The path of a launched projectile contains the vertex (5, 120) and the point (25, 80) on the boundary. If all the experiments that followed met or exceeded this path, which quadratic inequality in standard form contains the points in the later experiments?
Answers
The equation for the path of a launched projectile contains the vertex (5, 120) and the point (25, 80) on the boundary is shown in the graph.
What is a parabola?It is defined as the graph of a quadratic function that has something bowl-shaped.
The path of the launched projectile will a parabola.
We have the vertex of the parabola (5, 120)
The standard equation in terms of vertex (h, k)
[tex]\rm y = a(x-h)^2+k[/tex]
Plug the points:
[tex]\rm y = a(x-5)^2+120[/tex]
To find the value of “a” plug point (25, 80)
[tex]\rm 80 = a(25-5)^2+120[/tex]
a = -1/10
Plug this into the equation;
The path of the equation:
[tex]\rm y = \dfrac{-1}{10}(x-5)^2+120[/tex]
Thus, the equation for the path of a launched projectile contains the vertex (5, 120) and the point (25, 80) on the boundary is shown in the graph.
Learn more about the parabola here:
brainly.com/question/8708520
#SPJ1
Related Questions
Can a prism have the same volume and surface area EXPLAIN PLEASE URGENTLY ANSWER PLEASE
Answers
Answer:
Two figures can have the same volume but different surface areas. For example: A rectangular prism with side lengths of 1 cm, 2 cm, and 2 cm has a volume of 4 cu cm and a surface area of 16 sq cm. A rectangular prism with side lengths of 1 cm, 1 cm, and 4 cm has the same volume but a surface area of 18 sq cm.
The length of a rectangle is "a" inches and the width is 3 inches more than its length. find the perimeter and the area
Answers
Answer:
Step-by-step explanation:
Givens
Length = a
Width = a + 3
Formulas
P = 2L + 2w
Area = L * w
Solution
Perimeter
P = 2L + 2w
P = 2*a + 2(a + 3) Remove the Brackets
p = 2a + 2a + 6 Combine
P = 4a + 6
Area
Area = L * w
Area = a (a + 3)
Area = a^2 + 3a
Put the following equation of a line into slope-intercept form, simplifying all fractions.
12y−15x=84
Answers
The equation in slope-intercept form is y = (5/4)x + 7.
We have,
The slope-intercept form of a linear equation is given by y = mx + b, where "m" is the slope and "b" is the y-intercept.
To write the equation 12y - 15x = 84 in slope-intercept form, simplify the fractions and solve for y:
12y = 15x + 84
y = (15x + 84) / 12
y = (5x + 28) / 4
y = (5/4)x + 28/4
y = (5/4)x + 7
Thus,
The equation in slope-intercept form is y = (5/4)x + 7.
Learn more about equation of a line here:
https://brainly.com/question/23087740
#SPJ3
a square pyramid measuring 7 in along each edge of the base with a height of 12 in
Answers
Answer:
196 in^3
Step-by-step explanation:
Volume of pyramid = 1/3 base * height
= 1/3 (7x7) (12) = 196 in^3
4.5x67=
6/5x78=?
20-100=+3,000
Answers
6/5x78=63.6
20-100+3000=2920
8 tenths + 34 hundredths =
A 42 tenths
B 42 hundredths
c 114 tenths
D 114 hundredths
Answers
Answer:
D
Step-by-step explanation:
114 hundredths
Answer:
42 hundredths
Step-by-step explanation
Normally do 34+8 then add the hundredths since 34 hundredths is the bigger value
The price of a visit to the dentist is $25. If the dentist fills any cavities, an additional charge of $75 per cavity gets added to the bill. If the dentist finds x cavities, what will the cost of the visit be? Write your answer as an expression.
Answers
c = 75x + 25
HELP, I WILL GIVE YOU MANY POINTS (60)!
While using a skipping rope, Emily jumps 52 times in 60 seconds. Jumping at this
same rate, how many times does Emily jump in 75 seconds?
Answers
Answer:
65 times in 75 seconds
Step-by-step explanation:
52 × 75 = 3,900
3,900 ÷ 60 = 65
Solve the following system of equations. Show all work and solutions.
y = 3x^2 + 6x + 4
y = −3x^2 + 4
Answers
Answer:
y = 4, x = 0
y = 1, x = -1
Step-by-step explanation:
[tex]y = 3 {x}^{2} + 6x + 4[/tex]
[tex]y = - 3 {x}^{2} + 4[/tex]
[tex] \: [/tex]
Since both of them are equal to y, we can just equate them and solve.
