please help! the approximate path of a projectile launched from 100 m above the ground is given by f(×)= -5×^2+40+100, where f(×) represents the height × seconds after it is released into the air. use the info to answer the questions below. 1. what is the factored form of the equation? 2 how long will it take the projectile to reach the ground?
Answer:
Part 1) [tex]f(x)=-5(x-10)(x+2)[/tex]
Part 2) After 10 seconds.
Step-by-step explanation:
We have the function:
[tex]f(x)=-5x^2+40x+100[/tex]
Where f(x) represents the height x seconds after it is released into the air.
Part 1)
First, let's distribute a -5 out of the function:
[tex]f(x)=-5(x^2-8x-20)[/tex]
Now, let's factor. We want to pick two number that multiplies to -20 and adds to -8.
We can use -10 and 2. So:
[tex]f(x)=-5(x^2+2x-10x-20)[/tex]
Factor:
[tex]\begin{aligned}f(x)&=-5(x^2+2x-10x-20) \\ f(x)&=-5(x(x+2)-10(x+2)) \\ f(x)&=-5(x-10)(x+2) \end{aligned}[/tex]
Hence, our factored form is:
[tex]f(x)=-5(x-10)(x+2)[/tex]
Part 2)
We want to find after how many seconds does it take for the projectile to reach the ground.
If it reaches the ground, the height above the ground, f(x), will be 0.
So, we can set f(x) equal to 0 and solve for x. Instead of using the original equation, we can use the factored form. So:
[tex]0=-5(x-10)(x+2)[/tex]
Zero Product Property:
[tex]x-10=0\text{ or } x+2=0[/tex]
Solve for x:
[tex]x=10 \text{ or } x=-2[/tex]
Since x measures time, -2 does not make sense in this context.
Therefore, our solution is x=10.
So, after 10 seconds, the projectile will hit the ground.
Write the slope-intercept form of the equation of the line whose slope = -1 and y-intercept = 5.
Answer:
ask your mom for the answer
Step-by-step explanation:
thank me later
Answer: y= -1x+ 5
Step-by-step explanation:
Y = slope x + y- intercept
the difference of 7 and the reciprocal of y in a mathematical phrase
Answer:
kljnm
Step-by-step explanation:
ok
this and you get an A
The following is an example of the ____________
(a+b)+c=a+(b+c)
A.Commutative Property
B.Identity Property
C.Distributive Property
D.Associative Property
Answer:
D.Associative Property
Step-by-step explanation:
Answer:
D. Accociative Property
Step-by-step explanation:
You switched around the parenthesis!
What is 2.53 Times 57.62
Answer:
145.7786
simplified to 145.78
Step-by-step explanation:
Answer:
The answer is 145
how much time will it take for the plane to land?
Answer:
Again assuming we're cleared for immediate take off, it takes around 20 minutes to climb to cruise altitude, at an average ground speed of (say) 200 knots. This means we've covered about 70 miles, which the cruising aircraft would have covered in just over 10 minutes. So this final phase has cost us another 10 minutes
Find the slope of the line passing through the points (6, 1) and (6,-6).
Answer:
Slope = undefined
Step-by-step explanation:
Slope = (y2 - y1)/(x2 - x1)
(6, 1)
(6, -6)
1 - (-6)/6 - 6= 7/0
Slope = undefined
For reference:
0/x = 0
x/0 = undefined
Hope this helps!
La mitad de la edad que tenia anahí hace 27 años equivale a la cuarta parte de la edad que tendrá dentro de 5 años. ¿ qué edad tiene actualmente anahí?
Responder:
59 años
Explicación paso a paso:
Asumir que:
Edad actual = x
Edad 27 años atrás = x - 27
Edad dentro de 5 años = x + 5
La mitad de la edad de hace 27 años = 1/2 (x - 27)
Cuarto de edad dentro de cinco años = 1/4 (x +5)
0,5 (x - 27) = 0,25 (x + 5)
0.5x - 13.5 = 0.25x + 1.25
0.5x - 0.25x = 1.25 + 13.5
0,25 veces = 14,75
Dividir por 0,25
0,25x / 0,25 = 14,75 / 0,25
x = 59
Por lo tanto, la edad de Anahí ahora es de 59 años.
La edad actual de Anahí es de 59 años.
Sabemos por la pregunta que la mitad de la edad que tenía Anahí hace 27 años equivale a la cuarta parte de la edad que tendrá dentro de 5 años.
Para escribir esto como una ecuación, sea y la edad actual;
1/2(s - 27) = 1/4(y + 5)
El MCM de 2 y 4 es 4 por lo tanto;
4/2(y - 27) = 4/4(y + 5)
2(s - 27) =(y + 5)
2y - 54 = y + 5
2y -y = 5 + 54
y = 59
La edad actual de Anahí es de 59 años.
Más información sobre ecuaciones: https://brainly.com/question/2263981
What is the distance between the points (2, 3) and (5, -4)?
Answer:
7.6158
Step-by-step explanation:
HELP PLEASEE
Erica went to the amusement park and purchased tickets. She bought ferris wheel tickets and roller coaster
tickets. She bought a total of 12 tickets for $36.50. The ferris wheel tickets cost $2.75 each and the roller
coaster tickets cost $3.25 each. Find the number of ferris wheel tickets and roller coaster tickets that Erica
bought.
