Answer:
A.
Step-by-step explanation:
'The difference' means minus or subtraction. 'plus' and 'increased' are both for addition.
Brainliest please!
Given the following equation where A = Area of a rectangle and w = width of the rectangle, what value of 'w' would maximize the area?
A = LW
P = 2L+2W
P = 100
w should be 625 units
w should be 25 units
w should be 0 units
w should be 50 units
Answer:
the second option : w should be 25 units
Step-by-step explanation:
the area of the rectangle is length×width = L×W
the perimeter of a rectangle = 2L + 2W
now, we know that the perimeter is 100 units.
and we have to find the best length of W, that will then define L (to keep the 100 units of perimeter) and maximizes the area of the rectangle.
in other words, what is the maximum area of a rectangle with perimeter of 100 (and what are the corresponding side lengths)?
now, w = 625 is impossible. that side alone would be bigger than the whole perimeter.
W = 0 would render the whole rectangle to a flat line with L = 50 because of
100 = 2L + 2W = 2L + 0 = 2L
L = 50
and A = L×W = 50×0 = 0
an area of 0 is for sure not the largest possible area.
w = 50 would cause L = 0
100 = 2L + 2W = 2L + 2×50 = 2L + 100
0 = 2L
L = 0
and with L = 0 the same thing happens as with W = 0 : a flat line with 0 area.
so, the only remaining useful answer is W = 25
100 = 2L + 2W = 2L + 2×25 = 2L + 50
50 = 2L
L = 25
A = L×W = 25×25 = 625 units²
and indeed, the maximum area for a given perimeter is achieved by arranging the sides to create a square.
Find the measure of the missing angle using the triangle angle sum theorm.
Answer:
20 degrees
Step-by-step explanation:
One angle is 70 degrees and the other is 90. Angles of a triangle add up to 180. 180 - 70 - 90 = 20. The final angle is 20 degrees.
The function g(x) = x2 is transformed to obtain function h:
h(x) = g(x − 3).
Which statement describes how the graph of h is different from the graph of g?
A. The graph of h is the graph of g horizontally shifted right 3 units.
B. The graph of h is the graph of g horizontally shifted left 3 units.
C. The graph of h is the graph of g vertically shifted up 3 units.
D. The graph of h is the graph of g vertically shifted down 3 units.
Answer:
A
Step-by-step explanation:
The graph of h(x) = (x-3)^2. The (x-3) indicates that the graph is shifted horizontally right 3 units because the change takes place inside the parantheses. Because the units are being subtracted, the graph will shift to the right. I highly recommend using Desmos to find your answer next time.
Frogs are released into a pond where there are no other frogs of this species. The
function f(t) can be used to model the population of this new species after t years.
Below are 4 forms of the function that model this situation. Which form most clearly
shows the monthly population growth?
Answer:
[tex]f(t)=12(1.0139)^{12t}[/tex]
Step-by-step explanation:
Let the initial number of frogs = 12
And their population is growing with the annual growth rate = 16.68% per year
Function modeling the population after 't' years will be,
[tex]P(t)=12(1+r)^{t}[/tex]
Here, r = Annual growth rate
t = Number of years
If we convert the annual growth rate to monthly growth rate,
Expression modeling the population will be,
[tex]f(t)=12(1+\frac{r}{12})^{12t}[/tex]
[tex]=12(1+\frac{16.68}{12})^{12t}[/tex]
[tex]=12(1.0139)^{12t}[/tex]
Therefore, [tex]f(t)=12(1.0139)^{12t}[/tex] will be the answer.
Solve the system of equations using the substitution method.
y = 5x
7x + 2y = -17
(x, y) = ( , )
PLSSS HELP
Answer:
1. = 5 10 15 20 25
2. 2 4 6 8 10 12 14
X, y =10
Point A is the incenter of △PQR. Find each measure
Answer:
[tex]\angle ARU=40^{\circ}[/tex]
AU=20 units
[tex]m\angle QPA=35^{\circ}[/tex]
Step-by-step explanation:
We are given that
[tex]\angle ARQ=40^{\circ}[/tex]
AT=20 units
Point A is the incenter of triangle PQR.
Incenter is that point where three angle bisector of triangle meets.
AR is the bisector of angle R of triangle PQR.
Therefore, [tex]\angle ARQ=\angle ARU=40^{\circ}[/tex]
All right triangles are similar when two triangles are similar then the ratio of their corresponding sides are equal.
Right angled triangle ATP and Right triangle AUP are similar.
Therefore,
[tex]\frac{AT}{AU}=\frac{AP}{AP}=1[/tex]
[tex]\frac{20}{AU}=1[/tex]
[tex]AU=20[/tex]units
AP is the angle bisector of angle P of triangle PQR
[tex]\angle APQ=\angle APU[/tex]
[tex]3x+2=4x-9[/tex]
[tex]2+9=4x-3x[/tex]
[tex]x=11[/tex]
Using the value of angle x
[tex]\angle APQ=3x+2=3(11)+2[/tex]
[tex]\angle APQ=35^{\circ}[/tex]
Hence, the measure of angle QPA=35 degree
The incenter of a triangle is the point of intersection of all the three interior angle bisectors of the triangle. This point is equidistant from the sides of a triangle.
Angle ARU = 40 degree
Length of AU = 20
Angle QPA = 35 degree
Here a figure is attached.
Since, AR is angle bisector of angle URK.
So, ∠ARU = ∠ARK = 40 degree
Since, incenter point is equidistant from the sides of a triangle.
So, AT = AU = AK = 20
Since, PA is angle bisector of angle QPU.
So, ∠QPA = ∠UPA
3x + 2 = 4x - 9
4x - 3x = 9 + 2
x = 11
Substituting value of x in angle 3x + 2
We get, ∠QPA = 3(11) + 2 = 35 degree
Learn more:
https://brainly.com/question/1620555
Ibrahim likes to run a loop around the park near his house that is ⅞ mile long. There is a water fountain ½ way around the loop. Ibrahim stopped to get a drink of water at the water fountain. How far did Ibrahim run?
Answer:
7/16 mile
Step-by-step explanation:
Distance of the loop = 7/8 mile
Distance of Water fountain = 1/2 of the Distance of the loop
= 1/2 of 7/8
Ibrahim stopped to get a drink of water at the water fountain. How far did Ibrahim run?
= 1/2 of 7/8
= 1/2 * 7/8
= (1 * 7) / (2 * 8)
= 7/16
Ibrahim ran 7/16 mile to drink water at the water fountain around the loop
The probability that Sara wins a raffle is given by the expression n/n+3
Write down an expression, in the form of a combined single fraction, for the probability that Sara does not win.
Answer:
3/(n + 3)
Step-by-step explanation:
The given probability that Sara wins a raffle draw, P = n/(n + 3)
Given that the sum of all probabilities is 1, we get
The probability that Sara does not win, Q = 1 - P
Therefore;
Q = 1 - n/(n + 3) = (n + 3) - n/((n + 3) = 3/(n + 3)
The probability that Sara does not win, Q = 3/(n + 3)
Help Now!!!!
The Base Of A triangle prism
Answer:
Volume=Area × height
=35×7
volume = {245} m³
OAmalOHopeO
Answer:
Since the area of the triangle(base) is known we now multiply it to the height so we can get the volume.
7 x 35 = 245 m3 is your answer
You can picture it too:
(sorry my drawing is bad with the marker)
10 men painted 3 identical houses in 5 hours, working at a constant rate. How many houses would it take 20 men to paint 12 such houses, working at the same constant rate?
THE answer is
10 hours
F(x)=-3x^2+4x+4
G(x)=x(-7x-7)
Which expression is equal to f(x)+g(x)
Answer:
A
Step-by-step explanation:
f(x)+g(x)=-3x^2+4x+4+x(-7x-7)= -3x^2+4x+4 -7^2-7x
= -10x^2-3x+4
I need help with this I don't understand
Answer:
Sin ? = 4/7
? = arcSin (4/7)
? = 35° (rounded to the nearest degree)
So the answer is 35°
Answered by GAUTHMATH
Which expression is equivalent to the given expression?
