The correct option that describes the number and type of solutions of the quadratic equation is: There are two unequal real solutions. The correct answer alternative is option a.
The discriminant of a quadratic equation is the part of the equation under the square root in the quadratic formula, which is b² - 4ac. In the given equation, 2x² - 7x + 4 = 0, the values of a, b, and c are 2, -7, and 4, respectively.
To compute the discriminant, we plug in these values into the formula:
Discriminant = b² - 4ac
= (-7)² - 4(2)(4)
= 49 - 32
= 17
The discriminant is 17.
To determine the number and type of solutions of the quadratic equation, we look at the value of the discriminant. If the discriminant is greater than 0, there are two unequal real solutions. If the discriminant is equal to 0, there is one real solution. If the discriminant is less than 0, there are two imaginary solutions.
Since the discriminant in this case is 17, which is greater than 0, there are two unequal real solutions. Therefore, the correct answer is (a) There are two unequal real solutions.
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If 270 students bought a cheese pizza or a pepperoni pizza, how many lunches were sold on Friday?
Option Percent
Cheese Pizza 50
Pepperoni Pizza 40
Fried Chicken 10
If each lunch costs $3.50, how much money will the cafeteria earn from all of the lunches?
The cafeteria earned $945 from all of the lunches sold on Friday.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Let us calculate the number of students who bought each pizza.
Number of students who bought cheese pizza = 50% of 270 = 0.5 x 270 = 135
Number of students who bought pepperoni pizza = 40% of 270 = 0.4 x 270 = 108
Total lunches sold = Number of cheese pizzas sold + Number of pepperoni pizzas sold + Number of fried chicken sold
= 135 + 108 + 27
= 270
Therefore, a total of 270 lunches were sold on Friday.
To calculate how much money the cafeteria earned from all of the lunches, we can multiply the total number of lunches sold by the cost of each lunch:
Total earnings = Total lunches sold x Cost per lunch
= 270 x $3.50
= $945
Therefore, the cafeteria earned $945 from all of the lunches sold on Friday.
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In A parallelogram MNPQ if MN=12cm what is PQ
In A parallelogram MNPQ with MN=12cm, MQ = 10 cm
a) The length of side PQ is equals to the 12 cm.
b) The measure of angle Q is equals to the 155°.
In a geometry, a parallelogram is a simple quadrilateral with
two pairs of parallel sides. The opposite sides are of equal length.the opposite angles of are of equal measure.We have a parallelogram MNPQ, with
Side length, MN = 12cm
Other side length, MQ = 10 cm
Measure of angle M is = 25°
Also, MN|| PQ and MQ||NP
a) From the definition of parallelogram, the length of side MN is parallel to PQ and are of equal length. So, PQ = MN
= 12 cm
b) By the definition of parallelogram, opposite angles of a parallelogram are of equal measure. So, the measure of angle P = measure of angle M = 25°
Also, measure of angle N = measure of angle Q = x
Sum of all interior angles of quadrilateral
= 360°
=> m∠P + m∠N + m∠M + m∠Q = 360°
=> 25° + x + 25° + x = 360°
=> 2x + 50° = 360°
=> 2x = 310°
=> x = (310/2)° = 155°
Hence, required value of measure of angle Q is 155°.
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Complete question:
In A parallelogram MNPQ if MN=12cm , MQ = 10 cm and mZM = 25°. What is a)PQ
b) measure of angle Q
Find the balance of a savings account after 212 years if the simple interest earned each quarter is 0. 35% and the principal is $450
A $450 principal and a simple interest rate of 0.35% each quarter for 212 years would result in a savings account balance of $3768.
Amount and simple interestWe can use the formula for simple interest to solve this problem:
Simple Interest = Principal x Rate x Time
where Rate is the interest rate as a decimal, and Time is the time in years.
The quarterly interest rate is 0.35% / 4 = 0.00875, and the time is 212 years, or 848 quarters.
Plugging in these values, we get:
Simple Interest = $450 x 0.00875 x 848 = $3318
Therefore, the balance of the savings account after 212 years would be:
Balance = Principal + Simple Interest = $450 + $3318 = $3768
Therefore, the balance of the savings account after 212 years with a simple interest rate of 0.35% each quarter and a principal of $450 would be $3768.
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Can you do Step by Steps for this problem, please.
