Answer:
a) the platform is 110 feet above the ground.
b) It takes 8.69 sec for the rock to hit the ground
Step-by-step explanation:
This situation is modelled by the following function: [tex]f(x) = -5x^2 + 40x + 30\\[/tex]
We need to answer the following questions.
a) How high above the ground is the platform?
First we find x using the formula: [tex]x=-\frac{b}{2a}[/tex]
we have b = 40 and a = -5
Putting values and finding x
[tex]x=-\frac{b}{2a}\\x=-\frac{40}{2(-5)}\\x=-\frac{40}{-10}\\x=4[/tex]
Now putting x=4 in the function to find how high above the ground is the platform
[tex]f(x) = -5x^2 + 40x + 30\\Put\:x=4\\f(4)=-5(4)^2+40(4)+30\\f(4)=-5(16)+160+30\\f(4)=-80+160+30\\f(4)=110[/tex]
So, the platform is 110 feet above the ground.
b) How long does it take for the rock to hit the ground? Show all work to receive full credit!
We will factorise the given function [tex]f(x) = -5x^2 + 40x + 30[/tex] to find the time taken to hit the ground.
We can solve the equation using quadratic formula: [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
We have a =-5, b=40, c=30
Putting values and finding x
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\x=\frac{-40\pm\sqrt{(40)^2-4(-5)(30)}}{2(-5)}\\x=\frac{-40\pm\sqrt{1600+600}}{-10}\\x=\frac{-40\pm\sqrt{2200}}{-10}\\x=\frac{-40\pm46.9}{-10}\\x=\frac{-40+46.9}{-10},x=\frac{-40-46.9}{-10} \\x=-0.69,x=8.69[/tex]
So, we get values of x: x = -0.69 and x=8.69
As time cannot be negative, so we take x=8.69
So, It takes 8.69 sec for the rock to hit the ground
I need hellpppp please help meee
Answer:
i believe >
Step-by-step explanation:
what is the last number to put in the following question i am confused ..
Answer:
2^6
Step-by-step explanation:
2^6=64
2x2x2x2x2x2=64
it's 2 to the power of 6
Hey, Whats The answer please explain your answer marking brainliest:D...............................
Answer:
B. Kevin is correct. Amy did not line up the decimals correctly.
Step-by-step explanation:
Answer: B
Step-by-step explanation:
B- kevin is correct because amy did not line up the decimals correctly
What is [tex]\frac{2}{5}[/tex] as a decimal
Answer:
0.4
Step-by-step explanation:
2 x 20=40
5 x 20=100
40/100= 0.40 simplified as 0.4
Answer:
2/5 as a decimal is 0.4
Step-by-step explanation:
2 divided by 5 would equal 0.4
How long is the carrot?
Answer:
4 3/4 inches
Step-by-step explanation:
Answer:
[tex]4\frac{3}{4}[/tex]
Step-by-step explanation:
13x + 9 equals 6x - 12
Answer: okay is that a question?
Step-by-step explanation:
Answer:
[tex]given \\ 13x + 9 = 6x - 12 \\ = > 13x - 6x = - 12 - 9 \\ = > 7x = - 21 \\ = > x = \frac{ - 21}{7} \\ = > x = - 3[/tex]
it may be helpful for youif any problem then consulting with mefactorise 7t-6u+5t-4u
Answer:
-2u(3+2) + t(7+5)
Tip: arranging the like terms next to each other helps to keep things from getting messy.
Find the angle of elevation
from point C to point A.
A
?
59°
402 m
C
B
Angle of elevation = [?]°
I have 17 warnings how am I not banned from the app yet?
You should ask a moderator
Solve Each Equation PLS SHOW WORK
|5k-8| / 10 = 2
|5k-8| / 10 is a fraction btw
Answer:
The maximum value of k = 5 ³/₅ and the minimum value of k = -2 ²/₅
Step-by-step explanation:
Given;
[tex]\frac{|5k-8|}{10} = 2\\\\|5k-8| = 20[/tex]
Simplifying further;
5k - 8 = 20 ------- (1)
5k - 8 = -20------(2)
Solving equation (1)
5k - 8 = 20
5k = 28
k = 28 /5 = 5 ³/₅
Solving equation (2)
5k - 8 = -20
5k = -20 + 8
5k = -12
k = -12 / 5 = -2 ²/₅
Thus, the maximum value of k = 5 ³/₅ and the minimum value of k = -2 ²/₅
please help first answer will be marked brainiest
Answer:
6x
Step-by-step explanation:
add sides up
**NEED THIS WITHIN 5 MINS** Stan’s employer pays for 45% of his annual health insurance premium of $4,567.00. Stan pays the remaining balance by having it deducted in equal amounts from his 26 paychecks throughout the calendar year. How much will Stan have deducted from each paycheck?
Answer:
$88.3
Step-by-step explanation:
Here 42% of annual health premium($5450)=*5450
=$2289
This amount is being paid by the company means it is deducted amount in one year.
One year has 26 paychecks so above amount divided by 26 is rebate amount in each paycheck.
Deducted amount=
=$88.30
3. State what additional information is required in order to know that the triangles are congruent by the SSS Triangle Congruence Postulate
The additional information required in order to know that the triangles are congruent by the SSS Triangle Congruence Postulate is that Line ML is equivalent to line YL. Option A
What is the SSS congruence postulate?The SSS congruence theorem states that If all the sides of one triangle are equivalent to the corresponding three sides of the second triangle, then, the two triangles are said to be congruent.
From the diagram given, we have;
Triangles NLMTriangle LNYFor the three sides of triangles NLM to be equivalent to that of LNY;
Line MN must be equal to line YL
Thus, the additional information required in order to know that the triangles are congruent by the SSS Triangle Congruence Postulate is that Line ML is equivalent to line YL. Option A
Learn more about SSS congruence theorem here:
https://brainly.com/question/27997251
#SPJ1
ASAP PLZ HELP ME WITH THE QUESTION
Answer:
(0, 0)
Step-by-step explanation:
None
Solve the system of equations using the substitution method.
y=2+56x
4x−3y=3
Enter your answer in the boxes.
(___,___)
Answer:
(6,7)
Step-by-step explanation:
took the test, was correct.
x= 6, y=7
solve for the first variable in one of the equations, then substitute the result into the other equations.
The value of x is 0.05 and y is 4.8 for given system of equations.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given system of equations are
y=2+56x...(1)
4x−3y=3...(2)
Substitute (1) in equation (2)
4x-3(2+56x)=3
4x-6+168x=3
172x-6=3
Add 6 on both sides
172x=9
Divide both sides by 172
x=9/172
x=0.05
Now plug in x value in equation 1
y=2+56(0.05)
=2+2.8
y=4.8
Hence, the value of x is 0.05 and y is 4.8 for given system of equations.
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ2
4. Paula drew a map of her neighborhood on a coordinate grid. A grocery store is located at point (5,-4). A park is located at point (-5,4). Paula's house is located halfway between the grocery store and the park. A school is located halfway between Paula's house and the park. What are the coordinates of the school?
Answer:
Midpoint Formula= (x1+x2)/2, (y1+y2)/2
Plug in the numbers
Answer= (0, 0)
I hope this helps you!!
Help pls! 10 points!
HELP ME FIND X ASWELL PLEASE USING THE SAME KITE
Answer:
a=18units
x=99°
y=108°
Step-by-step explanation:
Perimeter=sum of lengths around the kite.
Given that two sides each are congruent:
P=12+12+a+a
60=24+2a
60-24=2a
36=2a
a=36/2=18
x=99°
y+99+99+54=360°(sum of interior angles of a quadrilateral)
y+252=360
y=360-252
y=108°
Need help for this one!!
Which of the following is equivalent to 7(a + 4) + 15?
7a + 43
7a + 19
7a + 60
28a + 15
Answer:
7a + 43
Step-by-step explanation:
Let's simplify step-by-step.
7(a+4)+15
Distribute:
=(7)(a)+(7)(4)+15
=7a+28+15
Combine Like Terms:
=7a+28+15
=(7a)+(28+15)
=7a+43
Answer:
7a + 43
Step-by-step explanation:
Given:
7(a + 4) + 15
Solve:
Distribute:
7(a + 4) + 15
7 × a = 7a7 × 4 = 28Now we have:
7a + 28 + 15
Add the numbers:
28 + 15 = 437a + 43
Therefore, 7a + 43 is equivalent to 7(a + 4) + 15.
Kavinsky.
another trigonometry question
i just want this test to be over >-
Answer:
e) cos(90-x)
Step-by-step explanation:
sinx=cos(90-x)
ASAP PLS HELP ME with this
Answer:
160
Step-by-step explanation:
there are 3 rectangles in the irregular figure cut across them with your pen by drawing lines and indicate using dimensions.
1. 4 by 6 =24
2. 6 by 11 =66
3. 7 by 10= 70
add them altogether
=160
Jamal makes $186 a week at his job. He plans to save 5% of his paycheck for a P.Y.F account. How much money will Jamal put in his P.Y.F account this week.
Answer:
$9.30
Step-by-step explanation:
Answer:
Jamal will put $9.30 in his P.Y.F. account this week.
Step-by-step explanation:
Jamal makes $186 a week. He plans to save 5% of that in his P.Y.F. account.
%5 of $186 is $9.30 ($186/20).
This week, he will put $9.30 in his P.Y.F. account.
Hope this helps!
A pair of dice is tossed. what is the probability of getting sum of 5 or 9?
A)7/9
B)5/9
C)1/9
D)2/9
Answer:
[tex]Probability = \frac{2}{9}[/tex]
Step-by-step explanation:
Given:
A pair of dice
Required
Determine the probability of a sum of 5 or 9
Let the sample space of the first die be S1 and the second, S2
[tex]S_1 = {1,2,3,4,5,6}[/tex] --- 6 outcomes
[tex]S_2 = {1,2,3,4,5,6}[/tex] --- 6 outcomes
Number of sample space, n is:
[tex]n = 6 * 6[/tex]
[tex]n = 36[/tex]
Next, we list out all possibilities of obtaining a sum of 5
[tex]Sum\ of\ 5 = \{(1,4),(2,3),(3,2),(4,1)\}[/tex]
n(Sum5 )= 4
Next, we list out all possibilities of obtaining a sum of 9
[tex]Sum\ of\ 9 = \{(3,6),(4,5),(5,4),(6,3)\}[/tex]
n(Sum9)= 4
The required probability is then calculated as:
[tex]Probability = \frac{n(Sum9)}{Total} + \frac{n(Sum5)}{Total}[/tex]
[tex]Probability = \frac{4}{36} + \frac{4}{36}[/tex]
Take LCM
[tex]Probability = \frac{4+4}{36}[/tex]
[tex]Probability = \frac{8}{36}[/tex]
Simplify
[tex]Probability = \frac{2}{9}[/tex]
Identify the slope shown in the linear equation below. y = - 5x + 3
Answer:
Slope: -5 Y-intercept: 3
Step-by-step explanation:
the slope intercept of a linear equation is:
y=mx+b
were m is slope. and b is the y intercept
therfore the problem is:
y=-5x+3
m=-5 so the slope is -5
b=3 so the y-intrercept is 3
Answer:
-5
Step-by-step explanation:
The slope is always in front of the x
Can you please help me with 6
Answer:
Third choice, 3/4
Step-by-step explanation:
Add all the cubes together, 12 + 5 + 3 = 20
There's a 12/20, which is 3/5, chance you'll get a green cube
5/20, which is 1/4, chance you'll get a blue cube
And there's a 3/20 chance you'll get a yellow cube
The probability of not getting a blue cube is 12/20 + 3/20 = 15/20 = 3/4
Write y=−4x−4 in standard form .
Answer:
Y=-4x-4= [tex]x=- \frac{y+4}{4}[/tex]
Step-by-step explanation:
Answer: The answer is x=–y+4/4?
Step-by-step explanation:
the clock below shows what time mason mom drop him off for practice. what time does his mom drop him off
Answer:
4:05?
Step-by-step explanation:
Answer:
?
Step-by-step explanation:
This doesn't make sense.
what is the slope of the line described by the equation below y-6=-2(x-8)
Answer:
-2
Step-by-step explanation:
you have to rearange in the form of
y=mx+b, where m is the slope
y -6= -2( x-8)
y = 6 -2x + 16
y= -2x +22
slope is -2
Simplify the expression by combining like terms.
15 + 12z– 5z + 4y- 7
Answer: = 4y + 7z + 8
Answer:
7z+4y+8
Step-by-step explanation:
Collect the like terms so 12z-5z would be 7z, then since there is only 1 y term it would be 4y, and -7 + 15= 8