This situation also emphasises how important it is to be conscious of one's surroundings and potential hazards when performing tasks like tossing a flying disc.
When you threw the flying disc into the air, it encountered an obstacle in the form of a tree branch, which caused it to change its trajectory. As a result, the disc's momentum slowed down, and it eventually came to a rest on a nearby roof.
This phenomenon is an example of how external forces can alter an object's motion and ultimately affect its final position.
Additionally, this scenario highlights the importance of being aware of one's surroundings and potential obstacles when engaging in activities such as throwing a flying disc.
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Rewrite the two equations in the form (x−p)^2=q.
0=x^2-10x+10
x^2+26x+167.5=0
Answer:
(x - 5)^2 = 15 and (x + 13)^2 = 3
Step-by-step explanation:
Sure, I can help you with that.
Let's start with the first equation:
0 = x^2 - 10x + 10
To rewrite this equation in the form (x - p)^2 = q, we need to complete the square.
First, let's factor out the coefficient of x^2:
0 = 1(x^2 - 10x + 10)
Next, we want to add and subtract a value that will allow us to complete the square inside the parentheses. In this case, we will add and subtract (10/2)^2 = 25:
0 = 1(x^2 - 10x + 25 - 25 + 10)
Now we can rearrange the terms inside the parentheses and simplify:
0 = 1((x - 5)^2 - 15)
Finally, we can rewrite the equation in the desired form by adding 15 to both sides:
15 = (x - 5)^2
So the first equation in the form (x - p)^2 = q is:
(x - 5)^2 = 15
Now let's move on to the second equation:
x^2 + 26x + 167.5 = 0
Again, we need to complete the square to rewrite this equation in the form (x - p)^2 = q.
First, let's factor out the coefficient of x^2:
x^2 + 26x + 167.5 = 1(x^2 + 26x + 167.5)
Next, we want to add and subtract a value that will allow us to complete the square inside the parentheses. In this case, we will add and subtract (26/2)^2 = 169:
x^2 + 26x + 167.5 = 1(x^2 + 26x + 169 - 169 + 167.5)
Now we can rearrange the terms inside the parentheses and simplify:
x^2 + 26x + 167.5 = 1((x + 13)^2 - 1.5)
Finally, we can rewrite the equation in the desired form by adding 1.5 to both sides:
1.5 = (x + 13)^2 - 1.5
So the second equation in the form (x - p)^2 = q is:
(x + 13)^2 = 3
Using the digits 1 to 9, without repeating, fill in the blanks to create a system of equations that intersect at x=1
The exponential function system that intersects as x = 1, is [tex]y = 3(1)^x[/tex] and [tex]y = \frac{6}{8} \times (4)^x[/tex].
What is an exponential function?The formula for an exponential function is [tex]f(x) = a^x[/tex], where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.
The d Here are two different exponential functions of the required form that intersect at x = 1 -
[tex]y = 3(1)^x[/tex]
[tex]y = \frac{6}{8} \times (4)^x[/tex]
In the first equation, a = 3, and b = 2.
Plugging in x = 1, we get -
[tex]y = 3(1)^1[/tex]
y = 3 × 1
y = 3
So the point of intersection of this equation with the x-axis is (1, 3).
In the second equation, a = 6/8 , and b = 4.
Plugging in x = 1, we get -
[tex]y = \frac{6}{8} \times (4)^1[/tex]
y = 3/4 × 4
y = 3
So the point of intersection of this equation with the x-axis is also (1, 3).
So, both of these equations intersect at x = 1 and are of the form [tex]y = a \times b^x[/tex].
Therefore, the equations are [tex]y = 3(1)^x[/tex] and [tex]y = \frac{6}{8} \times (4)^x[/tex].
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Complete reference question:
6x^2 + 60x + c what is c so to make it a perfect square trinomial
The calclulated value of c to make a perfect square trinomial from 6x^2 + 60x + c is 150
Calculating the value of c to make a perfect square trinomialTo make a quadratic trinomial a perfect square trinomial, we need to add a constant term that is equal to half of the coefficient of the x-term, squared.
In other words, we need to find a value of c such that:
6x^2 + 60x + c = Perfect square trinomial
Divide through by 6
So, we have
x^2 + 10x + c/6 = Perfect square trinomial
Take the coefficient of x
k = 10
Divide by 2
So, we have
k/2 = 5
Square both sides
(k/2)^2 = 25
This means that
c/6 = 25
So, we have
c = 150
Therefore, to make the trinomial 6x^2 + 60x + c a perfect square trinomial, we need to choose c = 150.
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What is the quotient of 13 and 0.4
A. 5.2
B. 52
C. 3.25
D. 32.5
Show work please.
Answer:
The quotient of 13 and 0.4 can be found by dividing 13 by 0.4.
13 ÷ 0.4 = (13/1) ÷ (2/5) = (13/1) × (5/2) = 65/2 = 32.5
So the answer is D. 32.5.
Step-by-step explanation:
The quotient of 13 and 0.4 is 32.5. The method involves directly dividing 13 by 0.4, either manually or using a calculator.
Explanation:The student is asking for the quotient of 13 and 0.4. Quotient means the result of a division operation. In this case, we divide 13 by 0.4. Here's how:
Firstly, we divide 13 by 0.4 directly using a calculator or manually.The result is 32.5.So, the quotient of 13 and 0.4 is 32.5. Therefore, the answer is (D) 32.5.
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2 1/4-6/7=
2 5/12-blank=2/3
7 1/12-5 3/8=
blank+7/10=2 9/20
To subtract 6/7 from 2 1/4, we need to find a common denominator. The least common multiple of 7 and 4 is 28, so we can convert 2 1/4 to 9/4 and 6/7 to 24/28. Then we can subtract:
9/4 - 24/28
= 63/28 - 24/28
= 39/28
Therefore, 2 1/4 - 6/7 = 39/28.
To solve for the blank in 2 5/12 - blank = 2/3, we can start by converting 2 5/12 to an improper fraction:
2 5/12 = (2*12 + 5)/12 = 29/12
Then we can subtract 2/3 from both sides:
2 5/12 - 2/3 = blank
To subtract these fractions, we need to find a common denominator. The least common multiple of 3 and 12 is 12, so we can convert 2/3 to 8/12. Then we can subtract:
29/12 - 8/12
= 21/12
= 7/4
Therefore, the blank in 2 5/12 - blank = 2/3 is 7/4.
To subtract 5 3/8 from 7 1/12, we need to find a common denominator. The least common multiple of 8 and 12 is 24, so we can convert both mixed numbers to improper fractions:
7 1/12 = (712 + 1)/12 = 85/12
5 3/8 = (58 + 3)/8 = 43/8
Then we can subtract:
85/12 - 43/8
= 85/12 - (433)/(83)
= 85/12 - 129/24
= 5/24
Therefore, 7 1/12 - 5 3/8 = 5/24.
To solve for the blank in blank + 7/10 = 2 9/20, we can start by converting 2 9/20 to an improper fraction:
2 9/20 = (2*20 + 9)/20 = 49/20
Then we can subtract 7/10 from both sides:
blank + 7/10 - 7/10 = 49/20 - 7/10
Simplifying the right side:
49/20 - 7/10 = (492)/(202) - (74)/(104) = 98/40 - 28/40 = 70/40 = 7/4
Therefore, blank + 7/10 - 7/10 = 7/4, and solving for blank:
blank = 7/4
Therefore, the blank in blank + 7/10 = 2 9/20 is 7/4.
Rachel ran 3 miles when she was training for a race. How many feet did she run?
15,840 feet
5,280 feet
10,560 feet
14,840 feet
To convert miles to feet, we need to multiply the number of miles by the number of feet in one mile. There are 5,280 feet in one mile. So, to find out how many feet Rachel ran, we can multiply 3 miles by 5,280 feet/mile:
3 miles x 5,280 feet/mile = 15,840 feet
Therefore, Rachel ran 15,840 feet. Answer: 15,840 feet.
