Plane A 4 hours to travel 2300 miles.
Plane takeoff angle.
Angel
During take off, a plane leaves the ground and travels in a straight line until it reaches a height of 10 km. The distance the plane flies during take off should be in the range 57 km to 62 km. What is the smallest possible angle that the path of the plane could make with the ground? Give your answer in degrees to 1 d. p.
Let's assume that the plane travels a distance of x km during take off and reaches a height of 10 km. Then, using trigonometry, we can find the angle θ between the ground and the path of the plane:
tan(θ) = 10/x
We want to find the smallest possible angle θ, which means we need to maximize x. From the given information, we know that x must be in the range 57 km to 62 km. Therefore, to maximize x, we choose x = 62 km.
Plugging this into the equation above, we get:
tan(θ) = 10/62
θ = arctan(10/62) ≈ 8.8°
Therefore, the smallest possible angle that the path of the plane could make with the ground is approximately 8.8 degrees.
Angel
Xochitl spots an airplane on radar that is currently approaching in a straight line, and that will fly directly overhead. The plane maintains a constant altitude of 7425 feet. Xochitl initially measures an angle of elevation of 19° to the plane at point A. At some later time, she measures an angle of elevation of 37° to the plane at point B.
Find the distance the plane traveled from point A to point B. Round your answer to the nearest foot if necessary
Let's assume that the distance from Xochitl to point A is d1 and the distance from Xochitl to point B is d2. We want to find the distance the plane traveled from point A to point B, which is the difference between d1 and d2.
From the given information, we can set up the following two equations:
tan(19°) = 7425/d1
tan(37°) = 7425/d2
Solving for d1 and d2, we get:
d1 = 7425/tan(19°) ≈ 22977.6 feet
d2 = 7425/tan(37°) ≈ 13060.2 feet
Therefore, the distance the plane traveled from point A to point B is:
d1 - d2 ≈ 9917.4 feet ≈ 3021 meters
Rounding to the nearest foot, we get that the distance the plane traveled from point A to point B is approximately 9917 feet.
Angel
Plane B is flying 75mph 75 mph faster than Plane A. Find the time it takes for Plane A to travel 2300 2300 miles if it takes Plane B the same amount of time to travel 2600 2600 miles.
Let's start by using the formula for distance, rate, and time:
distance = rate x time
Let's assume that Plane A's speed is r mph. Then we know that Plane B's speed is r + 75 mph.
We also know that Plane A travels 2300 miles and Plane B travels 2600 miles. Since they take the same amount of time to travel their respective distances, we can set up the following equation:
2300/r = 2600/(r + 75)
To solve for r, we can cross-multiply and simplify:
2300(r + 75) = 2600r
2300r + 172500 = 2600r
300r = 172500
r = 575 mph
Now that we know Plane A's speed, we can use the formula for distance, rate, and time to find the time it takes for Plane A to travel 2300 miles:
distance = rate x time
2300 = 575 x time
time = 4 hours
A die is rolled. Find the probability of the given event.
Answer:
(a) [tex]\frac{1}{6}[/tex] ≈ 0.167%
(b) [tex]\frac{3}{6}[/tex] = 50%
(c) [tex]\frac{1}{6}[/tex] ≈ 0.167%
Step-by-step explanation:
We Know
A dice has 6 faces.
Numbers: 1, 2, 3, 4, 5, 6
(a) The number showing is a 2;
The probability is : [tex]\frac{1}{6}[/tex] ≈ 0.167%
(b) The number showing is an even number;
The probability is : [tex]\frac{3}{6}[/tex] = 50%
(c) The number showing is greater than 5;
The probability is : [tex]\frac{1}{6}[/tex] ≈ 0.167%
Find the exact value of b
An algebraic expression is described as 14 more than the product of
3 and the difference of z and 9. What is the value of this expression
when z = 17?
The value of the expression is 38 when z = 17.
What is the value of this expression when z = 17?Given that, an algebraic expression is described as 14 more than the product of 3 and the difference of z and 9.
First, we write the expression:
The difference of z and 9 means we subtract 9 from z. We then take this result and multiply it by 3.
Finally, we add 14 to the product of 3 and the difference of z and 9.
3(z - 9) + 14
Where z represents the value that we want to substitute into the expression.
Substituting z = 17, we get:
3(z - 9) + 14
3(17 - 9) + 14
3(8) + 14
24 + 14
38
Therefore, the value of the expression is 38.
Learn more about algebraic expressions here:https://brainly.com/question/28382633
#SPJ1
The attendance at Longwood middle school his first football game of the season is 437 people eat it at the second game is 4 to 76 people determine the approximate percent increase in attendance between the first and second game round your answer to the nearest 10th%
Approximate percent increase in attendance between the first and second game is 8.9%.
What is the approx. percentage increase in attendance between the first and second football games?
To calculate the percent increase in attendance between the first and second game, we can use the formula:
percent increase =
[(new value - old value) / old value] x 100%
where the old value is the attendance at the first game and the new value is the attendance at the second game.
Substituting the given values, we get:
percent increase = [(476 - 437) / 437] x 100%
percent increase = (39 / 437) x 100%
percent increase ≈ 8.92%
Rounding to the nearest tenth percent, we get the approximate percent increase in attendance between the first and second game as 8.9%.
To learn more about Approximate percent, visit: https://brainly.com/question/29652870
#SPJ9
Please help to solve b
a. The probability that a randomly selected American who moved in 2004 was an owner is 0.31. b. 0.38 c. 0.03 .
Describe probability ?Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. For example, the probability of flipping a fair coin and getting heads is 0.5, because there are two equally likely outcomes (heads or tails).
a. Probability that a randomly selected American who moved in 2004 was an owner:
Total number of Americans who moved in 2004 = (11.7 + 2.8 + 0.3 + 18.7 + 4.5 + 1.0) million = 38 million
Number of Americans who moved in 2004 and were owners = 11.7 million
Therefore, the probability that a randomly selected American who moved in 2004 was an owner is:
11.7 million / 38 million = 0.31 (rounded to the nearest hundredth)
b. Probability that a randomly selected American who moved in 2004 moved within the same state:
Total number of Americans who moved in 2004 = (11.7 + 2.8 + 0.3 + 18.7 + 4.5 + 1.0) million = 38 million
Number of Americans who moved in 2004 and moved within the same state = 11.7 million + 2.8 million
Therefore, the probability that a randomly selected American who moved in 2004 moved within the same state is:
(11.7 million + 2.8 million) / 38 million = 0.38 (rounded to the nearest hundredth)
c. Probability that a randomly selected American who moved in 2004 was a renter who moved to a different country:
Total number of Americans who moved in 2004 = (11.7 + 2.8 + 0.3 + 18.7 + 4.5 + 1.0) million = 38 million
Number of Americans who moved in 2004 and were renters who moved to a different country = 1.0 million
Therefore, the probability that a randomly selected American who moved in 2004 was a renter who moved to a different country is:
1.0 million / 38 million = 0.03 (rounded to the nearest hundredth)
To know more about randomly visit:
https://brainly.com/question/29073331
#SPJ1
1 kg of cat food costs £6.38 How much does 9 kg of cat food cost? Give your answer in pounds (£).
Answer: 9 kg of cat food costs £57.42.
Step-by-step explanation: 1 kg of cat food costs £6.38, so you must multiply the cost by 9 to see how much 9 kg is worth.
6.38 x 9 = 57.42
Therefore, 9 kg of cat food is £57.42.
Mary takes a sightseeing tour on a helicopter that can fly 378 miles against a 35 mph headwind in the same amount of time it can travel 630 miles with a 35 mph tailwind. Find the speed, in miles per hour, of the helicopter.
Answer:
The speed of the helicopter is 160mph.
Step-by-step explanation:
The speed of the helicopter is 160mph.
Speed
Speed =Distance/Time
450miles/s-35mph = 702miles/s+35
450×s+35 = 702×s-35
450s+15,750 = 702s-24,570
Collect like terms
702s-450s = 15,750 + 24,570
252s= 40,320
Divide both side by 252s
s= 40,320/252
s= 160mph
Inconclusion the speed of the helicopter is 160mph.
In a recent year and author wrote 191 check, use the poisson distribution to find the probability that on a random select today he wrote at least one check
The probability that on a random select today he wrote at least one check is 0.407
How to solveLet X be the no.of checks the author wrote in a day
Average,
u = 191 checks per year
191/365
= 0.5233/ day
X~Poisson ( u- 0.5233)
The p.m.f of X is given by
P(X=x) =
The probability that, on a randomly selected day, he wrote at least one check = P(
= 1 - P( X < 1)
= 1 - P(X=0)
= 1 - e^-0.5233 x 0.5233^0/0!
