Answer:
{12, 4, -6}
Step-by-step explanation:
The relation is given by the equation as 12x + 6y = 24 ........... (1)
Now, the domain of this function is {-4, 0, 5}
We have to find the range of this function corresponding to the given domain.
Now, for x = - 4,
12(-4) + 6y = 24 {From equation (1)}
⇒ 6y = 72
⇒ y = 12
Now, for x = 0,
12(0) + 6y = 24 {From equation (1)}
⇒ 6y = 24
⇒ y = 4
Now, for x = 5,
12(5) + 6y = 24 {From equation (1)}
⇒ 6y = -36
⇒ y = -6
Hence, the range for the relation is {12, 4, -6} (Answer)
Marty ordered three extremely accurate and scientific water-balloon launchers from a mail order catalog (one for himself and two for his friends). The total price including shipping charges was $50. If the total shipping cost was $5, how much did each launcher cost?
Answer:
The price of each launcher is $ 15 .
Step-by-step explanation:
Given as :
The total price of three water balloon launchers including shipping charges = $50
The cost of the three shipping = $ 5
So, The price of water balloon launchers excluding shipping charges = $50-$5 = $ 45
Now,
∵ The price of 3 balloon launcher = $45
∴, The price of 1 balloon launcher = [tex]\frac{45}{3}[/tex] = $15
Hence The price of each launcher is $ 15 . Answer
Write the quadratic equation whose roots are 4 and 5, and whose leading coefficient is 4.
The quadratic equation whose roots are 4 and 5, and whose leading coefficient is 4, is: [tex]\[\bo{4x^2 - 36x + 80 = 0}\][/tex]
Step 1
To write a quadratic equation with given roots and a specified leading coefficient, we can use the fact that if p and q are the roots of a quadratic equation, the equation can be written as:
[tex]\[a(x - p)(x - q) = 0\][/tex]
where a is the leading coefficient.
Given roots: [tex]\( p = 4 \)[/tex] and [tex]\( q = 5 \)[/tex]
Leading coefficient: [tex]\( a = 4 \)[/tex]
Step 2
Let's substitute these values into the equation:
[tex]\[4(x - 4)(x - 5) = 0\][/tex]
Now, we need to expand this equation. First, expand the product [tex]\((x - 4)(x - 5)\):[/tex]
[tex]\[(x - 4)(x - 5) = x^2 - 5x - 4x + 20 = x^2 - 9x + 20\][/tex]
Step 3
Next, multiply this expression by the leading coefficient [tex]\( 4 \)[/tex]:
[tex]\[4(x^2 - 9x + 20) = 4x^2 - 36x + 80\][/tex]
Thus, the quadratic equation whose roots are 4 and 5, and whose leading coefficient is 4, is:
[tex]\[\bo{4x^2 - 36x + 80 = 0}\][/tex]
f(x) 3x^2+x-3 g(x)=x^2-5x+1 find f(x)-g(x)
Answer:
2x² + 6x - 4
Step-by-step explanation:
f(x) - g(x)
= 3x² + x - 3 - (x² - 5x + 1) ← distribute
= 3x² + x - 3 - x² + 5x - 1 ← collect like terms
= 2x² + 6x - 4
Answer:
f(x) - g(x) = 2x² - 4x - 2
Step-by-step explanation:
f(x) = 3x² + x - 3
g(x) = x² - 5x + 1
f(x) - g(x)
3x² + x - 3 - x² - 5x + 1
3x² - x² - 5x + x - 3 + 1
= 2x² - 4x - 2
f(x) - g(x) = 2x² - 4x - 2
Help please I don’t get this
Answer:
y = -2x - 1
Step-by-step explanation:
Formula is y = mx + b
m = slope
slope = change in y/change in x = (-1 - 3) / (0 - -2) = -4/2 = -2
So equation is now y = -2x + b
To find b, substitute any value from the table into the equation. Let's use (-2,3)
y = -2x + b
3 = -2(-2) + b
3 = 4 + b
-1 = b
So equation is y = -2x - 1
Answer:
C. This can be found by looking at when x=0. If y=-1, then that means that the y intercept is -1, so plug in 1 to either one of the middle two equations and see if it works.
Step-by-step explanation:
What is the simplified form of 2n ^ 2/3 * 3n^ 3 / 4
Answer: N^5/2 thats the answer thank you :)
The system of equations is graphed on the coordinate plane.
y=x−1y=−2x−4
What are the coordinates of the solution to the system of equations.
Answer:
(-1,-2)
Step-by-step explanation:
Hope it helps!
Answer:
the correct answer is (-1,-2)
Step-by-step explanation:
F=9/5c+32 a is there a constant of proportionality? Explain your reasoning
yes because in a standard form that that equation is in, it'd be y=mx=b. the m represents the constant of proportionality or the rate of change. another name for it is the slope. in this case, the 9/5 is the m & c is x. meaning that, there is one & it is 9/5
Solve the system of linear equations by addition
x+y=-9
x+y=5
Answer:
No Solution.
Step-by-step explanation:
x+y=-9
x+y=5
------------
x+y=-9
-(x+y)=-5
---------------
x+y=-9
-x-y=-5
-------------
0=-14
If you buy a home and make a relatively small down payment, what happens to the monthly payments and total payment for you loan?
Answer:
Both monthly payment and total payment will increase.
Step-by-step explanation:
If I buy a home and make a relatively small down payment, then the due payment will be more.
If I pay for my home through a bank and I fix the number of installments to pay back the due amount after down payment (say, monthly installment for 5 years), then the amount of installment payment will definitely increase if my down payment is less.
Again, if the down payment is less, the remaining amount to pay back will rise and the bank calculates interest on the remaining amount to pay. Therefore, the amount of interest will rise in value and finally the total payment after interest for my loan will increase. (Answer)
: Create a story or context for this number sentence
50 1/2 divided by 1/4 + 202
Answer:
Tommy has 202 Chocolates with him in, his uncle gave him 50 1/2 bars of Chocolate each bar is further divided in 1/4 pieces to make 1 chocolate. Find the total number of Chocolates Tommy has?
Step-by-step explanation:
Given:
[tex]\frac{50\frac{1}{2}}{\frac{1}{4}}+202[/tex]
The Story can be created as :
Tommy has 202 Chocolates with him in, his uncle gave him 50 1/2 bars of Chocolate each bar is further divided in 1/4 pieces to make 1 chocolate. Find the total number of Chocolates Tommy has?
At the market, 8 apples cost $4dollar. How much do 9 apples cost?
Answer: $4.50 for 9 apples
Step-by-step explanation: To find out how much it is for 1 apple, we need to find the unit price of 1 apple which is the cost per apple.
Since we know that it costs $4 for 8 apples, to find the cost for 1 apple, we need to divide 8 into $4 or 4 divided by 8 which is 0.5 of 50 cents per apple.
Since we know that it costs 50 cents per apple, to find the cost for 9 apples, we will need to multiply .50 by 9.
(.50) (9) = 4.50
Therefore, it will cost $4.50 for 9 apples.
what is half of 7 minutes and 24 seconds
Step-by-step explanation:
7 minutes are 7*60=420 seconds
420+24=444
444:2=222 seconds
222 seconds are 3minutes and 42 seconds
Answer:3.7 is half of 7 minutes and 24 seconds
Step-by-step explanation:
Barry is selling magazine subscriptions for a school fundraiser. He has already sold 15 subscriptions. He plans to sell 3 subscriptions per week until he reaches a total of 30 subscriptions sold. How many weeks will it take Barry to achieve his goal.
Answer:
5 more weeks
Step-by-step explanation:
5 more weeks if he already sold 15. 10 more weeks if you exclude the 15 he already sold.
5p = 1/15
what does p equal?
Answer:
(:5) 5p=1/15 (:5)
p=1/3
Answer:
p= .3333333
Step-by-step explanation:
use the rational exponent property to write an equivalent expression for
[tex] \sqrt[5]{n ^{4} } + 3 - 12[/tex]
Using the rational exponent property, an equivalent expression for[tex]\(x^{3/4}\[/tex] can be written as[tex]\(\sqrt[4]{x^3}\).[/tex]
Explanation:The rational exponent property states that for any real number a and positive integer[tex]\(n\), \(a^{m/n} = \sqrt[n]{a^m}\)[/tex] . Applying this property to the given expression[tex]\(x^{3/4}\[/tex] ), where (m = 3) and (n = 4), we can rewrite it as [tex]\(\sqrt[4]{x^3}\)[/tex] . This is derived by taking the fourth root of [tex]\(x^3\),[/tex] which is equivalent to raising [tex]\(x^3\)[/tex] to the power of[tex]\(1/4\).[/tex]
To further understand this, consider the original expression [tex]\(x^{3/4}\).[/tex] This represents the fourth root of [tex]\(x^3\)[/tex] , as the numerator 3 indicates the power to which x is raised, and the denominator 4 indicates the root. Expressing it as [tex]\(\sqrt[4]{x^3}\)[/tex] provides a clearer representation of the same mathematical concept, emphasizing the fourth root of [tex]\(x^3\).[/tex]
In mathematical notation, the rational exponent property is a useful tool for simplifying expressions involving fractional exponents. It allows us to transform expressions between radical form and exponent form, providing flexibility in mathematical manipulations and aiding in the understanding of the underlying concepts.
Find 4(6a−5)−(9a+1).
Answer:
15a-21
Step-by-step explanation:
could be wrong though
3/10 11/12 5/8 in Oder from least to greatest
Answer: 5/8 11/12 3/10 I think
Step-by-step explanation:
Find common denominators (LCM is 120).
3/10 = 36/120
11/12 = 110/120
5/8 = 75/120
Now, we can put them from least to greatest.
3/10, 5/8, 11/12
______
Best Regards,
Wolfyy :)
write an equation that is not a linear function explain why it is not linear
Answer:
x=y^2
Step-by-step explanation:
cause the definition of equation is one x correspond to one y,but one y can correspond to 2 x,
the picture I give to you a x correspond to 2 y
The function that does not represent the straight curve and has a varying rate of change are nonlinear functions.
What are functions?Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
here,
According to the question,
A nonlinear equation is given as,
y = x²
Now plotting the curve,
When we see that the relationship does not contain a straight line, and has a varying rate of change are nonlinear functions.
So this function is not linear.
Thus, the function that does not represent the straight curve and has a varying rate of change are nonlinear functions.
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The variables y and x have a proportional relationship, and y = 7 when x = 2.
What is the value of y when x = 5?
Enter your answer in the box.
y = 17.5 when x = 5
Step-by-step explanation:
When two variables are in direct proportion i.e. change in one variable causes change in other variable it can be expressed mathematically as:
y∝x
when the proportionality symbol is removed a proportionality constant is introduced
So,
[tex]y = kx[/tex]
Putting y = 7 and x = 2
[tex]7 = k * 2\\k = \frac{7}{2}\\k = 3.5[/tex]
So the expression will be:
[tex]y = 3.5x[/tex]
Now putting x = 5
[tex]y = 3.5 * 5\\y = 17.5[/tex]
Hence,
y = 17.5 when x = 5
Keywords: Proportion, variables
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There are 450 children that attend a high school. Of those students. 23%
are in the marching band. How many students are not in the marching
band?
Answer:
The number of students not in the marching band is 346.5
Step-by-step explanation:
Given as :
The total number of children that attend a high school = 450
The percentage of students in the marching band = 23 %
Let The number of students not in the marching band = x
Now ,
∵ The percentage of students in the marching band = 23 %
∴ The percentage of students not in the marching band = 100 % - 23 % = 77 %
So, The number of students not in the marching band = 77 % of the total number of students in the school
I.e The number of students not in the marching band = 77 % × 450
Or , The number of students not in the marching band = [tex]\frac{77}{100}[/tex] × 450
∴ The number of students not in the marching band = 346.5
And The number of students in the marching band = 450 - 346.5 = 103.5
Hence The number of students not in the marching band is 346.5 Answer
What is the equation of a line in slope intercept form that passes through the points (-4,3) and (-2,4)
Answer:
y=1/2x+5
Step-by-step explanation:
y-y/x-x for slope
4-3/-2-(-4) 1/2
Answer:
y= --2/4+5
Step-by-step explanation:
The expression x2 - 36y2 is equivalent to
Answer:
(x + 6y)(x - 6y)
Step-by-step explanation:
The expression x² - 36y² can be factored.
Since the expression is a difference (subtraction) between two numbers that are square (x² = x*x and 36y² = 6y*6y), the factoring can be done as a "difference of squares".
The rules is generalized as: [tex]x^{2} - y^{2} = (x - y)(x+y)[/tex]
To factor x² - 36y², take each square roots for each of the numbers and add and subtract between them.
x² - 36y²
= (√x² + √36y²)(√x² - √36y²)
= (x + 6y)(x - 6y)
What are the possible values of the missing term of the geometric sequence 6,....,13.5?
Answer:
THE ANSWER IS 1.5
Step-by-step explanation:
13.5 is the 3rd and last value. 6 is the first value.
