The graph of the quadratic parent function is reflected across the x-axis, then shifted 5 units down and 4 units right. Write the equation of the new function in vertex form.
Answers
Answer:
y = -(x -4)² -5
Step-by-step explanation:
-f(x) is a reflection of f(x) across the x-axis.
f(x) -5 is a translation down by 5 units.
f(x -4) is a translation right by 4 units.
Applying these transformations to y = x² gives, successively, ...
y = -x²
y = -x² -5
y = -(x -4)² -5 . . . . . . the new equation in vertex form
This is about reflection of graphs.
y = -(x - 4)² + 5
We are told the graph is that of the quadratic parent function. Now, in transformations of quadratic functions, the parent function of the quadratic group is usually expressed as;
y = x²
- Now, we are told that this quadratic parent function is reflected across the x-axis. This means the value of the y-coordinate will become negative and we have;
-y = x²
- It is now shifted 5 units down. This means we will now have;
-y = x² - 5
- It is now shifted 4 units down. This means we now have;
-y = (x - 4)² - 5
Dividing through by -1 to get;
y = -(x - 4)² + 5
Read more at; brainly.com/question/19333139
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When adding and subtracting fractions
of the remaining children get off, leaving the bus only half full.
How many children were on the bus at the start?
Answers
Answer:
12
Step-by-step explanation:
If there are x children on the bus at the start, after the first stop, there are (x-3) remaining. After two stops, the number on the bus is ...
x/2 = x -3 -(1/3)(x -3)
Multiplying by 6, we have ...
3x = 6x -18 -2(x -3)
3x = 4x -12 . . . . simplify
12 = x . . . . . . . . add 12-3x
There were 12 children on the bus at the start.
_____
Check
After 3 got off at the first stop, there were 12-3 = 9 remaining. 1/3 of those, or 9/3=3 got off at the second stop, so 9 -3 = 6 remained. This is half the original number, as required.
Final answer:
Let X represent the number of children on the bus originally. The equation formed is 2/3*(X - 3) = X/2, and when we solve it, we find that X equals 12 which indicates that there were 12 children on the bus at the start.
Explanation:
Let's denote the number of children on the bus at the start as X. After the first stop, the number of children on the bus became X - 3, because 3 children got off. After the second stop, a third of the remaining children got off, so the number of children on the bus became 2/3*(X - 3). According to the problem, after all the stops, the bus was half full. Therefore, we can set up an equation: 2/3*(X - 3) = X/2.
To solve the equation, we can multiply all terms by 6 to clear out the fractions and obtain the equation: 4*(X - 3) = 3X. This simplifies to 4X - 12 = 3X which simplifies further to X = 12, meaning there were initially 12 children on the bus.
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Answers
Donnell practiced for 7 hours while Marcus practices the piano for 4 hours.
How to form an equation?
Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
In other words, an equation is a set of variables that are constrained through a situation or case.
Let's say the number of hours piano played by Donnell is D while by Marcus is M.
Then,
Since Donnell practiced the piano 3 hours longer than Marcus.
D = 3 + M ⇒ D - M = 3
And,
Together, Marcus and Donnelly practiced the piano for 11 hours.
D + M = 11
By adding
2D = 14
D = 7
And,
M = 11 - 7 = 4
Hence "Donnell practiced for 7 hours while Marcus practices the piano for 4 hours".
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and the number of hours Marcus practiced be m.
We can set up a system of equations.
d = m + 3
m + d = 11
Substitute the value of d that's in the first equation, into the second equation.
m + (m + 3) = 11
2m + 3 = 11
2m = 8
m = 4
Marcus practiced for 4 hours. Since Marcus and Donnell, together, practiced 11 hours, Donnell practiced for 11-4=7 hours.
Answers
+5684
9999 So 5684 is the greatest number you can write.
Final answer:
The greatest number that can be added to 4315 without having to regroup is 5644. When added together, the sum doesn't result in a carryover to the next place value.
Explanation:
In Mathematics, particularly arithmetic, regrouping is the process of making groups of tens when adding or subtracting two numbers. When the question asks for the greatest number that can be added to 4315 without having to regroup, we are essentially looking for a number that when added to 4315 doesn't result in a carryover to the next place value.
Considering the number 4315, you would notice that the units digit is 5, the tens digit is 1, the hundreds digit is 3, and the thousands digit is 4. This means for each position we can add a number up to 9 without needing to regroup. Hence, the greatest number you can add to 4315 without needing to regroup would be 5644 (which gives 9 in the units place, 1+5=6 in the tens place, 3+4=7 in the hundreds place, and 4+4=8 in the thousands place).
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Answers
Answer:
Hi,
Step-by-step explanation:
Answers
Answer:
irrational
Step-by-step explanation:
√2 is irrational
Answer:
It would be and irrational number!
Answers
Number 12 have factors 12 = ( 1,2,3,4,6,12)
Number 18 have factors 18= ( 1,2,3,6,9,18 )
According to this we can conlude that numbers 12 and 18 have in common (1,2,3 and 6).
Good luck!!!
2 and 6 can go into it evenly