Answers
Given:
The equation of a parabola is given as,
[tex]y=x^2-5[/tex]The objective is to find the axis of symmetry of the parabola.
Explanation:
The general formula to find the axis of symmetry of a parabolic equation is,
[tex]x=-\frac{b}{2a}\text{ .. . . . . (1)}[/tex]From the given equation,
[tex]\begin{gathered} a=1 \\ b=0 \\ c=-5 \end{gathered}[/tex]On plugging the obtained values in equation (1),
[tex]\begin{gathered} x=-\frac{0}{2(1)} \\ x=0 \end{gathered}[/tex]Hence, the axis of symmetry of the parabola is at x = 0.
Related Questions
What is standard form of the parabola y - 4 = -(x - 1)^2
Answers
Answer:
Given that,
The equation of the parabola is,
[tex]y-4=-(x-1)^2[/tex]To find the standard form of the parabola.
Explanation:
Given equation is,
[tex]y-4=-(x-1)^2[/tex]From the definition we know that, standard form of the parabola is of the form,
[tex]y=a(x-h)^2+k[/tex]The standard form of the parabola is,
[tex]y=-(x-1)^2+4[/tex]Answer is: option B
[tex]y=-(x-1)^2+4[/tex]Jessica owns a sword, a set of wooden nunchucks, a giant wooden club, and a deadly pair of fists. She also owns a wooden shield and a set of medieval knight's armor. If she can only take one weapon and one piece of defensive equipment, what is the probability she will choose something made of metal?
Answers
The probability of choosing something made of metal is 0.5.
Let the wooden shield and set of medieval knight's armor be a combination 1.
And the sword, a set of wooden nunchucks, a giant wooden club, and a deadly pair of fists be a combination 2.
Al the wooden piece of combination 2 will come under one category and the metal piece be in another category.
Similarly, in combination 1 wooden piece is in one category, and the metal piece is in another category.
Therefore, the probability of the combination of metal from combination 1 and combination 2 of the metal category would be,
(1 ÷ 2) × ((2 ÷ 4) + (1÷2)) = 0.5
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1.Using geometry vocabulary, describea sequence of transformation that maps p onto figure q.2. write transformation mapping rule for the sequence you describe in part (a)P:(-1,2) (-1,4) (-4,2)(-4,4)Q:(2,-2) (2,-5) (4,-2) (4,-5)
Answers
First, we transform the coordinates of the vertices of P 270° anticlockwise.
The 270° anticlockwise transformation rule, T, is defined as:
[tex]T\colon(x,y)\to(y,-x)_{}[/tex]Therefore,
[tex]T(-1,2)=(2,1)[/tex][tex]\begin{gathered} T(-1,4)=(4,1) \\ T(-4,2)=(2,4) \\ T(-4,4)=(4,4) \end{gathered}[/tex]Let the resultant shape be named P'
Hence,
P': (2,1), (4,1) (2,4) (4,4)
Next
We translate the resultant shape downwards by 6 units.
The transformation rule, S, for moving downwards by 6 units is given by:
[tex]S\colon(x,y)\to(x,y-6)_{}[/tex]Therefore,
[tex]S(2,1)=(2,1-6)=(2,-5)[/tex][tex]\begin{gathered} S(4,1)=(4,1-6)=(4,-5) \\ S(2,4)=(2,4-6)=(2,-2) \\ S(4,4)=(4,4-6)=(4,-2) \end{gathered}[/tex]Hence, the image of S on P' is : (2,-2) (2,-5) (4,-2) (4,-5)
This is illustrated by the image below
I need to now the answer for a and b
Answers
Knowing that there is a total of 250 6th grade students that participated in the challenge:
a. You can identify that:
-The percentage of students that participated in lifting leights is 8%.
A percent can be written as a decimal number by dividing it by 100:
[tex]\frac{8}{100}=0.08[/tex]Therefore, the number of students that participated in that exercise is:
[tex](250)(0.08)=20[/tex]- The percentage of students that participated in running is 30%.
Therefore, the number of them that participated in this exercise is:
[tex](250)(\frac{30}{100})=75[/tex]- Notice that the percentage of students that participated in swimming is 5%.
Hence, the number of them that participated in this exercise is:
[tex](250)(\frac{5}{100})\approx13[/tex]b. Notice that the number of students who chose walking is:
[tex](250)(\frac{17}{100})\approx43[/tex]Therefore, the total number of students that chose swimming, walking, and lifting weight is:
[tex]13+43+20=76[/tex]Notice that that number is greater than the number of students who chose running.
Hence, the answers are:
a. Lifting Weights:
[tex]20\text{ students}[/tex]Running:
[tex]75\text{ students}[/tex]Swimming:
[tex]13\text{ students}[/tex]b. Joseph is right, because there are 76 students who chose swimming, walking, and lifting weights, and there are 75 students who chose running.
I need help what would be the 20th term in this sequence? 7, 14, 21, 28, 35... NUMBER 7
Answers
Cm, this is the solution:
This is the sequence given:
7, 14, 21, 28, 35
d = 7 (Common difference)
An = 7n (Arithmetic sequence)
The 20th term is:
A20 = 7 * 20
A20 = 140
If there is 1/3 of quantity A for every 4/9 of quantity B, how much of quantity A is there for 2/5 of quantity B?
Answers
Answer:
3/10 ths of A
Step-by-step explanation:
Find out how many 4/9 ths there are
2/5 / 4/9 = 2/5 * 9/4 = 18/20
Now multiply the number of 4/9ths ( which is 18/20) by 1/3
1/3 * 18/20 = 6/20 = 3/10ths of A
select functions f and g such that the ratio of function f to function g is equal to the function h.
Answers
What is required is that our choice should satisfy the equation:
[tex]f(x)\text{ = g(x) }\times\text{ h(x)}[/tex]By observation and trial, we obtain :
[tex]\begin{gathered} g(x)=x^2\text{ - x -2} \\ h(x)\text{ = x - 4} \end{gathered}[/tex]When we multiply, we have:
[tex]\begin{gathered} (x^2\text{ - x - 2) (x -4)} \\ =x^3-4x^2-x^2\text{ + 4x - 2x + 8} \\ =x^3-5x^2\text{ + 2x + 8} \end{gathered}[/tex]Hence,
[tex]f(x)=x^3-5x^2\text{ + 2x + 8}[/tex]In summary,
[tex]\begin{gathered} f(x)=x^3-5x^2\text{ + 2x + 8} \\ h(x)\text{ = x - 4} \\ g(x)=x^2\text{ - x -2} \end{gathered}[/tex]What is the distance between the points (4,3) and (1,-1) on the coordinateplane?
Answers
ANSWER
A. 5 units
EXPLANATION
The distance between two points (x₁, y₁) and (x₂, y₂) is given by the Pythagorean Theorem,
[tex]d=\sqrt[]{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]In this case, the points are (4, 3) and (1, -1). The distance between them is,
[tex]d=\sqrt[]{(4-1)^2+(3-(-1))^2}=\sqrt[]{3^2+(3+1)^2}=\sqrt[]{3^2+4^2}=\sqrt[]{9+16}=\sqrt[]{25}=5[/tex]Hence, the distance between the given points is 5 units.
Which expression describes the distance between point A and point B on the number line?
Answers
Answer:
2 -(-3)
Step-by-step explanation:
Find the domain and range. Then use the drop down menu to select the correct symbols to indicate your answer in interval notation. If a number is not an integer then round it to the nearest hundredth. To indicate positive infinifty ( \infty ) type the three letters "inf". To indicate negative infinity(-\infty ) type "-inf" with no spaces between characters.positive quadratic with closed end point at (-5,2) and open end point at (3,2) vertex=(-1,0)The domain is:AnswerAnswer,AnswerAnswerThe range is: AnswerAnswer,AnswerAnswer
Answers
• For domain { -5 ≤x < 3 } : [ -5 ;3),
( take notice of the square bracket that indicates a closed dot/ circle, and open bracket that indicates open circle/dot)
• For range : { 0≤ y≤ 2} : [0;2]
( take note that our graph extends up to y -value = 2 , our minimum being 0 , we put close brackets because it starts at 0 and end at 2 .)
