Answer:
x=3.00 or x= 8.00
Explanation:
Let us denote side of the cut-out square as x inches
Then base of box = 16-2x by 6-2x
The volume = V = (16-2x)(6-2x)
= 96-3x-12x+4x
dV/dx = 96-44x+4x^2
= 0 for a max V
divide by 4
X^2 -11x +24=0
Using quadratic formula to solve the equation
X= (11± √11^2-(4×1×24)/2
(11± √25)/2
x= 3 or 8inches
From the equation of volume = V = x(16-2x)(6-2x)
Substitute
let x = 3 , V = 3(16-6)(6-6) = 0
let x = 8 , V = 8(16-16)(6-16) = 0
Therefore, the maximum volume exist at both point x=3 or x= 8
greater than (−8) but less than (−2)
Answer:
-8 < x < -2
start number line at -10 and end it at 0
draw an open circle* over the dash indicating -8 and -2
connect the open circles
*open circle because it is less than and greater than, not less than or equal to and greater than or equal to
Answer:
-8<x<-2
Step-by-step explanation:
yw luv :D
Colin leaves school to go home. He walks 3 blocks south and then 9 blocks west. If Colin could walk in a straight line to the school, what is the exact distance between Colin and the school?
Answer:
9.48*
Step-by-step explanation:
This is a right triangle. The formula for solving the Hypotenuse, or the longest side of the right triangle is A^2 + B^2 = C^2. If we put the numbers from the problem into the formula this is what we get :
3^2 + 9^2 = C^2
9 + 81 = C^2
90 = C^2
9.48 = C
* This is rounded, the exact number is closer to 9.486832980505138. Your class should tell you what to round to.
Answer:
The answer would be A. 3√10 blocks
Step-by-step explanation:
I have had this question and its 3√10 blocks.
Hope this helps you other people :))
Based on the table, which best predicts the end
behavior of the graph of f(x)?
As x, f(x) —, and as x->-0, f(x) →..
As x 700, f(x) →, and as x -→-00, f(x) →--.
As x, f(x) →-00, and as x———00, f(x)
As x -+-0, f(x) →-00, and as x->-00, f(x) -
->
-→-00
Answer:
The correct option is;
As x → ∞ f(x) → -∞, and as x → -∞ f(x) →∞
Step-by-step explanation:
The values given are;
x, f(x)
-4, 18
-3, 9
-2, 6
-1, 3
0, 0
1, -3
2, -6
3, -9
4, -18
Based on the table, as the magnitude of x increases in the positive direction, the magnitude of f(x) increases in the negative direction
Therefore, the correct option that best predicts the end behavior of the graph of f(x) is As x → ∞ f(x) → -∞, and as x → -∞ f(x) →∞.
Please answer it now in two minutes
Answer:
8.4 in
Step-by-step explanation:
Solution:-
- We consider the large right angle triangle namely, " XVW "
- We will recall all the trigonometric ratios that are applicable to all right angled triangles.
- While we are dealing with trigonometric ratios we have the following terms that needs to be correlated with the given specific problem:
Hypotenuse ( H ): Side opposite to 90 degrees angle
Base (B): The side adjacent to the available angle ( θ )
Perpendicular (P): The side opposite to the available angle ( θ )
- We will go ahead and mark our respective sides as follows:
Angle ( θ ) : 34°
Hypotenuse ( H ) : XW = 15 in
Base ( B ) : VW
Perpendicular ( P ) : VX
- Now recall all the trigonometric ratios studied:
sin ( θ ) = P / H = VX / XW
cos ( θ ) = B / H = VW / XW
tan ( θ ) = P / B = VX / VW
- Now choose the appropriate trigonometric ratio with two values given and one ( VX ) that needs to be determined as follows:
sin ( θ ) = P / H = VX / XW
sin ( 34° ) = VX / 15
VX = 15*sin ( 34° )
VX = 8.387 .. ( 8.4 ) in
What is the measure of Angle D F E? Triangle D E F. The exterior angle to angle F is 142 degrees. 38 degrees 52 degrees 118 degrees 142 degrees
as the exterior angle is known
sum of that angle and f angle = 180
142 + f = 180
f = 180 - 142
f = 38
Answer:
38
Step-by-step explanation:
Add the angle and f angle (180)Now add 142 + f = 180 Now subtract 180 - 142 (= f) Finally you get your answer 38Hope this helps you :)
A ballasted roof is flat and covered with gravel to hold the roofing material in place. Adam plans to cover the roof in the diagram with gravel.
