Answer:
Step-by-step explanation:
h = - 16t ^ 2 + 50t + 4
maximum height take the first derivative of h (calculus if you are taking it)
h' = -32t + 50 set this equal to zero
0 = -32t +50
t = 50/32
t = 1.5625 now plug t = 1.5625 into the height equation
h = - 16(1.5625) ^ 2 + 50(1.5623) + 4
h = 43.0625 ft
you can also find the maximum height by graphing the function and locating the peak value (much easier)
how long to reach the ground h = zero
0 = - 16(t) ^ 2 + 50(t) + 4
use the quadratic equation to solve this or graph the function h(t) and find the roots (much easier) and you will find that
t = -0.078 and 3.203 seconds
obviously the negative root makes no sense unless he time travelled so
t = 3.203 seconds
The weights of 11 swimmers in the team were recorded by the coach and the average
weight was 86 pounds. Three swimmers whose weights were 88 pounds, 79 pounds,
and 83 pounds left the team. What was the new average?
Answer:
87
Step-by-step explanation:
87 x 11= 946
946-88-79-83=696
696/8 = 87
3b.) Nora is buying a used car valued at $22,730. It is expected to
depreciate an average of 9.5% each year. Predict the value of Nora's car in
6 years.
Help ??
Answer:
$12487.86
Step-by-step explanation:
Given data
Cost of car= $22,730
Rate of decrease= 9.5%
Time= 6 years
We can predict the value by using the exponential decay function'
A= P(1-r)^t
substitute
A= 22730(1-0.095)^6
A= 22730(0.905)^6
A= 22730*0.5494
A=$12487.86
Hence the value will be $12487.86
Find the value of x in the isosceles triangle below.
need this ASAP! Please include an explanation if possible
Answer:
x = 64
Step-by-step explanation:
Remark
The markings on the triangle tell us that the sides are equal. There is no marking on the third side, so it is not equal to the other two. The important fact is the angles opposite equal sides are also equal. That means that the angle on the lower right is equal to x.
Equation
So you have two angles = to x.
x + x + 52 = 180 All triangles have interior angles of 180
2x + 52 = 180 Combine the like terms on the left.
- 52 -52 Subtract 52 from both sides
2x = 128 Divide by 2
2x/2 = 128/2
x = 64
Which statements are true about the graph of y s 3x + 1 and y 2 -x + 2? Check all that apply.
O The slope of one boundary line is 2.
O Both boundary lines are solid.
A solution to the system is (1, 3).
O Both inequalities are shaded below the boundary lines
O The boundary lines intersect.
===========================================================
Explanation:
Let's go through each of the answer choices to see which are true and which are false.
----------------
Choice A
The general slope intercept form is y = mx+b
m = slope and b = y intercept.
For y = 3x+1, the boundary line of the first inequality, the slope is 3.
For y = -x+2, the slope is -1.
None of the slopes are 2.
Choice A is false.
We'll use the concept of slope again in choice E.
----------------
Choice B
The "or equal to" part of the inequality sign is what directly determines the boundary line being solid. This is because we include points on the boundary.
Choice B is true.
----------------
Choice C
Plug x = 1 and y = 3 into the first inequality
[tex]y \le 3x+1\\\\3 \le 3(1)+1\\\\3 \le 3+1\\\\3 \le 4\\\\[/tex]
The last inequality is true, so the first inequality is true when (x,y) = (1,3). This makes (1,3) a solution to [tex]y \le 3x+1\\\\[/tex]
Repeat those steps for the other inequality given to us
[tex]y \ge -x+2\\\\3 \ge -1+2\\\\3 \ge 1\\\\[/tex]
which is also true, so that makes (1,3) also a solution to [tex]y \ge -x+2\\\\[/tex]
The point (1,3) is a solution to both inequalities at the same time, making it a solution to the system overall.
Choice C is true
----------------
Choice D
When y is fully isolated, the "less than" inequality indicates the shading is below the boundary. This is due to us considering points of y coordinates smaller than the boundary line. So we'll shade below the boundary for [tex]y \le 3x+1\\\\[/tex]
We don't do the same for [tex]y \ge -x+2\\\\[/tex]. Instead, we'll shade above the solid boundary line.
Choice D is false.
