Answer:
The golf ball was in the air for 4 seconds.
Step-by-step explanation:
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]
[tex]\Delta = b^{2} - 4ac[/tex]
In this question:
We have to find the amount of time it takes for the ball to hit the ground. We have that:
[tex]d(t) = -2t^2 + 7t + 4[/tex]
Which is a quadratic equation with [tex]a = -2, b = 7, c = 4[/tex].
How long is the golf ball in the air?
We have to find t for which [tex]d(t) = 0[/tex]
So
[tex]-2t^2 + 7t + 4 = 0[/tex]
[tex]\Delta = b^{2} - 4ac = (7)^2 - 4(-2)(4) = 81[/tex]
[tex]t_{1} = \frac{-7 + \sqrt{81}}{2*(-2)} = -0.5[/tex]
[tex]t_{2} = \frac{-7 - \sqrt{81}}{2*(-2)} = 4[/tex]
Time is a positive measure, so t = 4.
The golf ball was in the air for 4 seconds.
PLS HELP ASAP!
Shown below is a cylinder. Calculate the volume using 3.14 for π
Answer:
V = 678.24 cm^3
Step-by-step explanation:
Formula for volume of a cylinder:
the radius is half of the diameter (12/2 = 6)
[tex]V = \pi r^{2} h\\V = \pi 6^{2} 6\\\\V = 678.24[/tex] cm^3
Answer:
678.24 cm^3
Step-by-step explanation:
The volume of a cylinder is given by
V = pi r^2 h where r is the radius and h is the height
We know the diameter
r =d/2 = 12/2 = 6
V = 3.14 * 6^2 * 6
678.24 cm^3
I need help plzzz
How can you construct the perpendicular bisector of segment RS by folding a piece of paper
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Answer:
(c) fold it so R lies on top of S
Step-by-step explanation:
The crease will be the perpendicular bisector of RS when R and S are equidistant from it. That can be accomplished by folding the paper so points R and S lie on top of each other.
Solve for X.
A. 10.96
B. 4.88
C. 0.04
D. 5.34
Answer:
4.88
Step-by-step explanation:
That may be the question
which exponential equation is equivalent to the logarithmic equation below? log478=a
A. 478^10 = a
B. a^10 = 478
C. 478^a = 10
D. 10^a = 478
What is the slope of a line perpendicular to the line whose equation is x + 2y = 2. Fully simplify your answer.
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Answer:
2
Step-by-step explanation:
We can solve for y to find the slope of the given line.
x +2y = 2
2y = -x +2 . . . . . subtract x
y = -1/2x +1 . . . . divide by the coefficient of y
The slope is the x-coefficient, -1/2.
Any perpendicular line will have a slope that is the opposite reciprocal of this:
-1/(-1/2) = 2
A perpendicular line will have a slope of 2.
ANSWER ASAP!! Use the substitution method to solve the system of equations. 3x+7y=1 and y=x-7
Answer:
x=5
y = -2
(5,-2)
Step-by-step explanation:
3x+7y=1 and y=x-7
Substitute the second equation in for y in the first equation
3x+7( x-7)=1
Distribute
3x+ 7x - 49 = 1
Combine like terms
10x - 49 =1
Add 49 to each side
10x-49+49 = 1+49
10x = 50
Divide by 10
10x/10 = 50/10
x = 5
Now find y
y = x-7
y = 5-7
y = -2
Will Mark Brainlest Help pls
Answer:
13
HOPE THIS HELPS YOU......
A rectangular room has a perimeter of 70m what could be the length of the longest side of the room
Answer:
34
Step-by-step explanation:
70-2=68
side 1 & 3=1m each
68 divided by 2 = 34
side 2 & 4 = 34m each
A mouse is trapped in a maze. To
find his way out, he walks 15 m,
makes a 90° left turn, walks 8 m,
makes another 90° left turn, and
walks 10 m. What is the magnitude
of the resultant vector?
Answer: Approximately 9.43 meters
The more accurate version is 9.4339811320566 but that's not exact.
This is exact magnitude is sqrt(89)
=======================================================
Explanation:
Let's draw an xy grid for this. Place the starting point at (0,0) which I'll call point A. Now let's say the mouse goes east 15 meters. That would move it to (15,0) which is marked as point B. Refer to the diagram below.
From point B, we move to C which is at (15,8). So the mouse has gone 8 meters north. It might help to turn the page so that the east direction is facing completely north, and then look to the left and you'll see "north". In other words, each 90 degree left turn is a 90 degree counterclockwise turn.
After doing another 90 degree counterclockwise turn, the mouse will move 10 meters westward. It moves from C(15,8) to D(5,8). Point D is the final position of the mouse.
-----------------------
A(0,0) was the initial position and D(5,8) is the final position
The vector v is
v = <5,8>
This is because we basically are saying "the mouse ultimately moved 5 meters east and 8 meters north" when going from start to finish. We're ignoring the intermediate stops along the way.
------------------------
Recall that for any vector of the form
v = <a,b>
the magnitude of that vector is
|v| = sqrt(a^2+b^2)
this is the length of the vector based on the pythagorean theorem.
Applying this formula gets us
|v| = sqrt(5^2+8^2)
|v| = sqrt(89)
|v| = 9.43398 approximate
This represents the straight line distance from start to finish, where we ignore any intermediate stops. So this isn't the distance the mouse travels (since it goes from A to B, to C to D). Instead, it's the distance it would travel if it wanted to take the shortest path from A to D.
Answer:
Step-by-step explanation:
9.4 for acellus
Can somone help me solve this
Answer:
solid shade above
Step-by-step explanation:
graph line same way you would if it was an equal sign
all the y's that are greater are above the line
its solid because is greater than OR equal to. Equal to includes the line itself as a set of solutions
The base of a triangle is 9cm correct to the nearest cm.
The area of this triangle is 40 cm2 correct to the nearest 5 cm?.
Calculate the upper bound for the perpendicular height of this triangle.
Answer:
can you show the picture plz
Use the listing method to write the following set \ 1,2,3\; [0, 1, 2, 3] O (1, 2)
f(x)=2x^2-x-6 g(x)=4-x (f+g)(x)
[tex] \large \boxed{(f + g)(x) = f(x) + g(x)}[/tex]
The property above is distribution property where we distribute x-term in the function.
Substitute both f(x) and g(x) in.
[tex] \large{ \begin{cases} f(x) = 2 {x}^{2} - x - 6 \\ g(x) = 4 - x \end{cases}} \\ \large{f(x) + g(x) = (2 {x}^{2} - x - 6) + (4 - x)} \\ \large{f(x) + g(x) = 2 {x}^{2} - x - 6 + 4 - x}[/tex]
Évaluate/Combine like terms.
[tex] \large{f(x) + g(x) = 2 {x}^{2} - 2x - 2} [/tex]
The function can be factored so there are two answers. (Both of them work as one of them is factored form while the other one is not.)
[tex] \large{(f + g)(x) = 2 {x}^{2} -2x -2}[/tex]
Alternative
[tex] \large{(f + g)(x) = 2({x}^{2} -x - 1)}[/tex]
Answer
(f+g)(x) = 2x²-2x-2(f+g)(x) = 2(x²-x-1)Both answers work. The second answer is in factored form.
Let me know if you have any doubts!
kelly bought two dozen apples she found 1/3 of them were rotten how manu apples were rotten
the answer is 8 apples were rotten
Answer:
8 apples are rotten.
Step-by-step explanation:
2*12=24 . There are 12 apples in a dozen.
24/3=8
Insurance companies need to maintain a certain amount in reserved funds in order to pay anticipated claims. The average monthly claim amount for the last 60 months for company A was $7,500,000 and the (sample) standard deviation was $1,200,000.
(a) Find a 95% upper confidence bound on the average monthly claim amount.
(b) The regulations on the reserves will be strengthened in the near future. According to the new regulations, insurance companies that do not have sufficient amount in reserve will be subject to a significant penalty. Company A wants to adjust the target reserve amount accordingly, by computing a new upper bound on the average monthly claim amount. Should the company recalculate an upper confidence bound with a higher or a lower level of confidence? Briefly explain why. Then compute a 99.95% upper confidence bound on the average monthly claim amount.
Answer:
a ) Upper bound of CI is 7803483.87
b) The new upper bound is 8039767.74
Step-by-step explanation:
From sample data:
sample size n = 60
sample mean x = 7500000
Sample standard deviation s = 1200000
a) Confidence Interval 95 % then significance level α = 5 % o α = 0.05
α/2 = 0.025 z(c) from z-table is z(c) = 1.96
CI 95 % = ( x ± z(c) * s/√n
CI 95 % = ( 7500000 ± 1.96 * 1200000/√60
CI 95 % = ( 7500000 ± 303483.87 )
CI 95 % = ( 7196516.13 ; 7803483.87)
Then upper bound of CI is 7803483.87
b) The company has to decrease the significance level equivalent to widen the confidence interval.
If CI now is 99.95 % significance level is α = 0.0005 and
α/2 = 0.00025 z(c) for that α/2 is from z-table z(c) ≈ 3.486
CI 99.95 % = ( x ± z(c)*s/√n
CI 99.95 % = 7500000 ± 3.486*1200000/ √60
CI 99.95 % = (7500000 ±539767.74)
CI 99.95 % = ( 6960232.26 ; 8039767.74)
The new upper bound is 8039767.74
Answer and I will give you brainiliest
Answer:
x = 60 degree
Step-by-step explanation:
90 + 90 + 2x - 10 + 2x + 2x + 10 = 540 degree (sum of 5 interior angles)
180 + 6x = 540
6x = 540 - 180
x = 360/6
x = 60 degree
The area of a triangle is 2/5 square feet. What is the base of the triangle if the height is 6/5 feet?
24/25 feet
25/24 feet
2/3 feet
3/2 feet
Answer:
2/3 feet.
Step-by-step explanation:
The formula for finding the area of a triangle is A = (B x H)/2. Or, area is equal to base times height, all divided by two. In your case, we don't know the base. If we substitute in values, we get 2/5 = (B x 6/5)/2.
Next, we have to multiply both sides by two, to cancel the "/2." That results in 4/5 = B x 6/5. Then, to isolate the variable, we have to divide both sides by 6/5. 4/5 ÷ 6/5 is 4/5 x 5/6. The fives cancel out, and we are left with 4/6.
Finally, we simplify! 4/6 simplifies to 2/3.
Consider the following equation. -2x + 6 =[-2/3] + 5
Answer:
that's my answer
hope it helps
What is the MEDIAN or Q2 of the data set: 24, 25, 29, 30, 31, 31, 32, 34, 34?
Answer:
31
Step-by-step explanation:
Median = middle number in terms of value
Usually the first step is to list the numbers in order from least to greatest however the numbers are already listed in order from least to greatest
24, 25, 29, 30, 31, 31, 32, 34, 34
We the just go to the middle number
The middle number would be 31
So we can conclude that the median is 31
for which of the following equations (-4, -3 ) not a solution
A. 2y - 3x = 6
B. -3x = 4y
c. y = 1 + x
D. 5x + 2y = -26
Part
The number 3.14 is a rounded value of the mathematical quantity . If you replace 3.14 with 1, what is the exact formula for the circumference in
terms of the diameter, d, and in terms of the radius, r?
B IV x x
Font Sizes
А
E1 E2
Characters used: 0/15000
Submit
I need help
Answer:
C = 2(3.14)r
C = (3.14)d
Step-by-step explanation:
Circumference in terms of radius:
[tex]c \: = 2\pi \: r[/tex]
So replacing pi with 3.14 you would get 2(3.14)r
Circumference in terms of diameter:
[tex]c = d\pi[/tex]
So replacing pi with 3.14 you would get d(3.14)
Please help me please ! Quick
Answer:
4,2 is tge answer due to the interaction point plus it says the solution is at the interaction.
Answer:
C. I think
Step-by-step explanation:
Choose all the points that would be acceptable points to choose to test for shading for −3(m+7)≥−24
Answer:
m≤1
Step-by-step explanation:
The given inequality is :
−3(m+7)≥−24
Dividing both sides by -3.
(m+7) ≤ 8
Subtract 7 from both sides,
(m+7)-7 ≤ 8-7
m≤1
Hence, this is the required solution.
what is the largest six-digit base five number? How do you know?
Answer:
999999.9>repeating
Step-by-step explanation:
.1 more and it will be 7 digits and not 6 Hope this helps :D
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Answer:
444444₅ = 15624₁₀
Step-by-step explanation:
It will be 1 less than the smallest 7-digit base-5 number. That number is 5^6 = 15625, so the largest 6-digit base 5 number is 15624 in decimal. In base 5, it is 6 of the largest base-5 digits:
444444₅ = 15624₁₀
__
The digits of the number cannot be any larger than the largest base-5 digit. The base-5 digits are 0 to 4, so the largest is 4.
Plz help me solve this algebra
Answer:
Step-by-step explanation:
[tex]16^{\frac{24}{64}} =16^{\frac{4*2*3}{4*2*8}}\\\\=(2^{4})^{\frac{3}{8}}\\\\=2^{4*\frac{3}{8}}\\\\=2^{\frac{3}{2}}=2^{3*\frac{1}{2}}\\\\=\sqrt{2*2*2}\\\\=2\sqrt{2}[/tex]
)Which statement best describes the area of the triangle shown below?
A coordinate grid is shown with a triangle.. The base is 4 units, and the height is 4 units.
It is one-half the area of a rectangle of length 4 units and width 2 units.
It is one-half the area of a square of side length 4 units.
It is twice the area of a rectangle of length 4 units and width 2 units.
It is twice the area of a square of side length 4 units.
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Answer:
(b) It is one-half the area of a square of side length 4 units.
Step-by-step explanation:
The triangle described can be formed by drawing the diagonal through a square 4 units on a side. Such a diagonal cuts the square cleanly in half, so the area of the triangle is half the area of the square.
Answer:
B
Step-by-step explanation:
Hope you have a nice day! :o)
1;3;5;7…(determine the value of the 19th term of the sequence)
Answer:
37
Step-by-step explanation:
fistly find how much different
3-1=2 5-3=2 7-5=2
so for the next and next value just plus two until the 19th then you will get 37
=============================================================
Explanation:
a = 1 is the first term
d = 2 is the common difference, since we add 2 to each term to get the next term.
The nth term is a+d(n-1) which becomes 1+2(n-1). That simplifies to 2n-1
The last step is to plug in n = 19 and you should get 2(19)-1 = 37
Maria has 24 dollars. If cokes are 3 dollars and
hotdogs are 4 dollars, which inequality represents the
possibilities of how she can spend the 24 dollars:
Answer:
do 24 divide 3
then 24-4
have maria debate if she wants large quantities of hot dogs or cokes
If the measure of angle 2 Is (4x+10)degrees and the measure of angle 3 is (3x-5)degrees, what is the measure of angle 2 in degrees?
Answer:
110°
Step-by-step explanation:
4x+10 + (3x-5) = 180
7x + 5 = 180
7x = 175
x = 25
∠2 = 4(25) + 10 = 110
The measure of angle 2 in degrees, when both lines are perpendicular, is approximately 58.56 degrees.
To find the measure of angle 2 when the lines are perpendicular, we can set up an equation. Since the angles are formed by perpendicular lines, we know that the sum of angle 2 and angle 3 will be equal to 90 degrees. Mathematically, we can write this as:
(4x + 10) + (3x - 5) = 90
Now, let's solve the equation to find the value of x. First, combine like terms:
4x + 3x + 10 - 5 = 90
7x + 5 = 90
Next, isolate x by subtracting 5 from both sides:
7x = 85
Finally, divide by 7 to solve for x:
x = 85 / 7 ≈ 12.14
Now that we have the value of x, we can find the measure of angle 2 by substituting x back into its expression:
Angle 2 = 4x + 10
Angle 2 = 4(12.14) + 10
Angle 2 ≈ 48.56 + 10
Angle 2 ≈ 58.56 degrees
To know more about angle here
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For brainlest answer
Answer:
3..
Step-by-step explanation:
dont know the explanation sry i m beginner so .
