Suppose the path of a baseball follows the path graphed by the quadratic function ƒ(d) = –0.6d2 + 5.4d + 0.8 where d is the horizontal distance the ball traveled in yards, and ƒ(d) is the height, in yards, of the ball at d horizontal yards. Identify the domain and range that matches this situation.
Answers
Answer:
Domain is all real numbers
Range is
[tex]y\le 12.95[/tex]
Step-by-step explanation:
The given function is
[tex]f(d)=-0.6d^2+5.4d+0.8[/tex]
This is a maximum quadratic function therefore the domain is all real numbers.
Let us complete the square to find the vertex.
[tex]f(d)=-0.6(d^2-9d)+0.8[/tex]
[tex]f(d)=-0.6(d^2+9d)+-0.6(\frac{9}{2})^2- -0.6(\frac{9}{2})^2+ 0.8[/tex]
[tex]f(d)=-0.6(d-\frac{9}{2})^2+\frac{243}{20}+ 0.8[/tex]
[tex]f(d)=-0.6(d-\frac{9}{2})^2+\frac{259}{20}[/tex]
Therefore the range is
[tex]y\le \frac{259}{20}[/tex]
[tex]y\le 12.95[/tex]
See graph
Answer:
Domain:
[tex][0,9.146][/tex]
Range:
[tex][0,12.95][/tex]
Step-by-step explanation:
we are given
a baseball follows the path graphed by the quadratic function
[tex]f(d)=-0.6d^2+5.4d+0.8[/tex]
where
d is the horizontal distance the ball traveled in yards
ƒ(d) is the height, in yards, of the ball at d horizontal yards
Domain:
we know that domain is all possible values of x for which any function is defined
So, for finding domain , we will take smallest x-value to largest x-value
so, we can set f(d)=0 and find zeros
[tex]-0.6d^2+5.4d+0.8=0[/tex]
we can use quadratic formula
[tex]d=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]d=\frac{-54\pm \sqrt{54^2-4\left(-6\right)8}}{2\left(-6\right)}[/tex]
[tex]d=-\frac{\sqrt{777}-27}{6},\:d=\frac{27+\sqrt{777}}{6}[/tex]
[tex]d=-0.14579,d=9.146[/tex]
we know that d is a horizontal distance
and distance can never be negative
so, domain will be
[tex][0,9.146][/tex]
Range:
Since, this is quadratic equation
so, it is also equation of parabola
so, firstly we will find vertex of parabola
Suppose, we have
[tex]ax^2+bx+c=0[/tex]
Vertex is
[tex]x=\frac{-b}{2a}[/tex]
so, we can compare
a=-0.6
b=5.4
c=0.8
now, we can find vertex
[tex]x=\frac{-5.4}{2\times -0.6}[/tex]
[tex]d=4.5[/tex]
now, we can find y-value
[tex]f(4.5)=-0.6(4.5)^2+5.4(4.5)+0.8[/tex]
[tex]f(4.5)=12.95[/tex]
we can see
that leading coefficient is -0.6
which is negative
so, parabola opens downward
so, range will be
[tex][0,12.95][/tex]
Related Questions
Margo has a coin collection. She was given 1 coin as a gift, and she adds 3 coins per year. Which of the graphs below represents Margo's coin collection?
A) graph of line going through 1, 2 and 3, 4
B) graph of line going through 1, 1 and 3, 3
C) graph of line going through 1, 4 and 3, 10
D) graph of line going through 1, 2 and 2, 5
Answers
Answer:
Option C) graph of line going through 1, 4 and 3, 10
Step-by-step explanation:
Let y equal to Margo's coin collection
Let x equal to number of years
At the begining x=0, y=1 → Point=(x,y)→Point=(0,1)
She adds 3 coins per year, then y=1+3x
At x=1, y=1+3(1)=1+3→y=4→Point=(x,y)→Point=(1,4)
At x=3, y=1+3(3)=1+9→y=10→Point=(x,y)→Point=(3,10)
The graph of line going through (1, 4) and (3, 10), then the option C is the correct.
