Answer:
[tex]y=3x^2+12x+17[/tex]
Step-by-step explanation:
The equation in vertex form is [tex]y=a(x+2)^2+5[/tex].
We can use the point [tex](1,32)[/tex] to solve for [tex]a[/tex].
[tex]32=a(1+2)^2+5 \\ \\ 27=9a \\ \\ a=3 \\ \\ \\ \therefore y=3(x+2)^2 + 5 \\ \\ =3(x^2+4x+4)+5 \\ \\ =3x^2+12x+12+5 \\ \\ =3x^2+12x+17[/tex]
A cannonball is shot with a velocity of 90 m/s. If its vertical velocity at the top of its arc is 0 m/s and the horizontal velocity at the top of its arc is 45 m/s, at what angle was it shot?
The measure of the angle when a cannonball is shot will be 60°.
What is a vector?The quantity which has magnitude, and direction, and follows the law of vector addition is called a vector.
A cannonball is shot with a speed of 90 m/s. Assuming its upward speed at the highest point of its curve is 0 m/s and the flat speed at the highest point of its bend is 45 m/s.
We know that in projectile motion, the horizontal velocity does not change.
Let 'x' be the angle it shot. Then the cosine of the angle x is the ratio of horizontal velocity to the resultant velocity when it is shot. Then we have
cos x = 45 / 90
cos x = 1/2
cos x = cos 60°
x = 60°
The proportion of the point when a cannonball is shot will be 60°.
More about the vector link is given below.
https://brainly.com/question/13188123
#SPJ1
What does 5 more than mean?
'5 more than' means that a number is 5 units greater than the original number, using the concept of addition.
Addition (usually signified by the plus symbol +) is one of the four basic operations of arithmetic, the other three being subtraction, multiplication and division.The addition of two whole numbers results in the total amount or sum of those values combined. The example in the adjacent image shows a combination of three apples and two apples, making a total of five apples. This observation is equivalent to the mathematical expression "3 + 2 = 5" (that is, "3 plus 2 is equal to 5").
Besides counting items, addition can also be defined and executed without referring to concrete objects, using abstractions called numbers instead, such as integers, real numbers and complex numbers. Addition belongs to arithmetic, a branch of mathematics. In algebra, another area of mathematics, addition can also be performed on abstract objects such as vectors, matrices, subspaces and subgroups.
Now, let us understand the meaning.
Let the original number be x.
'5 more than a number' implies x + 5.
This means that the new number, x + 5, is greater than the original number, x, by 5 units. We also have to keep in mind, [tex]x + 5 > x[/tex].
Hence, the final meaning is 5 units greater than the original number.
To learn more about addition, visit the link:
brainly.com/question/29464370
#SPJ4
the graph at right shows the situation after the u.s. removes a tariff on imports of canned tuna.
The supply-demand curve after US removed tariff on imports is provided. The customer surplus is denoted by area A+B+C+D, loss in producer surplus by A and government loss in revenue by C.
When supply is equal to the demand we get the equilibrium quantity produced and equilibrium price.
The initial price P0 is less than the equilibrium price and thus there is excess demand of the product and thus there is import. When tariff is removed price again drops increasing the excess demand and thus more product is imported.
Consumer surplus is the amount the customer saves as price set by the supplier is less than the amount the consumer is ready to pay. As the customer is ready to pay at P0, the customer surplus when price drop to P1 is given by area A+B+C+D.
The loss in producer surplus is denoted by the area A. As the tariff is removed, the loss in revenue for government is denoted by the area C.
--The question is incomplete, answering to the question below--
"The graph at right shows the situation after the U.S. removes a tariff on imports of canned tuna.
Which areas show the gain in consumer surplus?
A. C
B. A+B+C+D
C. A
D. B+C+D
Which area shows the loss in producer surplus?
A. B+C+D
B. A + B
C. A
D. A+B+C+D
Which area shows the loss in government tariff revenue?
A. A
B. C
C. A+B+C+D
D. B+C+D"
To know more on consumer surplus
https://brainly.com/question/29737905
#SPJ4
Sienna has 534 pounds of grapes. She eats 18 pound and gives 212 pounds to her brother.