= 1 - e^-0.5233 x 1/
= 1 - 0.59256
= 0.407
Read more about probability here:
https://brainly.com/question/24756209
#SPJ1
Use the Distributive Property to write an equivalent expression for -5(4+7y)
= -5( + )
Answer:
y = -3/7
Step-by-step explanation:
In March 2011, a California newspaper predicted that the price of gasoline in two years would be $4.10. The newspaper claimed that the prediction would be within 2% of the actual price of gasoline in March 2013. Given the data in the table, determine the percent error of the prediction. Was the newspapers claim correct or incorrect. Provide work or an explanation to justify your answer.
The newspaper's claim was incorrect, as the percent error of the prediction was 0.76%, which is greater than 2%.
What is percent error?It is the difference between the observed value and the true value, expressed as in percentage. It is used to quantify how accurately a given measurement, prediction or other value matches the true value.
The percent error of the prediction can be calculated using the following formula:
[(Predicted Price - Actual Price) / Actual Price] × 100.
For this problem, the percent error
= [(4.10 - 4.069) / 4.069] × 100
= 0.76%.
Therefore, the newspaper's claim was incorrect since the percent error did not fall within the specified 2%.
In this case, the newspaper's prediction of the price of gasoline in two years did not match the true value as closely as expected, since the percent error was 0.76%.
For more questions related to prediction
https://brainly.com/question/2088661
#SPJ1
A vertical number line labeled 30 to 40 with tick marks every one unit. Point A appears slightly above the tick mark 35.
A vertical number line labeled 30 to 40 with tick marks every one unit. Point A appears slightly above the tick mark 35.
What is
A
Astart color #9e034e, start text, A, end text, end color #9e034e rounded to the nearest whole number?
What is
A
Astart color #9e034e, start text, A, end text, end color #9e034e rounded to the nearest ten?
Point A rounded to the nearest whole Number is 35, and rounded to the nearest ten is 40.
Let's analyze the vertical number line and Point A:
1. The number line is labeled 30 to 40, with tick marks every one unit.
2. Point A is slightly above the tick mark 35.
Now, we need to round Point A to the nearest whole number and the nearest ten.
To round to the nearest whole number:
1. Observe the position of Point A on the number line.
2. Since Point A is slightly above 35, it's closer to 35 than 36.
3. Therefore, Point A rounded to the nearest whole number is 35.
To round to the nearest ten:
1. Observe the position of Point A (35) in relation to the tens (30 and 40) on the number line.
2. Since 35 is exactly halfway between 30 and 40, it is equidistant from both.
3. In this case, we round up to the next ten, which is 40.
4. Therefore, Point A rounded to the nearest ten is 40.
In summary, Point A rounded to the nearest whole number is 35, and rounded to the nearest ten is 40.
To Learn More About Number
https://brainly.com/question/26460978
SPJ11
Find the composition of transformations that
map ABCD to EHGF.
Reflect over the [? ]-axis, then translate
(x+[],y+[]).
Note: Enter x or y for axis.
4
7.
B C
o
Y
D
-1
3
2
0
2
3
H
4
Help
the composition of transformations that map ABCD to EHGF is a reflection over the y-axis followed by a translation by (4,7).
What is axis reflection ?
An axis reflection is a transformation in geometry that involves reflecting a point, a line, or an object across a given axis. In two dimensions, there are two axes of reflection: the x-axis and the y-axis.
When reflecting over the x-axis, all points stay in the same horizontal position but change their vertical position, so a point (x,y) is reflected to (x,-y).
When reflecting over the y-axis, all points stay in the same vertical position but change their horizontal position, so a point (x,y) is reflected to (-x,y).
Axis reflections can be used to transform geometric shapes such as polygons, circles, or lines. These transformations have important applications in various fields, including physics, engineering, computer graphics, and art.
To find the composition of transformations that map ABCD to EHGF, we first need to determine the individual transformations that are needed.
Reflecting over the y-axis will change the x-coordinates of the points, but leave the y-coordinates unchanged. So, to reflect over the y-axis, we negate the x-coordinates of the points.