The "Freshman 15" refers to the belief that college students gain 15 lb (or 6.8 kg) during their freshman year. Listed in the accompanying table are weights (kg) of randomly selected male college freshmen. The weights were measured in September and later in April. Use the listed paired sample data, and assume that the samples are simple random samples and that the differences have a distribution that is approximately normal. Complete parts (a) through (c)....Question content area top rightPart 1September April
Answers
ANSWER :
EXPLANATION :
Find GH. BC 19 GH 9x - 3 FE 5х + 1 option A: 2 option B: 6 option C: 15. option D: 51
Answers
Since FE and BC are given to be parallel, the figure BCEF is a trapezium.
The line GF divides the sides BF and CE equally. Hence, we can say that GH is parallel to side FE and BC.
Hence, the trapeziums BCHG and FEHG are similar.
Hence, the ratio between sides can be expressed as,
[tex]\frac{\text{BC}}{GH}=\frac{GH}{FE}[/tex][tex]\begin{gathered} \frac{19}{9x-3}=\frac{9x-3}{5x+1} \\ 95x+19=(9x-3)^2 \\ 95x+19=81x^2-2\times3\times9x+9 \\ 95x+19=81x^2-54x+9 \end{gathered}[/tex][tex]0=81x^2-149x-10[/tex]Using discriminant method, the equation can be solved as,
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x=\frac{-(-149)\pm\sqrt[]{(-149)^2-4\times81\times(-10)}}{2\times81} \end{gathered}[/tex]The positive solution to the equation is x≈2.
So,
[tex]\begin{gathered} GH=9\times2-3 \\ =15 \end{gathered}[/tex]Hence, GH=15.
need help with math paper only one page
Answers
Proportional relation
The slope
The blue slope is negative and the green one is positive, if you realize it your slope has to be positive.
To calculate the slope (m)
y = m x +b
m = (y2-y1)/ (x2-x1)
____________________
You can take two points from the graph for example
Points (x, y)
Point 1 (0, 0); x1= 0 ; y1= 0
point 2 (300, 450); x2= 300 ; y2= 450
m = (450 - 0)/ (300 - 0)
m = 45/ 30
m = 3/2
_____________________
The equation that represents the graph
y= 3/2 x
________________________________
Table
Grams of fish (x); the number of calories (y)
y= 3/2 x
x= 300 Grams of fish
y= 3/2 (300)
y= 450
450 calories
______________
x= 1
y= 3/2 (1)
y= 3/2 = 1.5
1.5 calories
_____________
x= 1000
y= 3/2 (1000)
y= 3000/2 = 1500
1500 calories
_______________________
y = 2001 calories
y= 3/2 x
2001 = 3/2 x
x= 2001 *2/3
x= 1334
1334 grams of fish
... Rotate the following polygon 90* CCW. List the new image coordinates. Write the general Coordinate 10 -10 The general rule for 90 degrees counter xy) > (30)
Answers
The general rule for 90* CCW rotation of a figure about the origin, is:
[tex]\mleft(x,y\mright)\to(-y,x)[/tex]By definition, the original figure is called "Pre-Image" and the new figure is called "Image".
Knowing the coordinates of each point of the figure, you can apply the rule shown. So you get that points of the new image are:
[tex]\begin{gathered} A\mleft(2,3\mright)\rightarrow A^{\prime}(-3,2) \\ B\mleft(5,3\mright)\rightarrow B^{\prime}(-3,5) \\ C\mleft(1,5\mright)\rightarrow C^{\prime}(-5,1) \\ D\mleft(6,5\mright)\rightarrow D^{\prime}(-5,6) \end{gathered}[/tex]Therefore, the answers are:
1. The general rule is:
[tex](x,y)\to(-y,x)[/tex]2. Knowing the points of both figures, you can draw them. The graph is:
3. The new image coordinates are:
The mass of a car is 2276kg rounded to the nearest kilogram.
The mass of a person is 60.6kg rounded to 1 decimal place.
Write the error interval for the combined mass, m, of the car and the person in the form _______
Answers
The error interval for car and person are:
2275 ≤ 2276 < 2276.5 and 60.55 ≤ 60.6 < 60.65 respectively.
