Draw a diagram of the archway modeled by the equation y = x^2 + 5x + 24. Fine and label the y-intercept and the x-intercepts on the sketch. Then find and label the width of the archway at its base and the height of the archway at its highest point, assuming the base of the archway is along the x-axis
Answers
Answer:
1) Please find the attached drawing of the archway created with MS Excel
2) The y-intercept is (0, 24)
The x-intercepts are (-3, 0), and (8, 0)
3) The width of the archway at its base is 11
The height of the archway at its highest point = 30.25
Step-by-step explanation:
1) Please find the attached drawing of the archway created with MS Excel
2) The y-intercept is (0, 24)
The x-intercepts are (-3, 0), and (8, 0)
3) The width of the archway at its base is 11
The height of the archway at its highest point = 30.25
Step-by-step explanation:
The given function representing the archway is y = -x² + 5·x + 24
1) Please find attached the required drawing of the archway created with MS Excel
2) The y-intercept is given by the point where x = 0
Therefore, we have, the y-value at the y-intercept = -0² + 5×0 + 24 = 24
The y-intercept = (0, 24)
The x-intercept is given by the point where y = 0
Therefore, the x-values at the x-intercept are found using the following equation;
0 = -x² + 5·x + 24
x² - 5·x - 24 = 0
By inspection, we have;
x² - 8·x + 3·x - 24 = 0
x·(x - 8) + 3·(x - 8) = 0
∴ (x + 3) × (x - 8) = 0
Either (x + 3) = 0, and x = -3, or (x - 8) = 0, and x = 8
Therefore, the x-intercepts are (-3, 0), and (8, 0)
3) The width of the archway at its base = The distance between the x-values at the two x-intercepts
∴ The width of the archway at its base = 8 - (-3) = 11
The highest point of the arch is given by the vertex of the parabola, y = a·x² + b·x + c, which has the x-value of the vertex = -b/(2·a)
∴ The x-value of the vertex of the given parabola, y = -x² + 5·x + 24, is x = -5/(2×(-1)) = 2.5
Therefore;
The y-value of the vertex, is y = -(2.5)² + 5×2.5 + 24 = 30.25 = The height of the archway at its highest point
∴ The height of the archway at its highest point = 30.25
The vertex of the parabola is at (-2.5, 17.75). And the y-intercept of the parabola is at (0, 24).
What is the equation of the parabola?Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.
Then the equation of the parabola will be given as,
y = a(x - h)² + k
The equation of the parabola is given as,
y = x² + 5x + 24
Convert the equation into a vertex form, then we have
y = x² + 5x + 25/4 - 25/4 + 24
y = (x + 5/2)² + 71/4
y = (x + 2.5)² + 17.75
The vertex of the parabola is at (-2.5, 17.75). The y-intercept of the parabola is given as,
y = (0)² + 5(0) + 24
y = 24
The y-intercept of the parabola is at (0, 24).
More about the equation of the parabola link is given below.
https://brainly.com/question/20333425
#SPJ2
Related Questions
Find the area of a rectangle & triangle! NEED HELP ASAP
Answers
Answer:
For rectangle: A=wl
Step-by-step explanation:
Multiply the length by the with to find the answer
Marla was given the point (1, 3), (2, 1), and (-2, -15). She was asked to find a quadratic function that fit these 3 given points. Marla created a system of three equations with three variables to solve the problem and then used the matrix functions on her graphing calculator to find the equation. Which equation can be written given these 3 points?
Answers
The quadratic equation is given by y = -2x² + 4x + 1
The standard form of a quadratic equation is given by:
y = ax² + bx + c
At point (1, 3):
3 = a(1)² + b(1) + c
a + b + c = 3 (1)
At point (2, 1):
1 = a(2)² + b(2) + c
4a + 2b + c = 1 (2)
At point (-2, -15):
-15 = a(-2)² + b(-2) + c
4a - 2b + c = -15 (3)
Solving equations 1, 2 and 3 simultaneously gives:
a = -2, b = 4, c = 1
The quadratic equation is given by y = -2x² + 4x + 1
Find out more on quadratic equation at: https://brainly.com/question/1214333
Help me please I need help
Answers
Answer:
a)25%
b)5%
Step-by-step explanation:
hope it will help goodbye
triangle abc has an area of 6 and a perimeter of 12. if the triangle is dilated by a scale factor of 3 centered at the origin, what is the area and perimeter of its image, triangle a'b'c'?
Answers
Answer:
perimeter: 36 unitsarea: 54 square unitsStep-by-step explanation:
The perimeter is multiplied by the scale factor:
image perimeter = 3 × original perimeter = 3×12 = 36 units
The area is multiplied by the square of the scale factor:
image area = 3² × original area = 9×6 = 54 square units
‼️DUE TODAY‼️
(Question in the picture)
Answers
Answer:
I Don't know
Step-by-step explanation:
I don't know I don't know I don't know
Y=ax^2 +bx +c
Where c represents the y intercept
In the equation it represents the height
So option c is correct
Please mark as brainliest if it’s correct
I need help to find the radius
Answers
Answer:
Step-by-step explanation:
i think 0.6
Which is an equivalent ratio of yellow cans to blue cans?
