Answer:
The maximum height the projectile reaches is 100 feet
Step-by-step explanation:
Notice that the given equation representing the height of the projectile is a quadratic equation which negative leading coefficient (-16). Such type of equations would have a parabola that branches downwards as its graph.
therefore, what we need to find is the coordinates of the top vertex of that parabola. We can use for such the typical formula for the x-position of the vertex of a parabola with standard equation:
[tex]f(x)=ax^2+bx+c[/tex]
with x-position of the vertex given by:
[tex]x_v=\frac{-b}{2a}[/tex]
Then in our case ([tex]H(t)=-16t^2+16t+96[/tex]) we have:
Horizontal position of the vertex given by:
[tex]t_{vertex}=\frac{-16}{2(-16)} =\frac{1}{2}[/tex]
and now we can find the maximum height plugging this value into the height expression:
[tex]H(t)=-16(\frac{1}{2}) ^2+16\,(\frac{1}{2})+96=-4+8+96=100\,\,ft[/tex]
Which expression has the greatest value?
(1 + 2)3
(15 - 1)0
(5-2) 2
(2 x 4)1
Answer:
(1+2)3
Step-by-step explanation: it equals 9 the the other expressions equal 8 0 and 6 so option one is the greatest value.
What is a regular Polygon? Name all the types of polygon.(HELP ASAP)
Answer:
A regular polygon is a polygon with sides of equal length. Some examples include, a equilateral triangle, square, regular pentagon, regular hexagon, regular heptagon, regular octagon, regular nonagon, regular decagon...
so 90/7 divided by 1 and three-fourths i keep trying but i keep getting a different answer what would be the best estimate
Answer:
see below
Step-by-step explanation:
90/7 ÷ 1 3/4
Change to an improper fraction
90/7 ÷ (4*1+3)/4
90/7 ÷7/4
Copy dot flip
90/7 * 4/7
360 /49
The exact answer is 7 17/49
To estimate I would round 49 to 50 and 360 to 350
350/50 is approximately 7 and since I rounded the numerator down and the denominator up, the answer would be a little higher
What is the length of BC in the right below?
Answer:
B. 17
Step-by-step explanation:
Pythagorean Theorem: a² + b² = c²
We have a and b, so:
8² + 15² = c²
c = √(8² + 15²)
c = 17
And we have our final answer!
Answer:
To find the length of BC we use Pythagoras theorem.
BC² = AB² + AC²
AB = 8 AC = 15
BC² = 8² + 15²
BC = √64 + 225
BC = √ 289
BC = 17
BC is 17
Hope this helps.
quick plz....When √98- √128 is simplified it is equal to:
A,15√2
B, -√30
C. -√2
D. 10√3
Answer:
[tex]-\sqrt{2}[/tex]
Step-by-step explanation:
[tex]\sqrt{98} -\sqrt{128}[/tex]
[tex]\sqrt{49 \times 2} -\sqrt{64 \times 2}[/tex]
[tex]\sqrt{49} \sqrt{2} -\sqrt{64} \sqrt{2}[/tex]
[tex]7\sqrt{2}-8\sqrt{2}[/tex]
[tex]=-\sqrt{2}[/tex]
3x2 + 2x - 5 and -4 + 7x2
Answer:
3×2+2x-5
6-5+2x
1+2x
-4+7×2
-4+14
10
Which statement is true for the numbers 2.5 and -2.5? A. On the horizontal number line, 2.5 and -2.5 are equal and are located on the same point. B. On the horizontal number line, -2.5 is located to the left of zero and 2.5 is located to the right of zero. C. On the horizontal number line, 2.5 and -2.5 are both located to the right of zero. D. On the horizontal number line, 2.5 is located to the left of zero and -2.5 is located to the right of zero.
Answer:B
Step-by-step explanation: because when u draw the number line all the negative numbers is written at the left side of the zero and all positive numbers are found at the right side of the zero
Answer: I believe it’s B
Step-by-step explanation:
A school allots £1500 to spend on a trip to the theatre. Theatre tickets have a regular cost of £35 each and are on offer for 1/5 off A train ticket for the day will cost £15 each. If 2 teachers and the maximum number of students attend, how much money will the school have left over?
