Answer:
-3+[tex]4x^{2}[/tex]
Step-by-step explanation:
Rose graphs this equation as shown x^2-4x+y^2=0 Rose correctly found the what but incorrectly found the what to correct her graph she could what
The equation [tex]x^2-4x+y^2=0[/tex] can be rewritten as [tex]x^2-4x+4+y^2=4[/tex], which is equivalent to [tex](x-2)^2 + y^2 = 2^2[/tex]. This is the equation of a circle centered at (2,0) with a radius of 2.
How to graph this equation?To graph this equation, you could plot the center point (2,0) and then draw a circle with a radius of 2 around that point. Alternatively, you could find a few points on the circle by plugging in values for x and solving for y (or vice versa), and then plot those points to sketch the circle.
If Rose found the correct equation but incorrectly graphed it, she could try using the correct center point and radius to sketch the circle more accurately. Alternatively, she could check her work to see where she made a mistake in graphing the equation.
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On a piece of paper, use a protractor to construct △ABC with m∠A=30° , m∠B=60° , and m∠C=90° .
Which statements about the triangles are true?
Select each correct answer.
AC BC
a c is greater than b c
AC>AB
a c is greater than a b
AC
Answer:
AC<BC = 30+60=90 < 60+90= 150
Step-by-step explanation:
AC>AB 30+90= 120 > 30+60=90
AC<BC 30+60=90 < 60+90= 150
linear equations in one variable
Answer:
x = [tex]\frac{3}{5}[/tex]
Step-by-step explanation:
[tex]\frac{x+1}{3}[/tex] - [tex]\frac{x-1}{2}[/tex] = [tex]\frac{1+2x}{3}[/tex]
multiply through by 6 ( the LCM of 2 and 3 ) to clear the fractions
2(x + 1) - 3(x - 1) = 2(1 + 2x) ← distribute parenthesis on both sides
2x + 2 - 3x + 3 = 2 + 4x
- x + 5 = 2 + 4x ( subtract 4x from both sides )
- 5x + 5 = 2 ( subtract 5 from both sides )
- 5x = - 3 ( divide both sides by - 5 )
x = [tex]\frac{-3}{-5}[/tex] = [tex]\frac{3}{5}[/tex]
Lisa uses her railcard to buy a ticket.
She gets off the normal price of the ticket.
The normal price of the ticket is £24.90
Work out how much Lisa pays for the ticket.
The discount percentage is different, the amount that Lisa pays will also be different.
What exactly is the discounted method?The act of estimating the present value of a future payment or series of cash flows that will be received in the future is referred to as discounting. A discount rate (also known as a discount yield) is the rate at which future cash flows are discounted back to their present value.
We need to know what percentage of the regular ticket price Lisa saves with her railcard. We cannot calculate the exact amount Lisa pays for the ticket without this information.
Assuming Lisa receives a 1/3 discount with her railcard, we can calculate the cost of her ticket as follows:
Discounted price = Regular price minus discount amount
Normal price x Discount percentage = Discount amount
Discount rate = 1/3 = 33.33% (rounded to two decimal places)
Discount amount = £24.90 multiplied by 33.33% = £8.30 (rounded to two decimal places)
Price after discount = £24.90 - £8.30 = £16.60 (rounded to two decimal places)
As a result, if Lisa receives a 1/3 discount with her railcard, she will pay£16.60 for the ticket. However, if the discount percentage is different, Lisa's payment will be different as well.
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Lisa uses her railcard to buy a ticket.
She gets off the normal price of the ticket.
The normal price of the ticket is £24.90
Work out how much Lisa pays for the ticket.
three fair, standard six-faced dice of different colors are rolled. in how many ways can the dice be rolled such that the sum of the numbers rolled is 10? (mathematics teacher calendar problem)
There are a total of 27 combinations that give a sum of 10 when rolling three dice.