[tex] \: [/tex]
[tex]3 {x}^{2} + 6x + 4 = - 3 {x}^{2} + 4[/tex]
[tex]3 {x}^{2} + 6x + 4 + 3 {x}^{2} - 4 = 0[/tex]
[tex]6 {x}^{2} + 6x = 0[/tex]
[tex]6x(x + 1) = 0[/tex]
[tex]6x = 0[/tex]
[tex]x = 0[/tex]
[tex] \: [/tex]
[tex]x + 1 = 0[/tex]
[tex]x = - 1[/tex]
[tex] \: [/tex]
[tex]for \: x = 0[/tex]
[tex]y = 3( {0})^{2} + 6(0) + 4[/tex]
[tex]y = 4[/tex]
[tex] \: [/tex]
[tex]for \: x = - 1[/tex]
[tex]y = 3( { - 1})^{2} + 6( - 1) + 4[/tex]
[tex]y = 1[/tex]
[tex] \: [/tex]
[tex]values \: of \: x \: and \: y \: for \: the \: system \: of \: equations \: are[/tex]
y = 4, x = 0
y = 1, x = -1
The system of equations has been solved and the solution set of the equation are (-1,1) and (0,4).
What is a system of equation?A system of equation is the set of equation in which the finite set of equation is present for which the common solution is sought.
The first equation given as,
y = 3x² + 6x + 4
The second equation given as,
y = -3x² + 4
Equate the value of y from both equation as,
3x² + 6x + 4=-3x²+4
3x²+3x²+6x+4-4=0
6x²+6x=0
6x(x+1)=0
x=0:x=-1
Put these values of x, in first equation,
y = 3(-1)^2 + 6(-1) + 4
y = 3 - 6 + 4
y=1
Put 0 on the place of x,
y = 3(0)^2 + 6(0) + 4
y = 0 +0+ 4
y=4
Thus, the system of equations has been solved and the solution set of the equation are (-1,1) and (0,4).
Learn more about the system of equations here;
https://brainly.com/question/13729904
#SPJ1
Can a right triangle have the side lengths 4 mm, 13 mm, and 10 mm?
Justify your reasoning.
Answers
Step-by-Step Explanation:
Using Pythagoras Theorem,
Hypotenuse^2 = 1st Side^2 + 2nd Side^2
Consider the longest number, ie. 13mm as the Hypotenuse.
=> 13^2 = 4^2 + 10^2
=> 169 = 116
LHS is not Equal to RHS
Therefore, this denies the Pythagoras Theorem. Hence, a Right triangle cannot have these side lengths.
Answer:
No, because the given values do not produce a correct equation when plugged into the Pythagorean Theorem.
Step-by-step explanation:
To solve this question, we can use the Pythagorean Theorem. (Also called Pythagoras Theorem)
The Pythagorean Theorem is true for ALL right triangles, meaning that if the side lengths don't work for it, the given triangle can not be a right triangle.
The theorem simply states that the sum of the squares of the two legs must add up to the square of the hypotenuse.
Note that the hypotenuse of a triangle is the side opposite to the right angle.
The Pythagorean Theorem can be easily written as the following expression:
a^2+b^2=c^2
This is where a and b are the legs and c is the hypotenuse.
We can plug our given values in to see if it's correct.
If it is a right triangle, the longest side will always be the hypotenuse, so we can safely set c as 13.
4^2+10^2=13^2
Simplify to see if it's true
16+100=169
116≠169
Therefore, a right triangle can not have these given side lengths.
Hope that helps, please let me know if you have any further questions!
A line passes through two sides of a rectangle.
12
34
56
78
The measure of Z1 is 50 degrees. What is the measure of 26?
O 50 degrees
80 degrees
130 degrees
O 150 degrees
Answers
Answer:
34
80 degrees
Step-by-step explanation:
I RELLAY HOPES THIS HELPS YOU PLEASE
Which angle in this quadrilateral is an obtuse angle?
Angle J
Angle K
Angle L
Angle M
Answers
Answer:
Where is the quadrilateral? You haven't inserted a picture.
Which graph represents the function?
f(x)=x(x+2)
Answers
Answer:
The bottom graph on the right, check the image below:
Explanation:
Substitute the x value with 1,
f(1)=1(1+2)=3
f(2)=2(2+2)=8
f(-1)=-1(-1+2)=-1
f(-2)=-2(-2+2)=0
Please help quickly! Will give points to 1st right answer!
the table below represents a logarithmic function f(x)
Answers
The domain of the logarithm function is (0, ∞) and the range of the logarithm function will be (-∞, ∞)
What are domain and range?The domain means all the possible values of the x and the range means all the possible values of the y.
The table is shown below.
Let the logarithm function with the variables x and y. Then we have
y = logₐ x
At x = 25, the value of y will be 2. Then the value of a will be
2 = logₐ 25
2 = 2 logₐ 5
1 = logₐ 5
Then 1 can be written as
1 = log₅ 5
Then on comparing, the value of a will be
a = 5
Then the logarithm function will be
y = log₅ x
Then the domain of the logarithm function is (0, ∞) and the range of the logarithm function will be (-∞, ∞)
More about the domain and range link is given below.
https://brainly.com/question/12208715
#SPJ1
What is the circumference of a circle that has a diameter of 12 feet?
Answers
Find the solution set of the inequality: 8x+2 > 34
x > or < or >= or =
Answers
Inequality are expressions that are not separated by an equal sign. The solution to the given system of equation is x > 4
Inequality functionInequality are expressions that are not separated by an equal sign.
Given the inequality
8x+2 > 34
Subtract 2 from both sides
8x + 2 - 2 > 34 - 2
8x > 32
Divide both sides by 8
8x/8 = 32/8
x > 4
Hence the solution to the given system of equation is x > 4
Learn more on inequality here: https://brainly.com/question/24372553
#SPJ1
Please help this assignment is due in 20 mins!
Jayvalyn is buying milk. She needs 4 liters. A half-liter of milk costs $2.86. A 200-milliliter container of milk costs $1.19. What should Jayvalyn buy so she gets 4 liters at the lowest price?
Answers
Answer:
the half liter
Step-by-step explanation:
200 mL :
4,000 mL in 4 liters.
4,000/200=20
20x1.19=23.8
half liter :
4x2=8
8x2.86=22.88
Jada's property has a shape of a parallelogram with the
dimensions shown. If the perimeter of the property is 300
feet, what is the value of x?
x + 75
X +45
Answers
2x+120=300
-120 -120
2x=180
/2 /2
X=90
what’s the reason? help
Answers
Answer:
adjacent exterior angles
x equals 80
Calculate the value of A please ?
Answers
A=7(4)+13
A= 28+13
A=41
casey sight the top of an 84 foot tall lighthouse at an angle of elevation of 58. if casey is 6 feet tall how far is he standing from the base of the lighthouse
Answers
lighthouse
Step-by-step explanation:
A right angle triangle is formed. The height of
the lighthouse represents the opposite side
of the right angle triangle. The distance, h
from the lighthouse to where Casey is
standing represents the adjacent side of the
right angle triangle. Casey's line of sight
along the angle of elevation represents the
hypotenuse.
To determine h, we would apply
the tangent trigonometric ratio.
Tan 0, =opposite side/adjacent side.
Therefore,
Tan 58 = 84/h
h = 84/tan 58 = 84/1.6
h= 52.5 feet
How much of your lawn can you mow with
one gallon of gas, if you maintain the rate
of ⅕ gallon of gas per ⅛ of a lawn?
Answers
Answer:
5/8
Step-by-step explanation:
1/5 x 5
1
1/8 x 5
5/8
Pleease help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
SOLUTION: sqrt(8^2+4^2)=8,9 and rounds up to 9
which expression represents 5 times the sum of 24 and 7?
a. 5 x 24 + 7
b. 5 x 24 x 7
c. 5 + 24 + 7
d. 5 x (24 x 7)
e. 5 x (24 +7)
Answers
Answer:
e
Step-by-step explanation:
the sum of 24 and 7 is 24 + 7 and multiplying this by 5 gives
5 × (24 + 7)
Answer:
e.
Step-by-step explanation:
24 + 7 = 31
5 * 31 = 155.
which fraction is equal to 5
Answers
good evening! Can someone please answer this, ill give you brainliest and your earning 50 points. Would be very appreciated.
Answers
Answer:
Part (a)From inspection of the diagram, the pattern is:
Step 1: 1² + 1
Step 2: 2² + 2
Step 3: 3² + 3
Let x = step number
Let y = total number of squares
Therefore, the equation that represents the relationship is:
y = x² + x
Part (b)x² relates to the large square made up of small squares (top part of the image of each step)
x relates to the rectangle of small squares (bottom part of the image of each step)
y is the total number of small squares in the image of each step.
The pattern is
1+14+29+3More simply
1²+12²+23²+3So for an integer n
y=n²+n#b
n² is pair of boxes at top side
n is boxes underneath
Solve by taking a square root: (x + 7)2 - 10
Answers
Answer:
2x+4
Step-by-step explanation:
Trust me
Shane and Abha earned a team badge that required their team to collect no less than 200020002000 cans for recycling. Abha collected 178178178 more cans than Shane did.
What is the solution set of the inequality?
Answers
The solution set of the inequality is represented as [911,∞)
How to find the solution set of the inequality?let
x be the number of cans collected by Shane.
Therefore,
Since, Abha collected 178 more cans than Shane did.
Therefore,
Abha = 178 + x
Hence,
Also, Shane and Abha earned a team badge that required their team to collect no less than 2000 cans for recycling.
Therefore,
x + 178 + x ≥ 2000
2x + 178 ≥ 2000
2x ≥ 2000 - 178
2x ≥ 1822
x ≥ 1822 / 2
x ≥ 911
learn more on inequality here: https://brainly.com/question/12018375
#SPJ1
Which is a factor of the polynomial f(x) = 6x4 – 21x3 – 4x2 24x – 35? 2x – 7 2x 7 3x – 7 3x 7
Answers
A factor of the polynomial f(x) = 6x⁴ - 21x³ - 4x² + 24x - 35 is 2x - 7
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Given the polynomial:
f(x) = 6x⁴ - 21x³ - 4x² + 24x - 35
The polynomial can be further simplified to:
f(x) = (2x - 7)(3x³ - 2x + 5)
A factor of the polynomial f(x) = 6x⁴ - 21x³ - 4x² + 24x - 35 is 2x - 7
Find out more on equation at: https://brainly.com/question/2972832
#SPJ4
Answer:
2x-7
Step-by-step explanation:
TLDR verified answer, correct on edge 2023
Help me find the area here! 6th grade math
Answers
63 cm2
hope it helps
you
63 CM answer