HELPPP PLEASE
Answer:
42.5
Step-by-step explanation:
will give BRAINLIEST
Find the area of each circle
. Round to the nearest tenth.
Answer:
13: 312yd squared
14: 907.5 rounded up but not rounded is 907.46
Step-by-step explanation:
this is because the formula is pi*r^2 so you'd
Step by step:
1. 20yd/2= 10 to get the radius for 13
2. substitute r in the formula pi*r^2 for 10 making it pi*10^2
3. multiply 10 by itself, 10*10=100
4. multiply pi by 100, 3.14*100= 314
314yd^2 is the answer for 13
14:
1. 34ft/2=17 to get the radius for 14
2. substitute r on the formula pi*r^2 for 17 making it pi*17^2
3. multiply 17 by itself, 17*17=289
4. multiply pi by 289, 3.14*289=907.46
5. round 907.46 to the nearest tenth, 907.5
907.5ft^2 is your answer
hope this helps :)
NEED HELP ASAP. WILL GIVE BRAINLIEST
Which statement describes the equivalent vectors?
The magnitudes are 10, and the direction angles are about 18º
The magnitudes are 10, and the direction angles are about 162°
The magnitudes are 100, and the direction angles are about 18°
The magnitudes are 100, and the direction angles are about 162º.
Answer:
A) The magnitudes are 10, and the direction angles are about 18º
Step-by-step explanation:
got it right on edge :)
The statement describes the equivalent vector is A) The magnitudes are 10, and the direction angles are about 18º.
How to find the cross product of two vectors?Suppose that two vectors in consideration are u and v, then their cross product is evaluated as:
[tex]u \times v = |u|.|v|.sin(\theta)\hat{n}[/tex]
where
the normal unit vector whose direction is decided by right hand thumb rule, and theta is the angle between u and v vector.
The two bars around a vector represents the magnitude of that vector.
Cross product returns the result as a vector itself.
From the given graph we can conclude that the magnitudes are 10, and the direction angles are about 18º.
The statement describes the equivalent vector is A) The magnitudes are 10, and the direction angles are about 18º.
Learn more about vectors here;
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(6th grade math)
adrian has 50$ she spent 12.45 at the movies and 10.19 at the bowling alley. how much money does she have left?
Answer:
$27.36
Step-by-step explanation:
To find how much she spent you add the costs of the movie and bowling alley: 22.64
Now you subtract that from the amount of money you had to get: 27.36
Hope this helps!
Answer:
Adrian has $27.36 left.
Step-by-step explanation:
First add up the total Adrian spent!
12.45 + 10.19 = 22.64
Now subtract that amount from $50
50.00 - 22.64 = 27.36
Therefore, Adrian has $27.36 left
Determine the seating capacity of an auditorium with 30 rows of seats if there are 20 seats in the first row, 24 seats in the second row, 28 seats in the third row, and so on
Answer:
The seating capacity of the auditorium is 2,340.
Step-by-step explanation:
This question relates to an Arithmetic Progression (AP).
An Arithmetic Progression (AP) is a sequence of numbers in which the differences of every two consecutive numbers or terms are constant or the same.
Therefore, the seating capacity can be calculated using the an arithmetic progression (AP) formula as follows:
Seating capacity = (n / 2) * (2a_1 + (n - 1)d) ...................... (1)
Where;
n = number of rows = 30
a_1 = Number seats in the first row = 20
d = Common difference = 24 - 20 = 28 - 24 = 4
Substituting the values into equation (1), we have:
Seating capacity = (30 / 2) * ((2 * 20) + ((30 - 1) * 4))
Seating capacity = 15 * (40 + (29 * 4))
Seating capacity = 15 * (40 + 116)
Seating capacity = 15 * 156
Seating capacity = 2,340
Therefore, the seating capacity of the auditorium is 2,340.
3(x + 3) – 2 < 4 or 1 – x ≤ –1
Answer:
eu singer nuştiu
terog scuză
work out the inverse function
y=x-2
Answer:
x + 2
Step-by-step explanation:
Replace the x with y.
Making is x = y -2
Solve for x=y-2
and you get x+2
Answer:
x+2
Step-by-step explanation:
When doing inverse functions, you switch the x and y.
x = y-2
Then you solve for y (add the 2 to the other side to get "y" by itself)
y = x+2
A line passes through (0, 2) and has a slope of 13 .
What is the equation of the line in slope-intercept form?
y=13x+2
y=13x−2
y=−13x+2
I don't know.
Answer:
y=1/3x+2
Step-by-step explanation:
Assuming that all of the '13' 's are suppost to be 1/3, it is y=1/3x+2
The equation of the line in slope intercept form is
[tex]y= \frac{1}{3} x+2[/tex]
Given :
A line passes through (0, 2) and has a slope of 1/3
The equation of a line in slope intercept form is y=mx+b
where m is the slope and b is the y intercept
From the given information , we know that slope [tex]m=\frac{1}{3}[/tex]
The line passes through (0,2) that is our y intercept b
b= 2
Replace slope [tex]m= \frac{1}{3}[/tex] and b=2 in slope intercept form y=mx+b
[tex]y= \frac{1}{3} x+2[/tex]
The equation of the line in slope intercept form is
[tex]y= \frac{1}{3} x+2[/tex]
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Neil bought 4 baseballs for a total of $15.25. If the baseball were the same cost, about how much did each baseball cost?