30 ft.
21 ft.
13 ft.
57 ft.
27 ft.
52 ft.
The area that Adam plans to cover with gravel is
weight of gravel on the roof will be
If the weight of the gravel is 12 pounds per square foot, the total
ling
2,702 square feet
Next
2,374 square feet
2,222 square feet
2,031 square feet
Answer:
[tex] Area = 2,031ft^2 [/tex]
Total weight of gravel on the roof = [tex] 24,372 pounds [/tex]
Step-by-step Explanation:
The area Adams planned to cover with gravel can be divided into 3 rectangles as shown in the diagram attached.
We would have 3 rectangles. See the attachment below to check out how we arrive at the dimensions of the 3 rectangles.
Area of rectangle = L*W
Area to be covered by gravel = area of rectangle 1 + area of rectangle 2 + area of rectangle 3
Area to be covered with gravel = [tex] (30*17) + (13*9) + (52*27) [/tex]
[tex] Area = (30*17) + (13*9) + (52*27) = 2,031ft^2 [/tex]
Total weight of gravel on the roof = 12 pounds per square foot multiplied by total area of the roof to be covered = [tex] 12 * 2031 = 24,372 pounds [/tex]
Answer:
2031 and 16925
Step-by-step explanation:
Solve the equation and show the solution set on a number line: |x+5|=x+5
Answer: x ≥ -5
Step-by-step explanation:
First, let's see how the function f(x) = IxI works:
if x ≥ 0, IxI = x
if x ≤ 0, IxI = -x
Notice that for 0, I0I = 0.
Ok, we want that:
|x+5| = x+5
Notice that this is equivalent to:
IxI = x
This means that |x+5| = x+5 is only true when:
(x + 5) ≥ 0
from this we can find the possible values of x:
we can subtract 5 to both sides and get:
(x + 5) -5 ≥ 0 - 5
x ≥ -5
So the graph in the number line will be a black dot in x = -5, and all the right region shaded.
something like:
-7__-6__-5__-4__-3__-2__-1__0__1__2__3__4__ ...
ASAP PLEASE A box contains 6 red, 3 white, 2 green, and 1 black (in total 12) identical balls. What is the least number of balls necessary to take out randomly (without looking) to be sure of getting at least one red ball?
Answer:
7 is the least.
Step-by-step explanation:
Their are 12 balls, and 6 of them are red. if you are to pick every single ball except the red ones, you cut the number of balls in half, and are left with 6 red balls, and 6 balls picked. Your next pick must be a red ball, making 7 picks.
The value 4 is a lower bound for the zeros of the function shown below.
f(x) = 4x^3 – 12x^2 – x + 15
A) True
B) False
Answer:
False roots are x = -1 or x = 5/2 or x = 3/2
Step-by-step explanation:
Solve for x:
4 x^3 - 12 x^2 - x + 15 = 0
The left hand side factors into a product with three terms:
(x + 1) (2 x - 5) (2 x - 3) = 0
Split into three equations:
x + 1 = 0 or 2 x - 5 = 0 or 2 x - 3 = 0
Subtract 1 from both sides:
x = -1 or 2 x - 5 = 0 or 2 x - 3 = 0
Add 5 to both sides:
x = -1 or 2 x = 5 or 2 x - 3 = 0
Divide both sides by 2:
x = -1 or x = 5/2 or 2 x - 3 = 0
Add 3 to both sides:
x = -1 or x = 5/2 or 2 x = 3
Divide both sides by 2:
Answer: x = -1 or x = 5/2 or x = 3/2
Answer:
False
Step-by-step explanation:
f(x) = 4x³ - 12x² - x + 15
Set output to 0.
Factor the function.
0 = (x + 1)(2x - 3)(2x - 5)
Set factors equal to 0.
x + 1 = 0
x = -1
2x - 3 = 0
2x = 3
x = 3/2
2x - 5 = 0
2x = 5
x = 5/2
4 is not a lower bound for the zeros of the function.
help me Please!!!!!!!