We have,
The possible outcomes in the sample space for rolling three dice:
S = {(1, 1, 1), (1, 1, 2), (1, 1, 3), (1, 1, 4), (1, 1, 5), (1, 1, 6),
(1, 2, 1), (1, 2, 2), (1, 2, 3), (1, 2, 4), (1, 2, 5), (1, 2, 6),
(1, 3, 1), (1, 3, 2), (1, 3, 3), (1, 3, 4), (1, 3, 5), (1, 3, 6),
(1, 4, 1), (1, 4, 2), (1, 4, 3), (1, 4, 4), (1, 4, 5), (1, 4, 6),
(1, 5, 1), (1, 5, 2), (1, 5, 3), (1, 5, 4), (1, 5, 5), (1, 5, 6),
(1, 6, 1), (1, 6, 2), (1, 6, 3), (1, 6, 4), (1, 6, 5), (1, 6, 6),
(2, 1, 1), (2, 1, 2), (2, 1, 3), (2, 1, 4), (2, 1, 5), (2, 1, 6),
(2, 2, 1), (2, 2, 2), (2, 2, 3), (2, 2, 4), (2, 2, 5), (2, 2, 6),
(2, 3, 1), (2, 3, 2), (2, 3, 3), (2, 3, 4), (2, 3, 5), (2, 3, 6),
(2, 4, 1), (2, 4, 2), (2, 4, 3), (2, 4, 4), (2, 4, 5), (2, 4, 6),
(2, 5, 1), (2, 5, 2), (2, 5, 3), (2, 5, 4), (2, 5, 5), (2, 5, 6),
(2, 6, 1), (2, 6, 2), (2, 6, 3), (2, 6, 4), (2, 6, 5), (2, 6, 6),
(3, 1, 1), (3, 1, 2), (3, 1, 3), (3, 1, 4), (3, 1, 5), (3, 1, 6),
(3, 2, 1), (3, 2, 2), (3, 2, 3), (3, 2, 4), (3, 2, 5), (3, 2, 6),
(3, 3, 1), (3, 3, 2), (3, 3, 3), (3, 3, 4), (3, 3, 5), (3, 3, 6),
(3, 4, 1), (3, 4, 2), (3, 4, 3), (3, 4, 4), (3, 4, 5), (3, 4, 6),
(3, 5, 1), (3, 5, 2), (3, 5, 3), (3, 5, 4), (3, 5, 5), (3, 5, 6),
(3, 6, 1), (3, 6, 2), (3, 6, 3), (3, 6, 4), (3, 6, 5), (3, 6, 6),
(4, 1, 1), (4, 1, 2), (4, 1, 3), (4, 1, 4), (4, 1, 5), (4, 1, 6),
(4, 2, 1), (4, 2, 2), (4, 2, 3), (4, 2, 4), (4, 2, 5), (4, 2, 6),
(4, 3, 1), (4, 3, 2), (4, 3, 3), (4, 3, 4), (4, 3, 5), (4, 3, 6),
(4, 4, 1), (4, 4, 2), (4, 4, 3), (4, 4, 4), (4, 4, 5), (4, 4, 6),
(4, 5, 1), (4, 5, 2), (4, 5, 3), (4, 5, 4), (4, 5, 5), (4, 5, 6),
(4, 6, 1), (4, 6, 2), (4, 6, 3), (4, 6, 4), (4, 6, 5), (4, 6, 6),
(5, 1, 1), (5, 1, 2), (5, 1, 3), (5, 1, 4), (5, 1, 5), (5, 1, 6),
(5, 2, 1), (5, 2, 2), (5, 2, 3), (5, 2, 4), (5, 2, 5), (5, 2, 6),
(5, 3, 1), (5, 3, 2), (5, 3, 3), (5, 3, 4), (5, 3, 5), (5, 3, 6),
(5, 4, 1), (5, 4, 2), (5, 4, 3), (5, 4, 4), (5, 4, 5), (5, 4, 6),
(5, 5, 1), (5, 5, 2), (5, 5, 3), (5, 5, 4), (5, 5, 5), (5, 5, 6),
(5, 6, 1), (5, 6, 2), (5, 6, 3), (5, 6, 4), (5, 6, 5), (5, 6, 6),
(6, 1, 1), (6, 1, 2), (6, 1, 3), (6, 1, 4), (6, 1, 5), (6, 1, 6),
(6, 2, 1), (6, 2, 2), (6, 2, 3), (6, 2, 4), (6, 2, 5), (6, 2, 6),
(6, 3, 1), (6, 3, 2), (6, 3, 3), (6, 3, 4), (6, 3, 5), (6, 3, 6),
(6, 4, 1), (6, 4, 2), (6, 4, 3), (6, 4, 4), (6, 4, 5), (6, 4, 6),
(6, 5, 1), (6, 5, 2), (6, 5, 3), (6, 5, 4), (6, 5, 5), (6, 5, 6),
(6, 6, 1), (6, 6, 2), (6, 6, 3), (6, 6, 4), (6, 6, 5), (6, 6, 6)}
Now,
The combination where the sum is 10 is 27.
ie.
{(1, 3, 6), (1, 4, 5), (1, 5, 4), (1, 6, 3), ........, (6, 1, 3), (6, 2, 2,), (6, 3, 1)}
Thus,
There are 27 ways of combination where the sum is 10.
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f(x)=3x^2+12+11 in vertex form
Answer:
y = -3(x - 2)^2 + 1. Explanation: x-coordinate of vertex: x = -b/(2a) = -12/-6 = 2 y-coordintae of vertex: y(2) = -12 + 24 - 11 = 1
Step-by-step explanation:
Answer:x-coordinate of vertex:
x = -b/(2a) = -12/-6 = 2
y-coordinate of vertex:
y(2) = -12 + 24 - 11 = 1
Vertex form:
y = -3(x - 2)^2 + 1
Check.
Develop y to get back to standard form:
y = -3(x^2 - 4x + 4) + 1 = -3x^2 + 12x - 11.
Step-by-step explanation:
Suppose the water depth during low tide at a certain bay is about 3.0 m, and at high tide it is about 9.0 m. The natural period of oscillation is about 12 hours, and on a particular day, high tide occurred at 6:45 a.m. Find the amplitude (in meters) of the model. Xm
The amplitude of the model is 3.0 meters.
The amplitude of a harmonic oscillator represents the maximum displacement from the equilibrium position. In the case of tidal oscillations, the equilibrium position is the average water level.
The amplitude of the model can be determined by considering the difference between the high and low tide water depths, which represents the maximum displacement of the water from the average level. Dividing this difference by two gives us the amplitude of the model.
The amplitude of the model can be found using the formula:
Xm = (H - L)/2
where H is the high tide water depth, L is the low tide water depth, and Xm is the amplitude of the model.
Substituting the given values, we get:
Xm = (9.0 - 3.0)/2
Xm = 3.0 meters
Therefore, the amplitude of the model is 3.0 meters.
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find the volume of the largest rectangular box with edges parallel to the axes that can be inscribed in the ellipsoid(x^2/4) + (y^2/64) + (z^2/49) = 1Hint: By symmetry, you can restrict your attention to the first octant (where x,y,z=0), and assume your volume has the form V=8xyz. Then arguing by symmetry, you need only look for points which achieve the maximum which lie in the first octant.What is the maximum volume?
The volume of the rectangular box is given by using the Lagrangian multiplier theorem is 172.435 cubic units.
It states that any local maxima or any local minima of the function are calculated under the equality constraints.
The equation of ellipsoid is given as,
[tex]\frac{x^2}{4} +\frac{y^2}{64} +\frac{z^2}{49} =1[/tex]
Let the edges of the required rectangular box be x, y, and z.