Answer:
36.9
Step-by-step explanation:
sinJ=[tex]\frac{21}{35}[/tex]
J= [tex]sin^{-1}[/tex][tex]\frac{21}{35}[/tex]
J= 36.9
A photocopier can copy 4 pages every 2 seconds. How long will it take to copy 120 pages draw a digram to solve the problem
Answer: First we have to check the information they are giving in the problem. do we can see that the photocopier can copy 4 pages every 2 seconds.
so with this info we can calculate the ratio, or the number of copies that can be done in one second:
So we made a rule of 3 to solve that
So, if the photocopier can print 2 copys every second, the we can calculate the the time that takes to print 120 pages:
solving this rule of 3:
so is going to take 60 seconds to copy 120 pages.
What is the area of the following composite figure? Round to the nearest whole. I NEED THE ANSWER ASAP.
Answer:
141 inch^2
Step-by-step explanation:
13×7= 91 for the rectangle
13-5=8
diameter of circle=8
radius=4
area if circle=4^2 times π
=16×π
=16π
16π+91=141.2654....
to the nearest whole= 141 inch^2 I think
A probability of 4/5 indicates an event is likely to happen.
Yes, a probability of 4/5 indicates that an event is likely to happen.
What is Probability?Probability refers to the measure of the likelihood of an event occurring, typically expressed as a number between 0 and 1. It is used to quantify uncertainty and is widely used in various fields such as mathematics, statistics, economics, science, and engineering.
Yes, a probability of 4/5 indicates that an event is likely to happen. It means that out of 5 possible outcomes, 4 outcomes are favorable to the event. In other words, there is an 80% chance that the event will occur.
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Solve (w-2)^(2)-54=0, where w Simplify your answer as much as If there is more than one solution, If there is no solution, click "No so
The solutions to the equation (w-2)^(2)-54=0 are w = 2, w = 9, and w = -6.
The equation (w-2)2 - 54 = 0 can be solved by factoring.
Let's start by writing the equation as: (w-2)(w-2) - 54 = 0
We can factor out (w-2) to get: (w-2)(w2 - 4w - 54) = 0
Now we can factor the second part of the equation, by splitting the middle term (4w) to get: (w-2)(w-9)(w+6) = 0
Now we have three equations, which we can solve separately:
w - 2 = 0 → w = 2
w - 9 = 0 → w = 9
w + 6 = 0 → w = -6
Therefore, the solutions to the equation (w-2)2 - 54 = 0 are w = 2, w = 9, and w = -6.
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y=5x2+3x-2 maximum minimum?
Answer:
its 0183
Step-by-step explanation:
jfirst queal then u have to divided then zjs
Answer: It is a minimum
Step-by-step explanation:
It is a minimum because the coefficient (5) is positive.
the item to the trashcan. Click the trashcan to cle Solve this equation by completing the square. 3x^(2)-4x=-2
The solutions to this 3x^(2)-4x=-2 are x=(2/3)+i*√(2/9) or x=(2/3)-i*√(2/9).
To solve this equation by completing the square, we need to first rearrange the equation and then complete the square for the x terms. Here are the steps:
1. Rearrange the equation:
3x^(2)-4x=-2 becomes 3x^(2)-4x+2=0
2. Divide the entire equation by the coefficient of the x^(2) term:
(3x^(2)-4x+2)/3=0/3 becomes x^(2)-(4/3)x+(2/3)=0
3. Complete the square by adding the square of half the coefficient of the x term to both sides of the equation:
x^(2)-(4/3)x+(2/3)+(4/3)^(2)/4=(4/3)^(2)/4 becomes x^(2)-(4/3)x+(4/9)=(4/3)^(2)/4-(2/3)
4. Simplify the right side of the equation:
(4/3)^(2)/4-(2/3)=(16/9)/4-(2/3)=(4/9)-(2/3)=(4/9)-(6/9)=-(2/9)
5. Factor the left side of the equation:
(x-(2/3))^(2)=-(2/9)
6. Take the square root of both sides of the equation:
x-(2/3)=+/-sqrt(-(2/9))
7. Solve for x:
x=(2/3)+/-sqrt(-(2/9)) becomes x=(2/3)+i*sqrt(2/9) or x=(2/3)-i*sqrt(2/9)
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On an analog clock, the hour hand rotates 30 degrees as the second hand rotates 21,600 degrees. Which equation correctly relates the variables defined below?
h: angular motion of the hour hand, in degrees
s: angular motion of the second hand, in degrees
Step-by-step explanation:
the ratio is 30/21600 = 3/2160 = 1/720
that means for every degree the hour hand moves, the second hand does 2 full rotations (2×360°).
h = s×30/21600 = s/720
FYI :
as there are 12 hours on a clock, every hour means 360/12 = 30° rotation for the hour hand.
so, for each hour the second hand moves 21600°.
that means 21600/360 = 60 full rotations.
that means one rotation of the second hand is 1 minute.
so, the second hand is truly a second hand (counting the seconds).