Answer:
Step-by-step explanation:
School allots £1500 to spend on a trip to the theatre.
Theatre tickets have a regular cost of £35 each and are on offer for 1/5 off
therefore 4/5*35 = 28 for the tickets
:
A train ticket for the day will cost £15 each.
therefore total cost for each: 28 + 15 = 43 pounds each
:
If 2 teachers and the maximum number of students attend, how much money will the school have left over?
:
let s = no. of students
43(s+2) =< 1500
43s + 86 =< 1500
43s =< 1500 - 86
43s =< 1414
s =< 1414/43
s =< 32.88, 32 students max
:
find how much left over. plus 2 teachers = 34 people
1500 - 43(34) =
1500 - 1462 = 38 pounds left over
Simon makes 30 cakes He gives 1/5 of the cakes to sali He gives 10% of the cake to Jane What fraction of 30 does he have left
Answer:
7/10 or 0.7 or 70% left.
Step-by-step explanation:
Since he gives 1/5 of the cake to Sali, he gave 1/5 * 30 = 6 cakes away to Sali. Since 10% is 1/10, he gave away 1/10 * 30 = 3 cakes away to Jane. He has a total of 30 - 3 - 6 = 21 cakes left. 21/30 = 7/10, or 0.7, or 70% left.
Answer: 21/30
Explanation this is because 1/5of 30 is 6 and 10 percent of 30 is 3
6+3=9
30-9=21
Therefore Simon has 21/30 cakes left
I hope it helps
Evaluate the following expression
Answer:
Hope this is correct
Step-by-step explanation:
HAVE A GOOD DAY!
Sound waves are emitted from a fishing boat. Some of the sound waves are reflected by fish and detected back at the boat.The shortest time between the sound waves being emitted and detected is 0.26 s. The speed of sound in water is 1500 m/s.A) Calculate the distance between the boat and the nearest fish.
Answer:
195 m.
Step-by-step explanation:
The time for the sound waves to reach the fish is 0.26/2 = 0.13 seconds.
Distance = speed * time
= 1500 * 0.13
= 195 m.
find the sum 12x^2+3x+6
Answer:
[tex]3(8x ^{2} + x + 2)[/tex]
factor out 3 polynomial 8xsqurd +x+2 not factored as it doesn't have any rational roots
Answer:
This cannot be simplified any further.
Step-by-step explanation:
Suppose a local vendor charges $2 per hot dog and that the number of hot dogs sold per hour is given by , where is the number of hours since 10 AM, .
Complete Question:
Suppose a local vendor charges $2 per hot dog and that the number of hot dogs sold per hour is given by [tex]x(t) = -4t^2 + 20t + 60[/tex], where is the number of hours since 10 AM:
a) Find an expression for the revenue per hour as a function of x, R(x)
b) Find and simplify, R(x(t))
Answer:
a) R(x) = 2x
b) [tex]R(x(t)) = -8t^2 + 40t + 120[/tex]
Step-by-step explanation:
a) This is a very trivial exercise.
[tex]x(t) = -4t^2 + 20t + 60[/tex]
The number of hot dogs sold per hour is given by x
Charge per hot dog = $2
An expression of revenue per hour,R, as a function of the number of hot dogs sold per hour, x, is therefore: R(x) = 2x
b) [tex]x(t) = -4t^2 + 20t + 60[/tex]
R(x(t)) = 2(x(t))
[tex]R(x(t)) = 2(-4t^2 + 20t + 60)\\R(x(t)) = -8t^2 + 40t + 120[/tex]
11. The formula for finding a number that's the square root of the sum of another number n and 6 is
A. x = √n + 6.
B. x = √n + 6.
C. x = √n + √6.
D. x = √n6.
Answer:
x = [tex]\sqrt{x+6}[/tex]
Step-by-step explanation:
The question states that it is the square root of the sum of both n and 6. That means n and 6 are added first before square rooted. Between B and C, choose the answer that has the parenthesis around x and 6, like (x + 6).
