To determine whether the system of equations is consistent and independent, consistent and dependent, or inconsistent, we need to first solve the system of equations to find the value of x and y that satisfy both equations.
To solve the system of equations, we can first solve the first equation for y:
y = −3x + 1
Next, we can substitute this expression for y into the second equation and solve for x:
2y = −6x + 2
2 * (−3x + 1) = −6x + 2
−6x + 2 = −6x + 2
0 = 0
Since the two equations are equivalent, the system of equations is consistent and dependent, meaning that there is only one possible solution (x = 0, y = 1) that satisfies both equations.
If f(x)=|x−5| 2, find f(3). responses 10 10 6 6 4 4 0
If the function f(x) = |x-5| + 2, then the value of f(3) is 4
The function
f(x) = |x-5| + 2
The function is defined as the mathematical statement that shows the relationship between the independent variable and the dependent variable. The function consist of different variables, numbers and mathematical operators
Here the function consist of the absolute value symbol.
|-a| = a
The absolute value of the positive and the negative number will be always positive.
The function is f(x) = |x-5| + 2
Then,
f(3) = |3-5| + 2
= |-2| + 2
= 2 + 2
= 4
Therefore, the value of f(3) is 4
I have answered the question in general, as the given question is incomplete
The complete question is:
If f(x)=|x−5| + 2, find the value of f(3).
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PLEASE HURRY!
Write and solve the inequality that represents negative one eighth is less than the product of negative two thirds and a number.
A: negative one eighth is less than negative two thirds y where y is less than three sixteenths
B: negative one eighth is less than or equal to negative two thirds y where y is greater than negative three sixteenths
C: negative two thirds is less than negative one eighth y where y is less than one twelfth
D: negative two thirds is greater than negative one eighth y where y is greater than negative one twelfth
The solution to the inequality statement is x < 3/16
How to determine the solution to the inequality?From the question, we have the following parameters that can be used in our computation:
negative one eighth is less than the product of negative two thirds and a number.
Express as numbers and operators
So, we have
-1/8 < -2/3x
Divide both sides by -2/3
So, we have the following representation
1/8* 3/2 > x
Evaluate the produdts
3/16 > x
Rewrite as
x < 3/16
Hence, the solution is x < 3/16
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you round_trip drive to work is 4 3/10 miles how many miles do you drive to and from work in 3 days?
Answer:
12.9 or 12 9/10
Step-by-step explanation:
4 3/10 or 4.3 x 3
12.9 or 12 9/10
10. dice when a pair of dice is rolled, what is the probability tha tthe sum of the dice is 5, given that exactly one of the dice shows a 3?
The probability sum of the dice is 2/11.
Let A be the event that the sum of dots is 5, then
A={(1,4), (2,3), (3,2), (4,1)}
n(A)=4
And, B is the event that one die shows a "one"
B={(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (3,1), (4,1), (5,1), (6,1)}
n(B)=11
The Event that some of the dots are five and one of the die shows "one".
A intersection B = {(1,4), (4,1)}
Since n(A) = 36 (thirty-six possible samples of two dice)
P(A)=4/36
P(B)=11/36
P(A intersection B)=2/36
So, the required probability is
P(A|B)=P(A intersection B)/P(B) =2/11
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what is sue's position x if her home is the origin? assume the positive direction is to the right.
If Sue's home is the origin and the positive direction is assumed to the right, then her position is 2 mi.
Therefore, the answer is 2mi.
Origin depends on the frame of reference, it depends on from where the observer is viewing.
From the figure, distance between home and Sue = 2 - 0 = 2mi
and the distance between Cinema and Sue = 5 - 2 = 3mi
Sue's position is 2mi right to her home and 3mi left to the Cinema. So if her home is the origin and positive direction is to the right x is +2 mi.
--The question is incomplete without the figure, answering to the figure attached--
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What is the slope of the line that passes through the points (-7,-2) and
(-15, -14)? Write your answer in simplest form.
Answer:
Step-by-step explanation:
To find the slope of a line that passes through two points, we can use the slope formula, which is written as follows:
slope = (y2 - y1) / (x2 - x1)
Where (x1, y1) and (x2, y2) are the coordinates of the two points.
