Using quadratic function concepts, it is found that:
1) The equation is [tex]y = -0.08x^2 + 4x[/tex]
2) The minimum distance is of 2.64 yards, and the maximum is of 47.36 yards.
A quadratic equation has the following format:
[tex]y = ax^2 + bx + c[/tex]
In this problem:
The ball was kicked from the ground, thus [tex]y(0) = 0[/tex], which means that c = 0.Item 1:
The vertex is: [tex]V(x_v,y_v)[/tex], in which:
[tex]x_v = -\frac{b}{2a}[/tex]
[tex]y_v = -\frac{\Delta}{4a} = -\frac{b^2 - 4ac}{4a}[/tex]
In this problem, it is (25,50). Thus:
[tex]-\frac{b}{2a} = 25[/tex]
[tex]-b = 50a[/tex]
[tex]b = -50a[/tex]
[tex]-\frac{b^2 - 4ac}{4a} = 50[/tex]
[tex]-b^2 = 200a[/tex]
[tex]-(50a)^2 = 200a[/tex]
[tex]-2500a^2 - 200a = 0[/tex]
[tex]200a(-12.5a - 1) = 0[/tex]
Then, as [tex]a \neq 0[/tex]
[tex]a = -\frac{1}{12.5} = -0.08[/tex]
[tex]b = -50a = -50(-0.08) = 4[/tex]
Thus, the equation, in standard form, is:
[tex]y = -0.08x^2 + 4x[/tex]
Item 2:
The distances are the values of x for which:
[tex]y = 10[/tex]
Then
[tex]-0.08x^2 + 4x = 10[/tex]
[tex]-0.08x^2 + 4x - 10 = 0[/tex]
Which is a quadratic equation with [tex]a = -0.08, b = 4, c = -10[/tex]. Then:
[tex]\Delta = 4^2 - 4(-0.08)(-10) = 12.8[/tex]
[tex]x_{1} = \frac{-4 + \sqrt{12.8}}{2(-0.08)} = 2.64[/tex]
[tex]x_{2} = \frac{-4 - \sqrt{12.8}}{2(-0.08)} = 47.36[/tex]
The minimum distance is of 2.64 yards, and the maximum is of 47.36 yards.
A similar problem is given at https://brainly.com/question/24713268
Please give a detailed explanation
[tex]\displaystyle \large \boldsymbol{} (7 \sqrt[5]{6x-10}) ^2 +\backslash\!\!\!8=\frac{49}{x^{-\tfrac{2}{5} }} +\backslash\!\!\!8 \\\\\\ 49\!\!\!\! \diagup \sqrt[5]{(6x-10)^2} = 49\!\!\!\! \diagup \cdot \sqrt[5]{x^2} \ \ ; \\\\\\ (6x-10)^2=x^2 \\\\ (6x-x-10)(6x+x-10) =0 \Rightarrow x_1=2 \ ; \ x_2=\frac{10}{7 }[/tex]
3.5m/min = how manny miles/hour
Answer:
[tex]\sf\longmapsto0.13 miles/hour[/tex]
Step-by-step explanation:
Firstly we have to use the formula to find the miles/hour
[tex]\sf\longmapsto \: Formula:Divide \: the \: speed \: value \: by \: 26.822.[/tex]
[tex]\sf\longmapsto \: 3.5 \div 26.822[/tex]
[tex]\sf\longmapsto \: 0.13 miles/hour[/tex]
Show 2 + 5 in number line.
Please show the process of your result. Thank you! :D
Answer:
[tex]3\sqrt{7}[/tex] Is correct answer
Step-by-step explanation:
In pic
(Credits: Symbolab)
(Hope this helps can I pls have brainlist (crown)☺️)
Express the ratio of 300 miles to 25 gallons of gasoline as a untie rate
Answers:
12 miles per gallon
1.2 miles per gallon
50 miles per gallon
32 miles per gallon
Answer:
12 miles per gallon (answer A)
Step-by-step explanation:
300:25
Divide each side by 25:
12:1
12 is your answer
Hope that helps
Solve the problem based on the picture
Step-by-step explanation:
those are the x values in the graph above
now the slope
first, find the derivative = (-2*x)/(9+(6*x^2)+x^4)+(50*Cos(x))/(3+x^2)+((-100*x)*Sin(x))/(9+(6*x^2)+x^4)
