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3 years ago

Need help writing a quadratic equation from a function given the graph, screenshot posted of the question

Mathematics

1 answer:

Maslowich3 years ago

6 0

Hello from MrBillDoesMath!

Answer: g(x) = (x+3) ^2 + 3

Discussion:

First, the graph looks like the parabola y = x^2 BUT its smallest y-value is +3. That suggests the equation g(x) = x^2 + 3 BUT the parabola is shifted 3 units to the left. This suggest we take our last guess (x^2 +3) and shift it 3 units to the left, giving g(x) = (x+3)^2 + 3

Note that g(-3) = (-3 +3)^2 + 3 = 3

Regards, MrB

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Nachelle is 1.45 meters tall. At 11 a.m., she measures the length of a tree's shadow to be 23.05 meters. She stands 18.9 meters

GREYUIT [131]

Step-by-step explanation:

this creates 2 similar triangles.

that means all angles are the same. and all the side lengths of one triangle correlate to the corresponding side lengths of the other triangle by the same multiplication factor.

her shadow is 23.05 - 18.9 = 4.15 m long.

the factor between the shadow lengths is then

4.15 × f = 23.05

f = 23.05 / 4.15 = 5.554216867...

the same factor now applies to the relation of the heights :

1.45 × 5.554216867... = 8.053614458... m

rounded the tree is 8.05 m tall.

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2 years ago

Lelani has 64 baseball cards. This is 4 times as many baseball cards as Paul has. How many baseball cards does Paul have?

NemiM [27]

Answer:

Step-by-step explanation:

64 divided by 4 is 16. Paul has 16 baseball cards.

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2 years ago

Read 2 more answers

Which of these systems of equations shows the solution for the graph?

I am Lyosha [343]

Answer:

Step-by-step explanation:

Note that one of the lines is simply y=-1 for any x, so we can dismiss the only answer without y=-1. That rejected answer is A)

Now let's notice, that the other line is decreasing y when increasing x. That tells us that in the equation y = ax + b, a has to be negative. This brings us to reject option D).

What is the y of that line for x = 0? Because y = ax + b, for x = 0 we will get the value of b. This is called the intercept. The line is at y=4 for x=0, so we know that the b in the equation must be positive 4. This fits answer C, but rejects answer B). And so, we have found that C) is the only possible answer.

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3 years ago

Some people think it is unlucky if the 13th day of a month falls on a Friday. Show that in every calendar year (non leap or leap

MakcuM [25]

We will set a variable, d, to represent the day of the week that January starts on. For instance, if it started on Monday, d + 1 would be Tuesday, d + 2 would be Wednesday, etc. up to d + 6 to represent the last day of the week (in our example, Sunday). The next week would start over at d, and the month would continue. For non-leap years:
If January starts on d, February will start 31 days later. Following our pattern above, this will put it at d + 3 (28 days would be back at d; 29 would be d+1, 30 would be d+2, and 31 is at d+3). In a non-leap year, February has 28 days, so March will start at d+3 also. April will start 31 days after that, so that puts us at d+3+3=d+6. May starts 30 days after that, so d+6+2=d+8. However, since we only have 7 days in the week, this is actually back to d+1. June starts 31 days after that, so d+1+3=d+4. July starts 30 days after that, so d+4+2=d+6. August starts 31 days after that, so d+6+3=d+9, but again, we only have 7 days in our week, so this is d+2. September starts 31 days after that, so d+2+3=d+5. October starts 30 days after that, so d+5+2=d+7, which is just d. November starts 31 days after that, so d+3. December starts 30 days after that, so d+5. Remember that each one of these expressions represents a day of the week. Going back through the list (in numerical order, and listing duplicates), we have d, d, d+1, d+2, d+3, d+3, d+3, d+4, d+5, d+5, d+6 and d+6. This means we have every day of the week covered, therefore there is a Friday the 13th at least once a year (if every day of the week can begin a month, then every day of the week can happy for any number in the month).
For leap years, every month after February would change, so we have (in the order of the months) d, d+3, d+4, d, d+2, d+5, d, d+3, d+6, d+1, d+4, and d+6. We still have every day of the week represented, so there is a Friday the 13th at least once. Additionally, none of the days of the week appear more than 3 times, so there is never a year with more than 3 Friday the 13ths.

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3 years ago

4) The triangle on the right is an equilateral Find the value of X and Y

ozzi

Answer:

angle Y is 29 degrees

angle X is 120 degrees

Step-by-step explanation:

Well, if the triangle is an equilateral, then all the angles are equal to

60 degrees

that means the the angle at the top point is 60+31 = 91 degrees

the right point is 60 degrees

every triangle has 180 degrees total

180 - (91+60) = 29 degrees

NOW FORGET ABOUT THE EQUILATERAL FOR A BIT

180 = 31+x+29

simplify

180 = 60+x

subtract 60 from both sides

120 = x

7 0

3 years ago