Given the points (-7, -2) and (-15, -14), we can substitute their coordinates into the slope formula to find the slope of the line:
slope = (-14 - (-2)) / (-15 - (-7))
= -12 / -8
= 3/2
Therefore, the slope of the line that passes through the points (-7, -2) and (-15, -14) is 3/2. In simplest form, this is equal to 1.5.
A group of students is asked if they travel
Students travelling Students not by car
travelling by car 14 to school by car. Here
are the results. 11 a) What percentage of
these students do not travel to school by
car? % No of students b) 14 of these
students travel by car. Number of cars in
one car Some of these travel in the same
car. Fill the missing frequency in the table.
c) Work out the mean number of students
in each car
The percentage of those that don't travel by car will be 44%.
How to calculate the percentage?It's important to note that a percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
In this case, 14 students travel by car and 11 don't travel by car. The total number of students will be:
= 11 + 14.
= 25
Therefore, the percentage of those that don't travel by car will be:
= 11 / 25 × 100
= 44%
The percentage is 44%.
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What is a written description of x − 14?
Answer: The written description of x - 14 is given as the difference of variable x and integer 14 gives x -14.
Step-by-step explanation:
Calculate the answer using a math operator is referred to as a mathematical operation.
Basic mathematical operations are addition, multiplication, subtraction and division.
Let x be a variable,
And 14 is an integer.
By using mathematical operations,
The difference of x and 14 can be given as,
x - 14.
According to the american dental association, 8% of adults have never had a cavity. A dental graduate student contacts an srs of 1000 adults and calculates the proportion p in this sample who have never had a cavity
The proportion of people who never had a cavity is 0.92.
What are ratio and proportion?A ratio is a comparison between two similar quantities in simplest form.
Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.
In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.
Given, 8% of adults have never had a cavity. A dental graduate student contacts an srs of 1000 adults.
8% of 1000 is,
= (8/100)×1000.
= 80.
Now, The proportion of people who never had a cavity is (1000 - 80)/100.
= 920/1000.
= 92/100.
= 0.92 proportion of people never had a cavity.
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Pls help I’ll put in a picture
Answer:
2 < x < 26
Step-by-step explanation:
The length of the side of a triangle must be less than the sum of the lengths of the other two sides of a triangle.
Therefore:
12+14>x
x<26
However, the following must also be true:
x+12>14 (The sum of x and 14 will always be greater than 12 because 14>12, so we don’t need to include that in the inequality)
So, x>2.
This means that the answer is 2<x<26
Is anyone good at this math
Answer:
x = 3
Step-by-step explanation:
4 + x = 7 Subtract 4 from both sides of the equation
4 - 4 - x = 7 - 4 Simplify
x = 3 X equals 3
Answer:
x = 3
Step-by-step explanation:
4 + x = 7
x + 4 - 4 = 7-4 = 3
x = 3
To solve for x, subtract 4 from both side of the equation. This leaves x by itself on the left side of the equation. Next subtract 4 from 7 to get the solution, x = 3.
Rida writes a fitness blog. At a certain point, she has 6,218 followers. Then the following events happen, in order:
92 people stop following Rida's blog.
417 people start following Rida's blog.
The number of followers doubles.
Use the drop-down menus to answer the questions below.
CLEAR CHECK
An expression that models this series of events is
.
Zuberi also writes a fitness blog. His current number of followers is equal to 3(945−120)+312. A possible series of events that led to this number of followers would be:
An expression that models the series of events is 2(6,218 - 92 + 417).
The possible events are:
120 followers stop following Zuberi's blog.
The number of followers triples.
312 followers start following Zuberi's blog.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
At a certain point, she has 6,218 followers.
Events happened in order:
92 people stop following Rida's blog.
417 people start following Rida's blog.
The number of followers doubles.
An expression that models this series of events.
= 2(6,218 - 92 + 417)
The current number of followers.
= 3 (945 - 120) + 312
The possible events.
120 followers stop following Zuberi's blog.
The number of followers triples.
312 followers start following Zuberi's blog.
Thus,
An expression that models the series of events is 2(6,218 - 92 + 417).
The possible events are given above.
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Three years ago Joseph was three times older than Agnes in 2 years times the sum of their ages will be 75 years. Determine their present ages
Answer:
Hey, answer is attached.
Step-by-step explanation:
Hope this helps.
PLS HELP
What is the range of f(x) = |x| + 7?
−7 ≤ y < ∞
−∞ < y ≤ −7
0 ≤ y < ∞
7 ≤ y < ∞
The range of the function f(x) = |x| + 7 is given by the option presented as follows:
7 ≤ y < ∞.
How to obtain the range of a function?The range is composed by the set containing all the values assumed by the output of the function, that is, all the numeric values assumed by the function.
In the context of this problem, the function is defined as follows:
f(x) = |x| + 7.
The parent function is the absolute value function g(x) = |x|, which gives the distance of a point x from the origin, assuming real values of at least 0, as a distance cannot be negative.
The addition by 7 means that the parent function was translated up seven units, meaning that the minimum value assumed by the range is seven, and the range of the function is given by the last option given as follows:
7 ≤ y < ∞.
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which of the three methods of assigning probabilities is used when we are dealing with sampling (as a method of determining probabilities)? no need to explain.
Random sampling methods of assigning probabilities is used when we are dealing with sampling.
Random sampling is a method of assigning probabilities used when dealing with samples of a population. It involves randomly selecting a sample from the population and then using that sample to estimate the probabilities of different outcomes. This is done by calculating the proportion of the sample that falls into each category. For example, if you are trying to determine the probability of a certain outcome, you would randomly select a sample from the population and then count how many of the individuals in the sample fall into that category. The probability of the outcome would then be calculated by dividing the number of individuals in that category by the total number of individuals in the sample.
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uppose we wanted the margin of error for the 90% confidence level to be about 1.5%. how large of a survey would you recommend?
confidence level to be about 1.5%. Then the survey would you recommend is 1537
The first thing is to apply the corresponding formula of this case, it is the calculation of a sample size without knowing the population. The equation is as follows, let n be the sample size:
n = (z * s / E) ^ 2
We know that z the corresponding z score of 95% of the confidence level, that this case is 1.96.
s, is the standard deviation and has a heat of 10.
Finally E, would be the error that is 0.5.
Now it's just replace in the formula:
n = (1.96 * 10 / 0.5) ^ 2 = 1536.64, that is approximately the sample must be 1537.
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What is the answer to this question
Answer:
Step-by-step explanation:
a because if you divide everything under the fraction number you get answer a
The solution for the given expression is x = 4³/₅. The correct option is B.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the expression is x - 17⁴/₅ = -13¹/₅. The given expression will be solved as,
x - 17⁴/₅ = -13¹/₅
x = 17⁴/₅ -13¹/₅
x = 89 / 5 - 66 / 5
x = 23 / 5
x = 4³/₅
The expression will be equivalent to x = 4³/₅.
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Decrease by
15 %
Increase by
85 %
Determine the Input
A number went into this machine and 50 came out.
What number went in?
To determine the input number, we can use the following steps:
Calculate the change in the input number as a percentage of the input number. In this case, the input number decreased by 15%, so the change is -0.15 * input number.
Add the change to the output number to find the input number. In this case, the output number is 50, so the input number is 50 + (-0.15 * input number).
Solve for the input number. In this case, we can solve for the input number by rearranging the equation and solving for x:
input number = 50 / (1 - 0.15)
input number = 50 / 0.85
input number = 58.82
Therefore, the input number is 58.82.
Note that this process can also be used to determine the output number given the input number and the percentage change. For example, if the input number is 100 and it increases by 85%, the output number would be:
output number = 100 * (1 + 0.85)
output number = 100 * 1.85
output number = 185
Answer:
[tex]x \times \frac{85}{100} \times \frac{185}{100} = 50[/tex]
[tex]x = 50 \times \frac{ {100}^{2} }{85 \times 185} [/tex]
[tex]31.8[/tex]
it seems to be a long number so I rounded
There might be a mistake because I wasn't able to check.
Kala's parents give her simple interest on any money she saves for college. Which equation and solution represents the total interest, T, earned when the principal amount is $100, the
annual simple interest rate is 1%, and the number of years is 10
Answer:
The interest earned is $10.00
Step-by-step explanation:
Interest = principal x rate x time
I= 100(.01)(10)
I = 10
What i the equation of the line that pae through the point (-1,5)(−1,5) and ha a lope of -3
The equation of the line is y = -3x + 2.
What is the slope of a line?
A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.
Both the net change in the y-coordinate and the net change in the x-coordinate are represented by Δy and Δx, respectively.
As a result, m = change in y/change in x = Δy/Δx is the formula for the change in y-coordinate with respect to the change in x-coordinate.
where "m" represents a line's slope.
Given that, the line passes through the point (-1,5) with slope of -3.
The equation of line passes through (x₁, y₁) with slope m is
y - y₁ = m(x - x₁)
Putting x₁ = -1, y₁ = 5 and m = -3.
y - 5 = -3(x - (-1))
y - 5 = -3x - 3
y = -3x + 2
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Graph the image of this figure after a dilation with a scale factor of 3 centered at
(−7, −6). Use the polygon tool to graph the dilated figure. *picture Below*
Answer:
See the picture below
Step-by-step explanation:
You start from the center given (-7,-6), then count how many spaces from the center to that point. Take that number and triple it to find the new point. I drew lines so that you could see the path of two of the points.
The path that I did not draw was from the point (-3,-2). If you start at (-7,-6) you will have to move 4 spaces to the right and 4 spaces up to get to (-3,-2) Now triple that. You will move 12 spaces to the right and 12 spaces up for the new point of (5,6)
Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42
Answer:
[tex] \sf \: x = 25[/tex]
Step-by-step explanation:
Given equation,
→ (x - 7)2 = 36
Now the value of x will be,
→ 2(x - 7) = 36
→ (2 × x) - (2 × 7) = 36
→ 2x - 14 = 36
→ 2x = 36 + 14
→ 2x = 50
→ x = 50/2
→ [ x = 25 ]
Hence, the value of x is 25.
Answer:
x = 25
Step-by-step explanation:
(x-7)2 = 36
divide both sides by 2
x-7 = 18
add 7 to both sides
x = 25
Solve the inequality 3(x-2) + 1 ≥x + 2(x + 2).
O A. x≤ 4
OB. x ≥-5
OC. no solution
OD. all real numbers
Answer: no solution
Step-by-step explanation:
1. distribute through both sides to get 3x-6+1 ≥ x+2x+4
2. then combine like terms to get 3x-5 ≥ 3x+4
3. then make sure like terms are together on either side -> 3x -3x ≥ 4+5 ->
4. since the 3x-3x = 0, there are no solutions
A rectangular yard measuring 40ft by 53ft is bordered (and surrounded) by a fence. Inside, a walk that is 4ft wide goes all the way along the fence. Find the area of this walk. Be sure to include the correct unit in your answer. helpppppp plssss for my final
Area of the walk that goea around the rectangular yard is 680 sq. ft.
What is a Rectangle ?A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason.
Rectangles can also be referred to as parallelograms since their opposite sides are equal and parallel.
The rectangle's characteristics are listed below:
There are four vertices and four sides.Every vertex has an angle of 90 degrees.Equal and parallel sides are on the opposing sides.Intersect each other diagonallyThe perimeter is equal to double the length plus width of the object.the product of its length and width determines its area.It has four right angles and is a parallelogram.All inner angles added together equal 360 degrees.Dimension of the yard is
width = 40 ft
length = 53ft
Dimension of the yard without the walkway is
Width =40 - 4*2 = 40 - 8 = 32 ft
Length = 53 - 4*2 = 53 - 8 = 45 ft
Area of the yard = Width * Length = 40 * 53 = 2120 sq. ft
Area of the yard wtihout the walk = 32 * 45 = 1440 sq. ft
Therefore the area of the walk is = Area of yard - Area of yard without walk = 2120 = 1440 = 680 sq. ft.
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Draw a line PQ and take a point A outide it. Uing ruler and compa , draw a line through A parallel to PQ
Using a ruler and compass, draw a line through point A parallel to line PQ by first drawing a line segment from A to any point on PQ. Then, use the compass to draw an arc from the other end of the line segment to the other point on PQ. Finally, use the ruler to draw a line through the arc, parallel to PQ.
Drawing a line parallel to an existing line can be done using a ruler and compass. First, draw a line segment from point A to any point on line PQ. Then, use the compass to draw an arc from the other end of the line segment to the other point on PQ. This arc should intersect with the first line segment. Finally, use the ruler to draw a line through the arc, parallel to PQ. This line will be parallel to PQ since it is the same distance from each point on the original line. The use of the compass ensures that the resulting line is the same distance away from the original line throughout, thus resulting in a line parallel to PQ.
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What transformation took place to get from triangle ABC to triangle A’B’C’? Be specific.
What transformation took place to get from triangle A’B’C’ to triangle A”B”C”? Be specific.
We can see two transformations.
1) ΔABC → ΔA'B'C', it is a translation 10 units left and 2 units up.
T(-10, 2)2) ΔA'B'C' → ΔA''B''C'', it is a reflection across the x-axis.
R(x-axis)Lucy wants to plant 218 flowers in her garden. If there are 32 flowers in a box, how many boxes of flowers will Lucy need to order?
Answer:
Step-by-step explanation:
She could order 7 boxes. if each box has 32 flowers, then you would multiply 6 by 32 which is 192. If you subtract 218 from 192 you get 26. meaning that if she orders 6 boxes of 32 flowers then she would only have 192 flowers and there would be 26 flowers remaining, so then it's better for her to order 7 boxes it's better to have more than what she wants instead of having less than what she wants... that way she is able to plant 218 flowers even if there are some left.
an agriculturalist working with australian pine trees wanted to investigate the relationship between the age and the height of the australian pine. a random sample of australian pine trees was selected, and the age, in years, and the height, in meters, was recorded for each tree in the sample. based on the recorded data, the agriculturalist created the following regression equation to predict the height, in meters, of the australian pine based on the age, in years, of the tree. Predicted height = 0.29 + 0.48(age) Which of the following is the best interpretation of the slope of the regression line?
The height increases by 0.48 meters each year.
The available regression equation is: Predict height= 0.29 + 0.48 (age).
Here, the predict height is dependent variable and the age is in-dependent variable.
Intercept = 0.29
Slope = 0.48
The given regression equation indicates the y on x model and the intercept coefficients of the regression equation is 0.29 and the slope is 0.48.
The height increases, an average, by 0.48 m per year.
Because co-efficient of slope variable indicate the positive sign and we increase 1 year in age then automatically height increased is 0.48 m.
The height increases, on average, by 0.48 meter each year.
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The available regression equation is: Predict height= 0.29 + 0.48 (age).
Here, the predict height is dependent variable and the age is in-dependent variable.
Intercept = 0.29
Slope = 0.48
The given regression equation indicates the y on x model and the intercept coefficients of the regression equation is 0.29 and the slope is 0.48.
PLEASE HEP ASAP GOT TEN MINS LEFT TILL DUE
Answer:
a ≈ 3.009075116
Step-by-step explanation:
cos(α) = adj/hyp
cos(53°) = a/5
a = 5 * cos(53°)
a ≈ 3.009075116
Joe asked a bank teller to cash a $570 check using $20 bills and $50 bills, If the teller gave him a total of 15 bills, how many of each type of bill did he receiver
Answer:
9 $50 bills and 6 $20 bills
Step-by-step explanation:
Let f = number of $50 bills.
Let t = number of $20 bills.
f + t = 15
50f + 20t = 570
f = 15 - t
50(15 - t) + 20t = 570
750 - 50t + 20t = 570
-30t = -180
t = 6
f + t = 15
f + 6 = 15
f = 9
Answer: 9 $50 bills and 6 $20 bills