How many pounds of grapes does Sienna have left?
Answer: 304 Pound of Grapes
Step-by-step explanation:
Sienna has 534 grapes. She eats 18 pounds of grapes.
[tex]534-18[/tex]
[tex]=516[/tex]
She gives 212 pounds of grapes to her brother.
[tex]516-212[/tex]
[tex]=\fbox{304 grapes left}[/tex]
What are the 3 methods used to calculate volume?
3 methods used to calculate volume are-
Volume by Space SolverCalculate Volume Using Density and MassVolume by Displacement SolverDefine the three method to find volume?Volume by Space SolverEvery physical object takes up space, and you may determine the volume of some of these by counting their individual parts. The volume of objects with straightforward shapes, such as cones, rectangular prisms, sphere, and cylinders, can be determined using this method most easily.
Calculate Volume Using Density and MassThe definition of density is the mass of an object per unit of volume. Therefore, using the equation: If you understand the object's density and can weigh it, you can calculate its volume.
volume = weight / density
Volume by Displacement SolverYou might not be able to precisely gauge an object's physical dimensions if it has an unusual shape.
The volume that is displaced when an object is submerged in a liquid and perhaps a gas can be measured as a substitute. This approach to measuring volume is widely popular and, when used properly, very precise.To know more about the volume of cube, here
https://brainly.com/question/19891526
#SPJ4
The stationary section is on isle 14, one row over from the scents and perfumes.
The correct spelling are of the following words is Caucion :caution ,Isle :aisle and Cents :sents
The scent of her perfume is the signifier, and the feminine and romantic association she makes with the scent is the signified.
In linguistics, the concepts of signifier and signified are seen in Saussure's theory of the sign. A sign is formed by the pair signifier/signified. Signifier is a word, an image, anything that has a material form. Signified is the meaning attributed to the signifier by an individual. That means the same signifier can have different signifieds according to the each person. For Mary, the signifier "floral perfume" presents as its signified the "feminine and romantic" feeling. To a different person - myself, for instance -, a floral perfume does not have the same meaning. I do not see it as romantic or feminine. Instead, because the sweet smell gives me a headache, that has become my signified for it.
The stationary section is on isle 14, one row over from the perfumes and cents.
Hence Caucion :caution
Isle :aisle
Cents :sents
the complete question is
Correct the misspellings in these sentences.
Please use caucion when entering this area as the floor can be slippary.
The stationary section is on isle 14, one row over from the perfumes and cents.
Hence Caucion :caution
Isle :aisle
Cents :sents
learn more about of spelling here
https://brainly.com/question/15225461
#SPJ4
a line ray or segment that divides a segment into two congruent parts at a 90° angle
A line, line segment, or ray that divides an angle into two congruent angles is called an angle bisector.
What are supplementary angles example?
Supplementary angles are those angles that sum up to 180 degrees. For example, angle 130° and angle 50° are supplementary angles because sum of 130° and 50° is equal to 180°. Similarly, complementary angles add up to 90 degrees.
What do you mean by angle bisector?
If the angle is divided by the line and the angle is divided such that the angles are equal to each other then the line is called the angle bisector.
The word congruent means equal of the things. In this, the angles are congruent to each other which means the angles are equal to each other.
Thus, the black space is to be filled by the angle bisector.
More about the angle bisector line is given below.
brainly.com/question/3642603
#SPJ4
Answer the question please
Answer:
81 degrees
Step-by-step explanation:
Because of exterior angles u=u-41+u-40
Solve:
u=2u-81
0=u-81
u=81
Let x^{3}-5 x^{2}-17 x+21=0x
3
−5x
2
−17x+21=0 be a polynomial equation.
a) Find all potential rational solution(s) using the Rational Root Theorem. Separate multiple solutions with commas if necessary.
Preview
b) Find all the distinct, actual rational solution(s). Separate multiple solutions with commas if necessary. If no solutions exist, enter \text{None}None.
By Rational Root Theorem, all rational roots of the polynomial equationx³-5x²-17x+21 = 0x is (x−3)(x+1)(x+7).