The translation (x+4, y+7) will move each point 4 units to the right and 7 units up.
Therefore, the composition of transformations is:
Reflect over the y-axis by negating the x-coordinates:
A'(-2, 3), B'(-4, 2), C'(-4, 0), D'(-2, -1)
Translate by (4,7):
A''(2, 10), B''(0, 9), C''(0, 7), D''(2, 6)
Therefore, the composition of transformations that map ABCD to EHGF is a reflection over the y-axis followed by a translation by (4,7).
To know more about axis visit :-
https://brainly.com/question/27946240
#SPJ1
Which of these would you expect to have a positive correlation? Check all that apply. HINT: There are two correct selections. Question 1 options: The number of TV shows you watch and the age of your car The shoe size of that adult and the salary they earn The value of a car and the age of the car The pages of a book you read and the time you spend reading that book A person's years of experience at a job and their salary A person's grade on a test and the number of missed homework assignments leading up to that test
What is the equation of the line that has a slope of -1 and passes through the point (4,1) in slope-intercept form?
y=-1x-4
y = -1x +5
y=-1x-5
y = -1x +3
Answer:
[tex]1 = - 1(4) + b[/tex]
[tex]1 = - 4 + b[/tex]
[tex]b = 5[/tex]
[tex]y = - 1x + 5[/tex]
help me please and if you are frogy... thanks for the anwers
Answer:
59 degrees
Step-by-step explanation:
Since all of those angles would add up to 180 degrees (since they are on a line), we need to subtract 31 degrees (from angle VYT) and 90 degrees (from the right angle on angle WYX) from 180 to get the measure of angle VYW:
180-31-90 = 59.
happy to help :)
45 points, need answers ASAP!!! Match each definition with the correct vocabulary word. The variable whose values result from counting or measuring something. The variable (often x) that does not depend on that of another. The variable (often y) whose value depends on that of another. The variable that has two or more groups, but there is no intrinsic ordering to the groups.
Answer:
Step-by-step explanation:
The matches are:
The variable whose values result from counting or measuring something: quantitative variableThe variable (often x) that does not depend on that of another: independent variableThe variable (often y) whose value depends on that of another: dependent variableThe variable that has two or more groups, but there is no intrinsic ordering to the groups: nominal variableDaisy and Oscar make £90 at a car boot sale. The split the money in the ratio 5:4. How much money did each of them make?
Answer:
Daisy made 50 and Oscar made 40.
Step-by-step explanation:
Daisy: Oscar: total
5 4 5+4 = 9
Taking the total made and dividing by 9.
90/9 = 10
Multiply each term in the ratio by 10.
Daisy: Oscar: total
5*10 4*10 9*10
50 40 90
Daisy made 50 and Oscar made 40.
find the length of the third side if necessary round to the nearest tenth
The length of the third side of the triangle is 8.
What is the length of the third side?The image is that of a right angled triangle. A right angled triangle is a triangle in which one of the angles measure 90 degrees. The sum of angles in the triangle measure up to 180 degrees.
In order to determine the length of the third side, the Pythagoras theorem would be used.
The Pythagoras theorem: a² + b² = c²
where a = length
b = base
c = hypotenuse
In the triangle, 15 is the length and 17 is the hypotenuse.
a² + 15² = 17²
a² = 17² - 15²
a = √(17² - 15² )
a = √(289 -225)
√64 = 8
To learn more about Pythagoras theorem, please check: https://brainly.com/question/14580675
#SPJ1
Based on the line graph shown, how did stock prices perform between March 2015 and August 2015?
A. The stock price increased.
B. The stock price decreased.
C. There is not enough information to make a determination.
D. There was no change.
Option C. Based on the given line graph, it is not possible to determine how stock prices performed between March 2015 and August 2015 as there is no information provided for that time period.
The line graph only provides information for the period from January 2015 to March 2015 and from August 2015 to November 2015. The information provided on the graph shows how the stock prices performed during those time periods. Therefore, there is not enough information on the graph to determine how the stock prices performed between March 2015 and August 2015. It is possible that the stock prices increased, decreased, or remained the same during that time period, but the graph does not provide any information to confirm any of those possibilities.
