After rotating the triangle counterclockwise by 270 degrees, the new coordinates of the vertices would be (3, -1), (-4, 2), and (3, 5).
How to Find the New Coordinates of a Triangle after a Rotation?To rotate a point counterclockwise around the origin by 270 degrees, we can use the following transformation rules:
[tex]New_x = -y[/tex]
[tex]New_y = x[/tex]
Let's apply these rules to each vertex of the triangle and find the new coordinates:
For the first vertex (-3, 1):
[tex]New_x = -1[/tex]
[tex]New_y = -(-3) = 3[/tex]
So, the new coordinates for the first vertex after rotating counterclockwise by 270 degrees are (3, -1).
For the second vertex (2, 4):
[tex]New_x = -4[/tex]
[tex]New_y = 2[/tex]
The new coordinates for the second vertex after rotating counterclockwise by 270 degrees are (-4, 2).
For the third vertex (5, -3):
[tex]New_x = -(-3) = 3[/tex]
[tex]New_y = 5[/tex]
The new coordinates for the third vertex after rotating counterclockwise by 270 degrees are (3, 5).
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The scatterplot above displays the relationship between the amount of food hippopotamuses eat per day and their age. Describe and explain any associations and data features on the scatterplot. Then, use the variables on the graph to interpret the relationship that is shown.
The scatter plot shows a [positive linear] association.
How to determine the association of the scatterplotFrom the question, we have the following parameters that can be used in our computation:
The image of the scatter plot
On the scatter plot, we can see that
The points appear to be on a straight line
Also, we can see that
As the x values increases the y values increases
This represents a positive linear association.
Hence, the association is a positive linear association.
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Regina is comparing two checking accounts. One has a monthly fee of $12
and a per-check fee of $0.10, and the other has a monthly fee of $9 and a per-
check fee of $0.25. What is the minimum number of monthly checks Regina
needs to write for the first account to be a better option?
A. 15
B. 30
OC. 21
OD. 20
The minimum number of monthly checks Regina needs to write for the first account to be a better option is 21 or more. Answer C. 21 is one of the suggested choices.
To solve this problemOn the basis of the quantity of checks written, we can compare the overall costs of the two accounts.
Let's calculate the total cost for each account based on the given information:
First Account:
Monthly fee: $12
Per-check fee: $0.10
Total cost = Monthly fee + (Per-check fee * Number of checks)
Second Account:
Monthly fee: $9
Per-check fee: $0.25
Total cost = Monthly fee + (Per-check fee * Number of checks)
We must determine the point at which the first account's total cost is less than the second account's total cost. Let's construct the formula:
$12 + ($0.10 * Number of checks) < $9 + ($0.25 * Number of checks)
Simplifying the equation
$12 - $9 < ($0.25 - $0.10) * Number of checks
$3 < $0.15 * Number of checks
Dividing both sides by $0.15:
$3 / $0.15 < Number of checks
20 < Number of checks
Therefore, the minimum number of monthly checks Regina needs to write for the first account to be a better option is 21 or more. Answer C. 21 is one of the suggested choices.
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3. Solve: 5 x 4+ (1+1) + 5 = *
Your answer
Answer:
27
Step-by-step explanation:
We can solve by using order of operations (PEMDAS), which shows us the order in which we're supposed to perform mathematical operations:
Parentheses,Exponents,Multiplication/DivisionThe / comes from the fact that you do these operations from left to right as multiplication and division have the same level of priority in an equation/operation.
and Addition/Subtraction.Like multiplication/division, the / comes from the fact that you do these operations from left to right as addition and subtraction also have the same level of priority in an equation/operation.
Step 1: Simplify inside the parentheses:
5 * 4 + (1 + 1) + 5
5 * 4 + 2 + 5
Step 2: Multiply 5 and 4:
20 + 2 + 5
Step 3: Add 20 and 2:
22 + 5
Step 4: Add 22 and 5 to get your answer:
27
Thus, 5 *4 + (1 + 1) + 5 = 27
Danielle Stevenson receives a commission of 6.5% for selling a $160,000 house. One-half of the commission goes to the broker, and one-half of the remainder to another salesperson. Stevenson receives the rest. Find the amount she receives.
Answer:
Danielle Stevenson receives $2,600 from selling the $160,000 house.
Step-by-step explanation:
To find the amount Danielle Stevenson receives from selling the house, we'll follow these steps:
Calculate the commission earned by Danielle Stevenson: Commission = 6.5% * $160,000.
Commission = 0.065 * $160,000 = $10,400.
Determine the broker's share: Broker Share = 0.5 * Commission.
Broker Share = 0.5 * $10,400 = $5,200.
Calculate the remaining amount after the broker's share: Remaining Amount = Commission - Broker Share.
Remaining Amount = $10,400 - $5,200 = $5,200.
Determine the salesperson's share: Salesperson Share = 0.5 * Remaining Amount.
Salesperson Share = 0.5 * $5,200 = $2,600.
Finally, calculate the amount Danielle Stevenson receives, which is the remaining portion after the broker and salesperson's shares: Amount Danielle Receives = Remaining Amount - Salesperson Share.
Amount Danielle Receives = $5,200 - $2,600 = $2,600.
Therefore, Danielle Stevenson receives $2,600 from selling the $160,000 house.
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Please help I don’t understand thank you have a blessed day
By evaluation, the values of the rational function are f(11) = - 1 / 12 and f(- 2) = 1, respectively.
How to evaluate a rational function
In this problem we find the case of a rational function that must be evaluated at two different x-values: x = 11, x = - 2. The procedure is summarized below:
Write the entire expression.Substitute on x with the given value.Simplify the expression by algebra properties.Now we proceed to present the complete procedure:
f(11) = 11 / (11 + 1) - 1
f(11) = 11 / 12 - 1
f(11) = 11 / 12 - 12 / 12
f(11) = (11 - 12) / 12
f(11) = - 1 / 12
f(- 2) = (- 2) / (- 2 + 1) - 1
f(- 2) = - 2 / (- 1) - 1
f(- 2) = 2 - 1
f(- 2) = 1
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The graph show the probability distribution of a
random variable.
What is the value of P(2 < X <5)?
O 0.30
O 0.35
O 0.40
O 0.45
0.3
0.25
0.2
0.15
0.1
0.05
1
Probability Distribution
2
3 4
S.
9.
N
B
The solution is : the value of P(2≤X≤5) is 0.50.
Here, we have,
given that,
The graph show the probability distribution of a random variable.
we know that,
The probability distribution of a random variable X is P(X = xi) = pi for x = xi and P(X = xi) = 0 for x ≠ xi. The range of probability distribution for all possible values of a random variable is from 0 to 1, i.e., 0 ≤ p(x) ≤ 1.
so, we have,
P(2≤X≤5)
=P(x=2)+ P(x=3)+ P(x=4)+ P(x=5)
= 0.2+ 0.1 +0.05+0.15
= 0.50
Hence, The solution is : the value of P(2≤X≤5) is 0.50.
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What is 35 degree angle in standard position?
After using ruler and following the steps described below
We get the standard position of 35 degree.
The given angle is = 35 degree
To draw standard position of angle:
We proceed it to draw by ruler
So, in order to get position,
Follow the following steps:
1: Draw a straight line with your ruler.
2: Place your protractor on the line and align the base of the protractor with the line.
3: Find the 35 degree mark on the protractor and make a small mark on the line at that point.
4: Move your protractor to the mark you just made.
5: Align the base of the protractor with the line and make another small mark on the line at the 35 degree mark.
6: Draw a straight line connecting the two points you just marked.
And there you have it! A 35 degree angle drawn on paper.
And after following these steps we get the standard potion angle 35 degree.
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Can someone help find the surface area, then round the answer to the nearest whole number please?
The Surface Area of cylinders are: 100 yd² , 264 m², 226 mm²
The Surface Area of Can is 219 cm².
We know the formula for Surface Area of Cylinder
= 2πrh
1. Radius = 2 yd
Height = 8 yd
So, Surface Area of Cylinder
= 2πrh
= 2 x 3.14 x 2 x 8
= 100 yd²
2. Radius = 7 m
Height = 6 m
So, Surface Area of Cylinder
= 2πrh
= 2 x 3.14 x 6 x 7
= 264 m²
3. Radius = 3 mm
Height = 12 mm
So, Surface Area of Cylinder
= 2πrh
= 2 x 3.14 x 3 x 12
= 226 mm²
4. Radius = 3.5 cm
Height = 10 cm
So, Surface Area of Can
= 2πrh
= 2 x 3.14 x 3.5 x 10
= 219 cm²
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Dos horas y media ¿A cuántos minutos equivale?
Answer:
90 minutos
Step-by-step explanation:
una hora es 60 minutos y media es 30 minutos.
Please help me answer this question
For the function [tex]A(t)=4000e^0^.^0^4^t[/tex] the value of A'(8) is $220 and the value of [tex]A'(t)=160e^0^.^0^4^t[/tex]
The given function is [tex]A(t)=4000e^0^.^0^4^t[/tex] gives the balance after t years.
The initial investment is 8000
4% is the compounded interest.
Now differentiate with respect to t
[tex]A'(t)=0.04(4000)e^0^.^0^4^t[/tex]
[tex]A'(t)=160e^0^.^0^4^t[/tex]
Now let us find the value of A'(8)
Plug in t as 8
[tex]A'(8)=160e^0^.^0^4^(^8^)[/tex]
A'(8)=220.3
Hence, the value of A'(8) is $220 and the value of [tex]A'(t)=160e^0^.^0^4^t[/tex]
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What is the value of x *
7+5x
47°
Answer: X = 8
Step-by-step explanation:
47 - 7 = 40
40 / 5 = 8
x = 8
you and a friend have created a carnival game for your classmates. you plan to charge $1 for each time a student plays, and the payout for a win is $5. according to your calculations, the probability of a win is .05 what is your expected value for this game?
Answer:
The expected value for this game is -$0.75, indicating that, on average, players would expect to lose $0.75 per game.
Step-by-step explanation:
Expected Value = (Probability of Winning * Payout for Win) - Cost of Playing
In this case:
Probability of Winning = 0.05
Payout for Win = $5
Cost of Playing = $1
Expected Value = (0.05 * $5) - $1
Expected Value = $0.25 - $1
Expected Value = -$0.75
Elon sent a chain letter to his friends, asking them to forward the letter to more friends.
The relationship between the elapsed time,
�
tt, in days, since Elon sent the email, and the total number of people who receive the email,
�
(
�
)
P(t)P, left parenthesis, t, right parenthesis, is modeled by the following function:
P(t)=4⋅3t
Complete the following sentence about the daily rate of change in the number of people who receive the email.
Every day, the number of people who receive the email
by a factor of
.
Every day, the number of people who receive the email grows by a factor of 3.
What is an exponential function?In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:
[tex]f(x) = a(b)^x[/tex]
Where:
a represents the initial value or y-intercept.x represents x-variable.b represents the rate of change, common ratio, decay rate, or growth rate.Based on the information provided above, an exponential function for the total number of people who received the email is given by;
[tex]P(t) = 4(3)^t[/tex]
By comparison, we have the following parameters;
Initial value, a = 4.
Growth rate, b = 3.
In conclusion, the number of people who receive the email from Elon every day grow by a factor of 3.
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Raina wants to buy a new house but needs money for the down payment. Her parents agree to lend her money at an annual rate of 6%, charged as simple
interest. They lend her $7000 for 5 years. She makes no payments except the one at the end of that time.
Answer the following questions. If necessary, refer to the list of financial formulas.
(a) How much total interest will Raina have to pay?
(b) What will the total repayment amount be (including interest)?
$
X
a. Raina will have to pay a total of $2100 in interest.
b. The total repayment amount, including interest, will be $9100.
How to Calculate Total Interest?To calculate the total interest and total repayment amount, we can use the formula for simple interest:
Simple Interest = Principal * Rate * Time
(a) Total interest:
Principal = $7000
Rate = 6% per year
Time = 5 years
Total Interest = Principal * Rate * Time
= $7000 * 0.06 * 5
= $2100
(b) Total Repayment Amount = Principal + Total Interest
= $7000 + $2100
= $9100
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A square piece of sheet metal (24 in x 24 in)
is used to make an open box (no lid). Equal
squares are cut out of each corner, and the
edges are folded up to make the box.
What is the maximum volume, V, of the box?
The maximum volume of the box is 864 cubic inches.
Let side length of the square cut from each corner is x inches.
After cutting the squares from each corner, the remaining dimensions of the sheet metal will be:
Length: 24 - 2x inches
Width: 24 - 2x inches
Height: x inches
So, the volume of the box
V = (24 - 2x) (24 - 2x) x
V = x(24 - 2x)²
To find the maximum volume, we can take the derivative of V with respect to x, set it to zero, and solve for x:
dV/dx = (24 - 2x)² - 2x(24 - 2x) = 0
4x² - 96x + 576 = 0
Solving the quadratic equation,
x = 6 and x = 12.
We can substitute x = 6 into the volume equation to find the maximum volume:
V = 6(24 - 2(6))²
V = 6(12)²
V = 6 x 144
V = 864 cubic inches
Therefore, the maximum volume of the box is 864 cubic inches.
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A student scored 80% on a test. If the test had 50 questions worth one point each, how many questions did the student answer correctly?
Answer:
40
Step-by-step explanation:
All questions are worth the same, 1 point each.
80% of 50 = 0.8 × 50 = 40
Answer: 40
Answer:
40
Step-by-step explanation:
80/100*50 = 40
I need help with this math
Answer:
500 and 4.3
Step-by-step explanation:
A decigram is one-tenth of a gram and a kilometer is one-thousandth of a meter. Using this information, we must multiply the given amounts by the values.
5000 × 0.1 = 500
4300 × 0.001 = 4.3
Thus, the answers [in order] are 500 and 4.3
Hope this helps and feel free to ask any questions.
What is the x of 4(40)-10
please helpppp me i can not figure this out it is an attachment
If they both start riding at the same time and ride at their current rates, the time is that A. Amy will have to wait 0.5 minute for Sebastian.
How to explain the informationLet v be the speed of Amy and Sebastian.
Option A states that Amy will have to wait 0.5 minutes for Sebastian. This implies that Sebastian is faster than Amy since he catches up to her within half a minute.
Therefore, Amy will have to wait 0.5 minute for Sebastian. This was calculated thus:
V = 3.0 - 2.5
v = 0.5
Therefore, Amy will have to wait 0.5 minute for Sebastian.
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Part of the population of 5,250 elk at a wildlife preserve is infected with a parasite. A random sample of 50 elk shows that 8 of them are infected. How many elk are likely to be infected? Based on the sample, there will likely be infected elk in the wildlife preserve.
The likely population of the infected elk in the wildlife preserve is 840.
What is the likely population of the infected elk?A sample is a smaller group of the population. A sample is a representation of the population.
The fraction of infected elks in the sample to the total sample would be the same of the infected elks in the population to the total population of the elks.
Population of the infected elk = (infected elks in the sample / total sample) x number of elks in the preserve
(8/50) x 5250
= 0.16 x 5250 = 840
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what’s is the surface area of this rectangular prism?
Answer:
220 in²
Step-by-step explanation:
surface area = [area of the 4 vertical faces] + area of the base + area of top.
surface area = [2(4 X 10) + 2(5 X 10)] + (4 X 5) + (4 X 5)
= (80 + 100) + 20 + 20
= 220 in²
Triangle ABC is shown. Use the graph to answer the question.
triangle ABC on a coordinate plane with vertices at 1 comma negative 2, 9 comma negative 2, 5 comma 2
Determine the coordinates of the image if triangle ABC is translated 5 units down.
A′(−4, −2), B′(4, −2), C′(0, 2)
A′(1, −7), B′(9, −7), C′(5, −3)
A′(1, 3), B′(9, 3), C′(5, 7)
A′(6, −2), B′(14, −2), C′(10, 2)
If triangle ABC is translated 5 units down, the coordinates of the image vertices are A′(1, −7), B′(9, −7), C′(5, −3).
The correct option among the given choices is A′(1, −7), B′(9, −7), C′(5, −3).
To determine the coordinates of the image if triangle ABC is translated 5 units down, we need to subtract 5 from the y-coordinate of each vertex of the triangle.
The given vertices of triangle ABC are A(1, -2), B(9, -2), and C(5, 2).
To translate the triangle 5 units down, we subtract 5 from the y-coordinate of each vertex.
The new coordinates of the vertices after the translation are:
A': (1, -2 - 5) = (1, -7)
B': (9, -2 - 5) = (9, -7)
C': (5, 2 - 5) = (5, -3)
Therefore, the correct option among the given choices is A′(1, −7), B′(9, −7), C′(5, −3).
In summary, if triangle ABC is translated 5 units down, the coordinates of the image vertices are A′(1, −7), B′(9, −7), C′(5, −3).
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Zara's car depreciates at a rate of 14% per year.
By what percentage has Zara's car depreciated after 5 years?
Give your answer to the nearest whole number.
NO SPAM.
Answer:
53%
Step-by-step explanation:
You want to know the depreciation of car value after 5 years if it is 14% per year.
MultiplierThe multiplier of value each year is ...
1 + growth rate = 1 + (-14%) = 0.86
When the value has been multiplied by that 5 times, it has been multiplied by ...
0.86^5 ≈ 0.4704
This represents a change in value from the original value of ...
0.4704 -1 = -0.5296 = -52.96% ≈ -53%
Zara's car has depreciated by 53% after 5 years.
<95141404393>
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Match each sine or cosine value to its equivalent measure
The equivalent sine and cosine values are as follows:
cos(74°) = sin(16°)cos(57°) = sin(33°)sin(32°) = cos(58°)sin(43°) = cos(47°)What is the relationship between sine and cosine angles?The relationship between sine and cosine angles is:
sinθ = cos(90 - θ)
This equation is known as the complementary angle identity for sine and cosine. It states that the sine of an angle is equal to the cosine of its complementary angle (90 degrees minus the original angle).
For example, if we have an angle theta = 30 degrees, its complementary angle would be 90 - 30 = 60 degrees.
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What is the end behavior of:
(2x ^ 2 - 5) / (x ^ 2 - 1)
A) x -> ∞ : f(x) -> 0
B) x -> ∞ : f(x) -> 2
C) f(x) -> - ∞ : x -> ∞
D) x -> ∞ : f(x) -> ∞
The given function does not have an end behavior because it is not a polynomial function.
What is the end behavior of a function?The end behavior of a function refers to how the function behaves or approaches as the input values (x-values) of the function become extremely large (approaching positive infinity) or extremely small (approaching negative infinity).The long term behavior of the function when x moves towards the ends of the coordinate plane can be predicted.
In a polynomial function, the leading coefficient and degree of the function often determine the polynomial function.
The given function is;
f(x) = 2x² - 5 / x² - 1
The end behavior of this function does not exist because this is not a polynomial.
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What is 50% of half of 10?
Answer:
2.5
Step-by-step explanation:
half of 10 is 10/2 = 5
so 50% of 5 is 2.5
a function that has a degree of 5 must have which one of the following?
a. 5 real zeros
b. 4 turning points
c. a maximum
d. at least one real 0
A function that has a degree of 5 must have the following: d. at least one real 0.
What is a polynomial function?In Mathematics and Geometry, a polynomial function is a mathematical expression which comprises intermediates (variables), constants, and whole number exponents with different numerical value, that are typically combined by using specific mathematical operations.
Generally speaking, the degree of a polynomial function is sometimes referred to as an absolute degree and it is the greatest exponent (leading coefficient) of each of its term.
In conclusion, a function that has a degree of 5 is referred to as a quintic function and it is characterized by an odd degree, can't have more than 4 turning points, and must have at least one real zero.
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Investor C decided to purchase a home that costs $600,000 with a 40% down payment loan, a 3.00% annually fixed rate for a 30 year term, and one payment per month. What is the monthly payment for this mortgage?
Step-by-step explanation:
To calculate the monthly payment for a mortgage, you can use the formula for a fixed-rate mortgage:
Monthly Payment = (P * r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
P = Loan amount (in this case, the home cost minus the down payment)
r = Monthly interest rate (annual rate divided by 12 and converted to decimal)
n = Total number of payments (number of years multiplied by 12)
Given:
Home cost = $600,000
Down payment = 40% of the home cost = 0.4 * $600,000 = $240,000
Loan amount = Home cost - Down payment = $600,000 - $240,000 = $360,000
Annual interest rate = 3.00%
Loan term = 30 years
First, calculate the monthly interest rate:
Monthly interest rate = (Annual interest rate / 100) / 12 = (3.00 / 100) / 12 = 0.0025
Next, calculate the total number of payments:
Total number of payments = Loan term * 12 = 30 * 12 = 360
Now, substitute the values into the formula:
Monthly Payment = ($360,000 * 0.0025 * (1 + 0.0025)^360) / ((1 + 0.0025)^360 - 1)
After performing the calculations, the monthly payment for this mortgage is approximately $1,520.06.
I hope I was helpful
What is the value of x?
Solving a simple equation, we can see that x = 35.
How to find the value of x?The 3 lines with an arrow that go to the left are parallel lines, thus, the relation between the sets of values in each of the sides must be the same ones.
Then we can take the quotients between the respective values, and these quotients must be equal, so we can write:
30/12 = x/14
And now we can solve that equation for x, we will get:
x = 14*(30/12)
x = 35
That is the value of x.
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Find the area of the shaded region. Round to the nearest tenth if necessary.
A. 332.1 cm
B. 210 cm
C. 201.3 cm
D. 205.8 cm
The area of the shaded region, obtained by finding the area of the composite figure is the difference between the area of the square and the area of the triangle and semicircle composite figure.
5. The area of the shaded region is about 205.8 cm squared. The correct option is therefore;
D. 205.8 cm squared
What is a composite figure?A composite figure is a figure that is composed two or more regular figures.
The area of the shaded region can be found by considering the unshaded region as a composite figure consisting of a triangle and a semicircle.
The area of the unshaded semicircle = π × 24²/8 = 72·π
The area of the triangular part of the unshaded region = (1/2) × 24 × 12 = 144
Area of the square = 24 × 24 = 576
Therefore, the area of shaded region = 576 - (72·π + 144) ≈ 205.8
The area of the shaded region ≈ 205.8 cm squared
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