The customer service department of a company found that the relationship between the number of minutes a customer spends on hold when telephoning and the customer's level of satisfaction on a 10-point scale can be approximated by the equation y=10−0.1x
, where x
is the number of minutes on hold and y
is the level of satisfaction. What does 0.1 represent in the equation?
In the equation y = 10 - 0.1x, the coefficient 0.1 represents the slope of the line.
Define slopeit represents the rate of change of y with respect to x, which is the amount by which y changes for every unit increase in x.
In this case, the slope is negative (-0.1), which means that as the number of minutes on hold (x) increases by 1 unit, the level of satisfaction (y) decreases by 0.1 units.
In other words, the longer a customer spends on hold, the lower their level of satisfaction is likely to be. The slope is a key parameter in the equation and provides valuable information about the relationship between the two variables.
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Round 7.19 to the nearest tenth
Answer:
7.2
Step-by-step explanation:
The 1 looks at the number to the right of it. If the number to the right is 5 or more, the 1 moves up to a 2. Hope this helps!
144q-15
as a product of two factors
144q-15 can be expressed as a product of two factors: 3 and (48q-5). The greatest common factor between 144q and 15 is 3:144q = 3 x 48q15 = 3 x 5, so we can factor out the common factor.
What is factor of algebraic expression?The number or algebraic expression that divides another number or expression completely or with no remainder is factor of that expression ,1 is a factor of every number. It is also the smallest factor of a number. or we can say a factor of a number is defined as an exact divisor of the given number. example, the factors of 20 are 1, 2, 4, 5, 10, and 20.
Given that an equation 144q-15
express 144q-15 as a product of two factors,
we can use factorization by grouping:
144q-15 = 12*12q - 3*5 = 3(412q - 5)
Therefore, 144q-15 can be expressed as the product of two factors:
3(48q-5)
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1. Give the rule for translating a point 4 units left and 8 units up. (2 points)
2. After the translation, where is A located? (2 points)
2. After the translation, where is A located? (2 points) Now reflect the figure over the y-axis. Answer the questions to find the coordinates of A after the reflection. 3. Give the rule for reflecting a point over the y-axis. (2 points)
4. What are the coordinates of A after the reflection? (2 points)
5. Is the final figure congruent to the original figure? How do you know? (2 points)
The image of the original figure after the translation and reflection is congruent to the original figure.
Translation over a point is what?A particular type of transformation on the coordinate plane called translation keeps the size of the point or geometrical shape constant while only changing the position. Along the x-axis and y-axis in the coordinate system, the point or the figure can be moved in any direction, including up, down, right, left, and multiple directions.
1. By taking away 4 from the x-coordinate and adding 8 to the y-coordinate, we can translate a point 4 units left and 8 units up.
2. Point A after translation is situated at (-2, 9).
3. We negate the x-coordinate and leave the y-coordinate unaltered to indicate a point over the y-axis.
4. Point B is obtained by reflecting point A over the y-axis (2, 9).
5. Indeed, the resulting representation is consistent with the original figure since the rigid transformations of translation and reflection maintain angles and distances. As a result, the original figure's picture after translation and reflection corresponds to the original figure.
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HELLLP FAST
Mathamatics
Answer:
512 ft and 1,232 ft
Step-by-step explanation:
area is length x width
the pool's area can be calculated doing 32ft x 16ft
the area of the pool is 512 ft
the deck's area can be calculated doing 28ft x 44ft
the area of the deck is 1,232 ft
you're welcome<3
if you borrow $1,000 for 4 years at an annual interest rate of 8% what is e total amount of money you will pay back
The total amount of money you will pay back when borrowing $1,000 for 4 years at an annual interest rate of 8% with annual compounding is $1,360.50.
How does compound interest work?The interest you receive is referred to as compound interest. Using simple math, you can see how this works: if you have $100 and it generates 5% interest annually, you will have $105 at the end of the first year.