10:12
30:25
18:16
5:6
Answers
Answer: 30:25
Step-by-step explanation:
notice how there are 6 yellow and 5 blue
so if we multiply both by 5 then we get
30:25
Xavier's living room is rectangular and measures 3 meters by 3 meters. Beginning in one
corner, Xavier walks the length of his living room and then turns and walks the width. Finally,
Xavier walks back to the corner he started in. How far has he walked? If necessary, round to
the nearest tenth.
Answers
16 =
ОА. 4
ОВ. 3
ОС. 8
O D. 6
Answers
Answer:
A. 4
Step-by-step explanation:
I hope this helps you!!!
The diagram shows a map of three land masses, numbered region 1, region 2, and region 3, connected via bridges over water. Each bridge can be traversed in either direction. (diagram is attached)
Show that there are 10 walking routes that start and end in region 2, crossing over water exactly twice. Assume each bridge, when crossed, is fully traversed to the next land mass.
Answers
Answer:
Explanation
Step-by-step explanation:
If you look closely, every route connected to region 2 could go to either region 1 or 3, which each could go back to region 2 in 3 different formats. For example the top bridge of region 2, could go through region 1, then region 3 then to the middle bridge of region 2. This can happen for all three of the other route when going backs and works for all bridges in region 2.
how to graph transformations of quadratic functions
Answers
Answer:
Shift "h" units to the right, "k" units up, and reflect over the x or y axis when needed.
Step-by-step explanation:
1) I want to talk about reflections first.
Reflections across the x-axis --> [tex]y = ax^2[/tex], a is the coefficient. if a is negative, then the equation should be reflected across the x-axis. This is known as a vertical reflection. Reflections across the y-axis --> [tex]y=a(bx)^2[/tex], b is the coefficient. If b is negative, then reflect the equation over the y-axis. There are cases where the reflection across the y-axis does not change anything. But, let's say its [tex]y=(x-3)^2[/tex]... the reflection across the y-axis is different (that equation is: [tex]y=(-x-3)^2[/tex] )2) Rigid transformations
Horizontal transformations (to the left or right): [tex]y=a(bx-h)^2[/tex], factor out b from "bx-h" and whatever h equals is the units to the right. If h is a negative number, then you move to the left. Vertical transformations (up and down): [tex]y = a(bx-h)^2+k[/tex]... k is just the units up... if k is negative then we move it down.Example (check image for visual)
We transform [tex]y = x^2[/tex] to [tex]y = -(-x-3)^2+3[/tex] , you move right 3, then reflect across the x-axis, then reflect across y-axis, then move 3 up.
--------------------------------------------------------------------------------------------------------------
Note: In the image, the red line is the original function, the blue one is the transformed function. See if you can follow along with the verbal instructions I gave above.
Please help me Find the slope no links or bots please and thank you I really need help
Answers
Answer:
B) -7/4
General Formulas and Concepts:
Algebra I
Slope-Intercept Form: y = mx + b
m - slope b - y-interceptStep-by-step explanation:
Step 1: Define
Identify.
y = -7/4x + 4
Step 2: Break
Slope m = -7/4
y-intercept b = 4
Plc help! Factor completely 2a^3b-ab^3-1 2/3ab^3-a^3b-4 1/2a^2b-1/2a^2b
Answers
Answer:
116−−√
110−−√
14√
18√
Step-by-step explanation:
PLEASE SOLVE ALL W STEPS WORTH 30 PTS
Answers
Answer:
Step-by-step explanation:
I'll leave you to round
7.)
x= amount invested at time 0
[tex]x*e^{18*.07}=25000\\x=7091.35066249[/tex]
8.)
[tex]7091.35066249(1+\frac{.045}{4})^{4*36}=35510.594803[/tex]
8b.)
In the first investment we had a yield of: 25000-7091.35=17908.65
In the second investment we had a yield of: 35510.5948-7091.35=28419.24
While it may seem like the second investment had the higher return (because it had the higher yield) the first one has the highest yield because it's being compounded more often and at a higher rate
9e +4= -5e + 14+ 13e
step by step pls
Answers
Answer:
e = 10
Step-by-step explanation:
9e +4= -5e + 14+ 13e
combine like terms on left side of the equation : -5e + 13e = 8e
9e + 4 = 8e + 14
subtract 8e from both sides : 9e - 8e = e and 8e - 8e cancels out
e + 4 = 14
subtract 4 from both sides : 4 - 4 cancels out and 14 - 4 = 10
we're left with e = 10
7363626x726=???? Helpppppp
Answers
Answer:
The answer is 5345992476
Step-by-step explanation:
Original price of coat: $100.00 Discount: 21%
Answers
Answer:
$79
Step-by-step explanation:
A store owner bought 15001500 pencils at \$0.10$0.10 each. If he sells them for \$0.25$0.25 each, how many of them must he sell to make a profit of exactly \$100.00$100.00
Answers
Based on the information given, the number of pencils that should be sold will be 1000 pencils.
Let the number that should be sold be x.
A store owner bought 1500 pencils at $0.10 each. Therefore, the cost price will be:
= 1500 × $0.10 = $150
Profit = Selling price - Cost price
100 = 0.25x - 150
0.25x = 100 + 150
0.25x = 250
x = 250/0.25
x = 1000
Therefore, 1000 pencils should be sold.
Learn more about equations on:
https://brainly.com/question/13802812
what is the area of the square units ? W (11,2), X (11,8), Y (14,8), Z (14,2)
Answers
Answer:
18 units²
Step-by-step explanation:
Find the side lengths then multiply the length and width to find the area.
Slope= -1/2 Y-intercept =4
Answers
Answer:
no I'm pretty sure it's wrong
Step-by-step explanation:
the y intercept for that to right us -4
Help meee please thank you will mark brainlist….
Answers
Answer:
It's 47 because it's an isosceles triangle.
Step-by-step explanation:
Answer:
F is equal to 47
Step-by-step explanation:
G is equal to F
Hello da 234234r32 ef3qew3e2wr3qefwasdwasd
Answers
Find the length of OP.
Answers
Answer:
OP = 84
Step-by-step explanation:
The triangle is equilateral meaning all angles equal and all sides are equal.
5y - 6 = 4y + 12
y - 6 = 12
y = 12 + 6
y = 18
Now
OP = 4y + 12
OP = 4(18) +12
OP = 84
x+y=5
x-1=y
Please help
Answers
Rearrange the second to give
x - y = 1
Add the two equations
(x + y) + (x - y) = 5 + 1
2x = 6
x=3
Substitute 3 into either equation
3 - 1 = y
y = 2
WHAT DOES AN ANIMAL BREEDER DO?????????
I LITERALLY NEED HELP ON THIS ONE!!
Some school commercial thingy.
Answers
Answer:
Breeders cross animals of the same species with desirable traits to create desirable offspring.
Step-by-step explanation:
you need to prepare 50 portions of broccoli flowers. A prepared portion weighs 0.090kg. Trimmings account for 25% of the total weight. How much broccoli do you need to order ?
Answers
The amount of broccoli needed to be ordered to prepare 50 portion of broccoli flower is 3.375 kg.
You need to prepare 50 portions of broccoli flowers.
A prepared portion weighs 0.090 kg.
Trimming accounts for 25% of the total weight.
Therefore, to find how much broccoli is needed to order can be calculated as follows:
Trimming account for 25% of 0.090 = 0.0225 kg The remaining weight(broccoli) required = 0.090 - 0.0225 = 0.0675 kgTherefore,
the broccoli needed to be ordered = 0.0675 × 50 = 3.375 kg
learn more on percentage here: https://brainly.com/question/25304304?referrer=searchResults
System practice problems
Answers
Looking at the first system of equations,
16x - 10y = 10
-8x - 6y = 6
If we multiply both sides of the second equation by 2, the coefficient of x is exactly the negative of the coefficient of x in the first equation.
-8x - 6y = 6
⇒ 2 (-8x - 6y) = 2 (6)
⇒ -16x - 12y = 12
By combining this new equation with the first one, we can eliminate x and solve for y :
(16x - 10y) + (-16x - 12y) = 10 + 12
⇒ -22y = 22
⇒ y = -1
Then we just solve for x by replacing y in either equation.
16x - 10y = 10
⇒ 16x - 10 (-1) = 10
⇒ 16x + 10 = 10
⇒ 16x = 0
⇒ x = 0
The main idea behind elimination is combining the given equations in just the right amount so that one of the variables disappears. The "right amount" involves using the LCM of the coefficients of a given variable. In this example, the x-coefficients had LCM(8, 16) = 16, so we only had to scale one of the equations (the one with -8x) to cancel all the x terms.
If we wanted to eliminate y first instead, we first note that LCM(6, 10) = 30. To get 30 as a coefficient on y, in the first equation we would have multiplied by 3:
16x - 10y = 10
⇒ 3 (16x - 10y) = 3 (10)
⇒ 48x - 30y = 30
And in the second equation, we would have multiplied by -5 (negative so that upon combining the equations, we end up with -30y + 30y = 0):
-8x - 6y = 6
⇒ -5 (-8x - 6y) = -5 (6)
⇒ 40x + 30y = -30
Now combining the two scaled equations gives
(48x - 30y) + (40x + 30y) = 30 + (-30)
⇒ 88x = 0
⇒ x = 0
We then solve for y :
16x - 10y = 10
⇒ -10y = 10
⇒ y = -1
so we end up with the same solution as before.
Please help me with percentages.
Answers
Answer:
I think the answer would be 10%.
Please help me asap
ty :)
Answers
Answer:
y = -3x - 3
Step-by-step explanation:
Subtract 3x both sides
y = -3 - 3x
y = -3x + (-3)
.this is all the question
Answers
Answer:
Answer: 2
Step-by-step explanation: