The actual bridge deck measures 4,320 square feet in size.
First, we need to convert the scaled dimensions to actual dimensions. Since the scale is 60:1, we need to multiply the scaled dimensions by 60 to get the actual dimensions.
The scaled length of the bridge deck is 36 inches, so the actual length is:
36 inches x 60 = 2,160 inches
The scaled width of the bridge deck is 4 4/5, or 24/5, inches. So the actual width is:
24/5 inches x 60 = 288 inches
To find the area of the actual bridge deck in square feet, we need to convert the actual dimensions to feet and then multiply:
Actual length in feet = 2,160 inches ÷ 12 inches/foot = 180 feet
Actual width in feet = 288 inches ÷ 12 inches/foot = 24 feet
Area in square feet = Actual length x Actual width = 180 ft x 24 ft = 4,320 square feet
Therefore, the area of the actual bridge deck in square feet is 4,320 square feet.
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When the sun is at its highest point in the sky, Hong goes to fly a kite in a flat field. He lets out 42.9 feet of string, and the spool of string is 3.4 feet above the ground. The shadow that the kite makes (directly below the kite on the ground) is 16.5 feet away from Hong. How high is the kite off the ground? Round your answer to two decimal places.
The height of the kite off the ground is approximately 17.87 feet rounded to two decimal places.
To solve the problem can use similar triangles.
Let's draw a diagram:
A
|\
| \
h | \ x
| \
|____\
d B
Point A represents the kite, point B represents the tip of the kite's shadow on the ground and point D represents the point directly below the spool of string on the ground.
The height of the kite represented by h.
The length of the string is 42.9 feet so the distance from point A to point D is also 42.9 feet.
The distance from point B to point D is 16.5 feet.
These two lengths to find the length of segment AB:
AB/AD = BD/AD
AB/42.9 = 16.5/42.9
AB = 16.5
So AB is 16.5 feet.
Now we can use the similar triangles to find h.
We have:
h/x = AB/AD
h/x = 16.5/42.9
h = x × 16.5/42.9
We need to find x.
The spool of string is 3.4 feet above the ground and we know that the kite is directly above the spool when it is at its highest point in the sky.
So the height of the kite above the ground is the same as the height of the spool above the ground plus the length of string that has been let out:
x = 3.4 + 42.9
= 46.3
Now we can substitute this value of x into the previous equation to find h:
h = 46.3 × 16.5/42.9
= 17.87
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Thorium 234 is a radioactive isotope that decays according to the eqaution At=A0e^-10.498t, where A0 is the initial amount present and At is the amount present after t years. is the amount present after t years. If you begin with 1000 grams of strontium 90,
(a) How much thorium 234 will be left after 0.5 years? Round your answer to the nearest tenth of a gram.
------------------- grams
(b) When will 115 grams of thorium 234 be left? Round your answer to the nearest tenth of a year.
-------------------- years
Answer: yes 2,0193-029712123,
Step-by-step explanation:
Sketch a graph of a polynomial function with a positive leading coefficient and zeros at x = 4, 2, and
-1 (multiplicity 2).
The graph of the polynomial function with a positive leading coefficient and zeros at x = 4, 2, and -1 (multiplicity 2) is given by the image presented at the end of the answer.
How to define the functions?We are given the roots for each function, hence the factor theorem is used to define the functions.
The function is defined as a product of it's linear factors, if x = a is a root, then x - a is a linear factor of the function.
Considering the zeros of the function, the linear factors are given as follows:
x - 4.x - 2.(x + 1)² -> due to the zero of multiplicity 2 at x = -1.Considering the leading coefficient of a = 1, the function is defined as follows:
f(x) = (x - 4)(x - 2)(x + 1)²
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MO
C
15 in
115
The triangle above has the following measures.
Use the 45 45 90 Triangle Theorem to find the
length of the hypolenuse Include correct units
Show all your work
The length of the hypotenuse of the triangle is b = x√2 units
Given data ,
Let the triangle be represented as ΔABC
And , the triangle is a 45 - 45 - 90 triangle
So , the two legs are congruent to one another and the non-right angles are both equal to 45 degrees
And , the sides are in the proportion x : x : x√2
Now , the length of the sides of the triangle are
The measure of base BC = a units = x
The measure of height AB = c units = x
So , the measure of the hypotenuse of the triangle is = x√2 units
Hence , the triangle is solved and hypotenuse AC = x√2 units
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A student is saving money to go on a school field trip. The graph shows the relationship between the number of weeks the student has been saving, x, and the total dollar amount they have saved, y.