How do you find rational solution using Rational Root Theorem?The rational root theorem, also known as the rational root test, is an algebraic theorem that states that for a polynomial equation with integer coefficients to have a solution (root) that is a rational number, the leading coefficient (the coefficient of the greatest power) must be divisible by the fraction's denominator and the constant term (the one without a variable) must be divisible by the fraction's denominator.
It is given that,
x³-5x²-17x+21 = 0x
Factor the left side of the equation,
(x−1)(x−7)(x+3)=0
If any of the factors on the left side of the equation equals 0, the entire expression equals 0.
x−1=0
x−7=0
x+3=0
Set, x−1equal to 0 and solve for x.
x−1 equal to 0.
x−1=0
Add 1 to both sides of the equation.
x=1
Set, x−7 equal to 0 and solve for x
Set x−7equal to 0.
x−7=0
Add 7 to both sides of the equation.
x=7
Set x+3 equal to 0and solve for x.
Set x+3 equal to 0.
x+3=0
Subtract 3 from both sides of the equation.
x= −3
The final solution is all the values that make (x−1)(x−7)(+3)=0 true.
x=1,7,−3.
Hence, By Rational Root Theorem, all rational roots of the polynomial equationx³-5x²-17x+21 = 0x is (x−3)(x+1)(x+7).
To learn more about Rational Root Theorem refer to:
https://brainly.com/question/27991702
#SPJ1
Joshua has a points card for a movie theater. He receives 60 rewards points just for signing up. He earns 5.5 points for each visit to the movie theater. He needs at least 245 points for a free movie ticket. Which inequality can be used to determine vv, the minimum number of visits Joshua needs to earn his first free movie ticket?
The inequality that can be used to determine v, the minimum number of visits Joshua needs to earn his first free movie ticket is 5.5v + 60 ≥ 245
The minimum number of visits Joshua needs is approximately 34 visits.
How to write and solve inequality?Points needed for a free movie ticket = at least 245 pointsPoints earned for signing up = 60 pointsPoints earned for each visit to the movies = 5.5 pointsNumber of visits Joshua needs to earn his first free movie ticket = v5.5v + 60 ≥ 245
Subtract 60 from both sides
5.5v ≥ 245 - 60
5.5v ≥ 185
divide both sides by 5.5
v ≥ 185 / 5.5
v ≥ 33.63636363636363
Approximately,
v ≥ 34
Therefore, the minimum number of visits Joshua needs to earn his first free movie ticket is approximately 34 visits
Read more on inequality:
https://brainly.com/question/25275758
#SPJ1
Is reflection and rotation the same?
Reflection is the act of flipping a figure over a line. The act of rotating involves turning a figure a predetermined distance around a point. And hence, reflection and rotation is not the same.
What is reflection?In mathematics, a reflection is an isometric mapping from a Euclidean space to itself with a set of fixed points called the hyperplane, also referred to as the axis or plane of reflection.
The image created by a reflection is the figure's mirror image in the axis or plane of reflection.
Rotation:
The concept of rotation in mathematics has its roots in geometry.
Any rotation is a movement of a certain area while maintaining at least one point. It may be used to describe, for instance, how a rigid body moves around a fixed point.
So, we can say that flipping a figure over a line is called reflection. Rotation is the process of turning a figure a specific amount around a point.
Therefore, reflection is the act of flipping a figure over a line. The act of rotating involves turning a figure a predetermined distance around a point. And hence, reflection and rotation are not the same.
Know more about reflection here:
https://brainly.com/question/26642069
#SPJ4
What is the slope of 3x 5y =- 9?
3x - 5y=-9 has a [tex]\frac{-3}{5}[/tex] slope.
A line's steepness can be determined by looking at its slope. To find the slope of a line, you need to have the equation of the line in the form y = mx + b, where m is the slope and b is the y-intercept (the point at which the line crosses the y-axis).
To put the equation 3x - 5y = -9 in this form, you can start by isolating the y term on one side of the equation:
3x - 5y = -9
-5y = -3x - 9
y = (-3/5)x - (9/5)
The slope of the line is therefore -3/5.
The complete question is:-
What is the slope of 3x - 5y =- 9?
