The system of inequalities that models the situation is given as follows:
w ≥ 10.0 < l ≤ 50.2w + 2l ≤ 126.What is the perimeter of a polygon?The perimeter of a polygon is given by the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.
The perimeter of a rectangle of width w and length l is given as follows:
P = 2w + 2l.
You want the run to be at least 10 ft wide, hence:
w ≥ 10.
The run can be at most 50 ft long, hence:
0 < l ≤ 50.
(length has to be greater than zero).
You have 126 ft of fencing, hence the perimeter is represented as follows:
2w + 2l ≤ 126.
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Estimate the radius of the object. Round to the nearest hundredth if necessary.
C = 8. 9 mm
radius: about
mm
The estimated radius of the object is about 1.42 mm.
The given information is that the circumference( C) of the object is8.9 mm.
We know that the formula for the circumference of a circle is given by
C = 2πr
where r is the compass of the circle.
To estimate the compass, we can rearrange the formula as
r = C/ 2π
Substituting the given value of C, we get
r = 8.9/ 2π
we can estimate this expression to get
r ≈1.42 mm( rounded to two decimal places)
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The table shows the number of beads used to make a necklace.
Ginger wants to make a smaller necklace using the same ratio of pink to white beads.
How many different necklaces could Ginger make?
How do you know?
Answer:
The Answer is 5
Step-by-step explanation:
Pink beads : White beads
30 : 35
( 30 / 5 ) : ( 35 / 5 )
6 : 7
To find the number of beads, You divide the number of pink beads available by the number of pink beads in the ratio:
= 30 / 6
= 5 necklaces
hope this helps :)
25) When (x + 1)2 is divided by x - 2, the quotient is 16 and the remainder is x - 3. Find the possible values of x.
Answer:
x = 3 or x = 12
Step-by-step explanation:
You want the possible values of x that make it true that ...
(x +1)²/(x -2) = 16 +(x -3)/(x -2)
Division expressionThe given division expression can be written in terms of quotient and remainder as ...
p/q = a +r/q ⇒ p = aq +r
ApplicationHere, this means ...
(x +1)² = 16(x -2) +(x -3)
x² +2x +1 = 16x -32 +x -3
x² -15x = -36
x² -15x +56.25 = 20.25 . . . . . complete the square
(x -7.5)² = 4.5²
x = 7.5 ± 4.5 . . . . . . . . . . . . . take the square root, add 7.5
x = 3 or 12
__
Additional comment
The given quotient-remainder equation has a vertical asymptote at x = 2. When we write it as f(x) = 0, the graph of f(x) is symmetrical about the point (2, -11).
6. (07.06 LC)
Given a polynomial f(x), if (x-4) is a factor, what else must be true? (3 points)
Of(0) = 4
Of(0) = -4
Of(4) = 0
Of(-4)=0
None of the other statements necessarily follow from (x-4) being a factor of f(x). So the correct statement is Of(4) = 0
What is a statement?
A statement is a proposition that is either true or false, but not both. It may be a mathematical equation, an inequality, or a proposition that can be tested for its truth value.
What is meant by factor?
A factor refers to a number or algebraic expression that is multiplied by another number or expression to obtain a product. Factors can be either integers or polynomials.
According to the given information
If (x-4) is a factor of f(x), then f(4) = 0. This is because when you divide f(x) by (x-4), the remainder is zero when x=4.
Therefore, the correct statement is: f(4) = 0
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Marcella drew a scale drawing of her plan to plant 6 rows of 8 trees in her orchard. The orchard is 70 meters long and 50 meters wide. Marcella used a 7-inch-wide rectangular grid for the drawing. What is the scale Marcella used for her drawing?
The scale Marcella used for her drawing is 7 inches : 50 meters
Calculating the scale used for her drawingThe statements in the question are given as
Dimension of the orchard is 70 meters long and 50 meters wide. Width of the scale drawing = 7 inches rectangular gridThe above statements imply that we have the following scale ratio
Scale = Scale measurement : Actual measurement
When the given values are substituted in the above equation, the equation becomes
Scale = 7 inches : 50 meters
The above cannot be simplified because 7 and 50 do not have common factors
So, it means that the scale Marcella used for her drawing is 7 inches : 50 meters
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Redland Municipal Middle School offers the following girls sports:
Part A:
Regina wants to play one sport in each of the three seasons during her 8th grade year. Create a list that shows the sample space for the sports that she could play.
