Please help!!
A ball is thrown straight up from a height of 3 ft with a speed of 32 ft/s. Its height above the ground after x seconds is given by the quadratic function y = -16x^2 + 32x + 3. Explain the steps you would use to determine the path of the ball in terms of a transformation of the graph of y = x^2.
Answers
y = -16x² + 32x + 3
Write the equation in the standard form for a parabola.
y = -16[x² - 2x] + 3
= -16[(x-1)² - 1] + 3
= -16(x-1)² + 16 + 3
y = -16(x-1)² + 19
This equation shows that the parabola is downward, has its vertex at (1,19), and has its axis of symmetry at x = 1.
A plot of the graph is shown below.
Transformations of y = x².
The equation for the parabola can be obtained from y = x² in the following steps:
1. Shift right by 1 to obtain y = (x-1)².
2. Dilate by -16 to obtain y = -16(x-1)².
3. Shift up by 19 to obtain y = -16(x-1)² + 19.
Answer:
-4
16
2
16
Step-by-step explanation:
got it right.
Related Questions
how to find the factor of a trinomial?
Answers
Factor 3x^2 - 4x - 15
first multiply the first number by the last That is 3 * -15 = -45
Now we need to find 2 factors of -45 which will when added give - 4 ( the coefficient of x)
-9 and = 5 look like the ones so we write
3x^2 - 9x + 5x - 15
Now factor this by grouping:-
= 3x(x - 3) + 5(x - 3)
x - 3 is common to the 2 parts so we have:-
(3x + 5)(x - 3) <-------- These are your factors
Any trinomial can be factored in this way.
18 POINTS PLUS BRAINLIEST FOR CORRECT ANSWER
Find the equation of the line perpendicular to y=−2 that passes through the point (4, −2).
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Anything perpendicular to this horizontal line will be a vertical line. All vertical lines are of the form x = k where k is some fixed value.
In this case, the answer is x = 4 because want the vertical line to go through (4,-2). In other words, we want all points on the vertical line to have x coordinate of 4.
Side Note: the slope of y = -2 is 0 while the slope of x = 4 is undefined.
if you cross multiply 10 over 2.4=15 over x
Answers
IOx = 36
x = 3.6
This may make me look dumb but idk what to do. I need answers please
Answers
Angle 2: 90 degrees - It is a right angle
Angle 4: 36 degrees (explained above)
Angle 5: 90 degrees - It is a right angle. It is also an opposite angle to angle 2, and is therefore equal to it.
Since the two diagonal lines are parallel, the angles will relate to each other.
Angle 7: 126 - It will be 180 - angle 10 (because a straight line = 180)
Angle 8: 54 - It is opposite to angle 10, and is therefore equal
Angle 9: 126 - It will be 180 - angle 8 (because a straight line = 180). It is also an opposite angle 7, and is therefore equal
Angle 10: You already figured this one out! :)
Angle 11: 36 degrees - A triangle is 180, and angles 11, 5, and 8 all make up a triangle. Therefore, 180 - angle 5 - angle 8 = angle 11
Angle 12: 144 degrees - It will be 180 - angle 13 (because a straight line = 180).
Angle 13: 36 degrees - it is opposite to angle 11, and is therefore equal
Angle 14: 144 degrees - it is opposite to angle 12, and is therefore equal
I hope this helps!
i don't understand what i'm supposed to do i wrote down the given but what's next i don't understand geometry
Answers
notice the tickmarks, is a given, that those sides are congruent.
now, look at the side at the bottom, the BC side, is really shared by both triangles, and therefore, the same length for both. Meaning we might as well put a tickmark on that one too.
so the triangles are congruent because all sides are equal on each, that is [tex]\bf \boxed{S}ide\qquad \boxed{S}ide\qquad \boxed{S}ide[/tex]
What is the equation of the line in slope-intercept form?
Answers
The equation of the line in slope-intercept form is
[tex]y = \frac{3}{5} x + 3[/tex]
EXPLANATION
The slope intercept form of a line is given by
[tex]y = mx + c[/tex]
Where [tex]m[/tex]is the slope and [tex]c[/tex]
is the y-intercept.
We can read any two points from the graph and use it to determine the slope of the line.
