Suppose Paul kicks a soccer ball straight up into the air with an initial velocity of 96 feet per second. The function f(x) = -16t2 + 96t gives the height, in feet, of the soccer ball after t seconds. This function is shown in the graph below.
How long will it take for the ball to hit the ground? Write your answer as an integer.
Answers
The ball will come to ground after 6 seconds.
We have a function of time given by -
f(x) = [tex]-16t^{2} +96t[/tex]
that gives the height of the ball in feet at ' t ' second.
We have to find out after how much time the ball will hit the ground.
In the question given to us above, the type of motion discussed is called ?The type of motion discussed in the above question is a two - dimensional projectile motion.
We have - h(t) = f(x) = [tex]-16t^{2} +96t[/tex]
Now, in order to find out the time at which the ball will hit the ground again, we will equate h(t) = f(x) = 0
[tex]-16t^{2} +96t=0\\-16t(t - 6)=0\\-16t =0\;\;\;\;\;\;t -6 = 0[/tex]
Now, time can never be 0.
Hence -
t - 6 = 0
t = 6 seconds.
Hence, the ball will come to ground after 6 seconds.
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Related Questions
You borrow $10,000 to buy a carThe simple interest rate is 3%. You pay the loan oft after 6 years. What is the total amount you paid for the loan?
Answers
Answer:
Step-by-step explanation:
Amount loaned = $10,000
Interest rate = 3%
Duration = 6 years
10,000 / 100 x 3/1 × 6
= 300 × 6
= 1800 + 10,000
Total Amount to pay
= $11,800
The three sides of a triangular lot are represented by x , 2 x , and 3 x + 2. Find each side if the perimeter of the triangular lot is 362 feet. The lengths of the sides of the triangle are :
Answers
Answer:
60 ft, 120 ft, 182 ft
Step-by-step explanation:
Hi there,
To find the perimiter of a polygon, you need to add of all of the sides.
So, let's do that:
x + 2x + 3x+2
Since we are given the perimeter, we make what we just did above, equal to the perimeter
x + 2x + 3x +2 = 362
Combine lke terms...
6x + 2 = 362
Subtract 2 from both sides to start to isolate the variable...
6x = 360
Divide both sides by 6 to isolate x...
x = 60
But we're not done yet...
The length of the first side is 60 ft, the length of the second side is 2*60 which is 120 ft, and the length of the third side is 3*60 + 2 which is 182 ft.
Let's check...
Does 60 + 120 + 182 = 362?
362 = 362
Our answers are right
Hope this helps! Stay safe!
- Emily
The sum of three numbers is 10. Two times the second number minus the first number is equal to 12. The first number minus the second number plus twice the third number equals 7. Find the numbers. Listed in order from smallest to largest, the numbers are
Answers
Answer:
The answer to your question is x = -2, y = 5 and z = 7
Step-by-step explanation:
Data
first number = x
second number = y
third number = z
Process
1.- Write equations to solve this problem
x + y + z = 10 Equation l
2y - x = 12 Equation ll
x - y + 2z = 7 Equation lll
2.- Solve equation ll for x
x = 2y - 12
3.- Substitute the previous equation in equation l and lll
(2y - 12) + y + z = 10 (2y - 12) - y + 2z = 7
2y - 12 + y + z = 10 2y - 12 - y + 2z = 7
3y + z = 10 + 12 y + 2z = 19
3y + z = 22
4.- Solve for y and z
-2(3y + z = 22)
y + 2z = 19
-6y - 2z = -44
y + 2z = 19
-5y + 0 = -25
y = -25/-5
y = 5
-Find z
5 + 2z = 19
2z = 19 - 5
2z = 14
z = 14/2
z = 7
5.- Find x
x + 5 + 7 = 10
x = 10 - 5 - 7
x = -2
Listed in order from smallest to largest: -2, 5, 7.
Let's denote the three numbers as follows:
- First number: x
- Second number: y
- Third number: z
We have three equations based on the given information:
1. x + y + z = 10
2. 2y - x = 12
3. x - y + 2z = 7
We can solve this system of equations to find the values of x, y, and z.
