The steps to graph the absolute value functions are given below.
We have,
Absolute value functions of form f(x) = |ax + b| have a characteristic shape, which depends on the values of a and b.
Here are some general guidelines for graphing these functions:
Find the y-intercept:
To find the y-intercept of the graph, set x=0 and solve for y.
This gives f(0) = |b|, so the y-intercept is at the point (0,|b|).
Find the x-intercept(s):
To find the x-intercepts of the graph, set y = 0 and solve for x.
If b > 0, there are two x-intercepts: x = -b/a and x = b/a.
If b = 0, there is one x-intercept at x=0.
If b < 0, there are no x-intercepts.
Determine the direction of the graph:
If a > 0, the graph opens upwards, like a "V".
If a < 0, the graph opens downwards, like an upside-down "V".
Determine the vertex:
The vertex is the point where the graph changes direction.
If a > 0, the vertex is at (-b/a, 0).
If a < 0, the vertex is at (b/a, 0).
Sketch the graph:
Use the information above to sketch the graph of the absolute value function.
Plot the y-intercept, the x-intercept(s), and the vertex, and then draw a smooth curve connecting these points.
Thus,
The graph of the absolute value functions is given above.
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Select the correct answer.
If the graphs of the linear equations in a system are parallel, what does that mean about the possible solution(s) of the system?
A. There is no solution.
B. There is exactly one solution
C. There are infinitely many solutions
D.The lines in a system cannot be parallel.
If the graphs of the linear equations in a system are parallel: A. There is no solution.
How to interpret Linear equation Graph?The general form for the equation of a line is:
y = mx + c
where:
m is slope
c is y-intercept
Usually, for two equations to have a solution, they must intersect each other.
However, If the graphs of the two equations are parallel lines, then there will be no solution, and the system is called an inconsistent system because the two lines will never intersect each other.
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employees receive a 10% discount their shopping at Tesco stores. calculate the weekly benefit to an employee who on average spend£14 each weekday and £22 on each day at the weekend.
The weekly benefit of the employees is A = £ 11.40
Given data ,
Let's calculate the weekly benefit for an employee who spends an average of £14 each weekday and £22 on each day of the weekend, considering the 10% discount they receive at Tesco stores.
First, we'll calculate the total amount spent on weekdays and weekends separately:
Amount spent on weekdays = £14/day x 5 days/week = £70/week
Amount spent on weekends = £22/day x 2 days/week = £44/week
Next, we'll calculate the total amount spent in a week by adding the amounts spent on weekdays and weekends:
On simplifying the equation , we get
Total amount spent in a week = £70 + £44 = £114
Now, we'll calculate the 10% discount on the total amount spent:
10% of £114 = £11.40
Hence , the weekly benefit to the employee who receives a 10% discount on their shopping at Tesco stores would be £11.40
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solve (2x - 3) (x + 2) = 0
Answer:
x=3/2
x=-2
Step-by-step explanation:
Find the value of a
Answer is 3
Step-by-step explanation:
Use the Ratio Test since Ratio Test guarantee absolutely convergence.
[tex] \frac{ ( - 1) {}^{k + 1}(k + 1) {}^{a} }{5 {}^{k + 1}(3(k + 1) } \times \frac{5 {}^{k}(3k) }{(k) {}^{a} ( - 1) {}^{k} } [/tex]
This simplifes to
[tex] \frac{( - 1) {}^{k} ( - 1) ((k + 1)!) {}^{a} }{5 {}^{k}(5)(3k +1) ! } \times \frac{5 {}^{k} (3k)!}{( - 1) {}^{k} (k!) {}^{a} } [/tex]
[tex] \frac{ - (k + 1) {}^{a} }{5(3k + 3)(3k + 2)(3k + 1)} [/tex]
Take the absolute value
[tex] \frac{(k + 1) {}^{a} }{5(3k + 3)(3k + 2)(3k + 1)} [/tex]
In order for this series to be convergent,
the limit as k approaches infinity must be less than 1.
In order for this series to have a limit less than 1, our numerator and denominator degree must be equal or the denominator must have the larger degree.
