Find the midpoint of the following segment created by these pairs of endpoints: (0, 1), (0, 5)
1: (1, 5)
2: (0, 2.5)
3: (0, 3)
4: (5, 1)
the height of a football in the air t seconds after it is thrown can be modeled by the function y=-16t^2+96t+3, where y are measured in feet and t is time. What is the maximum height that the football reaches? How long did it take the football to reach the maximum height? At what times will the football be above the ground at 122 feet?
The maximum height the football reaches is 147 feet, and it takes 3 seconds for the football to reach that height. To determine when the football is above 122 feet, the equation is set equal to 122 and solved for time t.
To find the maximum height reached by the football, we need to determine the vertex of the parabolic function given by y = -[tex]16t^2[/tex] + 96t + 3. Since the coefficient of [tex]t^2[/tex]is negative, the parabola opens downwards, and the vertex will give us the maximum height.
To find the time at which the maximum height occurs, use the formula t = -b/2a, where a is the coefficient of [tex]t^2[/tex] and b is the coefficient of t.
In this equation, a = -16 and b = 96, so t = -96/(2 x -16) = 3 seconds. Plugging this back into the original equation gives us the maximum height: y = -16[tex](3)^2[/tex] + 96(3) + 3 = 147 feet.
To determine when the football is above 122 feet, we set the equation equal to 122 and solve for t:
122 = -[tex]16t^2[/tex] + 96t + 3. We simplify and solve the quadratic equation, which may yield two possible times, one during the ascent and one during the descent of the football's path.
The length of a rectangle is 4 inches less than twice its width. if the area of the rectangle is 70 square inches, what are its dimensions?
Match the definition with the terms.
1. a portion of a large group
2. choosing a sample so that every member has an equal chance of being chosen
3. choosing a sample from people who are under 15 years old
4. using the responses of a small group to make conclusions about the large group.
random sample
sample
biased sample
estimating from a sample
Random sample - choosing a sample so that every member has an equal chance of being chosen (this is the absolute definition of random sampling)
Sample - a portion of a large group is termed as a sample.
Biased sample - choosing a sample from people who are under 15 years old (biased sampling states that all the members of a group are not included in survey)
Estimating from a sample - using the responses of a small group to make conclusions about the large group.(estimation means roughly judging something based on some sample )
Lena's penny bank is 1/2 full. After she removes 200 pennies, it is 3/10 full. How many pennies can Lena's bank hold?
1. y - 5/3 =1 2. Combine like terms: -21a + 16a 3. Simplify the expression: 9a - b - 2a - 10b 4. 5(x + 10) + x 5. -4n + 7 + 2n = 1 Thanks for everything!!
p(x) is a polynomial with integer coefficients and p(-3) = 0.
Which statements must be true? Choose all that apply.
x + 3 is a factor of the polynomial.
x - 3 is a factor of the polynomial.
-3 is the constant term of the polynomial.
p(x) can have at most 3 linear factors.
Answer:
x + 3 is a factor of the polynomial.
Step-by-step explanation:
We have been given that p(x) is a polynomial with integer coefficient.
Also p(-3)=0
Since, p(-3) =0, hence, we can say that -3 is a zero of the polynomial.
Now, we apply factor theorem.
Factor Theorem: If 'a' is a zero of a function f(x) then (x-a) must be a factor of the function f(x).
Applying this theorem, we can say that (x+3) must be a factor of the polynomial.
Hence, first statement must be true.
Answer: The correct option is (A) (x + 3) is a factor of the polynomial.
Step-by-step explanation: Given that p(x) is a polynomial with integer coefficients and p(-3)=0.
We are to select the true statement from the given options.
Factor Theorem: If q(x) is a polynomial with integer coefficients and q(a) = 0, then (q - a) will be a factor of q(x).
Here, it is given that
p(x) is a polynomial with integer coefficients and p(-3) = 0.
Therefore, by Factor theorem, we can say that (x-(-3)), ie., (x + 3) is a factor of the polynomial p(x).
Thus, (x + 3) is a factor of the polynomial.
Option (A) is CORRECT.
Transversal CD←→ cuts parallel lines PQ←→ and RS←→ at points X and Y as shown in the diagram. If m∠CXP = 106.02°, what is m∠SYD? 73.98° 90° 106.02° 180°
If m∠CXP = 106.02°, m∠SYD is 73.98°. Among the given ones the correct option is 1.
What is Transversal?In geometry, a transversal is a line that intersects two or more other lines in a plane.
When a transversal intersects two parallel lines, it forms a set of eight angles, including alternate interior angles, alternate exterior angles, corresponding angles, and consecutive interior angles.
If the lines PQ←→ and RS←→ are parallel, then the alternate interior angles formed by transversal CD←→ are congruent. Therefore, we have:
m∠CXP = m∠DYX (alternate interior angles)
m∠CXD + m∠DXP = 180° (linear pair)
We can use these two equations to find m∠SYD. First, we need to find m∠CXD, which is the same as m∠YXC because they are vertical angles. We know that:
m∠CXP = 106.02°
So, we can use the linear pair equation to find m∠DXP:
m∠CXD + m∠DXP = 180°
m∠DXP = 180° - m∠CXD
Substituting m∠CXD = m∠YXC, we get:
m∠DXP = 180° - m∠YXC
Now, using the alternate interior angles equation, we can replace m∠CXP with m∠DYX:
m∠DYX = m∠CXP = 106.02°
Finally, we can use the linear pair equation again to find m∠SYD:
m∠DYX + m∠SYD = 180°
m∠SYD = 180° - m∠DYX
m∠SYD = 180° - 106.02°
m∠SYD = 73.98°
Therefore, m∠SYD is 73.98°, i.e., option 1.
For more details regarding Transversal, visit:
https://brainly.com/question/13618693
#SPJ7
Rationalize the denominator of sqrt -9 / (4-7i) - (6-6i) ...?
Answer:
-3-6i/5 is the answer it was also correct on the test ! :D
Glenn has a beginning balance of $840 in his checking account. He has a deposit of $375 and withdraws $250 from the ATM. If the ATM fee is $3, what is his new balance?
$718
$212
$962
$572
The population of a town increases at the rate of 1% each year. today the town’s population is 8,500. what will the population be in five years?
Population of the town after 5 years = 8933.59.
What is Population growth rate?Population growth rate is defined as the change in the size of the population with respect to the time.
The growth rate is usually written as the ratio of the annual increase or decrease in population to the entire population of that year.
The formula for finding the future population is,
P(F) = P(R) [ 1 + r]ⁿ , where
P(F) = Future population
P(R) = Present population
r = Growth rate
n = Number of years
From the question, we have
P(R) = 8500, r = 1% = 0.01 and n = 5
Substituting these values in the main equation,
P(F) = 8500 [ 1 + 0.01 ]⁵
P(F) = 8500 × 1.01⁵
P(F) = 8933.59
Hence, the population of the town after 5 years if the rate of increase in population is 1% = 8933.59
To learn more about population growth rate, click:
https://brainly.com/question/14122627
#SPJ2
16 lizards have stripes on there tails . the ratio of lizards with white tails to those with yellow tail stripes is 1:2 . how many lizards have yellow tail stripes
What is 2576 divided by 3?
2576 divided by 3 is equal to 859 with a remainder of 2.
Explanation:When dividing 2576 by 3, you can divide each digit individually. Start with the first digit, 2. Since 2 is less than 3, you can't divide it evenly, so you move to the next digit. The next digit is 5. With 5, you can divide it evenly by 3, which gives you 1. Now, subtract 3 from 5, which gives you 2. Bring down the next digit, which is 7. The new dividend is 27. Divide 27 by 3, which gives you 9 with no remainder. Finally, bring down the last digit, which is 6. The new dividend is 26. Divide 26 by 3, which gives you 8 with a remainder of 2. So, 2576 divided by 3 is equal to 859 with a remainder of 2.
What is an equation for the line with slope 2/3 and y-intercept 9?
Answer:
[tex]y=\frac{2}{3}x+9[/tex]
Step-by-step explanation:
We can describe a line using the following equation :
[tex]y=ax+b[/tex]
Where ''a'' and ''b'' are real numbers.
In the equation, the number ''a'' is the slope of the line. If we want a line with slope [tex]\frac{2}{3}[/tex] ⇒
[tex]y=\frac{2}{3}x+b[/tex]
The intersection of a line with the y-axis can be calculated replacing [tex]x=0[/tex] in the equation ⇒
[tex]y=(\frac{2}{3}).(0)+b\\y=b[/tex]
The interception is the real number ''b''. We want that interception to be 9
⇒
[tex]y=\frac{2}{3}x+9[/tex] is the equation of the line with slope [tex]\frac{2}{3}[/tex] and that intersects the y-axis at the point [tex](0,9)[/tex]
how many tens and ones are in 25
The town of Goodland, Kansas, claims that it has one of the world's largest easels. It holds an enlargement of a van Gogh painting that is 24 feet wide. The original painting is 58 cm wide and 73 cm tall. If the reproduction is similar to the original, what is the height of the reproduction to the nearest foot?
What is the most misleading aspect of this graph that might lead one to the wrong conclusion?
connecting the data points with a line
scale of the y-axis
scale of the x-axis
spacing of the grid
(graph attached)
what is 3[10-(27÷9)]?
You need to sell 250 candy bars at $2 each. If you meet your goal, the total amount of money you will have is measured in the _____. ...?
Which ratio is equivalent to 24:2824:28 ?
A.4:74:7
B.12:1612:16
C.18:2118:21
D.48:5848:58
Answer:
C
Step-by-step explanation:
How will the solution of the system y > 2x + and y < 2x + change if the inequality sign on both inequalities is reversed to y < 2x + and y > 2x + ?
Answer:
The System of inequality is ,
1. y > 2 x + p
2. y < 2 x + p
Suppose we assign some values to p and q and draw its graph
And, then the inequality sign on both inequalities is reversed
3. y < 2 x + p
4. y > 2 x + p
And , then draw it's graph
it has been found that, the solution set of both the inequality remains same.That is there is no point or set of points , which satisfy both the system of inequality.
The system has no solution.
Answer:
There is no solution to the system in its original form. There are no points in common. If the signs are reversed, the system has an intersection with an infinite number of solutions.
Step-by-step explanation:
edge - 2023 :)
SOMEONE PLEASE HELP ME!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Kevin gets an auto loan of $12,000 at 8% annual interest. The terms of his loan state that he has to pay $292.96 each month for 4 years. How much total interest will he have to pay?
$384
$960
$1171.84
$2062.08
A five-sided solid has the numbers 1, 2, 3, 4, and 5. What is the probability of rolling two five-sided number solids and getting a sum of either a 3 or an 8?
A. 6/625
B. 9/625
C. 6/25
D. 1/5
Answer:
The answer is D. 1/5 hopefully this helps!
Which construction is illustrated above?
A) a perpendicular to a given line from a point on the line
B) a line segment congruent to a given line segment
C) The perpendicular to a given line from a point not on the line
D) the perpendicular bisector of a line segment
solve for z
[tex] \sqrt{ z^{2}+8z } +4=z [/tex]
Geoffrey wrote the following paragraph proof showing that rectangles are parallelograms with congruent diagonals.
According to the given information, quadrilateral RECT is a rectangle.
By the definition of a rectangle, all four angles measure 90°.
Segment ER is parallel to segment CT and segment EC is parallel to segment RT by the Converse of the Same-Side Interior Angles Theorem.
Quadrilateral RECT is then a parallelogram by definition of a parallelogram.
Now, construct diagonals ET and CR. Because RECT is a parallelogram, opposite sides are congruent.
Therefore, one can say that segment ER is congruent to segment CT.
Segment TR is congruent to itself by the Reflexive Property of Equality.
The _______________ says triangle ERT is congruent to triangle CTR.
And because corresponding parts of congruent triangles are congruent (CPCTC), diagonals ET and CR are congruent.
Robyn opened a bank account to save her birthday money. it was paying 3.75% interest. then the interest rate went up by 0.65%. how much is her new interest rate?
The weight of 8 science books is 28 pounds. what is the weight of 11 science books?
Answer:
Weight of 11 books =38.5 pounds
Step-by-step explanation:
Weight of 8 science book = 28 pounds
Weight of 11 science books = ?
If 8 science books -----------------------28 pounds
then 11 science books ---------------------?
Cross multiplying, we have
Weight of 11 books = (11 * 28)/8
= 308/8
= 38.5 pounds
Solve for w.
2w=12-4w
Simplify your answer as much as possible.
At the end of the calendar year, the a/p department creates _____ forms for non-incorporated individuals paid over $600.00
Answer:
The Form 1099-MISC
Step-by-step explanation:
At the end of the calendar year, the a/p department creates 1099 MISC forms for non-incorporated individuals paid over $600.00
The Form 1099-MISC is an IRS tax return document used to give miscellaneous payments made to non employees like contractors etc, during the calendar year. This is recorded when at least $600 in services, rents and other payments are made.