To learn more about stock prices please click on below link.
https://brainly.com/question/1674639
#SPJ1
Jayden has 8 5/6 cups of rice. He uses 3 1/4 cups to make dinner. How many cups of rice does Jayden have left
Answer: 5 [tex]\frac{7}{12}[/tex] cups
Step-by-step explanation:
Subtract whole number values:
8 - 3 = 5 cups
Subtract fractions:
* Get common denominators
5/6 ➜ 10/12
1/4 ➜ 3/12
* Subtract
10/12 - 3/12 = 7/12
Answer:
5 7/12 cups
Answer:
67/12 cups of rice
Step-by-step explanation:
We Know
Jayden has 8 5/6 cups of rice.
8 5/6 = 53/6
He uses 3 1/4 cups to make dinner.
3 1/4 = 13/4
How many cups of rice does Jayden have left?
We Take
53/6 - 13/4 = 212/24 - 78/24 = 134/24 = 67/12
So, Jayden has 67/12 cups of rice left.
I need help with this please
Finding the total volume of a composite figure requires breaking it down into simpler shapes and then adding up their volumes.
How to find the volume of a composite figure>To find the total volume of a composite figure, you'll need to break it down into simpler shapes and calculate their individual volumes.
Then, you can add up these volumes to get the total volume of the composite figure.
Here are the general steps you can follow:
Identify the simpler shapes: Look for the individual shapes that make up the composite figure, such as cubes, rectangular prisms, pyramids, cylinders, or spheres.
Calculate the volume of each shape: Use the appropriate formula for each shape to find its volume. For example, the volume of a cube is calculated by multiplying the length, width, and height of the cube.
Add up the volumes of all the simpler shapes: Once you have found the volume of each simpler shape, add them up to get the total volume of the composite figure.
Adjust for overlapping shapes: If there are any overlapping shapes, subtract the volume of the overlapped portion to avoid double-counting.
Check your work: Double-check your calculations and make sure your final answer makes sense based on the dimensions of the composite figure.
Overall, finding the total volume of a composite figure requires breaking it down into simpler shapes and then adding up their volumes.
Read more about volume here:
https://brainly.com/question/27710307
#SPJ1
help pls show ur work
The polygons are similar, therefore the missing lengths are: 12) 4; 13) 24
13. The triangles are similar by the SAS similarity theorem; 14. They are not.
How to Find the Sides of Similar Triangles?Recall that every pair of corresponding sides of similar triangles are always proportional to each other.
11. Let the missing side be x.
x/24 = 6/36
x/24 = 1/6
Cross multiply
6x = 24
x = 24/6
x = 4
12. x/20 = 36/30
x/20 = 6/5
Cross multiply:
5x = 120
x = 120/5
x = 24
13. m<VWU ≅ m<SWR based on vertical angles theorem [one pair of congruent included angles]
WV/WS = 40/5 = 8
WU/WR = 40/5 = 8 [two pair of proportional sides]
Therefore, both triangles are similar by the SAS similarity theorem.
14. The triangles are not similar because:
56/24 ≠ 28/13
Learn more about similar triangles on:
https://brainly.com/question/21874653
#SPJ1
Part C
Now you will attempt to copy your original triangle using only two of its sides and the included angle:
Using point E as the center, draw a circle with a radius equal to the length of
, which you calculated in part B.
Using point E as the vertex and
as one side of the angle, create an angle that is equal to the measure of
. Draw ray
Locate the intersection of the ray and the circle, and label the point F.
Complete
by drawing a polygon through points D, E, and F.
Take a screenshot of your results, save it, and insert the image below
After answering the prοvided questiοn, we can cοnclude that Tο circle cοmplete the cοpied triangle, draw a pοlygοn thrοugh pοints D, E, and F.
What is circle?A circle appears tο be a twο-dimensiοnal cοmpοnent that is defined as the cοllectiοn οf all pοints in a jet that are equidistant frοm the hub. A circle is typically depicted with a capital "O" fοr the centre and a lοwer sectiοn "r" fοr the radius, which is the distance frοm the οrigin tο any pοint οn the circle.
The fοrmula 2r gives the girth (the distance frοm the centre οf the circle), where (pi) is a prοpοrtiοnality cοnstant rοughly equal tο 3.14159. The fοrmula r² cοmputes the circumference οf a circle, which refers tο the amοunt οf space inside the circle.
