Answer:
D. -2
Step-by-step explanation:
19 = x + 12 + 11 + x
Solve for x
Combine like terms
x + x = 2x
12 + 11 = 23
We now have
19 = 23 + 2x
Subtract 23 from both sides
19 - 23 = -4
23 - 23 cancels out
We now have -4 = 2x
Divide both sides by 2.
-4/2 = -2
2x/2 = x
x = -2
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]
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
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:
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.
last question. 50 points!
w=-1.5
w=2
Answer:
Solution given:
[tex]\sqrt{2w²-19w+31}+2=7-2w[/tex]
again
keep square root alone
[tex]\sqrt{2w²-19w+31}=7-2w-2[/tex]
solve subtraction of 7-2
[tex]\sqrt{2w²-19w+31}=5-2w[/tex]
Squaring on both side
[tex](\sqrt{2w²-19w+31})²=(5-2w)²[/tex]
2w²-19w+31=5²-2*5*2w+4w²
take terms one side
2w²-19w+31-25+20w-4w²=0
-2w²+w+6=0
2w²-w-6=0
doing middle term factorisation
2w²-(4-3)w-6=0
2w²-4w+3w-6=0
take common from each two term
2w(w-2)+3(w-2)=0
(w-2)(2w+3)=0
either
w=2
or
W=-3/2=-1.5
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.
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)
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.
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
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 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]
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.
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)
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
3. Simplify the expression 5a - 4b - 2[a - (2b + c)]
Answer:
[tex]{ \tt{5a - 4b - 2{ (a - (2b + c))}}} \\ = { \tt{5a - 4b - 2a + 4b - 2c}} \\ { \tt{ = (5 - 2)a + ( - 4 + 4)b - 2c}} \\ { \tt{ = 3a - 2c}}[/tex]
Answer:
Step-by-step explanation:
5a - 4b -2[a - 2b + c] = 5a - 4b -2a + 4b - 2c {Distributive property}
= (5a - 2a) + (4b - 4b) - 2c {Group like terms}
= 3a - 2c
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.
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 ratio of 4 km to 3200 m.
Answer:
5:4 or 1.25:1
Step-by-step explanation:
Convert 4km to meters.4000m to 3200m.Divide by 800m.Left with 5 to 4.Simplify this expression.
Can anyone help pls
Answer:
Step-by-step explanation:
I have 7,800 dollars and rent is 625.55 what is the yearly amount?
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
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.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)
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 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.
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
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
160 pupils in a sports centre are surveyed. The pupils can only use the swimming pool, the gym and the tennis courts. 21 pupils use the swimming pool, the gym and the tennis courts. 55 pupils use the swimming pool and the gym. 48 pupils use the gym and the tennis courts. 40 pupils use the tennis courts and the swimming pool. 11 pupils use the swimming pool only. 7 pupils use the gym only. 35 pupils use the tennis courts only. Find the probability to select a pupil that uses the tennis courts.
Answer:
0.6375 = 63.75% probability to select a pupil that uses the tennis courts.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
Total:
In total, there are 160 pupils.
Uses the tennis courts:
21 pupils use the swimming pool, the gym and the tennis courts.
48 pupils use the gym and the tennis courts, which adds 48 - 21 = 27 to the number of those who use the tennis courts.
40 pupils use the tennis courts and the swimming pool, which adds 40 - 21 = 19 to the number of those who use the tennis courts.
35 use the tennis courts only.
So
21 + 27 + 19 + 35 = 102 use the tennis courts.
Find the probability to select a pupil that uses the tennis courts.
102 out of 160, so:
[tex]p = \frac{102}{160} = 0.6375[/tex]
0.6375 = 63.75% probability to select a pupil that uses the tennis courts.
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
