How do variables help you model real-world situations? Give an example of a model that uses variables and explain how it helps people make predictions.
You are given 4x-2y=12 and -4x-9=54. You are asked to find the order of the ladder. However, you did not specify which variable represents the ladder. I will just solve for both of the variables. I will be applying the substitution method.
Let 4x-2y=12 equals equation one and equation 2 for -4x-9=54.
4x-2y=12
4x=12+2y
x=3+1/2y
substitute this x to the equation 2
-4x-9y=54
-4(3+1/2y )-9y=54
Y=-6
X=3+1/2y = 3+1/2(-6) = 3+(-3) = 0
Barrie had stamps he gave 1/8 of them to tom if he gave 15 stamps to tom how many stamps did Barrie have at first
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]
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?
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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Which number sentences show how to solve the problem?
A pair of socks costs $5.00. A package of 3 pairs costs $12.00. How much would you save if you buy 2 packages instead of 6 individual pairs?
Choose all answers that are correct.
A.
6 × 5 = 30, 2 ×12 = 24, and 30 – 24 = 6
B.
12 – 5 = 7, 7 x 2 = 14, and 14 – 6 = 8
C.
12 ÷ 3 = 4, 5 – 4 = 1, and 1 × 6 = 6
D.
12 ÷ 3 = 4, 4 × 5 = 20, and 20 – 12 = 8
Answer:
a is the answer
Step-by-step explanation:
first you divded 12.00
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.
because the angles in a rectangle are 90 degrees it is not a parallelogram true or false? please explain why
seven subtracted from 4 times a number (x) is more than 13
what polynomial could you add to 3x^4 - 9x^3 + 5x^2 - x + 7 to get a sum of 3+4x^4 + 3x-x^3 + 3x^2
For normally distributed data, what proportion of observations have z-scores satisfying the following conditions:
0.62 < z < 2.92
The diameter of a beach ball is 10 inches. How many cubic inches of air can the beach ball hold? Use 3.14. Round to the nearest tenth of a cubic inch.
8;7 ratio is boys out of 195 campers
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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what is the product of any integer and -1
Please I need help with number 9 !!!! For brainlest answer and thanks !!!!!
which whole number is closest to √149
What two-dimensional cross-sections could we create by slicing a sphere?
convert 2.998m/s to km/h and to miles per hour
1 meter per second = 3.6 km per hour
2.998 x 3.6 = 10.7928 km per hour
1 KM per hour = 0.621371 mph
10.7928 x 0.621371 = 6.706
6.706 miles per hour
round answer as needed
what is the slope of (4,3.5),(-4,3.5)
A square patio has an area of 200 square feet how long is each side of the patio to the nearest 10th
a string was 4m long. she gave 1/4m of it to her sister and 3/4m to her friends. how much string had she given away?
Choose the correct simplification of (3xy6)2(y3)3
A.9x2y21
B.6x2y21
C.9x2y14
D.6x2y14
Answer: A. [tex]9x^2y^{21}[/tex]
Step-by-step explanation:
The given expression : [tex](3xy^6)^2(y^3)^3[/tex]
Using laws of exponents :
[tex]a^m*a^n=a^{m+n}\\\\(a^m)^n=a^{mn}[/tex]
To simplify the given expression :
[tex](3xy^6)^2(y^3)^3\\\\=(3)^2(x)^2(y^6)^2(y^{3\times3})\\\\=9x^2y^{12}\times y^9\\\\=9x^2y^{12+9}\\\\=9x^2y^{21}[/tex]
Therefore, [tex](3xy^6)^2(y^3)^3=9x^2y^{21}[/tex]
Which of the following is equivalent to the complex number
[tex]i ^{34}[/tex]
:
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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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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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
PLEASE HELP {It costs 5,700 every one sixth of an hour to build a hotel how many cents does building a hotel cost per second?}
Identify all sets to which the number 3.1214122144 . . . belongs. Choose from irrational,rational,whole,and integer
How do variables help you model real-world situations? Give an example