The formula you need to use is an= 3r^n-1
13.5=3r^3-1
THE REASON YOU USE 3 IS BECAUSE IN TOTAL THERE ARE 3 TERMS AND WE ARE SOLVING FOR ONE MISSING TERM.
Now we bring 3 over to 13.5 to get r alone because we are solving for r
13.5/3 =r^2
Now we want to get rid of the square root. So we...
√13.5/3 =√r^2
The final answer is 1.5=2
[tex] \frac{1}{3}x - 5 + 171 = x[/tex]
Answer:
x=249
Step-by-step explanation:
1/3x-5+171=x
1/3x+166=x
166=x-1/3x
166=2/3x
x=166/(2/3)
x=(166/1)(3/2)
x=498/2
x=249
A rectangular auditorium seat 2842 people. The number of seats in each row exceeds the number of rows by 9. Find the number of seats in each row.
Answer:25,578
Step-by-step explanation:
Multiply 2,842 by 9
The price of a toaster increase 10% to $40. What is the original price of the toaster before the increase?
Answer:
36.36
Step-by-step explanation:
We can express 10% as a decimal by multiplying it by (1/100), resulting in 0.1. Therefore, adding 0.1 of the original price, or x, to the price will result in 40, so x+0.1*x=40
= 1.1x
Dividing both sides by 1.1, we get that x, or the original price, is $36.36 (approximately).
Mary covered her kitchen floor with
10 tiles. The floor measures 6 feet long
by 5 feet wide. The tiles are each 3 feet
You have to write an equation though not solve it.
long and w feet wide.
Final answer:
The question pertains to writing an equation for a mathematics-related scenario, emphasizing the importance of understanding equations as expressions of concepts rather than just tools for calculation.
Explanation:
The subject of this question appears to revolve around forming an equation that could pertain to a mathematics problem. The use of mathematical equations to convey concepts is crucial; they aren't just mechanisms for inserting and churning numbers, but they are sentences that express concepts precisely and purposefully. Writing out such equations in both words and symbols ensures comprehension of the underlying reasoning.
Moreover, when teaching mathematics, it's beneficial to allow students to create their own formulas. This practice not only solidifies the understanding of concepts but also emphasizes that the symbols used in equations are arbitrary and that what matters is the concept they represent.
Remembering the correct order of operations is essential, which can be recalled with the mnemonic 'Please Excuse My Dear Aunt Sally.' Also, an iterative relation often used in advanced mathematics is not an equation per se, but rather a set of instructions for approximating a solution. This iterative process requires a different approach compared to straightforward equation solving.
is this a function ?
Answer:
No
Step-by-step explanation:
For the relation to be a function
Each value of x from the domain ( values on left ) must map to exactly one unique value of y in the range ( values on the right )
Here x = 0 → 0 and 1 ( that is 2 values from the range )
Thus this does not represent a function
I need the answer and if you could please explain step by step
Umm sir where is the Graff we need it to solve the problem
Answer:
we need a graph to solve this. please provide the graph and we will be happy to help you!
Step-by-step explanation:
An airliner is 9.34 feet wide. The airline wants to install 5 seats in each row. The seats are each 1.46 feet wide. Rounded to the nearest tenth, about how much space would be left for the aisle?
About 2.0 feet space will be left for aisle.
Step-by-step explanation:
Width of airliner = 9.34 feet
Width on one seat = 1.46 feet
Seats to install = 5
Width of 5 seats = 5*1.46 = 7.3 feet
Space left for aisle = Width of airliner - width of 5 seats
[tex]Space\ left\ for\ aisle=9.34-7.3\\Space\ left\ for\ aisle=2.04\ feet[/tex]
Rounding off to nearest 10th
Space left for aisle = 2.0 feet
About 2.0 feet space will be left for aisle.
Keywords: multiplication, subtraction
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To find the space left for the aisle, we first calculate the total seat width (5 seats × 1.46 feet/seat) and subtract it from the airliner width (9.34 feet), resulting in 2.0 feet of space for the aisle when rounded to the nearest tenth.
Explanation:To calculate the available space for the aisle in an airliner, we first determine the total width consumed by the seats. Since each seat is 1.46 feet wide and there are 5 seats in a row, we multiply the width of one seat by the number of seats:
1.46 feet/seat × 5 seats = 7.3 feet
Next, we subtract the total width of the seats from the total width of the airliner to find the space left for the aisle:
9.34 feet (total width) - 7.3 feet (width of seats) = 2.04 feet
Therefore, rounded to the nearest tenth, there would be approximately 2.0 feet of space left for the aisle.