Answer:
The is is 1
Step-by-step explanation:
I NEED HELP QUICK! PLEASE AND THANK YOU
The solution set, using properties of exponents is { 3/4 }.
How to find the solution set ?The solution set to ( 2 ³ˣ . 2 ˣ ) ˣ ⁻ ¹ = 8 can be found by using the properties of exponents in the following manner :
( 2 ^ ( 3 x + x ) ) ^ ( x ^ ( - 1 ) ) = 8
( 2 ^ ( 4 x ) ) ^ ( x ^ ( - 1 ) ) = 8
2 ^ ( 4 x * x ^ ( - 1 ) ) = 8
2 ^ ( 4 x * x ^ ( - 1 ) ) = 2^3
4 x * x ^ ( - 1 ) = 3
4 * x ^ ( 0) = 3
4 x = 3
x = 3/4
The solution set is { 3 / 4 }.
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can someone explain how five is the correct answer.
The number of unique preference orders that are represented in the table would be B. Five.
How to find the number of unique preference orders ?An individualized preference order is one way to assign a hierarchal ranking to an assortment of options. This ordering is recognized as "unique" because each item is assigned its own rank, with no two elements sharing the same level of priority.
From what is shown on the table, we have Voters 2, 4, 5 and 7 having a unique order. From these four voters, we therefore have four unique preference orders.
However, there is another unique preference order which is the shared preference order of Voters 1. 3 and 6 because this is unique preference order shared by three people.
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Question 4 Dennis purchases a new bicycle from the bike shop. Using the output expenditure model, the purchase of the bicycle would be an example of business investment government spending consumer spending net exports
Using the output expenditure model, the purchase of the bicycle would be an example of C) consumer spending.
What is consumer spending?Consumer spending is the expenditure made for the purchase of final goods and services by individuals and households.
In this situation, Dennis as a consumer is not a business organization, government institution, or an exporter, but an individual.
The expenditure for the purchase of a new bicycle is an expense for a final good.
Thus, under the output expenditure model, the purchase of a new bicycle is not a business investment, government spending, or a net export, but it is a consumer spending.
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d to fil
table.
(a) Does the parabola open upward or downward?
O upward
O downward
(b) Find the coordinates of the vertex.
(D
vertex:
(c) Find the intercept(s).
For both the x- and y-intercept(s), make sure
to do the following.
. If there is more than one, separate them
with commas.
If there are none, select "None".
x-intercept(s):
y-intercept(s):
(d) Find the equation of the axis of symmetry.
equation of axis of symmetry:
The graph is interpreted below
(a) the parabola open downward
(b) the coordinates of the vertex is (1, 9)
(c) the intercept(s)
x-intercept(s): (-2, 0) and (4, 0)
y-intercept(s): (0, 8)
(d) the equation of axis of symmetry: x = 2
How to find the intercepts of the parabolaTo find the intercepts of a parabola, you need to determine the points where the parabola intersects the x-axis (x-intercepts) and the y-axis (y-intercept).
Examining the graph shows that the points are
x-intercept(s) (Roots): (-2, 0) and (4, 0)
y-intercept(s): (0, 8)
Also, investing the graph shows that the graph opens upward and the vertex which is the maximum point is (1, 9)
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The length of a rectangle measures two more than three times the width if the area is 40 ft.² find the dimensions of the rectangle
Answer:Therefore, the dimensions of the rectangle are 14 ft by 4 ft.