Katherine is considering two new cell phone plans she doesn’t want to spend more for minutes she won’t use one plan allows up to 250 minutes per month for $49 and the other plan allows up to 350 minutes per month for $65 in the last six months she used 1470 minutes use estimating an exact answer to you to determine the best cell phone plan for Katherine
Answers
Answer: The plan with 250 minutes is best because she Maximus uses only 245 minutes per month so just 5 min to spare. Also i used mental math
Step-by-step explanation:
1470 divided by 6 equals= 245 minutes exactly unless Katherine had rounded her answer
Final answer:
To determine the best cell phone plan for Katherine, compare the cost per minute for each plan. The second plan, which allows up to 350 minutes per month for $65, has a lower cost per minute.
Explanation:
To determine the best cell phone plan for Katherine, we need to compare the cost per minute for each plan.
For the first plan, Katherine gets 250 minutes for $49, which means the cost per minute is $49/250 = $0.196 per minute.
For the second plan, Katherine gets 350 minutes for $65, which means the cost per minute is $65/350 = $0.1857 per minute.
Since the cost per minute is lower for the second plan, Katherine should choose the plan that allows up to 350 minutes per month for $65.
please help 5 pts
The Questions
An item sells for $40. the sales tax on the item is 8%. What is the sales tax and total cost?
Answers
Explanation: First you need to find what 8% of 40 would be. In order to do this you need to convert the 8% into a decimal. You do this by multiplying the percent with the whole. In this case, the whole is 40 so if you multiply them you get 3.20 (or 3.2 it's the same thing). That would be the sales tax. To get the total cost you simply add the sales tax with the item.
Solve for x in the equation?
a/(2x-c) = -1
Answers
Answer:
[tex]\frac{c-a}{2}[/tex]
Step-by-step explanation:
given [tex]\frac{a}{2x-c}[/tex] = - 1 ( cross- multiply )
- (2x - c ) = a ( distribute left side )
- 2x + c = a ( subtract c from both sides )
- 2x = a - c ( multiply both sides by - 1 )
2x = c - a ( divide both sides by 2 )
x = [tex]\frac{c-a}{2}[/tex]
Answer:
x = [tex]\frac{(a - c)}{-2}[/tex]
Step-by-step explanation:
a/(2x-c) = -1
The first step is to multiply both sides by (2x - c)
(2x - c)a/(2x-c) = -1(2x - c)
a = -2x + c
a - c = -2x + c - c
a - c = -2x
Divide both side by -2
(a - c)/-2 = x
∴ x = [tex]\frac{(a - c)}{-2}[/tex]
8.1 + -3.5 = what?
Please help this is due soon! Thank youu
Answers
Answer:
4.6
Step-by-step explanation:
8.1 + (-3.5) = 8.1 - 3.5
4.6
identify the property that the statement illustrates
Answers
Answer:
6 units away from 0.
Step-by-step explanation:
when move to 6 you count the units.