Why
If the numerator has a larger degree, our test would make this divergent, so the limit would be infinity
Since the denominator have 3 binomials, our power for the denominator will be 3, this the numerator having a degree of 3 or less as well.
So one of the answer is 3.
determine he measures of the angles
Answer:
45
Step-by-step explanation:
Evaluate the expression
12-3y divided by 2 + y(2y-4 divided by y) for y = 3
A florist wants to determine if a new additive would help extend the life of cut flowers longer than the original additive. The florist randomly selects 20 carnations and randomly assigns 10 to the new additive and 10 to the original additive. After three weeks, 6 carnations placed in the new additive still looked healthy and 2 carnations placed in the original additive still looked healthy. The difference in proportions (new – original) for the carnations that still looked healthy after three weeks was 0.4. Assuming there is no difference in the additives, 200 simulated differences in sample proportions are displayed in the dotplot.
Using this dotplot and the difference in proportions from the samples, is there convincing evidence that the new additive was more effective?
A. Yes, because a difference in proportions of 0.4 or more occurred 7 out of 200 times, meaning the difference is statistically significant and the new additive is more effective.
B. Yes, because a difference in proportions of 0.4 or less occurred 193 out of 200 times, meaning the difference is statistically significant and the new additive is more effective.
C. No, because a difference in proportions of 0.4 or more occurred 7 out of 200 times, meaning the difference is not statistically significant and the new additive is not more effective.
D. No, because a difference in proportions of 0.4 or less occurred 193 out of 200 times, meaning the difference is not statistically significant and the new additive is not more effective.
C. No, because a difference in proportions of 0.4 or more occurred 7 out of 200 times, meaning the difference is not statistically significant and the new additive is not more effective.
====================================================
Explanation:
If the new additive was more effective than the old one, then the difference in proportions (new - old) should be fairly large.
Count the dots over the x axis labels of "0.4" through "0.6"
5 dots over "0.4"1 dot over "0.5"1 dot over "0.6"That makes 5+1+1 = 7 dots total.
There are 7 instances where the difference of proportions is 0.4 or larger.
This is out of 200 observations, so 7/200 = 0.035 = 3.5% of the differences have 0.4 or larger.
This is not very significant. The general rule of thumb is to use 5% as the threshold. Some stats textbooks will use 10%. Other times your teacher will specify the significance level. The Greek letter alpha is often used.
Because 3.5% < 5%, we consider the new additive to not be that effective compared to the original additive.
When signing the lease for his $750.00 per month rental property. Stanley will have to pay the first and last months rent and a security deposit equal to 30% of one month's rent. If Stanley currently earns an average bi-weekly net pay of $1,050.00, determine what percent of his monthly pay he will need to save if he wants to save enough money to sign the lease in three month.
Answer:
Step-by-step explanation:
tax
A baker produces 400 brownies a day at a cost of 25 cents per brownie. If all the brownies are sold each day, what is the minimum selling price per brownie to make a daily profit of at least $420?
The minimum selling price per brownie to make a daily profit of at least $420 is $1.30.
What is the minimum selling price per brownie to make a daily profit of at least $420?Given that: A baker produces 400 brownies a day at a cost of 25 cents per brownie.
Let's begin by calculating the total cost of producing 400 brownies a day:
Cost per brownie = 25 cents = 0.25 dollars
Total cost = 400 × 0.25 = 100 dollars
To make a daily profit of at least $420, the total revenue should be:
Total revenue = Total cost + Minimum profit
Total revenue = 100 + 420 = 520 dollars
The minimum selling price per brownie to achieve this revenue can be calculated as:
Selling price per brownie = Total revenue / Number of brownies produced
Selling price per brownie = 520 / 400
Selling price per brownie = 1.3 dollars
Therefore, the minimum selling price is $1.30 per brownies.
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Complete the ratio table
The missing values from ratio table are 17 and 28.
We have table as
3 1
48 16
51 x
78 26
84 y
So, the ratio are in proportion then
48 / 16 = 51 /x
3 = 51/x
x= 51/3
x = 17
and, 3/1 = 84/y
y= 84/3
y= 28
Thus, the values are 17 and 28.
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The ratio of two numbers is 1 to 3 and the sum of their squares is 250. Find the numbers.
