Answer:
The ball is in the air for about 5.873 seconds.
Step-by-step explanation:
The function:
[tex]f(x)=-5x^2+20x+55[/tex]
Models the height of a ball x seconds after it is thrown in the air.
And we want to find the total time the ball is in the air.
So, we can simply find the time x at which the ball lands. If it lands, its height f above the ground will be 0. Thus:
[tex]0=-5x^2+20x+55[/tex]
We will solve for x. Dividing both sides by -5 yields:
[tex]0=x^2-4x-11[/tex]
The equation is unfactorable, so we can use the quadratic formula:
[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
In this case, a = 1, b = -4, and c = -11. So:
[tex]\displaystyle x=\frac{-(-4)\pm\sqrt{(-4)^2-4(1)(-11)}}{2(1)}[/tex]
Evaluate:
[tex]\displaystyle\begin{aligned} x&=\frac{4\pm\sqrt{16+44}}{2}\\&=\frac{4\pm\sqrt{60}}{2}\\&=\frac{4\pm2\sqrt{15}}{2}\\&=2\pm\sqrt{15}\end{aligned}[/tex]
Approximate:
[tex]x_1=2+\sqrt{15}\approx5.873\text{ or } x_2=2-\sqrt{15}\approx-1.873[/tex]
Since time cannot be negative, our only solution is the first choice.
So, the ball is in the air for about 5.873 seconds.
find the measure of arc VF. (look at the picture provided) please help
Answer:
60degrees
Step-by-step explanation:
Using the theorem that states that angle at the vertex is half the difference of the angles at the intercepted arcs
Angle at vertex can be gotten by taking the difference of 119 and 65
Angle at the vertex = 119 - 65
Angle at the vertex = 54
Hence;
54 = 1/2(168-VF)
Cross multiply
54 * 2 = 168-VF
108 = 168 - VF
VF = 168 - 108
VF = 60degrees
Hence the measure of arc VF is 60degrees
PLEASE HELP LAST ONE
Answer:
please the answer is C which is; x is about 4•0 and y is about 14•6
is y = 5x + 2 greater than y = 3x + 15
Answer:
no y = 3x +15 is greater
Step-by-step explanation:
20 divide ( 4 + 1) x 2
Answer:
[tex]\bf\huge{8}[/tex]
Step-by-step explanation:
Given that:20 divide ( 4 + 1) x 2To find:simplify formulas used:BODMASwhere,
B = bracket O = ofD = division M = multiplication A = addition S = subtraction explanation:⟼ 20 ÷ ( 4 + 1 ) × 2
⟼ 20 ÷ (5) × 2
⟼ 20 ÷ 5 × 2
⟼ 4 × 2
⟼ 8
∴ 20 ÷ ( 4 + 1 ) × 2 = 8.
Hence simplified ☑️Find the value of X in this hexagon
Answer:
x = 130°
Step-by-step explanation:
number of sides = 6
the sum of the total interior angles = (6 x 180) - 360 = 720°
x = 720 - 125 - 120 - 100 - 120 - 125 = 130°
The number of minutes spent talking on the phone, m, and the amount of a cell phone bill, a. What is the independent variable
can someone please help me?!?!?!?!?!?!? 25 POINTS!!!!!! NO LINKS!!!!!
Answer:
1) (1.5a , 2b)
2) a
3) (1.5a , b)
Help please 10 pointssss
Answer:
c
Step-by-step explanation:
A DVD has a diameter of 14 cm. What is the area of the DVD in square centimeters? Round your answer to the nearest hundredth.
a. 153.86
b. 43.96
c. 2461.76
d. 615.44
Answer:
A
Step-by-step explanation:
Area of a circle = [tex]A = \pi r^{2} \\[/tex]
R = 1/2 diameter
R = 14 / 2 = 7
A = π(7)²
A = 153.86
Answer:
a
Step-by-step explanation:
Can someone please help me in math?
Answer:
yes
Step-by-step explanation:
What you don't know. which chapter is hard for you?
Count the possible combinations of 3 letters chosen from A, B, C, D. The possible combinations of 3 letters are __.
