The solution to the System of equations is x = -9 and y = 8
We have the equation x - y = -1 and the equation x = -9. We can use the second equation to substitute the value of x in the first equation and solve for y.
Given x = -9, we substitute this value into the first equation:
(-9) - y = -1
Simplifying, we have:
-9 + y = -1
To isolate y, we can add 9 to both sides of the equation:
-9 + 9 + y = -1 + 9
This gives us:
y = 8
Therefore, the solution to the system of equations is x = -9 and y = 8.
We can check this solution by substituting the values of x and y back into the original equations:
Equation 1: x - y = -1
Substituting x = -9 and y = 8:
-9 - 8 = -1
Simplifying, we have:
-17 = -1
The equation is true, so our solution is valid.It is important to note that the solution provided is derived from the given equations and standard algebraic methods.
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Which value is a solution to the inequality x 4
Answer:
0
Step-by-step explanation:
x < 4 means all numbers less than 4, excluding 4 itself.
4.5 > 4.
5 > 4.
so 0 is the solution
Answer:
4
Step-by-step explanation:
interval notation ( negative infinity, 4)
A 10 kg ball moves at a speed of 15m/s. The ball collides with a wall causing it to rebound in the opposite direction at a speed of 23 m/s.
Calculate the impulse on the ball?
Answer:
The impulse on an object is equal to the change in momentum of the object. In this case, the ball's initial momentum is 10 kg * 15 m/s = 150 kg m/s. After the collision, the ball's final momentum is -10 kg * 23 m/s = -230 kg m/s.
The change in momentum of the ball is: -230 kg m/s - 150 kg m/s = -80 kg m/s.
So, the impulse on the ball is -80 kg m/s.
Serial numbers for a product are to be made using 4 letters followed by 4 digits. the letters are to be taken from the first 9 letters of the alphabet, with no repeats. the digits are to be taken from 0-9 with no repeats. How many serial numbers can be generated?
Answer:
15,240,960 numbers
Step-by-step explanation:
To solve this were going to use the principle of permutations. The formula for permutation is given as
P = n! / (n - r)!
Now, the question specifically stated that repeats aren't tolerated, thus for the needed number of serial numbers would be gotten by multiplying the permutation is 4 and 9, by that of the permutation of 4 and 10.
We then have something that is looking like this
Permutation of 4 and 9.
P = 9! / (9 - 4)!
P = 9! / 5!
P = 362,880 / 120
P = 3,024
Permutation of 4 and 10
P = 10! / (10 - 4)!
P = 10! / 6!
P = 3,628,800 / 720
P = 5,040
Multiplying both together would then fetch us our final answer
N = 5,040 * 3,024
N = 15,240,960
Need help solving this!
Answer:
A = 4πcm, 6πcm²
B = 45°, 35πcm²
C = 12m, 18.7πm or 19πm
Step-by-step explanation:
Formulas used...
Length of an arc of a sector = (¢/360)×2πr
Area of sector = (¢/360)×πr²
¢ means the angle given or used
Write √(-12) in simplest radical form
Answer: \(2i\sqrt{3}\)
where \(i = \sqrt{-1}\)
====================================================
Work Shown:
\(x = \sqrt{-12}\\\\x = \sqrt{-1*4*3}\\\\x = \sqrt{-1}*\sqrt{4}*\sqrt{3}\\\\x = i*2*\sqrt{3}\\\\x = 2i\sqrt{3}\\\\\)
Therefore, \(\sqrt{-12} = 2i\sqrt{3}\)
------------
Explanation:
The basic steps are to factor the radicand such that we pull out the -1 and we also pull out the largest perfect square factor. That way we can then apply the rule \(\sqrt{A*B} = \sqrt{A}*\sqrt{B}\) to break up the root and simplify.
What is x^2+10x+25 ——————- x^2-2x-35 in simplest form? State any restrictions on the variable. The simplified form is _______.
We are to simplify:
x^2+10x+25
x^2-2x-35
Lets factor x² + 10x + 25: (x + 5)²
= (x + 5)²
x² -2x-35
Let's factor x² - 2x - 35: (x + 5)(x - 7)
= (x + 5)²
(x + 5)(x - 7)
= Apply exponent rule: a^b+c = a^b . a^c
(x + 5)² = (x + 5)(x + 5)
= (x + 5)(x + 5)
(x + 5)(x - 7)
cancel out common factor: x + 5
= x + 5
x - 7
ILL GIVE YOU BRAINLIST !!! HAVE TO SHOW WORK !!!!
Answer:
-10
Step-by-step explanation:
h(t)=−2(5−t−1)
or
h(−2)=−2(5−(−2)−1)
=−2(52−1)
=−2(51)
=−2(5)
=−10
helo please show work
Answer:
Step-by-step explanation:
Solution:
We can simplify the ratio 305 : 60 by dividing both terms by the greatest common factor (GCF).
The GCF of 305 and 60 is 5.
Divide both terms by 5.
305 ÷ 5 = 61
60 ÷ 5 = 12
Therefore:
305 : 60 = 61 : 12
What is 2x2 + 1000 x 1000
Answer: 2x2 + 1000 x 1000 = 1000004
Step-by-step explanation: you add on 5 0's to the one and 2x2 = 4 so add on the 4 also
Answer:
1000004
Step-by-step explanation:
First we do can separate it into the parentheses: (2*2) + (1000*1000)
= 4 + 1000000
= 1000004
what is the variable in this expression 5x2+x+7?
Answer:
x
Step-by-step explanation:
Janet owns a plot of land that is perfectly square. She knows that the area of the plot is between 2000 and 2100 square feet. what is the value for the side of the plot of land?
Based on the area of the plot, the side of the plot can be determined to be between 44.72 ft and 45.82 ft
If you have the area of a square, you can calculate the length of one side of that square by:
= √Area
If the area is 2,000 ft², the side would be:
= √2,000
= 44.72 ft
If the area is 2,100 ft², the side would be:
= √2,100
= 45.82 ft
In conclusion, the value of a side is between 44.72 ft and 45.82 ft.
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Consider the trash bag problem. Suppose that an independent laboratory has tested trash bags and has found that no 30-gallon bags that are currently on the market have a mean breaking strength of 50 pounds or more. On the basis of these results, the producer of the new, improved trash bag feels sure that its 30-gallon bag will be the strongest such bag on the market if the new trash bag’s mean breaking strength can be shown to be at least 50 pounds. The mean of the sample of 40 trash bag breaking strengths in Table 1.9 is x⎯⎯x¯ = 50.560. If we let µ denote the mean of the breaking strengths of all possible trash bags of the new type and assume that σ equals 1.68:
(a) Calculate 95 percent and 99 percent confidence intervals for µ. (Round your answers to 3 decimal places.)
95 percent confidence intervals for µ is [, ].
99 percent confidence intervals for µ is
The 95 percent confidence intervals for µ is (50.049, 51.071) and for 99 percent confidence intervals is (49.903, 51.247).
What is confidence interval?
A confidence interval is defined as the estimate's mean plus and minus the estimate's range.
We are given that the mean(x) = 50.560, s = 1.68, and the sample size is over 30.
Using the formula, we get
95% confidence interval
⇒Mean(x) (+/-) 1.96 (1.68/v40)
⇒(50.560 - 0.511 , 50.560 + 0.511)
⇒(50.049, 51.071)
99% confidence interval
⇒Mean(x) (+/-) 2.576 (1.65/v40)
⇒(50.560 - 0.672, 50.560 + 0.672)
⇒(49.888, 51.232)
Hence, the 95 percent confidence intervals for µ is (50.049, 51.071) and for 99 percent confidence intervals is (49.903, 51.247).
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simplify 8+3{x-2[x+5(x3)]}
the correct answer is negitive one hundred eighty (-180)
A multiple-choice examination has 20 questions, each with five possible answers, only one of which is correct. Suppose that one of the students who takes the examination answers each of the questions with an independent random guess. What is the probability that he answers at least seventeen questions correctly? (Round your answer to three decimal places.)
Answer:
The probability that the student answers at least seventeen questions correctly is \(8.03\times 10^{-10}\).
Step-by-step explanation:
Let the random variable X represent the number of correctly answered questions.
It is provided all the questions have five options with only one correct option.
Then the probability of selecting the correct option is,
\(P(X)=p=\frac{1}{5}=0.20\)
There are n = 20 question in the exam.
It is also provided that a student taking the examination answers each of the questions with an independent random guess.
Then the random variable can be modeled by the Binomial distribution with parameters n = 20 and p = 0.20.
The probability mass function of X is:
\(P(X=x)={20\choose x}\ 0.20^{x}\ (1-0.20)^{20-x};\ x =0,1,2,3...\)
Compute the probability that the student answers at least seventeen questions correctly as follows:
\(P(X\geq 17)=P (X=17)+P (X=18)+P (X=19)+P (X=20)\)
\(=\sum\limits^{20}_{x=17}{{20\choose x}\ 0.20^{x}\ (1-0.20)^{20-x}}\\\\=0.00000000077+0.000000000032+0.00000000000084+0.000000000000042\\\\=0.000000000802882\\\\=8.03\times10^{-10}\)
Thus, the probability that the student answers at least seventeen questions correctly is \(8.03\times 10^{-10}\).
The question is in the picture
Answer:
16
Step-by-step explanation:
18,903
a crew will arrive in one week and begin filming a city for a movie. the mayor is desperate to clean the city streets before filming begins. two teams are available, one that requires 300 hours and one that requires 500 hours. if the teams work together, how long will it take to clean all the streets?
If the teams work together it take 187.5 hours to clean all the streets.
What is Fraction?The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.
The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.One team makes 1/300 of the job per hour.
and, other team makes1/500 of the job per hour.
If they work together the tam can make
= 1/300 + 1/500
= 5 /1500 + 3 /500
= 8/1500
= 1/ 187.5
So, the two teams will make the job in 187.5 hours working together.
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A number has 7 in its thousands place and is less than 54,00. How many such numbers are there?
There are 9,000 numbers that have 7 in the thousands of places and are less than 54,000.
Consider the possible digits in the hundreds, tens, and one's places.
Thousands of places: There is only one possibility, which is 7.
Hundreds place: Any digit from 0 to 9 is possible.
Tens place: Any digit from 0 to 9 is possible.
One place: Any digit from 0 to 9 is possible.
Since the number is less than 54,000, the digit in the hundreds place cannot be 5.
So, there are 9 possible digits (0 to 9, except 5) for the hundreds place, and 10 possible digits (0 to 9) for the tens and one's places.
So, the total number of such numbers is:
9 x 10 x 10 x 10 = 9,000
Therefore, there are 9,000 numbers that satisfy the given condition.
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What are the intercepts of the graph of
the equation 4y - x = 8
Answer:
x intercept: (-8,0)
y intercept: (0,2)
You spend 3 hours at a museum.
You spend 1/4 of your time in the dinosaur exhibit, and 2/5 on
the Egyptian exhibit, and the rest of your time in the natural history exhibit. How many minutes do you spend in the natural history exhibit?
In linear equation,The number of exhibits Mrs. Johnson's class can see if they spent 3 hours at the museum and they plan to spend 1/4 of an hour at each exhibit is 12 exhibits.
What is the most effective way to explain linear equations?
An x-y linear relationship, or two variables in which the value of one of them (often y) relies on the value of the other one, is what is known as a linear equation in two variables (usually x). In this scenario, y is referred to as the dependent variable because it depends on the independent variable, x.
Convert hour to minutes:
1 hour = 60 minutes
Total number of hours they will spend at the museum = 3 hours
= 3 × 60 minutes
= 180 minutes
Number of hours spent at each exhibits = 1/4 of an hour
= 1/4 × 60 minutes
= 15 minutes
Number of exhibits they can see = Total number of hours they will spend at the museum ÷ Number of hours spent at each exhibits
= 180 minutes / 15 minute
= 12 exhibits
Therefore, the number of exhibits they can see is 12 exhibits.
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Find the approximate area of the shaded region. Use 3.14 for pi
The area of the shaded region of the rectangle is approximately 573.92 square feet.
What is the area of the shaded region?The figure in the image is that of a rectangle with a semi-circle inscribed in it.
The area of rectangle is expressed as:
Area = Length × Width
The area of semi-circle is expressed as:
Area = 1/2 × πr²
To determine the area of the shaded region, we simply subtract the area of the semi-circle from the area of the rectangle.
Area of shaded region = area of rectangle - area of semi-circle
Area of shaded region = ( Length × Width ) - ( 1/2 × πr² )
From the image:
Length = 40 ft
Width = 20 ft
Radius r = 12 ft
Plug the values into the above formula:
Area of shaded region = ( Length × Width ) - ( 1/2 × πr² )
Area of shaded region = ( 40 × 20 ) - ( 1/2 × 3.14 × 12² )
Area of shaded region = ( 800 ) - ( 226.08 )
Area of shaded region = 573.92 ft²
Therefore, the area is approximately 573.92 square feet.
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What is an angle that is adjacent to <2?
(PLEASE)
Answer:
∠3 and ∠1 are correct
Step-by-step explanation:
adjacent angles are next to each other with a common vertexand side
Unit 2: Exponents and Exponential Functions
Find the average rate of change for the function f(x)=3x+17
Using the intervals of x=3 to x=6
Show ALL your work to receive credit
3 is the average rate of change for the function .
What in mathematics is a function?
An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable).
Mathematics is rife with functions, and the sciences depend on them for constructing physical relationships.
function f(x)=3x+17
the average rate of change over the interval of x=3 to x=6 would be calculated as shown below
a = 3
b = 6
f(a) = f(3) = 3(3) + 17 = 26
f(b) = f(6) = 3(6) + 17 = 35
Average rate of change = (35 - 26)/(6 - 3) = 3
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3. A taxi cab company charges $3.00 for 1 minute and $5.50 for 6 minutes.
a) Calculate the slope. What does it mean according to the question?
b) Calculate the y-intercept. What does it mean according to the question?
c) How much would it cost for a 30-minute cab ride?
d) How far could you travel for $50?
Answer:
a) 1/2
b)2.5
c)17.5
Step-by-step explanation:
The question gives you two points on the line. From this, you can calculate the slope. Since slope is m=\(y_2-y_1/x_2-x_1\), the work for question a is as follows:
m= 5.5-3/6-1
m=1/2 or 0.5
Now, you can use the information given to calculate the y-intercept. Use any of the two points to fill in x and y, and use the slope you just calculated to fill in for m. Fill in the equation and use algebra to isolate the variable and solve for b.
y=mx+b
3=0.5(1)+b
3-0.5=b+0.5-0.5
2.5=b
Finally, plug in all the numbers to find the answer for question c.
y=0.5x+2.5
y=0.5(30)+2.5
y=17.5
2a+c=162.97
how do you use the elimination method for this
When 'a' is 10, 'c' is approximately 142.97. You can repeat this process for different values of 'a' to find corresponding values of 'c'. Keep in mind that there are infinitely many solutions to this equation
To use the elimination method to solve the equation 2a + c = 162.97, we need another equation with the same variables. However, as there is only one equation given, we cannot apply the elimination method directly.
The elimination method typically involves adding or subtracting equations to eliminate one of the variables, resulting in a new equation with only one variable. Since we have only one equation, we don't have the opportunity to eliminate variables using another equation.
In this case, we can solve the given equation directly by isolating one variable in terms of the other. Let's solve for 'c':
2a + c = 162.97
Rearrange the equation to isolate 'c':
c = 162.97 - 2a
Now, we have an expression for 'c' in terms of 'a'. This equation represents a line in the 'a-c' coordinate plane. We can choose any value for 'a', substitute it into the equation, and calculate the corresponding 'c' value.
For example, let's say we choose 'a' = 10:
c = 162.97 - 2(10)
c = 162.97 - 20
c = 142.97
So, when 'a' is 10, 'c' is approximately 142.97.
You can repeat this process for different values of 'a' to find corresponding values of 'c'. Keep in mind that there are infinitely many solutions to this equation since we have one equation and two variables.
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The area of the triangle below is 23.4 square inches. What is the length of the base?
Answer:
zxcfghg
Step-by-step explanation:
xsdfghj
Please help me I need it please
will u do anything??
To determine customers opinion of their pricing, Home Depot randomly selects 60 check out lines during a certain week and surveys all customers in the check out line.
What type of sampling is used?
A. Systematic
B. Stratified
C. Convenience
Answer:
Cluster sampling
Step-by-step explanation:
The sampling technique used by Home Depot to select randomly 60 check out lines during a certain week in order to determine customers opinion of their pricing is called cluster sampling.
Cluster sampling is a sampling technique which is obtained by dividing the population into groups and selecting all individuals from within a random sample of the groups.
I think you omitted some options from the question which should include cluster sampling as the answer is not included in the options you gave in the question.
What is
\(|2-2x|=6\)?
Answer:
It is both -2 and 4
Step-by-step explanation: hope it helped!
A point in the table for the transformed function is
Answer:
linear function
Step-by-step explanation:
straight line then add up
Find the value of x such that the line containing (1,2) and (5,3) is perpendicular to the line containing (x,4) and (3,0)
The value of x that makes the line containing (1,2) and (5,3) perpendicular to the line containing (x,4) and (3,0) is x = 2.
To determine the value of x such that the line containing (1,2) and (5,3) is perpendicular to the line containing (x,4) and (3,0), we need to find the slope of both lines and apply the concept of perpendicular lines.
The slope of a line can be found using the formula:
slope = (change in y) / (change in x)
For the line containing (1,2) and (5,3), the slope is:
slope1 = (3 - 2) / (5 - 1) = 1 / 4
To find the slope of the line containing (x,4) and (3,0), we use the same formula:
slope2 = (0 - 4) / (3 - x) = -4 / (3 - x)
Perpendicular lines have slopes that are negative reciprocals of each other. In other words, if the slope of one line is m, then the slope of a line perpendicular to it is -1/m.
So, we can set up the equation:
-1 / (1/4) = -4 / (3 - x)
Simplifying this equation:
-4 = -4 / (3 - x)
To remove the fraction, we can multiply both sides by (3 - x):
-4(3 - x) = -4
Expanding and simplifying:
-12 + 4x = -4
Adding 12 to both sides:
4x = 8
Dividing both sides by 4:
x = 2
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