Let's use variables to represent the length and width of the rectangle. We know from the problem that:Length = 3 times the width + 2
Area = 40 ft²We can use the formula for the area of a rectangle to set up an equation:Area = length x widthSubstituting in the values we have:40 = (3w + 2)wExpanding the brackets and simplifying:40 = 3w² + 2wRearranging into a quadratic equation form:3w² + 2w - 40 = 0We can solve for w using the quadratic formula:w = (-2 ± sqrt(2² - 4(3)(-40))) / (2 x 3)
w = (-2 ± sqrt(484)) / 6
w = (-2 ± 22) / 6The two possible solutions are w = 4 and w = -6.67. Since width cannot be negative, we take the positive solution: w = 4 ft.To find the length, we can use the formula we established earlier:Length = 3w + 2
Length = 3(4) + 2
Length = 14 ft
. Two popcorn boxes are shown below. The boxes
have congruent openings and equal heights. If
the larger box of popcorn sells for $3.00, what
is a fair price for the smaller box?
The fair price for the smaller box should be $1.00.
How do we calculate?From the question, we have that the larger box of popcorn sells for $3.00 and the two boxes have congruent openings and equal heights, we then can make the assumption that the only difference between them is their volume.
The volume of a pyramid is found using the formula:
V = (1/3) B* h,
where 'B'= base area
'h' = height of the pyramid
In conclusion, we can say that The fair price for the smaller box should be $1.00 because a pyramid is 1/3 the volume of a prism.
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The complete question is attached
please help! I need a explanation on why it’s B and please use simple terms I could understand
The correct statement regarding the proportional relationships is given as follows:
D. The first bucket will be completely filled 11 minutes before the second bucket.
What is a proportional relationship?A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other.
The equation that defines the proportional relationship is given as follows:
y = kx.
In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.
For the first bucket, the equation is given as follows:
y = 0.4x.
Meaning that 0.4 gallons are inserted each minute, hence the time to insert 2 gallons is given as follows:
2/0.4 = 5 minutes.
For the second bucket, the constant is taken from the graph as follows:
k = 0.5/4
k = 0.125.
Hence the time is given as follows:
2/0.125 = 16 minutes.
Hence the difference is of:
16 - 5 = 11 minutes.
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The bar graph above shows the number of T-shirts of different colors sold by a store one week. The following
week, the store had a sale, and sales of each color T-shirt sold increased by about 50 percent from the
previous week. Of the following, which is closest to the number of green T-shirts sold the week of the sale?
0 15
0 20
045
0 60
The number of green t-shirts sold are 45.
Given that a bar graph showing the sell of t-shirts of 4 different colour,
It is saying that the sell has increased by 50% next week, we need to find the number of green t-shirts to be sold in next week,
So, the number of green t-shirts sold in previous week = 30
So this week the sell should have been increased by 50%
Therefore, the number of green t-shirts sold this week = 150/100 × 30
= 1.5 × 30 = 45
Hence the number of green t-shirts sold are 45.
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Which inequality represents the values of x for which triangle ABC exists
After considering all the given options we come to the conclusion that the inequality that represents the values of x for the give triangle ABC is 15/11 < x < 17/5, which is Option A.
Here, the sides of a triangle should gradually satisfy the triangle inequality theorem which projects that the summation of the lengths considering any two sides of a triangle should be bigger than or equivalent towards the length of the third side.
Then, for the given sides of triangle ABC,
3x+1 + 16 > 8x
Applying this inequality,
x > 15/11
So,
16 + 8x > 3x+1
Applying simplification
x < 17/5
Hence , the inequality that represents the values of x for which triangle ABC exists is 15/11 < x < 17/5.
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A triangle has one angle that measures 56° and one angle that measures 63⁰.
The measure of the triangle's third angle is
degrees.
The solution is
Answer:
61
Step-by-step explanation:
triangles add up to 180
56+63 is 119
180-119 to find the missing angle is 61
hope this helped
Determine if the table below represents a linear function. If so, what's the rate of change?  Question 9 options: A) Yes; rate of change = 4 B) No; it's a non-linear function. C) Yes; rate of change = 3 D) Yes; rate of change = 2
The given table represents a linear function with a constant rate of change of 2. Option D is the right answer.
To determine if the table represents a linear function and calculate the rate of change, let's examine the given values:
x | y
-----------
1 | 3
2 | 5
3 | 7
4 | 9
By looking at the y-values, we can observe that for every increase of 1 in x, the corresponding y-value increases by 2. This indicates a constant rate of change, suggesting that the table represents a linear function.