Given, the mass of a car is 2276 kg.
we are asked to determine the nearest kilogram.
the car: rounded to the nearest kilogram
so 2275 ≤ 2276 < 2276.5
therefore, a = 2275.5
and b = 2276.5
The mass of a person is 60.6 kg.
we need to round it to 1 decimal place.
the person: rounded to 1 decimal place,
so, 60.55 ≤ 60.6 < 60.65
therefore, a = 60.55
and b = 60.65
Hence the error interval for the combined mass, m, of the car and the person is 2275 ≤ 2276 < 2276.5 and 60.55 ≤ 60.6 < 60.65 respectively.
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Factor the following expression completely:
x² 18x + 80 =
Help please ad thanks!
Answers
Answer:
[tex]18 {x}^{3} + 80[/tex]
Step-by-step explanation:
[tex] {x}^{2} \times 18 {x}^{1} + 80 \\ {x}^{2 + 1} x18 + 80 \\ {x}^{3} x18 + 80 \\ 18 {x}^{3} + 80[/tex]
please help me out quickly huge point for grab please let your answer be correct
Answers
Answer:
first is T second is F
Step-by-step explanation:
And you're fine that on his way to work he waits time for the bus is roughly uniformly distributed between 8 minutes and 17 minutes 1 day he time his weight and writes down a number of minutes ignoring the 2nd run a solution to 3 decimal places
Answers
We have the waiting times uniformly distributed between 8 and 17 minutes. As he ignore the seconds, we have a discrete distribution with values 8 to 16.
We have to find what is the probaility that the waiting time is 10 minutes.
We can find this probability knowing that 10 is one class out of 17-8=9 classes with equal probability.
So the probability is:
[tex]P(X=10)=\frac{1}{9}\approx0.111[/tex]We now have to calculate the probability that the waiting time is between equal or higher 11 and less than 13. This include classes 11 and 12 (and not 13), so we include 2 classes out of 9. Then, the probability is:
[tex]P(11\le X\le13)=\frac{2}{9}\approx0.222[/tex]Answer:
P(X=10) = 0.111
P(11<=X<13) = 0.222
A car is traveling at 25 mph during rush hour. How far does the car travel in 3 minutes and 45 seconds? Round your answer to the nearest foot
Answers
Given:
The speed of car is 25 mph.
Explanation:
Determine the speed of car in foot per second.
[tex]\begin{gathered} 25\text{ mph=25 mph}\cdot\frac{1.46667\text{ fps}}{1\text{ mph}} \\ =36.6675 \end{gathered}[/tex]So car travel 36.6675 feet in 1 second.
Determine the time in seconds.
[tex]\begin{gathered} 3\text{ min 45 sec=3}\cdot60sec+45\text{ sec} \\ =180+45\text{ sec} \\ =225\text{ sec} \end{gathered}[/tex]Determine the distance travelled by car in 3 minutes 45 seconds.
[tex]\begin{gathered} 36.6675\cdot225=8250.1875 \\ \approx8250 \end{gathered}[/tex]So car travell 8250 feet.
Answer: 8250
Find the perimeter of a rectangle with width 20.0 inches and length 21.8 inches. Round your answer to the nearest tenth.
Answers
Given:
Length of the rectangle is 21.8 inches.
Width of the rectangle is 20.0 inches.
To find the perimeter of a rectangle:
Using the formula, we get
[tex]\begin{gathered} P=2(l+w) \\ =2(21.8+20.0) \\ =2(41.8) \\ =83.6\text{ inches} \end{gathered}[/tex]Hence, the perimeter of the rectangle is 83.6 inches.
You're flying from Joint Base Lewis-McChord (JBLM) to an undisclosed location 201 km south and 160 km east. Mt. Rainier is located approximately 56 km east and 40 km south of JBLM. If you are flying at a constant speed of 800 km/hr, how long after you depart JBLM will you be the closest to Mt. Rainier?
Answers
The time it would take to get closest to Mt Rainier, t ≈ 8.53 × [tex]10^{-3}[/tex] hours.
What is the separation of a line from a point?The perpendicular distance of a point to a line is the closest distance between them. The length of the perpendicular segment connecting a point to a line is the distance between them.
It would take roughly 5.12 minutes to go to the closest point to Mount Rainier.
The following justifies why the value is accurate:
The given parameters are;
The flight's direction is 201 kilometres south and 160 km east.
Mount Retainer is situated 56 kilometers east and 40 kilometers south of JBLM.
Flight velocity is 800 km/h.
The travel path's slope, in m, is given as follows:
m = -201/160
=1.2
The equation of the path is therefore;
y+201 = -1.2(x-160)
y = -1.2(x-160) - 201
The required slope for the perpendicular distance from the travel path to the Mt Rainier, m', is therefore;
m' = -1/m
Which gives;
m' = 1/1.2
The equation of the line is therefore;
y+ 40 = 1/1.2(x-56)
y = 1/1.2(x-56)-40
The coordinates of the point where the two lines meet is therefore;
-1.2(x-160)-201 = 1/1.2(x-56)-40
solving this we get
x = 22.46
y = -67.83
The magnitude of the distance in km is, d = 71.451
The time it will take to be closest to Mt. Rainier, t, is given as follows;
t = 71.451/800
t = 8.9×[tex]10^{-3}[/tex]
The time it would take to get closest to Mt Rainier, t ≈ 8.53 × [tex]10^{-3}[/tex] hours.
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You are a math tutor at your school.
On the last day of school, you bring in a bag of 48 pieces of candy for your students.
You want to share the candy equally with your 6 students.
How many pieces of candy will each student get?
CLEAR CHECK
54 pieces per student
42 pieces per student
8 pieces per student
0.13 piece per student
Answers
Reduce the current rate of 48 pieces per 6 students to 8 pieces per one student. Divide 48 pieces by 6 students to get 8 pieces per student.
What is called in probability?Probability is a branch of mathematics that deals with numerical descriptions of how likely an event is to occur or how likely a proposition is to be true. The probability of an event is a number between 0 and 1, where 0 indicates the event's impossibility and 1 indicates certainty. Probability and possibility are synonymous. It is a branch of mathematics that deals with the occurrence of a random event. The value ranges from 0 to 1. In mathematics, probability has been introduced to predict the likelihood of events occurring.The probability of an event occurring is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
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the following frequency data shows the number of States including the District of Columbia that favorite each party in the presidential popular vote in 1976 and 2012. Drag and drop the correct equations and inequalities into the boxes to complete the explanation
Answers
The conditional relative frequency that a state was won by the Democrat in 2012, given that a Democrat won the state in 1976 is: 12 (won by the Democrat in 2012 and also in 1976)/24(Total won by the Democrat in 1976)= 50 %
The conditional relative frequency that a state was won by the Republican in 2012, given that a Republican won the state in 1976 is: 12 (won by the Republican in 2012 and also in 1976)/27(Total won by the Republican in 1976)= 44.4 %
Since 44.4 % < 50%, the 2012 Republican candidate was slightly less likely to win a state that had voted for the party's candidate in 1976 than the Democratic candidate.
Jackie claims that points with the same x- and y- coordinates must lie in Quadrant l or Quadrant lll. Do you agree or disagree? Explain your answer.
Answers
It is known that in the I and III quadrants, the signs of the x- and y- are the same.
Jackie claims that the points with the same x - and y - coordinates must lie in the I or III quadrant.
His claim is true.
The points with the same x - and y - coordinates are of the form (a,a) or (-a,-a). If the point is of the form (a,a), it lies in the quadrant I
If the point is of the form (-a,-a), it lies in quadrant III.
Hello what is the question to both parts and what is the monthly payment
Answers
In general, the monthly payment formula is
[tex]M=\frac{P(\frac{r}{12})(1+\frac{r}{12})^n}{(1+\frac{r}{12})^n-1}[/tex]In our case,
[tex]P=19300,r=0.061,n=3\cdot12=36[/tex]Where r=6.1%=0.061 and the number of payments is 12months*3years=36 monthly payments. Thus, the answer is
[tex]\begin{gathered} \Rightarrow M=19300\cdot\frac{\frac{0.061}{12}(1+\frac{0.061}{12})^{36}}{(1+\frac{0.061}{12})^{36}-1} \\ \Rightarrow M=588.0182\ldots \\ \Rightarrow M\approx588.02 \end{gathered}[/tex]The monthly payment is $588.02
The probability a student at Jamal's school is in the band is 0.20. Jamal wants to estimate the probability that in 3 randomly selected students, at least 2 are in the band.