60 seconds in a minute (a full rotation by the second hand), that means each second corresponds to 360/60 = 6° rotation of the second hand.
Consider the following formula.
(x-50)/(s/squre root of n)
x = 45.3, s = 4.7, n = 48Evaluate this expression using the given
values. Round the result to two decimal places.
-12.87 ≈ -12.87
The given expression is:
(x-50)/(s/√n)
To evaluate it using the given values, we substitute the given values in the formula:
(45.3-50)/(4.7/√48) = -4.7/0.366 = -12.87
Rounding the result to two decimal places, we get:
-12.87 ≈ -12.87
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A watch was bought for 2,700 including 8% VAT. Find its price before the VAT was added.
Answer:
Let's assume that the price before adding the VAT is x.
We know that the VAT rate is 8%, which means that the VAT amount is 8% of x, or 0.08x.
The total price including VAT is the sum of the price before VAT and the VAT amount, so we can write:
Total price = price before VAT + VAT amount
or
2,700 = x + 0.08x
Simplifying this equation, we can combine like terms on the right-hand side to get:
2,700 = 1.08x
To solve for x, we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by 1.08:
x = 2,700 / 1.08
x = 2,500
Therefore, the price before VAT was added is 2,500.
[tex]\frac{10}{\sqrt{5} }[/tex]
Answer:
[tex]2 \sqrt{5} [/tex]
Is the simplified form
Step-by-step explanation:
Greetings!!!
Given expression
[tex] \frac{10}{ \sqrt{5} } [/tex]
factor the number 10:5.2
[tex] = \frac{5.2}{ \sqrt{5} } [/tex]
Apply radical rule
[tex]a = \sqrt{a} \sqrt{a} [/tex]
[tex]5 = \sqrt{5} \sqrt{5} \\ = \frac{ \sqrt{5} \sqrt{5}.2 }{ \sqrt{5} } [/tex]
Cancel the common factor :✓5
[tex] = \sqrt{5} .2 \\ = 2 \sqrt{5} [/tex]
If you have any questions tag me on comments
Hope it helps!!!
Answer:
2 * [tex]\sqrt{5}[/tex]
Step-by-step explanation:
Given: [tex]\frac{10}{\sqrt{5} }[/tex]
Using the basis formula, you simplify it to:
2×[tex]\sqrt{5}[/tex]
Which Values of x will make the expression?
The values of x that make the equation equals 0 are -3 and 3
How to determine the values of xThe equation given from the question is represented as
(6x^2 - 54)/(5x^2 - 20) = 0
The format of the above equation is that of a radical equation
For the expression to equal to 0, the numerator must be 0
So, we have
6x^2 - 54 = 0
Evaluate the like terms
6x^2 = 54
Divide both sides by 6
x^2 = 9
take the square root of both sides
x = -3 and x = 3
Hence, the solutions are -3 and 3
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7-5 skills practice parts of similar triangles
The answer is (1) x = 22.5; (2) x = 16.7; (3) x = 13.5; (4) x = 16.8; (5) x = 24.5; (6) x = 16.15; (7.a) height of the image on film is 11.2mm; (7.b) distance between camera and her friend is 1,875mm.
(1) We can see that in the given figure all three corresponding angles are congruent and all three corresponding sides are in equal proportion so, these are similar triangles.
As per properties of similar triangle:
Three pairs of corresponding sides are proportional i.e. Two pairs of corresponding sides are proportional and the corresponding angles between them are equal.
Therefore, [tex]\frac{32}{24} =\frac{30}{x}[/tex],
then by cross multiplying them, we get,
32x = 720
x = 720/32
x = 22.5
(2) As, this is already given that these are similar triangle and by applying the properties of similar triangle we get,
[tex]\frac{39}{26} =\frac{25}{x}[/tex]
39x = 650
x = [tex]16\frac{2}{3}[/tex]
x = 16.7
(3) As these are similar triangle again we can say that,
[tex]\frac{2x+1}{x+4} =\frac{40}{25}[/tex]
40(x + 4) = 25(2x + 1)
40x + 160 = 50x + 25
40x = 50x - 135
-10x = -135
(by cancelling (-) sign from both sides we get,
x = 135/10
x = 13.5
(4) By applying similar triangle's property, we can get
[tex]\frac{20}{30} =\frac{28-x}{x}[/tex]
20x = 840 - 30x
50x = 840
x = 840/50
x = 16.8
(5) As ΔJKL [tex]\sim[/tex] ΔNPR,
[tex]\frac{KM}{PT} =\frac{KL}{PR}[/tex]
[tex]\frac{18}{15.75} =\frac{28}{x}[/tex]
18x = 441
x = 441/18
x = 24.5
(6) As ΔSTU [tex]\sim[/tex] ΔXYZ,
[tex]\frac{UA}{ZB} =\frac{UT}{ZY}[/tex]
[tex]\frac{6}{11.4} =\frac{8.5}{x}[/tex]
6x = 96.6
x = 96.6/6
x = 16.15
(7.a) First we have to change 3 m and 140 cm into mm(millimeters).
So, 1m = 1000 mm
3m = 3000mm.
And 1cm = 10 mm
140cm = 1400 mm.
Then to find the height of the image on the film, we have to solve:
[tex]\frac{24}{3000} =\frac{x}{1400}[/tex]
by cross multiplication we get,
3000x = 33,600
x = 33,600/3000
x = 11.2 mm
the height of the image on the film is 11.2millimeters.
(7.b) For this also, we have to find x by solving the equation:
[tex]\frac{24}{3000} =\frac{15}{x}[/tex]
24x = 45,000
x = 45,000/24
x = 1,875 mm
The distance between camera and her friend is 1,875 millimeters.
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Full question is given below in the image.
y<|4x+1|-3 table and graphed
The table of values is added below and and the graph is attached
How to determine the table of values and graphFrom the question, we have the following parameters that can be used in our computation:
y < |4x + 1| - 3
To create a table of values for y < |4x + 1| - 3, we can choose different values of x and substitute them into the expression to find the corresponding values of y.
Let's choose some values of x: -2, -1, 0, 1, 2.
When x = -2, we have:
y < |4(-2) + 1| - 3
y < 4
When x = -1, we have:
y < |4(-1) + 1| - 3
y < 0
When x = 0, we have:
y < |4(0) + 1| - 3
y < |1| - 3
y < -2
When x = 1, we have:
y < |4(1) + 1| - 3
y < 2
When x = 2, we have:
y < |4(2) + 1| - 3
y < 6
Putting it all together, we have the following table:
x y values
-2 y < 4
-1 y < 0
0 y < -2
1 y < 2
2 y < 6
The graph is attached
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Hi urgent I need help today is my birthday all I ask is for anyone to help me with mark h questions the subject is algebra two mode, median and mean please this is serious and a cry for help if your interested please let me know also please feel free to ask for time zone and anything else thank you
Brainly will be issued as well
Answer:
Step-by-step explanation:
I am definitely willing to help anyone with algebra!
It seems you need explanations on mode, median and mean. First, let's remember that these terms are related to data sets.
Example: I have a list of grades in Algebra 2, which list off as 94, 94, 95, 96, 98, 99, 99, 99, 99, 100.
I want the mode, median and mean. The mode is the number that appears the most in a data set, the median is the number in the exact middle of a data set, and the mean is the average value of the data set.
Mode: The number that appears most in this list of grades is 99. My mode is 99, and usually people use this to represent the whole of a data set, especially when the mode appears in the majority of the data set, at least 80% of the data set.
Median: My median is basically the number in the middle of the list. Since I have an even number of 10 grades, I need to find the two numbers closest to the middle, which is 98 and 99, the fifth and sixth term. I find the average of these two numbers- (98+99)/2 = 98.5. This is my median grade. This is usually used to represent data sets when describing demographics.
Mean: This is the average of the whole data set, which means we add up all the numbers and divide them by the number of items there are. Since we have ten grades in the data set, I add (94+94+95+96+98+99+99+99+99+100)/10 = 97.3
This is my mean, which represents my average grade. The mean is used a lot when teachers create our report cards! Hope this helps, but if you need anything else, feel free to comment back on this. If you want, my electronic mail account is my username and I use g mail dot com. Feel free to each out, and Happy Birthday!
Which of the following is NOT a true statement? There are 2 possible answers. Choose one.
A. ∠EFC measures 80°
B. ∠BFC & ∠DFE have a sum of 90°
C. ∠AFD measures 130°
D. ∠AFB& ∠CFD are supplementary
Answer: C and D
Step-by-step explanation:
∠AFD measures 150°, not 130° and ∠AFB & ∠CFD are complementary, not supplementary.
25 Points Use Bisection Method to locate the root of f(x) = x/3 + In(x) - 1 on a closed interval [1,2]. Use 17 iterations to extract the root.
The Bisection Method is a numerical method used to find the roots of a function within a given interval. It works by repeatedly dividing the interval in half and checking which half contains the root until the desired level of accuracy is achieved. In this case, we are using 17 iterations to extract the root of the function f(x) = x/3 + In(x) - 1 on the closed interval [1,2].
To locate the root of f(x) = x/3 + In(x) - 1 on a closed interval [1,2] using the Bisection Method with 17 iterations, we will follow the steps below:
1. Define the function f(x) = x/3 + In(x) - 1
2. Set the initial values for the interval: a = 1 and b = 2
3. Start the iteration process by finding the midpoint of the interval: c = (a+b)/2
4. Evaluate the function at the midpoint: f(c) = f((a+b)/2)
5. Determine if the root lies in the left or right half of the interval by checking the sign of f(c)
6. If f(c) is positive, then the root lies in the left half of the interval, so we set b = c and repeat the process from step 3.
7. If f(c) is negative, then the root lies in the right half of the interval, so we set a = c and repeat the process from step 3.
8. Continue the iteration process until we have completed 17 iterations.
After 17 iterations, we will have narrowed down the interval to a very small range and the midpoint of this interval will be an approximation of the root of the function.
The Bisection Method is a numerical method used to find the roots of a function within a given interval. It works by repeatedly dividing the interval in half and checking which half contains the root until the desired level of accuracy is achieved. In this case, we are using 17 iterations to extract the root of the function f(x) = x/3 + In(x) - 1 on the closed interval [1,2].
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Solve the following system of equations using SUBSTITUTION METHOD.
SHOW YOUR WORK
Write your answer as an (x,y) point.
x= 4y - 1
3x + 2y = 25
The solution to the system of equations using the substitution method is (7,2).
Can the substitution approach be used to solve all equation systems?No, the substitution approach cannot be used to solve every system of equations. It can be challenging to replace one equation with another in some systems because they feature equations that are challenging or impossible to solve for one variable in terms of the other. Other approaches, such graphing or elimination, could be more useful in such circumstances.
Given that, the two equations are:
x= 4y - 1
3x + 2y = 25
Substitute x = 4y - 1 into the second equation:
3(4y - 1) + 2y = 25
12y - 3 + 2y = 25
14y - 3 = 25
14y = 28
y = 2
Substitute the value of y in equation:
x = 4y - 1
x = 4(2) - 1
x = 7
Hence, the solution to the system of equations using the substitution method is (7,2)
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Slope distance AB and BC measure 330.49m and 660.97 m,
respectively. The difference in elevation is 10.85 m for B and C. Using
the slope correction formula, determine the difference in elevation for
A and B if the horizontal length of line ABC is 991.45m. Assume the
line AB has a rising slope and BC has a falling slope.
The difference in elevation for A and B is the difference in elevation for line AB minus the slope correction: D = 330.422m
The slope correction formula is:
C = L * (D^2 / (2 * R)), Where:
- C is the slope correction
- L is the horizontal length of the line
- D is the difference in elevation
- R is the Earth's radius
For line BC, we can plug in the given values to find the slope correction:
C = 660.97m * (10.85m^2 / (2 * 6371000m))
C = 0.059m
For line AB, we need to find the difference in elevation first. We can do this by subtracting the slope correction from the slope distance:
D = 330.49m - 0.059m
D = 330.431m
Now we can plug in the values for line AB into the slope correction formula: C = 330.431m * (330.431m^2 / (2 * 6371000m)) C = 0.009m
The difference in elevation for A and B is the difference in elevation for line AB minus the slope correction:
D = 330.431m - 0.009m
D = 330.422m
Therefore, the difference in elevation for A and B is 330.422m.
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20% of $509 and how to work it out
Answer:
101.80
Step-by-step explanation:
Well this is fairly simple, if you can use a calculator. There not much to it so first you convert 20% to a decimal which is 0.2 or 0.20 either works. Then you multiply 0.2 by 509 to get 101.80. I used a calculator to multiply those two but Im not sure how else to do it without a calculator. Hope this helps.
Quadrilateral DEFG is a square. What is the value of t?
E
D
t =
3t+46
8t-19
G
F
as the quadrilateral is a square, all the sides will be equal to each other so DE is equal to DG.
3t + 46 = 8t - 19
-5t = -65
5t = 65
so t = 13
FACTORING POLYNOMIALS Factoring out a constant before Factor completely. 5x^(2)-55x+90
The factored form of the given polynomial is 5(x-9)(x-2).
To factor the given polynomial, 5x^(2)-55x+90, we first need to factor out the greatest common factor (GCF) which is 5. Factoring out the GCF will make the polynomial easier to factor completely.
5x^(2)-55x+90 = 5(x^(2)-11x+18)
Now, we need to factor the polynomial inside the parentheses completely. We can do this by finding two numbers that multiply to give us the constant term (18) and add to give us the coefficient of the x term (-11).
The two numbers that fit these criteria are -9 and -2. So, we can factor the polynomial inside the parentheses as follows:
x^(2)-11x+18 = (x-9)(x-2)
Putting it all together, we get the completely factored form of the given polynomial:
5x^(2)-55x+90 = 5(x-9)(x-2)
Therefore, the factored form of the given polynomial is 5(x-9)(x-2).
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Multiply the polynomials using a special product formula. Express your answer as a single polynomial in standard form. ,(2x-7)^(2)
The product of the polynomials is 4x^(2)-28x+49, which is a single polynomial in standard form.
What is polynomial?A polynomial is an expression consisting of variables, constants and coefficients, in which the exponents of the variables are either whole numbers or zero. It can be written in the form of a summation, where each term is the product of a coefficient and a variable raised to a power.
To multiply the polynomials using a special product formula, we can use the formula for squaring a binomial, which is (a-b)^(2)=a^(2)-2ab+b^(2). In this case, a=2x and b=7.
So, we can plug these values into the formula and simplify:
(2x-7)^(2) = (2x)^(2)-2(2x)(7)+(7)^(2)
= 4x^(2)-28x+49
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Use the image to determine the direction and angle of rotation.
90° clockwise rotation
270° clockwise rotation
90° counterclockwise rotation
180° counterclockwise rotation
After comparing the image and the figure, we found that the direction and angle of rotation are 180° counterclockwise rotation.
What is meant by the rotation of figures?A transformation known as a rotation involves turning the figure either clockwise or counterclockwise. The centre of rotation is the fixed location where the rotation occurs. The term "angle of rotation" refers to the amount of rotation. A figure can be rotated 90 degrees, or a quarter turn, in either a clockwise or counterclockwise direction. You have rotated the figure 180 degrees when you have spun it exactly halfway. The figurine may be rotated 360° by turning it all the way around. A counterclockwise turn has a positive magnitude because a clockwise rotation indicates a negative magnitude. Rotational symmetry exists in every regular polygon. When an object is rotated around its centre, it retains its original appearance. The object is then referred regarded as having rotational symmetry.
Let's write the coordinates of the original figure,
A = (1, -5)
B = (6, -2)
C = (6, -5)
D = (1, -8)
Now, if we rotate it 90 degrees counterclockwise, the coordinates are:
A' = ( 5, 1)
B' = (2, 6)
C' = (5, 6)
D' = (8, 1)
Now if we rotate it again 90 degrees counterclockwise, the coordinates are:
A'' = ( -1, 5)
B'' = (-6, 2)
C'' = (-6, 5)
D'' = (-1, 8)
Now from the figure, let's write the coordinates.
A' = ( -1, 5)
B' = (-6, 2)
C' = (-6, 5)
D' = (-1, 8)
This is the same as the coordinates of the second 90 degrees counterclockwise rotation.
Since we did two 90 degrees rotations, we can say we did a total of 180° counterclockwise rotation.
Therefore after comparing the image and the figure, we found that the direction and angle of rotation are 180° counterclockwise rotation.
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Answer: 180 degrees counterclockwise rotation.
Winnie purchased a new car for $54000. She has determined that it straight line depreciates to zero over 10 years. When she purchased the car she made at $8000 down payment and financed the rest with a four year loan at a 4.875%. You can also use the monthly payment formula from the last chapter to determine the monthly payment to the nearest cent.
a. Create an expense and depreciation function.
b. Graph these functions on the same axes.
c. Interpret the region before, at, and after the intersection point in light of the context of the situation.
The expense function consists of two parts: the monthly payment for the car loan and the monthly cost of depreciation. The monthly payment can be calculated using the following formula: P = (r(PV)) / (1 - (1+r)^(-n)) = $1,062.66 per month. The depreciation function will be a straight line from $54,000 to $0 over a period of 10 years (or 120 months).
What is a depreciation function?A depreciation function is a mathematical model that explains how the worth of an object decreases over time. It denotes the pace at which the worth of an asset depreciates over time.
In the given question,
a. The expense function will consist of two parts: the monthly payment for the car loan and the monthly cost of depreciation. The monthly payment can be calculated using the following formula:
[tex]P = (r(PV)) / (1 - (1+r)^(-n))[/tex]
where P is the monthly payment, r is the monthly interest rate (4.875%/12 = 0.40625%), PV is the present value of the loan (54,000 - 8,000 = 46,000), and n is the total number of payments (4 years x 12 months per year = 48). Plugging these values into the formula, we get:
[tex]P = (0.0040625(46000)) / (1 - (1 + 0.0040625)^(-48)) = $1,062.66 per month[/tex]
The depreciation function will be a straight line from $54,000 to $0 over a period of 10 years (or 120 months), so the monthly depreciation can be calculated as:
d = (54000 - 0) / 120 = $450 per month
Therefore, the expense function E(x) and depreciation function D(x) are:
E(x) = 1062.66 + 450x
D(x) = 450x
where x is the number of months since the car was purchased.
b. The graph of the expense function and depreciation function on the same axes is attached.
c. At the intersection point (around 66 months), the monthly loan payment becomes greater than the monthly depreciation cost, meaning that Winnie is paying more each month than the car is depreciating. After 66 months, the expense function is increasing faster than the depreciation function, so the total value of the car is decreasing rapidly. By the end of 120 months, the car will have depreciated to a value of $0 and Winnie will have paid a total of $62,719.20 in loan payments.
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At a carnival game, it cost Taylor $6 to toss 63 rings. Fill out a table of equivalent ratios and plot the points on the coordinate axes provided.
Graph is the collection of all points whose coordinates satisfy a given relation (such as a function).
What is coordinates?Coordinates of a point in a 2D plane, also known as cartesian coordinates, are two numbers or sometimes a combination of a letter and a number that tell us the exact location of a specific point on a grid. Here, the grid is known as a coordinate plane.
Let tosses be x and and dollars be y
Then we have, (x, y) as (63, 6)
So if in 6 dollars you get 63 tosses then 1 dollar you get = 63/6 = 10.5 tosses.
Then in 2 dollars we have = 10.5 × 2 = 21 tosses
As 21 tosses = 2 dollars
Then 42 tosses = 2 × 2 = 4 dollars
Thus, we have the table:
[tex]\boxed{\begin{array}{cc}\underline{\text{Tosses}}&\underline{\text{dollars}}&\\ \boxed{10.5}&2&\\42&\boxed4&\\63&6&\end{array}}[/tex]
To graph the given points, just correspond x as tosses and y as dollars.
Graph given in attachment
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Amna needs to make a total of 95 deliveries this week. So far she has completed 57 of them. What percentage of her total deliveries has Amna completed
If Anna has 95 deliveries to make and has delivered 57, she has completed 60% of the total deliveries.
To find the percentage of deliveries that Amna has completed, we can use the formula:
percentage = (part/whole) × 100
So in this case, the part is the number of deliveries Amna has completed, which is 57, and the whole is the total number of deliveries she needs to make, which is 95. Plugging these values into the formula, we get:
percentage = (57/95) × 100 %
percentage = 0.6 × 100 %
percentage = 60 %
Therefore, Amna has completed 60% of her total deliveries.
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