----------------
Choice E
If two lines have equal slopes, but different y intercepts, then we have parallel lines. Parallel lines never intersect.
If on the other hand, the slopes are different values, then the two lines will intersect somewhere on the xy grid. There will only be exactly one point of intersection.
The given system has boundary lines of slopes 3 and -1, for the first and second inequality respectively. Refer back to choice A. These differing slopes tell us that the boundary lines intersect somewhere.
Choice E is true
Let's go through all the options one at a time and look for the correct ones
Option 1: The slope of one boundary line is 2
We have 2 equations of lines, where the coefficients of are 3 and -1 respectively
because the coefficient of x denotes the slope of a line, we know that the lines have the slope 3 and -1, not 2
Hence, this option is Incorrect
Option 2: Both boundary lines are solid
In order for the boundary lines to be solid, the inequality must have an 'equal to', like ≤ (less than or equal to) or ≥ (greater than or equal to)
we can see that that's the case in our case and hence, this option is Correct
Option 3: A solution to the system is (1, 3)
To confirm this, we'll plug these coordinates into the given inequalities and see if it stands correct
y ≤ 3x + 1
3 ≤ 3(1) + 1
3 ≤ 4 which is correct because 3 is less than 4
Second equation:
y ≥ 2 - x
3 ≥ 2 - 1
3 ≥ 1
Which is also true because 3 is greater than 1
Now, we can say that (1 , 3) is a solution to the system because it satisfies both the equations and is Correct
Option 4: Both inequalities are shaded below the boundary lines
For an inequality to be shaded below the boundary line, it must have the ≤ inequality (in case of solid line) and < inequality (in case of dotted line)
because the second inequality listed includes the ≥ inequality, which was not mentioned above, it won't be shaded below
another way to think about it is that any 'greater than' inequality will shade everything above the line and the 'lesser than' inequality will shade below the line
which means that this option is Incorrect
Option 5: The boundary lines intersect
In order for the boundary lines to intersect, they must have have different slopes.
as we mentioned in the explanation of the first option, that the slopes of the lines is 3 and -1, which are different slopes
Therefore, this option is Correct
x^2=-28 square root method
Answer:
2i[tex]\sqrt{7}[/tex],-2i[tex]\sqrt{7}[/tex]
X-y=6, x+y=8, zx+zy=20
Answer:
Step-by-step explanation:
x = 6 + y
6 + y + y = 8
y = 1
x - 1 =6
x = 7
zx + zy = z(x + y) = 20
z = 2.5
Answer:
X = 7
Y = 1
Z = 2/5
Step-by-step explanation:
7-1 = 6
7+1 = 8
2/5 × 7 + 2/5 = 20
A line that passes through points (x, 4) and (6, -1) has a slope of 5/6. What value of x will yield the given slope?
A: x = -12
B: x = 0
C: x = -6
D: x = 12
The spinner has 8 congruent sections. What is the probability of
spinning a number divisible by 3 two times in a row?
Answer:
1/16 or 0.0625
Step-by-step explanation:
There are two numbers on the chart that are divisible by 3.
So the odds of spinning and getting one of those on the first try would be 2/8 or 1/4.
The odds are then multiplied by the chance of spinning it again on the second try, which would still be 1/4.
To get: 1/16
you have it $15 for the movie the cost of a movie ticket is $3 write an inequality to show how much money you can spend on treats.
Answer:
$3+x is less than or equal to $15
Step-by-step explanation:
I can't write the sign but it's < with a line under it
Step-by-step explanation:
y≥15-3
I am not sure
If Rashid faces north and then turns clockwise half a turn, in which direction does he face
Answer:naneeeeee
Step-by-step explanation:
if the radius of an argon atom is 0.0000000000098m, write in scientific notation
Answer:
90
Step-by-step explanation:
What is the value of n in the equation shown below?
2² x 21 = (24)3
Answer:
4
Step-by-step explanation:
i hope this helped :]
3 9 26
a. Use eoch digit once, make the smallest 4-digit number:
b. Use each digit once, moke the largest 4-digit number :
c. You can use one diga twice, make the smallest 4-digit number:
c. You con use one digit twice make the largest 4-digit number
.
I’m confused can somebody answer this?
14 is the asnwer because sqaure root of 200 is 14.14213562 and if you round that it is 14
In square units!!! Real answers only please no links!!!!
