To determine how the graph of the parent function [tex]y = x^2[/tex] is transformed to create the graph of the new function [tex]y = -(x – 1)^2 – 5[/tex], we need to analyze the individual transformations one by one Therefore the correct option is A.
1. Translation: (x – 1) This term inside the function represents a horizontal translation of the graph. When we subtract 1 from x, the entire graph is shifted to the right by 1 unit. Hence, this function is translated right 1 unit. 2. Reflection: (-) The negative sign outside the function reflects the graph across the x-axis. Thus, the graph opens downward.
3. Vertical Transformation: -5 The term -5 outside the function causes a vertical shift of the graph downward by 5 units. In summary, the graph of the new function [tex]y = -(x – 1)^2 – 5[/tex] undergoes the following transformations: - Translated right 1 unit due to (x – 1) - Reflected (opens downward) due to the negative sign - Translated down 5 units due to -5 Therefore, the correct answer is A. Translated right 1 and down 5 only
Hence the correct option is A
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Dr. Gilmore's research group tagged and released 800 squirrels for a study of a local park. Later, they trapped 430 squirrels, 43 of which had tags.
To the nearest whole number, what is the best estimate for the squirrel population?
Using proportions, it is found that the best estimate for the squirrel population is of 8000.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, 43 squirrels out of 430 had tags. Considering that in the entire population, 800 are tagged, and we want to find the total population, the rule of three is given by:
43 tagged - 430 squirrels
800 tagged - x squirrels
Applying cross multiplication:
[tex]43x = 430 \times 800[/tex]
[tex]x = \frac{430 \times 800}{43}[/tex]
[tex]x = 8000[/tex]
The best estimate for the squirrel population is of 8000.
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The cost of a business is the amount of money spent to start the business and keep it in operation. The revenue is the amouunt of
money the business earns from the sale of goods or services.
An online business called Muffins A-plenty started on January 1 of a recent year. The lines in the graph represent the cost function and
the revenue function of the first six months that Muffins A-plenty has been in operation.
Part A
Write equations to represent the cost function and the revenue function for this business,
Parts
The profit of a business equals revenue minus cost. First write an equation that represents the profit function for Muffins replenty using
the functions for cost and revenue, Then, predict the profit after 10 months of operation, found your answer to the nearest dollar. Provide
valid mathematical reasoning and calculations to support your answer,
The profit function of the business is the difference between the revenue and the cost functions
The equations of the cost and the revenue functions are: [tex]y = \frac 43x[/tex] and [tex]y = 0.5x + 3.5[/tex]The profit function is [tex]y = \frac 56x - 3.5[/tex]The profit after 10 months of operation is 29/6Part A: The equations to represent the functionsFor the revenue function, we have the following points
(x,y) = (0,0) and (6,8.0)
Since the line passes through the origin, the equation of the line would be:
[tex]y = \frac{y_1}{x_1} * x[/tex]
So, we have:
[tex]y = \frac{8.0}{6} * x[/tex]
[tex]y = \frac 43x[/tex]
For the cost function, we have the following points
(x,y) = (0,3.5) and (9,36) for x > 5
The equation of the line would be:
[tex]y = \frac{y_1-y_2}{x_1-x_2} * (x - x_1) + y_1[/tex]
So, we have:
[tex]y = \frac{6.5-3.5}{6-0} * (x - 0) + 3.5[/tex]
[tex]y = 0.5x + 3.5[/tex]
Hence, the equations of the cost and the revenue functions are: [tex]y = 0.5x + 3.5[/tex] and [tex]y = \frac 43x[/tex]
Part B: The profit functionThis is calculated as:
Profit = Revenue - Cost
So, we have:
[tex]y = \frac 43x - 0.5x - 3.5[/tex]
Evaluate the difference
[tex]y = \frac 56x - 3.5[/tex]
Part C: The profit after 10 months of operationSubstitute 10 for x in [tex]y = \frac 56x - 3.5[/tex]
[tex]y = \frac 56 * 10 - 3.5[/tex]
[tex]y = \frac {50}6 - 3.5[/tex]
Evaluate the difference
[tex]y = \frac {50-21}6[/tex]
[tex]y = \frac {29}6[/tex]
Hence, the profit after 10 months of operation is 29/6
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YALL PLEASE HELP ME
IDC ABOUT THE POINTS
Which ratio shows all circles are similar
Radius:area
Diameter: circumference
Area; circumference radius
Diameter:
Answer:
Diameter: Circumference
Step-by-step explanation:
Because this is Pi, which is the same for any circle.
what is it and why?
