Answer:
distance between the points (3,4) and (1,5) = 2.236
Step-by-step explanation:
The distance between two points is the length of the path connecting them. The shortest path distance is a straight line. In a 2 dimensional plane, the distance between points (X1, Y1) and (X2, Y2) is given by the Pythagorean theorem:
[tex]d = \sqrt {(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}[/tex]'
For:
[tex](X1, Y1) = (3, 4)\\\\(X2, Y2) = (1, 5)[/tex]
[tex]d = \sqrt {(1 - 3)^2 + (5 - 4)^2}\\\\d = \sqrt {(-2)^2 + (1)^2}\\\\d = \sqrt {{4} + {1}}\\\\d = \sqrt {5}\\\\d = 2.236068[/tex]
Answer:
Exact distance is [tex]\sqrt{5}[/tex]
Approximate distance is 2.2361
Round the decimal value however your teacher instructs.
====================================================
Work Shown:
I used the distance formula to get the following.
[tex](x_1,y_1) = (3,4) \text{ and } (x_2, y_2) = (1,5)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(3-1)^2 + (4-5)^2}\\\\d = \sqrt{(2)^2 + (-1)^2}\\\\d = \sqrt{4 + 1}\\\\d = \sqrt{5}\\\\d \approx 2.2361\\\\[/tex]
----------------
A slight alternative is to plot the points A(3,4) and B(1,5) and C(3,5).
Points A and B are the original points we were given. Point C helps form a right triangle. The hypotenuse is AB and the legs are AC and BC.
Leg AC = 1 unit and leg BC = 2 units
Use the pythagorean theorem [tex]a^2+b^2 = c^2[/tex] to plug in a = 1 and b = 2 to find that the hypotenuse is exactly [tex]c = \sqrt{5}[/tex] units long, which is the distance from A to B.
what number is equal to y????????????
1/2. (.5) 2. Frosty and the kids travel 2 miles through town in 2 hours. What is the unit rate per hour?~ is the question, can you show me how to find a unit rate?
EXPLANATION
Frosty and kids travel ---------------> 2 miles / 2 hours
The unit rate will be:
[tex]\text{unit rate = }\frac{2\text{ miles}}{2\text{ hours}}=\frac{1\text{ mile}}{\text{hour}}=\text{ 1mph}[/tex]I need assistance in intermediate algebra… Graph the solution to the inequality.Right the solution to the inequality both insert builder notation and interval notation
Answer:
Interval notation:
[tex]\lbrack-5,8)[/tex]Set-builder notation:
[tex]\lbrace x|-5≤x<8\rbrace[/tex]Plot of the solution:
Step-by-step explanation:
First, let's put the solution of the inequality into simpler words. We're looking for values of x that are between 5 and 8, including 5 and excluding 8.
This way, the interval notation for the solution is:
[tex]\lbrack-5,8)[/tex]As a set, we would read the solution as: "The set of all x's, such that x is greater or equal than -5 and less than 8 than 0". In set builder notation, this is:
[tex]\lbrace x|-5≤x<8\rbrace[/tex]The plot of the inequality would be:
Where the full end represents a square bracket and the empty end represents a parentheses.
The manager of a pizza restaurant recorded the total number of pizzas delivered after x weeks in this table. Which statement is true?
A. There was an increase of 83.5 pizzas each week from week 4 to week 6.
B. There was an increase of 34.5 pizzas each week from week 4 to week 6.
C. There was an increase of 50 pizzas each week from week 4 to week 6.
D. There was an increase of 28 pizzas each week from week 4 to week 6.
a) There was an increase of 83.5 pizzas each week from week 4 to week 6.
How to find the increase in pizza sales?Increase in no of pizzas from 4 to 5th week = 356 - 278 = 78
78 pizzas sales increased.
Increase in no of pizzas from 5 to 6th week = 445 - 356 = 89
89 pizzas sales increased.
On average = 78 + 89/2
= 167/2
= 83.5
Therefore,
There was an increase of 83.5 pizzas each week from week 4 to week 6.
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Which of the following polynomials has an even degree and a negative leading coefficient?
The function has an even degree if the the number of turns is an odd number.
The function has a negative leading coefficient if the behavior of the graph goes to the negative infinity.
From the choices, only this graph satisfied the conditions.
The graph has 3 turns (an odd number)
and it goes to the negative infinity.
if 150 bars equals 350 hars, and 200 gars equals 25 hars, how many bars is 112.5 hars
Answer:
48.214 bars
Step-by-step explanation:
112.5 hars * (150 bars / 350 hars) = 48.214 bars
A partial payment is made on the date indicated. Use the United States rule to determine the
balance due on the note at the date of maturity. (The Effective Date is the date the note was
written.) Assume the year is not a leap year.
The balance due on the note at the date of maturity is $___ (round to the nearest cent as needed)
The balance due on the note at the date of maturity is $1012.49
Given,
Principal = $2000
Int rate(r) = 5%
Effective date April 1
The partial payment date May 1
Maturity date June 1
partial payment is being made on May 1
Interest from April 1 to May 1 for 30 days and is calculated as:
$2000 x 0.05 x (30/365) = $8.21
Interest Amount deducted from the principal = $2000 - $8.21 = $1991.79
Amount applied to the principal = $1000 - $8.21 = $991.79
Principal due = $2000 - $991.79 =$1008.21
Interest on new principal $1008.215 will be for (61` - 30 ) is 31 days
interest due = $1008.21 x 0.05 x (31/365) = $4.28
Account due on maturity (Total due) is $1012.49
What is the principal amount ?
The principal is the amount of debt originally borrowed that remains unpaid. This amount does not include accrued unpaid interest related to the debt. The term can also refer to a principal participant in a contract or other transaction. Home loan equity is the amount of money originally borrowed by the lender, and it can also refer to the amount of money remaining when the loan is paid off.
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Start with 16÷8. Rewrite as an equivalent multiplication expression using the multiplicative inverse of 8.
Using the multiplicative inverse of 8, we will find the equivalent expression:
16*(1/8)
How to rewrite the quotient?
Here we have a quotient.
16/8
And we want to rewrite this as a product by using the multiplicative inverse of number 8.
Remember that for any number x, the multiplicative inverse y is such:
x*y = 1
Solving that for y we get:
y = 1/x
Then the multiplicative inverse of 8 is:
1/8
So, dividing by 8 (like in the quotient) is equivalent to multiply by (1/8), then we can rewrite the quotient as:
16/8 = 16*(1/8)
So the equivalent expression is 16*(1/8)
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Find volume and weight
The volume of the steel after the hole is cut is 32inches³.
The total weight of the drawing is 960 oz
What is the volume and weight?The volume of the shape that is being drawn is the difference in the volume of the rectangle and the volume of the hole. Th volume of an object is the amount of space that is in the object.
A rectangular prism is a three dimensional object that has 6 faces, 12 edges and 8 vertices.
Volume of a rectangular prism = length x width x height
3.77 x 9.32 x 1 = 35.14 inches³
The shape of the hole would be a cylinder. Thus, the formula for the volume of a cylinder would be used to determine the volume of the hole.
Volume of a cylinder = πr²h
Where:
π = 3.14 r = radius = diameter /2 = 1 h = height3.14 x 1² x 1 = 3.14 inches³
Volume of the steel after the hole is cut = 35.14 inches³ - 3.14 inches³ = 32inches³.
Total weight of the drawing = 32 inches x 30 = 960 oz
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Claire bought 5 kg of apples and 2 kg of bananas and paid altogether $22 Dale bought 4 kg of apples and 6 kg of bananas and paid altogether $33 Use matrices to find the cost of 1 kg of bananas
Answer:
$3.5
Explanation:
Let the cost of 1 kg of apples = x
Let the cost of 1 kg of bananas =y
Claire bought 5 kg of apples and 2 kg of bananas and paid altogether $22.
[tex]5x+2y=22[/tex]Dale bought 4 kg of apples and 6 kg of bananas and paid altogether $33.