What value for the constant,h, in the equation shown below will result in an onfinite number of solutions? Equation: 6x+18=h(3x+9) Answer choices: a. -2 b.-3 c.2 d.3
Answers
Answer:
c.2
Step-by-step explanation:
6x+18=h(3x+9)
To have an infinite number of solutions, the left and right side must be equal
Distribute the h
6x+18 = 3xh +9h
6x = 3xh
Divide by x
6x/x = 3xh/x
6 = 3h
Divide by 3
6/3 =3h/3
2 =h
Lets verify
18 = 9h
Divide by 9
18/9 = 9h/9
2 =h
h must be 2
A reta que passa pelos pontos (2,-1) e (6,4) intersecta o eixo das abcissas no ponto (x,0) onde x é igual a:
a) -2,8
b) 2,8
c) 0,15
d) 1,8
e) 1,6
Answers
Answer:
[tex]x=2.8[/tex]
Step-by-step explanation:
we are given that
line passes through (2,-1) and (6,4)
Firstly, we will find equation of line
First point is (2,-1)
x1=2, y1=-1
second point is (6,4)
x2=6 , y2=4
now, we can find slope
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
now, we can plug values
[tex]m=\frac{4+1}{6-2}[/tex]
[tex]m=\frac{5}{4}[/tex]
now, we can use point slope form of line
[tex]y-y_1=m(x-x_1)[/tex]
now, we can plug values
[tex]y+1=\frac{5}{4}(x-2)[/tex]
since, we have to solve for x from (x,0)
so, we can set y=0
and then we can solve for x
[tex]0+1=\frac{5}{4}(x-2)[/tex]
[tex]5\left(x-2\right)=4[/tex]
[tex]x-2=\frac{4}{5}[/tex]
[tex]x=\frac{14}{5}[/tex]
[tex]x=2.8[/tex]
HELP!!
a student finished 45 of her homework problems in class. if the ratio of problems she finished to problems she had left was 9:4, how many homework problems did she have total?
Answers
Answer:
60
Step-by-step explanation:
45 divided by 9 is 5. So you multiply 4 times 5. Which equals 20. So 20 plus 45 is 65. Hope you understand it.
Help with trig homework
Answers
Answer:
225 m
Step-by-step explanation:
Since we know they are similar triangles
8 15
---------- = -----------
120 bridge
Using cross products
8 * bridge = 15* 120
8* bridge = 1800
Divide each side by 8
8/8* bridge = 1800/8
bridge = 225
Answer:
225m
Step-by-step explanation:
the 2 triangles shown are similar by AAA
so their sides are in the same ratio
bridge/15 = 120/8
bridge length = 15*15 = 225m
Select all that apply question! See picture
Answers
Boots: $59.00, discount: 10 percent sales tax 5.5 percent
Answers
Answer:
Total cost of boots = $56.02
Step-by-step explanation:
$59 x 0.90 = $53.10
$53.10 x 1.055 = $56.02
or
59 x 0.10 = 5.9
59 - 5.9 = $53.10
53.10 x 0.055 = $2.92 tax
$53.10 + $2.92 = $56.02
Which statement is true about PQ in relation to the circumscribed circle ?
Answers
check the picture below.
Answer:
The answer is PQ is the diameter
Step-by-step explanation:
The formula for the circumference of a circle is C = 2r. What is one-fourth of the circumference of a circle that measures 12 centimeters around? If necessary, use 3.14 for .
Answers
The formula of a circumference is:
[tex]C=2\pi r[/tex]
r - radius
or
[tex]C=d\pi[/tex]
d - diameter
We have d = 12cm. Substitute:
[tex]C=12\pi\ cm[/tex]
One-fourth of the circumference:
[tex]\dfrac{1}{4}C=\dfrac{1}{4}\cdot12\pi=3\pi\ cm\approx3\cdot3.14=9.42\ cm[/tex]
Answer: 9.42 cm.PLEASE HELP WILL GIVE BRAINLIEST the number of students at north middle school is 1240 and is decreasing by 25 students per year. The number of students at south middle school is 800 and it is decreasing by 30 students per year. in how many years will the two schools have the same number of students?
Answers
Answer:
-88
Step-by-step explanation:
Let N(x) be the number of students at NMS for a certain number of years.
Let S(x) be the number of students at SMS for a certain number of years.
Let x be the number of years.
N(x)=1240-25x
S(x)=800-30x
When # of students is equal, N(x)=S(x). Therefore, we are looking for the value of x (# of years) when 1240-25x=800-30x
Subtract 1240 from each side
-25x=-440-30x
Add 30x
5x=-400
x=-88 years
Check your numbers.
