1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Shkiper50 [21]
3 years ago
12

1 A baseball is struck such that its position on a plane perpendicular to home plate can be described by the equation y = (x - 1

75)2 + 121, where x is the horizontal distance from the plate in feet and y is the vertical distance also in feet 250 Determine the position of the ball when it is at its highest point. ​
Mathematics
1 answer:
marshall27 [118]3 years ago
7 0

Answer:

21

Step-by-step explanation:

You might be interested in
The equation 2x2 − 12x + 1 = 0 is being rewritten in vertex form. Fill in the missing step. Given 2x2 − 12x + 1 = 0 Step 1 2(x2
Bezzdna [24]

Answer:

Part 1) 2(x-3)^{2}-17=0  (the missing steps in the explanation)

Part 3) (8, 4); The vertex represents the maximum profit

Part 4) x = 3.58, 0.42

Part 5) x = 6, x = 44; The zeros represent the number of monthly memberships where no profit is made

Part 6) 2(x − 7)2 + 118; x = $7

Part 7) The maximum height of the puck is 4 feet. −(x − 4)^2 + 6

Part 8) (x + 3)^2 − 4

Part 9) 2(x − 1)^2 = 4

Part 10) 8(x − 4)^2 + 592

Step-by-step explanation:

Part 1) we have

2x^{2} -12x+1=0

Convert to vertex form

step 1  

Factor the leading coefficient and complete the square

2(x^{2} -6x)+1=0

2(x^{2} -6x+9)+1-18=0

step 2

2(x^{2} -6x+9)+1-18=0

2(x^{2} -6x+9)-17=0

step 3

Rewrite as perfect squares

2(x-3)^{2}-17=0

Part 3) we have

f(x)=-x^{2}+16x-60

we know that

This is the equation of a vertical parabola open downward

The vertex is a maximum

Convert to vertex form

f(x)+60=-x^{2}+16x

Factor the leading coefficient

f(x)+60=-(x^{2}-16x)

Complete the squares

f(x)+60-64=-(x^{2}-16x+64)

f(x)-4=-(x^{2}-16x+64)

Rewrite as perfect squares

f(x)-4=-(x-8)^{2}

f(x)=-(x-8)^{2}+4

The vertex is the point (8,4)

The vertex represent the maximum profit

Part 4) Solve for x

we have

-2(x-2)^{2}+5=0

-2(x-2)^{2}=-5

(x-2)^{2}=2.5

square root both sides

(x-2)=(+/-)1.58

x=2(+/-)1.58

x=2(+)1.58=3.58

x=2(-)1.58=0.42

Part 5) we have

f(x)=-x^{2}+50x-264

we know that

The zeros or x-intercepts are the value of x when the value of the function is equal to zero

so

In this context the zeros represent the number of monthly memberships where no profit is made

To find the zeros equate the function to zero

-x^{2}+50x-264=0

-x^{2}+50x=264

Factor -1 of the leading coefficient

-(x^{2}-50x)=264

Complete the squares

-(x^{2}-50x+625)=264-625

-(x^{2}-50x+625)=-361

(x^{2}-50x+625)=361

Rewrite as perfect squares

(x-25)^{2}=361

square root both sides

(x-25)=(+/-)19

x=25(+/-)19

x=25(+)19=44

x=25(-)19=6

Part 6) we have

-2x^{2}+28x+20

This is a vertical parabola open downward

The vertex is a maximum

Convert the equation into vertex form

Factor the leading coefficient

-2(x^{2}-14x)+20

Complete the square

-2(x^{2}-14x+49)+20+98

-2(x^{2}-14x+49)+118

Rewrite as perfect square

-2(x-7)^{2}+118

The vertex is the point (7,118)

therefore

The video game price that produces the highest weekly profit is x=$7

Part 7) we have

f(x)=-x^{2}+8x-10

Convert to vertex form

f(x)+10=-x^{2}+8x

Factor -1 the leading coefficient

f(x)+10=-(x^{2}-8x)

Complete the square

f(x)+10-16=-(x^{2}-8x+16)

f(x)-6=-(x^{2}-8x+16)

Rewrite as perfect square

f(x)-6=-(x-4)^{2}

f(x)=-(x-4)^{2}+6

The vertex is the point (4,6)

therefore

The maximum height of the puck is 4 feet.