Lin drew this set of axes and plotted the points A=(1,2), B=(-3, -5), C=(5,7), D=(-4, -3), and E=(-4, 6) on them. Identify her mistakes! Which points were plotted incorrectly?
Answer:
B=(-3, -5)
Step-by-step explanation:
What is the equivalent radian measure for the angle 53?
9514 1404 393
Answer:
D (53π)/180
Step-by-step explanation:
There are π/180 radians in 1 degree, so in 53°, there are ...
53(π/180) radians = (53π)/180 radians
A cylindrical can is to be constructed for 80 cents. The cost of the material used for the top and the bottom is 3 cents per square inch, and the cost of the material used for the curved side is 2 cents per square inch. Express the volume of the can as a function of its radius. (Recall the volume of a cylinder is V
Answer:
V = r(40 - 3πr²)/2
Step-by-step explanation:
We know the area of a cylinder, A = 2πr² + 2πrh where r = radius and h = height.
Now, 2πr² = area of top and bottom and 2πrh = curved surface area
Since the cost of material for the top and bottom is 3 cents per square inch, the total cost of the materials for top and bottom = cost of material × area = 3 × 2πr² = 6πr²
Also, the cost of material for the curved is 2 cents per square inch, the total cost of the materials for the curved side = cost of material × area = 2 × 2πrh = 4πrh
The total cost of material = 6πr² + 4πrh
Since the total cost of material = 80 cents,
6πr² + 4πrh = 80
3πr² + 2πrh = 40 (1)
Now, the volume of a cylinder, V = πr²h
From (1), making h subject of the formula, we have
3πr² + 2πrh = 40
2πrh = 40 - 3πr²
h = (40 - 3πr²)/2πr
Substituting h into V, we have
V = πr²h
V = πr² (40 - 3πr²)/2πr
V = r(40 - 3πr²)/2
if there 10 students and 2/5 play soccer how many students play soccer?
Answer:
4
Step-by-step explanation:
2 out of 5 play so if there is 10 students 10*2/5 = 4 students
Answer:
4 students would play soccer
Step-by-step explanation:
To make the total students 10 instead of 5 we multiply the information by 2. 2/5 times 2 equals 4/10. So 4 out of 10 studento play soccer
Which of the following could be the equation of the function below?
y=0.5cos(2(x-pi/2))+2 y=0.5cos(4(x+pi/2))-2 y=0.5cos(4(x+pi))+2 y=0.5cos(2(x-pi))-2
Answer:
D y=0.5cos(2(x-pi))-2
Step-by-step explanation:
The Equation of the function is y=0.5 cos (4(x+π/2))-2
The correct option is B.
As, y=a cos (b(x+c))+d
Here, y max=-1.5 and y min=-2.5
So, d=(max + min)/2
d=(-1.5+(-2.5))/2
d=(-1.5-2.5)/2
d=(-4.0)/2
d=-2.0
and, the horizontal axis is
y=-2
Then, y= a cos(b(x+c))+(-2)
y=a cos (b(x+c))-2
The amplitude (a) is
a = max-d = d- min
a=-1.5-(-2)=-2-(-2.5)
a=-1.5+2=-2+2.5
a=0.5.
We have the period is π/2
P=2π/b
π/2=2π/b
πb=4π
b=4
Now, y=0.5 cos (4(x+c))-2
Thus, the required function is y=0.5 cos (4(x+π/2))-2.
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In parallelogram LMNO, the measure of N= 98° and the measure of 0= 82°. Find the measure of M.
Answer:
82
Step-by-step explanation:
180 - 98=82
The sum of two angels is 180
Lightbulbs of a certain type are advertised as having an average lifetime of 750 hours. The price of these bulbs is very favorable, so a potential customer has decided to go ahead with a purchase arrangement unless it can be conclusively demonstrated that the true average lifetime is smaller than what is advertised. A random sample of 50 bulbs was selected, the lifetime of each bulb determined, and the appropriate hypotheses were tested using Minitab, resulting in the accompanying output.
Variable N Mean St Dev SEMean Z P -Value
lifetime 50 738.44 38.20 5.40 -2.14 0.016
What conclusion would be appropriate for a significance level of .05? A significance level of .01? What significance level and conclusion would you recommend?