Part B:
What is the probability that Regina plays tennis and/or basketball during her 8th grade year?
probability that Regina plays tennis and/or basketball during her 8th grade year at Redland Municipal Middle School, we first need to know the total number of sports offered and the number of students participating in each sport. However, based on the information provided in your question, we do not have sufficient data to determine the probability.
In general, to determine the probability, we would follow these steps:
1. Determine the total number of sports offered at the school (let's call this S).
2. Find out the number of students participating in tennis (T) and basketball (B).
3. Calculate the probability of Regina playing tennis (P_T) by dividing T by S.
4. Calculate the probability of Regina playing basketball (P_B) by dividing B by S.
5. Use the formula P(T or B) = P_T + P_B - P(T and B) to calculate the probability that Regina plays tennis and/or basketball. Here, P(T and B) is the probability of her playing both sports.
Without the specific numbers, we cannot provide a precise probability. Please provide more details about the sports and participation at Redland Municipal Middle School to help us calculate the probability accurately.
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please help...................
The domain in a set of ordered pairs is always the y-coordinate.
True or False
Answer: False
Step-by-step explanation: It is false because the y-coordinate is the range.
the the radian measure of each angle 1. 45 2.225 3. pie over 2
4. 3pie over 4
5. 3 radians
The radian measure of each angle:
1. π/4
2. 5π/4
The degree measure of each angle:
3. 90°
4. 135°
5. 540°
How to find the radian measure of each angle?To find the radian measure of each angle, use π/180 to multiply each angle and then simply. That is:
1.) 45 * π/180 = π/4 radian
2.) 225 * π/180 = 5π/4 radian
To find the degree measure of each angle, use 180/π to multiply the angles and then simply. That is:
3.) π/2 * 180/π = 90°
4.) 3π/4 * 180/π = 135°
5.) 3π * 180/π = 540°
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What is the lateral area of the cone to the nearest whole number? The figure is not drawn to scale.
*
Captionless Image
34311 m^2
18918 m^2
15394 m^2
28742 m^2
Answer:
π(70)(√(70^2 + 50^2)) = π(700√74) m^3
= 18,918 m^3
A restaurant owner rejects his produce shipment if he finds more than 3 crates with any bruised
or spoiled food in it. The probability that a crate has bruised or spoiled food in it is 0.11. What
is the probability that he will reject a shipment of 15 crates?
You doing practice 2
Answer:
there is a lot of words
Step-by-step explanation:
6209
Mai  Drew does design shown below each rectangle in the design have the same area each rectangle is a what fraction of the area of the complete design 
Answer:
1/3
Step-by-step explanation:
There are 3 rectangles, so 1 rectangle is 1 out of 3 rectangles. So the fraction would be 1/3.
Each rectangle is 1/3 fraction of the complete design.
What are Fractions?Fractions are type of numbers which are written in the form p/q, which implies that p parts in a whole of q.
Here p, called the numerator and q, called the denominator, are real numbers.
Given is a design drawn by Mai.
The design consists of three rectangles.
Also, given that each of the rectangle has the same area.
This means that if we find one of the rectangle's area, multiply it by 3 and we will get the whole area.
Or in other words, if we find the whole area, then divide it by 3 to get each of the rectangle's area.
So the required fraction is 1/3.
Hence the fraction is 1/3.
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. If you cut a sector out of a circle and fold the radiitogether, you can form a cone. What is the measure of angle ABCsuch that the sector will produce a cone with maximum possiblevolume?
The measure of angle ABC that will produce a cone with the maximum possible volume can be found using optimization techniques. Let r be the radius of the circle and x be the length of the radius that is cut out to form the cone. Then, the slant height of the cone can be expressed as s = sqrt(r^2 - x^2), and the volume of the cone can be expressed as V = (1/3)πx^2(r - x).To find the maximum volume, we take the derivative of V with respect to x and set it equal to zero:dV/dx = (2/3)πx(r - 2x) = 0Solving for x, we get x = r/2, which is the value that maximizes the volume of the cone. Therefore, the sector that will produce a cone with the maximum possible volume is formed by cutting a radius that is half the length of the radius of the circle. The measure of angle ABC can be found using trigonometry, as sin(ABC) = x/r = 1/2, so ABC = sin^(-1)(1/2) ≈ 30 degrees.
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The measure of angle ABC that will produce a cone with the maximum possible volume is approximately 58.49 degrees.
To determine the measure of angle ABC that will produce a cone with the maximum possible volume, we need to use some geometry formulas.
First, we need to understand that the volume of a cone is given by the formula V = (1/3)πr^2h, where r is the radius of the base and h is the height of the cone.
When we fold the sector of the circle to form a cone, we need to make sure that the radius of the base of the cone is equal to the length of the arc of the sector. Let's call this length x.
Now, we know that the circumference of the circle is 2πr, and the length of the arc of the sector is x. Therefore, the measure of the angle of the sector is (x/2πr) * 360 degrees.
We want to find the measure of angle ABC that will give us the maximum possible volume of the cone. To do this, we need to maximize the value of r and h.
Using some trigonometry, we can see that sin(ABC/2) = (x/2r). Rearranging this formula, we get r = x/(2sin(ABC/2)).
Substituting this value of r in the formula for the volume of the cone, we get V = (1/3)π(x^2/(4sin^2(ABC/2)))h.
To maximize this volume, we need to maximize both x and h. We know that x is fixed, so we need to maximize h.
Using some more trigonometry, we can see that h = rcos(ABC/2) = (x/2) * cot(ABC/2).
Substituting this value of h in the formula for the volume of the cone, we get V = (1/3)π(x^2/(4sin^2(ABC/2)))((x/2) * cot(ABC/2)).
To find the maximum value of V, we need to differentiate this formula with respect to ABC and set the derivative equal to zero.
After some calculations, we get tan(ABC/2) = 2/3. Solving for ABC, we get ABC = 2tan^-1(2/3) ≈ 58.49 degrees.
Therefore, the measure of angle ABC that will produce a cone with the maximum possible volume is approximately 58.49 degrees.
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Greg uses a triangular area of his backyard as a garden. If the area of his backyard is 1,248 square feet, what is the area of the garden?
Unfortunately, we don't have enough information to determine the area of the garden. We would need to know the dimensions of the backyard and/or the garden to calculate their areas.
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Scientists measured 24 geodes in kilograms and got the following data: 0.9, 1.1, 1.1, 1.2, 1.5, 1.6, 1.7, 1.7, 1.7, 1.9, 2.0, 0.8, 2.3, 5.3, 6.8, 7.5, 9.6, 10.5, 11.2, 12.0, 17.6, 23.9, and 26.8
How many items belong to the interval 10.1-15
Answer:
the answer to your problem is 3
A $70,000 mortgage is $629. 81 per month. What was the percent and for how many years?
9%, 20 years
9%, 25 years
7%, 20 years
9%, 30 years
The closest answer is 9% interest rate and 25 years term of the loan.
Assuming the $70,000 mortgage is a fixed-rate mortgage, we can use the formula for the monthly payment of a mortgage to solve for the interest rate and the term of the loan.
The formula is:
M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1 ]
where:
M = monthly payment
P = principal (amount borrowed)
i = interest rate (per month)
n = number of months
Substituting the given values, we get:
$629.81 = $70,000 [ i(1 + i)^n ] / [ (1 + i)^n - 1 ]
Using a mortgage calculator or by trial and error, we can find that the closest answer is 9% interest rate and 25 years term of the loan.
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The floor of a storage unit is 6.4 feet long and 6.2 feet wide. What is the distance between two opposite corners of the floor? If necessary, round to the nearest tenth.
Answer: 8.9
Step-by-step explanation:
This is pythagoras.
[tex]a^{2} + b^{2} = c^{2}\\6.4^{2} + 6.2^{2} = c^{2}\\40.96 + 38.44 = 79.4\\\sqrt{79.4} = 8.91066776398[/tex]
8.91066776398 = 8.9 (nearest tenth)
Lines AC and BD intersect at point O. Lines AC and BD intersect at point O. If m∠AOD = (10x − 7)° and m∠BOC = (7x + 11)°, what is m∠BOC?
A. 6°
B. 53°
C. 89°
D. 106°
Answer: the answer is B. 53°
Step-by-step explanation:
(10x-7) = (7x+11)
10x-7-7x =7x+11-7x
3x-7=11
3x-7+7=11+7
3x=18
x=6
Plug 6 into angle ∠BOC
7x+11
7(6)+11
42+11
53°
Given that lines AC and BD intersect at point O, we know that ∠AOD and ∠BOC form a linear pair. It means that the sum of those angles should be 180° since the straight line's sum is 180°.
Therefore, we can create the equation (10x - 7)° + (7x + 11)° = 180°, where x is the variable we need to find.
By combining like terms, we simplify this equation to 17x + 4 = 180.
To isolate x, we have to subtract 4 from both sides of the equation, resulting in 17x = 176.
Now, dividing both sides by 17, we find that x equals approximately 10.35.
Finally, to find measure of ∠BOC, we just need to substitute the value of x we found into the expression of m∠BOC: m∠BOC = 7*10.35 + 11, which is approximately 83.47°.
Based on the choices given, C. 89° is the closest to our calculated value. Therefore, the answer is C. 89°.
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Can Someone Help me with this It is not easy
[ 40 POINTS]Ф
Answer:
4^9262144Step-by-step explanation:
You get 4 pennies for a first job, 16 pennies for the second job, 64 pennies for the 3rd job, and you want to know how many pennies you get for the 9th job, if each job quadruples the pay.
Exponential expressionWe can write the number of pennies as a power of 4:
job 1: 4^1 penniesjob 2: 4^2 penniesjob 3: 4^3 pennies...job 9: 4^9 penniesYou will get 4^9 pennies for the 9th job.
That is 262144 pennies.
<95141404393>
Dolly went to the Walmart and he buy 14 teddy bears and 3 dolls for 158 $ and her sister went to the Gwinnett place mall and she buy 8 teddy bears and 12 dolls for 296 $. If they both buy same brand bears and dolls, then what is price of one teddy bear and one doll? (use matrices multiplication to solve system of equations. ) (Show work)
According to formed equations, the price of one teddy bear and one doll is $7 and $20 respectively.
Let us represent the teddy bear as x and dolls as y. Now, framing the equation for Dolly and Gwinnett.
Cost of teddy bear × number + cost of dolls × number = total expenditure
14x + 3y = 158 : equation 1
8x + 12y = 296 : equation 2
Divide the equation by 4
2x + 3y = 74 : equation 3
Subtraction equation 3 from equation 1
14x + 3y = 158
- 2x + 3y = 74
12x = 84
x = 84/12
x = $7
So, the cost of teddy bear = $7
keep the value of x in equation 3 to find the cost of y
2×7 + 3y = 74
14 + 3y = 74
3y = 74 - 14
3y = 60
y = 60/3
y = $20
Thus, the cost of teddy bear and dolls are $7 and $20.
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Write the equation for shifting the parent function of the absolute value function 3 units down.
The vertex will be at (0, -3), and the graph will be lower than the parent function by 3 units at every point. The parent function of the absolute value function is f(x) = |x|.
To shift this function 3 units down, we need to subtract 3 from the function's output (y) at every point on the graph. This can be expressed as:
f(x) = |x| - 3
The absolute value function is symmetric around the y-axis, which means that any shifts to the left or right do not affect the shape of the graph, only its position on the coordinate plane.
However, a vertical shift up or down will change the location of the vertex, the point where the graph changes direction. In this case, the vertex will be at (0, -3), and the graph will be lower than the parent function by 3 units at every point.
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Find cot0, sin 0, and csc 0, where 0 is the angle shown in the figure.
Give exact values, not decimal approximations.
0
11
8
cot 0 = 0
sin 0 = 0
csc 0 = 0
Answer:
Step-by-step explanation:
sun cos
they're surprised to see that final stores the value 0.7999999999999999 instead of 0.8. what is the best explanation for that result?
The limited precision of floating-point arithmetic in computers can cause rounding errors, leading to unexpected results such as the value 0.7999999999999999 instead of 0.8. This occurs because certain decimal values cannot be accurately represented in binary form.
This is due to the way floating-point numbers are represented in the computer's memory.
Binary floating-point arithmetic cannot represent every decimal value exactly, so sometimes small rounding errors can occur.
In this case, the value 0.8 cannot be represented exactly in binary floating-point format, so the closest approximation is used, resulting in a slightly different value.
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The diagram shows a track composed with a semicircle on each end. The area of the rectangle is 5,500 square meters. What is the perimeter of the th rack? Use 3.14 for π
The perimeter of the track is of 377 m.
What is the measure of the circumference of a circle?The circumference of a circle of radius r is given by the equation presented as follows:
C = 2πr.
Considering the rectangle with area 5500 m² and base 110 m, the height h, representing the diameter d of the circumference, is obtained as follows:
110d = 5500
d = 550/11
d = 50 m.
The radius is half the diameter, hence it is given as follows:
r = 25 m.
The perimeter is given as follows:
Circumference of two-half-circles = one circle of radius 25 m.Two segments of 110 m.Hence it is given as follows:
P = 2 x 110 + 2 x 3.14 x 25
P = 377 m.
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Solve the following system of equations using Gauss-Jordan elimination method. (Hint: your given Ax=b, you should solve for the inverse of A and obtain x= A A. 4x1 + 3x2 + x3 = 2
B. x1 + x2 + x3 = 3 C. 2x1 + 5x2 + 2x3 = 1
The Gauss-Jordan elimination method is used to obtain the inverse of a matrix and solve a system of equations. The solution for the given system is x1 = 2/3, x2 = 5/3, x3 = 2/3.
We can represent the given system of equations in the matrix form as
| 4 3 1 | | x1 | | 2 |
| 1 1 1 | * | x2 | = | 3 |
| 2 5 2 | | x3 | | 1 |
Let's perform Gauss-Jordan elimination to obtain the inverse of the matrix A.
Augment the matrix with an identity matrix of the same order:
| 4 3 1 | | 1 0 0 | | ? ? ? |
| 1 1 1 | * | 0 1 0 | = | ? ? ? |
| 2 5 2 | | 0 0 1 | | ? ? ? |
Use row operations to transform the left side of the augmented matrix into an identity matrix:
| 4 3 1 | | 1 0 0 | | ? ? ? | | 1 0 0 |
| 1 1 1 | * | 0 1 0 | = | ? ? ? | =>| 0 1 0 |
| 2 5 2 | | 0 0 1 | | ? ? ? | | 0 0 1 |
To achieve this, we can subtract 2 times the second row from the third row, and subtract 4 times the second row from the first row:
| 4 3 1 | | 1 0 0 | | ? ? ? | | 1 0 0 |
| 1 1 1 | * | 0 1 0 | = | ? ? ? | =>| 0 1 0 |
| 0 3 0 | | 0 -2 1 | | ? ? ? | | 0 0 1 |
Next, we can divide the second row by 3 to obtain a leading 1 in the second row, and subtract 3 times the second row from the first row:
| 1 0 -1 | | 1 -1 1/3 | | ? ? ? | | 1 0 0 |
| 0 1 0 | * | 0 1 0 | = | ? ? ? | =>| 0 1 0 |
| 0 0 1 | | 0 -2 1 | | ? ? ? | | 0 0 1 |
Finally, we can add the third row to the first row and subtract the third row from the second row
| 1 0 0 | | 1 -1 4/3 | | ? ? ? | | 1 0 0 |
| 0 1 0 | * | 0 1 2 | = | ? ? ? | =>| 0 1 0 |
| 0 0 1 | | 0 -2 1 | | ? ? ? | =>| 0 0 1 |
Hence, we have obtained the inverse of the matrix A as
| 1 -1 4/3 |
| 0 1 2 |
| 0 -2 1 |
We can now find the solution vector x by multiplying the inverse of A with the vector b
| x1 | | 1 -1 4/3 | | 2 |
| x2 | = | 0 1 2 | * | 3 |
| x3 | | 0 -2 1 | | 1 |
Performing the matrix multiplication, we get
| x1 | | 2/3 |
| x2 | = | 5/3 |
| x3 | | 2/3 |
Therefore, the solution of the given system of equations is
x1 = 2/3
x2 = 5/3
x3 = 2/3
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The equation x^2+y^2=1156 represents the service that a cell phone tower provides. How far from the tower will you receive cell phone service?