To do this, he uses a simulation. He lets 1 represent a student who is in the band and 2, 3, 4, or 5 represent a student who is not in the band. He then uses a computer to randomly generate 3 random numbers from 1 to 5 twenty times. The results of these 20 trials are shown in this list.
233, 113, 131, 244, 414,344, 412, 132, 554, 454,334, 235, 125, 412, 254,232, 221, 342, 333, 313
Based on this simulation, what is the estimated probability that at least 2 of 3 randomly selected students are in band?
Enter your answer, as a decimal, in the box.
Answers
Answer:
0.45
Step-by-step explanation:
1) the required probability can be calculated as:
P=(number_trials_with_2or3_students_in_band)/(total_number_trials);
according to the formula above:
2) number of trials with 2 or 3 students in the band is:
233, 113, 131, 244, 414,344, 412, 132, 554, 454,334, 235, 125, 412, 254,232, 221, 342, 333, 313 - 9;
3) total number of trials is: 20.
finally, P=9/20=0.45
Answer: its 0.10
Step-by-step explanation:
i took da quiz heres proof
HELP ASAP BRAINLEST + 100 POINTS PLEASE I AM DESPERATE EASY 7TH GRADE
A TV show had 5.6 x 10^5 viewers in the first week and 4.1 x 10^5 viewers in the second week. Determine the average number of viewers over the two weeks and write the final answer in scientific notation.
9.7 x 10^10
9.7 x 10^5
4.85 x 10^10
4.85 x 10^5
Answers
Answer:
4.85 x 10^5
Step-by-step explanation:
First you want to find 5.6 x 10^5 into simplified form, which is 560000.
Then, you want to find 4.1 x 10^5 into simplified form, which is 410000.
Then you can add these numbers together to get 970000.
970000 into scientific notation is 9.7 x 10^5.
CORRECTION:
Answer should be based off of the AVERAGE viewers, not total.
Average viewers is 485000
485000 in scientific notation is 4.85 x 10^5
The average number of viewers over the two weeks are 4.85 x 10^5
A tv show had 5.6 x 10^5 viewers in the first week
and 4.1 x 10^5 viewers in the second week.
What is an average number:
This is the arithmetic mean, and is calculated by adding a group of numbers and then dividing by the count of those numbers.
To find the average number of viewers over the two weeks
Remove the decimal point.
5.6 x 10^5 write like this 560000
Similarly, 4.1 x 10^5 write like this 410000
Now, Solving the question
Therefore, the average will be
560000 + 410000
= 970000/2
=485000
=4.85 X 10^5
and 4.85 x 10^5
Thus , the average number of viewers over the two week 4.85 x 10^5
Questions in picture
Answers
A:
For the first graph the equation would be y=25x with y being the cost and x being the number of yards. Then put 40 for x so it is y=25(40) and solve.
The answer for graph is 1000
For the second table it costs 490 dollars to move 20 yards and 40 is double of 20 so double the cost.
The answer for table is 980
B:
The rate of change for graph is y=25x and that means for every yard shipped you pay 25 dollars
The rate of change for table is whatever the cost divided by the number of yards is i can't see the numbers
C:
In the first question the graph is 1000$ and the table is 980$ so the table would be cheaper
What's the answer please and thank you
Answers
step 1
Find the slope
we take the points
(5,-30) and (8, -48)
m=(-48+30)/(8-5)
m=-18/3
m=-6
step 2
Find the equation of the line in slope intercept form
y=mx+b
we have
m=-6
point (5,-30)
substitute
-30=-6(5)+b
-30=-30+b
b=0
therefore
y=-6xIs it possible to draw a triangle with a 6 mm side an 8 mm side in a 90° angle between them
Answers
Given:
Is it possible to draw a triangle with a 6 mm side an 8 mm side and a 90° angle between them?
The sides of 6 mm and 8 mm and 90° angle between them, so, the sides will be the legs of a right-angle triangle
the hypotenuse of the triangle will be calculated using the Pythagorean theorem as follows:
[tex]h=\sqrt{6^2+8^2}=\sqrt{36+64}=\sqrt{100}=10[/tex]So, the answer will be Yes, it is possible.