Answer:
C
Step-by-step explanation:
the solution to a system of equations given graphically is at the point of intersection of the 2 lines.
the lines here are parallel and never intersect. Thus there is no solution
Solve
6÷2(1+2)
Please tell me the answer
Answer:
9
Step-by-step explanation:
Follow the order of operations:
ParenthesesExponentMultiplication and DivisionAddition and SubtractionGiven expression: 6 ÷ 2(1 + 2)
Carry out the operation inside the parentheses first:
⇒ 6 ÷ 2(3)
⇒ 6 ÷ 2 × 3
Now multiply/divide by going left to right:
⇒ 3 × 3 = 9
Solution:
To solve this problem, we will need to use the "BODMAS".
Solving the expression:
[tex]\bullet \ \ 6 \div 2(1 + 2)[/tex]
First, simplify the expression inside the brackets.
[tex]\bullet \rightarrow 6 \div 2(3) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\ex\text{Bracket addition}][/tex]
Now, 2(3) can also be written as 2 × 3, as 2(3) and 2 × 3 are equivalent.
[tex]\bullet \rightarrow 6 \div 2 \times 3[/tex]
According to the BODMAS, division first.
[tex]\bullet \rightarrow 3 \times 3 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\ex\text{Division}][/tex]
According to the BODMAS, multiplication next.
[tex]\bullet \rightarrow \boxed{\bold{9}} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\tex\text{Multiplication}][/tex]
Thus, the solution to 6 ÷ 2(1 + 2) is 9.
In four years time Evie will be three times older than she was two years ago, How old will she be in one year
Answer: Evie will be 6 years old in one year.
2 years ago, Evie was 3 years old. Now, she is 5. 4 years after 5 would make her 9. 3*3=9
If In four years time Evie will be three times older than she was two years ago, then in one year's time Evie will be 6
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
In four years time Evie will be three times older than she was two years ago,
Let the age of Evie be x in one year.
By the given information we formulate a equation.
In four years time means we have to add 4 to the present age, x+4.
three times older than she was two years ago can be written as 3(x-2)
Now,
In four years time Evie will be three times older than she was two years ago
x + 4 = 3(x − 2)
Apply distributive property on RHS side
x+4=3x-6
x-3x=-6-4
-2x=-10
x=5
Therefore in one year's time Evie will be x+1 =6, 6 years old.
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slope- intercept form: y= -4/3x + 2
what is the standard form?
Answer:
4x-3y=-6
Step-by-step explanation:
90 POINTS!!
Haley has $155 in savings, and her brother Hank has $230. Hayley is saving $10 each week and her brother is spending $15 each week. After how many weeks will their savings account have the same amount of money in them?
Answer:
3 weeks
Step-by-step explanation:
Set the equations. Let "amount of weeks" be signified by the variable, x.
First, note that Haley starts with $155, and saves $10 each week:
10x + 155
Next, note that her brother has $230 saved and spends $15 each week:
230 - 15x.
Set the two equations equal to each other:
10x + 155 = 230 - 15x
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS. PEMDAS is the order of operations, and stands for:
Parenthesis
Exponents (& Roots)
Multiplications
Divisions
Additions
Subtractions
~
First, subtract 155 and add 15x to both sides of the equation:
10x (+15x) + 155 (-155) = 230 (-155) - 15x (+15x)
10x + 15x = 230 - 155
25x = 75
Next, divide 25 from both sides of the equation:
(25x)/25 = (75)/25
x = 75/25 = 3
3 weeks is your answer.
~
The men walked down the streets to the mine with their heads bent close to their chests. In groups of five or six they scurried on. It was impossible to recognize individuals from the small gaps between their caps, pulled down over their eyes, and the tightly bound scarves tied tightly over the bottom half of their faces
Is the inference true or false? The weather was cold, windy, and rainy.
Please select the best answer from the choices provided
T
F
What is the circumference of a circle with a radius of 84 inches? (Use 3.14 for Pi.)
Answer:
238.76
Step-by-step explanation:
I believe
Answer:
C≈527.79in
Solution
C=2πr=2·π·84≈527.78757in
If the area of a triangle whose base measures 3 cm is 6 sq.cm, then its height is
O 4 cm
O 2 cm
O 6 cm
O 5 cm
Answer:
then the height would be 2 because 3*2=6
Step-by-step explanation:
Answer:
4 cm
Step-by-step explanation:
area of triangle is: area = (base*height)/2.
since the area is 6 m^2, and base is 3 cm,
6 m^2 = (3 m*height)/2
12m^2 = 3 m*height
height = 4 m
Find the area of the trapezoid. The median is equal to 25cm and the height is 8cm. (btw if you explained how to find the base would help a lot) :)
The area of trapezium with a median of 25 cm and height of 8 cm = 200 cm².
What is the Area of a Trapezium?Area of trapezium = 1/2(a + b)h, where a and b are the parallel bases of the trapezium, and h is the height.
Note, median of a trapezium = half of the sum of the length of the two bases of a trapezium = 1/2(a + b). Therefore, the area of a trapezium with a given median would be:
A = median length × height
Given the following:
Median = 25 cmHeight = 8 cm.Area of trapezium = 25 × 8 = 200 cm².
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9) y + 3 = -(x + 5)
5
A) x + y = 5
C) x - y = 5
B) 2x + 5y = 0
D) 8x – 5 y=-25
Answer:
y+3=-(x+5)5
y+3=-5x-25
y+3+5x+25=0
y+5x+28=0
Make and test a conjecture about the given quantity.
18. The product of two negative even integers
19. The sum of two negative odd integers
20. The sum of two even integers and two odd integers
21. When you return from a run, your
friend states, “If you ran 1 mile, then
you ran 5280 feet." Your friend then
asks if you can write the statement as
a biconditional statement. Write the
biconditional statement and decide
whether it is true.
Answer:
18. The conjecture is: The product of two negative even integers is an even integer.
Testing: Let integers be -4 and -6. [Two negative even integers]
Then (-4) × (-6) = 24 [Even integer]
19. The conjecture is: Sum of two negative odd integers is a negative even integer.
Testing: Let the two negative odd integers be -3 and -7.
Then -3 + (-7) = -10 is a negative even integer
20. The conjecture is: Sum of two even integers and two odd integers is an even integer.
Testing: Let integers be 4, 12, 13, 17 (Two even integers and two odd integers)
Then 4 + 12 + 13 + 17 = 46 (Even integer)
21. The statement is: p------->q [If you ran 1 mile, then you ran 5280 feet]
Decide whether statement is true: So if p is True then q is also True.
Hence p------->q is True. So the given statement is True.
Step-by-step explanation:
18. The product of two negative even integers.
Let the integers be -2m and -2n, m and n are positive integers
Product in (-2m) × (-2n) = 4mn = 2(2mn)
= 2p, p = 2mn
The conjecture is: The product of two negative even integers is an even integer.
Testing: Let integers be -4 and -6. [Two negative even integers]
Then (-4) × (-6) = 24 [Even integer]
19. The sum of two negative odd integers.
Let the integers be -(2m + 1) and -(2n + 1), m and n are positive integers
Then -(2m + 1) + [-(2n + 1)] = -2m - 1 - 2n - 1
= -2m - 2n - 2
= -2(+m + 2 + 1)
= -2p, p = m + n + 1
The conjecture is: Sum of two negative odd integers is a negative even integer.
Testing: Let the two negative odd integers be -3 and -7.
Then -3 + (-7) = -10 is a negative even integer
20. The sum of two even integers and two odd integers.
Let the integers be 2m, 2n, 2p + 1, 2q + 1 (m, n, p, q are positive integers)
Then, 2m + 2n + 2p + 1 + 2q + 1 = 2(m + n + p + q + 1)
= 2r, r = m + n + p + q + 1
The conjecture is: Sum of two even integers and two odd integers is an even integer.
Testing: Let integers be 4, 12, 13, 17 (Two even integers and two odd integers)
Then 4 + 12 + 13 + 17 = 46 (Even integer)
21. Let p: You ran 1 mile
Let q: You 5280 feet
The statement is: p------->q [If you ran 1 mile, then you ran 5280 feet]
Since 1 mile = 5280 feet
So if p is True then q is also True.
Hence p------->q is True. So the given statement is True.
i need to find the x and the y
Answer: X=1 Y=-5
Step-by-step explanation:
−9x+2y+−2y=−19+−2y(Add -2y to both sides)
−9x=−2y−19 (Divide by 9 on both sides)
x= 2/9y+19/9 now Substitute 5(2/9y+19/9)+4y=-15=
46/9+95/9=-15 (simplify both sides)
46/9+95/9+-95/9=-15+-95/9 (Add (-95)/9 to both sides) =
46/9y=-230/9 (now divide both sides by 46/9) than equals
y=-5
for X we plug in -5 like this: X=2/9(-5)+19/9 now just evaluate than simplify both sides which equals: 1
The owner of a bike shop would like to analyze the sales data to determine if the business is growing, declining, or remaining flat. The owner has the following data: Sales Revenue Last Year =$125,000 Sales Revenue Current Year = $150, 000 What is the Sales Growth?.
The sales growth of the business of owner of a bike shop is $25000 and this business is growing.
What is sales growth?Sales growth is the amount of by which a business is growing. Sales growth is the difference of sales revenue of current year and the sales revenue of last year.
The owner of a bike shop would like to analyze the sales data to determine if the business is growing, declining, or remaining flat. The owner has the following data:
Sales Revenue Last Year =$125,000
Sales Revenue Current Year = $150, 000
As, the sales growth is the difference of sales revenue of current year and the sales revenue of last year. Thus, the sales growth of the business is,
[tex]\rm SG=150000-125000\\SG=25000[/tex]
Hence, the sales growth of the business of owner of a bike shop is $25000 and this business is growing.
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Please answer!! a b c or d?
Answer:
The reflection of a horizontal line has the same result as a rotation of 90 degrees clockwise.
Answer: Choice B
270 degree rotation clockwise
=======================================================
Explanation:
Notice that 270+90 = 360
Going 90 degrees in one direction is the same as going 270 degrees in the other direction because the two combine to a full 360 degree rotation.
Check out the image below for an example. In the example, the point P starts at (0,5). Doing either rotation mentioned will get us to (-5,0).
help me) 2y+x+3x-y
Simplify this expression by combining like terms
A boat heading out to sea starts out at Point AA, at a horizontal distance of 1206 feet from a lighthouse/the shore. From that point, the boat’s crew measures the angle of elevation to the lighthouse’s beacon-light from that point to be 9^{\circ} ∘. At some later time, the crew measures the angle of elevation from point BB to be 4^{\circ} ∘. Find the distance from point AA to point BB. Round your answer to the nearest tenth of a foot if necessary
Answer:
1525.6
Step-by-step explanation:
Question 10 of 40
Factor this polynomial completely.
x² - 81
O A. (x-2)(x - 9)
B. (x - 81)(x - 81)
C. (x+81)(x - 81)
O D. (x + 9)(x-9)
Answer:
D) (x + 9)(x-9)
Step-by-step explanation:
[tex]x^2-81[/tex]
Let's Rewrite 81 as → 9^2
[tex]x^2-9^2[/tex]
Now, apply difference two squares formula
[tex]\left(x+9\right)\left(x-9\right)[/tex]
~
help with math homework please! [ image attached + 15 point award ]
Answer:
40°
Step-by-step explanation:
As we have,
[tex]\rm\hookrightarrow[/tex]The Sum of all sides of a triangle is 180°
Now,
[tex]\rm\hookrightarrow 79+x+52+x+73=180\\\\\rm\hookrightarrow x=180-79-52-73\\\\\rm\hookrightarrow x=-12[/tex]
Again, finding the measure of ∡A by putting the value of x.
[tex]\rm\hookrightarrow x+52\\\\\rm\hookrightarrow -12+52\\\\\rm\hookrightarrow 40[/tex]
Find an equation for the line that passes through the points (-5, -5) and (3, 5)
Answer:
5x-4y+5=0.
Step-by-step explanation:
1) if the point A(-5;-5) and B(3;5), the formula is:
[tex]\frac{x-X_A}{X_B-X_A} =\frac{y-Y_A}{Y_B-Y_A}[/tex]
2) according to the formula above:
[tex]\frac{x+5}{3+5} =\frac{y+5}{5+5}; \ = > \ \frac{x+5}{4}=\frac{y+5}{5};[/tex]
or 5x-4y+5=0.
Which equation represents circle W?
Answer:
B (x - 6)² + (y + 4)² = 16
Step-by-step explanation:
From inspection of the graph:
center of the circle = (6, -4)radius = 4 unitsGeneral equation of a circle: (x - a)² + (y - b)² = r²
(where (a, b) is the center and r is the radius)
Therefore, substituting the given values into the equation:
equation of the circle: (x - 6)² + (y + 4)² = 16
Answer:
Answer B
Step-by-step explanation:
Centre of Circle (6,-4)
Radius = 4
Substitute in the Equation attached
[tex](x-h)^{2}+(y-k)^{2} =r^{2}[/tex]
[tex](x-6)^{2} +(y-(-4))^{2} =4^{2}[/tex]
[tex](x-6)^{2} +(y+4)^{2} =16[/tex]
Find the value of y. 4y² - 106 The value of y is
Answer:
7
Step-by-step explanation:
4y²-106=90
4y²=90+106
4y²=196
4y²/4=196/4
y²=49
y=√49
y=7
Find the circumference.
Answer:
[tex]2 \times 3.14 \times 6 = 37.68[/tex]
...
...
...
.
.
How many times greater is the value of 3 in 300 than the value of the 3 in 30
Answer:
ten times I hope I'm right
Step-by-step explanation:
3 × 100 = 300
3 × 10 = 30
sense 3 is what is being talked about, 3 in the 300 is 100 times and 3 in 30 is 10 times.
100 is 10 times 10
10 × 10 = 100
value is the total
how many times greater is the total of the 3 in both numbers
3 in 300 is 10 times the 3 in 30
hope this helps
Za and Zb are complementary angles. Za measures 44°.
What is the measure of Zb?
Answer:
zb = 46°
Step-by-step explanation:
za + zb = 90
44° + zb = 90°
90° - 44° = zb
zb = 46°
Instructions: Rewrite the equation in Slope-Intercept Form.
Answer:
y=−2/5x+2
Step-by-step explanation:
^
What is EC? please help me I will mark you as brainliest!
Step-by-step explanation:
DB/EC = AD/BE
5/EC = 4/12
5 = 4/12 EC
5×12/4 = EC
15 = EC
EC = 15
Julius currently pays the minimum monthly payment of $34.15 on his credit card, which has a balance of $1,289. his credit card has an apr of 20%. if julius wants to pay off the balance in 12 months, determine the monthly payments he needs to make. choose the following modification with the least cuts to his current expenses that will allow julius to pay off his credit card balance in 12 months. income wages $2,456.00 expenses rent $900.00 utilities $186.35 food/clothes $298.00 entertainment $330.00 car $385.00 credit card $34.15 cell phone $89.49 net income $233.01 a. julius can eliminate $31 from entertainment and $55 from food/clothes. b. julius can eliminate $80 from entertainment and $60 from food/clothes. c. julius can eliminate $18 from entertainment and $32 from food/clothes. d. the minimum payment is enough to pay off the balance within 12 months.
Julius can eliminate $31 from entertainment and $55 from food/clothes. Then the correct option is A.
What is APR?APR on a credit card is the way of saying that the interest you are charged over a year is equal to roughly of your balance.
Julius currently pays the minimum monthly payment of $34.15 on his credit card, which has a balance of $1,289.
His credit card has an APR of 20%.
If Julius wants to pay off the balance in 12 months, determine the monthly payments he needs to make.
Choose the following modification with the least cuts to his current expenses that will allow Julius to pay off his credit card balance in 12 months.
Income wages $2,456.00
Expenses rent $900.00
Utilities $186.35
Food/clothes $298.00
Entertainment $330.00
Car $385.00
Credit card $34.15
Cell phone $89.49
net income $233.01
The net amount will be over 12 months is 1432.92.
Monthly payback will be
[tex]\rm Monthly\ pay = \dfrac{1432.92}{12}\\\\Monthly\ pay = 119.41[/tex]
She was paying 105.68 dollars per month. Then the amount will be
Amount = 119.41 – 34.15 = 85.26
Julius can eliminate $31 from entertainment and $55 from food/clothes. Then the correct option is A.
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Answer:
a
Step-by-step explanation: