A = (1/2)(x)(y)
Let x = diagonal 1
Let y = diagonal 2
The product of xy = 144.
This means that x = 12 and y = 12.
So, 12 • 12 = 144
Each diagonal is 12 feet.
Prove:
72 feet = (1/2)(12)(12) feet
72 feet = (1/2)(144) feet
72 feet = 72 feet
To find the length of each diagonal of the rhombus, we'll use the relationship between the area of a rhombus and its diagonals. The formula for the area (A) of a rhombus in terms of its diagonals (d1 and d2) is given by:
\[ A = \frac{d1 \cdot d2}{2} \]
Additionally, we are given the product of the diagonals, which means:
\[ d1 \cdot d2 = 144 \]
Since we are also given the area of the rhombus, which is 72 square feet, we can write:
\[ 72 = \frac{d1 \cdot d2}{2} \]
\[ 144 = d1 \cdot d2 \]
We have two equations with two variables, which we can solve simultaneously. However, in this case, since both equations involve the product of d1 and d2, we can use the given product directly. We know that:
\[ 2 \cdot 72 = 144 \]
\[ d1 \cdot d2 = 144 \]
We can use a property of numbers that states that the product of two numbers is equal to the square of their average if and only if the two numbers are the same. However, here we are interested in finding two different numbers whose product is 144.
We can do this by breaking down 144 into pairs of factors and then checking which pair would satisfy the condition that their product divided by 2 is equal to 72. The pair of factors of 144 that add up to 144 when multiplied and divide to 72 when halved are the actual lengths of the diagonals.
One way to determine the pair is through the process of factoring 144:
\[ 144 = 1 \times 144 \]
\[ 144 = 2 \times 72 \]
\[ 144 = 3 \times 48 \]
\[ 144 = 4 \times 36 \]
\[ 144 = 6 \times 24 \]
\[ 144 = 8 \times 18 \]
\[ 144 = 9 \times 16 \]
\[ 144 = 12 \times 12 \]
We need to find two different factors since a rhombus's diagonals are not equal. Among the listed factors, the pair 18 and 8 satisfy the condition because:
\[ \frac{18 \cdot 8}{2} = \frac{144}{2} = 72 \]
So, the lengths of the diagonals of the rhombus are 18 feet and 8 feet.
Evaluate [16 ÷ (2 + 3 • 2)] + [4 • (36 – 25)]
Answer:
46
Step-by-step explanation:
There is an open + in the middle. It does not have any brackets around it. Therefore you do it at the very last.
Left side of the plus sign.
[16 ÷ (2 + 3*2)] Do the multiplication inside the parenthesis ( 2*3) first.
= [16 ÷ (2 + 6)] Add inside the parenthesis.
= [16 ÷ 8 ] Do the division
= 2
Right side of the open plus sign
[4 * (36 - 25)] Do the subtraction first.
[4 * 11 ] Do the multiplication
44
Now combine both right and left side.
2 + 44
46
The answer is 46.
46
I don’t think I helped
A restaurant offers the soup of the day in 10 ounce servings. Suppose 85 customers ordered the soup of the day on Monday. To the nearest tenth, how many gallons of the soup were sold on Monday?
A) 4.8 gallons
B) 5.5 gallons
C) 6.6 gallons **
D) 7.4 gallons
Answer:
C) 6.6 gallons
Step-by-step explanation:
10oz * 85 = 850oz
There are 128 ounces in a gallon.
850/128 = 6.64
Answer: Option 'c' is correct.
Step-by-step explanation:
Since we have given that
Number of servings = 85
Number of ounces per serving = 10 ounce
Total number of ounces would be
[tex]85\times 10\\\\=850[/tex]
As we know that
1 gallon = 128 ounces
So, Number of gallons of the soup were sold on Monday would be \
[tex]\dfrac{850}{128}\\\\=6.64\\\\\approx 6.6 \ gallons[/tex]
Hence, Option 'c' is correct.
Find the slope.
A 2
B -1/2
C -2
D 1/2
Answer:
-2
Step-by-step explanation:
I believe its -2 :) :3
HELP SOON!! 20+ points to the right answers!
class b median is 80
class a median is 77
the comparison tells me in terms of the situation the data represents is that class b did better than class a
Addition and subtraction are inverse operations.
true or false
That is very true.
In mathematics, an inverse operation is an operation that undoes what was done by the previous operation. The four main mathematical operations are addition, subtraction, multiplication, division. The inverse of addition is subtraction and vice versa. The inverse of multiplication is division and vice versa.
Addition and subtraction are indeed inverse operations. They are algebraic operations that do the opposite of one another and can thus 'undo' each other's effects.
Explanation:The statement that Addition and subtraction are inverse operations is indeed true. In mathematics, an inverse operation is an operation that undoes what was done by the previous operation. In the case of addition and subtraction, they do exactly that. For instance, if you were to add 3 and 4 to get 7, you can undo this operation by subtracting 3 or 4 from 7 which will give back the other original number. Hence, addition and subtraction are deemed as inverse operations.
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The surface area of a right cone which has a base diameter of six units and a height of eight units is:
Answer: [tex]A = 108.80\ units^2[/tex]
Step-by-step explanation:
The surface area of right cone is calculated by the following formula
[tex]A = \pi r *\sqrt{r^2 +h^2}+\pi r^2[/tex]
Where r is the radius of the cone and h is the height
In this case we know that the diameter d of the base is:
[tex]d=2r[/tex]
So the radius is:
[tex]r=\frac{d}{2}\\\\r=\frac{6}{2}\\\\r=3\ units[/tex]
and
[tex]h=8\ units[/tex]
So the area is:
[tex]A = \pi*3 *\sqrt{3^2 +8^2}+\pi(3)^2[/tex]
[tex]A = 108.80\ units^2[/tex]
Answer:
[tex]SA=108.8 units^2[/tex]
Step-by-step explanation:
The surface area of a right cone is given by
[tex]S.A=\pi r^2+\pi rl[/tex]
The relation between the slant height l, the radius r, and the height h, is
[tex]l^2=r^2+h^2[/tex]
[tex]l^2=3^2+8^2[/tex]
[tex]l^2=9+64[/tex]
[tex]l^2=73[/tex]
[tex]l=\sqrt{73}[/tex]
[tex]S.A=\pi \times 3^2+\pi \times3\times\sqrt{73}[/tex]
[tex]S.A=\pi \times 3^2+\pi \times3\times\sqrt{73}[/tex]
[tex]SA=108.8 units^2[/tex]
12
Which polynomial function has zeros at -3, 0, and 4?
1 f(x) = (x + 3)(x2 + 4)
2 f(x)=(x2 – 3)(x – 4)
3 F(x) = x(x + 3)(x – 4)
4 f(x) = x(x - 3)(x +4)
Answer:
3
Step-by-step explanation:
Given a polynomial with zeros x = a, x = b, x = c
Then the factors are (x - a), (x - b) and (x - c)
and the polynomial is the product of the factors
f(x) = k(x - a)(x - b)(x - c) ← k is a multiplier
here the zeros are x = - 3, x = 0, x = 4, thus the factors are
(x - (- 3)), (x - 0) and (x - 4), that is
(x + 3), x and (x - 4)
let k = 1, then
f(x) = x(x + 3)(x - 4) → 3
Answer:
F(x) = x(x + 3)(x – 4)
Step-by-step explanation:
The polynomial function has zeros at -3, 0, and 4 is F(x) = x(x + 3)(x – 4)
x(x + 3)(x – 4), set each part = 0 to find the solutions
x(x + 3)(x – 4) = 0
x = 0
x + 3 = 0; x = -3
x - 4 = 0; x = 4
The number of sports drinks in a cooler during practice is modeled by the equation y=648-24x where y is the number of ounces in the cooler after practice and x is the number of players at the practice who take drinks from the cooler.
Part A
Based on the information in the equation, press the hotspots of three statements that are true.
Hint: 648 is the starting point.
-24 is the slope (rate of change).
The answers are:
B. Before practice, there are 648 ounces of sports drink in the cooler.
C. Each plater drinks approximately 24 ounces of sports drink at practice.
E. For each additional player that takes a drink, there will be approximately 24 fewer ounces of sporks drink remaining after the practice.
Why?We are given the equation:
[tex]y=f(x)=648-24x[/tex]
Let's discard each of the given options in order to find the three correct options.
A. The cooler is meant to be used only by 24 players: False.
If we want to calculate how many players can use the cooler, we need to isolate "x" (rate of change) from the given equation, so, isolating we have:
[tex]f(x)=648-24x[/tex]
[tex]0=648-24x[/tex]
[tex]648=24x\\\\24x=648\\\\x=\frac{648}{24}=27[/tex]
We have that the cooler can be used by 27 players, so, the first option that states that "The cooler is meant to be used only by 24 players" is false.
B. Before practice, there are 648 ounces of sports drink in the cooler: True.
We have that before the practice when the cooler is not being used by any player (or there is no any player) has 648 ounces (full), we can calculate it making the variable "x" equal to 0, so, calculating we have:
[tex]f(x)=648-24x[/tex]
[tex]f(0)=648-24*(0)=648[/tex]
Therefore, we have that the statement "Before practice, there are 648 ounces of sports drink in the cooler." is true.
C. Each plater drinks approximately 24 ounces of sports drink at practice: True.
From the statement, we know that the rate of change is equal to (-24), and it's equal to the number of ounces that each player drinks.
Hence, we have that the statement "Each plater drinks approximately 24 ounces of sports drink at practice." is true.
D. If 24 players get drinks from the cooler, they will drink a total of 648 ounces of sports drink: False.
If we want to calculate the number of ounces that 24 players will drink, we need to use the slope value. If we know that each player drinks 24 ounces, so, to calculate how many ounces of sports drink will 24 players drink, we need to use the following equation:
[tex]DrankOunces=24oz*Players\\\\DrankOunces=24oz*24=576oz[/tex]
We have that 24 players will drink a total of 576 ounces, so, the statement "If 24 players get drinks from the cooler, they will drink a total of 648 ounces of sports drink." is false.
E. For each additional player that takes a drink, there will be approximately 24 fewer ounces of sporks drink remaining after the practice: True.
From the statement and the equation, we know that the slope (rate of change) is negative, meaning that for each player (x) it will be 24 fewer ounces of sports drink after practice, for example, calculating for 1 and 2 players, we have:
[tex]f(1)=648-24*1=624[/tex]
[tex]f(x)=648-24*2=600[/tex]
We can see that for each player, it will be 24 fewer ounces of sports drink after practice.
Hence, we have that the statement "For each additional player that takes a drink, there will be approximately 24 fewer ounces of sporks drink remaining after the practice." is true.
Therefore, the correct options are:
B. Before practice, there are 648 ounces of sports drink in the cooler.
C. Each plater drinks approximately 24 ounces of sports drink at practice.
E. For each additional player that takes a drink, there will be approximately 24 fewer ounces of sporks drink remaining after the practice.
Have a nice day!
Multiply this problem
12(17q+19)
Answer:
204q+228
Step-by-step explanation:
ANSWER
[tex]12(17q + 19) = 204q + 228[/tex]
EXPLANATION
The given expression is:
[tex]12(17q + 19)[/tex]
Recall the distributive property,
If a, b, and c are real numbers, then
a(b+c)=ab+ac
We apply this property to expand the parenthesis and obtain:
[tex]12(17q + 19) = 12 \times 17q + 12 \times 19[/tex]
[tex]12(17q + 19) = 204q + 228[/tex]
please help me!!
A. Zara is learning about surface area and volume in math class. She begins to notice that she can apply this geometry in everyday life. When her mom makes a jelly sandwich for her lunch, Zara notices it is similar to a rectangular prism and decides to measure its dimensions. She measures the length as 13 cm, the width as 10.8 cm, and the height as 3 cm, as shown below.
What is the volume of Zara's sandwich? Show your work.
B. What is the surface area of Zara's sandwich? Show your work.
C. Zara cuts her sandwich in half down the middle, dividing it into two equal pieces. She then stacks one half of the sandwich on top of the other, as shown below.
Zara concludes that stacking the pieces like this will result in a sandwich with a greater volume and a smaller surface area than the original sandwich.
Are Zara's conclusions correct? Explain how you know, and support your explanation with mathematical evidence.
Type your answers in the box below. Make sure to label each part with A, B, and C.
The volume of Zara's sandwich formed as a rectangular prism, is 421.2 cm³, calculated by multiplying the sandwich's length, width, and height. The surface area is 561.6 cm² which is calculated by adding the areas of each face of the prism. When the sandwich is cut and stacked, the volume remains the same, but the surface area increases.
Explanation:A. To find the volume of a prism (such as Zara's sandwich), we multiply the length by the width by the height. So, for Zara's sandwich, we would calculate the volume as follows (in cubic centimeters): 13cm × 10.8cm × 3cm = 421.2 cm³.
B. The surface area of a rectangular prism is calculated by 2lw + 2lh + 2wh (where l is the length, w is the width, and h is the height. Plugging in the dimensions Zara measured, we find the surface area to be: 2(13cm × 10.8cm) + 2(13cm × 3cm) + 2(10.8cm × 3cm) = 561.6 cm².
C. When Zara cuts her sandwich in half and stacks one half on top of the other, she is effectively doubling the height while keeping the length and width the same. However, since neither the volume nor surface area formulas have a square or cube factor in the height, the volume will be the same. As for the surface area, because the height is now equivalent to two sandwich halves, and the 'length' is not shared between the two halves, the surface area increases. So, Zara's conclusions are incorrect. The volume stays the same, while the surface area increases.
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a. The volume of Zara's sandwich is 421.2 cm³.
b. The surface area of Zara's sandwich is 561.6 cm².
c. Zara's conclusions are incorrect. The volume stays the same, while the surface area increases.
A. To calculate the volume of a prism (such as Zara's sandwich), multiply its length by breadth by height. So, for Zara's sandwich, the volume would be calculated as follows (in cubic centimeters): 13cm 10.8cm 3cm = 421.2 cm³.
B. A rectangular prism's surface area is computed as 2lw + 2lh + 2wh (where l is the length, w is the width, and h is the height). Using Zara's measurements, we calculate the surface area to be: 2(13cm 10.8cm) + 2(13cm 3cm) + 2(10.8cm 3cm) = 561.6 cm².
C. By cutting her sandwich in half and stacking one half on top of the other, Zara essentially doubles the height while maintaining the length and width. The volume, however, will be the same because neither the volume nor surface area formulae include a square or cube element in the height. The surface area grows since the height is now equivalent to two sandwich half and the 'length' is not split between the two halves. Zara's conclusions are thus wrong. The volume remains constant while the surface area grows.
Jenny, who rides a moped, takes 2 hours less to travel 60 miles than Maureen takes to travel 50 miles on her bicycle. Jenny travels 10 miles per hour faster than Maureen. (Hint: speed = distance ÷ time.)
Answer:
See below
Step-by-step explanation:
Givens
Jenny's Stats
t = m - 2
d = 60 miles
r = r1 + 10
Maureen's stats
d = 50 miles
t = m
r = r1
=======
60 = (r1 + 10) * (m - 2)
50 = r1 * m
m = 50/r1
60 = (r1 + 10)* (50/r1 - 2)
60 = 50 + 500/r1 - 2r1 - 20
60 = 30 + 500/r1 - 2r1
60r1 = 30r1 + 500 - 2*r1^2
30r1 = 500 - 2r1^2
2r1^2 + 30r1 - 500
This quadratic factors into
2 (r1 - 10)(r1 + 25)
r1 = 10 mph The 25 has no meaning.
m = 50/r1
m = 50/10
m = 5 hours
m - 2 = 3 hours.
someone please help me choose all answers that apply
First you must combine like terms (x and x)
2y + 2 + (x + x)
2y + 2 + 2x
^^^All have the number two in common so we can take a two out like so...
2 (y + 1 + x)
or
2(x + y + 1)
There fore the answer is A!
Hope this helped!
~Just a girl in love with Shawn Mendes
meg has 47 baby carrots to share equally with 6 friends. she puts an equal number of carrots on 6 plates.how manycarrots are left?
Answer:
5 carrots
Step-by-step explanation:
Since there are 6 friends, find the factor closest to 47. The closest one would be 6*7=42. Thus, the answer is 5 because every friend gets 7 carrots.
The amount Mike gets paid weekly can be represented by the expression 2.50a + 290, where a is the number of cell phone accessories he sell that week.
