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3 years ago

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Eorge and Maria decided to create a garden in their backyard. George works on the garden every third day and Maria works on the

garden every fourth day. If they worked on the garden today, the number of days until they work on the same day again would be .

1 answer:

Nikitich [7]3 years ago

7 0

Alright, lets get started.

Given that George is working in garden on each 3rd day.

Maria is working in garden on each 4th day.

Then they will not work together on days that are common multiples of 3 and 4.

The least common multiple of 3 and 4 is 12.

Means they will work together after 12 days from today. : Answer

Hope it will help :)

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To find out how fast a tree grows, you can measure its trunk. A giant red oak's diameter was 248 inches in 1965. The tree's diam

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Any times you see the phrase: "Rate of Change", or even sometimes just the word "Rate" think slope.

The word slope is just a fancy word that means the rate of change.

Rate of Change is just a fancy phrase meaning how much does something change over some amount of time.
So in this case our rate of change will have the units of inches per year.

Let's get to the problem at hand!
We'll need to find slope / the rate of change (the two are interchangeable with each other).
Let's go over the formula for slope:

m = (y2 - y1) / (x2 - x1)

First we will need to label each of the "coordinated points (the two numbers that go together in a pair)" with either (x1,y1) or (x2,y2).

A Giant Red Oak's diameter in 1965 was 248 inches. Keep in mind time is ALWAYS going to be X in rate of change problems (and most all problems for that matter).

(1965,248)
(X1,Y2)

(2005,251)
(X2,Y2)

Plug in the values into the equation!
m = (y2 - y1) / (x2 - x1)
m = (251 - 248) / (2005 - 1965)
m = (3) / (40)

Type that into a calculator to get a decimal value over 1.
m = 0.075 inches per 1 year.
Or...

m = 0.075in / 1 year

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B. If square-foot is on the x-axis then we can substitute for x in the equation and solve, and when we do, we get 2473.302 which is is B when rounded.

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Alinara [238K]

Answer:

a. Not Divisible

b. Divisible

c. Divisible

d. Divisible

e. Divisible

Step-by-step explanation:

To find the divisibility we need to follow the PEMDAS rule and check if the total value can be divided by the selected numbers without returning a remainder.

Let's begin with a:

$16^{5}+215$ by 33

$1,048,576 + 215$

$1,048,791$

We now then divide the total amount with 33.

$\dfrac{1,048,576}{33}$

= 31,781.5454

We can see that the value has a decimal point indicating that the total value divided by 33 will return a remainder. So it is NOT Divisible by 33.

Now let's continue on with the others.

$51^{7}-51^{6}$ by 25

$897,410,677,851 - 17,596,287,801$

$879,814,390,050$

We now then divide the total amount with 25.

$\dfrac{879,814,390,050}{25}$

= 35,192,575,602

The total value did NOT return a decimal point, therefore making the equation true. $51^{7}-51^{6}$ IS divisible by 25.

Next on we have:

$5^{5}-5^{4} +5^{3}$ by 7

$3,125 - 625 + 125$

As we know in the PEMDAS rule, that addition comes first. In this situation we have to read the equation from left to right and solve which ever comes first.

$2,500 + 125$

$2,625$

We now then divide the total amount with 7.

$\dfrac{2,625}{7}$

= 375

The total value did NOT return a decimal point, therefore making the equation true. $5^{5}-5^{4} +5^{3}$ IS divisible by 7.

$7^6+7^5-7^4$ by 11

$117,649+16,807-2,401$

$134,456-2,401$

$132,055$

We now then divide the total amount with 11.

$\dfrac{132,055}{11}$

= 12,005

The total value did NOT return a decimal point, therefore making the equation true. $7^6+7^5-7^4$ IS divisible by 11.

Last but not the least:

$5^{23}-5^{21}$ by 24

$11,920,928,955,078,125-476,837,158,203,125$

$11,444,091,796,875,000$

We now then divide the total amount with 24.

$\dfrac{11,444,091,796,875,000}{24}$

= 476,837,158,203,125

The total value did NOT return a decimal point, therefore making the equation true. $5^{23}-5^{21}$ IS divisible by 24.

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3 years ago

Determine if the graph is a function then state the domain and range.

nignag [31]

<h3><u>Explanation</u></h3>

A function is a set of relation that doesn't have repetitive domain. If we want to know if a graph is function or not, we have to do the line test.

<u>Line</u><u> </u><u>Test</u>

Draw a vertical line. Make sure that a line passes through a graph.
See if a line intercepts a graph more than one point or just only one.

<u>Result</u>

If a line intercepts a graph more than one point, it is not a function.

However, if a line only intercepts a graph just one point, it is indeed a function.

The given graph from the question is a function because it passes line test.

<u>Domain</u><u> </u><u>and</u><u> </u><u>Range</u>

Domain is the set of all x-values, meaning we only focus on x-axis or x-value only.

Range is the set of all y-values. We only focus on y-value or y-axis for Range.

<u>Determine</u><u> </u><u>Domain</u><u> </u><u>from</u><u> </u><u>Graph</u>

We can simply say that the domain is from starting domain or x-coordinate point to end x-coordinate point. For example, if a graph starts at x = -4 and ends at x = 2, we can say that - 4<=x=2.

<u>Determine</u><u> </u><u>Range</u><u> </u><u>from</u><u> </u><u>Graph</u>

Similar to Domain except Range starts from the minimum value or point to the maximum point or value. For example if a graph starts at min point = 6 and max point = 9. We can say that 6<=y<=9.

From the graph, the domain starts from negative infinity to positive infinity. Meaning that x can be any numbers. Hence, the domain is set of all real numbers. For range, the minimum value is 0 and max value is positive infinity. Therefore we write y>=0.

<h3><u>Answer</u></h3>

<u> $\begin{cases} x \in \mathbb{R} \\ y \geqslant 0 \end{cases}$ </u>

<u>Domain</u><u> </u><u>is</u><u> </u><u>set</u><u> </u><u>of</u><u> </u><u>all</u><u> </u><u>real</u><u> </u><u>numbers</u><u>.</u>

<u>Range</u><u> </u><u>is</u><u> </u><u>greater</u><u> </u><u>or</u><u> </u><u>equal</u><u> </u><u>to</u><u> </u><u>0</u><u>.</u>

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pychu [463]

Answer:

Step-by-step explanation:

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3 years ago

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