Simplify the expression using order of operation (11 - 8)^3 - 2 x 6
Answer:
500
Step-by-step explanation:
(11-3)^3-2x6
first evaluate 11-3-->8
then cube it-->8^3=512
then multiply 2x6-->12
then subtract the two-->512-12=500
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\huge\textsf{Just do PEMDAS}[/tex]
[tex]\huge\textsf{Parentheses}[/tex]
[tex]\huge\textsf{Exponents}[/tex]
[tex]\huge\textsf{Multiplication}[/tex]
[tex]\huge\textsf{Division}[/tex]
[tex]\huge\textsf{Addition}[/tex]
[tex]\huge\textsf{Subtraction}[/tex]
[tex]\mathsf{(11 - 8)^3 - 2\times 6}[/tex]
[tex]\mathsf{11 - 8 = \boxed{\bf 3}}[/tex]
[tex]\mathsf{3^3 - 2 \times 6}[/tex]
[tex]\mathsf{3^3 = 3\times 3\times 3 = 9\times 3 = \boxed{\bf 27}}[/tex]
[tex]\mathsf{27 - 2 \times6 }[/tex]
[tex]\mathsf{2\times 6 = \boxed{\bf 12}}[/tex]
[tex]\mathsf{27 - 12}[/tex]
[tex]\boxed{\mathsf{\bf= 15}}[/tex]
[tex]\boxed{\boxed{\huge\textsf{Answer: \bf 15}}}\huge\checkmark[/tex]
[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Help with Math Question 1
Answer:
Step-by-step explanation:
X is also 67° Like the interior angle
PLEASE HELP!!!!1!1!1! suppose one particular pyramid in egypt has a square base of side length 280 meters and a perpendicular height of 144 meters what is the surgace area of the pyramid?
Answer:
Pyramid Surface Area = .5 * Perim of Base * Slant Height
Slant Height^2 = 144^2 + 140^2
Slant Height^2 = 20,736 + 19,600
Slant Height^2 = 40,336
Slant Height = 200.8382433701
Surface Area = .5 * perim of base * slant height
Surface Area = .5 * 1,200 * 200.8382433701
Surface Area = 120,503 square meters
Source = www.1728.org/volpyrmd.com
Step-by-step explanation:
don’t mind the pencil writing
Answer:
Length = 22 cm
Width = 4 cm
Step-by-step explanation:
Area = 88 cm²
Length = x + 7
Width = x - 11
Area of rectangle = length*width
Therefore:
(x + 7)(x - 11) = 88
x(x - 11) +7(x - 11) = 88
x² - 11x + 7x - 77 = 88
Add like terms
x² - 4x - 77 = 88
x² - 4x - 77 - 88 = 88 - 88
x² - 4x - 165 = 0
Factorize
x² - 15x + 11x - 165 = 0
x(x - 15) +11(x - 15) = 0
(x + 11)(x - 15) = 0
x = -11 or x = 15
Let's use the positive number.
Therefore:
Length = x + 7
Plug in the value of x
Length = 15 + 7 = 22 cm
Width = x - 11 = 15 - 11 = 4 cm
Jamal borrowed $316 for nine months. He paid it off by paying $38.27 monthly.
What will he pay in finance charges?
The finance charge payed by Jamal is $28.43.
What is a word problem?A word problem is a verbal description of a problem situation. It consists of few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.
For the given situation,
Amount borrowed by Jamal for nine months = $316
His monthly payment = $38.27
Total amount payed by Jamal for nine months = [tex]9(38.27)[/tex]
⇒ [tex]\$344.43[/tex]
Thus his finance charge = [tex]344.43-316[/tex]
⇒ [tex]\$28.43[/tex]
Hence we can conclude that the finance charge payed by Jamal is $28.43.
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Answer Choices:
A. 0.26
B. 0.56
C. 0.52
D. 0.31
If you answer back with a link your comment will be reported.
will give brainliest ASAP PLEASE HELP!
Answer:
7k+7
41
Step-by-step explanation:
Distribute the 7 -
7(k+1)
7 * k = 7k
7*1 = 7
so 7k + 1
Insert 3 instead of x, so it reads -
[tex]5[/tex][tex](3)^{2}[/tex] - 4
[tex]3^{2} = 9[/tex]
9 * 5 = 45
45 - 4 = 41
Please no troll include work