What is the constant term in this expression and what does it represent?
Answer:
The 2.50a is the constant. He's getting paid 2.50 dollars weekly
Step-by-step explanation:
When theres a variable next to a number, that means that's the constant.
Answer:
no. Hes getting paid 290, guaranteed.
Step-by-step explanation:
...
what is the slope of (1,-3) and(-1,-3)
Answer:
slope = 0
Step-by-step explanation:
Calculate the slope m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (1, - 3) and (x₂, y₂ ) = (- 1, - 3)
m = [tex]\frac{-3+3}{-1-1}[/tex] = [tex]\frac{0}{-2}[/tex] = 0
Factored form of x^2+10x+5
Answer:
[tex]\large\boxed{x^2+10x+5=\left(x+5+2\sqrt5\right)\left(x+5-2\sqrt5\right)}[/tex]
Step-by-step explanation:
[tex]\text{Use the quadratic formula:}\\\\ax^2+bx+c=a\left(x-\dfrac{-b-\sqrt{b^2-4a}}{2a}\right)\left(x-\dfrac{-b+\sqrt{b^2-4ac}}{2a}\right)\\======================================[/tex]
[tex]\text{We have:}\ x^2+10x+5\to a=1,\ b=10\ \text{and}\ c=5\\\\\text{Substitute}\\\\b^2-4ac=10^2-4(1)(5)=100-20=80\\\sqrt{b^2-4ac}=\sqrt{80}=\sqrt{16\cdot5}=\sqrt{16}\cdot\sqrt5=4\sqrt5\\\\x_1=\dfrac{-10-4\sqrt5}{2(1)}=-5-2\sqrt5\\\\x_2=\dfrac{-10+4\sqrt5}{2(1)}=-5+2\sqrt5\\\\\bigg(x-\left(-5-2\sqrt5\right)\bigg)=\left(x+5+2\sqrt5\right)\\\\\bigg(x-\left(-5+2\sqrt5\right)\bigg)=\left(x+5-2\sqrt5\right)[/tex]
Which of the following are true statements?
Answer: Option A and Option B.
Step-by-step explanation:
You need to remember the logarithms properties:
[tex]log(a)+log(b)=log(ab)\\\\log(a)-log(b)=log(\frac{a}{b})\\\\log(a)^b=b*log(a)[/tex]
You can observe in Option A:
[tex]logM^p=p*logM[/tex] (This is true)
You can observe in Option B:
[tex]logM+logN=log(MN)[/tex] (This is true)
You can observe in Option C:
[tex]logM-logN=log(M-N)[/tex] (This is not true)
You can observe in Option D:
[tex](logM)^p=p*logM[/tex] (This is not true)
somebody i need help please
OK so first you find the square root of 363 which is 19.05255888325765 then you find the square root of 27 which is 5.196252422706632 then times that by 3 you get 15.5884572681199 so then you have 19.05255888325765 subtract 15.5884572681199 which equals 3.46410161513775
Hope this helped!
A falcon flying at a height of 200 yards spots a sparrow flying at a height of 150 yards. The location of the sparrow makes an angle of 40° from the horizontal line through the falcon's location. What is the distance x between the falcon and the sparrow? Assume that the ground beneath the birds is level.
Answer:
77.79 yard
Step-by-step explanation:
Given in the question that,
falcon flying at a height of 200 yards
sparrow flying at a height of 150 yards
Suppose, distance between Falcon and Sparrow = x yards
Step 1
Difference between the height of falcon and sparrow = 200-150 = 50 yards
Step 2
We will use Trigonometry Identity to find the distance between Falcon and Sparrow
SinФ = opposite / hypotenuse
Sin(40) = 50 / x
x = 50 / Sin(40)
x = 77.79 yard
Answer:
78
Step-by-step explanation:
A parallelogram has symmetry with respect to the point of intersection of its diagonals.
True
False
Use the remainder theorem to find the remainder for (x ^5 + 32) divided by (x+2) and state whether or not the binomial is a factor of the polynomial A:0; yes B: 0;no C: 1; yes D: -1; no
[tex]x+2[/tex] is a factor of [tex]x^5+32[/tex] because (by the remainder theorem) the remainder upon dividing [tex]x^5+32[/tex] by [tex]x+2[/tex] is [tex](-2)^5+32=0[/tex].