For instance, the graph passes through the points
[tex](-5,0)[/tex]and [tex](0,3)[/tex]
The slope can be found using the formula,
[tex]m= \frac{y_2-y_1}{x_2-x_1}[/tex]
This implies that,
[tex]m = \frac{ 3 - 0}{0 - - 5} [/tex]
[tex]m = \frac{ 3 - 0}{0 + 5} [/tex]
[tex]m = \frac{ 3 }{ 5} [/tex]
Also the y-intercept is
[tex](0,3)[/tex]
Therefore [tex]c = 3[/tex]
We substitute all these values in to the above equation to obtain,
[tex]y = \frac{3}{5} x + 3[/tex]
f(x)=x+7
if you know the domain is {-9,-3} then the range must be?
Answers
x F(x) = x + 7
-9 -9 + 7 = -2
-8 -8 + 7 = -1
-7 -7 + 7 = 0
-6 -6 + 7 = 1
-5 -5 + 7 = 2
-4 -4 + 7 = 3
-3 -3 + 7 = 4
So the range is {-2,4} <------ answer
5(x+2)7x+4 plz help idk what to do
Answers
70x + 5x = 75x
75x + 4
hope this helps
15 coins worth $3.15. if the coins are all quarters and dimes, how many quarters and dimes does she have?
Answers
If y varies directly as x and y is 18 when x is 5 which expression can be used to find the value of y when x is 11?
Answers
plug in given values:-
18 = k * 5
k = 18/5 = 3.6
so the equation of variation is y = 3.6x
when x = 11, y = 3.6 * 11 = 39.6 Answer
Answer:
The value of y is [tex]\frac{198}{5}[/tex] or 39.6.
Step-by-step explanation:
It is given that y varies directly as x and y. It means y is directly proportional to x.
[tex]y\propto x[/tex]
[tex]y=kx[/tex] .... (1)
where, k is constant of proportionality.
It is given that y is 18 when x is 5.
Substitute y=18 and x=5 in equation (1).
[tex]18=k(5)[/tex]
Divide both sides by 5.
[tex]\frac{18}{5}=k[/tex]
The value of k is [tex]\frac{18}{5}[/tex]. So, the relation between x and y is
[tex]y=\frac{18}{5}x[/tex] .... (2)
We need to find the value of y when x=11.
[tex]y=\frac{18}{5}(11)[/tex]
[tex]y=\frac{198}{5}[/tex]
[tex]y=39.6[/tex]
Therefore the value of y is [tex]\frac{198}{5}[/tex] or 39.6.
A rectangular room is three times as long as it is wide, and its perimeter is 48 meters. Find the length of the room.
Answers
x=3y and perimeter equation is 2x+ 2y = 48
2*3y + 2y = 48
6y + 2y = 48
8y= 48
y= 6 and x = 18
△JKL≅△QRS.
What is m∠Q?
Answers
we know that
If △JKL≅△QRS
then
the corresponding angles are congruent
so
m∠Q=m∠J
m∠R=m∠K
m∠S=m∠L
we have
m∠J=[tex]37\°[/tex]
therefore
the answer is
m∠Q=[tex]37\°[/tex]
Answer:
m∠Q = 37°
Step-by-step explanation:
It has been given that ΔJKL ≅ ΔQRS
∠J = 37° and ∠K = 105°
Since these triangles are congruent so we will apply the condition of ASA (theorem of congruence)
In ΔJKL and ΔQRS sides JK and QR along with their corresponding angles will be equal.
Side JK = side QR
and ∠K = ∠R = 105°
∠J = ∠Q = 37°
Therefore m∠Q = 37° will be the answer.
a=11+4b−4c?
A.c=a−4b−11
-------------
−4
B.c=a+b−11
------------
−4
C.c=a+4b+11
--------------
−4
D.c=a−b+11
------------
−4
Answers
At a baseball game, a vender sold a combined total of 112 sodas and hot dogs. the number of sodas sold was three times the number of hot dogs sold. find the number of sodas and the number of hot dogs sold.
