Solve the three equations in the table by factoring. Then enter those factors and the solutions in the table.
Equations: x^2 + 10 = 0, 4x^2 + 25 = 0, x^2 + 121 = 0
Factors: _______, ________, _______
solutions: _______,________, _______
Answers
Solutions are denoted by index. Most of the equations you listed has 2 solutions.
Number one cannot be factored using whole numbers.
Number two.
[tex]
4x^2+25=0\Longrightarrow(2x+5)(2x-5)=0 \\
x_1\Longleftrightarrow\boxed{2x+5=0\Longrightarrow x=-\dfrac{5}{2}} \\
x_2\Longleftrightarrow\boxed{2x-5=0\Longrightarrow x=\dfrac{5}{2}}
[/tex]
Number three.
[tex]
x^2+121=0\Longrightarrow(x+11)(x-11)=0 \\
x_1\Longleftrightarrow\boxed{x+11=0\Longrightarrow x=-11} \\
x_2\Longleftrightarrow\boxed{x-11=0\Longrightarrow x=11}
[/tex]
Hope this helps.
Check the picture for the correct answer:
Related Questions
Figure ABCD is a parallelogram.
What is the value of n?
Answers
Answer:
n = 17.
Step-by-step explanation:
The opposite angles of a parallelogram are congruent so we have:
4n - 2 = 2n + 32
4n - 2n = 32 + 2
2n = 34
n = 17.
if a+b+c=-2 and x+y=-9 what is 9x + 4b + 9y +4c + 4a
Answers
Answer:
-89
Step-by-step explanation:
9x + 4b + 9y +4c + 4a (9x+9y)+(4a+4b+4c) =9(x+y)+4(a+b+c)
but : a+b+c = -2 and x+y = -9
9x + 4b + 9y +4c + 4a = 9(-9)+4(-2) = - 81 -8 =-89
I need help please.
Answers
Answer:
Step-by-step explanation:
p^8 q^6 / p ^4 q^3
In this expression the base of numerator and denominator is same:
We will change the division into multiplication and the denominator will become numerator will negative exponents:
p^8 q^6 * p ^-4 q^-3
Now simplify the terms with same base
The exponents of the same base will be added
=p^8+(-4) q^6+(-3)
=p^8-4 q^6-3
=p^4 q^3
The answer is p^4 q^3....
. Solve the triangle. A = 32°, a = 19, b = 12 B = 19.6°, C = 148.4°, c ≈22.5 B = 19.6°, C = 128.4°, c ≈28.1 Cannot be solved B = 19.6°, C = 128.4°, c ≈16.9
Answers
Answer:
Step-by-step explanation:
sin(32)/19 = sin(B)/12
cross multiply
12 sin(32) = 19 sin(B)
sin(B) = 12 sin(32) /19 = 0.334686
B = sin°-1(0.334686)
B = 0.321272 radian
B = (0.321272)*180/pi degrees = 19.55°
C = 180-32-19.55 = 128.45°
sin(32)/19 = sin(128.45)/ c
cross multiply
c sin(32) = 19 sin(128.45)
c = 19 sin(128.45) /sin(32) =28.08....
Solve the equation by using the square root property.
2) (3z - 18)^2 +59 = 14
Answers
Answer:
Step-by-step explanation:
Z = i √5/3 +36
The given equation (3z - 18)^2 + 59 = 14 has no real solution because after isolating and simplifying the squared term, we would be taking the square root of a negative number, which is not possible in the real number system.
To solve the equation (3z - 18)^2 + 59 = 14 using the square root property, follow these steps:
Start by isolating the squared term:
(3z - 18)^2 = 14 - 59
Calculate the right side:
(3z - 18)^2 = -45
Since the equation involves squaring resulting in a negative number, which is not possible in the set of real numbers, this equation has no real solution.
It is important to note that squaring a real number always results in a non-negative number, so a square equal to a negative number indicates there are no real solutions to the equation.
The square root of a number is between 8 and 9. Which of the following could be the value of that number? Select all that apply.
a. 8.6
b. 74
c. 80
d. 81.5
Answers
The square root of 74 is approx 8.6 and that is between 8 and 9
The square root of 80 is approx 8.9 and that is between 8 and 9
~~hope this helps~~
Final answer:
Only options b (74) and c (80) could have their square roots between 8 and 9, as their values lie between 64 (8 squared) and 81 (9 squared).
Explanation:
To find which numbers could have their square roots lying between 8 and 9, we need to consider the squares of these two numbers. 8 squared is 64 and 9 squared is 81. Therefore, any number that has a square root between 8 and 9 must be greater than 64 and less than 81.
Option a (8.6): This number is too small since its square would be much less than 64.Option b (74): This is possible because 74 lies between the squares of 8 and 9.Option c (80): This is also possible for the same reason as option b.Option d (81.5): This number cannot have a square root between 8 and 9 as it is greater than 81.Thus, the values that could be the number with the square root between 8 and 9 are 74 and 80.
Find the sum of each pair of vectors and match it with the magnitude of the resultant vector. PLEASE HELP. Information on the picture
Answers
First of all, let's write this statement in vector form. For the fist vector we have:
Magnitude 3.5 m/s, direction angle 35°:
Let's say this is vector [tex]\vec{A}[/tex], so the magnitude is:
[tex]\left|\vec{A}\right|=3.5m/s[/tex]
And the direction is defined as:
[tex]\theta = 35^{\circ}[/tex]
So the components are:
[tex]Ax=\left|\vec{A}\right| cos\theta \\ \\ Ax=3.5 cos35^{\circ}=2.86m/s \\ \\ \\ Ay=\left|\vec{A}\right| sin\theta \\ \\ Ay=3.5 sin35^{\circ}=2m/s[/tex]
So vector [tex]\vec{A}[/tex] is:
[tex]\vec{A}=2.86i+2j[/tex]
For the second vector:
Magnitude 4 m/s, direction angle 150°:
Let's say this is vector [tex]\vec{B}[/tex], so the magnitude is:
[tex]\left|\vec{B}\right|=4m/s[/tex]
And the direction is defined as:
[tex]\theta = 150^{\circ}[/tex]
So the components are:
[tex]Bx=\left|\vec{B}\right| cos\theta \\ \\ Bx=4 cos150^{\circ}=-2\sqrt{3}m/s \\ \\ \\ By=\left|\vec{B}\right| sin\theta \\ \\ By=4 sin150^{\circ}=2m/s[/tex]
So vector [tex]\vec{B}[/tex] is:
[tex]\vec{B}=-2\sqrt{3}i+2j[/tex]
THE SUM OF THESE TWO VECTORS IS:
[tex]\vec{R}=\vec{A}+\vec{B}=(2.86i+2j)+(-2\sqrt{3}i+2j) \\ \\ \boxed{\vec{R}=-0.60i+4j}[/tex]
THE MAGNITUDE OF THE RESULTANT VECTOR IS:
[tex]\left|\vec{R}\right|=\sqrt{Rx^2+Ry^2} \\ \\ Rx=Ax+Bx \\ \\ Ry=Ay+By \\ \\ \\ \left|\vec{R}\right|=\sqrt{(-0.6^2)+(4)^2} \\ \\ \boxed{\left|\vec{R}\right|=4.05m/s}[/tex]
2. Magnitude 4.5 m/s, direction angle 55°, magnitude 3 m/s, direction angle 135°.Matches to 5.83 m/sMagnitude 4.5 m/s, direction angle 55°:
Let's say this is vector [tex]\vec{C}[/tex], so the magnitude is:
[tex]\left|\vec{C}\right|=4.5m/s[/tex]
And the direction is defined as:
[tex]\theta = 55^{\circ}[/tex]
So the components are:
[tex]Cx=\left|\vec{C}\right| cos\theta \\ \\ Cx=4.5 cos55^{\circ}=2.58m/s \\ \\ \\ Cy=\left|\vec{C}\right| sin\theta \\ \\ Cy=4.5 sin55^{\circ}=3.68m/s[/tex]
So vector [tex]\vec{C}[/tex] is:
[tex]\vec{C}=2.58i+3.68j[/tex]
For the second vector:
Magnitude 3 m/s, direction angle 135°:
Let's say this is vector [tex]\vec{D}[/tex], so the magnitude is:
[tex]\left|\vec{D}\right|=3m/s[/tex]
And the direction is defined as:
[tex]\theta = 135^{\circ}[/tex]
So the components are:
[tex]Dx=\left|\vec{D}\right| cos\theta \\ \\ Dx=3 cos135^{\circ}=-\frac{3\sqrt{2}}{2} \\ \\ \\ Dy=\left|\vec{D}\right| sin\theta \\ \\ Dy=3 sin135^{\circ}=\frac{3\sqrt{2}}{2}[/tex]
So vector [tex]\vec{D}[/tex] is:
[tex]\vec{D}=-\frac{3\sqrt{2}}{2}i+\frac{3\sqrt{2}}{2}j[/tex]
THE SUM OF THESE TWO VECTORS IS:
[tex]\vec{R}=\vec{C}+\vec{D}=(2.58i+3.68j)+(-\frac{3\sqrt{2}}{2}i+\frac{3\sqrt{2}}{2}j) \\ \\ \boxed{\vec{R}=0.46i+5.80j}[/tex]
THE MAGNITUDE OF THE RESULTANT VECTOR IS:
[tex]\left|\vec{R}\right|=\sqrt{(0.46)^2+(5.8)^2} \\ \\ \boxed{\left|\vec{R}\right|=5.83m/s}[/tex]
3. Magnitude 3 m/s, direction angle 70°, magnitude 3 m/s, direction angle 135°.Matches to 3.32 m/sMagnitude 4.5 m/s, direction angle 55°:
This is vector [tex]\vec{E}[/tex], so the magnitude is:
[tex]\left|\vec{E}\right|=3m/s[/tex]
Direction:
[tex]\theta = 70{\circ}[/tex]
Components:
[tex]Ex=\left|\vec{E}\right| cos\theta \\ \\ Ex=3 cos70^{\circ}=1.02m/s \\ \\ \\ Ey=\left|\vec{E}\right| sin\theta \\ \\ Ey=3 sin70^{\circ}=2.82m/s[/tex]
So:
[tex]\vec{E}=1.02i+2.82j[/tex]
For the second vector:
Magnitude 5 m/s, direction angle 210°:
[tex]\vec{F}[/tex]:
[tex]\left|\vec{F}\right|=5m/s[/tex]
Direction:
[tex]\theta = 210^{\circ}[/tex]
Components:
[tex]Fx=5 cos210^{\circ}=-\frac{5\sqrt{3}}{2} \\ \\ \\ Ey=5 sin210^{\circ}=-\frac{5}{2}[/tex]
Then:
[tex]\vec{F}=-\frac{5\sqrt{3}}{2} i-\frac{5}{2}j[/tex]
THE SUM OF THESE TWO VECTORS IS:
[tex]\vec{R}=(1.02i+2.82j)+(-\frac{5\sqrt{3}}{2}i-\frac{5}{2}j) \\ \\ \boxed{\vec{R}=-3.31i+0.32j}[/tex]
THE MAGNITUDE OF THE RESULTANT VECTOR IS:
[tex]\left|\vec{R}\right|=\sqrt{(-3.31)^2+(0.32)^2} \\ \\ \boxed{\left|\vec{R}\right|=3.32m/s}[/tex]
4. Magnitude 6 m/s, direction angle 120°, magnitude 2 m/s, direction angle 140°.Matches to 5.29 m/sMagnitude 6 m/s, direction angle 120°:
[tex]\left|\vec{W}\right|=6m/s[/tex]
Direction:
[tex]\theta = 120^{\circ}[/tex]
Components:
[tex]Wx=6 cos120^{\circ}=-3m/s \\ \\ \\ Wy=6 sin120^{\circ}=3\sqrt{3}m/s[/tex]
So:
[tex]\vec{W}=-3i+3\sqrt{3}j[/tex]
For the second vector:
Magnitude 2 m/s, direction angle 240°:
[tex]\vec{Z}[/tex]:
[tex]\left|\vec{Z}\right|=2m/s[/tex]
Direction:
[tex]\theta = 240^{\circ}[/tex]
Components:
[tex]Zx=2 cos240^{\circ}=-1 \\ \\ \\ Zy=2 sin240^{\circ}=-\sqrt{3}[/tex]
Then:
[tex]\vec{Z}=-i-\sqrt{3}j[/tex]
THE SUM OF THESE TWO VECTORS IS:
[tex]\vec{R}=(-3i+3\sqrt{3}j)+(-i-\sqrt{3}j) \\ \\ \boxed{\vec{R}=-4i+2\sqrt{3}j}[/tex]
THE MAGNITUDE OF THE RESULTANT VECTOR IS:
[tex]\left|\vec{R}\right|=\sqrt{(-4)^2+(2\sqrt{3})^2} \\ \\ \boxed{\left|\vec{R}\right|=5.29m/s}[/tex]
what is the area of the figure. please help show steps
Answers
Answer: [tex]143.99\ ft^2[/tex]
Step-by-step explanation:
We need to find the lenght AC and BC of the triangle by applying these identities:
[tex]cos\alpha=\frac{adjacent}{hypotenuse} \\\\sin\alpha=\frac{opposite}{hypotenuse}[/tex]
Then, AC is:
[tex]sin(45\°)=\frac{AC}{24}\\\\AC=24*sin(45\°)\\\\AC=16.97\ ft[/tex]
And BC is:
[tex]cos(45\°)=\frac{BC}{24}\\\\BC=24*cos(45\°)\\\\BC=16.97\ ft[/tex]
The area will be:
[tex]A=\frac{AC*BC}{2}[/tex]
Substituting values, we get:
[tex]A=\frac{(16.97\ ft)(16.97\ ft)}{2}=143.99\ ft^2[/tex]
A cylinder has a radius of 6 inches and is 15 inches tall. What is the approximate volume of the cylinder? Express the answer in terms of pi.
Answers
Answer:
The volume of cylinder = 540π inches²
Step-by-step explanation:
Points to remember
Volume of cylinder = πr²h
Where r - Radius of cylinder and
h - Height of cylinder
To find the volume of cylinder
Here r = 6 inches and height h = 15 inches
Volume = πr²h
= π * 6² * 15
= π * 36 * 15
= 540 πinches²
The volume of cylinder = 540π inches²
|
Which expression is equivalent to the following complex fraction?
.
Answers
Answer:
Yes, A is correct.
Solve for x.
5(x + 1) = 4(x + 8)
Answers
Answer:
x =27
Step-by-step explanation:
5(x + 1) = 4(x + 8)
Distribute.
5x + 5 = 4x + 32
Move x term onto one side.
x + 5 = 32
Move integer onto one side.
x = 27
Suppose f(x) = x^2. What is the graph of g(x) =f(4x)?
Answers
Answer:
your y-intercept is 0 and slope is 4 so any line with zero slope it will be horizontal
Answer: On mine it is D
Step-by-step explanation:
It is the small one facing up
Joe Bob wanted to find out how many hours of exercise the students at his school gets each week. He went to the school's gym and asked the following question:
"Do you work out every day like a healthy person, or are you a lazy couch potato who only works out once in a while?"
What is another way Joe Bob could word his question so that it does not contain any bias?
Answers
Although I am unsure what this question has to do with Mathematics, Joe Bob could simply say "How often do you work out in a week?"
Which polynomial is prime?
3x3 + 3x2 – 2x – 2
3x3 – 2x2 + 3x – 4
4x3 + 2x2 + 6x + 3
4x3 + 4x2 – 3x – 3
Answers
The prime polynomial out of the given options is 3x^3 + 3x^2 - 2x - 2.
Explanation:Out of the given polynomials, the polynomial that is prime is 3x3 + 3x2 - 2x - 2.
A polynomial is considered prime if it cannot be factored into a product of lower degree polynomials with integral coefficients.
In this case, the polynomial 3x3 + 3x2 - 2x - 2 is a cubic polynomial and cannot be factored further, so it is prime.
perform the indicated operation: (-1 1/2)(-3/2)
Answers
The operation (-1 1/2)(-3/2) gives 9/4 or 2 1/4 as a mixed number.
To perform the indicated operation: (-1 1/2)(-3/2), we need to multiply the two numbers.
First, convert the mixed number -1 1/2 to an improper fraction. It is -3/2 because 1 1/2 is equal to 3/2 and we keep the negative sign.Now, multiply the two fractions: -3/2 * -3/2.Since the signs are the same (both negative), the answer will be positive.Multiply the numerators: 3 * 3 = 9.Multiply the denominators: 2 * 2 = 4.So, the answer is 9/4, or 2 1/4 when converted to a mixed number.5.
The letters A, L, G, E, B, R, A are on 7 tiles in a bag, one letter on each tile. If you select tiles randomly from
the bag and place them in a row from left to right, what is the probability the tiles will spell out ALGEBRA?
(Lesson 19.2) (1 point)
Answers
Answer:
1/2520
Step-by-step explanation:
First you have to find out how many different combinations can be created
7×6×5×4×3×2×1 = 5040
There is only two combinations that will spell out algebra
2/5040= 1/2520
A combination of a conditional statement and its converse written in the “if and only if” form. Both the conditional and the converse must be true before writing this statement .
Answers
Answer:
An angle is 90° if and only if it is a right angle.
Explanation:
The statement is: If an angle is 90°, then it is a right angle.
The converse of this statement would be:
If an angle is a right angle, it is 90°.
Clearly, both the conditional and converse of this statement is true.
How would u solve this problem ?
Answers
Answer:
9×80=x×15
x=58lbs
Step-by-step explanation:
Considering no frictions applyd, the value of the report of the two forces ( F- the action force and R- the resistance force) equals the value of the report between the value of the distance from the folcrum to the rock and the value of the distance from the fulcrum to the active force
A company makes batteries with an average life span of 300
hours with a standard deviation of 75 hours. Assuming the
distribution is approximated by a normal curve fine the
probability that the battery will last:(give 4 decimal places for
each answer)
a. Less than 250 hours ___________
b. Between 225 and 375 hours __________
c. More than 400 hours ______________
Answers
Answer:
a) 0.2514
b) 0.6827
c) 0.0918
Step-by-step explanation:
Average life span of batteries = u = 300 hours
Standard deviation = s = 75 hours
Given that the distribution of life span of batteries is normally distributed, so we can use z-score to find the said probabilities.
Part a) Less than 250 hours
In order to find the probability that the life span of battery will be less than 250 hours we need to convert x = 250 into z-score and then use z-score to find the probability from the z-table.
The formula for z-score is:
[tex]z=\frac{x-u}{s}[/tex]
Using the values, we get:
[tex]z=\frac{250-300}{75}=-0.67[/tex]
From the z-table or z-calculator the probability of z-score being less than - 0.67 comes out to be 0.2514
P(z < -0.67) = 0.2514
Thus, the the probability that the life span of battery will be less than 250 hours is 0.2514
Part b) Between 225 and 375 hours
In order to find the probability that the life span of battery will be between 225 and 375 hours we need to convert them into into z-scores and then use z-score to find the probability from the z-table.
225 into z-score will be:
[tex]z=\frac{225-300}{75}=-1[/tex]
375 into z-score will be:
[tex]z=\frac{375-300}{75}=1[/tex]
Thus, from the z-table we now need to find that probability of z-score being in between -1 and 1. From the z-table this value comes out to be:
P(-1 < z < 1 ) = 0.6827
Thus, the probability that the life span of battery will be between 225 and 375 hours is 0.6827
Part c) More than 400 hours
In order to find the probability that the life span of battery will be more than 400 hours we need to convert x = 400 into z-score and then use z-score to find the probability from the z-table.
The formula for z-score is:
[tex]z=\frac{x-u}{s}[/tex]
Using the values, we get:
[tex]z=\frac{400-300}{75}=1.33[/tex]
From the z-table the probability of z score being more than 1.33 comes out to be:
P( z > 1.33) = 0.0918
Thus, the probability that the life span of battery will be more than 400 hours is 0.0918
The altitude of the hypotenuse of a right triangle divides the hypotenuse into segments of lengths 77 and 7. what is the length of the altitude?
Answers
Answer:
[tex]h=7\sqrt{11}\ units[/tex]
Step-by-step explanation:
The altitude to the hypotenuse of a right tringle is the geometric mean of the two segments that it divides the hypotenuse into.
1st segment = 77 units
2nd segment = 7 units
Altitude = h units
So,
[tex]h^2=77\cdot 7\\ \\h^2 =7\cdot 11\cdot 7\\ \\h=\sqrt{7\cdot 11\cdot 7}=7\sqrt{11}[/tex]
A rectangle has vertices at (-1,6), (-1,-2), (3,6), and (3,-2). Sara says the area of the rectangle is 16 square units and her
work is shown below
Steps
Step 1
Step 2
Step 3
Sara's Work
Base: 113-4
Height: 161+F2-4
Area: 4x4-16 square units
Where, if at all, did Sara first make a mistake in finding the area of the rectangle?
Step 1
Step 2
Step 3
no mistake
Answers
Answer:
Step 2
Step-by-step explanation:
Let
[tex]A(-1,6), B(-1,-2), C(3,6), D(3,-2)[/tex]
Plot the vertices to better understand the problem
see the attached figure
The area of the rectangle is equal to
[tex]A=bh[/tex]
we have
[tex]b=BD\\ h=BA[/tex]
step 1
Find the base b (BD)
[tex] B(-1,-2),D(3,-2)[/tex]
[tex]b=\left|3\right|+\left|-1\right|=4\ units[/tex]
step 1 is correct
step 2
Find the height h (BA)
[tex]B(-1,-2),A(-1,6)[/tex]
[tex]h=\left|6\right|+\left|-2\right|=8\ units[/tex]
step 2 is not correct
step 3
Find the area
[tex]A=(4)(8)=32\ units^{2}[/tex]
Therefore
Sara first make a mistake in finding the area of the rectangle in Step 2
Answer:
step 2
Step-by-step explanation:
Suppose you and some friends are going to the movies. The amount of money you spend for tickets varies directly with the number of people buying
tickets. If you spend $48 for six tickets, what is the constant of variation?
e r song to the movies. The amount of money you spend for tckets vantes directly w
6
Answers
Answer:
The constant variation, and the price of one ticket is 8.
Step-by-step explanation:
What is the number three thousand eighty expressed in scientific notation?
Answers
Answer:
3.08 x [tex]10^{3}[/tex]
Step-by-step explanation:
3080 = 3.08 x 1000 = 3.08 x [tex]10^{3}[/tex]
Which is the graph of f(x) =4(1/2)^x
Answers
Answer:
The graph in the attached figure
Step-by-step explanation:
we have
[tex]f(x)=4(\frac{1}{2})^{x}[/tex]
This is a exponential function of the form
[tex]y=a(b)^{x}[/tex]
where
a is the initial value
b is the base
r is the rate
b=1+r
In this problem we have
a=4 ----> initial value (y-intercept)
b=1/2
so
1+r=1/2
r=1/2-1=-1/2
r=-0.5=-50% ----> is negative because is a decrease rate
using a graphing tool
The graph in the attached figure
What is the length of the leg.s of the triangle below
Answers
Answer:
10
Step-by-step explanation:
What are the zeros of r(p) = -p2 + 14p?
Answers
[tex]-p^2 + 14p=0\\-p(p-14)=0\\p=0 \vee p=14[/tex]
Find the student's error in solving the following
inequality.
31 <-5x + 6
25 <-5x
-5
Answers
x>7
Step-by-step explanation:
when dividing by a (-)
the inequality sign changes
Answer:
"The student should have switched the direction of the inequality sign to get –5> x for a final answer."
and the second one is:
The student should have added 4 to all parts (left, middle, and right) to get 6 < –3x < 9.
Step-by-step explanation:
i got that on edge
where d is the length of the diameter. If d is a rational number, what can you conclude about the circumference?
Answers
Answer:
The circumference is a irrational number
Step-by-step explanation:
we know that
The circumference of a circle is equal to
[tex]C=\pi D[/tex]
where
D is the diameter
In this problem we have that
[tex]D=d\ units[/tex] ---> is a rational number
substitute
[tex]C=\pi (d)[/tex]
[tex]C=d\pi\ units[/tex]
Remember that
The number π is a irrational number
and
If you multiply a rational number by a irrational number, the result is a irrational number
therefore
The circumference is a irrational number
Marcos purchases a top-up card for his pre-paid cell phone. His remaining balance, B, can be modeled by the equation B=40−0.1n, where n is the number of minutes he's talked since purchasing the card.
a) How much money was on the card when he purchased it? $______. Which intercept is this? B-intercept or N-intercept?
b) How many minutes will he have talked when he runs out of money? $_____. Which intercept is this? B-intercept or n-intercept ?
c) What is the slope of this equation?________ . What are the units on the slope? Minute , dollars per minute ,minutes per dollars or dollars ?
Answers
Answer:
Part a) When Marcos purchased the card, the balance on the card was $40
This is the B-intercept
Part b) Mark will have spoken 400 minutes when he runs out of money
This is the n-intercept
part c) The slope of the equation is -0.1 and the units are dollars per minute
Step-by-step explanation:
we have
[tex]B=40-0.1n[/tex]
where
B is balance in dollars on the card
n is the number of minutes
Part a) How much money was on the card when he purchased it? $______. Which intercept is this? B-intercept or N-intercept?
we know that
The B-intercept is the value of B when the value of n is equal to zero
so
For n=0
substitute and find the value of B
[tex]B=40-0.1(0)=\$40[/tex]
therefore
When Marcos purchased the card, the balance on the card was $40
This is the B-intercept
Part b) How many minutes will he have talked when he runs out of money? $_____. Which intercept is this? B-intercept or n-intercept ?
we know that
The n-intercept is the value of n when the value of B is equal to zero
so
For B=0
substitute and find the value of n
[tex]0=40-0.1n[/tex]
[tex]0.1n=40[/tex]
[tex]n=400\ minutes[/tex]
therefore
Mark will have spoken 400 minutes when he runs out of money
This is the n-intercept
Part c) What is the slope of this equation?________ . What are the units on the slope? Minute , dollars per minute ,minutes per dollars or dollars ?
we have
[tex]B=40-0.1n[/tex]
This is is the equation of the line into slope intercept form
[tex]m=-0.1\frac{\$}{minute}[/tex] -----> slope of the equation
[tex]b=40[/tex] ------> the B-intercept
The units of the slope are dollars per minute
Marcos purchased a top-up card with an initial balance of $40 (B-intercept). He will run out of money after 400 minutes of call time (n-intercept). The charge rate is $0.1 per minute (slope).
Explanation:a) The money on the card when he purchased it is given by the constant term in the equation, which is $40. This is the B-intercept, because it is the value of B when n = 0 (meaning no minutes have been used).
b) Marcos will have run out of money when B = 0. To find this, set B = 0 and solve for n: 0 = 40 - 0.1n, which leads to n = 400. So, Marcos will have talked for 400 minutes when he runs out of money. This is the n-intercept. It represents the value of n when B = 0 (meaning there is no money left on the card).
c) The slope of this equation is -0.1. In the context of this problem, the slope represents the rate at which money is deducted from the balance for each minute of talk time. Therefore, the units on the slope are dollars per minute.
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The paragraph below comes from the rental agreement Susan signed when she opened her account at Super Video.
"All rentals are due back by midnight of the due date as printed on the transaction receipt. Any rental not received by midnight on the day it is due is subject to a late charge of $1.50 for each day it is late. Any rental not returned by the fifth day after the due date will be transferred to a sale. The Customer will then be required to pay the purchase price of the item in addition to five (5) days of late fees. The Customer will not be required to return the product once the total balance is paid."
As of today, Susan's movie is currently five days late. She knows that if she doesn't get the movie back tonight, she will be charged $9.99, the purchase price of the movie, plus five days' worth of late fees. A round trip cab ride to the video store will cost about $10.
Which of the following statements is true?
a.
Taking a cab to return the movie is the cheapest action. Susan should call a cab.
b.
It would cost about the same to keep or return the movie. Susan should keep it.
c.
Keeping the movie and paying the purchase price and late fees is the cheapest option.
d.
If Susan returns the movie, she should not have to pay late fees. She should return it.
ANSWER IS D
Answers
Answer:
c. Keeping the movie and paying the purchase price and late fees is the cheaper option.
Step-by-step explanation:
1. If Susan takes a cab and pays late fees
Cost of cab = $10.00
Late fees = 5 × 1.50 = 7.50
TOTAL = $17.50
2. If Susan keeps the movie
Purchase price of movie = $9.99
Late fees = 5 × 1.50 = 7.50
TOTAL = $17.49
Keeping the movie and paying the purchase price and late fees is the cheapest option.
a. is wrong. Taking a cab is the more expensive option.
b. is wrong. Susan contracted to return the movie, so she should try to do so.
c. is correct. This is a statement of fact, not a judgement call.
d. is wrong. Susan contracted to pay the late fees if she did not return the video (but she should still return it).