Answer:
1. x^2+5
2.x^2-6x+9
Step-by-step explanation:
these are just translations up and to the right.
since the f(x)=x^2
the transformations would be
1. g(x)=x^2+5
2.g(x)=(x-3)^2 = x^2-6x+9
You and eight friends plan a surprise party. Each of you contributes the same amount of
money m for food. Their mom also contributes $20.
a. Write an algebraic expression for the total amount of money contributed for food.
b. Evaluate your expression if each person contributed $10.50
Answer:
a. 9m + 8×$20 = $340
b. 9×$10.50 + 8×$10.50 = $178.50
Step-by-step explanation:
Its self-explanatory
Given f(x) = x² - 5x - 6 and g(x) =
x² - 6x, what are the domain restrictions
for (-)(x)?
A) x # +6
B) x = 0
C) x = 0,6
D) x = -2,6
The domain restrictions for (f/g)(x) are (c) x = 0, 6
How to determine the domain restrictions for (f/g)(x)?From the question, we have the following parameters that can be used in our computation:
f(x) = x² - 5x - 6
g(x) = x² - 6x
The composite function (f/g)(x) is calculated as
(f/g)(x) = f(x)/g(x)
substitute the known values in the above equation, so, we have the following representation
(f/g)(x) = (x² - 5x - 6 )/(x² - 6x)
For the domain restriction, we have
x² - 6x = 0
When solved, we have
x = 6 or x = 0
Hence, the domain restrictions for (f/g)(x) are (c) x = 0, 6
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Question
Given f(x) = x² - 5x - 6 and g(x) = x² - 6x, what are the domain restrictions
for (f/g)(x)?
A) x = +6
B) x = 0
C) x = 0,6
D) x = -2,6
In a warehouse, boxes are stacked such that they form 4 layers high and 5 boxes deep
going back. The layers are formed as follows: The bottom layer is 20 boxes wide and
5 boxes deep. The next layer is 16 boxes wide and 5 boxes deep. The next will be 12
boxes wide and 5 boxes deep. The top layer will be 8 boxes wide and 5 boxes deep.
A)Determine the number of boxes in the bottom 2 layers.
B)Develop a formula to calculate the number of boxes in n layers.
C)Use the formula from part b) to solve for the total number of boxes
needed to make up the 4 layers.
A) the total number of boxes in the bottom 2 layers is 100 + 80 = 180 boxes. B) Number of boxes in each layer = W(n) * D C) the total number of boxes needed to make up the 4 layers is 280 boxes.
How to determine the number of boxes in the bottom 2 layersA) To determine the number of boxes in the bottom 2 layers:
The bottom layer has a width of 20 boxes and is 5 boxes deep.
The second layer has a width of 16 boxes and is also 5 boxes deep.
Number of boxes in the bottom layer = 20 boxes wide * 5 boxes deep = 100 boxes
Number of boxes in the second layer = 16 boxes wide * 5 boxes deep = 80 boxes
Therefore, the total number of boxes in the bottom 2 layers is 100 + 80 = 180 boxes.
B) To develop a formula to calculate the number of boxes in n layers:
Let's denote the width of each layer as W and the depth of each layer as D.
The width of each layer follows the pattern: 20, 16, 12, 8.
We can observe that the width decreases by 4 units for each consecutive layer.
The formula to calculate the width of the nth layer can be written as:
W(n) = 20 - 4 * (n - 1)
Since each layer has a depth of 5 boxes, the number of boxes in each layer can be calculated as:
Number of boxes in each layer = W(n) * D
C) To use the formula from part B to solve for the total number of boxes needed to make up the 4 layers:
We want to calculate the total number of boxes in 4 layers.
Number of boxes in 4 layers = Number of boxes in the first layer + Number of boxes in the second layer + Number of boxes in the third layer + Number of boxes in the fourth layer
= W(1) * D + W(2) * D + W(3) * D + W(4) * D
= (20 - 4 * 0) * 5 + (20 - 4 * 1) * 5 + (20 - 4 * 2) * 5 + (20 - 4 * 3) * 5
= 20 * 5 + 16 * 5 + 12 * 5 + 8 * 5
Simplifying the expression, we get:
Number of boxes in 4 layers = 100 + 80 + 60 + 40 = 280 boxes
Therefore, the total number of boxes needed to make up the 4 layers is 280 boxes.
