.
h ( t ) = 112 t - 16 t²
When the rocket is 196 feet in the air:
196 = 112 t - 16 t²
16 t² - 112 t + 196 = 0
divide everything by 4 ( just makes numbers smaller and easier to work with)
4 t² - 28 t + 49 = 0
Now factor the equation:
( 2 t - 7 )² = 0
2 t - 7 = 0
2 t = 7
t = 7 : 2
t =
3.5 s
The rocket will be 196 feet in the air after 3.5 seconds.
Find the greatest common factor for the group of numbers. 12 , 28 , 24
Final answer:
The greatest common factor (GCF) of the numbers 12, 28, and 24 is found by identifying the smallest powers of their common prime factors, which are 2 and 3. Multiplying these together, 2 squared times 3, gives us the GCF of 12.
Explanation:
To find the greatest common factor (GCF) of the numbers 12, 28, and 24, we break each number down into its prime factors:
28 = 2 x 2 x 7
The smallest power of 3 that is common is just 3.
Therefore, the GCF of 12, 28 and 24 is 22 x 3 = 4 x 3 = 12.
A scale model of a human heart is 198 inches long. The scale is 34 to 1. How many inches long is the actual heart? Round your answer to the nearest whole number.
Find the equation of the quadratic function with zeros -1 and 1 and vertex at (0, -4).
Which of the following statements is false?
A. Opposite sides of a parallelogram are congruent.
B. A rhombus is a regular polygon.
C. The diagonals of a parallelogram bisect each other.
D. A rhombus is a parallelogram.
please explain
Find the value of each variable for the right triangles. Make sure all answers are in reduced radical form. Show your work.
Answer:
i) t = 5
ii) a = 3√7
iii) x =3√13
Step-by-step explanation:
We have right triangles.
Know the two sides of the triangle and need to find the third missing side.
In order to find the third side of the right triangle, we use pythagoras theorem.
It is,
(Hypotenuse)² = (base)² + (height)²
i)
13² = 12² + t²
169 = 144 + t²
t² = 25
t = 5.
ii)
12² = 9² + a²
144 = 81 + a²
144 - 81 = a²
a² = 63
a = √63
iii)
x² = 9² + 6²
x² = 81 + 36
x² = 117
x = √117
x = 3√13
if a number is tripled , it equals the product of four and the number diminished by two. find the number
How many reflectional symmetry does a regular hexagon have
Two mechanics worked on a car. the first mechanic worked for 5 hours, and the second mechanic worked for 15 hours. together they charged a total of $1450 . what was the rate charged per hour by each mechanic if the sum of the two rates was $160 per hour
Find the value of x if B is between A and C, AB = 4x – 9, BC = 3x + 5 and AC = 17.
Write the sum using summation notation, assuming the suggested pattern continues.
-1 + 2 + 5 + 8 + ... + 44
A) summation of negative three times n from n equals zero to fifteen
B) summation of the quantity negative one plus three n from n equals zero to fifteen
C)summation of negative three times n from n equals zero to infinity
D) summation of the quantity negative one plus three n from n equals zero to infinity
Erica purchased adult and youth tickets for a movie. She bought x adult tickets for $7 each and y youth tickets for $5. Write an expression that can be used to show the total cost, C, of all tickets.
Answer:
7x + 5y = C
Step-by-step explanation:
X is the number of people buying an adult ticket
Y is the number of people buying a youth ticket
Using this we can find C, cost
The value of a $225,000 house increases at a rate of 3.5% each year. Use a graph to predict the value of the house in 8 years.
A) ≈ $276,582
B) ≈ $286,263
C) ≈ $306,652
D) ≈ $296,282
The value of the house in 8 years. (D) ≈ $296,282
How to predict the value?The given parameters are:
Initial value, a = $225,000
Rate, r = 3.5%
The scenario is an illustration of an exponential growth function.
So, we have:
V(x) = a * (1 + r)^x
Substitute known values
V(x) = 225000 * (1 + 3.5%)^x
This gives
V(x) = 225000 * (1.035)^x
Next, we plot the graph of V(x)
See attachment
From the attached graph
V(x) = $296,282
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A person died leaving behind inheritance of Rs. 300000. Distribute the amount among 4 sons and 3 daughters so that each son gets double of what a daughter gets. Find the share of each when a debt of Rs. 80,000 was also to be paid.
The inheritance problem deals with distributing Rs. 300,000 among 4 sons and 3 daughters after a Rs. 80,000 debt is paid. Using algebra and ratios, it is determined that each daughter receives Rs. 20,000 while each son receives Rs. 40,000.
The situation given is that a person dies leaving behind an inheritance of Rs. 300,000, which must be divided among 4 sons and 3 daughters such that each son receives double what each daughter gets. Additionally, a debt of Rs. 80,000 is to be taken out of the inheritance before distribution.
First, we need to consider the debt. Subtracting the debt from the total inheritance, we have:
Total inheritance after debt = Rs. 300,000 - Rs. 80,000 = Rs. 220,000
Now, let's assume each daughter gets x amount. Therefore, each son gets 2x the amount. We can set up the equation accounting for all sons and daughters:
3x (daughters' shares) + 4(2x) (sons' shares) = Rs. 220,000
Simplifying:
3x + 8x = Rs. 220,000
11x = Rs. 220,000
x = Rs. 20,000 (share of each daughter)
Consequently, the share of each son will be double that of a daughter, which is:
2x = 2(Rs. 20,000) = Rs. 40,000 (share of each son)
jill traveled to the ferry office and back. the trip there took 5 hours and the trip back took 4 hours. she averaged 65 mph on the return trip. find the average speed of the trip there
We know from physics class that the formula for distance of a linear motion is given as:
d = v t
Where,
d = distance travelled
v = average velocity
t = time it took to reach the destination
Since the distance going to the office and back is just similar, therefore we can simply equate the two:
v1 t1 = v2 t2
Where 1 signifies going to the office and 2 signifies going back from the office. Therefore this yields to:
v1 * 5 hours = 65 mph * 4 hours
v1 = 52 mph
Answer: The average speed going to the office is 52 mph.
The average speed of Jill's trip to the ferry office was 52 mph, calculated by dividing the distance of 260 miles by the time of 5 hours.
To find the average speed of the trip there, we need to know the distance Jill traveled to the ferry office. Since she averaged 65 mph on the return trip which took 4 hours, the distance is calculated as speed x time, which equals 260 miles (65 mph x 4 hours).
The distance to the ferry office is the same as the distance back, so Jill also traveled 260 miles on the trip there. Given that the trip there took 5 hours, we can find the average speed by dividing the distance by the time. The average speed is 260 miles / 5 hours, which equals 52 mph.
I NEED THIS QUICK
Alvin’s first step in solving the given system of equations is to multiply the first equation by 2 and the second equation by –3. Which linear combination of Alvin’s system of equations reveals the number of solutions to the system?
9x + 4y = 36
6x + 2.5y = 24
After multiplying by the given coefficients and adding, the new equation obtained is:
8y - 7.5y = 0
after doing the calculations the answer is:
y = 0
x = 4
Because the two equations formed were independent, they had one solution
Answer:
its C
Step-by-step explanation:
what is the sum of 27 and 5 times a number is 187
Solve each system of equations by using elimination.
7)2t-u=17
3t+u=8
8)2j-k=3
3j+k==2
9)3c-2d=2
3c+4d=50
1. How many ways can you arrange the letters in the word MOMMY
A. 20
B. 25
C. 60
D. 120
2. A bag of marbles has 3 red, 2 blue and 5 white marbles in it. What is the probability of reaching in and selecting a white marble ?
a telephone pole casts a shadow that is 34 m long. find the height of the telephone pole if a statue that is 36cm tall casts a shadow 77cm long
How many hours is from 9:00am to 6:00 pm?
What is the length of the side opposite the 30° angle? HELP
HELP ASAP 30 POINTS
Evaluate f(3) for the piecewise function: f(x) = Which value represents f(3)?
–11
8
12.5
16
Answer:
-11
Step-by-step explanation:
Triangle END is translated using the rule (x, y) → (x − 4, y − 1) to create triangle E'N'D'. If a line segment is drawn from point E to point E' and from point N to point N', which statement would best describe the line segments drawn? (1 point
This answer is right!!!!! They are parallel and congruent.
PLEASE HELP!!!! If a function, f(x) is shifted to the left four units, what will the transformed function look like?
A bag contains 20 candies: 3 cherry, 4 orange, 7 lemon, and 6 grape. if two candies are selected simultaneously, what is the probability that they are both the same flavor?
Determine the slope of a line that makes an angle of 5pi/4 radians with the x-axis.
What is the product of any integer and –1?
A perfect circle figure has four lines of symmetry. True or false?
Use the equation mg sin A = umg cos A to determine the angle at which a waxed wood block on an inclined plane of wet snow begins to slide. Assume the coefficient of friction, u, is 0.17. 9.6º 42º 48º 22º
Using the friction equation mg sin A = μmg cos A and the given coefficient of friction (μ) of 0.17, the angle at which a waxed wood block begins to slide on wet snow is calculated to be approximately 9.6°.
Explanation:To find the angle at which a waxed wood block on an inclined plane of wet snow begins to slide, we can use the equation mg sin A = μmg cos A, where A is the angle of inclination, m is the mass of the block, g is the acceleration due to gravity, and μ is the coefficient of friction. Since the mass (m) and gravity (g) are both common factors on each side of the equation, they can be canceled out, leaving us with tan A = μ, where tan A is the tangent of the angle A, and μ is the coefficient of friction (0.17 in this case). Solving for A gives us A = arctan(μ). So, A = arctan(0.17), which calculates to approximately 9.6°. This is the angle at which the block begins to slide.
What is the graph of the function f(x) = the quantity of x squared plus 3 x plus 5, all over x plus 2
Answer:
Your answer is in the picture below
The graph approaches x=−2 asymptotically, has no x-intercepts, and the y-intercept of the graph is the point (0, 5).
Attached graph.
The graph of the function f(x) = (x² + 3x + 5 )/(x+ 2) is a parabola that is shifted to the left by 2 units.
The parabola is similar to the graph of the function y = x², but it is narrower because the denominator of the fraction is x + 2.
The graph also has a hole at the point (-2, 5), which is the point where the denominator of the fraction is 0.
Attached graph.
Here are the steps on how to sketch the graph of the function:
Sketch the graph of the function y = x².
Shift the graph to the left by 2 units.
Add a hole at the point (-2, 5).
The attached figure shows the graph of the function f(x) = (x² + 3x + 5 )/(x+ 2):
The graph of the function has the following features,
The domain of the function is all real numbers except for -2.
The range of the function is all real numbers except for 5.
The function has a minimum point at (-4, 1).
The function has a hole at the point (-2, 5).
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