To learn more about slope, refer:-
https://brainly.com/question/3605446
#SPJ4
Most Algebra 1 Formulas for needed for CST
The below would be most important Algebra 1 Formulas for CST.
Linear Equation:
[tex]Ax + By + C = 0[/tex]
Equation of Straight Line or Slope:
[tex]y = mx+b[/tex]
Point-slope form:
[tex]y-y_{1} = m(x-x_1)[/tex]
Slope when 2 points are given:
[tex]m = \frac{(y_2 - y_1)}{(x_2-x_1)}[/tex]
Quadratic Equation:
[tex]Ax^2 + Bx +C = 0[/tex]
When lines are parallel:
Slope of both lines are equal. [tex]m_1 = m_2[/tex]
When lines are perpendicular:
Slope of perpendicular lines are opposite reciprocals, meaning if the slope of a line [tex]l_1[/tex] is [tex]\frac{1}{2}[/tex]. The line [tex]l_2[/tex] perpendicular to [tex]l_1[/tex] is [tex]-\frac{2}{1}[/tex].
Work Formula:
Total Work Done = Number of Days [tex]\times[/tex] Efficiency
where Efficiency is inversely proportional to Time Taken.
To know more about Algebra, visit: https://brainly.com/question/24875240
#SPJ4
A carpet cleaner charges $59 for the first room and $30 for each additional room. A customer does not want to spend no more than $125 for having the carpets in his house cleaned. If r represents the additional rooms, write an inequality that represents the situation
The inequality could be represented by 59 + 30r ≤ 125
According to the given information
Money charged for first room = $59
Money charged for per additional room = $30
The money that the customer could pay = $125
So
We need to write the inequality to determine the situation
Let the number of carpets be r
Firstly , determining an expression for the cleaner charges
59 + 30*r
Since
The customer cannot pay more than $125
Hence
According to the given situation
59 + 30r ≤ 125
30r ≤ 66
r ≤ 2.2
The inequality could be represented by 59 + 30r ≤ 125
To know more about Inequality
https://brainly.com/question/11612965
#SPJ1
How do you know when a graph is inequality?
When plotting an inequality on a graph, treat the <, ≤, >, or ≥sign as an equals sign.
What is a graph of inequality?Treat the <, ≤, >, or ≥ sign as a = sign when putting an inequality on a graph.
Graph the equation as a dotted line if the inequality is either < or >.
Graph the equation as a solid line if the inequality is either ≤ or ≥.
How to Graph Linear Inequalities: Steps
(A) Always begin by separating the variable y from the inequality's left side.
(B) Symbolizing equality instead of inequality is step two.
(C) In the X, Y, XY, XY plane, graph the boundary line from step 2.
(D) The final step is to shade a portion or one side of the borderline.
Therefore, when plotting an inequality on a graph, treat the <, ≤, >, or ≥sign as an equals sign.
Know more about the graph of inequality here:
https://brainly.com/question/11234618
#SPJ4
What represents a function on a graph?
Use the vertical line test to determine whether a graph accurately represents a function. If a vertical line is moved across it and only ever touches it at one point, the graph is said to be a function. If the vertical line crosses the graph more than once, the graph is not a function.
What do we mean by a Graph of a function?Equations that have been solved for y are graphed as functions! In this instance, the graph of f(x) is the graph of y = x² - 3.
Making points for the graph is simple.
Select a value for the first coordinate, then calculate the second coordinate by evaluating f at that value
To establish if a graph reflects a function, use the vertical line test.
The graph is a function if a vertical line drawn across it is moved and only ever touches it at one point.
The graph is not a function if the vertical line crosses it at more than one location.
Therefore, use the vertical line test to determine whether a graph accurately represents a function. If a vertical line is moved across it and only ever touches it at one point, the graph is said to be a function. If the vertical line crosses the graph more than once, the graph is not a function.
Know more about the Graph of a function here:
https://brainly.com/question/24335034
#SPJ4
Write an equation or expression for the following. The quotient of twelve and a number is four times the number increased by one
Answer: quotient deals with addition and times deal with multiplication
12/(n*4+1)
What is the nature of the roots of x² − 3x 4 0?
The roots of the equation are x = (3 + iÂ√7)/2 and x = (3 - iÂ√7)/2.
The equation x^2 - 3x + 4 = 0 can be factored as (x - 4)(x - 1) = 0.
Therefore, the roots of the equation are x = 4 and x = 1.
To calculate this, we can use the Quadratic Formula:
x = [-b ± Â√(b^2 - 4ac)]/2a
In this equation, a = 1, b = -3, and c = 4
x = [-(-3) ± Â√((-3)^2 - 4(1)(4))]/2(1)
x = [(3) ± Â√(9 - 16)]/2
x = (3 ± Â√(-7))/2
x = (3 ± iÂ√7)/2
Therefore, the roots of the equation are x = (3 + iÂ√7)/2 and x = (3 - iÂ√7)/2.
Learn more about nature of the roots here :
https://brainly.com/question/12383696
#SPJ4
Is mean and SD the same?
Answer:
No, they are not the same
Step-by-step explanation:
Mean is simply the average sum of data. When Standard deviation is obtained from the average of the square of data
what is the slope if all y's are 5 in a table of data
Answer: 0 slope; horizontal line
what’s the surface area? & B and c
Answer:
Surface area: 502 ft^2
B) Volume
C) Surface area
Step-by-step explanation:
Surface area Formula: 2(lw + wh + lh) = 2(13*15+15*2+13*2)= 502 ft^2
B) Volume because it's asking how much it can hold
C) Surface area because it's asking like how much paint should Cover the thing, not how much it can hold
How do you find the inverse of x and y intercepts?
When the original graph is mirrored around the line y = x, the inverse function's graph may be determined, the domain of the inverse, f-1(x), corresponds to the range of the original function (x), the x intercept of f-1(x) is the y intercept of f, and the range of the inverse f-1(x) is the domain of f(x) (x).
What is a intercept theorem?The intercept theorem, also referred to as Thales' theorem, the basic proportionality theorem, or the side splitter theorem, is a crucial concept in basic geometry that discusses the ratios of different line segments that are produced when two intersecting lines are intercepted by a pair of parallels.
It is equivalent to the ratios in similar triangles theorem. It is typically credited to the Greek mathematician Thales. Despite the fact that its first known demonstration may be found in Euclid's Elements, it was known to the ancient Babylonians and Egyptians.
Similarity and the intercept theorem go hand in hand. It is equivalent to the idea of similar triangles in that it may be used to demonstrate both the qualities of similar triangles and the intercept theorem.
Hence, When the original graph is mirrored around the line y = x, the inverse function's graph may be determined, the domain of the inverse, f-1(x), corresponds to the range of the original function (x), the x intercept of f-1(x) is the y intercept of f, and the range of the inverse f-1(x) is the domain of f(x) (x).
To learn more about intercept theorem refer to:
https://brainly.com/question/16370160
#SPJ4
now let's look at the data from all the buffalo. if we calculate the 60% confidence interval for every buffalo's count (i.e. data sample), how many cis do we expect to contain the true mean? store your answer in theoretical hits. then we need to check our theoretical answer with our actual data. calculate the 60% confidence interval for each buffalo's count. then commpute how many of those cis contain the true mean. assume that the true mean is 25,000 . store this value in sample hits. does this value match the theoretical value?
For a 60% confidence interval, the number of cis that we expect to contain the true mean is of 60% of the total amount.
What is the interpretation of a x% confidence interval?The interpretation of a x% confidence interval it is x% likely that the population parameter(mean/proportion/standard deviation) is between a and b, which are the bounds of the confidence interval.
The bounds a and b of the confidence interval are given by the estimate plus/minus the margin of error.
The interpretation also means that out of n samples, the percentage which are expected to contain the true mean is of x, hence the percentage for this problem is of 60%, as it is the confidence level.
Missing InformationThe problem is incomplete, hence only the first part could be answered.
More can be learned about confidence intervals at https://brainly.com/question/17073112
#SPJ1
Which outcome did the Battle of San Antonio de Béxar have?
