Considering a quadratic equation, it is found that:
The maximum height of the volleyball is of 19.06 feet.The volleyball will hit the ground after 3.6 seconds.What is the quadratic equation for an object's height?Considering the height in feet, it is given by:
h(t) = -4.9t² + v(0)t + h(0)
In which:
v(0) is the initial velocity.h(0) is the initial height.In this problem, we have that h(0) = 6, v(0) = 16, hence the equation is given by:
h(t) = -4.9t² + 16t + 6
Which is a quadratic equation with coefficients a = -4.9, b = 16, c = 6. Hence the maximum height is found as follows:
[tex]\Delta = b^2 - 4ac = 16^2 - 4(-4.9)(6) = 373.6[/tex]
[tex]h_{MAX} = -\frac{\Delta}{4a} = -\frac{373.6}{-4(4.9)} = 19.06[/tex]
The maximum height of the volleyball is of 19.06 feet.
It hits the ground at the roots, hence:
The solutions are:
[tex]x_1 = \frac{-16 + \sqrt{373.6}}{-9.8} = -0.34[/tex]
[tex]x_2 = \frac{-16 - \sqrt{373.6}}{-9.8} = 3.6[/tex]
Time is a positive measure, hence:
The volleyball will hit the ground after 3.6 seconds.
More can be learned about quadratic equations at https://brainly.com/question/24737967
#SPJ1
Factor the polynomial 3x4 – 2x2 15x2 – 10 by grouping. which product is the factored form of the polynomial? (–x2 – 5)(3x2 2) (x2 – 2)(3x2 5) (x2 5)(3x2 – 2) (3x2 – 5)(x2 2)
The factor of the given polynomial are (3x^2-2)(x^2+5)
The polynomial
[tex]3x^4-2x^2+15x^2-10[/tex]
What is the factor of the polynomial?Factoring a polynomial is expressing the polynomial as a product.
The rearranged, grouped, and solved as follows
[tex]3x^4+15x^2-2x^2-10[/tex]
[tex]3x^4+15x^2-(2x^2+10)[/tex]
Factor out the common term
[tex]3x^2(x^2+5)-2(x^2+5)[/tex]
[tex](3x^2-2)(x^2+5)[/tex]
That is the third option is the correct option.
Therefore the factor of the given polynomial are (3x^2-2)(x^2+5)
To learn more about the factor method visit:
https://brainly.com/question/24380382
A point has zero dimension.
Q.A. True
• B. False
SUBMIT
Which expression is equal to
An item is regularly priced at $80. It is now priced at a discount of 70% off the regular price. What is the price now?
Answer:
$24
Step-by-step explanation:
PRICE=$80
DISCOUNT=70٪ OF $80=(70/100)×80=70×80/100=$56
HENCE DISCOUNT=$56
NOW THE PRICE=$80-$56=$24
I HOPE IT HELPED YOU
Answer: 24
Step-by-step explanation:
Multiply the original price by how much is being discounted.
80 x .70 = 56
Subtract the answer from the original price.
80 - 56 = 24
Select all of the equations that are equivalent to 3x+45=180
1. 3(x+45)=180
2. 3(x+15)=180
3. 3(x+15)=60
4. x+15=60
5. 3x=135
What is the quotient of (3x4 – 4x2 8x – 1) ÷ (x – 2)? 3x3 6x2 8x 24 – startfraction 47 over x minus 2 endfraction 3x3 6x2 8x 24 startfraction 47 over 3 x superscript 4 baseline minus 4 x squared 8 x minus 1 endfraction 3x3 6x2 8x 24 startfraction 47 over x minus 2 endfraction 3x3 6x2 8x 24 – startfraction 47 over 3 x superscript 4 baseline minus 4 x squared 8 x minus 1 endfraction
The quotient of (3x⁴ - 4x² + 8x - 1) ÷ (x - 2) is 3x³ + 6x² + 8x + 24
It can be expressed as 3x³ + 6x² + 8x + 24 + 47 / x - 2
What are the Quotients?Quotients is the number obtained by dividing one number by another.
