Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions. If the system has one solution, name it.
y= -x + 5 y= x - 3
Answers
Answer:
The system has one solution: (4,1)
Step-by-step explanation:
We have the equations:
1) Y = -X + 5
2) Y = X - 3
Replace the "value" of Y of the 2nd eq into the 1st eq:
(X - 3) = -X + 5
Now let's leave X alone in one side of the iquality:
X + X = 5 + 3
2X = 8
X = 8/2
X = 4
Now, having the value of X, replace it into any of the aquations, let's use the 2nd:
Y = X - 3
Y = 4 -3
Y = 1
The ONE solution of this equations system is (4,1), which is the point in the xy plane where the two lines intersect.
The following equation has:
Unique solution (one solution i.e. (4,1) )
Step-by-step explanation:The system of equation is given by:
y= -x + 5-----------(1)
and y= x - 3------------(2)
Now, on substituting the value of y from equation (1) into equation (2) we have:
[tex]-x+5=x-3[/tex]
On adding x on both the sides of the equation we have:
[tex]5=x+x-3\\\\5=2x-3[/tex]
on adding 3 on both the sides of the equation we have:
[tex]2x=5+3\\\\2x=8\\\\x=\dfrac{8}{2}\\\\x=4[/tex]
Now, on putting the value of x into equation (2) we have:
[tex]y=4-3\\\\y=1[/tex]
Hence, the solution is unique (one solution )
Also, the point of intersection of the graph of two equations is solution to the system of equations.
Related Questions
Which values are in the solution set of |x| -8 < 12?
Answers
There are 16 girls and 18 boys in a class. The teacher chooses a student’s name at random to answer a question. What is the probability that the teacher chooses a girl to answer the question?
A. 1/34
B. 1/16
C. 8/17
D. 8/9
Answers
Answer:C
Step-by-step explanation: The probability of choosing a girl is the number of girls over the total number of students. Since there are 16 girls and 16+18 students, 16/34=8/17. Hope this helps! (Could I please have brainliest?)
The probability of the teacher choosing a girl to answer the question is 8/17. The correct option is C.
To calculate the probability of the teacher choosing a girl to answer the question, we need to determine the ratio of the number of girls to the total number of students.
In the given class, there are 16 girls and 18 boys, making a total of 16 + 18 = 34 students.
The probability of selecting a girl is the number of favourable outcomes (girls) divided by the total number of possible outcomes (students).
Therefore, the probability is 16 (number of girls) / 34 (total number of students).
Simplifying this fraction, we have 8/17.
Hence, the correct option is C. 8/17, which represents the probability of the teacher choosing a girl to answer the question.
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Point M begins at (5,-2). Write the coordinates of Ry= 1 (M). Is this correctly illustrated
below?
Answers
Answer:
No
Step-by-step explanation:
The reflection (R) around the line y = 1 is not the point illustrated.
Notice that the original point M (5,-2) is THREE (3) units below the line y=1, therefore when doing the reflection, it should end up THREE units above the y=1 line.
That is, it should end up at the point (5,4 ) and not at (5,3) as is shown in the picture.
A store charges $6.96 for a case of mineral water. Each case contains 2 boxes of mineral water. Each box contains 4 bottles of minerals water. What is the cost of each bottle of mineral water?
Answers
The cost of each bottle of mineral water is $0.87.
Explanation:To find the cost of each bottle of mineral water, we need to divide the total cost of the case by the number of bottles in the case. A case contains 2 boxes and each box contains 4 bottles, so there are 2 x 4 = 8 bottles in a case. The cost of a case is $6.96, so the cost of each bottle is $6.96 divided by 8, which equals $0.87.
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The cost of each bottle of mineral water is $0.87.
Explanation:To find the cost of each bottle of mineral water, we need to divide the total cost of the case by the number of bottles.
The case of mineral water contains 2 boxes, and each box contains 4 bottles.
So, the total number of bottles in the case is 2 x 4 = 8.
Since the cost of the case is $6.96,
we can divide it by the number of bottles to find the cost of each bottle: $6.96 / 8 = $0.87.
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The total cost f(x), in dollars, for renting a car for a day and driving it x miles is shown:
f(x) = 90 + 0.11x
What does f(30) represent?
The number of dollars spent to rent the car for 30 days
The number of miles driven on the car in 30 days
The number of dollars it costs to drive the car 30 miles
The number of miles driven for a cost of $30
Answers
The total cost f(x), in dollars, for renting a car for a day and driving it x miles is shown:
f(x) = 90 + 0.11x
What does f(30) represent?
Answer:
The number of dollars it costs to drive the car 30 miles
option C. The number of dollars it costs to drive the car is 30 miles.
The total cost f(x), in dollars, for renting a car for a day and driving it x miles is shown:
f(x) = 90 + 0.11x.
What does f(30) represent?
It represents the number of dollars it costs to drive the car 30 miles.
How much gas will it take to drive 30 miles?1.5 gallons
Good luck on your trip. We hope that our "How much gas to drive 30 miles?" page made the trip planning a little easier for you.
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A computer company sells its products with a 6 month warranty for every $500 spent. How many months of warranty protection come with a $2000 purchase?
Answers
Answer:
24 months or 2 years
Step-by-step explanation:
For every 6 months it costs $500 then 1 year would be $1000 because there are 12 months in a year. Then just multiply that times 2 because they have $2000 then you would get 24 :)
Is 9/5 and 18/10 equivalent
Answers
Answer:
Yes.
Step-by-step explanation:
You can divide both the numerator (18) and the denominator (10) by 2 (also called simplifying) in order to get 9/5.
how do I show my work for this 50.04- 1.103
Answers
To show your work for the subtraction [tex]\(50.04 - 1.103\)[/tex], follow these steps:
1. Line up the Decimals:
Align the decimal points of both numbers, ensuring they are in the same vertical position.
[tex]\[ &50.040 \\ - &1.103 \end{align*} \][/tex]
2. Subtraction:
Begin subtracting from the rightmost column. Subtract 3 from 0, borrow 1 from 4, subtract 0 from 10, subtract 1 from 4, and subtract 1 from 5.
[tex]\[50.040 \\ - &1.103 \\ \underline{-} \end{align*} \][/tex]
[tex]\[ 48.937 \][/tex]
3. **Final Result:**
The result of [tex]\(50.04 - 1.103\)[/tex] is [tex]\(48.937\).[/tex]
By displaying each step of the subtraction process, you provide a clear and organized representation of your work.
Four more than five times a number is
two less than the number.
Answers
Answer:
4 + 5x = x - 2
Answer:
4 + 5x = x - 2
x=-1.5
Step-by-step explanation:
4 + 5x = x - 2
subtract 4 from both sides (or add negative whichever you prefer)
5x=x-6
now subtract x from both sides
4x=-6
now divide by 4
x=-1.5
This circle is centered at the origin, and the length of its radius is 4. What is
the equation of the circle?
Answers
Answer:
D. x² + y² = 4²
Step-by-step explanation:
The general equation of a circle is given in the attached graphic.
In this case, we can see that the center of the circle is at the origin i.e (0,0) and that the radius is 4 units.
the values for h, k and r in the general equation are as follows:
h = 0, k=0, r = 4
putting this into the general equation:
(x-h)² + (y-k)² = r²
(x-0)² + (y-0)² = 4²
x² + y² = 4²
The equation of the circle centered at the origin with a radius of 4 is:
x² + y² = 4².
Option D is the correct answer.
We have,
The equation of a circle centered at the origin (0, 0) with a radius of 4 can be written in the form:
[tex]x^2 + y^2 = r^2[/tex]
where (x, y) represents any point on the circle and r is the radius.
Substituting the given radius of 4 into the equation, we have:
x² + y² = 4²
x² + y² = 16
Therefore,
The equation of the circle centered at the origin with a radius of 4 is:
x² + y² = 4².
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Choose the function whose graph is given by:
Answers
Answer:
The answer to your question is letter A.
Step-by-step explanation:
A. This graph shows that is the sine graph, but it was moved to units up.
B. This is not the equation of the graph because the sine is negative then the graph should be inverted.
C. This is not the equation of the graph because the cosine graph starts in 1.
D. This is not the equation of the graph because it is cosine negative and the graph is different.
Answer:
[tex]y=sinx +2[/tex]
Step-by-step explanation:
We have to choose the function whose graph is given.
A.[tex]y=sinx+2[/tex]
Substitute x=0 then
[tex]y=0+2=2[/tex]
Therefore, y- intercept is at y=2.