Fοllοw these steps tο duplicate the οriginal triangle using οnly twο οf its sides and the included angle:
Find the pοint where the ray and the circle intersect. Place the tip οf the cοmpass at pοint E and draw an arc that intersects the circle twice. Label the pοint that is οn the same side οf side AC as pοint B as pοint F.
Tο cοmplete the cοpied triangle, draw a pοlygοn thrοugh pοints D, E, and F.
To know more about circle visit:
brainly.com/question/29142813
#SPJ1
PLEASE HELP THIS IS DUE TODAY
In conclusion the value that correctly fills in the blank in the table is 0.69.
Why it is?
To find the relative frequency of boys, we need to use the information given in the frequency table. We know that the total number of boys is 120 - 37 = 83, since the total number of students is 120 and the number of girls is 37.
We can then calculate the relative frequency for boys by dividing the number of boys who prefer math or social studies (40 + 43 = 83) by the total number of students (120):
Relative frequency for boys = (40 + 43) / 120 ≈ 0.69
Rounding to the nearest hundredth, we get:
Relative frequency for boys ≈ 0.69
Therefore, the value that correctly fills in the blank in the table is 0.69.
To know more about Frequency related questions, visit:
https://brainly.com/question/28104726
#SPJ1
same question still need answer:
Lee’s family had a garden in the shape of a right triangle. The total area of the garden is 16 square feet. If they expand the garden to form a triangle with twice the base and twice the height, by how much will they increase the size of their garden?
you say 48 is the answer but there is no step by step instruction shown. Please peovide step by step instruction
According to the question we can conclude that expanding the garden will increase its area by 48 square feet.
Let's call the base of the original right triangle "b" and the height "h". The area of the right triangle is given by the formula:
Area = (1/2) * base * height
So we have:
16 = (1/2) * b * h
When we factor in a single of the variables, then obtain:
b * h = 32
Now, the new triangle will have twice the base and twice the height of the original triangle, so the new base will be 2b and the new height will be 2h. The area of the new triangle is given by the formula:
(Half) * Additional Base * Increased Height = New Area
Plugging in the new values, we get:
New area = (1/2) * 2b * 2h
Simplifying:
New area = 2bh
Now we need to find by how much the area has increased, which is the difference between the new area and the old area:
Area increase = Current area minus Old area.
Area increase = 2bh - 16
Substituting bh = 32, we get:
Area increase = 2(32) - 16
Area increase = 48
Therefore, expanding the garden will increase its area by 48 square feet.
To know more about area visit:
brainly.com/question/951562
#SPJ9
Find the arithmetic mean of 4 and 18
Answer:
The arithmetic mean of two numbers is found by adding them together and dividing the sum by 2.
So, the arithmetic mean of 4 and 18 is:
(4 + 18) / 2 = 22 / 2 = 11
Therefore, the arithmetic mean of 4 and 18 is 11.
Step-by-step explanation:
Answer:
STEP 1:let the arithmetic mean be p, q, r hence 4,p, q, r, 18
STEP 2:U5=18=a+4d
a+4d=18
we're a=4 therefore
4+4d=18
STEP 3:4d/4=(18-4)÷4=14/4
d=14/4=3.5
p=U2=a+d=4+3.5=7.5
q=U3=a+2d=4+(2×7.5)
=
Write the equation for the function described, in STANDARD FORM.
A parabola has a y-intercept of -48. The x-intercepts of the parabola are -2 and 6.
Does your graph have a max or min?
In standard form: enter numeric answer only (no letters)
A=
B=
C=
STANDARD FORM is [tex]3x^2 + 24x + 32y + 192 = 0[/tex] ,parabola has a maximum point at its vertex, which is (2, -3).
what is equation of parabola in standard form:to write the equation for the given parabola in standard form, we need to use the vertex form of the equation of a parabola, which is:
[tex]y = a(x - h)^2 + k[/tex]
where (h, k) is the vertex of the parabola and 'a' is the coefficient that determines the shape and direction of the parabola.
We know that the x-intercepts of the parabola are -2 and 6. This means that the parabola intersects the x-axis at these two points. Therefore, the roots of the quadratic equation are -2 and 6.
We also know that the y-intercept of the parabola is -48, which means that the point (0, -48) lies on the parabola.
Since the parabola is symmetric about the vertical line passing through its vertex, the x-coordinate of the vertex is the midpoint of the x-intercepts, which is (6 - 2)/2 = 2.
