The correct answers are:
1. 2y=1.5x-2 ; and 4. -4y+3x=-2.
Explanation:
Using the first equation, we have the system
[tex]\left \{ {{3x-4y=2} \atop {2y=1.5x-2}} \right.[/tex]
The second equation can be written in standard form just as the first one. To do this, we will subtract 1.5x from each side:
2y = 1.5x-2
2y-1.5x = 1.5x-2-1.5x
-1.5x+2y = -2
This makes our system
[tex]\left \{ {{3x-4y=2} \atop {-1.5x+2y=-2}} \right.[/tex]
To solve this, we will make the coefficients of x the same; we do this by multiplying the bottom equation by 2:
2(-1.5x+2y=-2)
-3x+4y=-4
This gives us the system
[tex]\left \{ {{3x-4y=2} \atop {-3x+4y=-4}} \right.[/tex]
We solve this by adding the two equations:
[tex]\left \{ {{3x-4y=2} \atop {+(-3x+4y=-4)}} \right. \\\\\\0+0 = -4\\0=-4[/tex]
There is no solution to this.
For the second system, we will follow the same process, subtract 1.5x from each side of the second equation:
2y=1.5x-1
2y-1.5x = 1.5x-1-1.5x
-1.5x+2y = -1
To make the coefficients of x the same, multiply the second equation by 2:
2(-1.5x+2y=-1)
-3x+4y=-2
We will add the two equations to solve:
[tex]\left \{ {{3x-4y=2} \atop {+(-3x+4y=-2)}} \right. \\0+0=0\\0=0[/tex]
This means that the equations are of the same line and there are infinite solutions.
For the third system, the coefficients are already the same. We will cancel by subtracting the bottom equation from the top:
[tex]\left \{ {{3x-4y=2} \atop {-(3x+4y=2)}} \right. \\\\-4y-4y=2-2\\-8y=0\\\frac{-8y}{-8}=\frac{0}{-8}\\y=0[/tex]
Since we have a value for y, this has a solution.
For the last system, we will rearrange the second equation with the x term in front:
3x-4y=-2
Now we will subtract this from the first equation:
[tex]\left \{ {{3x-4y=2} \atop {-(3x-4y=-2)}} \right. \\-4y--4y=2--2\\0=4[/tex]
This has no solution.
Long division 112 divided by 10 please show working out
What is the sum of the polynomials? ( 8x^2 -9y^2-4x) + (x^2- 3y^2- 7x) answer options are in the pics
Answer: The correct option is (D) [tex]9x^2-12y^2-11x.[/tex]
Step-by-step explanation: We are given to find the following sum of the polynomials :
[tex]S=(8x^2-9y^2-4x)+(x^2-3y^2-7x)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To find the required sum, we need to add the coefficients of the same unknown variables with equal powers.
The sum of the polynomials in (i) is as follows :
[tex]S\\\\=(8x^2-9y^2-4x)+(x^2-3y^2-7x)\\\\=8x^2-9y^2-4x+x^2-3y^2-7x\\\\=(8+1)x^2-(9+3)y^2-(4+7)x\\\\=9x^2-12y^2-11x.[/tex]
Thus, the required sum of the polynomials is [tex]9x^2-12y^2-11x.[/tex]
Option (D) is CORRECT.
how do i find the degree of x and y?
q+5/9=1/6
what is q?
∠E and ∠F are vertical angles with m∠E=5x+10 and m∠F=7x−12 .
What is the value of x?
Answer: 11
Step-by-step explanation:
We are given that ∠E and ∠F are vertical angles with m∠E=5x+10 and m∠F=7x−12 .
We know that vertical angles are congruent, then their measures must be equal.
i.e. if ∠E and ∠F are vertical angles.
⇒ m∠E=m∠F
[tex]\Rightarrow\ 5x+10=7x-12[/tex] [Substitute the measures of ∠E and ∠F]
Subtract 5x from both sides , we get
[tex]10=2x-12[/tex]
Add 12 on both sides , we get
[tex]22=2x[/tex]
Divide both sides by 2 , we get
[tex]11=x[/tex] or x=11
Hence, the value of x= 11
How do I find the domain of a function
The domain of a function is the set of all possible input values that can be inserted into the function. The domain can be numerical or non-numerical, depending on what the function describes.
Explanation:In mathematics, finding the domain of a function involves identifying all possible values that can be inserted into the function. A function's domain can be a set of numerical values or a set of non-numerical values.
For example, if we have a function based on majors at a university, the domain could take form as X = {English, Mathematics, ...}, i.e., a list of all the majors offered at the university, plus undeclared, which are all possible inputs into the function.
Similarly, if we have a random variable X = hair color, then the domain of X would include all possible hair colors.
If the function is based on numerical variables, such as a Quadratic Function, the domain would be the set of all real numbers. For instance, the domain of Y = {0, 1, 2, ...} consists of the integers from zero up to a certain limit. Generally, the domain of a function is the set of all possible input values that will produce a value in the function.
