)$ , then the new location of A is:

$A(x',y') = (4,7)+(5,-3)$

$A(x',y') = (9, 4)$

The translated vector is $A(x',y') = (9, 4)$ .

4 0

4 years ago

Which is the first step needed to solve by substitution?

fredd [130]

$\begin{gathered} -x+y=-1 \\ 2x-y=3 \end{gathered}$

To solve the given system of equations for substitution you:

1. Solve in one of the equations a variable.

For the given options the one that is correct is solve the first equation for y, by adding x to both sides:

$\begin{gathered} -x+x+y=-1+x \\ y=-1+x \end{gathered}$

4 0

2 years ago

What is the difference? 2x7 - 8x7

kakasveta [241]

The answer is -42.

Hope it helps.

7 0

4 years ago

Read 2 more answers

<img src="https://tex.z-dn.net/?f=f%28x%29%3D%281-0.08%29%5E%7B%5Cfrac%7B1%7D%7B12%7D%20%7D%20%5E%7B%2812t%29%7D" id="TexFormula

oksano4ka [1.4K]

Answer:

See Below.

Step-by-step explanation:

We have:

$\displaystyle f(x)=(1-0.08)^{\frac{1}{12}(12t)}$

First, we can subtract within the parentheses:

$f(x)=(0.92)^{\frac{1}{12}(12t)}$

By the properties of exponents:

$f(x)=((0.92)^\frac{1}{12})^{12t}$

Approximate. Use a calculator:

$f(x)\approx (0.993)^{12t}$

Notes:

0.993 is only an approximation, hence the approximately equal sign.

I'm not given the context of the problem, but it's simpler to just simplify in the exponent like so (the fractions cancel):

$\displaystyle f(x)=(1-0.08)^{\frac{1}{12}(12t)}=(0.92)^t$

Full Problem:

The value of Sara's car decreases at a rate of 8% per year.

We will use the exponential decay formula with a set time, given by:

$f(x)=a(r)^{x/d}$

Where a is the initial value, r is the rate, x is the time that has passed (dependent on d), and d is the amount of time for one decrease.

For this problem, we can ignore the initial value.

And since the value decreases at a rate of 8% per year, r = 0.92 (we acquire this from 1 - 0.08).

Part 1) Per Month:

Since it decreases per month, d = 12.

$f(x)=(0.92)^{x/12}$

Approximate:

$f(x)=((0.92)^{1/12})^x\approx(.993)^x$

In this case, x is measured in months.

Part 2) Per Week:

Since it decreases per week, d = 52.

$f(x)=(0.92)^{x/52}$

Approximate:

$f(x)=((0.92)^1/52)^x\approx (.998)^x$

In this case, x is measured in weeks.

Part 3) Per Day:

So, d = 365.

$f(x)=(0.92)^{x/365}$

Simplify:

$f(x)=((0.92)^{1/365})^x\approx(.999)^x$

In this case, x is measured in days.

Part 4)

So, as d increases, our r increases as well.

Therefore, the smaller the time interval (from months to weeks to days), the higher our rate of decrease is.

8 0

3 years ago