Answer:C
Step-by-step explanation:
a^0=1 so youre left with 6ab/b8
then,
6a•b^(1-8)
6a•b^-7
therefore, 6a/b^7 is the answer
Show that 4^(x+2)+4^(x+1)+4^x is divisible by 7 for all positive integers of x.
Answer:
Below.
Step-by-step explanation:
4^(x+2)+4^(x+1)+4^x
= 4^x*4^2 + 4^x*4 + 4^4
= 4^x(16 + 4 + 1)
= 21*4^x.
As 21 is divisible by 7, 21*4^x is also divisible by 7 for all positive integers of x.
Thus the original expression must be also divisible by 7 for all positive integers of x.
American airlines requires that total outside dimensions (length+width+height) of a checked bag not exceed 62 inches.Suppose you want to check a bag whose height is same as its width.What is the biggest volumn bag of this shape that you can check on an american flight
Answer:
The maximum volume is 35316.4 in^3.
Step-by-step explanation:
Length + width + height is less than equal to 62 inches
Height = width = W
Let the length is L .
[tex]L + W + W = 62 \\\\L= 62 - 2 W\\\\Volume, V = L W H\\\\V = (62 - 2 W)\times W \times W\\\\V = 62 W^2 - 2 W^3\\\\\frac{dV}{dW}=124 W - 6 W^2\\\\So, \frac{dV}{dW} =0\\\\124 = 6 W\\\\W = 20.67 inches[/tex]
So, the maximum volume is
[tex]V =124\times 20.67\times 20.67 - 2 \times 20.67^3\\\\V =52978.86 - 17662.46 = 35316.4 inch^3[/tex]
Find the value of x. Write your answer in simplest form. WILL MAKE BRAINLIEST
============================================
Explanation:
Since we have an isosceles right triangle, the the length of the hypotenuse (let's call it y) is equal to sqrt(2) times the leg length x.
In other words, [tex]y = x*\sqrt{2}[/tex]
If we replaced y with 3*sqrt(2), then we could say,
[tex]y = x*\sqrt{2}\\\\3\sqrt{2} = x*\sqrt{2}[/tex]
in which we can see that x = 3 must be the case. Or you could divide both sides of that last equation by sqrt(2) to find x = 3.
-------------------------
Another method:
We'll use the pythagorean theorem
[tex]a^2+b^2 = c^2\\\\x^2+x^2 = \left(3\sqrt{2}\right)^2\\\\2x^2 = 3^2*\left(\sqrt{2}\right)^2\\\\2x^2 = 9*2\\\\2x^2 = 18\\\\x^2 = 18/2\\\\x^2 = 9\\\\x = \sqrt{9}\\\\x = 3\\\\[/tex]
We get the same answer as before.
Graph the function f(x) = - squared x + 2
One of the ways to graph this is to use plug in a few x-values and get an idea of the shape. Since the x values keep getting squared, there is an exponential increase on either side of the y-axis. You can see this by plugging in a few values:
When
x=0,f(x)=0
x=1,f(x)=1^2=1
x=2,f(x)=2^2=4
x=3,f(x)=3^2=9
x=4,f(x)=4^2=16
The same holds true for negative x-values to the left of the y-axis since a negative value squared is positive. For example,
x=−1,f(x)=(−1)2=1*−1=1
x=2,f(x)=(−2)2=−2*−2=4
The graph of f(x)=x^2 is called a "Parabola." It looks like this:
Simplify this expression.
Can anyone help pls
Answer:
Step-by-step explanation:
Can someone help me with this math homework please!
Answer:
The answers are options A and C.
They are (-2,0) and (0,0).
Step-by-step explanation:
x-intercept
(-2,0) and (0,0)
can someone answer this
Answer:sadwer
Step-by-step explanation:
write a expression to represent 6 fewer then the quotient of 8 and a number
Answer:
8/x-6
Step-by-step explanation:
When it says a number fewer, that means to put it behind rather than in the front.
Hope this helps!!:)
Answer:
The expression to represent the phrase is 8/x - 6.