The given expression is;
(3x⁴ - 4x² + 8x - 1) ÷ (x - 2)
Using synthetic division:
(3x⁴ - 4x² + 8x - 1) / (x - 2) = 3x³ + 6x² + 8x + 24 remainder 47
3x⁴ - 4x² + 8x - 1 → Dividend
x - 2 → Divisor
3x³ + 6x² + 8x + 24 → Quotient
47 → Remainder
The quotient is;
[tex]\rm =\dfrac{3x^4-4x^2+8x-1}{x-2}\\\\=\dfrac{(3x^3 + 6x^2 + 8x + 24)(x-2)}{x-2}\\\\=3x^3 + 6x^2 + 8x + 24[/tex]
Therefore, the quotient of (3x⁴ - 4x² + 8x - 1) ÷ (x - 2) is 3x³ + 6x² + 8x + 24
learn more on quotients:
brainly.com/question/13515262?
The quotient of (3x⁴ - 4x² + 8x - 1) ÷ (x - 2) would be 3x³ + 6x² + 8x + 24.
What are the Quotients?Quotients are the number that is obtained by dividing one number by another number.
The given expression
(3x⁴ - 4x² + 8x - 1) ÷ (x - 2)
(3x⁴ - 4x² + 8x - 1) / (x - 2) = 3x³ + 6x² + 8x + 24
remainder is 47
Here,
3x⁴ - 4x² + 8x - 1 = Dividend
x - 2 = Divisor
3x³ + 6x² + 8x + 24 = Quotient
47 = Remainder
The quotient is;
(3x⁴ - 4x² + 8x - 1) / (x - 2)
(3x⁴ - 4x² + 8x +24) (x - 2) / (x - 2)
3x³ + 6x² + 8x + 24
Therefore, the quotient of (3x⁴ - 4x² + 8x - 1) ÷ (x - 2) is 3x³ + 6x² + 8x + 24
learn more about quotients:
brainly.com/question/13515262?
Write −0.258
as a fraction in simplest form. ITS NOT 129/500
Write these as ordinary numbers:
A. 4×10³
B. 7×10⁹
C. 4×10⁰
= 4000
B. 7×10⁹= 7000000000
C. 4×10⁰= 4
( to convert back to ordinary form just move the decimal point according to the power. )
Answer:
A. 4000
B. 7000000000
C. 4
Step-by-step explanation:
A. 4×10³
= 4 × 1000
= 4000
B. 7×10⁹
= 7×1000000000
= 7000000000
C. 4×10⁰
(a⁰=1)
= 4×1
= 4
!!PLEASE PLEASE PLEASE PLEASE MARK ME THE BRAINLIEST!!
Parallelogram ABCD has the following vertices: A(3,6), B(6,8), C(9,6), and D(6,4). In two ut more complete sentences, explain how you can use the coordinates of the vertices to prove that parallelogram ABCD is a rhombus.
Explanation:
A rhombus is a parallelogram in which the diagonals are mutual perpendicular bisectors. The coordinates of the vertices can be used to show ...
the diagonals bisect each otherthe diagonals are perpendicularWhen both these conditions are met, the quadrilateral is a rhombus.
__
Mutual BisectorsThe diagonals will have the same midpoint (bisect each other) if the sum of the coordinates at the ends of one diagonal is the same as the sum of the end point coordinates of the other diagonal:
A +C = B +D
(3, 6) +(9, 6) = (6, 8) +(6, 4)
(3+9, 6 +6) = (6 +6, 8 +4)
(12, 12) = (12, 12) . . . . . . midpoints are the same; ABCD is a parallelogram
__
PerpendicularThe diagonals will be perpendicular if the sum of the products of the coordinate differences of their end points is zero.
AC⋅BD = (C -A)⋅(D -B) = (9 -3, 6 -6)⋅(6 -6, 4 -8)
= (6, 0)⋅(0, -4) . . . . . end point differences; we want their dot-product
= (6)(0) +(0)(-4) = 0 +0 = 0 . . . . diagonals are perpendicular
_____
Additional comment
The midpoints are computed as (A+C)/2 and (B+D)/2. We have multiplied each of them by 2 to simplify the arithmetic. Our resulting sums of (12, 12) must be divided by 2 to get the actual midpoint of the rhombus: (6, 6).