then substitute the X values
the slope at first point=0.00214262528
the slope at secondpoint=0.29521512101
the slope at the third point=0.29521512101
2. Find the value of x.
(1 point)
(5x)
(3x+28)
O 14
O20
O 12
O 19
Answer:
x = 14
Step-by-step explanation:
The triangle has 2 congruent legs and is isosceles with 2 base angles being congruent , then
5x = 3x + 28 ( subtract 3x from both sides )
2x = 28 ( divide both sides by 2 )
x = 14
Claire ate dinner at her favorite restaurant. When she received her bill, she wanted to
leave a 15% tip. What is the correct amount for Claire to tip, if the bill was $9.00?
Answer:
$1.35
Step-by-step explanation:
you multiply $9.00 (9) by 15% (.15). Which gives you 1.35.
Mira has $76 in her bank account and receives $11 in allowance every week. Write and expression to represent how much money she after w amount of weeks
Answer:
87w
Step-by-step explanation:
If she has $76 in her accoumt
and receives $11every week
76+11=$87
she would have$87xw in w amount of weeks
Answer:
76 + (11w)Step-by-step explanation:
Mira has $76 in her bank account and receives $11 in allowance every week. Write and expression to represent how much money she after w amount of weeks
----------------------------
76 + (11w)
Can someone help me, please?
Answer:
112
Step-by-step explanation:
Help ASAP I’ll mark you as brainlister
Consider the line y=-1/2x+9
What is the slope of a line parallel to this line?
What is the slope of a line perpendicular to this line?
Answer:
Parallel line: - 1/2
Perpendicular line: 2
Step-by-step explanation:
30 POINTS, WILL GIVE BRAINLIEST IF ONLY RIGHT
Which of these expressions is equivalent to log 200?
A) 2 + log 2
B) 2 + log 20
C) log 50 + log 150
D) log 250 – log 50
Answer:
ITS A ITS A ITS A
ANSWER = A
Step-by-step explanation:
All of the cheese slices at Chester's Cheesy Cafe have the same mass.
Chester finds that the total mass of 3 cheese slices is 27 grams.
What is the mass of one of the cheese slices?
grams
|2i+3j| is equal to:
Answer:
Step-by-step explanation:
|2i+3j|=√(2²+3²)=√(4+9)=√13
why did lil uzi vert get a diamond in his head
Answer:
Because he thought it would make him stand out.
PLEASE HELP ITS DUE REALLY SOON AND IM REALLY DESPERATE JUST ANSWER ANY QUESTION THAT YOU CAN AND PLS TELL ME WHICH ONE IT WAS. I WILL GIVE BRAINLIEST 5 STARS AND A THANKS PLS OMG :C SORRY THERE IS NOT A LOT OF POINTS :cCC
4. A: y= 2x + 6
B: y= x + 9
5. (3,12)
6. C: a pizza with 3 toppings will equal $12 at either restaurant
Find the missing side of the length, s. I need help!
Answer:
s = 12
Step-by-step explanation:
Since the triangles are similar then corresponding sides are in proportion, that is
[tex]\frac{AB}{XY}[/tex] = [tex]\frac{AC}{XZ}[/tex] , substitute values
[tex]\frac{6}{9}[/tex] = [tex]\frac{8}{s}[/tex] ( cross- multiply )
6s = 72 ( divide both sides by 6 )
s = 12
There are 4 times as many dogs as cats if the total number of dogs and cats is 20
how many dogs are there
Answer:5
Step-by-step explanation: 4*5=20
URGENT PLEASE HELP, respond to c, d, e, and f please !!
Answer:
Step-by-step explanation:
c. (18.5-17)/.9= 1.66666666667= 1.6667
d. .7107
e. .2185
f. 0.675=(x-17)/.9 x= 17.6075
I got ace in a week i felt so happy i wanna give someone branliest
2+2
Answer:
4
Step-by-step explanation:
2 plus 2 equals 4 lmk if you need more help
Answer:
4
Step-by-step explanation:
Plz help me, thx you
Answer:
transversal line is line A. parallel lines are B and C. corresponding to angle A is angle D. and alternate angle to E is G.