Therefore, the vertex of the parabola is (2, k), where k is the y-coordinate of the vertex.
Now we can use the vertex form
[tex]y = a(x - 2)^2 + k[/tex]
We need to determine the values of 'a' and 'k' to complete the equation.
Since the parabola passes through the point (0, -48), we can substitute x = 0 and y = -48 into the equation:
[tex]-48 = a(0 - 2)^2 + k[/tex]
-48 = 4a + k
Similarly, since the x-intercepts are -2 and 6, we can substitute x = -2 and x = 6 into the equation to get:
[tex]0 = a(-2 - 2)^2 + k[/tex]
0 = 16a + k
0 = a(6 - 2)^2 + k
0 = 16a + k
Solving these three equations for 'a' and 'k', we get:
a = -3/8 and k = -3
Substituting these values into the vertex form equation, we get:
[tex]y = (-3/8)(x - 2)^2 - 3[/tex]
Therefore, the equation for the parabola in standard form is:
[tex]3x^2 + 24x + 32y + 192 = 0[/tex]
This parabola has a maximum point at its vertex, which is (2, -3).
know more about minima visit :
https://brainly.com/question/29562544
#SPJ1
find the value of x there are 2 problems
Answer:
x = 70°
Y = 20°
Step-by-step explanation:
We Know
x + 20° = 90°
x = 70°
Y is the vertical angle to the 20° angle, meaning y must have the same measure as the 20° angle.
So, Y = 20°
Answer:
x=70
y=20
Step-by-step explanation:
We can see that y is a vertial angle and so it is 20 and x+20=90 wich means that x=70
A bond is worth $100 and grows in value by 4 percent each year. Explain why the value of the bond after t years is given by 100•1.04^t
The value of the bond is multiplied by the factor [tex](1 + 0.04)[/tex], which is the same as multiplying by 1.04. After t years, the value of the bond will be multiplied by this factor t times, giving the formula:
[tex]100(1.04)t[/tex].
So, the value of the bond after t years is given by 100 • 1.04t.
What is a factor?A factor in mathematics is an expression or number that divides another expression or number without producing a residue. In other terms, a factor is a unit of measurement that may be multiplied by another unit of measurement to yield a specific outcome.
For example, 2 and 3 are factors of 6, because 2 multiplied by 3 equals 6. Similarly, (x + 1) and (x - 3) are factors of the expression [tex]x^2 - 2x - 3[/tex], because when these factors are multiplied together, they produce the expression:
[tex](x + 1) \times (x - 3) = x^2 - 2x - 3[/tex]
The bond is worth $100 initially, and it grows in value by 4% each year. This means that after one year, the value of the bond will be:
[tex]100 + 0.04(100) = 100(1 + 0.04) = 100(1.04)[/tex]
In other words, the value of the bond after one year is the initial value (100) multiplied by a factor of 1.04.
Similarly, after two years, the value of the bond will be:
[tex]100(1.04) + 0.04(100)(1.04) = 100(1.04)^2[/tex]
After three years, the value of the bond will be:
[tex]100(1.04)^2 + 0.04(100)(1.04)^2 = 100(1.04)^3[/tex]
In general, after t years, the value of the bond will be:
[tex]100(1.04)t[/tex]
To know more about factor, visit:
https://brainly.com/question/25829061
Hey team can spend no more than $300 on shirts the team has already spent $80 how many more shirts for $15 each can I still buy Rite in inequality that represents the situation
He can buy less οr equal tο 14 shirts with the mοney left and The inequality that represents this situatiοn is s (stands fοr shirts) ≤ 14.
What is inequality?In Mathematics, it is the relatiοnship between twο values that are nοt equal. Inequality means twο values that are nοt equal. When the situatiοn is tο cοmpare the values, '≤' οr '≥' sign are used.
Hey team can spend nο mοre than $300 οn shirts the team has already spent $80.
300- 80 = 220
220/ 15 = 14.6
Let us say s be the number οf shirts.
Then the inequality will be s≤14
As the numbers οf shirts cant be a fractiοnal term sο we cοnvert the fractiοnal term tο the integer οne.
Hence, the inequality that represents the situatiοn is s≤14.
To know more about inequality
https://brainly.com/question/30238989
#SPJ1