The given equation represents the distance travelled by the object at time t.
The given equation is expressed as
-16t^2 + 48t + 160
At the point where it hits the ground, the distance woule be 0. Thus, we would so;ve the equation,
-16t^2 + 48t + 160=0
We would divide through by - 16. We have
t^2 - 3t - 10 = 0
We would find two terms such that their sum or difference is - 3t and their product is - 10t^2. They are 2t and - 5t. We have
t^2 + 2t - 5t - 10 = 0
By factorising, we have
t(t + 2) - 5(t + 2) = 0
(t + 2)(t - 5) = 0
t + 2 = 0 or t - 5 = 0
t = - 2 or t = 5
Since the time cannot be negative, the correct answer is
time = 5 seconds
in the diagram of JEA below, JEA = 90° and EAJ = 48°. Line segment MS connects points M and S on the triangle, such that EMS = 59°. Find the measure of JSM.
The value of m∠JSM is 17 degrees.
Given data;
The measure of the ∠JAE = 48 degrees.
The measure of the ∠AEJ = 90 degrees.
The measure of the ∠EMS = 59 degrees.
In triangle JEA;
By angle sum property, we know that;
∠JAE + ∠AEJ + ∠EJA = 180 degree
Substitute the given values in the above expression.
48 degree + 90 degree + ∠EJA = 180 degree
∠EJA = 42 degrees
The angle JMS is,
∠JMS = 180 - ∠EMS (Linear pair)
∠JMS = 180 degrees - 59 degrees = 121 degrees.
In triangle JMS,
By angle sum property, we know that;
∠JMS + ∠JSM + ∠EJA = 180 degree
121 degree + ∠JSM + 42 degree = 180 degree
∠JSM = 17 degree
Thus, the measure of ∠JSM is 17 degrees.
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Out of 210 racers who started the marathon, 187 completed the race, 16 gave up, and 7 were disqualified. What percentage did not complete the marathon?
The total number of racers who did not completed the marathon is given by the sum of those who gave up and those who were disqualified.
Then, 16 + 7 = 23 racers did not completed the marathon.
Therefore, is represent a total of 23/210 = 0.11 = 11% (rounded) of the total number of racers.
Hello! I need some assistance with this homework question, pleaseQ13
we have the new function
[tex]f(x)=\frac{2}{3}\mleft|x\mright|+3[/tex]The vertex of this function is the ordered pair (0,3)
The coordinates of the second point
(2,2) ------------> (2,f(2))
Find the value of f(2)
[tex]\begin{gathered} f(2)=\frac{2}{3}|2|+3 \\ f(2)=\frac{2}{3}\cdot(2)+3 \\ f(2)=\frac{4}{3}+3=\frac{13}{3} \end{gathered}[/tex]the new coordinates of point (2,2) are (2,13/3)
see the attached figure
4)Erica and Megan each improved theiryards by planting daylilies and shrubs.They bought their supplies from thesame store. Erica spent $200 on 9daylilies and 10 shrubs. Megan spent$185 on 13 daylilies and 5 shrubs. Whatis the cost of one daylily and the cost ofone shrub?Type text here
One daylily $10 and 1 shrub $11
1) Gathering the data from the question
Erica spent $200 on 9 daylillies and 10 shrubs
Megan spent $185 on 13 daylilies and 5 shrubs
9d+10s=200
13d+5s=185
2) Let's solve this system of linear equations now
9d+10s=200
13d+5s=185 Multiply by (-2)
9d +10s=200
-26d-10=-370
----------------------
-17d =-170
17d=170
d=10
9(10) +10s=200
90+10s-90=200-90
10s=200-90
10s=110
s=11
So the cost of one daylily is$10 and 1 shrub is $11
6. Solve by any method:3x - 2y = 6x + y = 2
we can take any equation and solve for any variable, for example y will solve x from the second equation
[tex]\begin{gathered} x+y=2 \\ x=2-y \end{gathered}[/tex]now replace the value of x on the first equation
[tex]\begin{gathered} 3x-2y=6 \\ 3(2-y)-2y=6 \\ \end{gathered}[/tex]simplify
[tex]\begin{gathered} 6-3y-2y=6 \\ 6-5y=6 \end{gathered}[/tex]and solve for y
[tex]\begin{gathered} -5y=6-6 \\ -5y=0 \\ y=\frac{0}{-5} \\ \\ y=0 \end{gathered}[/tex]Value of y is 0 now we can replace y=0 on any equation and solve for x
for example I will replace y=0 on the second equation to find x
[tex]\begin{gathered} x+y=2 \\ x+(0)=2 \\ x=2 \end{gathered}[/tex]Value of x is 2
If we want to represent the solution as a point, the solution is
[tex](2,0)[/tex]if 5 guys are putting yogurt in a girl's mouth and each liter is 5 liters how much is the girl carrying in her mouth ️️
5 guys are putting yogurt in a girl's mouth
Each of the yogurt is 5 liters
The total yogurt the girl is carrying = 5 x 5
= 25
The answer is 25 liters of yogurt
Two angles are complementary to each other. One angle measures 32°, and the other angle measures (12x − 20)°. Determine the value of x. 64 6.5 32.5 6
Answer:
B) 6.5
Step-by-step explanation:
Complementary angles are angles that are put together to equal 90 degrees.
Angle one is 32 degrees.
90-32= 58
So we need to get the number 58 for it to be complementary. The reason for this is because 32+58=90. Which would make it complementary.
When we plug in 6.5 we get 58, which is what we want.
12(6.5)- 20= 90
78-20=58
Hope this helps!!!
The value of x is 6.5.
Complimentary angles are known as angles which makes the sum of 90°.
The angles sum up to form a right angle. When two angles complement each other they sum up to be 90°.
According to question one angle - 32° and other angle [12x - 20].
⇒ 32 + [12x - 20] = 90
⇒ 12x - 20 = 58
⇒ 12x = 78
⇒ x = 6.5
Hence, the value of x is 6.5.
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How can i calculate the number of students that graduated from the university faculty of natural sciences in 2002? how can i determine the sector angle that will represent the number of graduates in each subject? how can i hence construct a pie chart of radius 4cm to represent the information given in the table?
A table showing the number of graduates by subject from a university's faculty of natural science in 2002.
1) To calculate the number of students that graduated, find the sum of the number of graduates from each subject.
[tex]9+15+19+12+5=60[/tex]The number of students that graduated is 60.
2) To determine the sector angle that will represent the number of graduates in each subject, divide the number of graduates in each subject by the total number of students and then multiply by 360º.
3) To construct a pie chart with radius, 4cm to represent the information, draw a circle of radius 4cm and partition it into sectors with central angles as calculated in (2) above.
Which number line represents the solution set for the inequality 3(8 - 4x) < 6(x - 5)?-5-4-3-2 -1 01+4123on++at-5-2+ o+1-1234501-5-4-3+o-2-1+1N+W+A+5++-5-4-3-2+o-1NT1345
To find the solution, lets first simplify the inequality:
[tex]undefined[/tex]Determine the concavity of the graph of f(x) = 4 - x^2 between x= -1 and x = 5 by calculating average rates of change over intervals of length 2. 1. The average rate of change over the interval 3 ≤ 2 < 5 =
Given the function:
[tex]f(x)=4-x^2[/tex]For the given function, we will determine the concavity between x = -1 and x = 5
By the average rate of change over the interval 3 ≤ x < 5
We will use the following formula:
[tex]\frac{f(5)-f(3)}{(5)-(3)}[/tex]First, we will find the value of f(5) and f(3)
[tex]\begin{gathered} x=5\rightarrow f(5)=4-5^2=-21 \\ x=3\rightarrow f(3)=4-3^2=-5 \end{gathered}[/tex]Substitute into the formula:
So, the average rate of change will be as follows:
[tex]\frac{f(5)-f(3)}{(5)-(3)}=\frac{(-21)-(-5)}{5-3}=\frac{-16}{2}=-8[/tex]As the average rate of change is negative, the concavity of the graph will be concave down
which of the following reflective symmetries apply to the hexagon?
The line y = -7x/3 is a line of symmetry to the given hexagon while the line y=x is not a line of symmetry to it
This makes the answer to the first statement Yes and the second statement No. That is
Reflective symmetry over the line y=-7x/3 -------------------Yes
Reflective symmetry over the x-axis ------------------------------------No
use the display of data to find the mean, median, mode, and midrange 10,3, 11,3, 12,4, 13,5, 14,2, 15,3
The mean, median, mode and midrange of the given data is 7.92, 7.5, 3 and 8.2 respectively.
What is median and midrange?The mid-way between the least value and the greatest value of the data set is called the midrange, and the median is the middle number in a sorted list of numbers.
Given a data 10,3, 11,3, 12,4, 13,5, 14,2, 15,3
Mean = (2+3+3+3+4+5+10+11+12+13+14+15)/12 = 7.92
Median = 15/2 = 7.5
Mode = 3
Midrange = (2+15)/2 = 8.2
Hence, The mean, median, mode and midrange of the given data is 7.92, 7.5, 3 and 8.2 respectively.
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Write the equation of a sine or cosine function to describe the graph. Please help I’ve tried but I keep missing something like finding the c/b. Thanks in advance!!!
Since the function starts at it maximum value, let's use a cosine function to represent it:
[tex]f(x)=A+B\cos(C(x+D))[/tex]Since the midline of the periodic function is y = 2, we have A = 2.
The period of the function is 4pi/3, so we have:
[tex]\begin{gathered} T=\frac{2\pi}{C}\\ \\ \frac{4\pi}{3}=\frac{2\pi}{C}\\ \\ \frac{2}{3}=\frac{1}{C}\\ \\ C=\frac{3}{2} \end{gathered}[/tex]Since the function already starts at its maximum value, there is no horizontal phase shift, so D = 0.
The amplitude is 1 (it goes up and down 1 unit from the midline), so we have B = 1.
Therefore the function is:
[tex]f(x)=2+\cos(\frac{3}{2}x)[/tex]What would be the correct way to solve this?[tex] {x}^{2} - 5x - 84[/tex]
Answer:
(x + 7 ) ( x - 12 )
Explanation:
We know that if we multiply any two expressions x + a and x + b then we have
[tex](x+a)(x+b)=x^2+(a+b)x+ab[/tex]Now similarly,
[tex]x^2+(a+b)x+ab=x^2-5x-84[/tex]meaning
[tex]\begin{gathered} a+b=-5 \\ ab=-84 \end{gathered}[/tex]In other words, what are the two numbers that if I add them together I get -5 and If I multiply them I get -84. The answer comes from educated guesses. We guess that if we add 7 and -12 we get 5 and if we multiply then we get -84; therefore,
[tex]\begin{gathered} a=7 \\ b=-12 \end{gathered}[/tex]Hence, the expression can be factored as
[tex]=x^2-5x-84=(x-12)(x+7)[/tex]which is our answer!
there are 550 students how many teachers were there be in ratio form
The ratio of teacher to student is equivalent so teacher to the student ratio is same for all the school A, B, C and D.
Equate the teacher to school ratio for school A and school C to obtain the number of teachers in school C.
[tex]\begin{gathered} \frac{15}{330}=\frac{x}{550} \\ x=\frac{15\cdot550}{330} \\ =25 \end{gathered}[/tex]The number of teacher is school C is 25.
Equate the teachers to students ratio for the school A and school D to obtain the number of students in school D.
[tex]\begin{gathered} \frac{15}{330}=\frac{36}{y} \\ y=\frac{36\cdot330}{15} \\ =792 \end{gathered}[/tex]
The number of students in school D is 792.
in the figure above
Since AB is tangent to the circle, the angle BAO equals π/2.
The same happens to BC, so the angle BCO also equals π/2.
Now, for any quadrilateral, the sum of the internal angles is 2π. Therefore:
ABC + AOC + BAO + BCO = 2π
ABC + 3π/7 + π/2 + π/2 = 2π
ABC = 2π - 3π/7 - π/2 - π/2 = π - 3π/7 = (7π - 3π)/7
ABC = 4π/7
Describe in words where cube root of 30 would be plotted on a number line.
Between 3 and 4, but closer to 3
Between 3 and 4, but closer to 4
Between 2 and 3, but closer to 2
Between 2 and 3, but closer to 3
Cube root of 30 is 3.107.
How to find cube root of a number?
Cube root is the number that needs to be multiplied three times to get the original number.
The cube root of a number can be determined by using the prime factorization method. In order to find the cube root of a number:
Step 1: Start with the prime factorization of the given number.
Step 2: Then, divide the factors obtained into groups containing three same factors.
Step 3: After that, remove the cube root symbol and multiply the factors to get the answer. If there is any factor left that cannot be divided equally into groups of three, that means the given number is not a perfect cube and we cannot find the cube root of that number.
We have to find the cube root of 30.
Prime factorization of 30 = 2*3*5.
Therefore the cube root of 30 = ∛(2*3*5)= ∛30 .
As ∛30 cannot be reduced further, then the result for the cube root of 30 is an irrational number as well.
So here we will use approximation method to find the cube root of 30 using Halley's approach:
Halley’s Cube Root Formula: ∛a = x[(x³ + 2a)/(2x³ + a)]
The letter “a” stands in for the required cube root computation.
Take the cube root of the nearest perfect cube, “x” to obtain the estimated value.
Here we have a = 30
and we will substitute x = 3 because 3³ = 27< 30 is the nearest perfect cube.
Substituting a and x in Halley's formula,
∛30 = 3[(3³ + 2*30)/(2*3³ + 30)]
= 3[(27+60)/(54+30)]
= 3(87/84)
= 3*1.0357
∛30 = 3.107.
Therefore the cube root of 30 is 3.107.
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10. Quadrilateral PQRS with P(-5,1). Q(-2,6), R(3,7), and S(6,4); dilate by a factor of 1/2 12 a. Is this an enlargement or reduction? How do you know? 14 b. What are the vertices of the image after the transformation?
a.
The dilation is a reduction, this comes from the fact that the dilation factor is less than 1.
b.
A point after a dilation is given as:
[tex](x,y)\rightarrow(kx,ky)[/tex]where k is the dilation factor.
In this case we need to divide all the coordinates by two, then we have that:
[tex]\begin{gathered} P^{\prime}(-\frac{5}{2},\frac{1}{2}) \\ Q^{\prime}(-1,3) \\ R^{\prime}(\frac{3}{2},\frac{7}{2}) \\ S^{\prime}(3,2) \end{gathered}[/tex]Determine the area of the figure: 1.5 cm 5 cm 5.5 cm Your answer
We can add the are of the 3 rectangle, so we get that the area is:
[tex]A=1.5\cdot5+1.5\cdot5+1.5\cdot0.5=15.75\operatorname{cm}[/tex]solve 10 + 15x - 30 = 40
We have the next equation
[tex]10+15x-30=40[/tex]We sum similar terms
[tex]15x-20=40[/tex]then we clear x
[tex]\begin{gathered} 15x=40+20 \\ 15x=60 \\ x=\frac{60}{15} \\ x=4 \end{gathered}[/tex]the value of x=4
Name the relationship between the pair of angles and find the value of x.
Consecutive interior angles (Same side)
x = -8
Explanations:The two angles are 136 + x and x + 56
The two angles are consecutive-interior angles because they are on the same side of the transversal.
Note that consecutive -interior angles are supplementary and they add up to 180 degrees.
Applying this rule to the diagram shown:
(136 + x) + (x + 56) = 180
136 + 56 + x + x = 180
192 + 2x = 180
2x = 180 - 196
2x = -16
x = -16 / 2
x = -8
A bank pays 3% per annum compound interest, calculate how much interest would you get if you invested £45 for 3 years
Answer:
405
Step-by-step explanation:
don't forget to follow rate like
8. Determine the most precise name for quadrilateral PQRS.-8 -6P(-1, 1)-4 -28642-2-4-6-8Q(0, 2)R(1, 1)2S(0, -2)468
Answer:
[tex]Kite[/tex]Explanation:
Here, we want to determine the most precise name for the quadrilateral
At first sight, the image plot looks like a kite. We will have to confirm this using the properties of a kite
One of the important properties is to check that the diagonals intersect at right angles
Looking at the plot, QS and PR must be perpendicular
This is correct as they meet at right angles at the line through the origin
Also, for us to have a kite, PQ and QR must be equal
This is also correct as PQ and QR are equal in length
Furthermore, PS and RS must be equal in length
This is alo correct as the two are equal in length
We thus conclude that the quadrilateral is a kitecohis is als
plot looks like a kite. We will have to confirm this using the properties of a kite
plot looks like a kite. We will have to confirm this using the properties of a kite
using this input output machine,f(x)=?input. 2,3,5,7output. 9,15,33,59x^2+x+3x^2-x+3x^2+x-3x*2-5
We have values of x and f(x) and choices for the expression of f(x).
We can easily found the correct option just evaluating the expressions in the x values and see which have the correct value of f(x):
For x=2 the outpur=f(x)=9:
[tex]\begin{gathered} x^2+x+3\Rightarrow2^2+2+3=4+5=9,\text{ Correct!!!} \\ x^2-x+3\Rightarrow2^2-2+3=4+1=5 \\ x^2+x-3\Rightarrow2^2+2-3=4-1=3 \\ x\cdot2-5\Rightarrow2\cdot2-5=4-5=-1 \end{gathered}[/tex]You can evaluate in the other values of x and proof that the corretc option is the first.
The vertices of a figure are A(1, -1), B(5.-6), and C(1, - 6). Rotate the figure 90 counterclockwise about the origin. Find the coordinates of the image. Polygon Undo Redo x Reset 7A 6. 5 4 3 2. 1 --7-6-5--4 -3 -2 -1 1 1 2 a 4 - 2 -3 -5 -6 -7 The coordinates of the image are:
The vertices of the given figure are
A(1, -1), B(5.-6), and C(1, - 6).
