Answer:
1) Using properties of the quadratic equation:
Here the height equation is:
h(t) = -16t^2 + 32t + 6
We can see that the leading coefficient is negative, this means that the arms of the graph will open downwards.
Then, the vertex of the quadratic equation will be the maximum.
Remember that for a general quadratic equation:
a*x^2 + b*x + c = y
the x-value of the vertex is:
x = -b/2a
Then in our case, the vertex is at:
t = -32/(2*-16) = 1
The maximum height will be the height equation evaluated in this time:
h(1) = -16*1^2 + 32*1 + 6 = 22
The maximum height is 22ft
2) Second method, using physics.
We know that an object reaches its maximum height when the velocity is equal to zero (the velocity equal to zero means that, at this point, the object stops going upwards).
If the height equation is:
h(t) = -16*t^2 + 32*t + 6
the velocity equation is the first derivation of h(t)
Remember that for a function f(x) = a*x^n
we have that:
df(x)/dx = n*a*x^(n-1)
Then:
v(t) = dh(t)/dt = 2*(-16)*t + 32 + 0
v(t) = -32*t + 32
Now we need to find the value of t such that the velocity is equal to zero:
v(t) = 0 = -32*t + 32
32*t = 32
t = 32/32 = 1
So the maximum height is at t = 1
(same as before)
Now we just need to evaluate the height equation in t = 1:
h(1) = -16*1^2 + 32*1 + 6 = 22
The maximum height is 22ft
Which of the following is an arithmetic sequence?
0-2,4, -6, 8,...
O 2, 4, 8, 16,...
O-8, -6, -4,-2....
This is because we are adding the same thing to each term to get the next term. In this case, we're adding 2 each time
-8+2 = -6
-6+2 = -4
-4+2 = -2
and so on. This common 2 we're adding on is known as the common difference.
Mark the points A(5, 5) and B(7.2). Draw a circle that has point A as the center and passes through point B. Measure and label the length of a
radius of the circle. What is the radius of circle A?
Answer:
i think 4 units im not sure though though
Step-by-step explanation:
Answer:
The radius of the circle A is 3.61 units.
Step-by-step explanation:
Got it right on edmentum
Help ASAP which option I mark brain list
Answer:the answer would be 4
Step-by-step explanation: you multiplied the 1 by 2, 2 by 4, 3 by 6.
What is the value of x in the equation 5 x - y 5x - y = 30, when y = 15?
Answer:
x=7
Step-by-step explanation:
5x-15=30
add 15 to both sides
5x=45
divide by 5
x=7
What is the first term for an arithmetic sequence with a12 = 56 and a21=101?
Find the information in the diagram can you prove FDG and FDE
Given:
A diagram of two triangles.
To find:
Whether the triangles are congruent or not.
Solution:
In triangles DEF and DGF,
[tex]m\angle EDF\cong m\angle GDF[/tex] (Given)
[tex]\overline{DF}\cong \overline{DF}[/tex] (Reflexive property)
[tex]m\angle DFE\cong m\angle DFG[/tex] (Given)
Two corresponding angles and their included angles are congruent, so the triangles are congruent by ASA postulate.
[tex]\Delta DE F\cong \Delta DGF[/tex] (ASA congruence postulate)
Therefore, yes the triangles are congruent by ASA. Hence the correct option is A.
Answer: I’m going towards no bc they all are aaa and there no aaa in geometry
Step-by-step explanation:
if y^17-17 is divided by y+1 , the remainder is
Answer:
Step-by-step explanation:
a) We have 15! as the product of 1 to 15 natural numbers. Since 17 is prime there will be no factor common to these
By actual division we find
15! (mod 17) =16
From this we deduce
even 16! mod 17 = 16 = -1
According to Wilson theorem
(17-1)! = -1 mod 17
Thus verified 17 is prime
Hence 15! (mod 17) =-1=16
-----------------------
b) 2(26!) is divided by 29
Since 29 is prime
(29-1)! = -1 mod 29
28! = -1 mod 29 = 28
When divided this gives 25 as remainder
THANKS
0
⚠️❗️⚠️❗️⚠️ 100 POINTS HELP ME FIND BOTH AREAS TROLLS GET REPORTED AND THEN THE POINTS WOULD BE TAKEN AWAY❗️⚠️❗️⚠️❗️⚠️
Answer:
Pink: 114 square units
Turquoise: 183 square units
Step-by-step explanation:
Separate the shapes into triangles and rectangles.
Area of a rectangle = width × length
Area of a triangle = 1/2 × base × height
Pink shapeThis comprises of 2 triangles and 2 rectangles.
Area of bottom left triangle = 1/2 × 6 × 6 = 18 square units
Area of top right triangle = 1/2 × 5 × 4 = 10 square units
Area of bottom large rectangle = 6 × 11 = 66 square units
Area of upper small rectangle = 4 × 5 = 20 square units
Total area = 18 + 10 + 66 + 20
= 114 square units
Turquoise shape
This comprises of 1 triangle and 2 rectangles.
Area of triangle = 1/2 × (25 - 9 - 9) × (24 - 16 - 2)
= 1/2 × 7 × 6
= 21 square units
Area of middle rectangle = (25 - 9 - 9) × 16
= 7 × 16
= 112 square units
Area of right rectangle = 2 × 25
= 50 square units
Total area = 21 + 112 + 50
= 183 square units
Answer:
Pink is = 114 square units
Turquoise is = 83 square units
--
The shapes need to be converted into triangles and rectangles so we can use their area formula which is
rectangle = width × lengthtriangle = 1/2 × base × height1. TEALThis shape has one triangle and two rectangles!
So . .
Area of the triangle = A = [tex]\frac{1}{2}[/tex] × b × h
= 1/2 × 7 × 6 = 21² unitsA= middle rectangle = A= L x W
= 7 × 16 = 112² unitsA= right rectangle = L x W
=2 × 25 = 50² unitsIn all = 183² units
2 . PINK
This shape has two rectangles and two triangles
A = bottom large rectangle -- 6 x 11 = 66² unitsA = top right triangle -- [tex]\frac{1}{2}[/tex] x 5 x 4 = 10² unitsA = bottom left triangle -- [tex]\frac{1}{2}[/tex] x 6 x 6 = 18² unitsA = upper small rectangle -- 5 x 4 = 20² unitsIn all = 114² units
Math help please show all work thanks
Jessica and Martha each have a bag of cookies with unequal quantities. They have 30 cookies total between the two of them. Each of them ate 6 cookies from their bag. The product of the number of cookies left in each bag is not more than 80. How many more cookies will Jessica have Martha? If x represents the number of cookies Jessica started with, complete the statements below.
Answer:
x^2 - 30 + 224 ≥ 0
the amount of cookies Jessica has more than Martha is at least two
Step-by-step explanation:
J + M = 30
x - 12 < 80
Read the following excerpt from a magazine carefully, and complete the activities.
In Arizona, spring is the most beautiful time of year. The temperature usually ranges from sixty-five to ninety degrees Fahrenheit. Statistics show that the sun shines 89 percent of the time during the spring days.
Birds love Arizona in the spring. Children laugh and play, and families get together for picnics. Thousands of people like to go to the lake to water ski or swim, while others enjoy driving to the forest-covered mountains to camp and fish.
List at least one statement from each of the two paragraphs that is an opinion rather than a provable fact.
first paragraph:
second paragraph:
first paragraph: second paragraph:
Paragraph 1: Spring is the most beautiful time of the year - the Authors opinion and not fact.
Paragraph 2: Birds love the spring - Nobody knows how a bird is feeling, this is just based off of the Author trying to make a scenery for you.
Hoped this helped :)
Write the statement that represents 3 times the sum of 2 and 4"?
Answer:
Step-by-step explanation:
according to the question expression can be written as
=3(2+4)
How Many Inches Of Wood Is Needed To Frame An 8.5 By 11 inches Photograph?
Please help me with my work
Answer:
nooooooooooooooooooooooooooooooooooooooo
2. Jasmine ran 22 kilometers. One mile is approximately equal to 1.6 kilometers. Which
measurement is closest to the number of miles Jasmine ran?
a. 13.75 mi
b. 35.2 mi
c. 23.6 mi
d. 22 mi
Answer:
13.75
22/1.6 = 13.75
which set of sides would make a right angle
Answer:
PICTURE?