To calculate the rate of change, we can use the formula:
[tex]\[\text{{Rate of Change}} = \frac{{\text{{Change in y}}}}{{\text{{Change in x}}}}\][/tex]
Taking any two points from the table, let's choose (1, 3) and (2, 5):
[tex]\[\text{{Rate of Change}} = \frac{{5 - 3}}{{2 - 1}} = \frac{2}{1} = 2\][/tex]
The table provided exhibits a linear function with a constant rate of change. As the x-values increase by 1 from [tex]1[/tex] to [tex]4[/tex], the corresponding y-values increase by [tex]2[/tex] from [tex]3[/tex] to [tex]9[/tex]. This consistent change in y for each unit change in x indicates a linear relationship between the variables.
The rate of change, also known as the slope of the function, is determined by the ratio of the change in y to the change in x. In this case, the rate of change is [tex]2[/tex], meaning that for every increase of [tex]1[/tex] in [tex]x[/tex], the y-value increases by 2.
Thus, the table represents a linear function with a rate of change of [tex]2[/tex].
Therefore, the correct answer is D) Yes; rate of change = [tex]2[/tex].
NOTE: The given question is incomplete. The complete question is:
Determine if the table below represents a linear function. If so, what's the rate of change?
options:
A) Yes; rate of change = 4
B) No; it's a non-linear function.
C) Yes; rate of change = 3
D) Yes; rate of change = 2
Table:
x | y
-----------
1 | 3
2 | 5
3 | 7
4 | 9
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Pls hep!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
98 mm²
Step-by-step explanation:
This parallelogram has a base of 7 and height of 14 mm.
The height is the vertical distance between the two bases
The area = b x h = 7 x 14 = 98 mm²
[tex]\huge\mathcal{\fcolorbox{aqua}{azure}{\red{➳Aɳʂɯҽɾ}}}[/tex]
Refer the attachment for clarity:-
[tex] \colorbox{yellow}{\red{Formula\: Base\: x \:Height= Area}}[/tex]
[tex]\sf{\leadsto 7×14}[/tex]
[tex]{ \red{ \sf 98m {m}^{2} }}[/tex]
______________________________
[tex]\bold{Thank ~you~:)}[/tex]
Kara's Custom Tees experienced fixed costs of $500 and variable costs of $5 a shirt Write an equation that can be used to determine the total expenses encountered by Kan's Custom Tees Lef x be the number
of shirts, and let C(x) be the total cost of producing x shirts. Then, calculate the cost of producing 8 shirts
Kara's Custom Tees will spend $540 to produce 8 shirts.
To determine the total expenses encountered by Kara's Custom Tees, we can use the equation:
C(x) = fixed costs + (variable costs per shirt) * x
In this case, the fixed costs are $500 and the variable costs per shirt are $5. Therefore, the equation becomes:
C(x) = 500 + 5x
To calculate the cost of producing 8 shirts, we substitute x = 8 into the equation:
C(8) = 500 + 5 * 8
= 500 + 40
= $540
Therefore, Kara's Custom Tees will spend $540 to produce 8 shirts.
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Complete the table for the given rule.
Rule:
y = x/4
Answer: Given as (x, y) in order from top to bottom: (16, 4); (8, 2); (36, 9)
Step-by-step explanation:
Since we need to solve for x, we will solve this equation for x first.
Given:
y = [tex]\frac{x}{4}[/tex]
Multiply both sides of the equation by 4:
4y = x
Next, for each given y-value, we will substitute into the given rule we transformed and solve.
4y = x
4(4) = 16
4y = x
4(2) = 8
4y = x
4(9) = 36
Answer:
16
8
36
Step-by-step explanation:
move the /4 to H other side and you get y*4=x,
now put the number on the table and multiply by 4 to get X, for each value,
Translate each graph as specified below.
(a) The graph of is shown. Translate it to get the graph of .
(b) The graph of is shown. Translate it to get the graph of .
look at picture
The graph of the translations are attached
The red is the preimage while the blue is the image
How to complete the translation
The absolute value graph has equation f(x) = |2x| and the translation we want to obtain is y = f(x) + 4 and this is a translation 4 units up
This results to a graph of equation y = f(x) + 4 = |2x| + 4
For the parabolic graph, the equation is written as
y = a(x - 2)² - 3
solving for a using (0, -5)
-5 = a(0 - 2)² - 3
-2 = 4a
a = -1/2, then the equation is g(x) = -1/2 (x - 2)² - 3
Applying the translation, the equation will be
y = g(x + 2) = -1/2 (x - 2 + 2)² - 3 = -1/2 (x)² - 3
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Please can anyone tell me what the L.C.M of c, 3c , 3 is?