Substitute [tex]x=\frac{\pi}{2}[/tex]
[tex]y=sin\frac{\pi}{2}+2=1+2=3[/tex] because ([tex]\sin\frac{\pi}{2}=1[/tex])
Substitute [tex]x=-\frac{\pi}{2}[/tex]
Then we get
[tex]y=sin(-\frac{\pi}{2})+2=-sin\frac{\pi}{2}+2=-1+2=1[/tex]
[tex] sin (-x)=-sinx[/tex]
Therefore, given graph is [tex]y=sinx +2[/tex]
B.[tex]y=-sinx+2[/tex]
When Substitute [tex]x=-\frac{pi}{2}[/tex]
Then, [tex]y=-sin(-\frac{\pi}{2})+2=sin\frac{pi}{2}+2=1+2=3[/tex]
But in graph at [tex]x=-\frac{pi}{2}[/tex] , y=-1
So,It is not true.
C.[tex]y=cosx+2[/tex]
When x=0
then we get [tex]y=cos0+2=1+2=3[/tex] (cos 0=1)
But in graph y - intercept at y=2
So, it is false.
D.[tex]y=-cosx+2[/tex]
Substitute x=0
Then, we get
[tex]y=-cos 0+2=-1+2=1[/tex]
So, it is false.
Answer: [tex]y=sinx +2[/tex]
60 is 5 times as great as k.
Answers
Answer:
k=12
Step-by-step explanation:
60÷5=12
OR5+5+5+5+5+5+5+5+5+5+5+5=60
↑=12 5's
Hope this helps!!!
Brady
Answer:
It's 12
Step-by-step explanation:
60 = 5k
or, 60/5 =k
or, k=12
Hence, 60 is 5 times great as 12
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Two groups of students were asked how many pets they had. The table below shows the numbers for each group:
Company A 1 2 1 1 3 5 4 2 3
Company B 3 2 3 2 2 2 1 1 2
Based on the table, which of the following is true?
The interquartile range for Group A students is 0.5 less than the interquartile range for Group B students.
The interquartile range for Group A students is 1.5 more than the interquartile range for Group B students.
The interquartile range for Group A students is equal to the interquartile range for Group B students.
The interquartile range for Group A students is 1 more than the interquartile range for Group B students.
Answers
interquartile range for group B = 1
2.5 - 1 = 1.5 (to find the difference you subtract)
so the answer is: the interquartile range for group A students is 1.5 more than the interquartile range for group B students.
hope this was helpful!
Final answer:
After arranging the data for each company and calculating the first and third quartiles, we found that the interquartile range for Company A's students (IQR = 2) is 1 more than the interquartile range for Company B's students (IQR = 1).
Explanation:
The interquartile range (IQR) is a measure of the middle spread of a data set, calculated as the difference between the third quartile (Q3) and the first quartile (Q1). To find the interquartile range for each group of students, we will first need to arrange each company's data in ascending order and then find the values of Q1 and Q3 for each group.
For Company A, the data in ascending order is: 1, 1, 1, 2, 2, 3, 3, 4, 5. Q1 is the median of the first half (1), and Q3 is the median of the second half (3). Thus, IQR is 3 - 1 = 2.
For Company B, the data in ascending order is: 1, 1, 2, 2, 2, 2, 2, 3, 3. Q1 is the median of the first half (1.5), and Q3 is the median of the second half (2.5). So, IQR is 2.5 - 1.5 = 1.
Comparing the IQRs, we find that the interquartile range for Company A's students is 1 more than the interquartile range for Company B's students.
Find the difference quotient
Answers
Answer:
[tex]\large\boxed{\dfrac{f(x+h)-f(x)}{h}=4x+2h}[/tex]
Step-by-step explanation:
[tex]f(x)=2x^2+4\\\\f(x+h)=2(x+h)^2+4\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\f(x+h)=2(x^2+2xh+h^2)+4\qquad\text{use the distributive property}\\\\f(x+h)=2x^2+4xh+2h^2+4\\\\\text{Substitute to}\ \dfrac{f(x+h)-f(x)}{h}\\\\\dfrac{f(x+h)-f(x)}{h}=\dfrac{2x^2+4xh+2h^2+4-(2x^2+4)}{h}\\\\\dfrac{f(x+h)-f(x)}{h}=\dfrac{2x^2+4xh+2h^2+4-2x^2-4}{h}\\\\\text{combine like terms}\\\\\dfrac{f(x+h)-f(x)}{h}=\dfrac{4xh+2h^2}{h}\qquad\text{distribute}\\\\\dfrac{f(x+h)-f(x)}{h}=\dfrac{h(4x+2h)}{h}\qquad\text{cancel}\ h[/tex]
[tex]\dfrac{f(x+h)-f(x)}{h}=4x+2h[/tex]
Jacob is two years younger than his sister together they are are 26 how old is jacob
Answers
Answer:
14+12=26
Step-by-step explanation:
i worked it pls give brainliest
Answer:
jacob is 12 and his sister is 14. this is the correct answer.
Step-by-step explanation:
hope this helps.
find the least common denominator of the fractions 7/16 and 1/4
Answers
Answer:
16
Step-by-step explanation:
7/16 = 7/16
1/4 = 4/16
Help help me I need help my mom don’t wanna help me
Answers
Answer: 32÷4+3=11
Step-by-step explanation:
24÷3=8
A hot tub pump circulates 4 cubic feet of water per minute. How many cubic inches of water does it circulate per minute
Answers
12 inches= 1 foot
We have 4 feet
12*4=48
Therefore 48 cubic inches is the answer
Hope this helps!!!
A hot tub pump that circulates 4 cubic feet of water per minute circulates 6912 cubic inches of water per minute, as 1 cubic foot equals 1728 cubic inches.
Explanation:This question involves a conversion from cubic feet to cubic inches. 1 cubic foot is equivalent to 1728 cubic inches. Therefore, if the hot tub pump circulates 4 cubic feet of water per minute, we need to multiply 4 by 1728 to find out how many cubic inches that would be.
Using the multiplication rule for units, we get:
4 cubic feet x 1728 cubic inches/cubic foot = 6912 cubic inches
Therefore, the hot tub pump circulates 6912 cubic inches of water per minute>.
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Carmen sells cars at a dealership that pays her a monthly salary of $2500 plus a
commission of $125 for every car she sells. A competing dealership has offered her a
job that pays a greater monthly salary of $2700, but only gives $100 commission on
each car sold. How many cars would Carmen have to sell in a month to get the same
pay from either dealership?
Answers
Answer:
Carmen would have to sell 8 cars in a month to get the same pay from either dealership.
Step-by-step explanation:
Let c = cars sold
Dealership #1 = 2500 + 125c
Dealership #2 = 2700 + 100c
2500 + 125c = 2700 + 100c
125c - 100c = 2700 - 2500
25c = 200
c = 8
Find the linear function
represented by the graph.
The slope of the line is
The y-intercept of the line is at
What linear function is represented by the graph?
Answers
Answer:
The slope of the line is ⅓.
The y-intercept is at (0,3).
The linear equation for the line is:
y=⅓x+3
The linear function represented by the graph has a slope of 3 and a y-intercept of 9. The equation of the linear function is y = 3x + 9.
Explanation:The linear function represented by the graph has a slope of 3 and a y-intercept of 9. The slope of a line represents the rate of change of the y-values with respect to the x-values, while the y-intercept is the value of y when x=0. In this case, for every increase of 1 on the horizontal axis, the vertical axis increases by 3 units. The equation of the linear function is y = 3x + 9.
30. 3 x (5 + 6) = 33
33. 14 - (8 - 2) - 1 =
36. (3 + 2) × (4 + 6) =
39. 6 x 4 + 5) =
Answers
Answer:
39. 29
36. 50
33. 7
30. 33
Step-by-step explanation:
39. According to the Order of Operations, in this case, Subtraction & Addition are evaluated after Division & Multiplication:
[tex]6 \times 4 + 5 = 24 + 5 = 29[/tex]
36. Evaluate everything since everything is wrapped in parentheses:
[tex](3 + 2) \times (4 + 6) = 5 \times 10 = 50[/tex]
33. Evaluate everything inside of parentheses FIRST:
[tex]14 - (8 - 2) - 1 = 14 - 6 - 1 = 7[/tex]
I am joyous to assist you anytime.
xm=x+z ,solve for x, Algebra 1
Answers
Answer: x = z/(m-1).
Step-by-step explanation: xm - x = z
x (m - 1) = z ; x = z/(m-1).
Evaluate the expression -5-3+1
Answers
Answer:
The answer is -7
Step-by-step explanation:
-5 - 3 = -8
-8 + 1 = -7
Hope I helped :)
Answer:
-7
Step-by-step explanation:
The rule for subtraction, in this case it is -5-3, you change the subtraction sign to addition and use the opposite of the second number, making it -5+(-3) which is -8. Then, you add 1 to -8, and the rule for this specific expression is to take the absolute value of both -8 and 1, then subtract the two, making the expression as of now 8-1. Subtract them, and get 7, but you take the sign of whichever number had the greatest absolute value, which was -8, so now the answer is -7. That's how you get your answer
-5-3+1= -5+(-3)+1
-8+1= |-8|-|1|
8-1= -7 (because you take the sign with the greatest absolute value, which is -8.)
A regulation baseball field measures 90 feet between each base. What is the distance around the bases in meters?
Answers
assuming that the bases are placed correctly, the bases connected draw a square, each side being 90 ft long. We multiply 90 by the amount of sides(4) to find the total distance/perimeter = 360.
The distance around the bases in meters will be 27.432 meters.
How many meters are in 1 feet?
In one feet there are 0.3048 meters.
Given is a baseball field measures 90 feet between each base.
Distance between each base in feet = [d] = 90 feet
The distance between each base in meters will be -
D [meters] = 90 x 1 ft
D [meters] = 90 x 0.3048 meters
D [meters] = 27.432 meters
Therefore, the distance around the bases in meters will be 27.432 meters.
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math question: i write 17 text messages to friends each week for x weeks in a row. write an expression for total members
Answers
Answer:
[tex]17x = y[/tex]
Step-by-step explanation:
Since we know that you write 17 text messages a week. 17 will be our constant number, now then after you said for x weeks.
Meaning that x would be our variable cause we can put an input of any number, then put it next to 17 because that is how many times you text a week.
17x = y
17 (how many times you text per week) x (how many weeks) = y (texts in total)
what is 9.6 x 10^6 in standard form
Answers
If i^2 = −1 and x = i + 9, which is the result of squaring x?
Answers
Answer:
80 + 18i
Step-by-step explanation:
i² = -1
x = i + 9
x² = (i + 9)²
Applying; (a + b)² = a² + 2ab + b² concept,
x² = i² + 18i + 81
We know that i² = -1
So x² = -1 + 18i + 81
x² = 81 - 1 + 18i = 80 + 18i
The square of the complex number x = i + 9 is computed by squaring each term and combining the results, giving us 80 + 18i as the final squared value.
To square the complex number x = i + 9, we use the formula for squaring a binomial:
Square the first term: i² = -1.
Square the second term: 9² = 81.
Multiply the first term by the second term and by 2 for the middle term: 2 times i times 9 = 18i.
Sum all the terms together -1 + 81 + 18i = 80 + 18i.
So, the result of squaring x is 80 + 18i.
What is the number if 4 is 12.5 % of a number?
Answers
Answer: 4 is 12.5% of 32
Step-by-step explanation:
12.5/100 = 0.125
4/0.125 = 32
Unknown number in the question is [tex]32.[/tex]
Let the unknown number is [tex]n[/tex].
It has been given in the question that 4 is 12.5% of the unknown number,
Therefore, expression for the statement will be,
12.5% of [tex]n[/tex] = 4
[tex]\frac{12.5}{100}\times n=4[/tex]
[tex]\frac{1}{8}\times n=4[/tex]
[tex]n=8\times 4[/tex]
[tex]n=32[/tex]
Hence, unknown number is [tex]32[/tex].
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The sum of two numbers is 39 . The larger number is 5 more than the smaller number. What are the numbers?
Answers
the smaller and the larger number are
17 and 22 respectively
Step-by-step explanation:
let the numbers be x and y
from the expression; The sum of two numbers is 39 means that
x + y=39
let y be the smaller number and x be larger number.
but from the expression
The larger number is 5 more than the smaller is written as
x=5+y
put it in the first equation to get
5+y+y=39
5+2y=39
2y=39-5
2y=34
y=34/2
y=17
put the y value in the equation to get the x value
thus
x=5+y
x=5+17
x=22
Jennie is training for a race. On Tuesday She finished her sprint 0.305 second faster than on Monday. be How can you explain the meaning of 0.305 Solve this problem anyway you choose
Answers
Monday = X
Tuesday is 0.305 faster therefore
Tuesday = x+0.305
Answer: Hello there!
we know that on Tuesday, Jennie finished her sprint 0.305 seconds faster than on Monday, and we want to model this with math.
If we define x as the time in which she finished ger sprint on Monday, we can write the time for Tuesday as x - 0.305s
this is because she finished her sprint 0.305 seconds "faster", this means that she finished it in less time, so you need to subtract this number to the previous time.
Then the meaning of 0.305 is the amount of time that you need to subtract from the previous time, in order to get the actual time that she needs to finish the sprint.