From equation 2, we can isolate x:
x = 2y - 12
Now substitute the value of x in equations 1 and 3:
1. (2y - 12) + y + z = 10
3y + z = 22
3. (2y - 12) - y + 2z = 7
y + 2z = 19
Now we have a system of two equations with two variables (y and z):
1. 3y + z = 22
2. y + 2z = 19
Let's solve for one of the variables in terms of the other. From equation 2, we can isolate y:
y = 19 - 2z
Now substitute this value of y into equation 1:
3(19 - 2z) + z = 22
57 - 6z + z = 22
-5z = -35
z = 7
Substitute the value of z back into the equation for y:
y = 19 - 2(7)
y = 5
Now that we have values for y and z, we can substitute them back into the equation for x:
x = 2y - 12
x = 2(5) - 12
x = 10 - 12
x = -2
So, the numbers are:
First number: -2
Second number: 5
Third number: 7
Listed in order from smallest to largest: -2, 5, 7.
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What is the product of -9x (5-2x)
Answers
Answer:
Step-by-step explanation:
It s 55555555
Answer:
18x^2-45x
Step-by-step explanation:
-9x (5-2x)
=-9x X 5-(-9x) X 2x
=-9 X 5x+9 X 2xx
=18x^2-45x
I hope this helps!
What is the initial value of the function represented by this graph? (5 points) Question 7 options: 1) 1 2) 5 3) 6 4)
Answers
Answer:
Initial value is at t = 0
Y-intercept is the initial value
Which ordered pair is a solution of the equation?
y - 4= 7(x – 6)
Choose 1 answer:
A. Only 5,4
B. Only 6,5
C both 5,4 and 6,5
D. Neither
Answers
Evaluate 5 + (-4) +(-7) + 2.
Answers
Answer:
-4
Step-by-step explanation:
Solve for x
-18x+21>-15 or 20x-13>27
Answers
Answer:
all value of x are equal
Step-by-step explanation:
Large samples of women and men are obtained, and the hemoglobin level is measured in each subject. here is the 95% confidence interval for the difference between the two population means, where the measures from women correspond to population 1 and the measures from men correspond to population 2: negative 1.76 g divided by dl less than mu 1 minus mu 2 less than minus 1.62 g divided by dl−1.76 g/dl<μ1−μ2<−1.62 g/dl. complete parts (a) through (c) below.
a. what does the confidence interval suggest about equality of the mean hemoglobin level in women and the mean hemoglobin level in men? because the confidence interval includes nothing, it appears that there is a significant difference between the mean level of hemoglobin in women and the mean level of hemoglobin in men. (type an integer or a decimal. do not
Answers
Answer:
1. The mean hemoglobin level in men is not equal to the mean hemoglobin level in women and
2. There is more hemoglobin in the average man than in the woman
Step-by-step explanation:
The confidence interval is from
-1.76 g/dl < μ₁ - μ₂ < -1.62 g/dl
Here we note that the range in the confidence interval for the difference between the two means lie in the negative part of the number line which is indicative of that μ₁ - μ₂ ≠ 0 or μ₁ ≠ μ₂
That is the statistic of the confidence interval implies that the mean hemoglobin level in men is not equal to the mean hemoglobin level in women and
That there is more hemoglobin in the average man than in the woman.
40 - 5n = -2 need explanation as well
Answers
Answer: n = 8.4
Step-by-step explanation:
40 - 5n = -2
First, subtract 40 from each side of the equation
-5n = -42
Then, divide each side by -5
n = 8.4
The -5 and -42 cancel each other out when dividing, so n = 8.4 is positive.
