Mathematics High School

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

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

Answer 2

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

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.

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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

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Answers

Answer:

Answer: 2

Step-by-step explanation:

I need help to find the radius

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Answer:

Step-by-step explanation:

i think 0.6

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:

Please help me asap

ty :)

Answers

Answer:

y = -3x - 3

Step-by-step explanation:

Subtract 3x both sides

y = -3 - 3x

y = -3x + (-3)

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.

Help me please I need help

Answers

Answer:

a)25%

b)5%

Step-by-step explanation:

hope it will help goodbye

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-intercept

Step-by-step explanation:

Step 1: Define

Identify.

y = -7/4x + 4

Step 2: Break

Slope m = -7/4

y-intercept b = 4

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

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.

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

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

30:25 because there’s 6 blue cans and 5 yellow cans which means that you do 6x5 and 5x5

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 kg

Therefore,

the broccoli needed to be ordered = 0.0675 × 50 = 3.375 kg

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Please help me with percentages.

Answers

If there were no tip, each person would have to pay $5. They pay this much because if the bill is $50 and there are 10 people, would would calculate by 50 divided by 10 which would equal 5 so 10 people pay $5 dollars. The total would be $50.

Answer:

I think the answer would be 10%.

x+y=5
x-1=y
Please help

Answers

This is a simultaneous equation

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

16 =
ОА. 4
ОВ. 3
ОС. 8
O D. 6

Answers

Answer:

A. 4

Step-by-step explanation:

The area is multiplied by the square of the scale factor:

image area = 3² × original area = 9×6 = 54 square units

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

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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.

Help meee please thank you will mark brainlist….

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It's 47 because it's an isosceles triangle.

Step-by-step explanation:

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F is equal to 47

Step-by-step explanation:

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For rectangle: A=wl

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‼️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

The equation of a parabola is
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

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