Answer:
slope = - 2
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 2, 5) and (x₂, y₂ ) = (3, - 5)
m = [tex]\frac{-5-5}{3-(-2)}[/tex] = [tex]\frac{-10}{3+2}[/tex] = [tex]\frac{-10}{5}[/tex] = - 2
An object is launched from a platform. its height in meters X seconds after the launch is modeled by h(x)=-5x^2+20x+60 how many seconds after launch Will the object land on the ground
Answer:
6 seconds after launch.
Step-by-step explanation:
You should make sure there aren't odd symbols in your question when you post it.
Assuming it is just the equation -5x^2 + 20x + 60, if you graph it you can see the path of the ball. at x=0 this is the starting point It then hits the ground when it touches the x axis. So this is finding zeroes of a quadratic.
You could do this several ways; find a way to factor it, guess and check, the quadratic formula or completing the square. I will complete the square as that is what I am most used to. If you would like to see another let me know.
The first step in completing the square is making sure the x^2 has a coefficient of 1, so now it has -5 so we have to factor out -5 from the equation.
-5x^2+20x+60 = -5(x^2 - 4x - 12)
Now you only really need to focus on the factored expression, but I will continue writing everything. The next step is to find (b/2)^2 where b is the coefficient of the x term. In this case -4. so (b/2)^2 = (-4/2)^2 = 4.
Again, focusing on x^2 - 4x - 12 you want to add and subtract (b/2)^2 from that expression. since you are adding and subtracting you are not changing the value, but we can use this.
-5(x^2 - 4x - 12) = -5(x^2 - 4x - 12 + 4 - 4)
Here you want to rearrange it a bit. Originally c was the constant term, -12, now you want it to be the positive (b/2)^2, which is positive 4. also you can combine the two other constant terms. the original c and -(b/2)^2, but I will hold off for now so I don't do too much at once.
-5(x^2 - 4x - 12 + 4 - 4) = -5(x^2 - 4x + 4 - 12 - 4)
Now you focus on x^2 - 4x + 4. Hope fully you recognize this is the same as (x-2)^2. This always happens at this step of the process. also notice -2 = b/2. Using only variables here are the first steps.
ax^2 + bx + c
a(x^2 + (b/a)x + (c/a))
a(x^2 + (b/a)x + (c/a) + (b/(2a))^2 - (b/(2a)^2)
a(x^2 + (b/a)x + (b/(2a))^2 + (c/a) - (b/(2a))^2)
a((x + b/(2a))^2 + (c/a) - (b/(2a))^2)
Again, being able to make x^2 - 4x + 4 into (x-2)^2 or x^2 + (b/a)x + (b/(2a))^2 into (x + b/(2a))^2 willa lways happen. this is because if you expand (x + b/(2a))^2 you always get x^2 + (b/a)x + (b/(2a))^2.
Now I would combine the -12-4
-5(x^2 - 4x + 4 - 12 - 4) = -5((x - 2)^2 - 12 - 4) = -5((x - 2)^2 - 16)
If you redistribute the -5 you get vertex form, but I am going to stop here because I will just undo that in the next step. So this is the form you want. Finally we can find when it equals 0. So, you set this equal to 0 and use algebra to solve.
-5((x - 2)^2 - 16) = 0
Divide both sides by -5
(x-2)^2 - 16 = 0
add 16 to both sides
(x-2)^2 = 16
Take the square root of both sides, but also count botht he positive and negative version of the answer. the reason is both 2 and -2 squared get you 4.
x - 2 = +/-4
I am using +/- to indicate I am using both positive and negative 4. Now though add 2 to both sides. since you have +/- 4 you are going to get two different results. -4+2 and 4+2
x = -2 and 6.
now, the question wants times after x=0 (the start) so you only get 6. so x=6, or in other words 6 seconds after launch.
Let me know if you have any questions.
Answer:
6
Step-by-step explanation:
sorry no step by step explanation because I’m in a rush please mark me as brainliest bye have a great day !!! :D
If f(x) = \XI + 9 and g(x) = -6, which describes the range of (f + g)(x)?
O (f + g)(x) > 3 for all values of x
O (f + g)(x) < 3 for all values of x
O (f + g)(x) < 6 for all values of x
O (f + g)(x) > 6 for all values of x
Answer:
the first option
Step-by-step explanation:
well, 9 +(-6) = 3
so the equations last part is changed, but the rest stays the same
The range of (f + g)(x) is (f + g)(x) > 3 for all values of x.
What is a function?A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Gives are two function, f(x) = |XI + 9 and g(x) = -6, we need to find the range of (f + g)(x),
f(x)=|x|+9 and g(x)= -6
Taking the sum of the functions:
f(x) + g(x) = |x|+9 + (-6)
f(x) + g(x) = |x|+9 - 6
f(x) + g(x) = |x|+3
Due to the modulus of x which is positive,
Hence (f + g)(x) is greater to 3 for all values of x
Learn more about functions, click;
https://brainly.com/question/12431044
#SPJ7
ayuda porfavor es urgente
Can you please write a paragraph using this Key Terms: amphibians larvae salamanders emerge habitat dormant migrate escort
Answer:
DESCRIPTION: Large for a modern amphibian, the male California tiger salamander can reach up to 8.5 inches in length, the female up to seven. Adults have protruding eyes and long tails, and their slick bodies are mostly black with brilliant yellow spots and stripes on their back, sides, and tail. Larvae are greenish gray in color.
HABITAT: California tiger salamanders can be found in annual grasslands and oak woodlands with hot, dry summers and cool, rainy winters. For most of the year, they reside in underground burrows created and abandoned by small mammals. They need ephemeral pools for breeding.
RANGE: Historically these salamanders ranged throughout California's Sacramento and San Joaquin River valleys, the surrounding foothills, and the lower elevations of the state's central coast. Now their distribution is limited to disjunct vernal pool complexes in the northern part of their historical range. The northernmost and southernmost populations, residing in Sonoma and Santa Barbara counties respectively, are genetically distinct and geographically isolated from others.
MIGRATION: Once fall and winter rains begin, adult tiger salamanders emerge from underground hibernation habitat in mammal burrows and migrate to breeding ponds. After breeding, adults disperse back to uplands habitat to retreat underground. Adults may migrate long distances between summering and breeding sites: salamanders have been found along roads more than 1.2 miles from any known breeding ponds. Juvenile salamanders dispersing from ponds have been trapped more than 1,200 feet from their natal ponds.
BREEDING: Following early-winter rains, California tiger salamanders nocturnally emerge from their burrows and lay their eggs in newly formed vernal pools. After the eggs are fertilized internally, a female can lay up to 1,300, which she deposits individually or in small batches. Adults move back to their terrestrial burrows after breeding.
LIFE CYCLE: Within two weeks of egg fertilization, salamander larvae hatch, remaining in their natal pools for two to three months. By late spring or summer, once they reach metamorphosis, juveniles roam up to two miles away to hibernate in terrestrial habitat. Salamanders are thought to have lifespans of 10 years or more.
FEEDING: For the first six weeks of life, juveniles eat small crustaceans, algae, and mosquito larvae. Adult salamanders prey on aquatic insects, invertebrates, and tadpoles of Pacific tree frogs, California red-legged frogs, western toads, and spadefoot toads.
THREATS: The California tiger salamander is threatened by habitat destruction due to urban and agricultural development, habitat fragmentation, pesticides, hybridization with nonnative tiger salamanders, introduced diseases, and predation by nonnative species.
POPULATION TREND: Surveys showed that by 1993, the California tiger salamander had been extirpated from at least half of its historic localities. By 2004, only six tiger salamander meta-populations within 48 breeding ponds remained in Santa Barbara County, and by 2005, only seven viable tiger salamander breeding sites remained in Sonoma County.
Step-by-step explanation:
Divide (16m³-10m²+2m)÷2m
[tex]\huge\color{purple}\boxed{\colorbox{black}{♡Solution♡}}[/tex]
[tex]8 \: {m}^{2} - 5 \: m + 1[/tex] ✅
Step-by-step explanation:
[tex] \frac{(16 \: {m}^{3} - 10 \: {m}^{2} + \: 2m) }{2 \: m} \\ \\ = \frac {2 \: m \: (8 \: {m}^{2} - 5 \: m + 1)} {2 \: m} \\ \\ = 8 \: {m}^{2} - 5 \: m + 1[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{.}}}}}[/tex]
HELP i will give brainliest
all questions ;(
Answer:
1. The theoretical probability of rolling an even number and flipping heads is 25%.
2. The experimental probability of rolling a 1 and flipping tails is 15%.
3. The experimental probability of flipping heads is 40%.
4. I think around 7%.
5. I would expect to roll 3 and land on heads 8 times.
Step-by-step explanation:
I am not sure about number 4.
Have a nice day!
Ask me if you need my work. :-)
Write an equation to describe the relationship between x and y in the table shown:
Will give brainliest if correct!!
Answer:
The smallest increment is 10 V and the uncertainty is 5 V.
what are the coordinates of point V
Answer:
c is the and
no worries thank you to each of the Fourth of that mother you have any other questions please contact me
A line passes through the points (-2, 4) and (6, 16). Which of the following would not be
a correct equation of the line?
what is the total value of 6 in 24.63
Answer:
.60
Step-by-step explanation:
The values is 6 tenths
how do you determine the second deriviative of x^3-7x^2+36
Answer:
6x -14
Step-by-step explanation:
x^3-7x^2+36
Take the first derivative
3x^2 -14x
Now take the derivative again
6x -14
Answer:
6x - 14
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightCalculus
Derivatives
Derivative Notation
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Step-by-step explanation:
Step 1: Define
Identify
f(x) = x³ - 7x² + 36
Step 2: Differentiate
Basic Power Rule: f'(x) = 3x³⁻¹ - 2 · 7x²⁻¹ + 0Simplify: f'(x) = 3x² - 14xBasic Power Rule: f''(x) = 2 · 3x²⁻¹ - 1 · 14x¹⁻¹Simplify: f''(x) = 6x - 14Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Derivatives
Book: College Calculus 10e
Which statement is an example of the reflexive property of congruence? Help!
Answer:
In geometry, the reflexive property of congruence states that an angle, line segment, or shape is always congruent to itself. If ∠ A \angle A ∠A is an angle, then. \angle A \cong \angle A. ∠A≅∠A.
...
Reflexive property in proofs.
StatementsReasons3. a c = b c ac=bc ac=bc3. Substitution property of equality
En el autoservicio del barrio reciben al proveedor de gaseosas cada 8 dias,al de lacteos cada 3 dias y al de galletitas cada 12 dias . El 5 de abril fueron los 3. A¿Cuantos dias pasaran para qie se encuentren nuevamente?
Respuesta:
24 días
Explicación paso a paso:
Para calcular el día en que se volverán a reunir después del 5 de abril; tomamos el mínimo común múltiplo de la cantidad de días de cada visita:
Por lo tanto, tomamos el mínimo común múltiplo de 8, 3 y 12.
Múltiple de:
8: 8, 16, 24, 32, 40, 48
3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30
12:12, 24, 36, 48, 60
El mínimo común múltiplo es 24;
Todos se volverán a encontrar después de 24 días.
5 de abril + 24 días = 29 de abril
expand and simplify pla
Please help first real answer will get brainliest
Answer:
6
Step-by-step explanation:
a1(n-1) + D
d = 6
At age 25, you invest $1,500 that earns 8 percent each year. How much money will you have at age 65? $_____ (no comma) 32586.78 b. At age 40 you invest $1,500 that earns 11 percent per year. How much money will you have at age 65? $______ (no comma) 20378.20 In which case (a or b) would you have more money at age 65? Why?
Answer:
The Money Invested At age 25 earns more because it earns more Interest As compare to The Money Invested At age 40.
Step-by-step explanation:
According To the Question,
Given, A Person Invested $1,500 at Age of 25, With an 8% Per Annum Interest Rate.Thus, The Money He will have at age of 65 would be, [tex]$1,500 * (1.08)^{40}[/tex] = 32586.78$ . Here The Interest Earn in 40 Year Is 31086.78$.
And, the Same Person Invested $1,500 at Age of 40, With an 11% Per Annum Interest rate.Thus, The Money He will have at age of 65 would be, [tex]$1,500 * (1.11)^{25}[/tex] = $20378.20 . Here The Interest Earn in 25 Years Is 18878.20$.
⇒ Now, it is understood that the same amount invested for different periods of time & with a different interest rate, Since The Amount who get more Interest Would earn More. hence, The Money Invested At age 25 earns more because it earns more Interest As compare to The Money Invested At age 40.
What is f(5) for the function below?
f (x) = 6x – 10
Answer:
20
Step-by-step explanation:
f(5) = 6(5) - 10
= 30-10
=20
when x = 5, y = 20
Amit and Aman have a water tank of 44 litres. Amit uses 3/4 part of the water in water
tank and Aman yses 1/4 part of the water and out the quantity of water used by
both also find who is using much water than other and by how much. (3)
Answer:
i dont know
Step-by-step explanation:
Write the following as an inequality.
2 is less than w, and 7 is greater than or equal to w
Use w only once in your inequality.
Answer:
2 > w ≤ 7
Step-by-step explanation:
3/4 : 1/2 :: 27x : 14
Answer:
Step-by-step explanation:
Note: It is not mention what to find so than i am finding the value of x.
Given data:
3/4 : 1/2:: 27x: 14
Now,
[tex]x=\frac{1/2*27}{3/4*14} \\x=4.5[/tex]
Find the value of each variable
Answer:
Z = 65 Y = 115
Step-by-step explanation:
z+115 = 180
z=65
y + 65 +100+80= 360
y+245 = 360
y=115
Answer:
y = 115°
z = 65°
Step-by-step explanation:
*IMPORTANT* Straight line = 180° & Squares = 360°
1) 180° - 115° = 65°
z = 65°
2) 360° - 100° - 80° - 65° = 115°
Also, interior angles = exterior angles
If the pentagon below is to be reflected over the line y=x, what are the new coordinates of the vertices?
Answer:
K' (-2, -2)
L' (3, -2)
G' (4,0)
H' (3,2)
J' (-2, 2)
Step-by-step explanation:
list all the coordinates of the image, and apply the y=x rule of reflection. The line y=x states that the previous y is now in the x and vice versa.
K(-2, -2)
L(-2, 3)
G(0,4)
H(2,3)
J(2, -2)
–6(2 + a) = –48 please answer
Answer:
a = 6
Step-by-step explanation:
–6(2 + a) = –48
Divide each side by -6
–6(2 + a) / -6 = –48/-6
2+a = 8
Subtract 2 from each side
2+a-2 = 8-2
a = 6
7th grade Girl!
*urgent, pls pls pls help!* :(
(in the screenshot above. pleaseeeee! i’m desperate ahhhh :( )
A second-hand car costs $2400. The price falls by 25% when it is sold again. How much is it sold for?
Answer:
1,800$
Step-by-step explanation:
25% is 1/4th of the total amount. So...
Divide 2,400$ by 4 and get 600
Now, subtract 600 from 2,400.
Note:
Pls notify me if my answer is incorrect for the other users that will see this response. Thank you.
-kiniwih426
After studying the growing population of a certain species of fish, Dr. Goldthwait has determined that the population will grow
in such a way that the population each year will be 27 less than the square of the previous year's population. If he introduces
this species of fish to a new environment by placing a population of 15 fish, and the population grows according to his results
which of the following recursive formulas can be used to determine the number of fish that will be in the environment in the
future? Assume that the space for the population to grow is unlimited.
OA
NEXT = Now2 - 27 starting at 15
OB. NEXT = (NOW + 27) starting at 15
OC. NEXT = now? + 27 starting at 15
OD. NEXT =
(NOW - 27) starting at 15
Answer:
OB. NEXT
Step-by-step explanation:
Use the drop-down menus to complete the statements to match the information shown by the graph.
Find the length of AB pls and thank you
Answer:
x=4
AB=19
Step-by-step explanation:
in such a parallelogram the length of AD must be equal to the length of BC.
=>
18x = 17x + 4
x = 4
AB = 4x + 3 = 4×4 + 3 = 19
Maham has a number of apples. She could share my apples equally among 3, 4, or 5 people. What is the smallest number of apples Maham could have?
The value 60 is the LCM of 3, 4 and 5.
==================================================
Explanation:
LCM = lowest common multiple
To find the LCM, we list out the prime factorization of each number
3 = 3*14 = 2*25 = 5*1Ignoring the factors of 1, we have the unique primes of 2, 3, 5. There are 2 copies of '2', one copy of '3', and one copy of '5'. So we multiply this out to get 2*2*3*5 = 4*15 = 60
----------
If she had 60 apples, and wanted to give them to 3 friends, then each friend gets 60/3 = 20 apples
If instead, she had 4 friends, then each friend gets 60/4 = 15 apples.
Or if she had 5 friends, then each friend gets 60/5 = 12 apples.
For any of those three cases, there are no leftovers or remainders.
Any multiple of 60 will work (eg: 120 or 180), but 60 is the smallest such number that allows her to divide the apples this way without any leftovers.
Answer:
60
Step-by-step explanation:
60 / 3 = 15
60 / 4 = 20
60 / 5 = 12
They all divide evenly.