Which of the following points is a solution of the inequality y < |x - 2|?
(-2, 0)
(2, 1)
(2, 0)
Answer:
(-2,0)
Step-by-step explanation:
y < |x - 2|
Substitute the points in and check
(-2,0)
0 < |-2 - 2|
0 < |-4|
0 < 4 True
(2,1)
1 < |2 - 2|
1 < |0|
1 < 0 False
(2,0)
0 < |2 - 2|
0 < |0|
0 < 0 False
Will give brainiest
∆ABC and ∆PQR are similar. ∆ABC is dilated by a scale factor of 1.25 and rotated 45° counterclockwise about point B to form ∆PQR. The side lengths of ∆ABC are , 5 units; , 4.2 units; and , 4 units. Match each side of ∆PQR to its length.
see file attached
Answer:
QR=5.25 units
PR=5 units
PQ=6.25 units
In a recent storm, an 18-foot utility pole broke and fell leaving a 5-foot tall portion upright. How far is the top of the pole from the base of the pole?
Answer: [tex]12\ ft[/tex]
Step-by-step explanation:
Given
Total height of utility pole is 18 ft
After breakage, only 5 foot tall portion is standing
The fallen part is [tex]18-5=13\ ft[/tex] in length
From the figure, apply the Pythagoras theorem
[tex]\Rightarrow 13^2=x^2+5^2\\\Rightarrow x^2=169-25\\\Rightarrow x=\sqrt{169-25}\\\Rightarrow x=\sqrt{144}\\\Rightarrow x=12\ ft[/tex]
Thus, the fallen part is [tex]12\ ft[/tex] away from the base of the pole.
Jeanette wants to raise $3,200 in a marathon fundraiser. Her sponsers will donate
$35 for each (whole) kilometer she runs this summer.
The minimum amount Jeanette will have to run to reach her goal of $3, 200 is
kilometers.
Total amount she wants to raise = $3200
Amount she'll get for each kilometer = $35
So, number of kilometers she need to run
= Total amount she wants to raise/Amount she'll get for each kilometer
= $3200/$35
= 91.42....
Since her sponser is will donate only for whole kilometers she'll have to run 92 km.
Find the value of x if log636 = x.
Answer:
assuming that this is your question
[tex]log_{6} 36 = x[/tex]
[tex]6^{x} = 36[/tex]
x = 2
Note: your actual question log 636
is actually [tex]log_{10} 636 = x[/tex]
[tex]10^{x} = 636[/tex]
x = 2.803 (i am sure that tis not the question in your homework)
Step-by-step explanation:
find the value of 2/5 - 3
[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]
[tex]\sf{\dfrac{2}{5}-3 }[/tex] [tex]\sf{\dfrac{2-10}{5} }[/tex] [tex]\sf{\dfrac{-8}{5} }[/tex][tex]\sf{ }[/tex]
Find questions attached.
Show workings.
Answer:
Solution given:
7.<OYM=15°base angle of isosceles triangle
<OYL=50°base angle of isosceles triangle.
<OYL=<OYM+<MYL
50°=15°+<MYL
<MYL=50°-15°
<MYL=35°
again;
<MOL=35*2=70°central angle is double of a inscribed angle.
18.
Solution given:
<PQR+<PSR=180°sum of opposite angle of a cyclic quadrilateral is supplementary
<PQS+42°+78°=180°
<PQS=180°-120°=60°
<PQS=60°
<SPR=42°inscribed angle on a same arc is equal
:.<QPS=18°+42°=60°
<QSR=18°inscribed angle on a same arc is equal
again.
<PSR=78°
<QSR+<PSQ=78°
18°+<PSQ=78°
<PSQ=78°-18°
<PSQ=60°
In ∆ PQS
<PSQ=60°
<QPS=60°
<PQS=60°
In triangle ∆PQS all the angles are equal.
so it is a equilateral triangle.Which is the graph of f(x) = 3 (2/3)x ?
Step-by-step explanation:
.....................
I have 7,800 dollars and rent is 625.55 what is the yearly amount?