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Solve 2(5x + 9) = 6x+ 26.
A. x = -2
B. x= 11
C. x= -11
D. x = 2
what is the area of a circle with a diameter of 12in?
Answer:
113.1in^2 (round to 1dp)
Step-by-step explanation:
to calculate the area of a circle, you use the formula π\(r^{2}\) where r is the radius which in this case is 6 and the square of 6 is 36 so its 36π
which equals 113.0973355in^2 and 113.1in^2 if you round it to 1 decimal place
The formula for the area of a circle is:
Area = π x (radius)^2
where π (pi) is a mathematical constant approximately equal to 3.14159, and the radius is half of the diameter.
Given that the diameter of the circle is 12 in, we can find the radius by dividing the diameter by 2:
radius = diameter / 2 = 12 in / 2 = 6 in
Now we can substitute this value into the formula for the area:
Area = π x (radius)^2 = π x (6 in)^2
Using a calculator to approximate π as 3.14159, we get:
Area ≈ 3.14159 x (6 in)^2 ≈ 113.1 in^2
Therefore, the area of the circle with a diameter of 12 in is approximately 113.1 square inches.
A ski club charges $70 for a lift ticket and $20 per hour to ski. Jim paid at least $130 last week to ski. How many hours would he have skied.
Answer:
Step-by-step explanation: $130-$70 lift = $60/$20 per hour= 3 hours ski time
What are the x-intercepts of the graph below ?
Answer:
(3, 0)(-2, 0)Step-by-step explanation:
You want to identify the x-intercepts on the graph.
X-interceptAn "x-intercept" is a point where the graph crosses or touches (intercepts) the x-axis. The y-value there is always 0.
The given graph crosses the x-axis where x = -2 and x = 3. This means the x-intercept points are ...
(-2, 0) and (3, 0)
<95141404393>
The students calculate a chi-squared value of 92.86 and compare it with a critical value of 7.82. Which of the following best completes the chi-square good The null hypothesis cannot be rejected, and the students should conclude that the data fit a model of independent assortment. The null hypothesis cannot be rejected, and the students should conclude that the data may have resulted from genetic linkage. The null hypothesis can be rejected, and the students should conclude that the data fit a model of independent assortment The null hypothesis can be rejected, and the students should conclude that the data may have resulted from genetic linkage.
The students should draw the conclusion that the data might have been caused by the genetic connection if the null hypothesis is rejected.
Given information;
The students determine a crucial value of 7.82 and compare it to a chi-squared value of 92.86.
Which of the following results in the chi-square goodness-of-fit test being most complete?
The null hypothesis can be rejected, and the students should conclude that the data may have resulted from the genetic linkage.
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A survey found that the American family generates an average of 17.2 pounds of glass garbage each year. Assume the standard deviation of the distribution is 2.5 pounds. Find the probability that the mean of a sample of 40 families will be between 17.1 and 18.1 pounds. Assume that the sample is taken from a large population and the correction factor can be ignored. Round your final
answer to four decimal places and intermediate z-value calculations to two decimal places
The probability that the mean of a sample of 40 families will be between 17.1 and 18.1 pounds is given as follows:
0.5874 = 58.74%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by \(\mu\) and standard deviation symbolized by \(\sigma\) is obtained by the rule presented as follows:
\(Z = \frac{X - \mu}{\sigma}\)
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).The parameters for this problem are given as follows:
\(\mu = 17.2, \sigma = 2.5, n = 40, s = \frac{2.5}{\sqrt{40}} = 0.3953\)
The probability that the mean of a sample of 40 families will be between 17.1 and 18.1 pounds is the p-value of Z when X = 18.1 subtracted by the p-value of Z when X = 17.1, hence:
\(Z = \frac{X - \mu}{\sigma}\)
By the Central Limit Theorem:
\(Z = \frac{X - \mu}{s}\)
Z = (18.1 - 17.2)/0.3953
Z = 2.28
Z = 2.28 has a p-value of 0.9887.
Z = (17.1 - 17.2)/0.3953
Z = -0.25
Z = -0.25 has a p-value of 0.4013.
Hence:
0.9887 - 0.4013 = 0.5874 = 58.74%.
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hello fellow indians Question: Lawrence poured 27.328 L of water into a right rectangular prism- shaped tank. The base of the tank is 40 cm by 28 cm. When he finished pouring the water, the tank was ⅔ full. ( 1L=1,000 cm 3).
Answer: andres is 5 years old pls banned him he called e a mean word like the N word
Step-by-step explanation:
State the correct polar coordinate for the graph shown. It is not the option selected.
Answer:
Solution : Option D
Step-by-step explanation:
Let's start by listing two cases made possible when r is positive, in ( r, θ ). Remember that in polar coordinates a point is expressed in an ordered pair, where r is the distance from the pole (in this case 9, as it lies on the 9th circle) and theta is the directed angle from the positive x - axis.
( 9, θ ) here theta will be the angle to the terminal side with respect to the positive x - axis. This angle will be 60 degrees more than 90, or 90 + 60 = 150 degrees
( 9, θ ) and here theta will be the remaining degrees, or 360 - 150 = 210 degrees. Right away your solution will be (9, 210°)
In the square pyramid shown, points and are midpoints of the edges of one face. If the figure is sliced through points and and through the base, which best describes the shape of the resulting cross section? The picture shows a triangular prism. M and N are the points on the prism. A. rectangle B. trapezoid C. quadrilateral D. parallelogram
Based on the given information, we have a square pyramid with points M and N being the midpoints of the edges of one face. and forms a parallelogram. Option D
Since the base of the pyramid is a square, the cross section will consist of a square shape. Additionally, since the slice is made through the midpoints of the edges of the face, the resulting cross section will have parallel sides.
Considering these characteristics, we can conclude that the shape of the resulting cross section is a parallelogram. A parallelogram is a quadrilateral with opposite sides parallel. In this case, the opposite sides of the square cross section will be parallel, as the slice passes through the midpoints of the edges.
Therefore, the correct answer is D. parallelogram.
It's important to note that a triangular prism is not the correct answer because a triangular prism is a three-dimensional figure with two triangular bases and three rectangular faces. The cross section resulting from the given slice will not have the characteristics of a triangular prism. Option D.
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Together, kamela and Leo have 198 stamps. Kamela’s collection has 62 more stamps Thant Leon’s collection. How many stamps does Leo have?
Based on the information marked in the diagram
Answer:
I believe the answer is A. true
Answer:
True
Step-by-step explanation:
explain how to write function rule from the table below. Then write a function fule. x=0,2,4,6. y=2,1,0,-1
Both representations are equivalent and describe the same function.the function rule for this table is: f(x) = -1/2 x 2
What do you mean by Slope in Graph ?
The slope or gradient of a line is a number that describes both the direction and the steepness of the line. A slope of a line is the change in y coordinate with respect to the change in x coordinate.
To write a function rule for a given array, we need to determine how the values in the output column (y) relate to the values in the input column (x).
Looking at the given data, we notice that the output values decrease by 1 every time the input value increases by 2. This suggests that the function is linear and that we can use the slope-intercept form of a linear equation to represent it. .
The slope-intercept form of a linear equation is y = mx b, where m is the slope and b is the y-intercept. In this case, the slope m is -1/2 because the output values decrease by 1 every time the input values increase by 2. The y-intercept b is 2 because the output value is 2 when the input value is 0.
Therefore, the function rule for this table is:
f(x) = -1/2 x 2
where x is the input value and f(x) is the output value.
Alternatively, we can also represent the function in table entries, for example:
f(0) = 2
f(2) = 1
f(4) = 0
f(6) = -1
Both representations are equivalent and describe the same function.
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Use the drop-down menus to complete each equation so the statement about its solution is true. PLEASE HURRY
The solution of the given linear equation when
1. there is no solution, is x=-7.
2.one solution, is x=0.
What is a linear equation, exactly?
A linear equation is an equation which can be written in the form y = mx + b, where x and y are variables, m is the slope of the line, and b is the y-intercept. The slope represents the rate of change of y with respect to x, and the y-intercept is the point where the line crosses the y-axis.
Now,
If there is no solution, then the equation must be contradictory, meaning that it simplifies to a statement that is always false.
5x - 2x + 7 - x = 0
2x + 7 = x
1. x = -7, which leads to a contradiction.
Therefore,
there is no solution to the equation when x=-7.
If there are infinitely many solutions, then the equation must be an identity, meaning that it simplifies to a statement that is always true.
5x - 2x + 7 - x = 2x + 7 - x
2x + 7 = 2x + 7
This simplifies to 0 = 0, which is true for all values of x.
2. Therefore, there are infinitely many solutions to the equation.
If there is one solution, then the equation must be consistent, meaning that it simplifies to a statement that is true for only one value of x.
5x - 2x + 7 - x = 3x + 7
2x + 7 = 3x + 7
-x = 0
x = 0
Therefore,
3. the equation has one solution, x = 0.
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1815 + 0230 = subtract as n military time
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Answer: 20:45
I hope this helped!
<!> Brainliest is appreciated! <!>
- Zack Slocum
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Answer:
2045
Step-by-step explanation:
Find the equation of the given line.
Answer:
y=2/3x+1
Step-by-step explanation:
m= (slope)
b= (y-intercept
I need answer please
Answer:
The rate of change is -2
Step-by-step explanation:
formula we will use: G(x)= \(\frac{f(b)-f(a)}{b-a}\) [-1,2]
g(x)= \(x^3\)-5x
g(-1)=\(-1^3\)-5(-1)
g(-1)=-1+5
g(-1)=4
g(2)=\(2^3\)-5(2)
g(2)=8-10
g(2)=-2
so g(x)= \(\frac{(-2)-(4)}{(2)-(-1)}\)
g(x)= \(\frac{-6}{3}\)
g(x)=-2
Refer to the table summarizing service times (seconds) of dinners at a fast food restaurant. How many individuals are included in the summary? Is it possible to identify the exact values of all of the original service times?
Time (sec) Frequency
60 to 119 7
120 to 179 24
180 to 239 14
240 to 299 1
300 to 359 4
Answer:
Based on the provided information, the table summarizes service times (in seconds) of dinners at a fast food restaurant. To determine the number of individuals included in the summary, we can sum up the frequencies listed in the table:
7 + 24 + 14 + 1 + 4 = 50
Therefore, there are 50 individuals included in the summary.
Regarding the exact values of all the original service times, it is not possible to determine them precisely based on the given information. The table only provides ranges of service times and their corresponding frequencies. We can determine the range within which each individual's service time falls, but we cannot determine the exact value within that range.
A card is selected at random from an ordinary deck of 52 cards. What is the probability that it is either an ace or a spade
Answer: 4/13
Step-by-step explanation:
Number of cards in a deck = 52
Number of spades = 13
Number of aces = 4
Number of ace of spade = 1
Probability of either a spade or an ace :
P(spade or ace) = P(spade U ace)
P(spade U ace) = p(spade) + p(ace) - p(spade n ace)
Probability = required outcome / Total possible outcomes
P(spade) = 13 / 52
P(ace) = 4 / 52
P(spade n ace) = 1 / 52
P(spade U ace) = p(spade) + p(ace) - p(spade n ace)
= 13/52 + 4/52 - 1/52
= 16 / 52 = 4 /13
Eliminate the parameter in the equations x = t^1/3 and y = t – 4. How can the rectangular equation be described?
This is the rectangular equation described by the parameter equation x = t1/3 and y = t – 4.
Elimination of the parameter means to rewrite the equations in terms of only x and y. To do this, substitute t from one equation into the other equation. Here, the two equations are:x = t1/3 and y = t – 4Substitute t from the first equation into the second equation:y = (x^3) – 4Now the equation is in terms of x and y only.
This is the rectangular equation described by the parameter equation x = t1/3 and y = t – 4.The rectangular equation, y = (x^3) – 4 can be plotted on a graph. It is a cubic equation. The graph will look like a curve that passes through the point (0, -4) and continues to move towards infinity. The graph will be symmetric to the origin because the equation involves an odd power of x.
If the equation involved an even power of x, the graph would be symmetric to the y-axis. The graph will never touch the x-axis or y-axis, it will only approach them.In conclusion, the rectangular equation y = (x^3) – 4 is derived from the two parameter equations, x = t1/3 and y = t – 4. The graph of this equation is a cubic curve that is symmetric to the origin. The curve passes through (0, -4) and approaches the x and y-axes but never touches them.
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Can yall hel me with this pls
Answer:
X = 10
Z = 67
Step-by-step explanation:
We see that the angles are formed by the intersection of two lines.
Angles z and 67° are vertically opposite angles and therefore they are equal to each other
z°= 67°
Angles z and (7x + 43) are supplementary angles. The sum of these angles add up to 180°
z + 7x + 43 = 180
67 + 7x + 43 = 180
7x + 110 = 180
7x = 180 -110 = 70
x = 70/7 = 10
(1/3) to the power of 4
Step-by-step explanation:
\( (\frac{1}{3} ) {}^{4} \\ \\ = \frac{1}{81} \)
what are the powers of 3 through 1000? AND DONT JUST SAY A FEW I NEED ALL OF THEM
Answer:
1, 3, 9, 27, 81, 243, 729
Step-by-step explanation:
The powers of 3 are:
\(3^0 = 1\)
\(3^1 = 3\)
\(3^2 = 9\)
\(3^3 = 27\)
\(3^4 = 81\)
\(3^5 = 243\)
\(3^6 = 729\)
\(3^7 = 2187\)
And so on...
So through 1000: 1, 3, 9, 27, 81, 243, 729
Cakculate the Length of line x
The length of line x in the figure of the cube given is 19.
Calculate the length of the base of the cube, which is the diagonal of the lower sides :
base length = √10² + 6²
base length = √136
The length of x is the diagonal of the cube
x = √baselength² + 15²x = √(√136)² + 15²
x = √136 + 225
x = √361
x = 19
Therefore, the length of line x in the figure given is 19.
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what is the area of the cylinder rounded to the nearest whole number
Answer:
the area is 207
Step-by-step explanation:
The equation to solve the area of a cylinder is A=2πrh+2πr^2
The radius is the length from the outside to the center, 6 is the diameter so we could half that to get the radius, 3 and height is 8
A=2*3.14*3*8+2*3.14*3^2
A=6.28*3*8+6.28*9
A=18.84*8+56.52
A=150.72+56.52
A=207.24
207.24 rounded to the nearest whole number is 207 so your area is 207
Which algebraic expression are polynomials? Check all that apply
Answer:
A, B, E
Step-by-step explanation:
Edge21
two pounds of flour cost 1.20 .How much flour do you get per dollar?
1.67 pounds flour we get per dollar.
What does pounds mean in weight?Pound, avoirdupois weight unit equivalent to 16 ounces, 7,000 grains, or 0.45359237 kg, and troy and apothecaries' weight unit equal to 12 ounces, 5,760 grains, or 0.3732417216 kg The symbol lb comes from the Roman predecessor of the contemporary pound, the libra.
Given,
Cost for 2 pounds of flour = $ 1.20
Cost per pound of flour = $ 1.20 /2
= $ 0.20
Now for 2 dollar we get flour = 2 pounds.
for 1 dollar we will get flour = 2/1.20 pounds
= 1.6666 pounds
i.e. for 1 dollar we will get flour = 1.67 pounds.
So, 1.67 pounds flour we get per dollar.
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(14z - 10) and (177 + 4)". Find the measures of the angles.
Answer:
Step-by-step explanation:
A regular polygon is a polygon that is both equiangular and equilateral. All sides are equal length placed around a common center so that all angles between sides are also equal. When the number of sides, n, is equal to 3 it is an equilateral triangle and when n = 4 is is a square.