Answer:
[tex]\boxed{Option \ C}[/tex]
Step-by-step explanation:
[tex]Sin \ Y = \frac{Opposite }{Hypotenuse } = \frac{XZ}{XY}[/tex]
[tex]Cos \ Y = \frac{Adjacent}{Hypotenuse} = \frac{YZ}{XY}[/tex]
[tex]Tan Y = \frac{opposite}{adjacent} = \frac{XZ}{ZY}[/tex]
Answer:
[tex]\boxed{\mathrm{C}}[/tex]
Step-by-step explanation:
sin [tex]\theta[/tex] = Opposite/Hypotenuse
sin (Y) = [tex]\frac{XZ}{XY}[/tex]
cos [tex]\theta[/tex] = Adjacent/Hypotenuse
cos (Y) = [tex]\frac{YZ}{XY}[/tex]
tan [tex]\theta[/tex] = Opposite/Adjacent
tan (Y) = [tex]\frac{XZ}{YZ}[/tex]
A school counselor surveyed 90 randomly selected students about thé langages they speak. Of thé students surveyed 16 speak more than one langage fluently. Bases on thèse résults, How many of thé 1800 students at thé school can be expected to speak more than one langage fluently
Answer: 320 students
Step-by-step explanation:
From the question, we are informed that a school counselor surveyed 90 randomly selected students about thé langages they speak and thé students surveyed 16 speak more than one langage fluently. This means that 16/90 speak more than one language.
When 1800 students are surveyed, the number of students that can be expected to speak more than one langage fluently will be:
= 16/90 × 1800
= 16 × 20
= 320 students
In 1819, the United States purchased Florida from Spain for
$5 X 106. The area of Florida is about 6.6 x 104 square miles.
Which key strokes on a calculator will give the cost the
United States paid for each square mile of Florida?
Answer:
Option D. 5 EE 6 ÷ 6.6 EE 4
Step-by-step explanation:
Data obtained from the question include the following:
Area of land purchased = 6.6×10^4 square miles
Cost = $ 5×10^6
To determine the key strokes on a calculator which will give the cost the
United States paid for each square mile of Florida, let us calculate cost of 1 square mile.
This can be obtained as follow:
6.6×10^4 sq mile = $ 5×10^6
Therefore,
1 sq mile = $ 5×10^6 ÷ 6.6×10^4
In calculator, the key strokes will be:
5 EE 6 ÷ 6.6 EE 4
Answer:
Like Eduard22sly said D). 5 EE 6 ÷ 6.6 EE 4 is correct.
plus i took the test 100% :)
If x is an even number, the function fX) = 2x - 1 gives an odd number. Identify the set of odd numbers corresponding to this set of even
numbers: {0, 2, 4, 6, 8)
Answer:
{-1, 3, 7, 11, 15}
Step-by-step explanation:
we just substitute the set of even numbers in the function f(x) given to get our corresponding set of odds numbers
for 0
2(0)-1=0-1=-1
for 2
2(2)-1=4-1=3
for 4
2(4)-1=8-1=7
for 6
2(6)-1=12-1=11
for 8
2(8)-1=16-1=15
If the perimeters of each shape are equal, which equation can be used to find the value of x? A)(x+4)+x+(x+2)=1/2x+(x+3) B)(x+2)+x+(x+4)=2(1/2x)+2(x+3) C)2 (x) + 2 (x + 2)=2(1/2 x) + 2(x+3) D)x + (x + 2) + (x + 4) =2 (x + 3 1/2)
(x+2) + x + (x+4) = 2(1/2) + 2(x+3)
Step-by-step explanation:
They are equal to each other and the rectangle has 2x more perimeter
The triangle would be divided in half from that rectangle.
What the answer question now
Answer:
UW=41
Step-by-step explanation:
the tangent line and the radius always meet at a right angle(90 degrees)
UWV is a right angle triangle, apply the Pythagorean theorem:
a²+b²=c² (a=40, b=9, c=UW)
40²+9²=c²
c=√40²+9²=√1600+81=√1681
c= 41
A car bought for $20,000. Its value depreciates by 10% each year for 3 years. What is the car's worth after3 years?
Answer:
$14,580
Step-by-step explanation:
To start off, 10% of 20,000-one easy way to do this is to multiply 20,000 by 0.1, which is 10% in decimal form
-In doing that, you get 2,000
-Now the question says that the value is depreciated which means it goes down in value, so subtract 2,000 from 20,000 to 18,000
-the value of the car after one year is now $18,000
Now, let's move to the second year. This time find 10% of 18,000
-multiply 18,000 by 0.1 to get 1,800
-since the value is depreciating, or becoming less, we will subtract 1,800 from 18,000 to get 16,200
-the value of the car after two years is now $16,200
Finally, let's look at the value of the car after three years. Only this time, we will now find 10% of 16,200
-multiply 16,200 by 0.1 to get 1,620
-since value is being depreciated, or lessened, we will once again be subtracting. Subtract 1,620 from 16,200 to get 14,580
Therefore, the value of the car after three years is now $14,580.
Find the measure of arc JKM if angle KLM = 50 degrees.
Answer:
180°
Step-by-step explanation:
Answer:
180 = arc JKM
Step-by-step explanation:
Angle JM is a straight line so the angle is 180
Central Angle = Intercepted Arc
angle JM = arc JKM
180 = arc JKM
Find the x-intercepts of the graph
Answer:
(1,0) and (3,0)
Step-by-step explanation:
y=x^2-4x+3
To factor we need to know what numbers add up to -4 and multiply will equal to 3.
y=(x-3)(x-1)
The zeroes would be 3 and 1.
x=3 so y=0 for (x-3)
x=1 so y=0 for (x-1)
If right pls give me brainliest thank you.
Answer:
(1, 0) and (3, 0)
Step-by-step explanation:
[tex]y=x^2-4x+3[/tex]
Plug y as 0 to find the x-intercepts.
[tex]0=x^2-4x+3[/tex]
Factor right side.
[tex]0=x^2-1x-3x+3[/tex]
[tex]0=x(x-1)-3(x-1)[/tex]
[tex]0=(x-1)(x-3)[/tex]
Set factors equal to 0.
[tex]x-1=0\\x=1\\x-3=0\\x=3[/tex]
x=1 or x=3 when y=0
Which pairs of events describe independent events?
Answer:last one is the correct ans...
Step-by-step explanation:
Pleased to help u....
Solve the inequality
V/3+12>7
Answer:
V > -15
Step-by-step explanation:
[tex]\frac{V}{3} +12>7\\\\\frac{V}{3}>-5\\\\V>-15[/tex]
Answer:
V > -15
Step-by-step explanation:
V/3 + 12 > 7
V/3 > -5
V > -15
Carrie can inspect a case of watches in 5 hours.James can inspect the same case of watches in 3 hours.After working alone for 1 hour,Carrie stops for lunch.After taking a 40 minute lunch break,Carrie and James work together to inspect the remaining watches.How long do Carrie and James work together to complete the job?
Will mark brainlist if it correct and well explained
Answer:
It takes Carrie and James an hour and a half to finish the job.
Step-by-step explanation:
assuming they have to inspect ONE case of watches.
Carrie can inspect 1/5 case in one hour.
James can inspect 1/3 case in one hour.
Carrie worked alone for 1 hour, so she finished 1/5 of a case.
She leaves 4/5 case to finish.
She had lunch.
After that, Carrie and James worked together for x hours to finish the job.
When they work together, the finish 1/5+1/3 = 8/15 case per hour.
So time to finisher the remaining case
Time = 4/5 / (8/15)
= 4/5 * 15/8
= 3/2 hours
= an hour and a half.
Simplify 6c + 4d - c -7d
Answer:5c-3d
Step-by-step explanation: Collect the like terms such as 6c ,-c and 4d,-7d
Answer:
5c - 3d
Step-by-step explanation:
6c + 4d - c - 7d
Group like terms
6c - c + 4d - 7d
Add similar elements : 6c - c = 5c
5c + 4d - 7d
Add similar elements : 4d - 7d = - 3d
5c - 3d
I hope this helps
In 2010, the number of houses built in Town A was 25 percent greater than the number of houses built in Town B. If 70 houses were built in Town A during 210, how many were built in Town B
Answer:
The number of houses built in Town B is 56.
Step-by-step explanation:
We are given that in 2010, the number of houses built in Town A was 25 percent greater than the number of houses built in Town B.
Also, 70 houses were built in Town A during 210.
Let the number of houses built in Town B be 'x'.
So, according to the question;
Number of houses built in Town A = Number of houses built in Town B + 25% of the houses built in Town B
[tex]70 = x + (25\% \times x)[/tex]
[tex]70 = x(1+0.25)[/tex]
[tex]x=\frac{70}{1.25}[/tex]
x = 56
Hence, the number of houses built in Town B is 56.
Find the 9th term geometric sequence 1,1/2,1/2^2w. Please show the steps.
Answer:
9th term geometric sequence (a9) = 1 / 256
Step-by-step explanation:
Given:
Geometric sequence 1,1/2,1/2²
First term (a) = 1
Common ratio (r) = A2 / A1 = (1/2) / 1 = 1/2
Number of term (n) = 9
Find:
9th term geometric sequence (a9)
Computation:
[tex]an = ar^{n-1}[/tex]
a9 = ar⁹⁻¹
a9 = (1)(1/2)⁸
a9 = (1/2)⁸
a9 = 1/256
9th term geometric sequence (a9) = 1 / 256
PLZZ HELP Fill in the blank with the correct response. The slope of the graph of y = x is ___a0.
Answer:
1
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = x ← is in slope- intercept form
with slope m = 1
Answer:
1
Step-by-step explanation:
Two cars are traveling north along a highway. The first drives at 40 mph, and the second, which leaves 3 hours later, travels at 60 mph. How long after the second car leaves will it take for the second car to catch the first?
Answer:
Step-by-step explanation:
We will make a table and fill it in according to the information provided. What this question is asking us to find, in the end, is how long did it take the cars to travel the same distance. In other words, how long, t, til car 1's distance = car 2's distance. The table looks like this:
d = r * t
car1
car2
We can fill in the rates right away:
d = r * t
car1 40
car2 60
Now it tells us that car 2 leaves 3 hours after car 1, so logically that means that car 1 has been driving 3 hours longer than car 2:
d = r * t
car1 40 t + 3
car2 60 t
Because distance = rate * time, the distances fill in like this:
d = r * t
car1 40(t + 3) = 40 t+3
car2 60t = 60 t
Going back to the interpretation of the original question, I am looking to solve for t when the distance of car 1 = the distance of car 2. Therefore,
40(t+3) = 60t and
40t + 120 = 60t and
120 = 20t so
t = 6 hours.
Katya has $20.00 to spend at her college bookstore, where all students receive a 20% discount . katya wants to purchase a copy of a book that normally sells for $22.50 plus 10% sales tax. how much dose the book sell for dose katya have enough money bc bc?
Answer:
Katie is correct. You would take 20% of $22.50 (22.5 multiplied by .2). You would get $4.50 off of the book with the discount. So you would subtract 4.5 from 22.5 and get $18. Then you would take 10% of $18 for the sales tax. (18 multiplied by .1). You would get $1.80 towards sales tax. you would then add $1.80 to $18 and get $19.80
Step-by-step explanation:
Please help me with this question!! TRIGONOMETRY
Work Shown:
sin(angle) = opposite/hypotenuse
sin(35) = 10/x
x*sin(35) = 10
x = 10/sin(35)
x = 17.434467956211 make sure your calculator is in degree mode
x = 17.4
Answer:
[tex]\boxed{17.4}[/tex]
Step-by-step explanation:
sin [tex]\theta[/tex] = [tex]\frac{opposite}{hypotenuse}[/tex]
sin (35) = [tex]\frac{10}{x}[/tex]
x = [tex]\frac{10}{sin(35)}[/tex]
x = 17.4344679562...
x ≈ 17.4
What is the volume of the following rectangular prism? *picture shown below*
Answer:
27/2 units^3
Step-by-step explanation:
Formula for volume: l * w * h or a * h because l * w = area.
27/5 ( which is area ) * 5/2 ( the height ) = 27/2
i hope this helps
The volume of the following rectangular prism is 27/2 units^3
We know that the rectangular prism is a three-dimensional shape that has two at the top and bottom and four are lateral faces.
The volume of a rectangular prism = Length X Width X Height
We are given the dimensions as Length = 5/2
Area = 27/5
Here a * h because l * w = area.
Volume = Length X Width X Height
= area X Width
= 27/5 x 5/2
= 27/2
The volume is 27/2 units^3.
Learn more about a rectangular prism;
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Use De Morgan's laws to write negations for the statement. Sam is an orange belt and Kate is a red belt.
A. Sam is an orange belt or Kate a red belt.
B. Sam is not a red belt and Kate is not an orange belt.
C. Sam is not an orange belt and Kate is not a red belt.
D. Sam is not a red belt or Kate is not an orange belt.
E. Sam is not an orange belt or Kate is not a red belt.
Answer:
C. Same is not an orange belt and Kate is not a red belt.
Step-by-step explanation:
The negation for the statement is Sam is not an orange belt or Kate is not a red belt.
What is Negation of De- Morgan's Law?The negation of a conjunction is equivalent to the disjunction of the negation of the statements making up the conjunction. To negate an “and” statement, negate each part and change the “and” to “or”.
Given statement:
Sam is an orange belt and Kate is a red belt.
Now, to make the negation we have to consider the rule "To negate an “and” statement, negate each part and change the “and” to “or”."
So, the negation statement would be
Sam is not an orange belt or Kate is not a red belt.
Learn more about De Morgan's laws here:
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