The least common multiple ( LCM ) is A = 3c
Given data ,
Let the three numbers be represented as c , 3c and 3
Now , The prime factorization of each number is:
c: c
3c: 3 * c
3: 3
The LCM is the product of the highest power of each prime factor. In this case, the highest power of c is c, and the highest power of 3 is 3. Therefore, the LCM is:
LCM = c * 3 = 3c
Hence , the LCM of c, 3c, and 3 is 3c
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A point is located 5 units to the right origin along the x axis and 3 units up along the y-axis on a coordinate plane
Answer: (5, 3)
Step-by-step explanation:
this is just basic coordinate geometry. it tells you how far to go right and up.
An angle measures 14.2° more than the measure of its supplementary angle. What is the measure of each angle?
Answer:
Step-by-step explanation:
Let the angle be x
then its supplementary angle be 180 - x
x - ( 180 - x ) = 14.2
2x = 194.2
x = 97.1
angle = 97.1
supplementary angle = 180 - 97.1
= 82.9
Use the tree diagram to complete each statement.
The probability of no promotion, given that a salesperson hit the quota: A is
.
The probability of a promotion, given that a salesperson missed the quota: B is
.
The probability of no promotion, given that a salesperson missed the quota: C is
.
The probability that a salesperson hit the quota and got promoted: D is
.
The probability that a salesperson hit the quota, given that the salesperson was promoted is 0.88. Therefore, option D is the correct answer
From the tree diagram, there are two ways to obtain the promotion:
0.41 of 0.68 (hit the quota).
0.14 of 0.32 (did not hit the quota).
So, the probability of getting a promotion is:
P(A) = 0.41 × 0.68 + 0.14 × 0.32 = 0.3236.
The probability of both getting a promotion and hitting the quota is:
P(A and B) = 0.41 × 0.68 = 0.2788.
So, the conditional probability is:
P(B|A) = P(A and B)/P(A) = 0.2788/0.3236 = 0.88 (approximately).
Therefore, option D is the correct answer.
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"Your question is incomplete, probably the complete question/missing part is:"
Salespeople at a certain company must meet a quota each month. On average, they hit the quota 68% of the time. If a salesperson hits the quota, the probability of being promoted in the next six months is 0.41. If a person doesn’t hit the quota, the probability of being promoted is 0.14.
Use the tree diagram to determine the probability that a salesperson hit the quota, given that the salesperson was promoted.
A. 0.28
B. 0.32
C. 0.41
D. 0.88
Peter's restaurant is bringing in money from customers, and he needs to know how much he needs to pay off the bill for the electricity to run the place. To turn the electricity on, he has to pay $25. For every hour that the electricity is on, he has to pay $4. How many hours can he have the electricity on for if she makes a $49 profit?
Please answer with step-by-step instructions. Thank you.
Peter can have the electricity on for 18.5 hours if he wants to make a $49 profit.
We have,
Let's start by setting up an equation to represent the situation:
Profit = Revenue - Cost
We know that Peter's profit is $49, and we can find the revenue by multiplying the number of hours by the hourly rate:
Revenue = Hourly rate x Number of hours
The hourly rate is $4, and the cost includes the initial fee of $25 plus the hourly cost:
Cost = Initial fee + Hourly rate x Number of hours
Now we can substitute these equations into the profit equation and solve for the number of hours:
$49 = ($4 x Number of hours) - ($25 + $4 x Number of hours)
$49 = $4 x Number of hours - $25 - $4 x Number of hours
$49 + $25 = $4 x Number of hours - $4 x Number of hours
$74 = $4 x Number of hours
Number of hours = $74 / $4
Number of hours = 18.5
Thus,
Peter can have the electricity on for 18.5 hours if he wants to make a $49 profit.
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What do you know about the graphs of polynomials with positive end behavior compared to the graphs of polynomials with negative end behavior?
If "positive" end behavior:
1. The graph hits the x-axis
2. The arrows point in opposite directions
3. The arrows point in the same direction
4. The right arrow is up
5. The graph hits the y-axis
6. The right arrow is down
If "negative" end behavior:
1. The graph hits the x-axis
2. The right arrow is down
3. The graph hits the y-axis
4. The right arrow is up
5. The arrows point in the same direction
6. The arrows point in opposite directions
The end behavior of a polynomial with positive leading coefficient is either "up-up" or "down-down" depending on the degree of the polynomial the end behavior of a polynomial with negative leading coefficient is either "up-down" or "down-up" depending on the degree of the polynomial.
Actually, the end behavior of a polynomial refers to the behavior of the function as the input variable (usually x) approaches positive or negative infinity.
The end behavior of a polynomial is determined by the degree and leading coefficient of the polynomial.
If the degree of the polynomial is even and the leading coefficient is positive, then the end behavior is as follows:
As x approaches negative infinity, the graph of the polynomial approaches the x-axis from above (the arrows point in opposite directions).
As x approaches positive infinity, the graph of the polynomial approaches the x-axis from below (the arrows point in opposite directions).
If the degree of the polynomial is even and the leading coefficient is negative, then the end behavior is as follows:
As x approaches negative infinity, the graph of the polynomial approaches the x-axis from below (the arrows point in opposite directions).
As x approaches positive infinity, the graph of the polynomial approaches the x-axis from above (the arrows point in opposite directions).
If the degree of the polynomial is odd and the leading coefficient is positive, then the end behavior is as follows:
As x approaches negative infinity, the graph of the polynomial goes down to negative infinity (the arrows point in the same direction).
As x approaches positive infinity, the graph of the polynomial goes up to positive infinity (the arrows point in the same direction).
If the degree of the polynomial is odd and the leading coefficient is negative, then the end behavior is as follows:
As x approaches negative infinity, the graph of the polynomial goes up to positive infinity (the arrows point in the same direction).
As x approaches positive infinity, the graph of the polynomial goes down to negative infinity (the arrows point in the same direction).
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A new car is purchased for $41, 000 and over time its value depreciates by one half every 3 years. What is the value of the car 4 years after it was purchased, to the nearest hundred dollars?
The value of the car 4 years after it was purchased is $16,270.86.
What is the value of the car after 4 years?
Depreciation is when the value of an asset declines with the passage of time as a result of wear and tear.
The equation that would be used to determine the value of car with the passage of time would be an exponential equation.
Value of the car after t years = [tex]p(1 -r)^{\frac{t}{3}[/tex]
Where:
p = purchase price of the car r = rate of depreciation t = number of yearsValue of the car after 4 years = [tex]41,000(1 -0.5)^{\frac{4}{3}[/tex] = $16,270.86
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Which expression is equivalent to (z + 6)(z – 6)?
Answer:
[tex]z^{2} +z-36[/tex]
Step-by-step explanation:
Multiply
Which of the following statements are true?
Select all that apply.
A. 4 is a perfect cube.
B. 16 is a perfect square.
C. 2,197 is both a perfect square and a perfect cube.
D. 8 is a perfect cube.
E. 18 is neither a perfect square nor a perfect cube.
Answer:
B and D
Step-by-step explanation:
4²= 16
it's a perfect square
2³= 8
it's a perfect cube
Select the correct answer. Which equation represents a circle with center Z (-3,5) and a radius of 4 units? A. (x − 3)2 + (y + 5)2 = 4 B. (x − 3)2 + (y + 5)2 = 16 C. (x + 3)2 + (y − 5)2 = 4 D. (x + 3)2 + (y − 5)2 = 16
The correct equation which represents a circle with center Z (-3,5) and a radius of 4 units is,
⇒ (x + 3)² + (y - 5)² = 16
We have to given that;
In a circle,
Center = (- 3, 5)
Radius = 4
Since, The standard form of equation of circle is,
⇒ (x - h)² + (y - k)² = r²
Where, (h, k) = center
And, r is radius
Here, Center = (- 3, 5)
Radius = 4
Hence, The correct equation which represents a circle with center Z (-3,5) and a radius of 4 units is,
⇒ (x - (- 3))² + (y - 5)² = 4²
⇒ (x + 3)² + (y - 5)² = 16
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