Answers
Help solve x for this
Answers
6x = 120
x = 20
<GOF = 180 - 134 = 46
134 = 14 +6x
subtract 14 from each side
120 = 6x
divide each side by 6
x = 120/6 = 20
x = 20
ANGLE GOF = (360 - (134+134)) /2 = 92/2 = 46 degrees
Reaner Recycling shreds 7/8 ton of aluminum each day.The machines can shred 1/24 ton aluminum per cycle.How many cycles will be needed to shred the aluminum?
plz help I don't get it
Answers
168/8= 21
21 cycles will be needed to shred the aluminum.
Hope this helps!
Answer:
21.
Step-by-step explanation:
We have been given that Reaner Recycling shreds 7/8 ton of aluminum each day.The machines can shred 1/24 ton aluminum per cycle.
To find the number of cycles needed to shred the aluminum, we will divide amount of aluminium by 1/24 as:
[tex]\text{Number of cycles}=\frac{7}{8}\div \frac{1}{24}[/tex]
Convert into multiplication problem by flipping the 2nd fraction:
[tex]\text{Number of cycles}=\frac{7}{8}\times \frac{24}{1}[/tex]
[tex]\text{Number of cycles}=\frac{7}{1}\times \frac{3}{1}[/tex]
[tex]\text{Number of cycles}=7\times 3[/tex]
[tex]\text{Number of cycles}=21[/tex]
Therefore, 21 cycles will be needed to shred the aluminum.
Determine algebraically whether the function is even, odd, or neither even nor odd.
f(x)=x+ [tex] \frac{4}{x} [/tex]
a))Even
b))Neither
c))Odd
Answers
If 6 people in the United States each eat the average amount of popcorn for 5 years, how many quarts of popcorn will they eat.
Answers
68*5= 340.
340*6= 2,040 quarts of popcorn.
Hopefully this helps! :)
Is the value a an improper fraction less than 1 or greater than 1
Answers
Write a function rule for the area of a rectangle whose length is 6 ft more than its width. What is the area of the rectangle when its width is 12 ft?
Answers
=> x+6 will be the length.
Function: x(x+6)= x^2+6x
Area= 12^2+6.12= 216 ft
The area of the rectangle is 72 square ft and this can be determined by using the formula of the area of the rectangle.
Given :
Length is 6 ft more than its width.
The following steps can be used in order to determine the area of the rectangle when its width is 12 ft:
Step 1 - Let the length of the rectangle be 'L' and the width of the rectangle be 'W'.
Step 2 - According to the given data, length is 6 ft more than its width that is:
L = 6 + W
Step 3 - The formula of the area of the rectangle is given below:
A = LW
Step 4 - Substitute the value of 'L' in the above expression.
A = (6 + W)W
Step 5 - Now, at W = 6ft the area of the rectangle becomes:
A = (6 + 6)6
A = 72 square ft.
For more information, refer to the link given below:
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What is the value of c such that: x2 + 14x + c, is a perfect-square trinomial? A. 7 B. 98 C. 196 D. 49
Answers
First list greatest common factors of 49 which is 7 and 7
Second your second addition sign is telling you that both numbers are going to be the same
Third your first sign is telling you that both numbers are positive
So your equation is (x+7)(x+7) if you do the box method or any other formula you will com out with x² +14x+49
If you need additional help from this topic I will gladly send you my notes your welcome
The length of one base of a trapezoid is 19 less than five times the length of the other base. If the trapezoid has a height of 18 feet and an area of 477 ft squared, find the length of the longer base.
Answers
suppose the length of one base is x, then the other base is 5x-19
[(x+5x-19)*18]/2=477
[6x-19]*18=954
6x-19=53
6x=72
x=12
The longer base is 5*12-19=41
The length of the shorter base of the trapezoid is found by solving the equation generated by using the formula for the area of a trapezoid. After finding this length, it is substituted into the equation representing the length of the longer base to find its value, which is 76 feet.
Explanation:To solve this problem, let's denote the length of the shorter base of the trapezoid as 'a'. According to the problem, the length of the longer base is then 5a - 19. We also know that the area of a trapezoid is given by the formula: (1/2) * (sum of lengths of bases) * height. So, by substituting the given trapezoid area (477 ft squared) and height (18 ft) into the this formula, we get: 477 = 1/2 * (a + (5a - 19)) * 18. Solving this equation will give us the value of 'a'. As calculating 'a' we find it to be 19. After that, we insert 'a' into the longer base equation: 5a - 19, we find the length of the longer base to be 76 ft.
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geometry proof help please
Answers
so, because those two triangles, have HF in common, they also would have the bisected angle in common, and the other side as well, therefore, those EHF and GHF triangles are congruent by [tex]\bf \boxed{S} ide\quad \boxed{A} ngle\quad \boxed{S} ide[/tex].
namely, one side, then the angle and the other side stemming from that angle.
now, if those two triangles are congruent by SAS, then the last side must also be congruent too.
what is the value of the digit 7 in 43782
Answers
The value of the digit '7' in the number 43782 is 7000, because it's at the thousands place.
Explanation:In the number 43782, the value of the digit 7 is determined by its place in the number. In our decimal number system, each digit's value depends on its position starting from the right. If we start counting from right to left, the 1st place is units or ones place, 2nd place is tens place, 3rd place is hundreds place, 4th place is thousands place and so on. Here, the number '7' is located in the thousandth place. Therefore, the value of the digit 7 in 43782 is 7000.
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Help please!
Victoria is 4 years older than her neighbor. The sum of their ages is no more than 14 years.
Enter an inequality that can be used to represent this situation in the box, where x represents Victoria's neighbor's age.
Answers
What is the solution to the system of equations?
y = x + 3
x = –2
Answers
y= 1
Just plug in the x= -2 into the y system of equation. so y= (-2)+3
A car service charges a fixed fee of $3 plus $2 for each mile. Find the cost of a 7-mile ride. Let x=the number of miles.
Answers
3 + 2 times 7 miles (x) = 17
Hope this helps!!
What is the reference angle for a 240° angle
Answers
The reference angle for a 240° angle is 60 degree.
What is a Reference Angle?Reference Angle is the acute angle between the terminal side and the x axis. The value of reference angle is always positive and less than 90 degree.
The angle is 240 degree, for which the reference angle has to be determined.
The angle 240 degree lies in the third quadrant between 180 and 270 degree.
To determine the reference angle, the given angle will be subtracted by 180 degree.
=> 240 - 180
=> 60 degree
To know more about Reference Angle
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Which is an equivalent form of the equation 4x-y= 14
Answers
-y = 14 - 4x
y = -14 + 4x
Answer:
y = 4x - 14 is equivalent from of y = 4x - 14.
Step-by-step explanation:
Given : 4x-y= 14
To find : Which is an equivalent form of the equation.
Solution : We have given 4x - y = 14.
We can write it in slope intercept form y = mx + b
Where, m = slope , b = y intercept.
4x - y = 14.
On subtracting both sides by 4x
- y= -4x + 14.
On dividing both sides by -1.
y = 4x - 14.
Therefore, y = 4x - 14 is equivalent from of y = 4x - 14.
angle efg and angle gfh are a linear pair, the measure of angle efg equals 4n+20, and measure of angle gfh equals 3n+13. what are the measures of angle efg and angle gfh?
Answers
Answer:
∠EFG=104° and ∠GFH=76°
Step-by-step explanation:
Given information:∠EFG = (4n+20)°, ∠GFH = (3n+13)° and ∠EFG and ∠GFH are a linear pair.
If two angles are a linear pair, then the sum of those angles is 180°.
It is given that ∠EFG and ∠GFH are a linear pair.
[tex]\angle EFG+\angle GFH=180^{\circ}[/tex]
Substitute the given values.
[tex](4n+20)+(3n+13)=180[/tex]
Combined like terms.
[tex](4n+3n)+(20+13)=180[/tex]
[tex]7n+33=180[/tex]
Subtract 33 from both sides.
[tex]7n+33-33=180-33[/tex]
[tex]7n=147[/tex]
Divide both sides by 7.
[tex]n=21[/tex]
The value of n is 21.
[tex]\angle EFG=4n+20=4(21)+20=104^{\circ}[/tex]
[tex]\angle GFH=3n+13=3(21)+13=76^{\circ}[/tex]
Therefore, the measure of ∠EFG and ∠GFH are 104° and 76° respectively.