The internet service provider charges 40 cents for each extra hour used.
Also, he provides 40 hours of free service for every account.
Solved using linear equations.
Let the number of free hours provided by the internet service provider be x, and the charge for each extra hour be p cents.
Let the time consumed by Wells, Ted, and Vino be t1, t2, and t3 respectively.
Chargeable time used by Wells = t1 - x.
Cost for Wells = p(t1 - x).
Chargeable time used by Ted = t2 - x.
Cost for Ted = p(t2 - x).
Chargeable time used by Vino = t3 - x.
Cost for Vino = p(t3 - x).
Now, we are given that Wells and Ted, in total used 105 hours, that is, t1 + t2 = 105.
The cost for them together is $10 or 1000 cents.
This can be shown as the linear equation:
p(t1 - x) + p(t2 - x) = 1000.
or, p{(t1 - x) + (t2 - x)} = 1000,
or, p{(t1 + t2) - 2x} = 1000,
or, p(105 - 2x) = 1000,
or, p = 1000/(105 - 2x) ... (i).
Time consumed by Vino is given as 105 hours, thus, t3 = 105.
The total cost to Vino is given as $26 or 2600 cents.
This now can be shown as the linear equation:
p(t3 - x) = 2600,
or, {1000/(105 - 2x)}(105 - x) = 2600 {Substituting t3 = 105, and p = 1000/(105 - 2x)}.
This is the required linear equation in one variable.
It can be solved as follows:
{1000/(105 - 2x)}(105 - x) = 2600,
or, 105000 - 1000x = 273000 - 5200x,
or, 5200x - 1000x = 273000 - 105000,
or, 4200x = 168000,
or, x = 168000/4200 = 40.
Substituting x = 40 in (i), we get:
p = 1000/(105 - 2x),
or, p = 1000/(105 - 2(40)),
or, p = 1000/(105 - 80),
or, p = 1000/25,
or, p = 40.
Thus, the internet service provider charges 40 cents for each extra hour, and he provides 40 hours of free internet on every account.
The provided question is incomplete. The complete question is:
"An Internet service provider allows a certain number of free hours each month and then charges for each additional hour used. Wells, Ted, and Vino each have separate accounts. This month the total hours used by Wells and Ted was 105, and each used all of their free hours. Their total cost was $10. Vino used 105 hours by himself and had to pay $26. What is the number of cents charged for each extra hour?"
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Given: AC BD and AC and BD bisect each other.
Prove: BE EC
1) [tex]\overline{AC} \cong \overline{BD}[/tex] and [tex]\overline{AC}[/tex] and [tex]\overline{BD}[/tex] bisect each other (given)
2) [tex]ABCD[/tex] is a parallelogram (a quadrilateral with diagonals that bisect each other is a parallelogram)
3) [tex]ABCD[/tex] is a rhombus (a parallelgoram with congruent diagonals is a rhombus)
4) [tex]\overline{BE} \cong \overline{EC}[/tex] (halves of congruent segments are congruent)
state the domain and range of the following relation
x^2+y^2=16
The domain and range is [-4, 4] and [0, 4]
What is Domain and range?The domain of a function is the set of values that we are allowed to plug into our function.
The range of a function is the set of values that the function assumes.
x² + y² = 16
y = √16 - x²
For domain under root should not be negative quantity,
16 - x²≥0
16≥x²
So, x≤4 or x≥4
Thus, the domain is [-4, 4]
Range:
y is maximum at x=0, y=4
y is minimum at x=4, y=0
Thus, range = [0, 4]
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17.
Lincoln stands on the top of a building and fires a gun upwards. The bullet travels
according to the equation h = -16t² + 384t + 50, where h is the height of the bullet off
the ground in metres at t seconds after it was fired.
a) How far is Lincoln above the ground when he shoots the gun?
b)How high does the bullet travel vertically relative to the ground?
c)How long does it take the bullet to reach its greatest height?
d)After how many seconds (round to nearest 100th) does the bullet hit the ground?
please help asap!
Answer:
a) 50 meters
b) 2354 meters
c) 12 seconds
d) 24.13 seconds
Step-by-step explanation:
Hello!
a) How far is Lincoln above the ground when he shoots the gun?We need to really understand what the variables represent in this question. Given that t is time, and h is height, the time at which he shoots the bullet will be 0, as the bullet hasn't started traveling yet. This means that we can solve for the original height of the bullet by plugging in 0 for time in the equation.
Equation: [tex]h = -16t^2 + 384t + 50[/tex]
Plug in 0 for t:
[tex]h = -16t^2 + 384t + 50[/tex][tex]h = -16(0)^2 + 384(0) + 50[/tex][tex]h = 50[/tex]The height at which Lincoln shot the bullet is 50 meters.
We can also look at this graphically. The height of origin will simply be when the x-value (in this case t-value) is 0. That means it is the point at which the graph intersects the y-axis, known as the y-intercept.
Standard form of a Parabola: [tex]y = ax^2 + bx + c[/tex]
The y-intercept is the "c" value.
Given our equation: [tex]h = -16t^2 + 384t + 50[/tex]
The c-value is 50. This proves that the y-intercept is 50.
b)How high does the bullet travel vertically relative to the ground?We want to find the highest point of the graph. To do that, we can find the vertex.
We can utilize the Axis of Symmetry (AOS) to find the Vertex.
First, find the AOS using the formula: [tex]AOS = -\frac{b}{2a}[/tex]
a = -16b = 384Plug it into the formula:
[tex]AOS = -\frac{b}{2a}[/tex][tex]AOS = -\frac{384}{2(-16)}[/tex][tex]AOS = \frac{384}{32}[/tex][tex]AOS = 12[/tex]Plug in 12 for t in the equation:
[tex]h = -16t^2 + 384t + 50[/tex][tex]h = -16(12)^2 + 384(12) + 50[/tex][tex]h = -2304 + 4608 + 50[/tex][tex]h = 2304+50[/tex][tex]h = 2354[/tex]Therefore, the highest point of the bullet is 2354 meters.
c)How long does it take the bullet to reach its greatest height?We answered this in the last question. The t-value when h is at its highest is 12.
d)After how many seconds (round to nearest 100th) does the bullet hit the ground?We have to solve for the values of t when h is 0 (when it touches the ground).
Set the equation to 0, and solve using the quadratic formula.
Quadratic formula: [tex]x = \frac{-b\pm\sqrt{b^2 - 4ac}}{2a}[/tex]
[tex]x = \frac{-b\pm\sqrt{b^2 - 4ac}}{2a}[/tex][tex]x = \frac{-384\pm\sqrt{384^2 - 4(-16)(50)}}{2(-16)}[/tex][tex]x = \frac{-384\pm\sqrt{147456 +3200}}{-32}[/tex][tex]x = \frac{-384\pm\sqrt{150656}}{-32}[/tex][tex]x = \frac{-384\pm388.14}{-32}[/tex][tex]x = -\frac{4.14}{32}, x = \frac{772.14}{32}[/tex]We are only going to take the positive solution, as we can't have a negative time. The solution that doesn't work is called an extraneous solution.
[tex]x = \frac{772.14}{32}[/tex][tex]x = 24.13[/tex]It takes approximately 24.13 seconds for the bullet to hit the ground.
To prove that ΔAED ˜ ΔACB by SAS, Jose shows that StartFraction A E Over A C EndFraction = StartFraction A D Over A B EndFraction.
Triangle A E D is shown. Line segment B C is drawn from side A D to A E to form triangle A C B.
Jose also has to state that
The other equality which must be stated by Jose is that angles BAC and BAE are congruent and their measures are equal.
What other congruence statements must Jose state?It follows from the task content that Jose is trying to prove the congruence of both triangles by means of the Side-Angle-Side congruence theorem.
It therefore follows that since, Jose has identified that the ratio of corresponding sides are equal as indicated in the task content, the equality which Jose has to state is the angle congruence equality.
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Blending problems arise when one must decide which of two or more ingredients is to be chosen to produce a product.
No, it isn't true that blending problems arise when one must decide which of two or more ingredients is to be chosen to provide a product.
Given sentence "Blending problems ...............................supply a product."
We have to answer whether the given sentence is true or false.
We can say that the given sentence is fake. the sole objective functions allowed for applied math problems maximizing profits and minimizing costs.
Blinding problems are a typical application of mixed integer applied mathematics. They involve blending several resources or materials to make one or more products similar to a requirement. Mixed integer linear programs are linear problems during which some variables are required to require integer values.
Hence the given statement is fake regarding arise of blending problems.
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Question is incomplete because it should includes:
State whether the statement is true or false.
Can someone please help me with this?
Answer: -5
Step-by-step explanation:
When x = 8, y = -5.
The total surface area of this cuboid is 112^2
Find the value of x
length = 10cm
width = 2cm
Hight = x
The value of x is 3
How to solve for x?The given parameters are:
Length = 10cm
width = 2cm
Height = x
The surface area is calculated as;
Area = 2 *(lw + lh + wh)
So, we have:
2 * (10 * 2 + 2x + 10x) = 112
Evaluate the like terms and divide by 2
20 + 12x = 56
Subtract 20 from both sides
12x = 36
Divide by 12
x = 3
hence, the value of x is 3
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What kind of compound inequality is
4x-5≥3
Or
5-x > 8
?
a. hole
b. intersection
c. conjunction
d. union
Answer: D) union
======================================================
Explanation:
Let's solve the first inequality for x.
4x-5 ≥ 3
4x ≥ 3+5
4x ≥ 8
x ≥ 8/4
x ≥ 2
Now solve the other inequality
5 - x > 8
5 > 8+x
8+x < 5
x < 5-8
x < -3
The two solutions we get are x < -3 or x ≥ 2
These two regions do not overlap. The key word "or" connecting the original inequalities also applies to the solutions.
Either x is smaller than -3, OR it is 2 or larger
I recommend drawing out a number line and shading the appropriate regions. The two disjoint regions do not connect which means we have a union of the two regions.
convert 2.3 tn = _______ Ib show your work pls
What is the turning point of the parabola with the equation?
y=27(x-64)squared+43
A: (-64,-43) B: (64,43) C: (64,-43) D: (1728,43) E: (-64,43)
The turning point of the parabola is (64, -43)
What is a turning point?Turning point is that point on a parabolic curve in which the gradient of the curve changes value.
It is also the point on the curve in which the curve starts rising or falling.
Analysis:
[tex]27(x-64)^{2}[/tex] + 43
27(x-64)(x-64) + 43
27([tex]x^{2}[/tex] -64x -64x +4096) + 43
27[tex]x^{2}[/tex] -3456x +110592 +43
27[tex]x^{2}[/tex] -3456x +110635
at turning point dy/dx = 0
dy/dx = 54x - 3456
54x - 3456 = 0
54x = 3456
x = 3456/54 = 64
To find the value of y at x = 64
27[tex](64)^{2}[/tex] -3456(64) +110635
110592 - 221184 +110635 = -43
Therefore the turning point of the parabola is (64, -43)
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how to get more brancells?
Answer:
Read books, watch documentaries, exercise, anything that benefits your body and mind
Step-by-step explanation:
Slope BC and DE are both -0.4 what is their relationship
There are 10 circles and 6 squares. What is the simplest ratio of squares to total
shapes?
Answer:
The simplest ratio would be 5:3
Step-by-step explanation:
Both 10 and 6 can be divided by 2.
They turn into 5 and 3.
Since you can't make 5 and 3 any smaller, this will be the answer.
5:3
Hope this helped! :D
i honestly done know what to do (look at image)
Answer:
A is x - 4n / 3, B is 6k + 9n, C is 11k + 16n
Step-by-step explanation:
Pretty simple, you are adding the algebra grids, or substituting variables and making out an equation.
Solving for B: 4k + 6n + 2k + 3n = 6k + 9n
Solving for A: (2k + 3n) + x = 5k + 7n = x - 4n / 3
Solving for C: 6k + 9n + 5k + 7n = 11k + 16n
Please help ill give whoever answers the best the brainliest answer ;0
Answer:
This could be described by the stock market. Suppose you had stock of tesla that went up then flat then down
Step-by-step explanation:
you went for a walk : you started at home, walked away, first slower, then a little bit faster, stayed a little bit first at one place, then started walking back home, stayed a really short time at a second place and finally walked back home.
The perimeter of a triangle is 44cm. One side is 4cm shorter than the second side and twice as long as the third side. Find the length of each side of the triangle.
The 1st, 2nd, and 3rd sides of the triangle are 16, 20, and 8 respectively.
Given that the perimeter of the triangle is 44 cm.
Let us consider a side 's' which is 4 cm shorter than the second side.
That means the second side is 4 cm longer than s, hence the second side is s+4 cm in length.
We also have that the side of length s is of length twice as long as the third side.
Hence, the length of the third side is half that of s so, it is of length s/2.
Hence, at the end 44=s+(s+4)+(s/2)=s(2+1/2)+4
⇒ s(5/2)=40
⇒ s=8*2=16
So, the 1st, 2nd, and 3rd sides of the triangle are 16, 20, and 8 respectively.
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Which expression is equivalent to the following complex fraction? StartFraction negative 2 Over x EndFraction + StartFraction 5 Over y EndFraction divided by StartFraction 3 Over y EndFraction minus StartFraction 2 Over x EndFraction StartFraction negative 2 y + 5 x Over 3 x minus 2 y EndFraction StartFraction 3 x minus 2 y Over negative 2 y + 5 x EndFraction StartFraction x squared y squared Over (negative 2 y + 5 x) (3 x minus 2 y) EndFraction StartFraction (negative 2 y + 5 x) (3 x minus 2 y) Over x squared y squared EndFraction
The expression that is equivalent to the given complex fraction is; (-2y+5x) / (3x - 2y)
How to simplify algebraic fractions?The given algebraic sentence can be rewritten as;
((-2/x) + (5/y))/((3/y) - (2/x))
The LCM is xy and as such when we put it in the denominators of each fraction, we have:
((-2y + 5x)/xy)/((3x - 2y)/xy)
Putting 'xy' in the numerator and denominator of the whole fraction:
(-2y + 5x)/(3x - 2y)
The final expression we have is (-2y + 5x)/(3x - 2y)
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Answer:
its A -2y+5x ÷ 3x-2y
Step-by-step explanation:
Edge 2022
subtract 6x 2 −7x−2 from 6x^{2}-2x+6
Answer:
5x+8
Step-by-step explanation:
The from is the key word
That means the second term is first
6x^2 -2x +6 - (6x^2 -7x -2)
Distribute the minus sign
6x^2 -2x +6 - 6x^2 +7x +2
Combine like terms
5x+8
Which solution can be used to fill
in both blanks in the table? (1, 6)
(6, 1)
(7, 6)
(6, 7)
The solution which can be used to fill in both blanks in the table is; (6,7).
What is the solution for the system?It follows from the task content that the system given has been simplified to the point that;
3x = 18
x = 18/3 = 6.
Hence, the value of y can be evaluated as follows;
2y - x = 8. where (x=6.
2y = 8+6
y = 14/2 = 7.
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How many values of x will satisfy the equation |x-1| = | x+3|
The value of x that will satisfy the equation is x=-1.
We have given that,
[tex]\left|x-1\right|=\left|x+3\right|[/tex]
We have to solve the above inequality
What is inequality?
Inequality is a relation that makes a non-equal comparison between two numbers or other mathematical expressions.
Find the positive and negative intervals
[tex]x < -3,\:\:-3\le \:x < 1,\:\:x\ge \:1[/tex]
Solve the inequality for each interval
[tex]x < -3,\:\:-3\le \:x < 1,\:\:x\ge \:1[/tex]
[tex]\mathrm{No\:Solution}\quad \mathrm{or}\quad \:x=-1[/tex]
Therefore we get,
[tex]x=-1[/tex]
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The dot plots below show the ages of students belonging to two groups of painting classes:
Based on visual inspection, which group most likely has a lower mean age of painting students? Explain your answer using two or three sentences. Make sure to use facts to support your answer. (10 points)
On the base of visual inspection , it can be said that the Group A has an average lower than the Group B
What is a Dot Plot ?It is the simple form of data visualization , in which the frequency of a data is marked as dots on x and y axis.
The dot plot is given for two groups of 30 people , who go to painting class.
It has been asked that which group most likely has a lower mean age of painting students .
On the base of visual inspection , it can be said that the Group A has an average lower than the Group B
It can be said so as the dots are highest at the age of 19 in Group A , and the whole distribution lies between 9 to 19 age of people ,
while in Group B the age of the people is wide distributed and therefore the average age will be more ,
By calculation it is proved that the average age of Group A is 15.967
and the average age of Group B is 19.7.
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Try It #2
Use function notation to express the weight of a pig in pounds as a function of its age in days d.
Based on the weight of the pig and the age in days, the function notation would be w = f (d).
What function expresses the pig's weight in days old?The function will take the form of:
y = f(x)
y will be the weight and x will be the age of the pig in days.
The function would therefore be:
w = f (d)
In conclusion, the function notation to express the pig's weight is w = f (d).
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What is the main benefit of building a connection with your community
Answer: Being connected means greater opportunities to learn from each other, mine each other's wisdom, and help each other thrive. Connecting. By being more closely interconnected, each member of the community is able to enjoy a wider, richer network of resources, wisdom, connections, and support.
for what values of the variables are the following expressions defined 1/x+y
The expression is defined for all the real values except x = -y , y = -x.
What is an Expression ?An expression is a mathematical statement consisting of constants , variables and mathematical operators.
The expression given in the question is 1/(x +y)
An expression f(x) is undefined when the denominator = 0
f(x) = 1/(x +y)
For the denominator to be zero,
x = -y
or y = -x
So the expression is defined for all the real values except x = -y , y = -x
It can be written as
E = {x ∈ R ∧ x ≠ -y} or
E = {y ∈ R ∧ y ≠ -x}
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calculate AC to 1 decimal place ?
Step-by-step explanation:
first we need to find the length of CD, so that we can use Pythagoras to find AC.
to get CD we use again Pythagoras. there is a smaller right-angled triangle on top of the BCD rectangle.
so, AD = 11 = 4 + 7
7 = the vertical leg of the upper right-angled triangle.
the horizontal leg is congruent to CD and is
sqrt(16² - 7²) = sqrt(256 - 49) = sqrt(207).
AC² = sqrt(207)² + 11² = 207 + 121 = 328
AC = sqrt(328) = 18.11077028... cm ≈ 18.1 cm
Gotta need answers fast like asap, it’s geometry, just fill the blanks pls
Two or more triangles are said to be congruent if and only if they have equal lengths of sides and equal measures of angles.
Thus, the required proof is as shown below:
STATEMENTS REASONS
1. ΔABC and ΔDEC with AB ≅ DE;
BC ≅ EC; <1 ≅ <2 Given
2. <1 and < ABC; < 2 and <DEC are sup Sum of angles on a straight line
3. <ABC ≅ <DEC Congruent angles of similar triangles
4. ∴ΔABC ≅ ΔDEC Side-Angle-Side (SAS) postulate
5. ∴<ACB ≅ <DCE CPCTC postulate
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Im taking precalc over edge 2022 right now. Cramming right before the deadline LOL. If i complete things after the deadline do they count for late credit?
Step-by-step explanation:
♦ Solution ♦ :-
Given Information :
The ratio of heights of the two girls = 5:7
Assumption
Consider their height be 5X cm and 7X cm
The height of the first girl = 5X cm
But According to the condition mentioned in given problem
The height of the first girl = 192 cm
=> 5X = 192
=> X = 192/5
=> X = 38.4
Therefore, X = 38.4 cm
Now the height of the second girl = 7X cm
=> 7 × 38.4 cm
=> 268.8 cm
♦ Alternative Method♦ :-
The ratio of the heights of the two girls = 5:7
The height of the first girl = 192 cm
Assume that the height of the second girl = X cm
Therefore, 5:7= 192:X
=> 5/7 = 192/X
=> 5X = 7×192
=> X = (7×192)/5
=> X = 7× 38.4
=> x = 268.8 cm
♦ Answer ♦ :-
The height of the second girl is 268.7 cm
can you help me with this. step by step
Answer:
B The vertex is at (2,2)
Or could possibly be
C the axis of symmetry is x=2
What is the quotient of (x cubed 3 x squared minus 4 x minus 12) divided by (x squared 5 x 6)?
The quotient of [tex]x^{3}+3x^{2} -4x-12[/tex] divided by [tex]x^{2} +5x+6[/tex] is (x-2_.
Given the polynomial [tex]x^{3}+3x^{2} -4x-12[/tex] and [tex]x^{2} +5x+6[/tex] and the first expression or polynomial is divided by second.
Quotient is a number that is obtained by dividing two numbers. It can be of two numbers or two expressions. Remainder is a number or an expression left after division of two numbers.
To find the quotient of [tex]x^{3}+3x^{2} -4x-12[/tex] divided by , we have to divide the expression first.
We know that ,
Divident=Divisor*Quotient+remainder
[tex]x^{3}+3x^{2} -4x-12[/tex]=[tex]x^{2} +5x-6[/tex]*(x-2)-12
If we carefully watch the above equation and compares with the above formula then we can easily find that the value of quotient is (x-2).
Hence the quotient of [tex]x^{3}+3x^{2} -4x-12[/tex] divided by [tex]x^{2} +5x-6[/tex] is (x-2).
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Question is incomplete as the given expressions are incomplete as they should be like this:
[tex]x^{3}+3x^{2} -4x-12[/tex] and [tex]x^{2} +5x-6[/tex].
A line passes through the two points (0, -2) and (9, 1). what is the y y -coordinate of the point on this line whose x x -coordinate is 12? a. -6 b. 0 c. 2 d. 4
Answer: 2
Step-by-step explanation:
The slope of the line is
[tex]\frac{-2-1}{0-9}=\frac{1}{3}[/tex]
So, the equation of the line is [tex]y=\frac{1}{3}x-2[/tex].
Substituting in x=12,
[tex]y=\frac{1}{3}(12)-2=2[/tex]