Josie is a travel agent who loves to analyze data about the vacation destinations she books for her clients. She believes that the
more she knows about a destination, the better she can educate and prepare her clients to get the most enjoyment out of
their trips. She's recently been investigating the climate of Paradise Island, where one of her biggest clients, Jack, is planning to
visit. Her research of the temperature history of Paradise Island is vital to Jack's travel plans, as he has an ideal temperature
that he prefers for vacationing. In this task, you'll use technology and regression techniques to help Josie plan Jack's ideal
vacation to Paradise Island.
Part A
Josie has collected data that shows the average daily high temperature for several months over the last year. In her table
of data, month 1 can be interpreted as January, month 2 as February, and so on.
Month, x
Average Daily High Temperature, y
(°F)
50
56
1
2
3
67
5
84
6
89
7
98
92
84
9
10
12
58
button to insert a screenshot of your scatter plot in the
Answer:
The scatter plot for the data is attached below.
Step-by-step explanation:
The data collected by Joise for the average daily high temperature for several months over the last year is as follows:
Month X Average Daily High Temperature, Y (°F)
January 1 50
February 2 56
March 3 67
May 5 84
June 6 89
July 7 98
September 9 92
October 10 84
December 12 58
The scatter plot for the data is attached below.
How long is 139.5 minutes
Answer:
[tex]\mathrm{2.325 \: hours}[/tex]
Step-by-step explanation:
[tex]\frac{139.5}{60}=2.325[/tex]
[tex]\mathrm{2 \: hours\: 19.5 \: minutes}[/tex]
(25 POINTS) Write the inequality of the following graph?
Answer:
f(x) > -x + 2
Step-by-step explanation:
First I found the equation of the line.
The y intercept is at 2 so I know to add 2 at the end
The slope is -1 since it is going downwards
Since the top side is shaded, that represents greater than, if it was shaded downwards, it would be less than
Putting all that together, the equation is f(x) > -x + 2
Which equation is an example of the commutative property of multiplication?
O (4 + 21) = (21 + 4)
O (4 + 21)(3-51) = (3-51)(4 + 21)
(4 + 21(3-51) = (4 + 21)(3-51(1)
(4 + 21) = (4 + 21 + 0)
Answer:
the answer is (4 + 21)(3-51) = (3-51)(4+ 21)
The equation is an example of the commutative property of multiplication is 4 + 21)(3-51) = (3-51)(4 + 21).
What is Commutative Property?The commutative property is a mathematical statement that states that the order in which numbers are multiplied has no effect on the product.
According to the commutative property of multiplication, if we multiply two integers, the result will remain the same even if the positions of the integers are swapped.
Let A and B be the two integers, then;
A × B = B × A
As, we know commutative Property supports multiplication and Addition.
First, (4 + 21) = (21 + 4)
This is Commutative Property of Addition.
Second, (4 + 21)(3-51) = (3-51)(4 + 21)
This is Commutative Property of Multiplication
Third, (4 + 21(3-51) = (4 + 21)(3-51(1)
No property can be applied.
Fourth, (4 + 21) = (4 + 21 + 0)
This is expansion.
Learn more about Commutative Property here:
https://brainly.com/question/778086
#SPJ7
The number of milligrams of a certain medicine a veterinarian gives to a dog varies directly with the weight of the dog. If the veterinarian gives a 30-pound dog Three-fifths milligram of the medicine, which equation relates the weight, w, and the dosage, d? d = StartFraction 1 Over 50 EndFraction w d = three-fifths w d = 18 w d = 50 w
Answer:
Step-by-step explanation:
A direct variation equation is of the form
y = kx,
where, in words, it reads "y varies directly with x" or "y varies directly as x". In order to use this as a model, we have to have enough information to solve for k, the constant of variation. The constant of variation is kind of like the slope in a straight line. It rises or falls at a steady level; it is the rate of change.
We have that a vet gives a dose of three-fifths mg to a 30 pound dog. If the dose varies directly with the weight of the dog, then our equation is
d = kw and we need to find k in order to have the model for dosing the animals.
[tex]\frac{3}{5} =k(30)[/tex]
Divide both sides by 1/30 to get k alone.
[tex](\frac{1}{30})(\frac{3}{5})=k[/tex] and
[tex]k=\frac{1}{50}[/tex]
Our model then is
[tex]d=\frac{1}{50}w[/tex]
This means that for every pound of weight, the dog will get one-fiftieth of a mg of medicine.
Answer:
A
Step-by-step explanation:
Find 310% of 150. a number blank
Answer:
465
Step-by-step explanation:
Of means multiply
310% * 150
Change to decimal form
3.10 * 150
465
Answer:
465
Step-by-step explanation:
1 percent of 150 is 1.5.
Multiply 1.5 by 310 to 465
Alhondro wants to determine the average shoe size of all of male students in his school
the radius of wheel of a bicycle is 40 cm. taking pie =3.14, a)find tthe circumference of the wheel.b) find the distance covered by the bicycle in 200 complete revolution of the wheel.please ans this question. i beg you
Answer:
a)=251.2 cm b)=50240 cm
Step-by-step explanation:
a) The formula for calculating the circumference of a circle is c=d*pie, where D is the diameter of the circle.
Therefore, C = 2 * 40 * 3.14 = 251.2 cm
b) The distance covered by 200 revolutions of the wheel is 200 times the circumference, 200*251.2=50240 cm.So to think about this we can assume that there is a point A on the wheel, the distance that point A travels when it rotates 200 times.
Which of the graphs below would result if you made the leading term of the following function negative? f(x)=2x^4+2x+2
If we change the sign of the leading coefficient of the polynomial, the graph of the new polynomial will open downwards. The graphs can be seen at the end.
Which graph do we get when the leading coefficient is negative?Here we start with the polynomial:
[tex]f(x) = 2x^4 + 2x + 2[/tex]
The leading coefficient is one that multiplies the term with the largest exponent. In this case, is 2.
Changing its sign will cause the polynomial's arms now will open downwards (instead of upwards, as in the original polynomial).
The graphs of both functions can be seen below. The green is the original one, and the blue is the changed one.
If you want to learn more about polynomials:
https://brainly.com/question/4142886
#SPJ2
Abcd is a rectangle.
please answer very quickly
Answer:
ABD
Step-by-step explanation:
Need help people pls
Mr. Mole left his burrow and started digging his way down.
A represents Mr. Mole's altitude relative to the ground (in meters) after t minutes.
A= -2.3t – 7
How fast did Mr. Mole descend?
Answer:
He's descending at a pace of 2.3 meters per minute.
Step-by-step explanation:
This is because the equation shows us the slope or the speed he's going at.
A= -2.3t - 7
A= Altitude
-2.3 = Slope
- 7 is his starting altitude in meters
But every minute, t, he is going down 2.3 meters. It's easier to think about if you consider, A = y, and, t = x. Now you have the equation, y = -2.3x - 7.
And you graph it to see the progression in slope.
Can somebody help me with this ?? :)
Answer:
A.
Step-by-step explanation:
We have AC = DF, ∠A =∠D, so
we need AB = DE.
We get SAS congruence.
For the following geometric sequence find the explicit formula: {-1, 3, -9,...}
Answer:
[tex]a_{n}[/tex] = - 1 [tex](-3)^{n-1}[/tex]
Step-by-step explanation:
The explicit formula for a geometric sequence is
[tex]a_{n}[/tex] = a [tex](r)^{n-1}[/tex]
where a is the first term and r the common ratio
Here a = - 1 and r = 3 ÷ - 1 = - 3 , thus explicit formula is
[tex]a_{n}[/tex] = - 1 [tex](-3)^{n-1}[/tex]
Which linear inequality is graphed with y > –x – 2 to create the given solution set? y > x + 1 y x – 1 y < x + 1
Answer:
D
Step-by-step explanation:
I took the test, dont listen to the person above me:)
Answer:
y<x+1
Step-by-step explanation: