Final answer:
To solve these physics problems, we used vector mathematics to find the speed of the ball, its position after a certain time, the time it aligns with a certain point, and the speed of a player to intercept it. Additionally, we considered gravity as a factor for a more realistic model of the ball's motion.
Explanation:
Speed of the ball: To find the speed of the ball, we calculate the magnitude of the velocity vector (5i + 8j) m/s using the Pythagorean theorem, which results in \(\sqrt{5^2 + 8^2} = \sqrt{89}\) m/s.
Position vector after t seconds: We calculate the position vector at time t by using the initial position vector (2i + j) m and adding the product of the velocity vector and time t. This yields the formula (2i + j) + t(5i + 8j).
Time when the ball is due north of B: For the ball to be due north of B, their i-components must be equal. Given B's position vector is (10i + 7j), we set the i-component equal to 10 and solve for t, getting t = (10 - 2)/5 = 1.6 seconds.
Value of v for the running player: Since the player intercepts the ball after 1.6 seconds, and the ball's j-component of the velocity is 8 m/s, the player's velocity v must be the distance covered in the j direction divided by time, which is (8j - 7j)/1.6 = 0.625 m/s.
Physical factor for a more realistic model: One physical factor to make the model more realistic could be the effect of gravity on the ball's trajectory, which would cause the ball to follow a parabolic path rather than a straight line.
What is 9x-15+7x-7 in 2 numbers topic is Equivalent expressions
Comparing each pair of triangles,what conclusion can be reached about the unequal sides or angles
Answer: Can you attach a copy of the triangles?
Step-by-step explanation:
87 x (-22.57) ?????????
Answer:
1979.25
Step-by-step explanation:
the perimeter of an equilateral triangle is given as 15x +21.find the greatest common factor
Step-by-step explanation:
15x + 21= 3 (5x + 7)
Therefore, greatest common factor is (5x + 7)
billy was going to run 3/4 of thre trainjng course and jen was going rtn 1/2 of the course billy had finish 1/3 of the run while ken finish 1/2 of his run who run the farthest
Answer:
Therefore both Ken and Billy ran the same amount of the training course.
Step-by-step explanation:
i) Billy was going to [tex]\frac{3}{4}[/tex] th of the training course.
ii) Ken was going to run [tex]\dfrac{1}{2}[/tex] of the training course.
iii) Billy finished [tex]\frac{1}{3}[/tex] of his run Therefore Billy finished only [tex]\frac{1}{3} \times \frac{3}{4} = \frac{3}{12} = \frac{1}{4}[/tex] of the training course.
iv) Ken finished [tex]\dfrac{1}{2}[/tex] of his run Therefore Billy finished only [tex]\dfrac{1}{2} \times \dfrac{1}{2} = \dfrac{1}{4}[/tex] of the training course.
v) Therefore both Ken and Billy ran the same amount of the training course.
(WILL GIVE BRAINLIEST TO WHOEVER ANSWERS FIRST) Directed line segment is graphed below. Plot point R on the graph so that it splits into segments with a ratio of 1:2.
Explain how you determined your answer
Answer:
(0 , -1)
Step-by-step explanation:
WR = 4 + 2 = 6
WS = 1/3 x WR = 2 .... the point of 1:2 of WR
S (-2 + 2 , -4) i.e. (0,4)
The same reason: RQ = 1/3 x RY = 1/3 x (5 + 4) = 3
Q (-4 , -4 + 3) i.e. (-4, -1)
QP // RW
p (0 , -1)
The attic floor, ABCD in the model, is a square. The beams that support the roof are the edges of a block (rectangular prism) EFGHKLMN. E is the middle of AT, F is the middle of BT, G is the middle of CT and H is the middle of DT. All the edges of the pyramid in the model have length 12m.
Calculate the length of EF, one of the horizontal edges of the block.
Answer:
EF = 6m.
Step-by-step explanation:
Given that:
1) All the edges of the pyramid in the model have length 12m.
So, AB = 12m
2) E is the middle of AT, F is the middle of BT
So, EF is a line segment connecting the midpoints of ΔATB
So, by applying The Triangle Mid-segment Theorem
EF // AB and EF = 0.5 AB
So, EF = 0.5 AB = 0.5 * 12 = 6m
====================================
The Triangle Mid-segment Theorem:
The line segment connecting the midpoints of any two sides of a triangle has the following properties:
1) The line segment will be parallel to the third side.
2) The length of the line segment will be a half of the length of the third side.
Select the two figures that are similar to the 2 by 6 figure that shown.
Guys pls help this an imagine math problem here is the picture.
The value of two figures that are similar to the 2 by 6 figure are shown in figure 2 and figure 4.
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
The figure is type of 2 by 6.
Now,
Since, The figure is type of 2 by 6.
Which is equal to 1 by 3.
Clearly, In figure 1;
The size is 2 by 4.
It is equal to 1 by 2.
In figure 2;
The size is 1 by 3.
It is equal to 1 by 3.
In figure 3;
The size is 1 by 6.
It is equal to 1 by 6.
In figure 4;
The size is 3 by 9.
It is equal to 1 by 3.
Thus, The figure 2 and figure 4 is equal to the figure 2 by 6.
Learn more about the divide visit:
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(-102.74) divided (-3)
Answer:
34.246
Just divide both numbers
True or false: f(x) is a function.
A
2
f(x)
True, [tex]f(x)[/tex] is a function.
5z+3-3z in equivalent expression
Answer:
2z +3
Step-by-step explanation:
This question simply involves understanding what like terms are, and how to combine them.
Here, 5z and -3z are like terms, so we combine them by going 5z-3z = 2z
(i.e. we minus the coefficients, but the z stays unchanged).
Next, the number term of 3 in the middle cannot be combined with any other term, so it just stays in the expression.
Find the slope of the line that passes through the points (0,-3) and (4, 5).
Answer: 2
Step-by-step explanation:
to find this you use the equation
y2-y1
--------
x2-x1
so with your points tuat would be
5+3/4-0 (it becomes a plus bc two negatives= a positive
8/4=2
Solve for k
4.5 + 1.5k = 18 - 3k
What is k?
Please help I need to hand my assignment in an hour. Thanks all :)
Answer:
When solving equations the goal is to get the variable by itself so
4.5+1.5k=18-3k (first step is to subtract 4.5 from each side)
1.5k=13.5-3k (4.5-4.5=0, 18-4.5=13.5) (Next is to add 3k to each side)
4.5k=13.5 (1.5k+3k=4.5k, -3k+3k=0) (Last you divide both sides by 4.5)
k=3 (4.5/4.5=1, 13.5/4.5=3)
k=3
Hope this helps ;)
what is the solution to this problem? NEED ASAP PLS
Answer:
18
Step-by-step explanation:
2(x - 5) + 4 = 30
2x - 10 + 4 = 30
2x - 6 = 30
2x = 36
x = 18
Answer:
18
Step-by-step explanation:
2(x-5)+4=30
2(x-5)=30-4
2(x-5)=26
x-5=26/2
x-5=13
x=13+5
x=18
Which word phrase describes the algebraic expression x - 16.5?
16.5 decreased by x
x less 16.5
x more than 16.5
16.5 minus x
Answer:
x less 16.5
Step-by-step explanation:
"x -16.5" means 16.5 is subtracted from x. The resulting value is 16.5 less than x. The wording "x less 16.5" basically means "x minus 16.5" and/or "x reduced by 16.5".
__
Subtraction is not commutative, so "16.5 decreased (or reduced) by x", meaning "16.5 -x" or "16.5 minus x", is not the same thing.
3 1/10- 2 5/6 in simplest form
Answer:
[tex] \frac{4}{15} [/tex]
Step-by-step explanation:
[tex] 3 \frac{1}{10} - 2 \ \frac{5}{6} [/tex]
Convert the above mixed numbers to improper fractions through this simple approach: 3 × 10 + 1 /10 = 31/10. Similarly, 2 × 6 + 5 /6 = 17/6
[tex] \frac{31}{10} - \frac{17}{6} [/tex]
Take the LCM of the denominators and simplify. LCM = 60. Thus, 60/10 = 6; 6 × 31 = 186. Also, 60/6 =10; 10×17 =170 all divide by 60:
[tex] = \frac{186 - 170}{60} [/tex]
Common factors between the numerator and denominator is 4, therefore 16/4 = 4 and 60/4 = 15.
[tex] = \frac{16}{60} = \frac{4}{15} [/tex]
Therefore the answer is 4/15 in simplest form.
A wooden board is 3 yards and 1 foot long what is a equivalent length
Final answer:
To find an equivalent length for a wooden board that is 3 yards and 1 foot long, you convert yards to feet, using the fact that 1 yard equals 3 feet, and then add any remaining feet. The board is therefore 10 feet long in total.
Explanation:
Converting Yards to Feet:
A wooden board is 3 yards and 1 foot long. To find an equivalent length, we need to convert yards to feet because there are 3 feet in 1 yard. The calculation goes as follows:
First, we know that 1 yard equals 3 feet.
To convert 3 yards to feet, we multiply by 3: 3 yards × 3 feet/yard = 9 feet.
Next, we add the extra foot: 9 feet + 1 foot = 10 feet.
Therefore, the board is 10 feet long in total.
This process involves using equalities and conversion factors to change one unit of measurement to another while maintaining the same quantity.
150% of $90.00 pls help
Answer:$135
Step-by-step explanation: you divide it and get that answer
Answer:
$135
Step-by-step explanation:
90×1.5= 135 Hope this helps
the rational roots of a polynomial function f(x) can be written in the form p/q, where p is a factor of the leading coefficient of the polynomial and q is a factor of the constant term.
A true
B false
The statement is true. The rational roots of a polynomial can be written in the form p/q. The rational root theorem is used to determine these potential roots.
Explanation:The statement in the question is true.
The rational roots of a polynomial function can indeed be written in the form p/q, where p is a factor of the leading coefficient and q is a factor of the constant term. This is known as the Rational Root Theorem.
For example, if we have the polynomial function f(x) = 3x^3 - 7x^2 + 4x - 2, the leading coefficient is 3 and the constant term is -2. The potential rational roots would be of the form p/q, where p is a factor of -2 and q is a factor of 3. The factors of -2 are -1, 1, -2, and 2, while the factors of 3 are -1 and 3. Therefore, the potential rational roots would be:
p/q = -1/1 = -1p/q = 1/1 = 1p/q = -2/1 = -2p/q = 2/1 = 2p/q = -1/3 = -1/3p/q = 3/3 = 1Learn more about Rational Root Theorem here:https://brainly.com/question/31805524
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PLEASE HELP!! BRAINLIEST AND 50 POINTS!
For each scenario below, identify the variables and which variable depends on the other. Identify and explain whether the two variables have a positive association, a negative association, or no association. Then choose which scatter plot could represent the data.
(a) Marcus records the amount of lemonade that he sells each day and compares it to the temperature. He notices that when the temperature is warmer, he sells more lemonade.
(b) Ms. Lee compares the time runners spend training each day to their race times and notices that runners who spend more time training have faster race times.
(c) Tomika surveys her friends to see whether their height affects the amount of time they spend watching television. She finds that some of her taller friends watch a lot of television and some of them watch very little television.
(d) Marley compares the number of hours a person is in a mall to the amount of money the person has left in his or her wallet. She finds that the more time people spend in the mall, the less money they usually have left.
(e) Johanna read a study that stated that people who exercise more are expected to live longer.
Answer:
For the first scatter plot, the variables have a negative association, which matches the option D. X is the amount of time in the mall and Y is the remaining money.
For the second scatter plot, it is a positive association. This plot could match A, B, or E.
The third scatter plot shows no correlation whatsoever, which represents C. Tomika's friends' heights did not associate with how much time they watched TV.
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Brainliest would be appreciated! I'd be Expert by now, but I never get brainliest. You don't have to though, but it would make me happy. Thanks!
Free brainliest and what is 21/7?
Answer:
if your dividing then 3 but if you want 21 sevenths as a mixed number then it would be 3.
Step-by-step explanation:
to find the quotient, you need to find out what multiplied by 7 gives you 21. (thats easy 3) so there is your answer. to find the mixed version of 21 sevenths you need to divide 21 by 7 ( literally what i just showed...) and you get 3.
HOPE THIS HELPS!!!
Answer:
That would be 3 because 7x3 is 21.
Step-by-step explanation:
Perform the indicated operation.
(7x3 + 11x2 + 4x + 9)-(-x3 + 6x2 + 2x+6)
(7x3 + 11x2 + 4x +9)-(-x3 + 6x2 + 2x+6)=
(Simplify your answer. Do not factor.)
[tex](7x^3 + 11x^2 + 4x + 9)-(-x^3 + 6x^2 + 2x+6) = 8x^3+5x^2+2x+3[/tex]
Solution:
Given that we have to perform the indicated operation
Given polynomial is:
[tex](7x^3 + 11x^2 + 4x + 9)-(-x^3 + 6x^2 + 2x+6)[/tex]
Polynomial addition\subtraction is similar to arithmetic addition\subtraction
Add\subtract the terms of coefficients with same variable with same exponent
For example: [tex]x^3 -2x^3 = -x^3[/tex]
To subtract Polynomials, first reverse the sign of each term we are subtracting
Which means, reverse the sign of each term in second bracket
[tex]\rightarrow (7x^3 + 11x^2 + 4x + 9)-(-x^3 + 6x^2 + 2x+6)\\\\\rightarrow (7x^3 + 11x^2 + 4x + 9)+x^3 - 6x^2 - 2x-6\\\\\text{Remove the parenthesis in first bracket }\\\\\rightarrow 7x^3 + 11x^2 + 4x + 9+x^3 - 6x^2 - 2x-6\\\\\text{Group the similar terms }\\\\\rightarrow 7x^3+x^3+11x^2-6x^2+4x-2x+9-6\\\\\text{Combine the similar terms }\\\\\rightarrow 8x^3+5x^2+2x+3[/tex]
Thus the given operation is performed
What is the factorization of the trinomial below? 2x^2 +11x+15
Answer:
(2x+5)(x+3)
Step-by-step explanation:
2x^2+11x+15
(2x+5)(x+3)
Answer:
(2x+5)(x+3)
Step-by-step explanation:
Ms. Marigneaux's science class needs to
collect $68.00 for science materials for a class
project. In addition, the class will need
$100.00 to pay for an upcoming field trip. If
there are 29 students in the class, what is the
average amount each student must collect?
(Round to the nearest cent.)
If there are 29 students in class and they need to collect a total of 168, we can divide 168 by 29 to get $5.79. This means that each student must collect $5.79 in order for them to be able to purchase everything.
Solve the following compound inequality.
3x + 1 <-5 OR 5X-1 > 29
Answer:
3x + 1 <-5 is x<−2
5x-1> 29 is x>6
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Inequality Form:
x<−2
Isolate the variable by dividing each side by factors that don't contain the variable.
Inequality Form:
x>6
Final answer:
To solve the compound inequality 3x + 1 < -5 OR 5x - 1 > 29, solve each inequality separately. The solution is all real numbers that are either less than -2 or greater than 6.
Explanation:
To solve the compound inequality 3x + 1 < -5 OR 5x - 1 > 29, we need to solve each inequality separately and then find the union of the two solutions, since the word 'OR' indicates that a solution to either inequality will satisfy the compound inequality.
Solving the first inequality:
3x + 1 < -5
Subtract 1 from both sides: 3x < -6Divide by 3: x < -2Solving the second inequality:
5x - 1 > 29
Add 1 to both sides: 5x > 30Divide by 5: x > 6The solution to the compound inequality is the set of all real numbers that are either less than -2 or greater than 6.
Find the distance between the points (1, 2) and (4,3).
ANSWER: Exact Form: [tex]\sqrt{10}[/tex]
Decimal Form: 3.16227766
STEP-BY-STEP EXPLANATION:
(1, 2) and (4,3)
Use the distance formula to determine the distance between the two points.
Distance = \sqrt{(X2-X1)^{2 }+ (Y2-Y1)^{2} }
Substitute the actual values of the points into the distance formula.
\sqrt{(4-1)^{2 }+ (3-2)^{2} }
The result can be shown in multiple forms.
Exact Form: [tex]\sqrt{10}[/tex]
Decimal Form: 3.16227766
The distance between the given points is approximately 3.16 units.
To find the distance between the points (1, 2) and (4, 3), we use the distance formula derived from the Pythagorean Theorem, which calculates the distance between two points in a coordinate plane. The distance formula is:
d = √((x₂ - x₁)² + (y₂ - y₁)²).
Using this formula, we plug in the coordinates of the two points:
Let (x₁, y₁) = (1, 2)
Let (x₂, y₂) = (4, 3)
Substituting these values into the formula gives us:
d = √((4 - 1)² + (3 - 2)²)
d = √(32 + 12)
d = √(9 + 1)
d = √10
d ≈ 3.16
Therefore, the distance between the two points is approximately 3.16 units.
22% of a group of people voted in the last election. If 66 of the people voted, how many total people were there?
Answer:
300
Step-by-step explanation:
22% means 22 of 100
for every 100 persons 22 voted
for every x persons 66 voted.lets do the math to find what is the x
[tex] \frac{22}{100} = \frac{66}{x} [/tex]
[tex]x = \frac{66 \times 100}{22} [/tex]
x=300
Answer: 300
Step-by-step explanation:
we know that 22% is the same as 22/100 ( 22 over 100). We are trying to find the whole, which means we are already given the part which is 66. how can we get from 22 to 66? 22 multiples by 3 = 66 do the same to the bottom 100 multiplied by 3 is 300.
Choose Yes or No to tell whether each expression is equivalent to –43p – 25.
Answer:
–43p + (–25) is EQUIVALENT to –43p – 25.
Step-by-step explanation:
The options are MISSING.
The needed options are:
1. 25 – 43p
2. 25 – 43p
3. –25p –43
4. –43p + (–25)
Now, here the given expression is: –43p – 25
Taking each option and simplifying it , we get:
1. 25 – 43p
Here, the second term is NEGATIVE, but the first term (25) is POSITIVE.
⇒ 25 – 43p ≠ –43p – 25
Hence, 25 – 43p is NOT EQUIVALENT.
2. 25 – 43p
Here, the second term is NEGATIVE, but the first term (25) is POSITIVE.
⇒ 25 – 43p ≠ –43p – 25
Hence, 25 – 43p is NOT EQUIVALENT.
3. –25p –43
Here, the variable p is multiplied with (-25) and NOT (-43).
⇒ –25p –43 ≠ –43p – 25
Hence, –25p –43 is NOT EQUIVALENT.
4. –43p + (–25)
Here, both the given terms (43) and (25) are NEGATIVE.
Also, the varibale p is multiplied with (-43)
⇒ –43p + (–25) = –43p – 25
Hence, –43p + (–25) is EQUIVALENT.
Answer:
no no no no
Step-by-step explanation:
My brother needs help with this question
What Shape has 12 sides and 12 angles?
Answer:
A dodecagon.
what is the quadratic equation if the solutions are -9+ √65 /2, -9- √65 /2
Answer:
[tex]4x^2+72x+259=0[/tex]
Step-by-step explanation:
If [tex]x_1[/tex] and [tex]x_2[/tex] are the solutions to the quadratic equation, then this equation can be written as
[tex](x-x_1)(x-x_2)=0[/tex]
In your case,
[tex]x_1=-9+\dfrac{\sqrt{65}}{2}\\ \\x_1=-9-\dfrac{\sqrt{65}}{2}[/tex]
Then the equation is
[tex]\left(x-\left(-9+\dfrac{\sqrt{65}}{2}\right)\right) \left(x-\left(-9-\dfrac{\sqrt{65}}{2}\right)\right)=0\\ \\\left(x+9-\dfrac{\sqrt{65}}{2}\right)\left(x+9+\dfrac{\sqrt{65}}{2}\right)=0\\ \\x^2+9x+\dfrac{\sqrt{65}}{2}x+9x+81+\dfrac{9\sqrt{65}}{2}-\dfrac{\sqrt{65}}{2}x-\dfrac{9\sqrt{65}}{2}-\dfrac{65}{4}=0\\ \\x^2+18x+\dfrac{259}{4}=0\\ \\4x^2+72x+259=0[/tex]