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1. A painter earns $15 per hour. What is the minimum number of hours he must work to earn at least $200? Write an inequality to represent this situation and solve. Show your work. (Will get brainiest if you show all work)
So you know that he earns $15 per hour so we can write that as 15h, h = # of hours worked
We also know he has to earn AT LEAST $200, so putting all this together we form the inequality(=< means less than or equal to): 15h =< 200
so now we have to solve for h (number of hours worked):
15h =< 200
(divide both sides by 15)
h =< 13 1/3
So, the painter must work a minimum of 13 and 1/3 hours to earn at least $200.
Hope this helps! :)
3-5x in verbal expression
Name two congruent angles that measure 15
Which is the best estimate of -14 1/9 (-2 9/10)
If the correlation between variables is .60, what is the coefficient of alienation?
A group of students is counting the number of plastic bags placed in a landfill during a single day .What are the students doing?
A)collecting data
B)Drawing a conclusion
C)Stating a problem
D)Making a hypothesis
Answer:
A
Step-by-step explanation:
Write the slope intercept equation of a line that passes through points (-3,4) and (2, -6)
Give three solutions to the equation y = 3 x + 4 y=3x+4 . give your solutions as ordered pairs, using reduced fractions or integers for coordinates.
Final answer:
To find three solutions to the equation y = 3x + 4, you can choose different values for x and calculate the corresponding values of y. Three solutions are (0, 4), (1, 7), and (-1, 1).
Explanation:
The equation y = 3x + 4 represents a linear equation in slope-intercept form, where the coefficient of x is the slope and the constant term is the y-intercept. To find three solutions to this equation, we can choose different values for x and calculate the corresponding values of y.
If x = 0, then y = 4. So one solution is (0, 4).If x = 1, then y = 7. So another solution is (1, 7).If x = -1, then y = 1. So the third solution is (-1, 1).The temperature in a town is 36.6F during the day and -12.6F at night what is the temperature change from day to night
The temperature changes by 49.2F from day to night. You calculate this by subtracting the night temperature from the day temperature and remembering to treat subtraction of a negative as addition.
Explanation:The subject of your question is the calculation of temperature change, which is a simple subtraction problem in mathematics. Given a temperature of 36.6F during the day and a temperature of -12.6F at night, you can find the temperature change by subtracting the night temperature from the day temperature.
So, it will be 36.6F - (-12.6F) equals 49.2F. It's important to note here that subtracting a negative number is the same as adding a positive number which is why we add 12.6F instead of subtracting it.
This means, the temperature changes by 49.2F from day to night.
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A rectangular garden is fenced on all sides with 160 feet of fencing. The garden is 6 feet longer than it is wide. What is the area of the garden?
A builder wants to build a diagonal beam across a decorative window. If the window is 3 feet by 5 feet, then to the nearest hundredth, how long is the diagonal?
Answer:
12 square feet
Step-by-step explanation:
The ratio of men to women working for a company is 7 to 5 . if there are 105 men working for the company, what is the total number of employees?
Please help with this question: A brick company guarantees to fill a contractor's order to within 5% accuracy. A contractor orders 1,500 bricks. Please write and solve an absolute-value equation to find the maximum and minimum number of bricks guaranteed.
Kim has small wooden cube shaped blocks. To make the next size cube, she needs 8 blocks. Write a sequence to show the number of blocks needed for each increasingly larger cube. Include at least 6 terms in the sequence.
Use the graph below to answer the question that follows:
What trigonometric function represents the graph? (6 points)
Select one:
a. f(x) = −3 sin(x − pi over 2 )
b. f(x) = −3 cos(x − pi over 2 )
c. f(x) = 3 cos(x − pi over 2 )
d. f(x) = 3 sin(x − pi over 2 )
The trigonometric function which represents the graph is:
c) [tex]f(x)=-3\cos (x-\dfrac{\pi}{2})[/tex]
Step-by-step explanation:From the graph we may observe that when x=π/2 we have the value of the function f(x)= 3
Hence, we will check in which this point hold true:
a)
[tex]f(x)=-3\sin (x-\dfrac{\pi}{2})[/tex]
Now, when x=π/2 we have:
[tex]f(x)=-3\sin (\dfrac{\pi}{2}-\dfrac{\pi}{2})\\\\\\f(x)=-3\sin (0)\\\\\\f(x)=0\neq 3[/tex]
Hence, option: a is incorrect.
b)
[tex]f(x)=-3\cos (x-\dfrac{\pi}{2})[/tex]
Now, when x=π/2 we have:
[tex]f(x)=-3\cos (\dfrac{\pi}{2}-\dfrac{\pi}{2})\\\\\\f(x)=-3\cos (0)\\\\\\f(x)=-3\neq 3[/tex]
Hence, option: b is incorrect.
d)
[tex]f(x)=3\sin (x-\dfrac{\pi}{2})[/tex]
Now, when x=π/2 we have:
[tex]f(x)=3\sin (\dfrac{\pi}{2}-\dfrac{\pi}{2})\\\\\\f(x)=3\sin (0)\\\\\\f(x)=0\neq 3[/tex]
Hence, option: d is incorrect.
c)
[tex]f(x)=-3\cos (x-\dfrac{\pi}{2})[/tex]
Now, when x=π/2 we have:
[tex]f(x)=3\cos (\dfrac{\pi}{2}-\dfrac{\pi}{2})\\\\\\f(x)=3\cos (0)\\\\\\f(x)=3[/tex]
Similarly we will see that the value of this function matches all the points that on the graph.