Answer:
Step-by-step explanation:
5 and 15
5^2=25
15^2=225
225+25=250
Which expression is equivalent to 12/5x -2 A. 12x-2/5 B. 2(2/5x -1) C. 2/5(6x-10) D. 1/5(12x-10)
Answer:
The answer is D.
[tex] \frac{1}{5}(12x - 10)[/tex]
PLS HURRY I AM GIVING BRAINLIEST!!!
the question is in the photo!!
In the above triangle,
1) the sum of side 1 and 2 is: 4x² + 3x + 4
2) the length of side 3 is: 5x³-6x²-12
1) To find the sum of side 1 and side 2, we simply need to add them together.
Side 1 = 3x² - x - 1
Side 2 = x² + 4x + 5
Side 1 + Side 2 = (3x² - x - 1) + (x² + 4x + 5)
= 3x² + x² - x + 4x - 1 + 5
= 4x² + 3x + 4
Therefore, the sum of side 1 and side 2 is = 4x² + 3x + 4
2) We can derive the expression of the thried side by removing the expression in (1) above form the perimeter.
That is;
(5x³-2x² + 3x - 8) - (4x² + 3x + 4)
First we distribute the negative sign
= 5x³-2x² + 3x - 8 + -1 (4x² + 3x + 4)
= 5x³-2x² + 3x - 8 + -1 (4x²) -1( 3x) -1( 4)
= 5x³-2x² + 3x - 8 + -4x² - 3x - 4
Combining like terms we have
= (5x³) (-2x²+-4x²) + (3x +- 3x) + (-8 + - 4)
= 5x³-6x²-12
Hence the missing side (thrid side is) 5x³-6x²-12
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Here are some integers where a
a
b
C
d
d
d
The mode of the integers is 9
The median of the integers is 8
The range of the integers is 4
Work out the value of a, the value of b, the value of c and the value of d
We know that the mode of the integers is 9, which means that 9 occurs more frequently than any other number in the set of integers.
How to explain the mediWe also know that the median of the integers is 8, which means that when the integers are arranged in order from smallest to largest, the middle number is 8.
Finally, we know that the range of the integers is 4, which means that the difference between the largest and smallest integers in the set is 4.
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Pamela paid $8.95 for 5 pounds of bananas. How much will it cost to buy 2 pounds of bananas at the same rate?
Answer:
$3.58
Step-by-step explanation:
Because we know that the 2 lbs of bananas will be purchased at the same rate, the price per pound for 5 lbs of bananas is proportional to the price per pound for 2 lbs of bananas.
Thus, we can solve for price, p of 2 lbs of bananas by setting up a proportion:
[tex]\frac{8.95}{5}=\frac{p}{2}\\ \\ 17.90=5p\\\\3.58=p[/tex]
UCM college administrators claim that the average freshman enrollment over the last 10 years meets the university's capacity of 6,500 students. You believe hypothesize this is inaccurate and believe that UCM is underestimating the number of college freshman. Using a sample of 500
students, you determine a sample mean of 6,600 freshman. Assume o = 1,000 and a = .05.
The t-statistic value of the hypothesis is 2.236
The population mean is equal to 6,500 (H0: μ = 6500)
Alternative hypothesis:
The population mean is greater than 6,500 (Ha: μ > 6500)
We are given the sample mean (x) = 6,600, sample size (n) = 500, population standard deviation (σ) = 1,000, and level of significance (α) = 0.05.
First, we need to calculate the t-statistic using the formula:
t = (X - μ) / (σ / √n)
where X is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.
Substituting the given values, we get:
t = (6,600 - 6,500) / (1,000 / √500)
= 2.236
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NEED TO BE DONE ASAP ONLY HAVE 2MIN
Answer:
42 units³
Step-by-step explanation:
You want the volume of a rectangular prism that has a base area of 5 1/4 units² and a height of 8 units.
VolumeThe formula for the volume of a prism is ...
V = Bh
where B is the base area and h is the height perpendicular to the base.
Here, we have B = 5 1/4 u² and h = 8 u. The volume is ...
V = (5 1/4 u²)(8 u) = 42 u³
The volume of the prism is 42 cubic units.
In the diagram, angle adc is a central angle and angle measure adc = 60°. What is angle measure ABC?
The measure of angle ABC is 30 degrees. Option B
How to determine the valueIt is important to note the properties of a circle, they include;
Two circles are congruent if they have same radii.Diameter of a circle is the longest chord in the given circleSame chords of a circle subtend the same measure of angles at the center of the circleThe radius that is perpendicular to the chord divides the chord into twoAlso note that the measure of the angle at the circumference is half to twice the measure of the angle at the center.
From the information given, we have that;
<ADC = 60 degrees
This is the angle at the circle
Then,
<ABC is the angle at the circumference
<ABC = <ADC/2 = 60/2 = 30 degrees
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A car is driving away from El Paso with constant velocity. At 1 p.m., it is 145 miles away from El Paso. At 3 p.m., it is 275 miles away from El Paso.
Part A: Write a linear function that describes the distance (in miles) the car is from El Paso in terms of time (in hours after 12:00 p.m.).
The linear function that describes the distance (in miles) is therefore y = 65x + 80
How to solve for the linear functionWe have to find the slope and the intercept in other to get the linear function
The data points are:
(1, 145) and (3, 275).
m = (y2 - y1) / (x2 - x1)
fixing the data points we have
m = (275 - 145) / (3 - 1)
= 130 / 2
= 65
y = mx + b
(1, 145):
145 = 65(1) + b
b = 145 - 65
= 80
y intercept is 80
The linear function is therefore y = 65x + 80
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What is the measure of angle b?
Answer:60 degrees
Step-by-step explanation: The three angles of a triangle add to 180, a right angle is 90 so 180-90-30= 60.
DE bisects AC at point B. AC=a+23
and AB = 3a + 4. Find BC.
Y
X
13
2
X
(X) XS
X₁
IV
The values of AB and BC are equal and equal to
13 units.How to find BCInformation given in the problem includes
DE bisects AC at point B
AC = a + 23
AB = 3a + 4
From the definition of a bisector, point B divides AC into two equal sides, this means that
AB = BC = (1/2) * AC
Substituting the value of AC and AB
AB = 3a + 4 = (1/2) * (a + 23)
3a + 4 = (1/2) * (a + 23)
solving for a
2 * (3a + 4) = a + 23
6a + 8 = a + 23
6a - a = 23 - 8
5a = 15
a = 3
Then we have that:
AB = 3a + 4 = 3(3) + 4 = 9 + 4 = 13
and, AB = BC
so BC = 13
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The Statue of Liberty in New York Harbor stands at a height of about 305 feet. A group of students in a social studies class is building a scale model of the monument. If the students use a scale of 1 inch: 50 feet, about how tall will their model be? Round your answer to the nearest tenth of an inch if necessary.
Answer:
The answer to your problem is, 6.1 inches
Step-by-step explanation:
So we know that 1 inch of there model in real life is 50 feet.
Divide:
305 / 50
= 6.1 but we are going to use 6
Since it is 6 there model is 6 inches.
But remember we still have that 0.1 which we need to full fill for that:
Note that 6.1 will be in inches.
So it is done.
Thus the answer to your problem is, 6.1 inches
A hair dryer has a power of 1,200 W. How much electrical energy does it use in minutes?
Answer:
r 0.6 kWh to run for 30 minutes.
Answer:
ok so it takes 1200 watts for a hair dryer to run for a full hour, that means it takes 600 watts, or 600 Wh, or 0.6 kWh to run for 30 minutes
Step-by-step explanation:
The half-life of a certain element is 5 days. If you started with 948 grams of this element, how much remains after 30 days?
After 1 half-life, the amount of the element remaining is half of the original amount. After 2 half-lives, the amount remaining is half of the remaining amount after the first half-life. We can continue this pattern until we get to 30 days.
The number of half-lives in 30 days is 30/5 = 6.
So, after 1 half-life, the amount remaining is 948/2 = 474 grams.
After 2 half-lives, the amount remaining is 474/2 = 237 grams.
After 3 half-lives, the amount remaining is 237/2 = 118.5 grams.
After 4 half-lives, the amount remaining is 118.5/2 = 59.25 grams.
