Answer: Choice A
f(x) = (x + 2)^2 - 11
=========================================================
Work Shown:
y = x^2 + 4x - 7
y+7 = x^2 + 4x
y+7+4 = x^2 + 4x + 4
y+11 = x^2 + 4x + 4
y+11 = (x + 2)^2
y = (x + 2)^2 - 11
f(x) = (x + 2)^2 - 11
In the third step, I added 4 to both sides to complete the square for the x^2+4x portion. Notice that (x+2)^2 = x^2+4x+4. So I added 4 to fill in the missing piece needed to complete the square.
Put another way the '4' added to both sides is because we first divided the x coefficient 4 in half to get 4/2 = 2. Then you square it to get 2^2 = 4.
--------------------
Alternative Method (optional)
y = x^2 + 4x - 7 is in the form of y = ax^2+bx+c
where: a = 1, b = 4, c = -7
Plug those a,b values into the formula below
h = -b/(2a)
h = -4/(2(1))
h = -2
This is the x coordinate of the vertex.
Use it to find the y coordinate of the vertex.
y = x^2 + 4x - 7
y = (-2)^2 + 4(-2) - 7
y = -11
The vertex is located at (h,k) = (-2,-11)
We have the template y = a(x-h)^2 + k update to y = (x + 2)^2 - 11 after plugging in a = 1, h = -2, and k = -11.
Directions: Name each polygon and tell if it is regular or irregular.
Answer:
regular pentagon. 2 irregular. 3 irregular. 4 regular octagon. 5 regular nonagon. remember that regular polygon is a polygon that
The mean temperature for the first 7 days in January was 4 °C. The temperature on the 8th day was -1 °C. What is the mean temperature for the first 8 days in January?
Answer:
3.375 °C
Step-by-step explanation:
Mean temperature for first 7 days = 4 °C
⇒ Total temperature over first 7 days = 4 °C × 7 = 28 °C
Temperature on 8th day = -1 °C
[tex]\sf mean=\dfrac{\textsf{sum of all the numbers}}{\textsf{amount of numbers}}[/tex]
Therefore, mean temperature for first 8 days:
= [28 - 1] ÷ 8
= 27 ÷ 8
= 3.375 °C
determine the general rule for0,3,8,15
Answer:
a_n = n^2 − 1
Step-by-step explanation:
The numbers can be described as a polynomial with the following formula:
a1 = 1^2 − 1 = 1 - 1 = 0
a2 = 2^2 − 1 = 4 - 1 = 3
a3 = 3^2 − 1 = 9 - 1 = 8
a4 = 4^2 − 1 = 16 - 1 = 15
a5 = 5^2 − 1 = 25 - 1 = 24
A baker bakes 48 dozen doughnuts each morning. She sells 18 dozen
in her store and fills orders with the rest. Write a fraction to show the
portion of doughnuts the baker sells in her store. Be sure to simplify.
Answer:
30/48
Step-by-step explanation:
he work of a student to solve the equation 4(2x − 4) = 8 + 2x + 8 is shown below: Step 1: 4(2x − 4) = 8 + 2x + 8 Step 2: 6x − 8 = 16 + 2x Step 3: 6x − 2x = 16 + 8 Step 4: 4x = 24 Step 5: x = 6 In which step did the student first make an error and what is the correct step? Step 2; 8x − 4 = 2(6 + x + 6) Step 2; 8x − 16 = 16 + 2x Step 3; 6x − 2x = 16 − 8 Step 3; 6x + 2x = 16 + 8
Answer:
step 2: 8x-4=2(6+x+6)
Step-by-step explanation:
[tex]4(2x - 4) = 8 + 2x + 8 \\ 8x - 16 = 16 + 2x here \\ 8x - 2x = 16 + 16 \\ 6x = 32 \\ \frac{6x}{6} = \frac{32}{6} \\ x = 5[/tex]
Answer:
4(2x-4)=8+2x+8
8x-16=16+2x
8x-2x=16+16
6xboth sides over 6
x=5.3repiting
The graph of y=kcos(8x)
The x coordinate of point A that is shown on the graph is 3π/16.
How to explain the graph?From the information given, y = kcos(8x). Also, the axis of symmetry is given as kx.
Therefore, the x coordinate will be:
= π/8 + π/16
The LCM of 8 as 16 is 16.
= 2π/16 + π/16
= 3π/16
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Anybody please help thank you!
Answer:
alright well
from what I got x is 29.444 , y is 34 and angle b is 60 degrees
the correct answer is A.
