during a baseball game, a player's ball hit into the outfield is modeled by the equation h=-16t^2 + 65t. A bird flying across the field follows the path modeled by the equation h=8t+20. let t be the time since the ball is hit and h be the height. what do the intersection points of the equations represent?
Answer:
Intersection points are
(0.39,0) and (3.16,0)
Step-by-step explanation:
The equation of the outfield is [tex]h=-16t^2 + 65t[/tex]
The path equation is [tex]h=8t+20[/tex]
To find intersection of two equations , we make them equal and solve for t
[tex]-16t^2+65t= 8t+20[/tex]
Subtract 8t from both sides
[tex]-16t^2+57t=20[/tex]
Subtract 20 on both sides
[tex]-16t^2+57t-20=0[/tex]
Divide whole equation by -1
[tex]16t^2-57t+20=0[/tex]
Apply quadratic formula to solve for t
[tex]t=\frac{-b+-\sqrt{b^2-4ac}}{2a}[/tex]
a= 16, b=-57 and c=20
[tex]t=\frac{57+-\sqrt{(-57)^2-4(16)(20)}}{2(16)}[/tex]
[tex]t=\frac{57+-\sqrt{1969}}{32}[/tex]
[tex]t=\frac{57+\sqrt{1969}}{32}=3.16[/tex]
[tex]t=\frac{57-\sqrt{1969}}{32}=0.39[/tex]
write an equation to represent the relation. Then solve the equation. A number decreased by 30 is the same as 14 minus 3 times the number
x-30 =14-3x
subtract 1 x from each side
-30 =14-2x
subtract 14 from each side
-44 = 2x
x=-44/2 = -22
x=-22
check:-22-30 = -52
14-3(-22) = 14-66 =-52
both equations equal
X = -22
The modified expression, x3(2x + 5) – 4(2x + 5), has two terms with a common factor
part 2
Fred bakes 10 dozen cookies for the bake sale. He makes the following types of cookies:
. 1/2 chocolate chip
. 1/4 peanut butter
. 1/8 sugar cookies
. 1/8 oatmeal raisin cookies
4. How many of each type of cookie did Fred make? Show your work.
Chocolate chip_________
Peanut Butter _______
Sugar cookies ________
Oatmeal raisin_______
5. Unfortunately, Fred had some trouble in the kitchen and 3/5 of the peanut butter cookies were burned.
a. How many peanut butter cookies does Fred have left to sell? _____
b. Explain how you know this is correct.
600 is 10 times as much as
How do variables help you model real-world situations? Give an example
The ratio between the number of children (c) on a field trip and number of teachers (t) on the trips is (14)/(3). There are 70 children on the field trip. How many teachers are on the grip?
seven subtracted from 4 times a number (x) is more than 13
Bryce collected data about the amount of time each student in history class spends studying. if the range is 1, what does this reveal about the data?
answer both questions for brain
Answer:
19.SA of a cylinder = (2 * π * r²) + (2 * π * r * h)SA = (2 * π * 5²) + (2 * π * 5 * 20)SA = (2 * π * 25) + (2 * π * 5 * 20)SA = (2 * π * 25) + (2 * π * 5 * 20)SA = (157) + (628)SA = 785The answer is A. 785 square meters.20.SA of a rectangle = 2(wl + hl + hw)w = 15l = 4h = 14SA = 2(15*4 + 14*4 + 14*15)SA = 2(60 + 56 + 210)SA = 2(326)SA = 652The answer is B. 652 square centimeters.
Step-by-step explanation: I did the math and this is what I got.
Use long division to convert -45/8 to a decimal.
A. -5.625
B. -6.252
C. 5.625
D. 6.252
8;7 ratio is boys out of 195 campers
Lucy has to run two errands. She starts from home and travels 3 miles south to the post office. From the post office, she travels 4 miles east to the gas station. Then, from the gas station, she travels 5 miles to return home. The entire trip forms a triangle.
What was the smallest angle made in her trip?
It is at the gas station.
It is at Lucy’s home.
It is at the post office.
It depends on the direction Lucy is traveling.
Lucy starts from home and travels 3 miles south to the post office. From the post office, she travels 4 miles east to the gas station. As it is known south and east directions form right angle. Since the entire trip forms a triangle, this triangle is right with right angle at post office.
Call the vertices of this triangle P - post office, G - gas station, H - home. Then HP and PG are legs of this triangle and GH is hypotenuse.
From the given data:
HP=3;PG=4;GH=5;∠P=90°.The smallest angle is opposite to the smallest side. The smallest side is leg HP, so the smallest angle is G that is the angle at gas station.
Answer: correct choice is A.
In this exercise we have to mark the correct alternative corresponding to the location, so we have:
Letter A
The following information was then given by the statement:
Lucy starts from home and travels 3 miles south to the post officeFrom the post office, she travels 4 miles east to the gas station.Imagining the paths made by lucy as a triangle, we know that the longest path that corresponds to the hypotenuse will be from the gas station to her house, so:
HP=3;PG=4;GH=5;P=90°.We have:
[tex]180-90=90\\90/2=45\\45-15=30[/tex]
The smallest angle is at the gas station.
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What is the área of a circule with a radious of 3 meters use 3.14
what number is 26.8% of 67.5?
and
325% of what is 78.65?
what is the slope of (4,3.5),(-4,3.5)
For normally distributed data, what proportion of observations have z-scores satisfying the following conditions:
0.62 < z < 2.92
Identify all sets to which the number 3.1214122144 . . . belongs. Choose from irrational,rational,whole,and integer
What is P(0.6 ≤ z ≤ 2.12)?
The value of P(0.6 ≤ z ≤ 2.12) is, 26%
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
To Calculate the percent of a number , divide the number by whole number and multiply by 100.
Given that;
To find the value of P(0.6 ≤ z ≤ 2.12).
Now, We can simplify as;
P(0.6 ≤ z ≤ 2.12) = P( z ≤ 2.12) - P(z < 0.6)
So, From the Cumulative Standardized Normal Distribution table,
P( z ≤ 2.12) = 0.9830
P(z < 0.6) = 0.7257
Hence, We get;
P(0.6 ≤ z ≤ 2.12) = P( z ≤ 2.12) - P(z < 0.6)
P(0.6 ≤ z ≤ 2.12) = 0.9830 - 0.7257
P(0.6 ≤ z ≤ 2.12) = 0.2573
P(0.6 ≤ z ≤ 2.12) = 0.26
P(0.6 ≤ z ≤ 2.12) = 26%
Thus, The value of P(0.6 ≤ z ≤ 2.12) is, 26%
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A refrigerator contains 11 drinks 5 lemons drinks 3 apple drinks and 3 orange drinks. Abby is first in the line for drinks. Telly is second. What is the probability that Abby will get a lemon drink and Telly will get an orange drink.
Avery owns stocks in Ever Rise Corporation. The stock price increased by 120% over the past week. If the stock price was p last week, write two equivalent expressions that represent the current stock price and explain what their equivalence means. Substitute one or more variables into the expressions to prove them equivalent.
Answer:
Expression 1. P+1.2p
Expression 2. 2.2p
Step-by-step explanation:
These 2 equivalent expressions state that increasing a value by 120% is the same as multiplying the original value by 2.2.
Example: assume that p=50. The first expression gives p+1.2p=50+1.2(50) =110. The second expression gives 2.2p=2.2(50)=110
The two expressions 1.2p and p + 0.2p are equivalent, as they both represent the same relationship between the current stock price and the stock price last week.
What is the expression?
Expressions are defined as mathematical statements that have a minimum of two terms containing that variables or numbers.
If the stock price increased by 120% over the past week, then the current stock price is 120% of the stock price last week. This can be represented by the equation:
current price = 1.2p
Another way to represent the same relationship is to say that the current price is the stock price last week plus 120% of the stock price last week. This can be represented by the equation:
current price = p + 0.2p
To prove that these two expressions are equivalent, we can substitute a value for p into both equations and show that they give the same result. For example, if the stock price last week was $100, then:
current price = 1.2100 = $120
current price = 100 + 0.2100 = $120
Therefore, the two expressions are equivalent, as they both represent the same relationship between the current stock price and the stock price last week.
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How to round 4.253 to the nearest hundredths
A gardener uses a tray of 6 conical pots to plant seeds. Each conical pot has a radius of 3 centimeters and a depth of 8 centimeters. About how many cubic centimeters of soil are needed to plant the full tray? Round to the nearest cubic centimeter.
By definition, the volume of a cone is given by:
[tex] V = (\frac{1}{3}) * (\pi) * (r ^ 2) * (h)
[/tex]
Where,
r: radius of the circular base
h: height of the cone
Since we have 6 conical pots, then the total volume is:
[tex]Vt=6V[/tex]
[tex] Vt = 6 * (\frac{1}{3}) * (\pi) * (r ^ 2) * (h)
[/tex]
Substituting values we have:
[tex] Vt = 6 * (\frac{1}{3}) * (3.14) * (3 ^ 2) * (8)
Vt = 452.16 cm ^ 3
[/tex]
Rounding to the nearest cubic centimeter:
[tex] Vt = 452 cm ^ 3
[/tex]
Answer:
are needed 452 cm^3 of soil to plant the full tray
The cubic centimeters of soil are needed to plant the full tray is approximately 452cubic in
Volume of a coneThe formula for calculating the volume of a cone is expressed as:
V = 1/3πr²h
r is the radius = 3cm
h is the height = 8cm
Substitute
V = 1/3 * 3.14 * 3^2 * 8
V = 75.36 cubic cm
Since the gardener uses a tray of 6 conical pots to plant seeds, the total volume will be expressed as:
T = 6(75.36)
T = 452cubic in
Hence the cubic centimeters of soil are needed to plant the full tray is approximately 452cubic in
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What are the x-intercepts of the graph of the function f(x) = x2 + 5x − 36?