According to the given information:A = P*(1 + r/n)[tex]^(^n^*^t^)[/tex]
A is the total amount
P is the principal (initial amount borrowed), which is $1,000 in this case
r is the annual interest rate expressed as a decimal, which is 0.08 (8%)
n is the number of times the interest is compounded per year, which is usually 12 (monthly compounding) or 1 (annual compounding)
t is the time in years, which is 4 in this case
Assuming that the interest is compounded annually (n=1), we can plug in the values and simplify:
A = 1000*(1 + 0.08/1)¹⁴
= 1000(1.08)⁴
= 1000*1.3605
= $1,360.50
the total amount of money you will pay back when borrowing $1,000 for 4 years at an annual interest rate of 8% with annual compounding is $1,360.50.
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A bucket contains 50 lottery balls numbered 1-50. One is drawn at random. Find each probability.
P(less than 20)
Therefore the probability of drawing a ball with a number less than 20 is 0.38 or 38%.
How to find the probability ?Probability is a measure of an event's likelihood or chance of occurring. It is usually expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is unavoidable.
The probability of drawing a ball with a number less than 20 is calculated by dividing the total number of balls by the number of balls less than 20.
There are 19 balls numbered 1 through 19. As a result, the likelihood of drawing a ball with a number less than 20 is:
P(less than 20) = total number of balls / total number of balls = 19 / 50 = 0.38
So the chance of drawing a ball with a value less than 20 is 0.38, or 38%.
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what is the solution to this
Answer:
-2
Step-by-step explanation:
Which of the following is equivalent to 0=2x^(2)-16x-18 when completing the square?
Answer:
X=-1 or 9
Step-by-step explanation:
using the quadratic formula:
[tex]X=\frac{-b+-\sqrt{b^{2} -4ac} }{2a}[/tex]
X=-1
X=9
Find the next 2 terms in the geometric sequence: 4, 12, 36,
To solve using square roots, your quadratic must be in which format?
Answer:
0=-ax^2+bx+c
Step-by-step explanation:
58 points please urgent super urgent
4x=16
what is x
Answer:4? Think
Step-by-step explanation:
Please helpppp it’s urgent!!! Assume you have a balance of $3000 on a credit card with an APR of 24 %, or 2 % per month. You start making monthly payments of $200, but at the same time you charge an additional $100 per month to the credit card. Assume that interest for a given month is based on the balance for the previous month. How long does it take to pay off the credit card debt? Round your numbers to the nearest cent?
It will take around 3.72 months to pay off the credit card debt.
Explain about the annual percentage rate APR?The annual rate of interest that a person must pay on a loan or receives on a bank account is known as the annual percentage rate (APR).APR is utilized for everything, including credit cards, auto loans, and mortgages.The formula for APR is:
A = P * [tex](1 + r/n)^{nt}[/tex]
In which,
A = amount after compounding.
P = balance amount
r = rate of interest.
n = number of time compounded.
Initial balance: $30,000.
Payments per month = $200.
Expenses = $100
Balance amount = 30,000 - 12 *(200 - 100)
Balance amount = $28800
So, time taken for paying off credit card debt.
30,000 = 28800 [tex](1 + 0.24/1)^{1*t}[/tex]
[tex](1.24)^{t}[/tex] = 30,000 / 28800
[tex](1.24)^{t}[/tex] = 1.04
Solve by using logarithmic function.
t = ln (1.04) / 1.24
t = 0.31 year
t = 3.72 months
Thus, it will take around 3.72 months to pay off the credit card debt.
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Six pounds of raisins are distributed equally into five bags to make trail mix. How many pounds of raisins are in each bag
Answer: 1.2 pounds of raisins
Step-by-step explanation:
If six pounds of raisins are distributed equally into five bags, then each bag will have an equal amount of raisins. To find out how many pounds of raisins are in each bag, we can divide the total amount of raisins by the number of bags:
6 pounds ÷ 5 bags = 1.2 pounds per bag
Therefore, each bag will have 1.2 pounds of raisins.
help so i cna get out of class
Based on the given conditions, the lock solution is 205.
How to solve a lock?To solve the lock, to calculate the total score based on the given conditions:
Crocus: + 20
Daffodil: + 25
Snowflake: - 50
Tulip: + 30
Bird-Red: + 25, else + 10
Calculating the scores for each input:
TULIP: +30
CROCUS: +20
DAFFODIL: +25
TULIP: +30
DAFFODIL: +25
TULIP: +30
DAFFODIL: +25
CROCUS: +20
Total score = 30 + 20 + 25 + 30 + 25 + 30 + 25 + 20 = 205
Therefore, the solution for the lock is 205.
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Image transcribed:
SPRING NOW LOADING.
<IF CROCUS, THEN +20>
<IF DAFFODIL, THEN +25>
<IF SNOWFLAKE, THEN -50>
<IF TULIP, THEN +30>
<IF BIRD-RED, THEN +25, ELSE + 10>
TULIP
CROCUS
DAFFODIL
TULIP
DAFFODIL
TULIP
DAFFODIL
CROCUS
Solve Lock
Fred hires Trident Electrik Company to install a new light fixture. The electric company will charge an initial fee for the service call. In addition, the total cost of the job includes an installation fee that will depend on how long the job takes. This situation can be modeled as a linear relationship. 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 $25 $50 $75 $100 $125 $150 $175 $200 $225 $250 x y Time (hours) Total cost What does the y-intercept of the line tell you about the situation?
Answer:
Step-by-step explanation:
your mom
which of the following values are needed to determine the area of the trapezoid? choose all that apply
A. 5 mm
B. 6 mm
C. 8 mm
D. 10 mm
PLEASE PLEASE HELP ME!!!!!!!!
The trapezoid A’B’C’D is a dilation of the trapezoid ABCD. What is the scale factor of the dilation?
Simplify your answer and write it as a proper fraction, an improper fraction, or a whole number.
PLEASE LOOK AT PICTURE!!!!!!
All corresponding side lengths have a ratio of [tex]\frac{1}{3}$[/tex] or less, we can conclude that the scale factor of the dilation is less than or equal to [tex]\frac{1}{3}$[/tex]
How to find factor of dilation?We can use the distance formula to find the length of the sides of both quadrilaterals, and then find the ratio of corresponding side lengths to determine the scale factor of the dilation.
Let's start with the original quadrilateral ABCD. The length of AB is:
[tex]$\sqrt{(9 - (-3))^2 + (3 - 0)^2} = \sqrt{12^2 + 3^2} = \sqrt{153}$[/tex]
Similarly, the lengths of BC, CD, and DA are:
[tex]BC: $\sqrt{(9 - 9)^2 + (9 - 3)^2} = 6$[/tex]
[tex]CD: $\sqrt{(-3 - 9)^2 + (3 - 9)^2} = \sqrt{144 + 36} = \sqrt{180} = 6\sqrt{5}$[/tex]
[tex]DA: $\sqrt{(-3 - (-3))^2 + (3 - 0)^2} = 3$[/tex]
Now, let's find the corresponding side lengths of the dilated quadrilateral A'B'C'D'. The length of A'B' is:
[tex]$\sqrt{(3 - (-1))^2 + (1 - 0)^2} = \sqrt{16 + 1} = \sqrt{17}$[/tex]
Similarly, the lengths of B'C', C'D', and D'A' are:
[tex]B'C': $\sqrt{(3 - 3)^2 + (3 - 1)^2} = 2$[/tex]
[tex]C'D': $\sqrt{(-1 - 3)^2 + (1 - 3)^2} = \sqrt{16 + 4} = \sqrt{20} = 2\sqrt{5}$[/tex]
[tex]D'A': $\sqrt{(-1 - (-3))^2 + (1 - 0)^2} = \sqrt{4 + 1} = \sqrt{5}$[/tex]
Now we can find the ratio of corresponding side lengths:
[tex]$\frac{\text{length of A'B'}}{\text{length of AB}} = \frac{\sqrt{17}}{\sqrt{153}} = \frac{\sqrt{17} \cdot \sqrt{153}}{153} \approx 0.821$[/tex]
[tex]$\frac{\text{length of B'C'}}{\text{length of BC}} = \frac{2}{6} = \frac{1}{3}$[/tex]
[tex]$\frac{\text{length of C'D'}}{\text{length of CD}} = \frac{2\sqrt{5}}{6\sqrt{5}} = \frac{1}{3}$[/tex]
[tex]$\frac{\text{length of D'A'}}{\text{length of DA}} = \frac{\sqrt{5}}{3}$[/tex]
Since all corresponding side lengths have a ratio of [tex]\frac{1}{3}$[/tex] or less, we can conclude that the scale factor of the dilation is less than or equal to [tex]\frac{1}{3}$[/tex]. To find the exact scale factor, we can choose any two corresponding side lengths and take their ratio.
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You pick a card at random. 6 7 8 9 What is P(less than 8)?
Answer:
50% chance
ur welcome-ssq
Calculate the length between the points (2, 3)
and (5. 7)
A. 3
B. 4
C. 5
D. 6
can someone help me please
You deposit $6000 in an account earning 7% interest compounded monthly. How much will you have in the account in 5 years?
$
Step-by-step explanation:
FV = PV ( 1 + i)^n FV = future value ....what you are looking for
PV = present value = $ 6000
i = decimal periodic interest = .07/12
n = periods = 5 yr * 12 monts/yr = 60 periods
FV = $ 6000 ( 1 + .07/12)^60 = $ 8505.75
Pls help meee!!!
Anybody pls!!
Answer:
85 degrees.
Step-by-step explanation:
These are parallelograms, meaning the opposite sides are parallel. Since they are parallel, that the line EA becomes a transversal and a bisector for the angle CEK. That means the angle 8 and 3 are equivalent and 7 and 4 are equivalent. This is due to Same Side Interior Angles. These are two halves of the big angle. If the halves are equal, so are the angles. Therefore, CEK = CAK.
A tank in the shape of a hemisphere has a radius of 8 feet. If the liquid that fills the tank has a density of 98.9 pounds per cubic foot, what is the total weight of the liquid in the tank, to the nearest full pound?
Answer:
848,775 pounds
Step-by-step explanation:
The volume of a hemisphere with radius 8 feet is:
V = (2/3)πr^3 = (2/3)π(8^3) = 268.08 cubic feet
The weight of the liquid is given by:
W = V * ρ * g
where ρ is the density of the liquid and g is the acceleration due to gravity. Plugging in the values, we get:
W = 268.08 * 98.9 * 32.2 = 848,774.7 pounds
Rounding to the nearest full pound, the total weight of the liquid in the tank is 848,775 pounds.
Suppose Winston's annual salary as an accountant is $60,000 and his financial assets generate $4,000 per year in interest. One day, after deciding to be his own boss, he quits his job and uses his financial assets to establish a consulting business, which he runs out of his home. He outlays $8,000 in cash to cover all the costs involved with running the business and earns revenues of $150,000. What is Winston's economic profit?
$138,000
$150,000
$142,000
$78,000
Winston's economic profit based on the forgone salary of $60,000, and the revenue of $150,000 is $78,000. The correct option is therefore;
$78,000
What is an economic profit?An economic profit is a profit that accounts for both the explicit and implicit costs of a business. The economic profit is obtained from the difference between the total revenue and the costs including the opportunity costs.
The annual salary of Winston as an accountant = $60,000
The amount Winston's financial asset generates = $4,000 per year
The cost of running the business = $8,000
The amount Winston earns as revenue = $150,000
Therefore;
Winston's opportunity cost which is the forgone alternative, is the amount he earns as an accountant = $60,000
The interest of $4,000, earned from the financial asset = The cost of using the financial asset for the business
The cost of running the business = $8,000
The total cost = Opportunity cost + Cost of making use of the financial asset + The business running cost
The total cost = $60,000 + $4,000 + $8,000 = $72,000
The economic profit = The total revenue - The total cost
Therefore;
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