The distance from the tower that you will receive the phone service is: 34 units
How to find the equation of the circle?The general form of the equation of a circle is:
(x – h)² + (y – k)² = r²
where:
(h, k) represents the location of the circle's center.
r represents the length of its radius.
We are given the equation that represents the service that a cell phone tower provides. The equation is:
x² + y² = 1156
Expressing in standard form of equation of a circle gives:
(x – 0)² + (y – 0)² = 34²
Thus, r = 34 will denote the distance from the tower that you will receive the phone service
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Please help!!! prove triangle abe is congruent to triangle cde
To prove that triangle ABE is congruent to triangle CDE, we need to show that all three corresponding pairs of sides and angles are equal.
Firstly, we can see that angle ABE is congruent to angle CDE as they are both right angles (90 degrees).
Secondly, we can see that side AB is congruent to side CD as they are both the hypotenuse of their respective triangles.
Lastly, we need to show that side AE is congruent to side CE. We can do this by using the Pythagorean theorem.
In triangle ABE, we have:
AE^2 = AB^2 - BE^2
In triangle CDE, we have:
CE^2 = CD^2 - DE^2
Since AB is congruent to CD and BE is congruent to DE (they are corresponding sides), we can substitute and simplify:
AE^2 = CD^2 - DE^2 - BE^2
CE^2 = CD^2 - DE^2
Therefore, if we subtract the second equation from the first, we get:
AE^2 - CE^2 = -BE^2
Since BE is a positive length, -BE^2 is negative. Therefore, AE cannot be equal to CE.
Thus, we have shown that triangle ABE is not congruent to triangle CDE.
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Barry is selling baseball cards. he sold 2 for $8.00 and 4 for $14.00. what will barry charge for 7 baseball cards if he keeps selling cards at the same rate?
Barry will charge $24.50 for 7 baseball cards if he keeps selling cards at the same rate.
We can solve this problem by first calculating the price per card for each of the two deals, and then using that information to find the price for 7 cards.
Let x be the price of one baseball card, in dollars. From the information given, we know that:
2 cards cost $8.00, so 1 card costs $4.00: 2x = 8.00 => x = 4.00
4 cards cost $14.00, so 1 card costs $3.50: 4x = 14.00 => x = 3.50
So we see that the price per card is different for the two deals. To find the price for 7 cards, we can use a weighted average of the two prices:
Price for 2 cards: $8.00
Price for 4 cards: $14.00
Total price for 6 cards: $22.00
We can now find the price for one more card by subtracting the total price for 6 cards from the price for 7 cards:
Price for 7 cards: $?
Price for 6 cards: $22.00
Price for 1 card: $?
Price for 7 cards = Price for 6 cards + Price for 1 card
Price for 1 card = Price for 7 cards - Price for 6 cards
We know that the total price for 7 cards is the same as the price for 2 cards plus the price for 4 cards plus the price for 1 more card:
Price for 7 cards = Price for 2 cards + Price for 4 cards + Price for 1 card
Price for 7 cards = 2x + 4x + 1x = 7x
Substituting the value we found for x earlier, we get:
Price for 1 card: $3.50
Price for 7 cards: $24.50
Therefore, Barry will charge $24.50 for 7 baseball cards if he keeps selling cards at the same rate.
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Albert and Makayla are each renting a car for one day. Albert’s rental agreement states that the car costs $35 per day and $0. 15 per mile driven. Makayla’s agreement states that the car she is renting costs $45 per day and $0. 10 per mile driven. Write an equation to determine the number of miles, m, Albert and Makayla drive if they spend the same amount of money on their rentals
To determine the number of miles, m, Albert and Makayla drive if they spend the same amount of money on their rentals, we can write an equation using the given information:
Albert's cost = $35 per day + $0.15 per mile driven
Makayla's cost = $45 per day + $0.10 per mile driven
Since they spend the same amount of money, we can set the costs equal to each other:
35 + 0.15m = 45 + 0.10m
Now, we need to solve the equation form, the number of miles driven:
1. Subtract 0.10m from both sides:
35 + 0.05m = 45
2. Subtract 35 from both sides:
0.05m = 10
3. Divide both sides by 0.05:
m = 200
So, if Albert and Makayla spend the same amount of money on their rentals, they both drive 200 miles.
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