Then, the volume of the box in the first quadrant is V = xyz
Then we have,
[tex]\phi(x,y,z) = \frac{x^2}{4} +\frac{y^2}{64} +\frac{z^2}{49} -1[/tex]
By the Lagrange multiplier,
[tex](V_x,V_y,V_z) = \lambda (\phi_x, \phi_y,\phi_z)\\\\(yz,xz,xy)=\lambda(\frac{2x}{4},\frac{2y}{64},\frac{2z}{49} )\\\\xyz = \lambda\frac{x^2}{2},xyz =\lambda\frac{y^2}{32} ,xyz=\lambda\frac{2z^2}{49} \\\\x^2 = 2k, y^2=32k,z^2=49k/2[/tex]
Solving for k we have the value of k as k = 2/3.
Put k=2/3 in equation 2, we have
x² = 2*2/3 , y² = 32*2/3, z² = 49/2*2/3
x =±2/√3 , y= ±8/√3 , z = ±7/√3
Then the volume of the rectangular box will be
Volume = [tex]\frac{2}{\sqrt{3} } \frac{8}{\sqrt{3} } \frac{7}{\sqrt{3} }[/tex]
Volume = 172.435 cubic units.
Therefore, the value of volume of the rectangular box is 172.435 cubic units.
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What is the value of the expression?
1/2 ÷ 6
Answer:
0.25
Step-by-step explanation:
Answer:
1/12
Step-by-step explanation:
To solve this expression, we need to remember that division should be done before multiplication or addition/subtraction.
So we first simplify the expression by dividing 1/2 by 6:
1/2 ÷ 6 = 1/2 × 1/6
Next, we multiply the two fractions by multiplying their numerators and denominators:
1/2 × 1/6 = (1 × 1)/(2 × 6) = 1/12
Therefore, the value of the expression 1/2 ÷ 6 is equal to 1/12.
The measure of an angle is 40.6°. What is the measure of its supplementary angle?
Answer: 139.4
Step-by-step explanation:
a supplementary angle is equal to 180 so all we have to do is subtract 40.6 from 180
180 - 40.6 = 139.4
You ride your bicycle 40 meters. How many complete revolutions does the front wheel make?
solve the linear system using elimination. -5x+3y=19 and -5x+7y+11
Answer:
x = -5
y = -2
Step-by-step explanation:
-5x + 3y = 19
-5x + 7y = 11
Time the first equation by -1
5x - 3y = -19
-5x + 7y = 11
4y = -8
y = -2
Now put -2 in for y and solve for x
-5x + 3(-2) = 19
-5x - 6 = 19
-5x = 25
x = -5
Let's Check
-5(-5) + 3(-2) = 19
25 - 6 = 19
19 = 19
So, x = -5 and y = -2 is the correct answer.
10340000000 in standard form
Answer:
1034 x 10⁷
Step-by-step explanation:
the seven just means to multiply by 10 seven times
Let me know if this helps.
Draw and label the height of each parallelogram.
Based on the image given, the height of the parallelogram can be expressed as 2 units.
What is the height of a parallelogram?Parallelograms are two-dimensional figures that include four sides as rectangles. However, in parallelograms, the opposite sides are parallel and the vertical or horizontal sides are diagonal. Due to this, the height in a parallelogram can be determined by measuring the distance between the top and bottom lines. Based on this principle, the height of the parallelogram would be 2.
Note: Below I attach the missing image in this question:
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Write each function in terms of its cofunction. Assume that all angles in which an unknown appears are acute angles. cos(α+20∘)
The given function is cos(α+20°) and its cofunction can be expressed as cos(α+20°) = cos(α)sin(70°) - sin(α)cos(70°).
Therefore cos(α+20°) in terms of its cofunctions, we need to use the formulas for sin and cos of complementary angles.
The complementary angle of 20° is 70° because 20° + 70° = 90°.
So, we can rewrite cos(20°) as sin(70°) and sin(20°) as cos(70°).
Using the formula for the cosine of the sum of two angles, we can then substitute these values to get:
cos(α+20°) = cos(α)sin(70°) - sin(α)cos(70°)
Therefore, expression of cos(α+20°) in terms of its cofunctions is cos(α+20°) = cos(α)sin(70°) - sin(α)cos(70°).
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What’s the area of 5feet 12feet and 13feet, using 4(bxh)
The area of 5feet 12feet and 13feet, 30 square feet
Area calculation.the formula 4(bxh) is used to calculate the area of a rectangle, not a triangle. However, the dimensions 5 feet, 12 feet, and 13 feet are actually the sides of a right triangle (known as a Pythagorean triple), so we can use the formula for the area of a right triangle:
Area = 1/2 x base x height
where the base and height are the two legs of the right triangle.
Using the Pythagorean theorem, we can determine that the legs of the triangle are 5 feet and 12 feet, and the hypotenuse is 13 feet. Therefore, the area of the triangle is:
Area = 1/2 x 5 feet x 12 feet
Area = 30 square feet
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Choose the correct answer.
When you get the sum of a data set and divide by the number of values collected, you get the
A)quantitative data
B)qualitative data
C)median
D)mean
Kernels as Dot Products 2 1 point possible (graded) Which of the following feature vectors (x) produces the kernel K(x,x) = (x) - (x') (x) = [x1, x2, x3] O(x) = [₁ + x₂ + x3] (x) = [x₁, x₂ + x3] (x) = [x₁ + x3, x1 + x2] = x₁x₁ + x2x₂ + x3 x3 + x 2 x 3 + x 3 x 2
The feature vector that generates the kernel K(x, x) = (x) - (x') is given by (x) = [x1, x2 + x3].
The formula for kernel is K(x, y) = φ(x) · φ(y) and the dot product of two vectors is defined as (x) · (y) = x^Ty where x^T denotes the transpose of x.
Therefore, we can expand the given kernel to: K(x, x') = φ(x) · φ(x')= [x1, x2 + x3] · [x1, x2 + x3]'= [x1, x2 + x3] · [x1, x2 + x3]= x1x1 + (x2 + x3)(x2 + x3) The correct option is (x) = [x1, x2 + x3]
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Elena is testing out a new studying method and wants to know if it works. She decides to compare her spelling test scores from last week and this week. On last week's test, Elena spelled 16 out of the 20 words correctly. On this week's test, she spelled 13 out of the 15 words correctly. On which test did Elena get a higher ratio of correctly spelled words to total words?
Answer:
To determine which test Elena got a higher ratio of correctly spelled words to total words, we need to calculate the ratio of correctly spelled words to total words for each test and compare them.
For last week's test, the ratio of correctly spelled words to total words is:
16/20 = 0.8
For this week's test, the ratio of correctly spelled words to total words is:
13/15 ≈ 0.867
Since 0.867 is greater than 0.8, Elena got a higher ratio of correctly spelled words to total words on this week's test. Therefore, the new studying method appears to be working better for Elena. However, it is important to note that a single comparison is not sufficient to draw a definitive conclusion about the effectiveness of the studying method, and it would be beneficial for Elena to continue tracking her performance over a longer period of time.
Select the interval where
h
(
x
)
>
0
h(x)>0h, left parenthesis, x, right parenthesis, is greater than, 0.
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
−
1
<
x
<
0
−1
The correct statement regarding where the graph of h(x) = x³ has positive signal is given as follows:
x > 0.
How to classify a function as positive or negative?The graph of a function is positive in the regions where the function values are greater than zero, and negative in the regions where the function values are less than zero.
The comparisons to zero are given as follows:
Greater than zero -> above the x-axis.Less than zero -> Below the x-axis.Hence, considering the function defined by the rule y = x³, the graph of the function is classified as positive or negative as follows:
Negative for x < 0.Positive for x > 0.Missing InformationThe function is h(x) = x³, and it's graph is given by the image presented at the end of the answer.
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Will make you brainlist!
Answer:
x = -2 , y = 2
Step-by-step explanation:
label your equations (1) and (2) the question mention to use elimination method and make x the same for both. To do that multiply equation (1) by 2. than label it (3)so 3x becomes 6x adding the equation (2)+(3) cancels out -6x and 6x so you can find value of yuse value of y to find xhope this helps :)
In a certain class of 40students, 90% passed ssce mathematics examinations and 75% passed English. If 2 students failed both mathematics and English, what percentage of students passed both examinations
30% percent of the students passed both Mathematics and English.
What is Percentage?A rate, number, or amount in each hundred is known as a percentage
Let's use a Venn diagram to represent the information given in the problem. Let M be the set of students who passed Mathematics, E be the set of students who passed English, and F be the set of students who failed both.
We know that there are 40 students in the class, and 90% passed Mathematics, so the number of students who passed Mathematics is 0.9 × 40 = 36. Similarly, 75% passed English, so the number of students who passed English is 0.75 × 40 = 30.
We also know that 2 students failed both Mathematics and English, so we can label the F section with 2.
where the number in each section represents the number of students who passed the respective exam.
To find the percentage of students who passed both examinations (i.e., the intersection of M and E), we need to add the number of students in the M and E intersection to the F section, then subtract that from the total number of students (40), and finally divide by 40 to get the percentage. That is:
percentage of students who passed both exams = (M ∩ E + F) / 40 × 100%
= (28 + 2) / 40 × 100%
= 30%
Therefore, 30% of the students passed both Mathematics and English.
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The amount of daily daylight is unrelated to levels of depression in older adults. What type of hypothesis is this?
a) Null hypothesis
b) Alternative hypothesis
b) Research hypothesis
d) Nonsignificant hypothesis
The amount of daily daylight is unrelated to levels of depression in older adults. The hypothesis "The amount of daily daylight is unrelated to levels of depression in older adults" is an example of the null hypothesis.
A null hypothesis is a statement that there is no significant difference between two variables or a relationship between them.The null hypothesis assumes that the observed results or changes in the experiment or data are due to random fluctuations or errors in the measurement process. It is the default hypothesis that is typically tested against an alternative hypothesis.
A researcher tries to disprove or reject the null hypothesis by conducting experiments or collecting data to support the alternative hypothesis. If the null hypothesis is rejected, then the alternative hypothesis is accepted as true. However, if the null hypothesis cannot be rejected, then it remains as the plausible explanation for the observations or outcomes in the experiment.
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A triangle has one side with length 9 and another side with length 6. The angle opposite the side of length 6 measures 40. what is the measure of the angle opposite the side of length 9?
Answer: the angle opposite the side length 9 is 74.62 degrees I think .
Step-by-step explanation:
Which statements are true? Select each correct answer.
A. 40m^6 -4=4(10m^6-1)
B. 32m^4 +12m^3 =4m^3(8m +3)
C. 15m^3-6m=3m(5m^2 -6m)
D. 6m^2+18m=6m^2(1+3m)
Answer:
C. 15m^3-6m=3m(5m^2 -6m) is true.
D. 6m^2+18m=6m^2(1+3m) is true.
A. 40m^6 -4=4(10m^6-1) is not true.
B. 32m^4 +12m^3 =4m^3(8m +3) is not true.
Answer:
C. 15m^3-6m=3m(5m^2 -6m) is true.
D. 6m^2+18m=6m^2(1+3m) is true.
Step-by-step explanation:
The volume of this prism is 4950cm3. The area of the cross-section is 110cm2. Work out x .
Answer:
answer will be my albert enistein calculation is 4500000⁹7765⁵44³=6425786
Transaction ID
Items
1
Bread, Milk
2
Bread, Diaper, Beer, Eggs
3
Milk, Diaper, Beer, Coke
4
Bread, Milk, Diaper, Beer
5
Bread, Milk, Diaper, Coke
6
Bread, Coke, Eggs
7
Beer, Coke
8
Beer, Milk, Bread, Diaper, Eggs
9
Eggs, Diaper
10
Diaper, Beer
Calculate the support, Confidence, and Lift for each of the following rules
Please show work.
3
Rule:
Support
Confidence
Lift
1)
{Bread} -> {Milk}
2)
{Beer} -> {Eggs}
3)
{Beer, Bread} -> {Milk}
4)
{Bread, Eggs} -> {Diapers}
5)
{Milk, Bread} -> {Eggs, Coke}
6)
{Beer, Milk} -> {Bread, Diapers}
7)
{Bread, Milk, Eggs} -> {Diapers}
8)
{Bread, Eggs, Coke} -> {Diapers, Beer}
Confidence in math is the belief in one's ability to understand and solve mathematical problems. Developing confidence in math is important because it can help individuals overcome anxiety and fear of math, which can limit their performance and success in the subject.
1) {Bread} -> {Milk}:
Support: 5/10
Confidence: 5/7
Lift: 5/2.4
2) {Beer} -> {Eggs}:
Support: 4/10
Confidence: 4/9
Lift: 4/3
3) {Beer, Bread} -> {Milk}:
Support: 3/10
Confidence: 3/6
Lift: 3/1.8
4) {Bread, Eggs} -> {Diapers}:
Support: 4/10
Confidence: 4/7
Lift: 4/2.6
5) {Milk, Bread} -> {Eggs, Coke}:
Support: 4/10
Confidence: 4/7
Lift: 4/2.6
6) {Beer, Milk} -> {Bread, Diapers}:
Support: 3/10
Confidence: 3/6
Lift: 3/1.8
7) {Bread, Milk, Eggs} -> {Diapers}:
Support: 2/10
Confidence: 2/5
Lift: 2/2.2
8) {Bread, Eggs, Coke} -> {Diapers, Beer}:
Support: 2/10
Confidence: 2/5
Lift: 2/2.2
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Please help me please it would be very appreciated.
the equation of the quadratic function that is moved to the left three, up four, and stretched by a scale factor of two is [tex]y = 2(x + 3)^2 + 4.[/tex]
What is quadratic equation?
A quadratic equation is a type of polynomial equation of degree two, meaning it contains one or more terms that involve x raised to the power of two (i.e., x²
The equation of a quadratic function is generally given by:
[tex]y = a(x - h)^2 + k[/tex]
where (h, k) is the vertex of the parabola and "a" determines the shape of the parabola.
To move the function to the left by three units, we need to replace "x" with "(x + 3)" inside the parentheses:
[tex]y = a(x + 3 - h)^2 + k[/tex]
To move the function up by four units, we need to add four to the value of "k":
[tex]y = a(x + 3 - h)^2 + (k + 4)[/tex]
To stretch the function by a scale factor of two, we need to multiply "a" by two:
[tex]y = 2a(x + 3 - h)^2 + 2(k + 4)[/tex]
Combining these transformations, we get the final equation:
[tex]y = 2(x + 3 - 0)^2 + (0 + 4)[/tex]
[tex]y = 2(x + 3)^2 + 4[/tex]
Therefore, the equation of the quadratic function that is moved to the left three, up four, and stretched by a scale factor of two is [tex]y = 2(x + 3)^2 + 4.[/tex]
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45/43 as a percentage rounded to the nearest tenth of a percent
Answer:
104.7% to the nearest tenth.
Step-by-step explanation:
Multiply the fraction by 100:
= (45 x 100) / 43
= 104.651.
Can some one solve this and show their work please
Answer:
m = 2n = 7Step-by-step explanation:
we solve with two equations between the corresponding sides
9m = 7m + 4
9m - 7m = 4
2m = 4
m = 2
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check
9 x 2 = 7 x 2 + 4
18 = 18
this answer is good
n + 6 = 2n - 1
n + 7 = 2n
7 = n
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7 + 6 = 2 x 7 - 1
13 = 13
this answer is good