A. Mexican troops forced the Texans to retreat.
B. Both sides withdrew from the town.
C. Texans captured San Antonio.
D. Mexican soldiers demolished the Alamo.
Answer:
b
Step-by-step explanation:
both sides withdrew
subtract ( – 8r–2)–( – 5r–9)
Answer:[tex]-3r+7[/tex]
Step-by-step explanation:
given the equation
[tex](-8r-2)-(-5r-9)[/tex]
Distribute the negative
[tex]-8r-2+5r+9[/tex]
Combine like terms
[tex](-8r+5r)+(-2+9)[/tex]
[tex](-3r)+(7)=[/tex]
[tex]-3r+7[/tex]
Hope this helps!
Help Please :> Its for my homework I don't understand it :p
Answer:
>
Step-by-step explanation:
81 is greater than 64
Winter Wonderland charges children $0.50 per ride down the sledding hill plus an entrance fee. Todd sled down the hill 16 times and paid $18 for his time at winter wonderland.
What is the equation in y=mx+b form?
The equation of the amount to be paid by anyone using the ride in slope intercept form is; y = 0.5x + 10
How to write an equation in slope intercept form?The general form of the equation of a Line in slope intercept form is;
y = mx + b
where;
m is slope
b is y-intercept
Now, we are told that;
Amount charge by Winter Wonderland per child = $0.50
We are told that there is a separate entrance fee.
Amount of times todd sled down the hill = 16 times
Amount paid by todd = $18
Thus, using the slope intercept form, we have;
18 = 0.5(16) + b
18 = 8 + b
b = 10
Thus, the equation of this amount to be paid in slope intercept form is;
y = 0.5x + 10
Read more about Slope Intercept form at; https://brainly.com/question/1884491
#SPJ1
In a survey, one out of three people named blue as their favorite color. Two out of seven named red. If 1,092 people were included in the survey, how many named neither blue nor red as their favorite color?
By using fraction, it can be calculated that 416 people choose neither blue nor red as their favorite color.
What is fraction?
Suppose there is a collection and a part of the collection has to be taken. The part which is taken is called fraction. In other words, part of a whole is called fraction.
The upper part of the fraction is the numerator and the lower part of the fraction is called denominator.
This is a word problem on fraction.
Fraction of people choose blue as their favorite color = [tex]\frac{1}{3}[/tex]
Fraction of people choose red as their favorite color = [tex]\frac{2}{7}[/tex]
Fraction of people choose neither red nor blue as their favorite color =
[tex]1- (\frac{1}{3}+\frac{2}{7})\\\\1 - (\frac{7 + 6}{21})\\\\1-\frac{13}{21}\\\\\frac{21-13}{21}\\\\\frac{8}{21}[/tex]
Total number of people surveyed = 1092
Number of people choose neither red nor blue as their favorite color =
[tex]\frac{8}{21}\times 1092[/tex]
= 416
To learn more about fraction, refer to the link-
https://brainly.com/question/17220365
#SPJ1
What is the standard deviation of 25?
Variance's square root is always the standard deviation. √25 thus equals 5.
Describe the term standard deviation?Both the standard deviation and the variance are indicators of how far data deviates from the mean. Because the results are all in data form or units, S.D. provides accurate results. Variance produces squared data findings, making it challenging to compare to actual data. Therefore, it makes sense to compare findings using S.D. rather than variance.Saying that the median is 7, the mode is 2, and the variance is squared does not make much sense.
However, it makes sense to state that the data's median, mode, and standard deviation are 7, 2, and 4, respectively.
Variance produces squared findings that make it impossible to compare to actual data without. You can only understand differences from getting S.D.Thus,
√25 = 5.
Variance's square root is always the standard deviation.
To know more about the standard deviation, here
https://brainly.com/question/12402189
#SPJ4
Mrs. Ortega paid $188 for some jeans and T-shirts. A pair of jeans cost $26, and a T-shirt was $16 cheaper than a pair of jeans. If Mr. Ortega bought 3 pairs of jeans, how many T-shirts did she buy?
Answer:
A pair jeans=26$
:. 3 pair jeans=78$
1 t-shirt=10$
No of t-shirt=188$-78$/10$=11