Part 8) we have

x^{2}+6x+5

Convert to vertex form

Group terms

(x^{2}+6x)+5

Complete the square

(x^{2}+6x+9)+5-9

(x^{2}+6x+9)-4

Rewrite as perfect squares

(x+3)^{2}-4

Part 9) we have

2x^{2}-4x-2=0

This is the equation of a vertical parabola open upward

The vertex is a minimum

Convert to vertex form

Factor 2 the leading coefficient

2(x^{2}-2x)-2=0

Complete the square

2(x^{2}-2x+1)-2-2=0

2(x^{2}-2x+1)-4=0

Rewrite as perfect squares

2(x-1)^{2}-4=0

2(x-1)^{2}=4

The vertex is the point (1,-4)

Part 10) we have

8x^{2}-64x+720

This is the equation of a vertical parabola open upward

The vertex is a minimum

Convert to vertex form

Factor 8 the leading coefficient

8(x^{2}-8x)+720

Complete the square

8(x^{2}-8x+16)+720-128

8(x^{2}-8x+16)+592    

Rewrite as perfect squares    

8(x-4)^{2}+592

the vertex is the point (4,592)

The population has a minimum at x=4 years ( that is after 4 years since 1998 )

6 0
3 years ago
Applying Angle Relationships of Isosceles Triangles
soldi70 [24.7K]
(180(total angle measure of triangle)-50(EFG))/2(the other two angles have the same measure)=65


The angle CGE=180=CGF+EGF
180-65=CGF
115=CGF
8 0
3 years ago
Read 2 more answers
The cost of a council tax bill increased by 5%.
andreyandreev [35.5K]

The council tax bill before the increase is £1240

The equation that represents the percentage increase in council tax bill is :

percentage increase x t = £62

Where t represents the initial council tax bill - council tax bill before the 5% increase

5% x t = £62

0.05 x t = £62

Divide both sides of the equation by 0.05

t = £62 / 0.05 = £1240

To check if the answer derived is correct : 5% x 1240 = 62.

A similar question was answered here: brainly.com/question/12066598?referrer=searchResults

5 0
3 years ago
Write expanded form for six hundred and four hundred thirteen thousandths
lakkis [162]
64,013,000 =
<span>six hundred and four hundred thirteen thousandths =
60,000,000 + 4,000,000+10,000+3,000</span>
4 0
3 years ago
Evaluate the expression: 2x + 5 for x = 3
lubasha [3.4K]

Substitute the value of the variable into the equation and simplify.
11
11
5 0
3 years ago
Other questions:
  • A measure of ________ for a numerical data set describes how its values vary with a single number.
    15·1 answer
  • This is the third time I post this question and no one answered it can someone please help me​
    7·1 answer
  • the interval between the root and the third of a major triad is made up of ____ half steps . . A. three . B. four . C. five . D.
    5·1 answer
  • 1/2+3/5 for math and idk what it is
    14·2 answers
  • PLZZZ HELP I'LL GIVR U A MEDAL N FAN U
    6·2 answers
  • What's The Value Of X If X =3squared ?
    12·1 answer
  • What are all the coordinates that are solutions to the equation -2x + 4y = -10
    11·1 answer
  • Find c.<br> Round to the nearest tenth:
    12·1 answer
  • How many 3/4s are in 3 2/4
    10·1 answer
  • Complete the proof of the identity by choosing the rule that justifies each step.(1-cosx)(1+cosx)=sin^2x
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!