Lyle bought 3/8 of red grapes and 5/12 pound of green grapes how many pounds of grapes did he buy
Answers
Answer: 19/24
Step-by-step explanation:
3/8
+
5/12
=
(3 × 12) + (5 × 8)
8 × 12
=
76/96
=
76 ÷ 4
96 ÷ 4
=
19/24
Solve equation for z
Answers
Answer:
z = 7
Step-by-step explanation:
9z + 4 / 5 - 8 = 5.4
Add 8 to both sides.
9z + 4 / 5 = 13.4
Multiply 5 by both sides.
9z + 4 = 67
Subtract 4 from both sides.
9z = 63
Divide both sides by 9.
z = 7
Answer:
7 (rounded up)
Step-by-step explanation:
9z+4/5=13.5
Multiply both sides by 5
9z+4=67.5
Subtract both sides by 4
9z=63.5
Divide both sides by 9
z=7 (rounded up)
identify an equation in point-slope form for the line parallel to y=5x+2 that passes through (-6,-1)
Answers
Answer:
y = 5x + 29
Step-by-step explanation:
y=5x+2
Given equation is in the form of y=mx+b
Where m is the slope = 5
and b is the y intercept = 2
When the lines are parallel then their slopes are equal
So the slope of parallel line is also 5 (m=5)
Given that the line passes through (-6,-1)
We use point slope formula
y-y1= m (x-x1)
m=5, x1= -6, y1=-1
Plug in all the values
y - (-1) = 5(x-(-6))
y + 1= 5 (x+6)
y + 1= 5x + 30
Subtract 1 on both sides
y = 5x + 29
Either table C or Table D shows a proportional relationship. Plot all the points from the table that shows a proportional relationship. I'll post a picture of the graph. Table C is ( X= 2,4,6,8) and Y= ( 1,3,5,7). Table D is ( X= 2,6,8,10) and Y= ( 1,3,4,5).
Answers
Answer:
Step-by-step explanation:
A proportional relationship is a straight line through the origin that grows at a constant rate
For table C
The constant of proportionality is y/x
2/1 = 4/3 = 6/5 = 8/7 This is not true so this is not proportional
For table D
The constant of proportionality is y/x
1/2 = 3/6 = 4/8 = 5/10 This is true so this is proportional
All the members of a construction crew work at the same pace. Six of them working together are able to pour foundation in 22 hours. c How many hours would this job take if the number of workers increased by factor of 4?All the members of a construction crew work at the same pace. Six of them working together are able to pour foundation in 22 hours. c How many hours would this job take if the number of workers increased by factor of 4?All the members of a construction crew work at the same pace. Six of them working together are able to pour foundation in 22 hours. c How many hours would this job take if the number of workers increased by factor of 4?All the members of a construction crew work at the same pace. Six of them working together are able to pour foundation in 22 hours. c How many hours would this job take if the number of workers increased by factor of 4?All the members of a construction crew work at the same pace. Six of them working together are able to pour foundation in 22 hours. c How many hours would this job take if the number of workers increased by factor of 4?All the members of a construction crew work at the same pace. Six of them working together are able to pour foundation in 22 hours. c How many hours would this job take if the number of workers increased by factor of 4?
Answers
Answer:
5.5 h
Step-by-step explanation:
There is an inverse relationship between the time (t) it takes to do a job and the number (n) of workers (the more workers. the faster the work gets done).
t = k/n Divide both sides by n
t/n = k
If we have two different numbers of workers, then
t₁/n₁ = t₂/n₂ Multiply each side by n₂
t₂ = t₁ × n₁/n₂
t₂ = 22 × 1/4
t₂ = 5.5 h
plz somebody I need these and I'm failing math cause of these problems.
Answers
Answer:
1.A =113.04 cm^2
2.A =616 in^2
Step-by-step explanation:
To find the area of a circle we use the formula
A = pi * r^2 if we know the radius or
A = pi * (d^2/4) if we know the diameter
In problem 1 we know the radius
A = pi * r^2
A = pi * (6)^2
A = 36*pi
Using 3.14 for pi
A = 36* 3.14
A =113.04 cm^2
In problem 2 we know the diameter
A = pi * d^2/4
A = pi * (28)^2/4
A = pi 784/4
A = 196
Using 22/7 for pi
A = 196*22/7
A =616 in^2
Answer:
1. Area of the circle with 6 cm radius is [tex] 113.14 cm^2[/tex].
2. Area of the circle with 28 cm diameter is [tex] 616 cm^2[/tex].
Step-by-step explanation:
1. Radius of the circle ,r= 6 cm
Area of the circle , A= [tex]\pi r^2[/tex]
[tex]A=\pi (6 cm)^2=\frac{22}{7}\times 6 cm\times 6 cm=113.14 cm^2[/tex]
Area of the circle with 6 cm radius is [tex] 113.04 cm^2[/tex].
2. Diameter of the circle = d = 28 cm
Radius of the circle , r = [tex]\frac{28 cm}{2=14 cm[/tex]
Area of the circle , A= [tex]\pi r^2[/tex]
[tex]A=\pi (14 cm)^2=\frac{22}{7}\times 14 cm\times 14 cm=616cm^2[/tex]
Area of the circle with 28 cm diameter is [tex] 616cm^2[/tex].
What is √9/14 in simplest radical form? Enter your answer in the box.
Answers
Answer: (3√14)/14
Step-by-step explanation: you should go buy a scientific calculator Casio or a TI calculator not much about $10 i will help a lot
Ryan bought a guitar for $475.45. If he makes $9.25 per hour at his job, how many hours did he have to work to pay for the guitar? Explain how to find the answer and check it.
Answers
Answer: 51.4 hours
Step-by-step explanation: To figure out the answer to this equation you would divide the cost by how much you make, 475.45÷9.25=51.4
Ryan would need to work approximately 51.51 hours to earn enough money to pay for the guitar.
To find the number of hours Ryan had to work to pay for the guitar, we need to divide the cost of the guitar by his hourly wage.
Divide $475.45 (cost of the guitar) by $9.25 (Ryan's hourly wage):
$475.45 / $9.25
≈ 51.51
This calculation shows that Ryan would need to work approximately 51.51 hours to earn enough money to pay for the guitar.
To check the answer, multiply the number of hours (51.51) by Ryan's hourly wage ($9.25):
51.51 x $9.25 ≈ $476.33
The result is close to the cost of the guitar ($475.45), allowing for small discrepancies due to rounding or decimal approximations. Therefore, this confirms that Ryan would indeed need to work around 51.51 hours to cover the cost of the guitar.
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The height of a rectangular prism is found by dividing volume, V, by the base area, B. If the volume of the rectangular prism is represented by 6x2 – 2x + 8 and the base area is 2x – 4, which expression represents the height? 3x + 5 – 3x – 7 + 3x + 5 + 3x – 7 –
Answers
Answer:
[tex](3x+5)+\frac{28}{2x-4}[/tex]
Step-by-step explanation:
Since,
The volume of a rectangular prism = Base area × Height,
Given,
Volume of the rectangular prism = [tex]6x^2-2x+8[/tex]
Base area = 2x - 4
Let h be the height,
[tex]\implies 6x^2-2x+8=(2x-4)h[/tex]
[tex]\implies h = \frac{6x^2-2x+8}{2x-4}[/tex]
By long division ( shown below ),
[tex]h=(3x+5)+\frac{28}{2x-4}[/tex]
Which is the required expression that represents the height.
Answer:
[tex](3x+5) + \frac{14}{x-2}[/tex]
Step-by-step explanation:
We are given the following information in the question:
Volume of rectangular prism =
[tex]6x^2 - 2x + 8[/tex]
Area of base of prism =
[tex]2x -4[/tex]
Formula:
[tex]\text{Volume of Prism} = \text{Area of base}\times \text{Height of prism}\\\\\text{Height of prism} = \displaystyle\frac{\text{Volume of Prism} }{\text{Area of base}}[/tex]
Putting the values we, get,
[tex]\text{Height of prism} = \displaystyle\frac{6x^2 - 2x +8}{2x-4} = \frac{2(3x^2-x+4)}{2(x-2)}= (3x+5) + \frac{14}{x-2}[/tex]
Hence, the height of the prism is given by the expression [tex](3x+5) + \frac{14}{x-2}[/tex]
simplify this expression
17-a-2a-6+5a
please solve
Answers
Answer:
Answer: 2 a + 11
Step-by-step explanation:
Simplify the following:
5 a - a - 2 a - 6 + 17
Grouping like terms, 5 a - a - 2 a - 6 + 17 = (-a - 2 a + 5 a) + (17 - 6):
(-a - 2 a + 5 a) + (17 - 6)
-a - 2 a + 5 a = 2 a:
2 a + (17 - 6)
17 - 6 = 11:
Answer: 2 a + 11
The expression 17-a-2a-6+5a simplifies to 2a+11. This involves combining similar terms and simplifying the arithmetic.
Explanation:
In order to simplify the expression 17-a-2a-6+5a, we first need to gather like terms. In this expression, the like terms are -a, -2a, and +5a. When you add these together, you get 2a. Now, substitute this back into the expression. You now have 17+2a-6. If you simplify further by adding the plain numbers together, you get 2a+11. Therefore, the simplified expression is 2a+11.
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Dmitri brought 28 ounces of trail mix for $3.92. What is the unit rate?
Answers
Answer:
The unit rate is 0.14 cents per ounce.
Step-by-step explanation:
Divide 3.92 by 28 to find out how much the trail mix is per ounce.
The unit rate of Dmitri's trail mix purchase is $0.14 per ounce, calculated by dividing the total cost by the total weight.
To find the unit rate of Dmitri's trail mix purchase, we divide the total cost of the trail mix by the total weight of the trail mix. Dmitri bought 28 ounces of trail mix for $3.92, so we perform the following calculation:
Unit Rate = Total Cost / Total Weight
Unit Rate = $3.92 / 28 ounces
Unit Rate = $0.14 per ounce
Therefore, the unit rate is $0.14 per ounce. This means that for every ounce of trail mix, Dmitri paid $0.14.
what is an interger?
Answers
An integer is any whole number and it can be positive or negative. Integers cannot be fractions!
A few examples of integers are...
21, 4, -6666
Used paperback books are $0.25 and hardback books are $0.50. If you buy 3 paperback book and 5 hardback books, how much money do you spend
Answers
Answer:3.25$
Step-by-step explanation:
If one paperback book is 0.25 and you buy 3 of them, (0.25 x 3) is 0.75 and a hardcover is 0.50 per book, (0.50 x 5) is 2 dollars and 50 cents and if you add the two, you will get 3.25$
The amount of money to spend to buy 3 paperback books and 5 hardback books is,
⇒ $3.25
Given that,
The cost of Used paperback books is $0.25.
And, cost of hardback books is $0.50
Here, the cost to buy 3 paperback books is,
⇒ [tex]3 \times 0.25[/tex]
⇒ $0.75
And, the cost of 5 hardback books is,
⇒ [tex]5 \times 0.50[/tex]
⇒ $2.50
So, the total cost of 3 paperback books and 5 hardback books is,
⇒ $0.75 + $2.50
⇒ $3.25
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I think the answer is is either B or C
Confused
Answers
Answer:C
Step-by-step explanation:If she studies for 10 munites and t equals munite t would go next tp 10 then d would go under it.
Find the total cost to the nearest cent. $25 pants; 20% off
Answers
Answer:
$20.00
Step-by-step explanation:
"$25 pants, 20% off" is equivalent to (1.00 - 0.20)($25), or:
0.80($25) = $20.00
This is the total cost to the nearest cent.
Answer:
$20
Step-by-step explanation:
Lets find the discount
25 * .2 = 5
You get $5 off
Price - discount = price you pay
25-5 = 20