Hence, option: c is correct.
Given: f(x)=x²-3 and g(x)=x+1. What is the composite function gOf?
1. x²+2x-2
2. x²+2x-2
3. x²-2
For two given functions f(x) and g(x), the composite function
(g ° f)(x) is: g(f(x))
Here we will find that the correct option is the last one:
(g°f)(x) = x²-2
To get this, we know that:
g(x) = x + 1
f(x) = x² - 3
Then:
(g°f)(x) = g(f(x))
So here we just need to evaluate g(x) in f(x):
g(f(x)) = f(x) + 1 = ( x² - 3) + 1 = x² - 3 + 1 = x² - 2
Then the correct option is 3:
(g°f)(x) = x²-2
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Michael is three times as old as Margaret, and in 6 years he will be twice as old as her. How old was Michael when Margaret was born?
Answer:
12 years old
Step-by-step explanation:
m = Michael
a = Margaret
m = 3a
m+6 = 2(a+6)
m+6 = 2a+12
Two equations, two unknowns, so we can use substitution.
3a+6 = 2a+12
a+6 = 12
a = 6
Plug it back in.
m = 3(6)
m = 18
When Michael was 18, Margaret was 6. So when she was born (basically when she was 0) Michael was 18-6 = 12.
Answer:
Michael was 12 years old when Margaret was born.
Step-by-step explanation:
Let Michael be x and Margaret be y.
x=3y
x+6 (years) = 2(6+y) --> x+6=12+2y --> x=6+2y
Now that we have x, substitute x=3y:
6+2y=3y --> y=6
Now we have y, substitute again with x=3(6) --> x=18
So, Michael, x, is 18 years old. Margaret, y, is 6 years old. But, to find how old Michael was when Margaret was born, do 18 (Michael's age)-6 (Margaret's age) to get 12. So, Michael was 12 years old when Margaret was born. Hope that helped, sorry if I missed something... :D
The average gas mileage m in miles per gallon for a compact car is modeled by m(s) = -0.015(s - 47)^2 + 33, where s is the car's speed in miles per hour. The average gas mileage for an SUV is modeled by m(s) = -0.015(s - 47)^2 + 15. What kind of transformation describes this change, and what does this transformation mean?
15/16 × 5/6
Reduce your answers to simplest form
The sum of three consecutive even integers is 378. what is the largest of the three integers
The largest of the three integers is 127.
It is required to find the largest of the three integers.
What is integer?An integer is a whole number (not a fractional number) that can be positive, negative, or zero.
Given that:
Let's assume, that first number is "x", than second number will be "x + 1" and third one is "x + 2".
x + (x + 1) + (x + 2) = 378
x + x + 1 + x + 2 = 378
3x + 3 = 378
3(x + 1) = 378
Divide by 3
x + 1 = 126
x = 125
The first number is 125, second number is 126 and third number is 127.
So, the largest of the three integers is 127.
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PLEASE HELP WILL MARK THE BRAINLIEST
1. How many solutions can a quadratic equation have and why does it vary? How would the corresponding graphs look like?
2. Describe the process of graphing a quadratic equation without using graphing technology.
3. Apply the projectile formula to a real-world situation.
‼️correct answer will get brainliest‼️
Each week, Alfonso earns $85 for every shift he works at the theater and $15 for every dog-walking job. He uses the expression 85x + 15y to keep track of his earnings.
Part A: Identify the coefficients and variables in the expression. (3 points)
Part B: How many terms are in the expression, what are they, and how do you know? (4 points)
Part C: Which term in the expression shows the total earned from the dog-walking jobs? (3 points)
Find the mean of the integers -16,-27,21,-19,14,-3
The mean of the integers -16, -27, 21, -19, 14, -3 is found by adding together all the numbers to get -30, and then dividing by the total number of values, which in this case is 6. This results in a mean of -5.
Explanation:The solution to this problem falls under the branch of Mathematics known as Statistics, which is the study of collecting, analyzing, interpreting, presenting, and organizing data. The term mean is frequently used in statistics, and it refers to the average of a set of numbers. In this case, you are required to find the mean of the set of integers -16, -27, 21, -19, 14, -3.
To compute the mean, you need to follow a simple two-step process: Add together all the numbers in the set, and then divide the total by the number of items in the set. For the numbers given in your case (-16, -27, 21, -19, 14, -3), you add these together which gives you a total of -30. There are 6 numbers in the set, so the mean would be -30 divided by 6, which equals -5.
Therefore, the mean of the integers -16, -27, 21, -19, 14, -3 is -5.
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