Step-by-step explanation:
What is the slope of a line perpendicular to y=2x
Answer:
[tex]-\frac{1}{2}[/tex]
Step-by-step explanation:
To find the slope of a perpendicular line just calculate the anti-reciprocal of 2
Slope of the perpendicular line: [tex]-\frac{1}{2}[/tex]
The equation would be:
[tex]y=-\frac{1}{2} x[/tex]
Jim is going to plant lettuce in a rectangular area of his garden. The rectangle is 9 feet long and 8 feet wide. What is the area of this rectangle?
63 sq ft
72 sq ft
34 ft
17 ft
Answer:
72 sq ft
Step-by-step explanation:
cuz 8x9 is 72 hope it helps
Construct the graph of the equation given by solving for the intercepts. Show all of the steps in finding the
intercepts and then plot the intercepts to create the graph. Label the intercepts, as well as the asis on the
graph
Y=-1/4x-1
answer
x, y - intercepts are (0, -1) and (-4, 0)
Step-by-step explanation:
put x and y = 0 respectively in given equation to get intercepts
What team has not been to a super bowl
A. Texans
B. Lions
C. Browns
D. Jaguars
E. All Of The Above
goodluck :)
Answer:
E
Step-by-step explanation:
Im smart and watch this stuff thats how! lol
Find the measure of angle 3 if the measure of angle 8 is 40
degrees.
Answer:
3=140°
Step-by-step explanation:
x:35 = 20:28
For what value of x is the proportion shown
above true?
Answer:
25
Step-by-step explanation:
x = (20/28) * 35
x = 25
The test scores for a group
pupils are as folows:
7, 4, 3, 9, 1,8, 4, 5, 4 what is the modal Score?
Answer:
4
Step-by-step explanation:
has most number of
An animal shelter provides shelter for dogs and cats. The animal shelter currently has a total of 117 animals. If the number of cats is 3 more than 5 times the number of dogs, how many dogs and cats are currently at the animal shelter?
Answer:
98 cats and 19 dogs
Step-by-step explanation:
cat = c
dog = d
The animal shelter currently has a total of 117 animals
c + d = 117
c = 117 - d
the number of cats is 3 more than 5 times the number of dogs
c = 3 + 5d
subtitute c
117 - d = 3 + 5d
117 - 3 = 5d + d
114 = 6d
6d = 114
d = 114/6 = 19
so, the cat is 117-19 = 98
help finding volume
I've been working all day so please now I ask you guys to help me, please I am starving
:(
Answer and Step-by-step explanation:
For the first one, x is equal to 61 (180 - 63 - 56 = 61)
and y = 4
51 = 12y + 3
48 = 12y
y = 4
For the second one,
x = 11
11x - 4 = 117
11x = 121
x = 11
y = 5
17y - 8 = 12 + 13y
4y = 20
y = 5
#teamtrees #PAW (Plant And Water)
Which postulate proves these triangles are similar? (giving brainliest and thanks to all!)
Complete these ordered pairs for this equation.
(0, ), (-1,), (1, ) y=2x+1
Help
Answer:
The completed ordered pair are;
(0, 1), (-1, -1), and (1, 3)
Step-by-step explanation:
The ordered pair, (x, y), presents the corresponding values of 'x' and 'y' based on a given relationship, or equation
The given relationship between 'x', and 'y' is, y = 2·x + 1
Therefore, given that the x-values (first of two values, separated by the coma) are given, we have;
In the given incomplete pair (0, ), when x = 0, therefore, y = 2 × 0 + 1 = 1
The complete ordered pair is (0, 1)
Similarly, for (-1, ), we have;
When x = -1, y = 2 × (-1) + 1 = -1
The complete ordered pair is (-1, -1)
We also have for the incomplete pair, (1, )
When x = 1, y = 2 × 1 + 1 = 3
The complete ordered pair is (1, 3)
The completed ordered pair for the equation, y = 2·x + 1, are therefore;
(0, 1), (-1, -1), and (1, 3).
You have 12 liters of a juice blend that is 25% juice. How many liters of pure juice need to be added in order to make the blend 70% juice
The graph shows the relationship between the total amount of money that Carly will have left, y, if she buys x packs of baseball cards.
A graph titled Money Left after Purchase. The x-axis shows packs of cards bought, numbered 1 to 9, and the y-axis shows the money left (in dollars), numbered 2 to 18. Blue diamonds appear at points (1, 16), (2, 12), (3, 8), (4, 4), (5, 0).
How much money will she have if she doesn't buy any packs of baseball cards?
$16
$18
$19
$20