Step-by-step explanation:
Fahari kicks a ball on the ground into the air. One
second after being kicked, the ball reaches its
maximum height of 16 feet above the ground, and
2 seconds after being kicked, the ball is back on the
ground. A quadratic function models the height h(t) ,
in feet, of the ball t seconds after Fahari kicks it.
Which equation defines this relationship?
The equation that defines the relationship between the height and the time and models the position of the ball in time is the quadratic function y = - 8 · t² + 24 · t.
How to derive a quadratic function for the height of a ball
Quadratic functions are polynomials of grade 2 of the form y = a · t² + b · t + c, where t and y are the time and the height of the ball, in seconds and feet, respectively. To determine the value of the three coefficients we need to know three different points of the form (t, y).
If we know that (t₁, y₁) = (0 s, 0 ft), (t₂, y₂) = (1 s, 16 ft) and (t₃, y₃) = (3 s, 0 ft), then the quadratic function is:
a · 0² + b · 0 + c = 0 (1)
a · 1² + b · 1 + c = 16 (2)
a · 3² + b · 3 + c = 0 (3)
The solution to this system is a = - 8, b = 24, c = 0.
The equation that defines the relationship between the height and the time and models the position of the ball in time is the quadratic function y = - 8 · t² + 24 · t.
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Consider this cone with a diameter of 19 cm. A cone with diameter 19 centimeters and slant height of 31 centimeters. Use the drop-down menus to describe the cone measurements. What is the radius measure of the cone? cm What is the base area of the cone? Pi cm2 What is the surface area of the cone? Pi cm2
Answer:
1) Radius of the cone = 9.5 cm
2) BA = 90.25 π cm²
3) SA = 384.7 π cm²
Step-by-step explanation:
1) Radius of the cone = 9.5 cm
2) Base Area of the cone =
BA = (π)(9.5)²
BA = 90.25 π cm²
3) Surface Area of Cone =
SA = π(9.5)(9.5 + √(29.5)²+(9.5)²)
SA = 9.5π(9.5 + 31)
SA = 9.5π(40.5)
SA = 384.7 π cm²
Edge 2022
Consider the function FX equals -2/3 X -24 which conclusions can be drawn about F negative 1X select two options a F negative 1X has a slope of -2/3 F1X has a restricted domain of negative 1X has a slight intercept of zero -36 -1 and 7X intercept of -3 60 negative 1X has a range of all real numbers
The conclusions that can be drawn about f–1(x) are:
[tex]f^-^1(x)[/tex] has an x-intercept of (-36, 0)[tex]f^-^1(x)[/tex] has a range of all real numbers.Calculations and Parameters:Given:
[tex]f(x) = \frac{-2}{3}x - 24[/tex]
[tex]f(x) + 24 = \frac{-2}{3}x[/tex]
To find x, we would multiply both sides by -2/3
= [tex]x= \frac{-3}{2} (f(x) + 24)[/tex]
[tex]f^-^1(x) = -\frac{3}{2} (0) - 36[/tex]
[tex]f^-^1(x) = -36[/tex]
Therefore, [tex]f^-^1(x)[/tex] has an x-intercept of (-36, 0)
Furthermore, [tex]f^-^1(x)[/tex] has a range of all real numbers.
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0.2(7 + 2t) = 0.4t + 1.4
Answer:
all real numbers
Step-by-step explanation:
When you factor in the .2 on the left side you are left with 1.4 + .4t which is equal to the other side. And so, no matter what value for t you plug in, they will always be equal to eachother.
WHAT IS THIS HELP
if u put a bad answer i'll report
Answer:
C
Step-by-step explanation:
Two negatives cancel out and turn into a positive.
In the expression 11 - ( -3 5/8 ) there are two negative signs. If the parenthesis are removed, the two negative signs cancel out and turn into a positive and we are left with 11 +3 5/8
So the answer is C
This is super easy. Explanation, please!
The proposition given by definition of function "division" is false as [tex]\frac{f}{g} \ne {(1, 2)}[/tex] for the former function f = (9, 5) and the latter function g = (9, 0).
How to analyse a operation between two functions by propositional approach
In this question we have a definition of division between two functions, consisting in dividing each component of the ordered pair of the former function (f) by the component of the ordered pair of the latter function (g) such that resulting ordered pair is (1, 2).
We must check if the proposition is true for every ordered pair. Let analyze each case:
Case I
[tex]\frac{f}{g} = \left(\frac{1}{1}, \frac{6}{3} \right) = (1, 2)[/tex]
Case II
[tex]\frac{f}{g} = \left(\frac{9}{9}, \frac{5}{0} \right) = (1, NaN)[/tex]
Thus, the proposition is false.
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A flower bed is in the shape of a rectangle. It measures 7 yards long and 3 yards wide. David wants to use mulch to cover the flower bed. The mulch is sold by the square foot. Find the area of the flower bed in square feet.
The area of the rectangle is equal to 216ft^2.
We have given that,
A flower bed is in the shape of a rectangle.
It measures 7 yards long and 3 yards wide. David wants to use a mulch to cover the flower bed.
The mulch is sold by the square foot.
A yard is equal to 3 feet.
7 yards = 7(3) = 24 feet
3 yards = 3(3) = 9 feet
What is the formula for the area of the rectangle?
Area of the rectangle= Lw
Area of the rectangle= 24(9)
Area of the rectangle= 216 ft^2
Therefore the area of the rectangle is equal to 216ft^2.
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Conor’s monthly costs are £695 he wants to go on holiday and needs to save £680 how much does he need to save each month if he saves for 5 months
The amount of money Conor should save each month for 5 months is £136.
How much should he save each month?Division is the mathematical operation that is used to determine the quotient of a number. It involves grouping a number into equal parts using another number.
The amount of money Conor should save each month = total amount needed / number of month
£680 / 5 = £136
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Rose bought a bag of potatoes for $6.00 and some granola bars for $5.25 per package. Her total bill was $74.25. How many packages of granola bars did she buy? Enter your answer in the box.
Answer:
Rose bought 14 packages of granola bars.
Step-by-step explanation:
Total bill = 1 bag of potatoes + x amount of packages of granola bars
Total bill = $74.25
1 bag of potatoes = $6.00
1 package of granola bar = 5.25
We set the equation to:
74.25 = 6.00 + 5.25x
Subtract 6.00 from both sides:
68.25 = 5.25x
Divide both sides by 5.25 to leave x by itself
68.25/5.25 = 5.25x/5.25
13 = x
This means Rose bought 13 packages of granola bars.
Let's recheck our work by inputting x = 13 into the equation:
74.25 = 6.00 + 5.25(13)
74.25 = 6.00 + 68.25
74.25 = 74.25
Please help with question 2, 3 and possibly 4 if you can.
The solution of the inequality are (iii) and (iv)
The solution of the equality is x = 8.
The solution of the equality is x = 0.
How to solve inequality ?The solutions of the inequalities can be found as follows:
x³ + 3(5 - 2) ≥ 20 - 4
x³+ 3(3) ≥ 16
x³+ 9 ≥ 16
x³ ≥ 16 - 9
x³ ≥ 7
x ≥ ∛7
x ≥ 1.9
Therefore, (iii) and (iv) are solution.
4(72 - x²) = 3.12 - 4
288 - 4x² = 36 - 4
288 - 4x²= 32
-4x² = -256
x²= 256 / 4
x²=64
x= √64
x= 8
7(x + 12) = 7.12
7x + 84 = 84
7x= 84 - 84
7x= 0
x = 0
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If the property tax on a $250,000 home is $1200, what is the tax on a $120,000 home?
Answer:
well i mean it all depends were you live at
Step-by-step explanation:
in new york it will be $36,198. but in California it would be about $31,682 and Your average tax rate is 16.51% and your marginal tax rate is 24%.
how to find the area of a trapezium
3(5z-7) - 2 (9z-11) = 4 (8z-13) - 17
please help me. i’m very stressed.
[tex]\sqrt[n]{a^n}=a[/tex], therefore [tex]\sqrt[4]{5^4}=5[/tex].
Answer:
It is 5
Key solutions:
[tex]\left(\sqrt[n]{a}\right)^n=a[/tex]Step-by-step explanation:
Isolate the exponents and remove the square, giving you 5
[tex]\left(\sqrt[4]{5}\right)^4\\=5[/tex]
If you were charged $151 in taxes on a $3,020 purchase, you were charged Blank 1 % on the purchase.
Answer:
5 %
Step-by-step explanation:
3020 * x = 151 x is the percentage in decimal form
x = 151 / 3020 = .05 which is 5 %
A sum of Rs. 12,500 amounts to Rs. 16,500 in 4 years at the rate of simple interest. What is the rate of interest?
Answer:
100
Step-by-step explanation:
Answer:
The rate of interest is6.4 %
Step-by-step explanation:
Given : Principal (P) = Rs12500
Total amount (A) = Rs16500.
The time period (t) =5 years
To find : Rate of interest (R) = ?
Solution :
It is given that Principal (P) = Rs. 12500
Total amount (A) = Rs. 16500
The time period (t) =5 years
We have to find rate of interest (R).
We know the formula for simple interest as,
S.I. = A-P
= 16500±12500
= Rs. 4000
Now, to find rate of interest, use the formula for simple interest as
S.I. =
∴
∴ *R
∴
∴
∴R=6.4 %
∴ The rate of interest is6.4 %.
3. Find the measures of the angles in the figure.
Answer:
60° , 60° , 120° , 120°Step-by-step explanation:
NOTE :
the sum of the 4 interior angles of a quadrilateral is 360°.
…………………………………………
Then
h + h + 2h + 2h = 360
Then
6h = 360
Then
h = 360 ÷ 6 = 60
Then
2h = 2 × 60 = 120
If you rolled two dice, what is the probability
that you would roll a sum of 3?
second
1
first
2 3
5
4
6
1
[?]
1,1 1,2 1,3 1,4 1,5 1,6
2 2,1 2,2 2,3 2,4 2,5 2,6
3 3,1 3,2 3,3 3,4 3,5 3,6
4,1 4,2 4,3 4,4 4,5 4,6
5 5,1 5,2 5,3 5,4 5,5 5,6
6,1 6,2 6,3 6,4 6,5 6,6
6
Probability =
Desired Outcome
All Outcomes
Simplify your fraction, then enter the numerator AND DENOMINATOR.
Thank youuuu
Answer:
2 / 36 = 1/18
Step-by-step explanation:
there are 2 ways to get 3
1 then 2 or 2 then 1 , 2 out of a possible 36 outcomes
A. Gus buys cupcakes every Saturday morning. When he walks into the bakery, he always orders by saying, "Give me $10 worth of cupcakes." What does this tell you about Gus's elasticity of demand for cupcakes?
B. Use the graph believe to illustrate Gus’ demand for cupcakes. This line should only contain the two endpoints (X axis is quantity of cupcakes 0-25 going by 5s, Y axis is Price of cupcakes 0-6 going up by 2)
The thing that can be deduced from Gus's elasticity of demand for cupcake is that the demand for cupcakes is perfectly elastic.
What is elasticity of demand?It should be noted that elasticity of demand simply means the responsiveness to demand when there's a change in price.
Gus's elasticity of demand for cupcake is that the demand for cupcakes is perfectly elastic. This is when the percentage change in quantity demanded is infinite due to the price change.
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draw a point that belongs to the solution region of this system of inequalities. y>1.5^x + 4 y< 2/3x + 6
The point (1,6) belongs to the solution region of the system of inequalities.
How to determine the point in the solution region?The system of inequalities is given as:
y>1.5^x + 4
y< 2/3x + 6
Next, we plot both inequalities on a graph (see attachment)
From the attached graph, the point (1,6) is on the solution region of the inequalities
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2. If the parent function is y= 4*, which is the function of the graph?
2
4
y=-2(4)*
y=2(4)*
y=3(4)*
A function assigns the values. The function of the given graph is y=3(4)ˣ, thus, the correct option is C.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The complete question is:
If the parent function is y = 4ˣ, which is the function of the graph?
y = −2(4)ˣ
y = −3(4)ˣ
y = 3(4)ˣ
y = 2(4)ˣ
Since the graph intersect the y-axis at 3, and the parent function of the function is y=4ˣ, therefore, we can write,
y = A(4)ˣ
3 = A(4)⁰
3 = A × 1
A = 3
Hence, the function of the given graph is y=3(4)ˣ, thus, the correct option is C.
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graph linear equation 6x - 2y = 12
The graph of the linear equation 6x - 2y = 12 would be option C .
What is a linear equation?Linear equation is equation in which each term has at max one degree. Linear equation in variable x and y can be written in the form y = mx + c
Linear equation with two variables, when graphed on the cartesian plane with axes of those variables, give a straight line.
Subtract both sides from 6x, leaving you with the equation:
-2y = -6x + 12
Now, you divide all of the sides by -2,
y = 3x - 6
The graph of the linear equation 6x - 2y = 12 would be option C .
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This figure is a square, with side lengths as shown.
415 mm
What are the perimeter and the area of the square?
80
200
400
8√5 16√5
32√5
The perimeter of the square is,
The area of the square is_
millimeters.
square millimeters
The perimeter and area of the square are 16√5 mm and 80 mm²
How to find perimeter and area of a square?Perimeter of a square = 4L
where
l = lengthTherefore,
Perimeter of a square = 4 × 4√5
Perimeter of a square = 16√5 mm
Area of a square = l²
Area of a square = (4√5)²
Area of a square = 16 × 5
Area of a square = 80 mm²
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