[tex]4x+6y=33[/tex]We set up the system of linear equations as a matrix below:
[tex]\begin{bmatrix}{5} & {2} & \\ {4} & {6} & {}{}\end{bmatrix}\begin{bmatrix}{x} & \\ {y} & {}{}\end{bmatrix}=\begin{bmatrix}{22} & \\ {33} & {}{}\end{bmatrix}[/tex]We then solve for the variables x and y as follows.
[tex]\begin{gathered} \begin{bmatrix}{x} & \\ {y} & {}{}\end{bmatrix}=\begin{bmatrix}{5} & {2} & \\ {4} & {6} & {}{}\end{bmatrix}^{-1}\begin{bmatrix}{22} & \\ {33} & {}{}\end{bmatrix} \\ =\frac{1}{30-8}\begin{bmatrix}{6} & {-2} & \\ {-4} & {5} & {}{}\end{bmatrix}\begin{bmatrix}{22} & \\ {33} & {}{}\end{bmatrix} \\ =\frac{1}{22}\begin{bmatrix}{6} & {-2} & \\ {-4} & {5} & {}{}\end{bmatrix}\begin{bmatrix}{22} & \\ {33} & {}{}\end{bmatrix} \end{gathered}[/tex]We proceed to simplify further.
[tex]\begin{gathered} =\begin{bmatrix}{\frac{6}{22}} & {-\frac{2}{22}} & \\ {-\frac{4}{22}} & {\frac{5}{22}} & {}{}\end{bmatrix}\begin{bmatrix}{22} & \\ {33} & {}{}\end{bmatrix} \\ =\begin{bmatrix}{\frac{6}{22}\times22-\frac{2}{22}\times33} & {} & \\ {\frac{-4}{22}\times22+\frac{5}{22}\times33} & & {}{}\end{bmatrix} \\ =\begin{bmatrix}{6-3} & {} & \\ {-4+7.5} & & {}{}\end{bmatrix} \\ =\begin{bmatrix}{3} & {} & \\ {3.5} & & {}{}\end{bmatrix} \end{gathered}[/tex]Therefore:
x=3 and y=3.5.
The cost of 1 kg of bananas is $3.5.
In a random sample of 325 students at a university, 260 stated that they were nonsmokers. Based on this sample, compute a 99% confidence interval for the proportion of all students at the university who are nonsmokers. Then find the lower limit and upper limit of the 99% confidence interval. Carry your intermediate computations to at least three decimal places. Round your answers to two decimal places. (If necessary, consult a list of formulas.) Lower limit: $ ? Upper limit:
Confidence interval is written as
Sample proportion +/- margin of error
The formula for determining margin of error is
[tex]\begin{gathered} \text{margin of error = z }\times\text{ }\sqrt[\square]{\frac{pq}{n}} \\ \end{gathered}[/tex]where
z represents the z score corresponding to the confidence interval
p represents the sample proportion. It also means the probability of success
q represents the probability of failure
q = 1 - p
p = x/n
where
n represents the number of samples
x represents the number of success
From the information given,
n = 325
x = 260
p = 260/325 = 0.8
q = 1 - p = 1 - 0.8 = 0.2
To determine the z score, we would subtract the confidence level from 100 to get alpha, a
Thus
a = 1 - 0.99 = 0.01
a/2 = 0.01/2 = 0.005
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.005 = 0.995
The z score corresponding to the area on the z scores table is 2.576. Thus, the z score for a 99% confidence interval is 2.576
Thus, the 99% confidence interval is
[tex]\begin{gathered} 0.8\text{ }\pm\text{ 2.576 }\frac{\sqrt[\square]{0.8\times0.2}}{325} \\ 0.8\text{ }\pm\text{ 2.576 x 0.022} \\ 0.8\text{ }\pm0.057 \end{gathered}[/tex]Thus,
the lower limit is
0.8 - 0.057 = 0.743
the upper limit is
0.8 + 0.057 = 0.857
to determine whether the relation is a function. {(-6,15). (-12, -10), (-15, 11), (8, -14), (16, 1), (-10, -7)}.
The relation; {(-6,15). (-12, -10), (-15, 11), (8, -14), (16, 1), (-10, -7)} as given in the task content is; a function.
What kind of relation is a function?It follows from the task content that the relation is to be determined as being a function or not.
Since the definition of is such that; a function from a set X to a set Y assigns only one element of Y to each value of X.
In this regard, the set of possible values of x is called the domain of the function while the set y is called the range/codomain of the function.
Hence, since the relation given assigns only one y-value to each x-value, the relation given is therefore a function.
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(14−3 to the 2nd power +1) to the 2nd power1÷3⋅1/4
answers: 1, 3, 144, 432.
The solution to the expression (14−3 to the 2nd power +1) to the 2nd power1÷3⋅1/4 is 3
How to evaluate the expression?The expression is given as
(14−3 to the 2nd power +1) to the 2nd power1÷3⋅1/4
Rewrite the expression properly
So, we have
(14 - 3² + 1)² ÷ 3 * 1/4
Evaluate the exponent
So, we have
(14 - 9 + 1)² ÷ 3 * 1/4
Evaluate the sum and the difference
So, we have
6² ÷ 3 * 1/4
Evaluate the exponent of 6
So, we have
36 ÷ 3 * 1/4
This gives
36 x 1/3 x 1/4
Evaluate
3
Hence, the value of the expression is 3
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Subjects in an experiment take either an aspirin or a placebo as part of a study on heart attack prevention. The use of a placebo is an example of incorporating what aspect of successful experimental design?
Given the definitions of
blocking is the arranging of experimental units in groups (blocks) that are similar to one another
replication experiment is typically performed by obtaining test results on 20 samples of the same material and then calculating the mean, standard deviation, and coefficient of variation
randomized experiments are the experiments that allow the greatest reliability and validity of statistical estimates of treatment effects
in Control Experiment all variable factors have been kept constant and which is used as a standard of comparison to the experimental component in a controlled experiment
since
the sampling group could be either in group a or b (aspirin or placebo)
this expample is a blocking experiment
Correct answer
option A
A triangle with vertices (−1, 1), (2,−1), and (3, 0) is translated using the rule (x,y)→(x+2, y−6). What are the coordinates of the image?
The coordinates are (1, -5),(4, -7) and (5, -6)
What is Translation?
In mathematics, a translation is the up, down, left, or right movement of a shape. Because the translated shapes appear to be exactly the same size as the original ones, they are consistent with one another. Just one or more directions have been altered. There is no change in the shape because it is simply being moved from one location to another.
Given,
(−1, 1), (2,−1), and (3, 0)
The translation rule:
(x,y)→(x+2, y−6)
In the case (-1, 1):
(x, y)→(-1+2, 1−6)
(x, y)→(1, -5)
In case (2, -1):
(x,y)→(2+2, -1−6)
(x,y)→(4, -7)
In case (3,0):
(x,y)→(3+2, 0−6)
(x,y)→(5, −6)
Hence, The coordinates are (1, -5),(4, -7) and (5, -6)
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Please help! Create a scatterplot for the data in the table. Let English scores be X and History Scores be Y.
Part 2: draw line of fit
Part 3: choose two points, find slope, and record slope decimal
A way to pinpoint a point's location on the planet is through the use of a coordinate system. In most coordinate systems, a point's location is determined by two numbers called a coordinate. Each of these values represents the separation between the point and the origin, a fixed point of reference.
Explain about the coordinate system?A two-dimensional number line, such as two perpendicular axes, can be thought of as a coordinate system.
The x-axis stands for the horizontal axis, and the y-axis for the vertical axis.
A coordinate system's origin is its centre (in which the lines intersect). The axes cross if x and y are both 0.
The coordinates of the origin are (0, 0).
for the posed query.
"English score" is one of the independent variables on the x-axis.
The dependent variables "History score" are displayed on the y-axis.
The scattered points are used to plot the graph for the provided table.
Take note of these two points on the graph:
(x₁, y₁) = (60, 65) (60, 65)
(x₂, y₂) = (61, 61) (61, 61)
The slope will then be;
m = (y2 - y1)/(x2 - x1) is the slope.
the values in.
m = (61 - 65)/(61 - 60) (61 - 60)
m = -4
The slope is -4.
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can someone help me on this
Answer: A, D, E, should be correct because the others are equal
Step-by-step explanation:
help mee pleasee!!
thank you <3
The function for the cost C(x) of printing the newsletter is :
C(x) = 75 + 0.25x
In this question, we have been given the cost of producing a newsletter is an initial charge of $75 for formatting and editing plus $0.25 for printing each copy.
We need to express the cost C(x) of printing the newsletter as a function of x i.e., the number of copies printed.
Here $75 is the fixed cost.
And the cost of printing 'x' copies would be 0.25x
So, we get a function C(x) = 75 + 0.25x
Therefore, the function for the cost C(x) of printing the newsletter is :
C(x) = 75 + 0.25x
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One side of a rectangle is 7 feet shorter than twice and other side find the length of the shorter side if we also know that the perimeter of the rectangle is 100 feet.
The perimeter of a rectangle is 2(l+b).
The length and breadth of a rectangle are 31 ft and 19 ft respectively.
How to find the length and breadth of a rectangle?Let the other side of a rectangle = b
And the one side of a rectangle = l = 2b - 7 ft
The perimeter of a rectangle = 2(l+b) = 100 ft.
2(2b - 7+ b) = 100
2(3b - 7) = 100
3b - 7 = 50
3b = 57
b = 57/3ft
b = 19ft
l = 2b - 7
l = 2*19 - 7
l = 38 - 7
l = 31
l = 31ft
Therefore, length = 31 ft. and breadth = 19ft.
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solve in the substitution method pleasex - 2y = -5x + 5y = 2
To solve the system of equations:
[tex]\begin{gathered} x-2y=-5 \\ x+5y=2 \end{gathered}[/tex]by the substiturion method we need to solve one of the equations for one of the variables, then we substitute this value in the other equation and solve for the remaining variable. Let's apply this method to the system.
First we solve the first equation for x:
[tex]x=2y-5[/tex]now we plug this value in the second equation:
[tex]\begin{gathered} 2y-5+5y=2 \\ 7y=5+2 \\ 7y=7 \\ y=\frac{7}{7} \\ y=1 \end{gathered}[/tex]Hence y=1. Once we have the value of y we substiute it in the equation for x:
[tex]\begin{gathered} x=2(1)-5 \\ x=2-5 \\ x=-3 \end{gathered}[/tex]Therefore the solution of the system is x=-3 and y=1
Write the decimal as a fraction.0.6 = [?]Simplify your answer completely.
0.6 is a decimal and it can be converted to fraction by moving the dot to the right sides and dividing by the number of zero that existed by the dot movement to the right.
[tex]\begin{gathered} 0.6=\frac{6}{10}=\frac{3}{5} \\ \end{gathered}[/tex]The coordinates of the point U are (-1,6) and the coordinates of point V are(-9,6). What is the distance, in units, between the point U and point V?
The distance between two points (a,b) and (c,d) is given by
[tex]d=\sqrt[]{(c-a)^2+(d-b)^2}[/tex]Here u = (-1,6) and v=(-9,6)
Hence the distance is given by
[tex]\begin{gathered} d=\sqrt[]{(-9+1)^2+(6-6)^2_{}} \\ d=\sqrt[]{-8^2} \\ d=\sqrt[]{64} \\ d=8 \end{gathered}[/tex]Can anyone help me with this?
the difference b and 2 is less than 25
We are given the following word problem.
"The difference of b and 2 is less than 25"
Let us convert t
Is hollow a double consonant
Is HALLOW is double consonant. Yes, HALLOW is double consonant.
Given that,
We have to prove is HALLOW is double consonant.
What is double consonant?
A double consonant is a term that contains two consecutive consonant letters. For instance, the double consonant "nn" in tunnel. Words with a suffix, like "beginning," are usually found to have double consonants.
In conclusion, if a word has:
Syllable count: 2
Vowel one is short.
between each vowel, only one consonant sound is made.
Double that consonant after that! Like any other spelling rule in English literacy, this spelling strategy should be taught to pupils to help them learn how to double consonants together with other rules.
Here,
In hallow there is "ll"
Therefore, HALLOW is double consonant.
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Write a linear function f with the values f(-1) = -3 and f (2) = 6. A function is f(x) =
Answer:
The linear equation is;
[tex]f(x)=3x[/tex]Explanation:
Given that the function f(x) is a linear function;
[tex]f(x)=mx+b[/tex]let us derive the values of m and b.
At x=-1, f(-1)=-3;
[tex]\begin{gathered} f(-1)=m(-1)+b=-3 \\ -m+b=-3\text{ --------1} \end{gathered}[/tex]At x=2, f(2)=6;
[tex]\begin{gathered} f(2)=m(2)+b=6 \\ 2m+b=6\text{ ---------2} \end{gathered}[/tex]subtract equation 1 from 2;
[tex]\begin{gathered} 2m-(-m)+b-b=6-(-3) \\ 3m=9 \\ m=\frac{9}{3} \\ m=3 \end{gathered}[/tex]let's substitute the value of m into equation 2;
[tex]\begin{gathered} 2m+b=6 \\ 2(3)+b=6 \\ 6+b=6 \\ b=6-6 \\ b=0 \end{gathered}[/tex]Therefore, since we have the values of m and b we can substitute to get the equation f(x);
[tex]\begin{gathered} f(x)=mx+b \\ f(x)=3x+0 \\ f(x)=3x \end{gathered}[/tex]The linear equation is;
[tex]f(x)=3x[/tex]A packet of cream cheese contains six equal sectors of cheese when new. one of the sectors has been removed. If the packet has an internal diameter of 14cm and and internal depth of 2cm internally. calculate, correct to the nearest whole cm³, the volume of cheese remaining
The remaining area of the cream cheese pack will be 255.9 cm³.
What is the volume of a cylinder?
The volume of a cylinder is -
V = πr²h
Given is a packet has an internal diameter of 14cm and and internal depth of 2cm internally.
The volume of the cream cheese pack will be -
V[C] = πr²h
V[C] = π(d/2)²h
V[C] = 3.14 x 7 x 7 x 2
V[C] = 307.2
For six equal sectors, the volume of each sector = 307.2/6 = 51.3 cm³.
Remaining volume = 307.2 - 51.3 = 255.9 cm³
Therefore, the remaining area of the cream cheese pack will be 255.9 cm³.
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Answer to this question
Answer:
Either B or D
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
the general form of the absolute value function is
y = a | x - h | + k
where (h, k ) are the coordinates of the vertex and a is a multiplier
here (h, k ) = (2, 3 ) then
y = a | x - 2 | + 3
to find a substitute any other point on the graph into the equation
using (1, - 1 ) , then
- 1 = a | 1 - 2 | + 3
- 1 = a | - 1 | + 3
- 1 = a + 3 ( subtract 3 from both sides )
- 4 = a
then
f(x) = - 4 | x - 2 | + 3
is 0.49 a rational or irrational number? Explain how you know. PLS HELP
can you answer this ? Tavon has a gift card for $95 that loses $4 for each 30-day period it is not used. He has another gift card for $85 that loses $3.50 for each Ju-day period It Is not Write and solve an equation for the number or 30-dav periods unuthe value or the art cards will be equalD. What wil the value or each card be when thev have equa value?a. If x is the number of 30-day periods, then the equation can be used to find the number of 30-dav periods until the values of the aift(Type an equation. Use integers or decimals for any numbers in the equation.
If x is the number of 30 days period, the cost of gift cards after x days unused is,
[tex]95-4x[/tex]And for the second gift card:
[tex]85-3.50x[/tex]The equation for x is,
[tex]95-4x=85-3.50x[/tex]Solve the equation for x.
[tex]\begin{gathered} 95-4x=85-3.50x \\ 95-85=4x-3.50x \\ 10=0.5x \\ x=\frac{10}{0.5} \\ =20 \end{gathered}[/tex]So after 20 unused days, the value of cards are equal.
(b)
Substitute 20 for x in equation 95 - 4x to determine the value of the card.
[tex]\begin{gathered} 95-4\cdot20=95-80 \\ =15 \end{gathered}[/tex]So the value of cards, when they are equal, is $15.