There's also the sum of fifth powers formula,
[tex]a^5+b^5=(a+b)(a^4-a^3b+a^2b^2-ab^3+b^4)[/tex]
ANSWER
The correct answer is A
EXPLANATION
The given polynomial is
[tex]p(x) = {x}^{5} + 32[/tex]
According to the remainder theorem, if p(x) is divided by x+2 the remainder is p(-2).
If the remainder is zero then x+2 is a factor of f(x).
We plug in x=-2 into the function to obtain;
[tex]p( - 2) = { (- 2)}^{5} + 32[/tex]
[tex]p( - 2) = - 32 + 32[/tex]
[tex]p( - 2) = 0[/tex]
Since the remainder is zero, x+2 is a factor.
The correct answer is A
Mrs. Rodriguez has a blueprint of her new house. The actual living room has a width of 20 feet and a length of 24 feet. If the scale
used to make the blueprint is inch = 4 feet, what is the length of the living room on the blueprint?
12 inches
3 inches
5inches
6 inches
Answer:
D) 6 in
Step-by-step explanation:
The length is 24 feet. The blueprint scales 1 ft : ¹/₄ in.
So, we can set up a proportion: 1 ft / ¹/₄ in = 24 ft / x in
Cross-multiply: 24 * ¹/₄ = x
Multiply: x = 6 in
mia mowed 6 lawns in 2 hours. what was her rate of mowing in lawns per hour
Answer:
3 lawns per hour
Step-by-step explanation:
Divide the lawns by the time: 6/2=3
6/2 = 3
So, Mia mowed 3 lawns in an hour.
Answer: 6 divided by 2 equals 3
The general term for the sequence 3,9,27,81,243, .... is
Answer:
[tex]a_n=3(3)^{n-1}[/tex]
Step-by-step explanation:
We have the following sequence
3,9,27,81,243
Note that if you divide each term of the sequence between the previous term you get:
[tex]\frac{9}{3} = 3\\\\\frac{27}{9} = 3\\\\\frac{81}{27} = 3[/tex]
then the radius of convergence of the series is r.
therefore this is a geometrical series.
The formula to find the general term [tex]a_n[/tex] of the geometric sequence is:
[tex]a_n=a_1(r)^{n-1}[/tex]
Where
[tex]a_1[/tex] is the first term of the sequence
Then the general term for this sequence is:
[tex]a_n=3(3)^{n-1}[/tex]
PLEASE HELP Jane can make a handcrafted dream catcher in 6 days. Zena makes the same dream catcher in 4 days. If they work together making dream catchers, how many days will it take to make 15 dream catchers? A. 2. B. 15. C. 21. D. 36.
The answer is D, 36 days. In 36 days, Jane can make 6 dream catchers and Zena can make 9. 9+6=15
Answer:The correct answer is 36 days
Step-by-step explanation: Jane-1 in 6 days or 2 in 12 days..Zena-1 in 4 days or 3 in 12 days. So in 12 days together the girls can make 5 dream catchers. In 24 days they would have 10, and in 36 days they would have 15.
what is -3×^2+1467x-86940=0 ?
For this case we must solve the following quadratic equation:
[tex]-3x ^ 2 + 1467x-86940 = 0[/tex]
If we divide both sides of the equation by 3 we have:
[tex]-x ^ 2 + 489-28980 = 0[/tex]
The solutions will come from:
[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}[/tex]
Where:
[tex]a = -1\\b = 489\\c = -28980[/tex]
Substituting:
[tex]x = \frac {-489 \pm \sqrt {(489) ^ 2-4 (-1) (- 28980)}} {2 (-1)}\\x = \frac {-489 \pm \sqrt {239121-115920}} {- 2}\\x = \frac {-489 \pm \sqrt {123201}} {- 2}\\x = \frac {-489 \pm351} {- 2}[/tex]
The roots are:
[tex]x_ {1} = \frac {-489 + 351} {- 2} = \frac {-138} {- 2} = 69\\x_ {2} = \frac {-489-351} {- 2} = \frac {-840} {- 2} = 420[/tex]
ANswer:
[tex]x_ {1} = 69\\x_ {2} = 420[/tex]
60 POINTS!!! CAN SOMEBODY PLEASE HELP ME!! I DONT WANT TO FAIL THIS!
3. A rocket is launched vertically from the ground with an initial velocity of 64 .
(a) Write a quadratic function that shows the height, in feet, of the rocket t seconds after it was launched.