For a 90 counterclockwise about the origin, a coordinate, (x, y) would be (- y, x)
This means that after the 90 degrees rotation,
coordinate A would be (- - 1, 1) = (1, 1)
Coordinate B would be (- - 6, 5) = (6, 5)
Coordinate C would be (- - 6, 1) = (6, 1)
Pablo draws Rectangle P. He says that the area is greater than 50 square units. What could the missing side length be? Explain. P. ? units 6 units
Answer:
Explanation:
Here, we want to get the missing side length
From the question, it was said that the area is greater than 50 square units
What this mean is that the product of the width and length of the rectangle is greater than 50 square units
Therefore, the number in whch we will multiply by 6 must give us a result greater than 50 square units
The highest multiple of 6 closest to 50 is 48 while the closest multiple after 50 is 54
9 multiplied by 6 will give 54 square units
In essence, we can say that the missing side length is 9 square units
Can you pls help me with number 6 my treacher said that it was d but I got b is me correct or my treacher
Given the algebraic expression below
[tex]6a+4y+a+2a[/tex]Collect like terms
[tex]6a+2a+a+4y[/tex]Add possible like terms using the distributive property of algebra
[tex]\begin{gathered} (6+2+1)a+4y \\ 9a+4y \end{gathered}[/tex]Hence, the final answer is 9a + 4y
Option D is correct
Use Composition of FunctionsBOX OFFICE A movle theater charges $8.50 for each of the xtickets sold. The manager wants to determine how much the movietheater gets to keep of the ticket sales If they have to glve thestudlos 75% of the money earned on ticket sales t(x). If the amountthey keep of each ticket sale is k(x), which composition representsthe total amount of money the theater gets to keep?
Given: The amout charged per ticket is $8.50
If x tickets are sold
Then the total revenue (amount made) will be =>
[tex]8.5\text{ x }x\text{ = \$8.50x}[/tex]If t(x) represents how much the studio collects
and k(x) represents how much is kept
Given: t(x) = 75% then
k(x)= (100 -75)%= 25 %
So that
The total amount that will be kept will be
25% of $8.50x
=>
[tex]\frac{25}{100}\text{ x (\$8.50x) }[/tex][tex]\frac{25\text{ x \$8.50x}}{100}\text{ = }\frac{212.5x}{100}=\text{ \$2.125x}[/tex]The amount that will be kept will be
= > $2.125x
Where x is the number of tickets
By which Theorem or postulate is Change ABC congruent Change BAD?
Solution
we are given that
[tex]\begin{gathered} |AB|=|BC| \\ We draw the diagram as followsNotice the lettering on each triangle, they both represent the triangle we are given in the question
The postulate here is Sides, Angle, Sides (SAS)
Option C
Does the data set display exponential behavior? * {(0, 1), (1, 3), (2, 9), (3, 27)}
ANSWER
Yes, it does.
EXPLANATION
We want to check if the data set displays an exponential behavior.
An exponential function is one in which the values of the range (y values) increase by a certain factor.
The general form of an exponential function is:
[tex]y=a\cdot b^x[/tex]where a is the starting value
b = factor.
Now, we have to compare the data set with this kind of function.
To do that, we have to find a mock function of the data set using the first two data points to test each x value (domain) for each y value.
Basically, we will replace x in the function with a value and see if we get the correct y.
Therefore, when x = 0:
[tex]\begin{gathered} y=a\cdot b^0 \\ y=a\cdot1 \end{gathered}[/tex]From the data set, we see that, when x = 0, y = 1:
[tex]\begin{gathered} \Rightarrow1=a\cdot1 \\ a=1 \end{gathered}[/tex]That is the value of a.
Now, let us try when x = 1:
[tex]\begin{gathered} \Rightarrow y=1\cdot b^1 \\ y=b \end{gathered}[/tex]From the data set, we see that, when x = 1, y = 3:
[tex]\begin{gathered} \Rightarrow3=b \\ b=3 \end{gathered}[/tex]Now, we can say that we have an exponential function to test with:
[tex]y=3^x[/tex]So, let us test for the remaining values of x and y and see if they match the function.
[tex]\begin{gathered} \text{when x = 2:} \\ y=3^2 \\ y=9 \\ \text{when x = 3:} \\ y=3^3 \\ y=27 \end{gathered}[/tex]As we can see, each x value that goes into the function yields the exact y value as the data set. This means that the exponential function works for it.
Hence, the data set displays an exponential behavior.