The notion of "dot product" is a vector notion. Two vectors are perpendicular when their dot product is zero. The dot product is the scalar sum of the products of corresponding coordinates.
ok only 3 questions and going to sleep
WILL MARK BRAINLIEST
Answer:
71.2
Step-by-step explanation:
PEMDAS is Parentheses, Exponent, Multiplication, Addition, Subtraction
This is just the order you do the operations.
First, Parentheses.
Second, Exponents,
Third, Multiplication or Division
Last, Addition or Subtraction
So, in 6 x (2.4 + 10.3) - 5
We first do parentheses which is
(2.4 + 10.3) = 12.7
Now we have,
6 x 12.7 - 5
The next thing is multiplication
6 x 12.7 = 76.2
Now we have,
76.2 - 5
Lastly subtract,
76.2 - 5 = 71.2
Please help!!!
Danil, Gabriel and Hadley share some money in the ratios 3:5:9
The difference between the amount of money that Gabriel receives and the amount of
money that Hadley receives is 196 euros.
Work out the amount of money that Danil receives.
Answer:
Danil received 147 euros
Step-by-step explanation:
Let, Danil,Gabriel and Hardly share some money of 3x:5x:9x ratio then,
From the question,
9x - 5x= 196
or, 4x= 196
or, x = 196/4
or, x = 49 euros
Again,Danil received 3x share of money
=3*49
=147 euros
Answer:
Step-by-step explanation:
Ratio = 3 : 5 : 9
Money received by Danil = 3x
Money received by Gabriel = 5x
Money received by Hadley = 9x
Difference in the amount between Gabriel and Hadley = 196 euros
9x - 5x = 196
4x = 196
x = 196/4
x = 49
Money received by Danil = 3*49
= € 147
how much is 2.268 in dimes
Answer:
1 dime
Step-by-step explanation:
didvide 1 pound by the weight or the dime to get the answer
Will V − E + F always equal 2?
The expression V − E + F is an illustration of the Euler's formula.
The expression V − E + F is always 2
How to determine the true statement?The equation is given as:
V - E + F = 2
Where:
V represents the verticesE represents the edgesF represents the facesAccording to the Euler's formula, the relationship between V, E and F is:
V + F = 2 + E
Subtract E from both sides
V - E + F = 2
Hence, the expression V − E + F is always 2
Read more about Euler's formula at:
https://brainly.com/question/12274716
Write the slope-intercept form of equation.
9x + 3y = 27
slope intercept form: y = mx + b [ where m is slope and b is y-intercept ]
[tex]\dashrightarrow \ \sf9x + 3y = 27[/tex]
[tex]\dashrightarrow \ \sf 3y = 27 -9x[/tex]
[tex]\dashrightarrow \ \sf y = \dfrac{27 -9x}{3}[/tex]
[tex]\dashrightarrow \ \sf y = -3x + 9[/tex]
Here, the "slope is -3" and "y-intercept is 9"
Slope intercept form:-
y=mx+bNow convert
9x+3y=273y=-9x+273y=3(-3x+9)Cancel 3
y=-3x+9plane leaves the airport at 9:15 p.m. and travels at 560 km/h. how far away will it be at midnight?
t=2 hrs-------so 2 hrs after the second plane leaves it will catch the first plane
CK
720+240*2=600*2
720+480=1200
1200=1200
Question 1
The prism shown in the diagram has a volume of 39 units. What is the volume of the pyramid? Explain your reasoning.
Question 2
Consider this cone and pyramid, which have the same height, h. Planes parallel to the base cut through each solid at equal
heights, as shown.
Part A
What is the approximate area of each cross section of the cone and pyramid?
Type the correct answer in each box. Use numerals Instead of words.
Part B
Consider your results from part A. What conclusion can you draw about the volumes of the cone and pyramid? Explain
your reasoning.
Part C
The volume of the pyramid is one-third of the area of its base multiplied by its height, which is 144/3 pi h cubic units. Using
this measurement and your answer from part B, derive a formula for the volume of a cone.
The volume of the cone and pyramid are the same.
Formula for volume of cone = ⅓(144π × h)
What is the Volume of a Triangular Pyramid and a Cone?Volume of cone = ⅓[πr² × height of cone)
Volume of triangular pyramid = ⅓[(½bh × height of pyramid)]
Also note the following:
Area of a circle = πr²
Area of a triangle = ½bh
Part A:
Area of circle 1 = πr² = π(12²) = 144π units²
Area of circle 2 = πr² = π(6²) = 36π units²
Area of circle 3 = πr² = π(3²) = 9π units²
Area of triangle 1 = ½(24)(12π) = 144π units²
Area of triangle 2 = ½(12)(6π) = 36π units²
Area of triangle 3 = ½(6)(3π) = 9π units²
Part B: Based on our results in part A, the volumes of the cone and pyramid, having the same height are the same.
Part C:
Volume of pyramid = ⅓(144π × h)
Using this measurement and our conclusion in part B:
Formula for the Volume of a cone = ⅓(144π × h)
Learn more about the volume of cone and pyramid on:
https://brainly.com/question/16017622
The vertices of PQR are P(6, 1), Q(3,5), and R(11, 11). The length of segment PR is √125 units. Use the coordinates and geometric reasoning to show that PQR is a right triangle.Explain your reasoning and show your work
Check the picture below, so hmm we know that much, and we can also more or less see that PR is the longest side, let's check the length of the other two sides
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ P(\stackrel{x_1}{6}~,~\stackrel{y_1}{1})\qquad Q(\stackrel{x_2}{3}~,~\stackrel{y_2}{5})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ PQ=\sqrt{[3 - 6]^2 + [5 - 1]^2}\implies PQ=\sqrt{(-3)^2+4^2}\implies \boxed{PQ=5} \\\\[-0.35em] ~\dotfill\\\\ Q(\stackrel{x_1}{3}~,~\stackrel{y_1}{5})\qquad R(\stackrel{x_2}{11}~,~\stackrel{y_2}{11})~\hfill QR=\sqrt{[11 - 3]^2 + [11 - 5]^2} \\\\\\ QR=\sqrt{8^2+6^2}\implies \boxed{QR=10}[/tex]
if that's true, the triangle is indeed a right-triangle, then hmmmm most likely using the pythagorean theorem PR² = PQ² + QR², let's check
[tex](\sqrt{125})^2~~ = ~~5^2~~ + ~~10^2\implies 125=25+100\implies 125=125~~\textit{\Large \checkmark}[/tex]
Jenna concludes that (4, 9) is the solution to the system of these two equations. Which of the following justifies her conclusion?
Only these two lines contain the point (4, 9).
The point (4, 9) appears in both tables.
These two lines have the same rate of change.
These two lines are perpendicular to each other.
What is the value of the expression when a = 3 and b = 5?
3a+b−4
4
7
10
34
Beth and Leslie are trying to decide which one of them gets to portray the lead character in a student play. They will use a random number generator to produce an integer. If the integer that comes up is odd, Beth gets to play the lead, and if the integer is even, Leslie gets to play the lead. Having the random integer generated be in which interval will make this a fair decision?
A) from 2 to 10 B) from 3 to 15 C) from 5 to 20 D) from 5 to 25
The fair interval illustrates a sample space
The interval that will make a fair decision is from 5 to 20
How to determine the fair interval?From the question, we understand that:
Beth plays the lead, and if the integer is even, Leslie plays the lead, if otherwiseSince they choose odd and even integers, then the sample space must be divisible by the number of people (i.e 2 people)
The sample space (S) is calculated as:
S = Highest - Least + 1
A) from 2 to 10S = 10 - 2 + 1 = 9
B) from 3 to 15S = 15 - 3 + 1 = 13
C) from 5 to 20S = 20 - 5 + 1 = 16
D) from 5 to 25S = 25 - 5 + 1 = 21
Only 16 can be divisible by 2
Hence, the interval that will make a fair decision is from 5 to 20
Read more about sample space at:
https://brainly.com/question/10558484
The wood on the back deck of a house needs waterproofing. The shape of the deck is a rectangle with the length * 35 feet and a width of 5 yards. A gallon can of waterproof stain covers 80 square feet and costs $19.99 per can plus 7% sales tax. You go to the hardware store to purchase the waterproof stain needed to complete the job. You give the cashier $150.
How much change do you receive, or how much additional cash must you find in order to be able to pay for all of the
stain you need? You must show all calculations.
Area of Rectangle = length X width
You cannot split up a can of stain.
You must show all calculations.
You earn $1,166 gross taxable income every week, and have claimed no exemptions. assuming that you have no other sources of income, what is the amount of income tax withheld each week? for weekly gross income between 1,160 and 1,170 dollars and claiming no exemptions, 340 dollars will be withheld each week. a. $323 b. $337 c. $340 d. $344 please select the best answer from the choices provided a b c d
They are exempt from income tax and we would get the income tax withheld as $340.
What is tax?
The person does not have another source of income, and there are no exceptions that are claimed by the person.
The withheld tax which is held every week can be calculated as;
Amount of income tax = 30 % of 1,166
Amount of income tax = $339.6
Amount of income tax = $340
Hence, they are exempt from income tax and we would get the income tax withheld as $340.
Read more about taxable income here:
brainly.com/question/25641320
Please ANSWER
Amy is wrapping a present
that is a rectangular prism.
The height is 18 inches, the
width is 16 inches and the
length is 20 inches. What is the
least amount of wrapping
paper, in square inches, that
Amy needs to wrap the
present
The least amount of wrapping paper that Amy needs to wrap the present is 1936in².
What is Surface Area?Surface area is simply the amount of space covering the outside of a 3-dimensional object.
The surface area of a rectangular prism is expressed;
A = 2( wl + hl + hw )
Given the data in the question;
Height of the rectangular prism h = 18inWidth w = 16inLength l = 20inSurface area of the rectangular prism A = ?To determine the least amount of wrapping paper that Amy needs to wrap the present in the shape of a rectangular prism, we substitute our given values into the expression above.
A = 2( wl + hl + hw )
A = 2( (16in×20in) + (18in×20in) + (18in×16in) )
A = 2( 320in² + 360in² + 288in² )
A = 2( 968in² )
A = 1936in²
Therefore, the least amount of wrapping paper that Amy needs to wrap the present is 1936in².
Learn more about the surface area of a rectangular prism here: https://brainly.com/question/14987814
What is the Pythagorean triplet whose one member is 14
Answer:
14, 48 and 50
Step-by-step explanation:
Lars read that there are about
210,000 grains of salt in one
teaspoon.
How is 210,000 written as a power
of ten?
A. 210 X 104
B. 21 X 104
C. 21 X 108
D. 2.1 X 10^
Answer
the answer is a
Step-by-step explanation:
Can someone help me with this problem?
Answer:
30(2+1)
Step-by-step explanation:
Again, find common highest number. It is 30.
60/30 =2
30/30 = 1
so,
30(2+1)
Complete the equation below to make an equation that is equal to 1.
Answer: 5/10 +5/10 =10/10 =1
Step-by-step explanation: I don't think this requires much explanation. Any number with same numerator and denominator equals 1.
When you get 10/10, the first and second box can be figures that sum up to be 10.
It can be 7 and 3, it can be 6 and 4
helppppp................................/
Answer:
pounds and ounces
Randomly pick 25 fish from the entire pond and weigh each of them
Step-by-step explanation:
Centimeters, feet and inches measure length, not weight.
To find the average weight of fish living in a large pond, the scientist will randomly pick 25 fish from all over the pond. Next, each fish will be weighed. The weight of all 25 fish will be added and the total will be divided by 25. This will give you the average weight of a fish living in the large pond.
A glider flies 8 miles south from the airport and then 15 miles east. Then it flies in a straight line back to the airport. What was the distance of the glider's last leg back to the airport?
Answer:
17
Step-by-step explanation:
This flight makes a right triangle
The sides are 8 and 15. The hypotenuse isnt know and that is the answer.
8^2 + 15^2 = c^2
c^2 = 289
c = 17
Simplify. 2(x^2 + 5) - 3(x + 1) + 3
Please explain how you got your answer, I'm really confused!! :( I will mark Brainliest!
Answer:
2x^2+10-3x
Step-by-step explanation:
start by multiplying numberes into the parentheses.
2x^2+10-3x-3+3
now combine like terms
2x^2+10-3x