(b) Graph on the coordinate plane.
(c) Use your graph from Part 3(b) to determine the rocket’s maximum height, the amount of time it took to reach its maximum height, and the amount of time it was in the air.
Answer:
(A): The equation is h(t)= -16t^2 + 64t
(B): The vertex points are (2,64) and the t intercepts are 0 and 4
(C): I dont know c!! i need help!
PLEASE EXPLAIN WELL!!!
a) The graph of the function is illustrated below.
b) The rocket's maximum height is 64 feet, it takes 2 seconds to reach this height.
c) The total time it was in the air is 4 seconds.
(A) Quadratic Function: To model the height of the rocket as it moves upward, we use a quadratic function in the form h(t) = at² + bt + c, where h(t) represents the height of the rocket at time t seconds. Since the rocket is moving vertically, we consider the acceleration due to gravity, which is -32 feet per second squared. The initial velocity of the rocket is 64 feet per second, so the coefficient of the linear term, b, is 64.
The equation for the height of the rocket is: h(t) = -16t² + 64t
(B) Graphing on the Coordinate Plane: To graph the quadratic function, we plot points on a coordinate plane. The vertex of the parabola represents the maximum height of the rocket, and the t-intercepts correspond to the times when the rocket hits the ground. The vertex of a quadratic function in the form h(t) = at² + bt + c is given by the coordinates (t_v, h(t_v)), where
t_v = -b / 2a.
In this case,
t_v = -64 / 2(-16) = 2 seconds.
(C) Finding Rocket's Maximum Height and Time in the Air: The vertex point we found earlier is (2, 64). This means that the rocket reaches its maximum height of 64 feet after 2 seconds of flight. To find the maximum height, we plug the value of t_v back into the equation:
h(t_v) = -16(2)² + 64(2) = -16(4) + 128 = 64 feet.
The rocket's maximum height is 64 feet, and it takes 2 seconds to reach this height. To find the total time the rocket is in the air, we look at the t-intercepts on the graph, which correspond to the times when the rocket hits the ground. From the equation h(t) = -16t² + 64t, we set h(t) to 0 and solve for t:
0 = -16t² + 64t t(0) = 0 (corresponding to the initial time of launch) t(4) = 4 seconds.
The rocket is in the air for 4 seconds.
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what is the factored form of 11x-x^2=0
Answer: [tex]x(11-x)=0[/tex]
Step-by-step explanation:
Given the quadratic equation [tex]11x-x^2=0[/tex], you need to factor it.
In order to find the form asked of the given equation, you need to factor out the common factor of the terms.
You can observe that the common factor of the terms of the equation is: [tex]x[/tex]
Now, knowing this, you must factor out [tex]x[/tex]. Then you get the following form:
[tex]x(11-x)=0[/tex]
Therefore, the factored fom of the equation [tex]11x-x^2=0[/tex] is:
[tex]x(11-x)=0[/tex]
If the measure of arc AD = (6x – 80)° and 2G = (x + 2)°, what is the measure of G?
Answer:
The measure of G = 9.2°
Step-by-step explanation:
From the figure we can write,
The measure of <G is half the the measure of arc AD
To find the value of x
We have AD = (6x - 80)° and 2G = (x + 2)°
6x - 80 = (x + 2)
6x - 80 = x + 2
6x - x = 82
5x = 82
x = 82/5 = 16.4
To find the measure of <gG
m<G = (x + 2 )/2
= (16.4 + 2)/2 = 18.4 = 9.2
Therefore the measure of <G = 9.2°
What value can be written on the blank line to make the expressions equivalent?
48 + 54 = x(8+9)
Answer:
x=6
Hope This Helps! Have A Nice Day!!
Answer:
x=6
Step-by-step explanation:
[tex]48+54=x(8+9)\\\\102=8x+9x\\\\102=17x\\\\6=x[/tex]