Answers
(a) Let x be the variable. The variable will stand for the number of additional minutes used (in addition to the minutes built into the default plan). For example, if x = 10, then Allegra used 10 additional minutes on top of what her plan allows. If x = 0, then Allegra simply pays the $65 without any extra charge.
(b) The equation is 0.10x+65 = 73.40; the 65 represents the fixed cost of 65 dollars per month regardless of how many additional minutes you use. Then you add on 0.10x on top of that to get the total 0.10x+65, which is set equal to 73.40 as this is the given bill for this particular month.
(c) Solve the equation from part (b) to get...
0.10x+65 = 73.40
0.10x+65-65 = 73.40-65
0.10x = 8.40
0.10x/0.10 = 8.40/0.10
x = 84
(d) Allegra used 84 additional minutes as this is the solution to the equation mentioned in part (b) and solved in part (c). To check the answer, simply replace x with that value
0.10x+65 = 73.40
0.10x*84+65 = 73.40
8.4+65 = 73.40
73.40 = 73.40
The answer checks out
====================================
Problem 2
P = principal (amount deposited)
i = interest only
r = interest rate in decimal form
t = time in years
We are given the following:
i = 2800
r = 0.04 (decimal version of 4%)
t = 3.5
and we want to solve for P
i = P*r*t
2800 = P*0.04*3.5
2800 = P*0.14
2800 = 0.14P
2800/0.14 = 0.14P/0.14
20000 = P
P = 20000
Andrea should deposit $20,000 into the account (to earn $2,800 after 3.5 years; where the interest rate is 4%)
====================================
Problem 3
|4x-8| - 3x = 6x+2
|4x-8| - 3x+3x = 6x+2+3x
|4x-8| = 9x+2
4x-8 = 9x+2 or 4x-8 = -(9x+2)
4x-8 = 9x+2 or 4x-8 = -9x-2
9x-4x = -8-2 or 9x+4x = -2+8
5x = -10 or 13x = 6
x = -10/5 or x = 6/13
x = -2 or x = 6/13
The two possible solutions are:
x = -2 or x = 6/13
However, x = -2 does not work since
|4x-8| - 3x = 6x+2
|4(-2)-8| - 3(-2) = 6(-2)+2
|-8-8| + 6 = -12+2
|-16| + 6 = -10
16 + 6 = -10
22 = -10
which is false
Luckily, x = 6/13 does work and I'll leave that as an exercise to have you check it.
In short, the only answer is x = 6/13
Related Questions
A few years ago, a total of 2682 thousand people lived in the metropolitan areas of Las Vegas, Nevada, and Sacramento, California. Sacramento had 276 thousand more residents that Las Vegas. What was the population of each metropolitan area? 50 POINTS
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2,682,000 - 276,000 = 2,406000
2,406,000 / 2 = 1,203,000 lived in Nevada
1,203,000 + 276,000 = 1,479,000 lived in California
Your friend is looking at laptops for college, and is comparing the different screen sizes. Use the diagram and formula below to find the width of the laptop screen. Round your answer
D= W^2+H^2
(The image of the figure is a rectangle in half, the top side is D= 17inch the H= 9inch, W is blank)
Mutiple choices are
A. W= 16.7 inch
B. W= 9.9 inch
C. W= 8 inch
D. W= 14.4 inch
Answers
D ^ 2 = W ^ 2 + H ^ 2
We substitute the values:
D = 17inch
H = 9inch
Substituting:
17 ^ 2 = W ^ 2 + 9 ^ 2
We clear the value of W:
W = root (17 ^ 2 - 9 ^ 2)
W = 14.4 inch
Answer:
The width of the laptop screen is:
D. W = 14.4 inch
Answer:
The Answer is 14.4inch for Apex!
Step-by-step explanation:
Ellipses have symmetry through only their major axis?
True or False?
I think false. They have them through both major and minor.,
Answers
Please help with this.
Quadrilateral ABCD is inscribed in circle O.
What is m∠C ?
Enter your answer in the box.
Answers
When you have an polygon inscribed in a circle, the opposite angles are supplementary.
Therefore, we can write and solve the following equation.
2x + 3 + 4x + 3 = 180
6x = 174
x = 29
If you substitution 29 into the expression for C, you will find that C = 59.
2(29) + 1 = 59
Good luck,
MrEQ
100 POINTS!!!!!!!!!!!!!!! whats is 9 times 7 times 4777 times 2 plus 3636363636363 times 700 times 4 minus 5 time 6999999996950 plus 300 times 400
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I believe this is the correct answer
hope this helps
Hope this helps! Have a great day :)
PLEASE HELP ASAP! BRAINLIEST TO BEST/RIGHT ANSWER
Answers
Consider the diagram.
The congruence theorem that can be used to prove △LON ≅ △LMN is
SSS.
ASA.
SAS.
HL.
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We have been given an diagram and we are asked to find the congruence theorem that can be used to prove △LON ≅ △LMN.
We can see from our diagram that side LO of △LON equals to side LM of △LMN. We can also see that side ON △LON of equals to side MN of △LMN. Side LN equals to itself.
We can see that three sides of triangle LON are congruent to three sides of triangle LMN. Therefore, by SSS (Side-Side-Side) congruence △LON ≅ △LMN.
In need of some help please.
Answers
50^2 = x^2 +(x +34)^2
2500 = 2x^2 +68x + 1156
x^2 +34x -672 = 0
(x -14)(x +48) = 0
x = 14 or -48
The distance from the wall to the base of the ladder is 14 ft.
_____
7-24-25 is a Pythagorean triple. The dimensions here are double those values. It can be handy to know a few of the Pythagorean triples, as that can let you write down the answers to problems without having to go through the equations.
A bag contains 18 blocks numbered from 1 to 18. Two blocks are selected from the bag at the same time. Let event E = the two numbers differ by 11. How many outcomes are in E? A) 7 B) 14 C) 28 D) 292
Answers
Answer:
A) 7
Step-by-step explanation:
E is when the numbers differ by 11, so these pairs work:
(1, 12), (2, 13), (3, 14), (4, 15), (5, 16), (6, 17), (7, 18)
Thus, there are 7 outcomes where the numbers differ by 1
Pamela drove her car 99 kilometers and used 9 liters of fuel. She wants to know how many kilometers, (k), she can drive with 12 liters of fuel. She assumes the relationship between kilometers and fuel is proportional. How many kilometers can Pamela drive with 12 liters of fuel?
Answers
x km ... 12 liters
If the relationship is proportional, we have
[tex] \frac{99}{x} = \frac{9}{12} [/tex]
from where
[tex]x = \frac{99*12}{9}= \frac{1188}{9}=\bold{132} [/tex]
The answer is 132 kilometers.
If a and b are real numbers and if y = ax + b is a direct variation equation, what do you know about a and b?
Answers
We observe that the given equation is the generic equation of a line.
Where,
a = represents the slope of the line. That is, the rate of change of the given function. (in this case it is constant).
b = is the cut point with the y axis.
Please help :( 2 questions..
If c(x)=5/x-2 and d(x)=x+3 what is the domain of (cd)(x)?
And, if f(x)=7+4x and g(x)=1/2x, what is the value of (f/g)(5)?,
Answers
An angle measures 44° more than the measure of a supplementary angle. what is the measure of each angle?
Answers
The correct answers are:
68° and 112°.
Explanation:
Let x be the measure of the smaller angle.
The larger angle would then be x+44.
Since the angles are supplementary, their sum measures 180°. This gives us the equation:
x+(x+44) = 180
Combining like terms, we have
2x+44 = 180
Subtract 44 from each side:
2x+44-44 = 180-44
2x = 136
Divide each side by 2:
2x/2 = 136/2
x = 68
The smaller angle measures 68°.
The larger angle is 44° more:
68+44 = 112°
Please help on the circle question ASAP
Answers
314 = 3.14 * radius ^2
100 = radius ^2
radius = 10
A company developed the following linear model to help budget annual expenses over time. In this model, x represents the number of years after 2009, and y represents the expense budget (in dollars). Interpret the y-intercept. y = 189,785 + 37,896x
A. The company's expense budget for 2009 was $189,785.
B. The company's expense budget for 2008 was $37,896.
C. The company's expense budget for 2009 was $37,896.
D. The company's expense budget for 2008 was $189,785.
Answers
I believe this because since x is the years after 2009 then you wouldn't times that by the expense budget for that year or any year eliminating B and C. When finding the total expense budget for this you would have to take in account the budget from 2009 so that would lead it to add 189,758. Since we are talking about after 2009 then D would be eliminated since 2008 is before 2009.
I hope this helps! Good luck!
help help help me
please
Answers
-11/3-(-2/3)=-9/3=-3
4^(-3)=1/4³=1/64
the first choice is correct.
The answer is A
If a plane slices a cube through three points that are equidistant from one of its vertices, which of the following best describes the cross-section of the cube?
Answers
Imagine a object that is a cube, like a dice. Start at one vertice and measure down 3 edges the same distance.
Now, imagine that you cut through those 3 dots and cut off the corner. The resulting base of your new shape would be the cross section. It would be a triangle.
Answer:
Triangle
Step-by-step explanation:
A cube is a three-dimensional figure with six congruent square faces. The cube below is sliced by a plane through three points that are equidistant from one of its vertices.
The cross-section created by the plane is an equilateral triangle.
Therefore, traingle is the best choice.
(2x - 3y)(4x - y) Please help
Answers
(2x - 3y) (4x - y) = 8x² -14xy + 3y²
---------------------------------
Answer:8x² -14xy + 3y²
---------------------------------
AC←→ is tangent to the circle with center at B.
The measure of ∠ACB is 71°.
What is the measure of ∠ABC?
Enter your answer in the box.
m∠ABC = __ °
Answers
Answer: The value of m∠ABC = 19 °
Step-by-step explanation:
Since we have given that
AC is tangent to the circle with center at B.
The measure of ∠ACB = 71°
And we know that "Radius is the shortest distance from the center to the tangent".
So, Radius is always perpendicular to the tangent.
So, the measure of ∠BAC = 90°
Consider, ΔABC, we get that
[tex]\angle ABC+\angle BAC+\angle ACB=180^\circ\\\\\angle ABC+90^\circ+71^\circ=180^\circ\\\\\angle ABC=180^\circ-90^\circ-71^\circ\\\\\angle ABC=19^\circ[/tex]
Hence, the value of m∠ABC = 19 °
A bowling ball leaves a bowler's hand. An accelerometer inside the ball reads zero. Which of the following best describes what happens to the ball?
A. The ball speeds up.
B. The ball moves at a constant speed.
C. The ball curves toward the gutter.
D. The ball slows down.
Not quite sure what this means :( Thanks!! @perl :)
Answers
Draw a bar model to represent the expression m divided by 4
Answers
Bar models can be used to represent the quotient and the product of numbers or expressions
How to draw the bar modelRepresent the division of m by 4 with x.
So, we have:
[tex]\frac m4 = x[/tex]
Multiply both sides of the equation by 4
[tex]4 * \frac m4 = x * 4[/tex]
Evaluate the products
[tex]m = x * 4[/tex]
So, we have:
[tex]m =4x[/tex]
See attachment for the bar model
Read more about quotients at:
https://brainly.com/question/7068223
A 36-foot long fence is placed around a square garden. What is the length of one side of the garden? (1 point)
4 feet
6 feet
9 feet
12 feet
Answers
What equation is equivalent to 9^(x-3)=729?
Answers
The 2nd selection is appropriate.
Answer:
Next one is six
Step-by-step explanation:
Im doing the assignment rn, it always seems about halfway through an edge course brainly users lose braincells because they keep saying next one is 81.333
starting with 25 members a club doubled its membership every year write the function f(n) that expresses the number of members after six years
Answers
now, we know they're doubling every year, so the rate of growth is 100%, so whatever amount, + 100% is just double that much, therefore,
[tex]\bf \qquad \textit{Amount for Exponential Growth}\\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\to &25\\ r=rate\to 100\%\to \frac{100}{100}\to &1.00\\ t=\textit{elapsed time}\to &6\\ \end{cases} \\\\\\ A=25(1+1)^6\implies A=25(2)^6\implies A=1600[/tex]
The number of members after six years is 1600.
We have given that,
starting with 25 members a club doubled its membership every year write the function f(n) that expresses the number of members after six years.
What is the formula for exponential growth?
[tex]A=P(1+r)^t[/tex]
A=Amount
P=initial amount
r=rate
t=time
now, we know they're doubling every year, so the rate of growth is 100%, so whatever amount, + 100% is just double that much, therefore
[tex]A=25(1+1)^6\\A=25(2)^6\\A=1600[/tex]
Therefore we get the number of members after six years is 1600.
To learn more about exponential growth visit:
https://brainly.com/question/7920039
#SPJ2
Which relationship shows an inverse variation?
x: 2,3,4,5
f(x):1,4,9,16
x:1,2,3,4
f(x):2,8,18,32
x:1,2,3,4
f(x):4,3,2,1
X:2,4,6,8
f(x):12,6,4,3,
Answers
Answer:
x : 2,4,6,8
f(x) :12,6,4,3
This table represents the relationship of an inverse variation.
Step-by-step explanation:
We are asked to find which relationship shows an inverse variation.
Inverse variation means that there exist a constant 'k' such that:
f(x)=k/x
or, k=x·f(x)
1)
x : 2, 3, 4, 5
f(x): 1, 4, 9, 16
if x=2 and f(x)=1
k=2
but if x=3 and f(x)=4
we get: k=12.
Hence, we do not obtain a same constant k.
2)
x: 1,2,3,4
f(x):2,8,18,32
when x=1 , f(x)=2
⇒ k=2
when x=2 , f(x)=8
⇒ k=16
Hence, we did not get a same constant 'k'.
3)
x: 1,2,3,4
f(x):4,3,2,1
when x=1, f(x)=4
⇒ k=4
when x=2 , f(x)=3
⇒ k=6
Hence, we did not get a same constant 'k'.
4)
x :2,4,6,8
f(x) :12,6,4,3
when x=2 f(x)=12
⇒ k=2×12=24
when x=4 f(x)=6
⇒ k=4×6=24
when x=6 f(x)=4
⇒ k=6×4=24
when x=8 f(x)=3
⇒ k=8×3=24
Hence, we get a constant 'k=24' for all the values of x.
Hence, option: 4 shows relationship of an inverse variation.
x :2,4,6,8
f(x) :12,6,4,3
Suppose a normal distribution has a mean of 16 and a standard deviation of 4.
A value of 26 is how many standard deviations away from the mean?
−2.5
−1.5
1.5
2.5
Answers
(26 - 16) / 4 = 2.5
Answer:
Correct Answer is 2.5
Step-by-step explanation:
Easy Algebra 2 Rational Expressions question
Answers
x - 8 = 0
x = 8
Currently, the highest tax bracket in united state is____.
A. 1%
B. 10%
C. 0%
D. 35%
Answers
Answer:
35%
Step-by-step explanation:
A store sells 1 gallon of lemonade for 7 dollars and 1 quart of lemonade for 2 dollars. Horace has 11 dollars to buy 6 quarts of lemonade for a party.Explain whether he has enough money.
Answers
Jenny said i'm thinking of fraction that is equivalent to 2/6 the numerator is 8 less than the denominator what fraction is jenney thinking of
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Hope I helped!