$3.00
$64.00
$4.00
$3.81
Answer: your answer is $74.81 and you are welcome
Step-by-step explanation:
$3.00 +$64.00 + $4.00 +$3.81 = $74.81
Para la reforestación de un terreno por parcela se compraron 150 arboles de cedro y 210 arboles de guayacán para sembrarlos de tal forma que en cada parcela quede la misma cantidad de arboles de cada tipo ¿Cuál es el mayor numero de parcelas? ¿Cuántos arboles de cedro y cuantos arboles de guayaca se sembrar en cada parcela?
Answer:
a) 30 parcelas
b) Para árboles de cedro: 5 por parcela
Para árboles de Guayacán: 7 por parcela
Step-by-step explanation:
a) ¿Cuál es el mayor número de parcelas?
De la pregunta tenemos:
150 árboles de cedro y 210 árboles de guayacán
Para encontrar la mayor cantidad de parcelas, resolvemos usando los métodos del mayor factor común.
Encontramos los factores de 150 y 210
Los factores de 150 son: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150
Los factores de 210 son: 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210
Entonces el máximo común divisor es 30.
Por lo tanto, la mayor cantidad de parcelas que podemos tener es de 30 parcelas.
b) ¿Cuántos árboles de cedro y de guayacán plantar en cada parcela?
Para cedros
Tenemos 150 árboles de cedro
Por lo tanto, la cantidad de árboles de cedro por parcela = 150 ÷ 30 = 5 árboles de cedro por lote
Para los árboles de Guayacán
Tenemos 210 árboles de Guayacán
Por lo tanto, el número de árboles de Guayacán por parcela = 210 ÷ 30 = 7 árboles de Guayacán por lote
hi can someone help me with this
Answer:
=−12y+11.7 I believe it's that but I am not completely sure
I believe it is
What is the value of x
Answer:
x=39
Step-by-step explanation:
First I try to find the angle measurements for the rest of the angles inside the triangle. I saw that the 68 degrees and I notice that it was vertical angles, meaning that the inside is also 68. I then notice that the 107 and the other unknown angle besides x must be 180 when adding up, so I can do 180-107=73. Now I know that that angle is 73 degrees I can find x by solving this equation 180=73+68+x, which the answer comes out to be 39. so x=39.
Hope this helps you
The equations of four lines are given. Identify which lines are parallel.
Line 1: y= 2 - 6
Line 2: 3 - 2y = -1
Line 3: y = 4x + 6
Line 4: y+3= 1 (2-6)
Answer:
lines 1 and 4
Step-by-step explanation:
they are both horizontal lines because when solved equal a number without an x so they is no slope so they are horizontal and have the same slope which means they are parallel to each other
What is the first step of the following division problem?
Answer:
There is no picture
Step-by-step explanation:
But... if i were to answer to any problem first thing u do is set it up with the numbers when doing long division
Customers of a certain credit card earn points for using the card. The table below shows the number of points earned for the amount spent. ( Photo Attached )
Predicted number of points for spending $10 :
___
Will give Brainliest (:
Answer:
Just hit continue.
Step-by-step explanation:
The predicted amount is for the second button only.
Each dollar spent does not always earn the same number of points.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Customers of a certain credit card earn points for using the card.
The table shows the number of points earned for the amount spent.
Now, By the given table which shows the number of points earned for the amount spent.
⇒ Number of points in 4 dollars = 36
Hence, Number of points in 1 dollars = 36/4 = 9
⇒ Number of points in 7 dollars = 56
Hence, Number of points in 1 dollars = 56/7 = 8
⇒ Number of points in 9 dollars = 72
Hence, Number of points in 1 dollars = 72/9 = 8
Thus, We get;
⇒ Each dollar spent does not always earn the same number of points.
Learn more about the mathematical expression visit:
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A student builds a model of her bathroom. The scale is 1:25. In the scale model, the students bed is 3 inches long.
HOW LONG IS THE STUDENTS ACTUAL BED?
PLS HELP ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
75
Step-by-step explanation:
The answer is 75 because you have to cross mutiply:
1 3
25 x
3 x 25 is 75
What is the solution to the system of equations?
y= 1/3x-10
2x + y = 4
34756Step-by-step explanation:
please help this is due tomorrow!! (SQUARE ROOTS)
Ill give brainliest!! find the value
√b^6
3√-x^6
3√-y^9
What is the answer to this question?
will get awarded with brainliest!
(6x-7)(2x+5)
Write the equation of a line in slope intercept form that has a slope of -3 and passes through the point (0,7)
Write an algebraic expression that models the following statement:
Four times the sum of 'x' and '7'.
Answer:
4(x+7)
or 4x+28
Step-by-step explanation:
Here you go:)