After 5 half-lives, the amount remaining is 59.25/2 = 29.625 grams.
After 6 half-lives, the amount remaining is 29.625/2 = 14.8125 grams.
Therefore, after 30 days, 14.8125 grams of the element remains
Given that the perimeter of an equilateral triangle is 63 inches, find the height/altitude of the triangle.
The height of the triangle is h = 18.18 inches
Given data ,
In an equilateral triangle, all three sides are equal in length.
Let the length of each side be s
Now , the perimeter of the equilateral triangle is given as 63 inches, so we have:
Perimeter of the triangle = 3s = 63 inches
Dividing both sides by 3, we get:
s = 63/3 = 21 inches
Let's now plot an altitude from one of the equilateral triangle's vertex to the side's midway. As a result, two right-angled triangles will be formed, each with the hypotenuse "s" and sides "s/2" and "h"
From the Pythagoras theorem , we get
(h²) + ((s/2)^2) = s²
Substituting the values we found earlier for "s", we get:
(h²) + ((21/2)²) = 21²
Simplifying further, we have:
(h²) + (10.5²) = 21²
(h²) + 110.25 = 441
Subtracting 110.25 from both sides, we get:
h² = 330.75
On taking square roots on both sides , we get
h = √(330.75)
h ≈ 18.18 inches
Hence , the height of the equilateral triangle is 18.18 inches
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Is the function g(x)=8 linear or nonlinear?
Answer:
It's linear
Step-by-step explanation:
Answer:
Linear
Step-by-step explanation:
How to solve a 2 step inequality
Answer: To solve a two-step inequality, undo the addition or subtraction first, using inverse operations, and then undo the multiplication or division. The inverse operation of addition is subtraction and vice versa. Similarly, the inverse operation of multiplication is division and vice versa.
Step-by-step explanation:
find f(g(2)), g(f(2)) given f(x)=3x+5 and g(x)=-7x+6
The two compositions give:
f(g(2)) = -19g(f(2)) = -71How to evaluate the compositions?Here we have two functions:
f(x) = 3x + 5
g(x) = -7x + 6
And we want to fin the two compositions:
f(g(2))
g(f(2))
First, let's find g(2) = -7*2+ 6 = -14 + 8 = -8
Then:
f(g(2)) = f(-8) = 3*-8 + 5 = -19
Now the other one:
f(2) = 3*2 + 5 = 11
Evaluating g in that:
g(11) = -7*11 + 6 = -77 + 6 = -71
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A rectangular aquarium measures 21 inches long by 11 inches wide by 18 inches tall. If the aquarium is filled to the 15 inch mark, what is the volume of the water in the aquarium?
The volume of water in the aquarium up to the 15 inch mark is 3465 cubic inches.
What is the volume of the water in the aquarium?A rectangular prism is simply a three-dimensional solid shape which has six faces that are rectangles.
The volume of a rectangular prism is expressed as;
V = w × h × l
Where w is the width, h is height and l is length
The volume of water in the aquarium up to the 15 inch mark will be equal to the volume of a rectangular prism with a length of 21 inches, a width of 11 inches, and a height of 15 inches.
This is because the water level is 15 inches from the bottom of the aquarium.
Hence, the volume of water in the aquarium up to the 15 inch mark is:
V = l × w × h
V = 21 × 11 × 15
V = 3465 cubic inches
Therefore, the volume of water in the aquarium is 3465 cubic inches.
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If $x$ is a real number, find $49x^2+14x(19-7x)+(19-7x)^2$
The value of the expression is $-56x² + 266x + 261
What are algebraic expressions?Algebraic expressions are simply described as mathematical expressions that consists of coefficients, certain variables, terms, constants and factors.
Algebraic expressions are also identified with arithmetic operations, such as;
SubtractionMultiplicationDivisionAdditionBracketParenthesesFrom the information given, we have;
$49x^2+14x(19-7x)+(19-7x)^2
expand the bracket, we get;
49x² + 266x - 98x² + 361 - 7x²
Now, collect the like terms, we get;
49x² - 98x² - 7x² + 266x + 361
Add or subtract the values
$-56x² + 266x + 261
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