Answer:
x intercepts are (4,0) and (-9,0)
Step-by-step explanation:
The given function graphed f(x) = x² + 5x -36 and we have to find the x-intercepts.
Since x intercepts means points on x-axis which will have y-coordinates as zero.
so f(x) = x² + 5x - 36 = 0
x² + 9x - 4x - 36 = 0
x(x+9) - 4(x-9) = 0
(x-4)=0 ⇒ x = 4
or ( x+9) = 0 ⇒ x = (-9)
Therefore, x intercepts are (4,0) and (-9,0)
Considering the definition of function quadratic and roots, the roots or x-intercepts of the graph of the function f(x) = x² + 5x − 36 are 4 and -9.
Function quadraticThe function f(x) = ax² + bx + c
with a, b, c real numbers and a ≠ 0, is a function quadratic expressed in its polynomial form (It is so called because the function is expressed by a polynomial).
Definition of rootsThe roots are those values of x for which the expression is 0, so it graphically cuts the x-axis.
This can be solved by:
[tex]x1, x2=\frac{-b+-\sqrt{b^{2} -4ac} }{2a}[/tex]
x-intercepts of f(x) = x² + 5x − 36In this case you know that a=1, b= 5 and c= -36. So the roots can be determined as:
[tex]x1=\frac{-5+\sqrt{5^{2} -4x1x(-36)} }{2x1}[/tex]
[tex]x1=\frac{-5+\sqrt{25 +144} }{2}[/tex]
[tex]x1=\frac{-5+\sqrt{169} }{2}[/tex]
[tex]x1=\frac{-5+13}{2}[/tex]
[tex]x1=\frac{8}{2}[/tex]
x1= 4
and
[tex]x2=\frac{-5-\sqrt{5^{2} -4x1x(-36)} }{2x1}[/tex]
[tex]x2=\frac{-5-\sqrt{25 +144} }{2}[/tex]
[tex]x2=\frac{-5-\sqrt{169} }{2}[/tex]
[tex]x2=\frac{-5-13 }{2}[/tex]
[tex]x2=\frac{-18 }{2}[/tex]
x2= -9
Finally, the roots or x-intercepts of the graph of the function f(x) = x² + 5x − 36 are 4 and -9.
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Please I need help with number 9 !!!! For brainlest answer and thanks !!!!!
A survey showed that 30% of students bring their lunch to school. The survey polled 300 students. How many of the 300 students do Not bring their lunch to school?
3(n+11)-5n=-2(n-12)+9
The given equation simplifies to -2n + 33 = -2n + 33, where both sides are equal, hence 'n' can be any real number. Thus the equation has infinitely many solutions.
Explanation:This question pertains to solving a linear equation. The given equation is 3(n+11)-5n=-2(n-12)+9.
Let's solve this step by step:
First distribute 3 and -2 in the brackets (Order of Operations - BIDMAS/BODMAS). This will result in: 3n+33-5n = -2n + 24 + 9.Combine like terms on both sides of the equation to obtain: -2n + 33 = -2n + 33.Lastly you can see that both sides of the equation are equal, this means that n can be any real number.This indicates that we have infinitely many solutions because any value of 'n' satisfies this equation.
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What two-dimensional cross-sections could we create by slicing a sphere?
The ratio of trumpet players to tuba players at a high school is 5:2 Which statement is true?
A.2/5 of the total tuba and trumpet players are tuba players.
B.The number of trumpet players is 2.5 times the number of tuba players.
C.There are 2 trumpet players for every 5 tuba players.
D.If there are a total of 100 trumpet and tuba players, 52 of them are tuba players.
The ratio of trumpet players to tuba players at the high school is 5:2. There are 2 trumpet players for every 5 tuba players.
Explanation:The ratio of trumpet players to tuba players at a high school is 5:2. This means that for every 5 trumpet players, there are 2 tuba players. Therefore, option C is correct, which states that there are 2 trumpet players for every 5 tuba players.
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The hypotenuse of a right triangle is 37 mm. One leg of the right triangle is 12 mm. What is the length of the other leg?
Answer:
35 they are right
Step-by-step explanation: