For the functions f(x)=x² and g(x) = (4x)² the best statement is the graph of g(x) is vertically stretched by a factor of 4.
The function g(x) = (4x)² can be rewritten as g(x) = 16x²
Comparing this with f(x) = x², we can see that g(x) is equal to f(x) multiplied by 16.
Therefore, the graph of g(x) is the same as the graph of f(x) except that it is vertically stretched by a factor of 16.
The graph of g(x) is vertically stretched by a factor of 4.
Hence, for the functions f(x)=x² and g(x) = (4x)² the best statement is the graph of g(x) is vertically stretched by a factor of 4.
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URGENT!!!
Find the value of n in the picture above. Leave your answer in simplest radical form.
The value of n in the given triangle is given as follows:
[tex]n = 4\sqrt{5}[/tex]
What is the geometric mean theorem?The geometric mean theorem states that the length of the altitude drawn from the right angle of a triangle to its hypotenuse is equal to the geometric mean of the lengths of the segments formed on the hypotenuse.
The bases of the triangle are given as follows:
8 and 10.
Hence the altitude n is given as follows:
n² = 8 x 10
n² = 80
[tex]n = \sqrt{80}[/tex]
[tex]n = \sqrt{16 \times 5}[/tex]
[tex]n = 4\sqrt{5}[/tex]
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I’m stuck on these questions help
The coordinates of the point halfway between the origin and point B is [0, 5].
The coordinates of the midpoint of point A and point B is [5, 4].
The coordinates of the midpoint of point P and point Q is [7, 8].
How to determine the midpoint of a line segment?In order to determine the midpoint of a line segment with two (2) endpoints, we would add each point together and then divide by two (2):
Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]
For line segment BO, we have:
Midpoint of BO = [(0 + 0)/2, (10 + 0)/2]
Midpoint of BO = [0, 10/2]
Midpoint of BO = [0, 5].
For line segment AB, we have:
Midpoint of AB = [(2 + 8)/2, (4 + 4)/2]
Midpoint of AB = [10/2, 8/2]
Midpoint of AB = [5, 4].
For line segment QP, we have:
Midpoint of QP = [(7 + 7)/2, (10 + 6)/2]
Midpoint of QP = [14/2, 16/2]
Midpoint of QP = [7, 8].
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Given: Circle k(O) with OT ⊥ XY, OU ⊥ WZ, and ∠XOY ≅ ∠ZOW Prove: OT ≅ OU
50 points
Polygon JKLM is drawn with vertices J(−2, −5), K(−4, 0), L(−1, 2), M (0, −1). Determine the image coordinates of M′ if the preimage is translated 4 units up.
M′(−4, −1)
M′(4, −1)
M′(0, −5)
M′(0, 3)
Answer: M′(−4, −1)
Step-by-step explanation: m=-2 j+-5+4=M′(−4, −1)
Answer:
Option D
Step-by-step explanation:
DO THE MATH: Dade buys a new patio bench in Wooster, Ohio for the price of
$266.20 which includes a sales tax of 6.5%. What is the price of the patio bench
without sales tax? Round your answer to the nearest penny.
$265.27
$248.90
$249.99
$249.95
Price without tax is $249.95.
What is patio bench ?A patio bench is a common piece of outdoor furniture for a patio or deck. To fit varied outdoor locations and seating requirements, it can be produced in a number of forms and sizes and is often made of wood, metal.
We can multiply the total cost by (1 + tax rate) to get the cost of the patio bench sans sales tax.
(1 + 0.065) = 1.065
Price without tax = $266.20 / 1.065 = $249.9
Therefore, the correct answer is D) $249.95.
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Name the similar triangles. ΔBAC ~ ΔDEF , ΔBAC ~ ΔEDF, ΔBAC ~ ΔDFE, ΔBAC ~ ΔFED
Based on the angle-angle similarity theorem (AA), the similar triangles in the image given can be named as: ΔBAC ~ ΔEDF.
What are Similar Triangles?When two triangles have the same shape but have different sizes, it means the triangles have corresponding pairs of congruent angles and corresponding pairs of sides that are proportional to each other. The triangles are said to be similar.
The image given show two set of triangles that have two corresponding pairs of congruent angles, based on the angle-angle similarity theorem, it means that they are similar to each other.
Therefore, the similar triangles are:
ΔBAC ~ ΔEDF.
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Carved into the desert are a number of drawings that can only be seen from a helicopter, See if you can see my dilation inspired drawings of the drawings! Fill in the missing four pieces (either the scale factor, (AB) or (A'B')) with correct values from the "Number Bank".
For the humming bird X = 130m
For the monkey r= 2
For the trapezoid X = 110m
For the whale r = 7/2
How to calculate the scale factor of a given model?To calculate the scale factor of a given shape or model, the formula that should be used would be;
Scale factor = dimensions of bigger model/smaller model
For hummingbird:
X = 585/4.5
= 130m
For monkey ;
r= 440/220
= 2
For the trapezoid;
X= 165×2/3
= 330/3
= 110m
For the whale;
r= 420/120
= 7/2
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Your class is collecting bottled water for a service project. The goal is to collect 300
bottles of water. On the first day, Max brings in 3 packs of water with 6 bottles in each
pack. Sarah brings 6 packs with 6 bottles in each pack. How many bottles of water do
they still need to be brought?
Step-by-step explanation:
Goal: 300
Max brought: 3 × 6 = 18 bottles in total.Sarah brought: 6 × 6 = 3636 + 18 = 54300 - 54 = 246They still need 246 bottles.
If the quadratic formula is used to solve 2 -3 -1 = 0, what are the solutions?x2x
PLEASE HELP
If the quadratic formula is used to solve 2x² - 3x - 1 = 0, the solutions include the following: C. [tex]x = [\frac{3\; + \;\sqrt{17}}{4}, \frac{3\; - \;\sqrt{17}}{4}][/tex]
What is a quadratic equation?In Mathematics and Geometry, a quadratic equation can be defined as a mathematical expression that can be used to define and represent the relationship that exists between two or more variable on a graph.
In Mathematics, the standard form of a quadratic equation is represented by the following equation;
ax² + bx + c = 0
Mathematically, the quadratic formula is represented by this mathematical equation:
x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}
For the given quadratic equation 2x² - 3x - 1 = 0, we have:
[tex]x = \frac{-(-3)\; \pm \;\sqrt{(-3)^2 - 4(2)(-1)}}{2(2)}\\\\x = \frac{3\; \pm \;\sqrt{9 +8}}{4}\\\\x = \frac{3\; \pm \;\sqrt{17}}{4}[/tex]
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Complete Question:
If the quadratic formula is used to solve 2x² - 3x - 1 = 0, what are the solutions?
The equation f(x) = (x - 1)²2 - 2 is being
moved 3 units to the right and 3 units up, write
the new equation
The new equation after moving 3 units to the right and 3 units up is
[tex]f(x) = (x - 4)^{2} 2 + 1.[/tex]
How to move the equation rights and up?We need to change the equation to move the function [tex]f(x) = (x - 1)^{2} 2 - 2[/tex] three units to the right and three units up:
To shift the function three units to the right, replace x with (x - 3), which adjusts the graph three units to the right. [tex]f(x) = ((x - 3) - 1)^{2} 2 - 2[/tex], which simplifies to [tex]f(x) = (x - 4)^{2} 2- 2.[/tex]
To move the function three units up, multiply the equation by three.[tex]f(x) = (x - 4)^{2} 2 + 1[/tex] is the final equation.
The new equation is now [tex]f(x) = (x - 4)^{2} 2 + 1.[/tex]
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Is the answer 1479.20? Pic below
The expected profit for selling action movies is given as follows:
$15,583.20.
How to obtain the expected profit?The expected profit for selling action movies is obtained applying the proportions in the context of the problem.
The proportion of action movies on the last month is given as follows:
2150/(2150 + 1721 + 829 + 300) = 0.43.
Hence, out of 8000 movies, the expected number of action movies is given as follows:
0.43 x 8000 = 3440.
The expected profit for each movie is of $4.53, hence the expected profit for action movies is given as follows:
4.53 x 3440 = $15,583.20.
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circumference of OC 7.5 m F G 76° C APARUMORISCHER
Answer: 570OC^2mFG
Step-by-step explanation: I did this in school! Trust Me! You can report if wrong!
Factor the quadratic expression completely.
-3x^2+17x-20=
Answer:
To factor -3x^2 + 17x - 20 completely, we need to find two binomials that when multiplied together give us the original quadratic expression.
First, we can multiply the leading coefficient (-3) by the constant term (-20) to get -60. Then, we need to find two numbers that multiply to -60 and add up to the coefficient of the x-term (17). After some trial and error, we find that the two numbers are 12 and -5.
Now, we can rewrite the quadratic expression as:
-3x^2 + 17x - 20 = -3x^2 + 12x - 5x - 20
Next, we group the first two terms and the last two terms:
(-3x^2 + 12x) + (-5x - 20)
We can factor out 3x from the first group and -5 from the second group:
3x(x - 4) - 5(x + 4)
Now we can factor out a negative one from the second grouping:
3x(x - 4) - 5( -1)(x + 4)
And simplify:
3x(x - 4) + 5(x + 4)
Therefore, the quadratic expression -3x^2 + 17x - 20 can be factored completely as (3x - 5)(x - 4).
Prove that ABC AADC.
51
51
2
B
Statement
D
1 m/BAC = m_DAC = 51
AB = AD=4
Pick statement
AABCEAADe
Reason
Pick statement
Given
Segments are the same length as themselves,
Pick congruence criterion
a hint
congruence
ΔABC and ΔADC are congruent by SAS
We have,
From the figure,
We have,
ΔABC and ΔADC
∠BAC = ∠DAC = 51 ( given )
AB = AD = 4 ( given )
AC = AC ( common length )
This means,
ΔABC and ΔADC are congruent by SAS
Thus,
ΔABC and ΔADC are congruent by SAS
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A flower bed has the shape of a rectangle 5yards long 4 yards wide what is its area in square ft
The area of the flower bed is 180 square feet.
Area refers to the amount of space occupied by a two-dimensional shape or surface. It is measured in square units, such as square meters, square inches, or square centimeters. The area of a shape can be calculated by multiplying the length and width of the shape (in the case of a rectangle or square), or by using more complex formulas for other shapes, such as triangles or circles.
To convert yards to feet, we multiply by 3 since 1 yard = 3 feet.
The length of the rectangle in feet is 5 yards × 3 feet/yard = 15 feet.
The width of the rectangle in feet is 4 yards × 3 feet/yard = 12 feet.
The area of the rectangle in square feet is length × width = 15 feet × 12 feet = 180 square feet.
Therefore, the area is 180 square feet.
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Practice!
1.
In the diagram, JKLM~ EFGH.
C.
a.
b.
Find the scale factor of JKLM to EFGH.
k=
Find the values of x, y, and z.
x =
y =
Find the perimeter of each polygon.
4y + 4
H3G
11
zo
E 8 F
Z=
30
65°
M
20
D
K
L
Answer:
a. To find the scale factor of JKLM to EFGH, we can compare the corresponding sides:
JK/JH = KL/KG = LM/LF = x/x = 1
Therefore, the scale factor is 1.
b. Since JKLM~EFGH, the corresponding sides are proportional. We can set up the following ratios:
JK/EF = KL/FG = LM/FH = 1/1
JK/x = KL/20
LM/30 = 1/2
Solving for JK, KL, and LM:
JK = EF = x
KL = 20(1/2) = 10
LM = 30(1/2) = 15
c. To find the perimeter of JKLM, we add the lengths of its sides:
Perimeter of JKLM = JK + KL + LM + MJ
Perimeter of JKLM = x + 10 + 15 + x
Perimeter of JKLM = 2x + 25
To find the perimeter of EFGH, we can use the fact that corresponding sides are proportional:
FG = KL = 10
FH = LM = 15
EG = JK = x
EH = EF = x√2
Perimeter of EFGH = EF + FG + GH + EH
Perimeter of EFGH = x + 10 + 2z + x√2
We are not given a value for z, so we cannot calculate the perimeter of EFGH.
Note: The angle measures given in the diagram are not used in the calculations for this problem.
A rectangular room is 28 feet by 32 feet.
A scale drawing of the room has a perimeter is 12 inches.
What is the length of the shorter side of the room on the scale drawing?
The length of shorter side is 2.8 inch.
We have,
A rectangular room is 28 feet by 32 feet.
The Perimeter of scale drawing of room is 12 inches.
So, the perimeter of room
= 2(l +w)
= 2(28+ 32)
= 2(60)
= 120 feet
So, the scale factor is
= 120 / 12
= 10 inches
Thus, the length of shorter side is
= 28/10
= 2.8 inch
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The Venn diagram below shows the number of items in sets A and B.
An item is chosen at random.
a) Explain how we can tell from the Venn diagram that P(A) ≤ P(B) without doing any calculations.
b) Calculate P(A) and P(B) as fractions in their simplest forms.
B4
A1
9
A is inside B and 9 is outside the venn diagram
The probability of A would be lesser than or equal to that of B because A is a subset of B
Explaining P(A) ≤ P(B) from the Venn diagramFrom the question, we have the following parameters that can be used in our computation:
The Venn diagram
On the Venn diagram, we have
A is inside B
This means that A is a subset of B
And as such the probability of A would be lesser than or equal to that of B
Calculating P(A) and P(B)Here, we have
A = 1
B = 4
Outside = 9
So, we have
P(A) = 1/(1 + 4 + 9) = 1/14
P(B) = (1 + 4)/(1 + 4 + 9) = 5/14
Hence, the values of P(A) and P(B) are 1/4 and 5/14
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Kyle plans to estimate the area of the figure below by identifying the full and partial squares that make up the figure.
On a coordinate plane, a figure contains 40 full squares and 8 partial squares.
If Kyle uses the strategy, which statement best describes the figure?
The figure that Kyle plans to estimate the area of is likely a series of squares, either full or partially shaded, that do not form a perfect square or rectangle.
The figure that Kyle plans to estimate the area of contains 40 full squares and 8 partial squares. Based on this information, we can assume that the figure is composed of a grid or a series of squares that are either full or partially shaded. Kyle plans to use the strategy of identifying the full and partial squares that make up the figure to estimate its area.
If the figure is a perfect square or rectangle, Kyle can use the formula A = l x w to find its exact area. However, since the figure is not described as a specific shape, Kyle will need to use estimation to find its area. By identifying the full and partial squares, he can estimate the total number of square units that the figure covers. Kyle can then multiply this estimate by the size of each square unit to find an approximate area.
In conclusion, Using his strategy, Kyle can estimate the total area of the figure by identifying the full and partial squares and multiplying his estimate by the size of each square unit.
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23. As long as supplies last, the local animal shelter will give customers a free collar and name tag for each dog or cat
adopted this month. The shelter has the following collars: 5 blue, 8 green, 2 purple, and 5 brown. The name tags that
are available are 10 plastic, 4 leather, and 6 metal.
What is the probability that the first customer will randomly be given a brown collar?
The probability that the first customer will randomly be given a brown collar is given as follows:
0.25 = 25%.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
The total number of collars is given as follows:
5 + 8 + 2 + 5 = 20 collars.
5 of these collars are brown, hence the probability that the first customer will randomly be given a brown collar is given as follows:
p = 5/20 = 1/4 = 0.25 = 25%.
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Devaughn is 11 years younger than Sydney. The sum of their ages is 73. What is Sydneys age?
Let's use S to represent Sydney's age. According to the problem, Devaughn is 11 years younger than Sydney, so his age can be represented as S - 11. We also know that the sum of their ages is 73, so we can write an equation:
S + (S - 11) = 73
Simplifying this equation, we get:
2S - 11 = 73
Adding 11 to both sides, we get:
2S = 84
Dividing both sides by 2, we get:
S = 42
Therefore, Sydney is 42 years old.
Irma has $41,000 in a savings account that earns 2% interest per year. The interest is not compounded.To the nearest cent, how much will she have in total in 4months?
Identify all of the Independent Events
You randomly select and eat three chocolates out of the box
Drawing a marble out of a bag, replace it and draw another
Dominic picks an ice cream cone out of the freezer to eat, then Arianna picks one
Rolling a dice, then picking a block from a pile
Rolling a dice twice
Randomly picking a sock from a laundry basket to wear, then randomly picking a second one
Out of these events, the independent events are drawing a marble out of a bag, replacing it and drawing another and rolling a dice twice. So the correct option is 2 and 5.
Events that are independent are those in which the outcome of first event has no effect on the outcome of a second event. The independent event in each of the situations according to this definition are:
Drawing a marble out of a bag, replacing it, and drawing anotherRolling a dice twiceThe outcome of the first event in either of these situations have no effect on the outcomes of the second event.
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A company estimates that 0.8% of their products will fail after the original warranty period but within 2 years of the purchase, with a replacement cost of $200.
If they offer a 2 year extended warranty for $30, what is the company's expected value of each warranty sold?
Step-by-step explanation:
The expected value of each warranty sold can be calculated using the following formula:
Expected Value = (Probability of Failure without warranty x Replacement Cost without warranty) + (Probability of Failure with warranty x Replacement Cost with warranty) - Cost of Warranty
Probability of Failure without warranty = 0.8% or 0.008 (given)
Replacement Cost without warranty = $200 (given)
Probability of Failure with warranty = 0% (since the product is covered under warranty)
Replacement Cost with warranty = $0 (since the cost of replacement is covered under warranty)
Cost of Warranty = $30 (given)
Expected Value = (0.008 x $200) + (0 x $0) - $30
Expected Value = $1.60 - $30
Expected Value = -$28.40
The company's expected value of each warranty sold is -$28.40, which means that on average, the company can expect to lose $28.40 for every warranty sold. This is because the cost of the warranty ($30) is greater than the expected cost of replacement without the warranty ($1.60). Therefore, it is not beneficial for the company to offer the extended warranty.
HELP ASAP WILL GIVE TRUE 100 POINTS AND BRAINLIEST
The y-intercept represents the base price of $____for airfare from NYC.
Answer: THE ANSWER IS Blank 1: 200, Black 2: 1000, Blank 3: 800, Blank 4: 30+0.50x, Blank 5: y=50=0.30x.
Step-by-step explanation: Please give Brainliest.
Hope this helps!!!!
I can answer more questions for Brainlist.
Choose the equation for the graph.
a) y = 2x - 3| +1
b) y = -2|x - 3| +1
c) y = 2x - 3| - 1
d) y = -2|x + 3| -1
e) y = 2x + 3| +1
The calculated equation for the graph is y = -2|x + 3| - 1
Choosing the equation for the graph.From the question, we have the following parameters that can be used in our computation:
The absolute value graph
An absolute value function is represented as
y = a|x - h| + k
Where
Vertex, (h, k) = (-3, -1)
So, we have
y = a|x + 3| - 1
The graph faces down
So, a is negative
Possible value is a = -2
So, we have
y = -2|x + 3| - 1
Hence, the function is y = -2|x + 3| - 1
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Find the volume of figure two
Answer: 72
Step-by-step explanation:
V=lwh
=(3)(4)(6)
=72
Find the value of x for the following
The side has a length of 15 units.
Let us denote the length of the missing side by x. According to the Pythagorean theorem, the sum of the squares of the lengths of the two legs of a right triangle is equal to the square of the length of the hypotenuse. In mathematical terms, this can be written as:
side² + side² = hypotenuse²
Substituting the given values, we get:
x² + 8² = 17²
Simplifying this equation, we get:
x² + 64 = 289
Subtracting 64 from both sides, we get:
x² = 225
Taking the square root of both sides, we get:
x = 15
Therefore, the missing side has a length of 15 units.
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Statistics help!!!
I chose B and got it wrong, I still don’t understand how to get the correct answer or what that answer is, but I want to understand how to do it right !
What is the probability of rolling a single 6 sided dice three times and getting the following outcomes: 4, a number greater than two, and an
even number.
a) 4/9
b) 21/54 (wrong answer)
c) 1/27
d) 12/216
Answer:
I am not sure but I will say A I guess.
hello, pls help
The distance AB is divided in the specified ratio. Calculate the coordinates of the division point T. A=(3|2|-1), B=(-6|1|-2), 1:2 Please help me because i am not sure if i did it right: T=A+r*(B-A) T=(3,2,-1)+1/3*(-9,-1,-1) T=(0,5/3,-4/3) Is it right? Pls help me
Yes, your answer is correct.
The coordinates of the division point T are indeed (0, 5/3, -4/3).
We have,
To find the coordinates of the division point T, we use the formula:
T = A + r(B - A)
where r is the ratio in which AB is divided.
In this case, the ratio is 1:2, so r = 1/3 (since 1 + 2 = 3).
Substituting the given values.
T = (3, 2, -1) + (1/3)(-9, -1, -1)
T = (3, 2, -1) + (-3, -1/3, -1/3)
T = (0, 5/3, -4/3)
Thus,
The coordinates of the division point T are indeed (0, 5/3, -4/3).
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