Answer:
n=8.4
Step-by-step explanation:
To solve, we need to isolate the variable, n
40 -5n =-2
Subtract 40 from both sides
40-40-5n= -2 -40
-5n= -42
Divide both sides by -5
-5n/-5=-42/-5
n=42/5
n=8.4
What is the vertex form of the equation
y= -x^2+10x-30
Answers
Answer:
The answer to your question is Vertex = (5 , -5)
Step-by-step explanation:
Data
Equation y = - x² + 10x - 30
Process
1.- Add 30 units in both sides
y + 30 = -x² + 10x - 30 + 30
2.- Simplify
y + 30 = -x² + 10x
3.- Factor -1 in the right side
y + 30 = -(x² - 10x )
4.- Complete the perfect square trinomial
y + 30 - 5²= -(x² - 10x + 5²)
5.- Simplify
y + 30 - 25 = -(x² - 10x + 25)
y + 5 = -(x - 5)²
6.- Find the vertex
Vertex = (5 , -5)
What does vertex in graphs mean?
Answers
A bag contains 10 marbles of the same size that are red, yellow, and orange. The probability of picking a red marble is 10%. The probability of picking a yellow marble is 60%. Determine the probability of picking an orange marble from the bag and then classify the probability of picking an orange marble as likely or not likely to occur.
Answers
Answer:
30% not likely
Step-by-step explanation:
We have 10 marbles
The probability must equal 100%
10% red
60% yellow
----------------
70 %
That leaves 30% for orange
Orange is 30%
This is less than 50% so it is not likely to occur
Answer:
30%
not likely
Step-by-step explanation:
P(orange) = 100 - 10 - 60
= 30%
Less likely or not likely
is 29 a monomial please help
Answers
Answer:
it is
Step-by-step explanation:
Any number, all by itself, is a monomial, like 5 or 2700.
Answer:
Yes it is a monomial
Step-by-step explanation:
There's only one number, there's no operations to do so its a monomial :)
Esther needs a bin for her hair bows. A yellow bin has a length of 11.4 inches, a width of 4.2 inches, and a height of LaTeX: \frac{8}{3}8 3 inches. A red bin has a length of 9 inches, a width of 5.45 inches and a height of LaTeX: \frac{11}{5}11 5 inches. What is the volume of the bin with the greatest volume? Explain your answer.
Answers
Answer:
Yellow Bin
Step-by-step explanation:
Yellow Bin
Length = 11.4 inches,
Width = 4.2 inches,
Height = [tex]\frac{8}{3}[/tex]
Volume of the yellow bin=LWH[tex]=11.4 X 4.2 X \frac{8}{3}=127.68 \:cubic \:inches[/tex]
Red Bin
Length = 9 inches,
Width = 5.45 inches,
Height = [tex]\frac{11}{5}[/tex]
Volume of the red bin=LWH[tex]=9X 5.45 X \frac{11}{5}=107.91 \:cubic \:inches[/tex]
The yellow bin has a greater volume since 127.68 is greater than 107.91.
Write your own word problem that involves 1 1/3 -2/3 . Solve the problem, and explain what your solution means in terms of the problem that you wrote.
Answers
Answer:
If there are eleven apples to be shared between 3 boys and two bananas to be shared between 3 girls, find the difference between them.
Step-by-step explanation:
So there are 11 apples to be shared between 3 boys, which is represented mathematically as 11/3
And 2 bananas to be shared between 3 girls, which can be represented mathematically as 2/3, find the difference.
The difference between them would be 11/3 - 2/3
Solving this problem, they both have the same denominator, so we subtract the numerators directly.
11/3 - 2/3 = 9/3
Which is equals to 3.
So the difference between both of them is 3.
Fine the volume of the sphere. Leave the answer in terms of pi.
Answers
Given:
The area of the given sphere = 36π in²
To find the volume of the given sphere.
We need to find the radius first.
Formula
The area of a sphere [tex]A = 4\pi r^{2}[/tex]The volume of the sphere [tex]V = \frac{4}{3} \pi r^{3}[/tex]where, r be the radius of the sphere.
Now,
According to the problem,
[tex]4\pi r^{2} = 36\pi[/tex]
or,[tex]4r^{2} = 36\\[/tex] [ Eliminating π from both the side]
or, [tex]r^{2} = \frac{36}{4}[/tex]
or, [tex]r = \sqrt{9}[/tex]
or, [tex]r = 3[/tex]
So,
The radius of the sphere is 3 inches
Therefore,
The volume of the sphere is
[tex]V = \frac{4}{3} \pi (3)^{3}[/tex]
or, [tex]V = 36\pi[/tex]
Hence,
The volume of the sphere is 36π cube inches.
Rebeckah answered 42 of the 60 questions correctly on a test. Which method should she use to find the percent of questions she answered correctly? First, subtract 42 from 60 to find the ratio of questions answered correctly to total questions, which is . Then, add 40 to the numerator and denominator to find the percent: . First, find the ratio of questions answered correctly to total questions, which is . Then, add 40 to the numerator and denominator to find the percent: . First, subtract 42 from 60 to find the ratio of questions answered correctly to total questions, which is . Then, simplify the ratio to . Finally, multiply the numerator and denominator by 10 to find the percent: . First, find the ratio of questions answered correctly to total questions, which is . Then, simplify the ratio to . Finally, multiply the numerator and denominator by 10 to get
Answers
Answer:
The last option
Step-by-step explanation:
To find a percentage of something you need
[tex]\frac{expected}{total}*100[/tex]
The expected is correct marks, the total is the total amount - then you multiply by 100 to turn the decimal into a percentage.
Answer:
the answer is D
Step-by-step explanation:
Plz helppppppppppp me with these
Answers
Answer:
help with what tho
Step-by-step explanation:
Answer:
with what I can't see it
Step-by-step explanation:
Mr.Hawkins gets two bonus payments every year this year his bonus payment was 1/4of his salary his second payment was 1/8 of his salary what is the fraction for his combined bonus payments?
Answers
Answer:
3/8
Step-by-step explanation:
1/4 + 1/8 = 2/8 + 1/8 = 3/8
After you give the fractions a common denominator, you can add their numerators to find the numerator of the result.
Mr. Hawkins's combined bonus payments are 3/8 of his salary.
Please help, geometry
Answers
Step-by-step explanation:
As it is a quadrilateral so sum of all angles of quadrilateral is equal to 360°
14x - 11° + 8x + 7° + 5x + 18° + 10x + 13° = 360°
37x+ 27° = 360°
37x = 360° - 27°
37x = 333°
x = 333° / 37
Therefore x = 9°
Now
<B = 8 * 9° + 7° = 79°
Hope it will help you.
Answer: The answer is 79.0°
Step-by-step explanation:
A quadrilateral will always have 360° and four sides. Keep that in mind, that's a universal rule of geometry.
Here, the sum of all sides is equal to 360°. Therefore, we make an equation:
[tex](14x-11) + (8x+7) + (5x+18) + (10x + 13) = 360[/tex]
Simplify by adding and subtracting like terms.
[tex]37x +27=360[/tex]
Isolate x by first passing the 27 to the other side.
[tex]37x = 333[/tex]
Divide by 37 to isolate x.
[tex]x = 9[/tex]
To find m∠B, we plug in x to [tex](8x+7)[/tex]
which gives you: [tex](8*9+7) = 79[/tex]
The answer is 79.0°
Curious if it is correct? Let's double check.
Plug in the x=9 to all the x values and add them up. You should get 360, which makes the answer correct.
Evaluate the expression (2a)3
Answers
Hope this will help u
Final answer:
To evaluate the expression (2a)³, we cube the numeric term, resulting in 8, and multiply the exponent of the variable 'a' by 3, which gives us the final result of 8a³.
Explanation:
The expression given, (2a)³, requires us to cubing of exponentials. Cubing in mathematics involves raising a number or expression to the third power. In this case, the number 2 and the variable a are multiplied together first, and then that result is raised to the power of three. To evaluate this expression, you would do the following steps:
Cube the digit term in the usual way, which is 2 cubed or 23, which equals 8.Multiply the exponent of the exponential term by 3. Since the original expression has the variable 'a' to the first power, multiplying the exponent by 3 means 'a' will now have an exponent of 3.Combining these results, the expression (2a)³ becomes 8a³.
A radio antenna is kept perpendicular to the ground by three wires of equal length. The wires touch the ground at three points on a circle whose center is at the base of the antenna. If the wires touch the ground at (9,-19),(-21,-19), and(14,16), what are the coordinates of the base of the antenna?
Answers
Answer:
The coordinates of the base of the antenna is (-6. 1)
Step-by-step explanation:
Here we are required to find the center of a circle given points on the circumference
The equation of a circle is
(x - h)² + (y - k)² = r²
Where:
x and y are points on the circumference
h and k are coordinates of the center of the circle and
r = The radius of the circle
Since we have the values for the points on the circumference, we are left with three unknowns, which we can find with three equations as follows;
By plugging in the values for x and y at the respective points we get,
At (9, -19) → (9 - h)² + (-19 - k)² = r²...............(1)
At (-21, -19) → (-21 - h)² + (-19 - k)² = r².....,...(2)
At (14, 16 ) → (14 - h)² + (16 - k)² = r² ............(3)
Solving, we get from (1) (-19 - k)² = r² - (9 - h)²
Plugging in the value of (-19 - k)² in equation (2) we get
(-21 - h)² + r² - (9 - h)² = r²
So that (-21 - h)² - (9 - h)² = r² - r² = 0
and (-21 - h)² - (9 - h)² = 0 gives
60·h +360 = 0 or h = -6
Plugging in the value of h = -6 in equation (3) we get
(14 - (-6))² + (16 - k)² = r²
20² + (16 - k)² = r² .................(4)
similarly from equation (1) we get
(9 - (-6))² + (-19 - k)² = r²
15² + (-19 - k)² = r² ................(5)
Subtracting equation (5) from (4) gives
20² - 15² + (16 - k)² - (-19 - k)² = 0
Which gives
-70·k + 70 = 0
or k = 1
Therefore the coordinates of the base of the antenna = (-6. 1).
c^2=4? Anyone want to help?
Answers
Answer: c=2
Step-by-step explanation: the square root of c^2 equals the squae root of 4 which is 2 so your left with c=2
At Central High School, 85% of all senior girls attended and 65% of all senior boys attended the Spring Dance. Of all attendees, 20% won a prize. A. Assuming that the number of senior girls at Central High School is about equal to the number of senior boys, estimate the probability that a randomly selected senior won a prize at the dance. Explain. Enter your answer. B. Construct Arguments If you knew whether the selected student was a boy or a girl, would your estimate change
Answers
Answer:
a) 0.30 (30%)
b) Boy: 0.13 (13%) , Girl : 0.17 (17%)
Step-by-step explanation:
Given:-
- The probability of senior girls attend spring dance, P(GA) = 0.85
- The probability of senior boys attend spring dance, P(BA) = 0.65
- The probability that an attendee wins a prize, P(W) = 0.20
Find:-
Estimate the probability that a randomly selected senior won a prize at the dance.
Construct Arguments If you knew whether the selected student was a boy or a girl, would your estimate change
Solution:-
- First realize that the probability for any senior student to attends the spring dance and winning a prize are independent events.
- So for independent events, the probability that a "girl or a boy" attends the spring dance and wins a prize can be determined:
P ( GA & W ) = P(GA)*P(W) = 0.85*0.20 = 0.17 (17%)
P ( BA & W ) = P(BA)*P(W) = 0.65*0.20 = 0.13 (13%)
P ( (BA & W) U (GA & W) ) = P ( BA & W ) + P ( GA & W )
= 0.17 + 0.13
Answer = 0.3 (30%)
- So the estimate probability that a randomly selected senior won a prize at the dance is 0.3 or 30% of all attendee.
- If the randomly selected senior was a girl would be the proportion of people who won the prize.
P ( GA & W ) = 0.17 (17%)
- Similarly, If the randomly selected senior was a boy would be the proportion of people who won the prize.
P ( BA & W ) = 0.13 (13%)
Answer:
a) 30%
b) the estimate wouldnt change as far as the probabilities is been maintained. thre can only be a shift in the gender probability depending on whether there are more number of boys or girls.
Step-by-step explanation:
a) Prob( all senior girl attended) = 85%
Prob ( all senior boy attended) = 65%
Prob( won a price) = 20%
Prob( a senior girl attends and win a price) = 85% x 20%
= 17%
Prob ( a senior boy attends and win a price) = 65% x 20%
= 13%
Prob( a senior won a price) = 17% + 13%
= 30%
b) The estimate wouldnt change as far as the probabilities is been maintained. thre can only be a shift in the gender probability depending on whether there are more number of boys or girls.
if angle 5 is 120 degrees, what is the measure of angle 6?
Answers
Final answer:
Without more context, the measure of angle 6 cannot be determined from the given information that angle 5 is 120 degrees.
Explanation:
To determine the measure of angle 6, we need additional information about the context in which angle 5 and angle 6 are related. Since the question does not provide sufficient details, such as whether the angles are supplementary, complementary, or part of a geometric figure like a triangle or polygon, it's not possible to provide the measure of angle 6 based solely on the given information that angle 5 is 120 degrees. In geometry, the relationships between angles often depend on the shapes they are part of or the lines intersecting with them. If angle 5 and angle 6 are supplementary angles (angles that add up to 180 degrees), for instance, we could subtract the measure of angle 5 from 180 degrees to get angle 6. However, without more details, we cannot accurately provide the measure of angle 6.
If tan B = 1.6732, what is the measure of B to the nearest tenth of a degree
Answers
Answer:
59.1 °
Step-by-step explanation:
-Given that Tan B=1.6732
-Angle B is equivalent to the tan inverse of the tan B value:
[tex]\angle B=Tan^{-1}B\\\\\angle B=Tan^{-1}(1.6732)\\\\=59.1350\approx59.1\textdegree[/tex]
Hence, angle B is 59.1 °
To find the measure of angle B, you can use the inverse tangent function (arctan) to find the angle whose tangent is 1.6732.
The measure of angle B is approximately 59.7 degrees.
Explanation:To find the measure of angle B, you can use the inverse tangent function (arctan) to find the angle whose tangent is 1.6732. First, convert the tangent value to radians by using the formula tan(B) = opposite/adjacent. Then, take the arctan of B to find the measure in radians. Finally, convert the radians to degrees by multiplying by 180/pi.
Step-by-step:
Convert the tangent value to radians: tan(B) = opposite/adjacent => B = arctan(1.6732)Convert radians to degrees: B (in degrees) = B (in radians) * 180/piPlugging in the given value, B ≈ 59.7 degrees to the nearest tenth of a degree.
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Yasmin arrived home from play practice at 4:25 pm. The walk took 15 minutes. Practice began 20 minutes after the final bell and lasted for a half hour. When did school end
Answers
Answer:
Step-by-step explanation3:45
Answer:
3:20 p.m
Step-by-step explanation:
um i need help with this.
Answers
Answer:
none
Step-by-step explanation:
A student solved 3/x-4 =x/7 in six steps as shown.Which statement is an accurate interpretation of the students work
Answers
Answer:
A student solved 3/x−4=x/7 in six steps, as shown:
Step 1: 3=x(x−4)/7
Step 2: 21=x(x−4)
Step 3: 21=x^2−4(x)
Step 4: 0=x^2−4(x)−21
Step 5: 0=(x−7)(x+3)
Step 6: x=−3, x=7
Which statement is an accurate interpretation of the student's work?
A.The student solved the equation correctly.
B.The student made an error in step 2.
C.The student made an error in step 5.
D.Only x=7 is a solution to the original equation.
Option A is the right choice.
Step-by-step explanation:
Given:
An equation and its step-wise work.
We have to check whether the steps are correct or not.
The equation is:
⇒ [tex]\frac{3}{x-4} = \frac{x}{7}[/tex]
Solution:
⇒ [tex]21=x(x-4)[/tex] ...cross multiplying terms.
⇒ [tex]21=x^2-4x[/tex]
⇒ [tex]x^2-4x-21=0[/tex]
⇒ [tex]x^2-7x+3x-21=0[/tex] ...using middle term splitting
⇒ [tex]x(x-7)+3(x-7)=0[/tex]
⇒ [tex](x+3)(x-7)[/tex]
⇒ [tex]x=-3\ and\ x=7[/tex]
The student have solved the question correctly.