Answer:
Step-by-step explanation:
We are given the letters:
2
We write the possible permutations of 3 letters from the given list:
3
Because order is not important in a combination we cross out the duplicate pairs:
4
Answer:
4
Step-by-step explanation:
n! / r!(n-r)!
n = # of total objects
r = # grouped together at a time
4! / 3!(4-3)!
4
Abdul Hayee had and annual income of $ 21 500 in 2018.
His annual income increased to $ 22 790 in 2019.
Calculate the percentage increase.
Jane ordered a few moving boxes from a local store as she is relocating to Atlanta. She returned 28 damaged boxes. She allotted the remaining boxes equally for each of the four rooms from which her belongings had to be packed. If 5 boxes were used for each room, how many boxes did she receive from the store initially?
Answer:
17
Step-by-step explanation:
What’s the answer?!!!!!!!
Answer:
no
[tex] {16}^{2} + {35}^{2} is not equal {41}^{2} [/tex]
What would this answer be if i solved for x?
SOLVE FOR X
x + 67
x + 127
Answer:
X+67=0
X=-67
X+127=0
X=-127
Step-by-step explanation:
pie graphs anyone help????
PLEASE HELP I WILL MARK BRAINLIEST!!
Answer:
79 degrees.
Step-by-step explanation:
There are 7 total temperatures, 68, 82, 81, 82, 74, 75, and 91 degrees. To find the mean, we add all of the temperatures together and divide it by the number of tempuratures-- 7.
68+82+81+82+74+75+91 = 553.
553 / 7 = 79.
Hope this helps!
HELP ME PLEASE!
Jessica is planting a garden. It has the shape of a right triangle. She wants 4 plants for each square yard of area. How many plants does she want in the garden?
A right triangle has a base of length 9 yards and a height of 12 yards. The longest side has length 15 yards
Answer:
216 plants
Step-by-step explanation:
To answer this question :
Determine the area of a triangle Multiply the area of the triangle by the number of plants per square yardArea of a triangle = 1/2 x base x height
1/2 x 9 x 12 = 54 yards²
54 x 4 = 216 plants
help I literally got a 4/10 in my math test and my mom is like REALLLLY mad that she took my phone so I’m using my sisters ipad and she gave me advice on this app so i don’t even know if this could help but this is the page I need to complete/it’s for term 2 (week2) basically on my test well it’s apart of it so pls help- ~btw don’t look at the top cause I already completed it, I just need the 2 and 3 helppppp ima die ANDDD I used all the points I think that’s what it’s called~
Answer:
3/8 < 2/4
2/3 > 7/12
i could be wrong sorry
It should look like this:
Triangle XYZ is inscribed in semicircle O shown below such that YZ = 7 and YX = 10. Which of the following
is closest to the radius of the semicircle?
(1) 5.8
(2) 6.1
(3) 11.6
(4) 12.2
Answer:
(2) 6.1
tep-by-step explanation:
∠Y is a right angle, so ΔXYZ is a right triangle
[tex]XZ^{2} = XY^{2} + YZ^{2}[/tex]
[tex]XZ^{2} = 7^{2} + 10^{2}[/tex] = 49 + 100 = 149
XZ = [tex]\sqrt{149}[/tex] = 12.2
XZ is the diameter of the semicircle, therefore, the radius is 12.2/2 = 6.1
Graph y = x2 - 8x + 13
Answer:
Step-by-step explanation:
From the given x^2 - 8x + 13 we can find several points to graph to represent this quadratic function.
The y-intercept is (0, 13) and stems from letting x = 0.
b
The axis of symmetry is x = - -----
2a
-8
Since a = 1 and b = -8, the axis of symmetry is x = - ------- = 4
2(1)
and so the vertex is at (4, 4^2 - 8(4) + 13), or (4, -3)
If you want to go the extra mile, find the roots of the given equation. These are also your x-intercepts. One such intercept is (2. 0).
Plot these points and draw a smooth curve through them.
Hint: the parabolic graph opens up.
Please help write a rule to represent the secuence 3, -12, 48, ...
Answer:
multiply the value behind the other value
Step-by-step explanation:
3 x -12 = 48
-12 x 48 = -576
and so on
You roll a 6-sided die.
What is P(5)?
Answer:
1/6
Step-by-step explanation:
you have a 6 sided die that is numbered 1, 2, 3, 4, 5, and 6.
you roll it once, so the probability that you will roll a five is 1/6
this is because you only want one specific number so that goes on the numerator of the fraction.
then, you have to multiply how many sides you have on the die to the number of rolls. in this case we have one roll and six sides. so the six goes on the denomerator side of the fraction
Use 5 miles = 8 km to convert 18 mph to m/s.
Give your answer as an integer.
Answer:
8 m/s.
Step-by-step explanation:
18 miles = 18*8/5 = 28.8km
28.8 km = 28.8 * 1000
= 28,800 m.
There are 3600 seconds in an hour.
Therefore:
28800 meters per hour = 28800/3600
= 8 m/s.
Concept 9.6: Find measure of angle 2. Assume that any segments that appear to be tangent are tangent.
Answer:
<2= 113
Step-by-step explanation:
134/2=67
TANGENT LINES ARE SUPPLEMENTARY
180-67=113
I need help with math, I don't understand any of this type of stuff.
Answer:
option number three goes to square, option number two goes to trapezoid and las third option goes to rectangle.
Step-by-step explanation:
Jasmine bought a new stereo system for $480.50 if the tax rate is 6 1/2 what was the total cost of the stereo system?
Answer:
$511.7
Step-by-step explanation:
Given data
Cost of stereo system= $480.50
Tax= 6 1/2% = 6.5%
Let us find the amount of the tax
=6.5/100*480.5
=0.065*480.5
=$31.2
Hence the amount of the tax = $31.2
Therefore the total cost is
=31.2+480.50
=$511.7
Quintaveous’s father gave him a baseball card collection for his birthday. He told
Quintaveous that its current value is $250 and that each year the value will grow at
a rate of 10%. What is the approximate value of the card after 6 years?
Group of answer choices
$310
$500
$133
$443
Answer:
the approximate value after 6 years is $443
Step-by-step explanation:
The computation of the approximate value after 6 years is shown below:
= Current value × (1 + rate of interest)^number of years
= $250 × (1 + 0.10)^6
= $250 × 1.1^6
= $442.8903
= $443
Hence, the approximate value after 6 years is $443
Therefore the last option is correct
8a - 3 = 5(a + 7) + 3a
Answer: NO SOLUTIONS
Step-by-step explanation:
8a-3=5a+35+3a
8a-3=8a+35
-8a -8a
-3 does not equal to 35
NO SOLUTIONS
Answer: 8a=38+8a²
Step-by-step explanation:
8a-3=5(a+7)+3a
8a-3=5a+35+3a
8a-3=8a²+35
8a=35+3+8a² (I moved 3 to put it with 35 because they are the same, I couldn't do the same for 8a and 8a² because of the 2)
8a=38+8a²
HOPE IT WORK
PLEASE HELP !!!!!!! what is the coordinate of the vertex of the following parabola: (x-1)^2=12(y+2)
a. (-1, 2)
b. (1, 2)
c. (1, -2)
d. (0, 12)
The coordinate of the vertex of the parabola is option (C) (1,-2) is the correct answer.
What is the equation of the parabola?The set of all points in a plane that are equidistant from a fixed line and a fixed point (not on the fixed line) in the plane is a parabola. The fixed line is the ‘directrix’ and the fixed point is the ‘focus’. The point of intersection of the parabola with the axis is the vertex.
For the given situation,
The equation of parabola is [tex](x-1)^2=12(y+2)[/tex] ------ (1)
The diagram below shows the parabola and the vertex of the equation of parabola.
The general form of the equation of parabola is
[tex](x-h)^{2} =4a(y-k)[/tex]
Here the vertex is (h,k)
Now compare the equation 1 with this general form, we get
⇒ [tex]h=1[/tex] and [tex]k=-2[/tex]
Hence we can conclude that the coordinate of the vertex of the parabola is option (C) (1,-2) is the correct answer.
Learn more about equation of the parabola here
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