Gabriella is building a garden that is 3.6 m long by 7.77 m wide. What is the area of her garden?
simplify the problem 4 . 3 + 1 . 6 + 8 . 4 − 0 . 9
Answer:
13.4
Step-by-step explanation:
4.3+1.6=5.9
5.9+8.4=14.3
14.3-0.9=13.4
What did I do wrong 1st person answer get brainlist
Answer: you got the subtracted wrong.
Step-by-step explanation: 115 - 101 = (14)
you said 13
Number of College Faculty The number of faculty listed for a variety of private colleges that offer only bachelor’s degrees is listed below. Use these data to construct a frequency distribution with 7 classes, a histogram, a frequency polygon, and an ogive. Discuss the shape of this distribution. What proportion of schools have 180 or more faculty?
Answer: Number of College Faculty The number of faculty listed for a variety of private colleges which offer only bachelor’s degrees is listed below. Use these data to construct a frequency distribution with 7 classes, a histogram, a frequency polygon, and an ogive. Discuss the shape of this distribution. What proportion of schools have 180 or more faculty? 165 221 218 206 138 135 224 204 70 210 207 154 155 82 120 116 176 162 225 214 93 389 77 135 221 161 128 310 Source
Please answer these and find the slope intercept form for each one.
Best answer gets brainliest!
What is \frac{1.88x10^6}{2000} in scientific notation?
Answer:
Its actually 9.4 × 10²
Step-by-step explanation:
Show that (√7+i√3/√7-i√3 + √7-i√3/√7+i√3) is real
Answer:
Step-by-step explanation:
Step-by-step explanation:
[tex]\large\underline{\sf{Solution-}}[/tex]
Consider,
[tex]\rm \longmapsto\:\dfrac{ \sqrt{7} + i \sqrt{3} }{ \sqrt{7} - i \sqrt{3}} + \dfrac{ \sqrt{7} - i \sqrt{3} }{ \sqrt{7} + i \sqrt{3} } [/tex]
On taking LCM, we get
[tex]\rm \: = \: \dfrac{ {( \sqrt{7} + i \sqrt{3})}^{2} + {( \sqrt{7} - i \sqrt{3})}^{2} }{( \sqrt{7} + i \sqrt{3})( \sqrt{7} - i \sqrt{3})} [/tex]
We know,
[tex] \purple{\rm \longmapsto\:\boxed{\tt{ {(x + y)}^{2} + {(x - y)}^{2} = 2( {x}^{2} + {y}^{2})}}} \\ [/tex]
and
[tex] \purple{\rm \longmapsto\:\boxed{\tt{ (x + y)(x - y) = {x}^{2} - {y}^{2} \: }}} \\ [/tex]
So, using these Identities, we get
[tex]\rm \: = \: \dfrac{2\bigg[ {( \sqrt{7})}^{2} + {(i \sqrt{3}) }^{2} \bigg]}{ {( \sqrt{7}) }^{2} - {(i \sqrt{3})}^{2} } [/tex]
[tex]\rm \: = \: \dfrac{2(7 + 3 {i}^{2})}{7 - {3i}^{2} } [/tex]
We know,
[tex] \purple{\rm \longmapsto\:\boxed{\tt{ {i}^{2} = - 1}}} \\ [/tex]
So, using this, we get
[tex]\rm \: = \: \dfrac{2(7 - 3)}{7 + 3} [/tex]
[tex]\rm \: = \: \dfrac{2 \times 4}{10} [/tex]
[tex]\rm \: = \: \dfrac{4}{5} [/tex]
Hence,
[tex] \red{\rm\implies \:\boxed{\sf{ \dfrac{ \sqrt{7} + i \sqrt{3} }{ \sqrt{7} - i \sqrt{3}} + \dfrac{ \sqrt{7} - i \sqrt{3} }{ \sqrt{7} + i \sqrt{3} } \: is \: purely \: real}}}[/tex]
Eight identical pens cost $10.80.
a. Write an equation in the given box that represents the total cost, y, in dollars for a pens.