Answer:
a. $18.36 for 3 pizzas : k = 6.12
b. $4.17 for 3 pounds of bananas . k = 1.39
c. $16.48 for 4 pounds of potatoes . k = 4.12
d. 2 cups of flour to make 24 cookie . k = 12
Step-by-step explanation:
PROPORTIONALITY:
Two quantities x and y are said to proportional to each other
if for x ∝ y , x = y k.
Here, k is called the PROPORTIONALITY CONSTANT.
⇒[tex]x \propto y \implies k = \frac{x}{y}[/tex]
Now, for the given quantities:
a. $18.36 for 3 pizzas [box]
Here, [tex]k = \frac{x}{y} = \frac{18.36}{3} = 6.12[/tex]
So, the proportionality constant is 6.12.
b. $4.17 for 3 pounds of bananas [box]
Here, [tex]k = \frac{x}{y} = \frac{4.17}{3} = 1.39[/tex]
So, the proportionality constant is 1.39.
c. $16.48 for 4 pounds of potatoes [box]
Here, [tex]k = \frac{x}{y} = \frac{16.48}{4} = 4.12[/tex]
So, the proportionality constant is 4.12.
d. 2 cups of flour to make 24 cookies
Here, [tex]k = \frac{x}{y} = \frac{24}{2} = 12[/tex]
So, the proportionality constant is 12.
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)
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.
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
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 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
If you suspect that "hours studied" and "score on a math test" are positively correlated, what does that mean?
A. More hours of studying tend to go with higher scores on the test.
B. Fewer hours of studying tend to go with lower scores on the test.
C. More hours of studying tend to go with lower scores on the test.
D. Both A and B are true.
I think its D but im not sure completely
Answer:
D. Both A and B are true
Step-by-step explanation:
Why would you study to decrease scores? so C. Is automatically wrong. Now A. is true and B. is true. D says both A and B are true so D is correct.
Answer:
D
Step-by-step explanation:
D. Both A and B are true.
PLEASE SHOW YOUR WORK. thanks
Mrs. Bailey had 12 pieces of candy. She gave away some candy and has 3 pieces left. What is the percent decrease of candy?
Answer:
75%
The drawings will help
Refer to the first one to help understand the second.
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).
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:
find the HCF of following !! a) 15,63,99 B) 66,33,78
Answer:
(a) 3, (b) 3
Step-by-step explanation:
HCF is highest common factor. Each number is split into multiples while the common factors are then multiplied together.
(a) HCF of 15, 63, 99
15 = 3 X 5 ----------------------------- (i)
63 = 3 X 3 X 7 ---------------------------(ii)
99 = 3 X 3 X 11 ---------------------------(iii)
From the three equations, 3 is the only common factor; 3 appears in equations (i), (ii) and (iii)
hence the HCF of 15, 63 and 99 is 3
(b) HCF of 66, 33, 78
66 = 2 X 3 X 11 ----------------------------- (iv)
33 = 3 X 11 ---------------------------(v)
78 = 2 X 3 X 13 ---------------------------(vi)
From the three equations, 3 is still the only common factor; 3 appears in equations (iv), (v) and (vi)
hence the HCF of 166, 33, 78 is 3
[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
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
Learn more about multiplication at:
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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.
a circle has a circumference of 320π cm. what is it radius
Answer:
The radius of the circle is 160cm
Step-by-step explanation:
circumference of circle = 2πr
circumference = 320π cm
2πr = 320π
2r = 320
r = 160 cm
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.
Give your answer in its simplest form.
Use [tex]\frac{a^n}{a^m}=a^{n-m}[/tex].
[tex]
\dfrac{2m^2t^6}{m^4t^2}=2m^{2-4}t^{6-2}=\boxed{2m^{-2}t^4}
[/tex]
Hope this helps.
Answer:
2m⁻²t⁴
Step-by-step explanation:
Rule:
If aᵇ / aˣ, then aᵇ ⁻ ˣ
[tex]\frac{2m^2t^6}{m^4t^2} = 2 m^{2-4} t^{6-2} = 2m^{-2} t^{4}[/tex]
Please someone help with this and explain it as best as you can. Thank you ;)
Answer:
the answer is B
Step-by-step explanation:
Can someone please help me?
GEORGINA WAS GIVEN THAT THE LENGTH OF THE RECTANGLE WAS 2.5 INCHES LONGER THEN ITS WIDTH AND THE PERIMETER OF THE RECTANGLE WAS 75.4 INCHES.
FIND THE LENGTH AND WIDTH OF THE RECTANGLE Alegebraically. SHOW ALL WORK
Answer:
Length of the rectangle is [tex]18.85\ inches[/tex],and the width of the rectangle is [tex]16.35\ inches[/tex]
Step-by-step explanation:
Let the width of the rectangle be [tex]x[/tex] inches
Then
The length of the rectangle will be [tex]x+2.5[/tex] inches
So perimeter [tex]=2(length + width)[/tex]
Plugging the values:
⇒ [tex]2(x+x+2.5)=75.4[/tex]
⇒ [tex]2(2x+2.5)=75.4[/tex]
⇒ [tex]4x+10=75.4[/tex]
Subtracting [tex]10[/tex] from both sides.
⇒ [tex]4x=65.4[/tex]
⇒ [tex]x=\frac{65.4}{4}=16.35\ inches[/tex]
So the width of the rectangle is [tex]16.35\ inches[/tex]
And the length of the rectangle is [tex]18.85\ inches[/tex]
Sheila has $47 to buy graphing pads for her math class. Each pad costs $8,
How many pads can she buy? Do not include units in your answer.
Answer:
5 tablets can be bought
Step-by-step explanation:
47/8= 5
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
Give formula to calculate Selling price when profit is given in percentage.
the diameter of the sweep of the main rotor of the eh101 helicopter is 18.6 meters. A toy model of it has a sweep of 31 centimeters. What is the scale of the model?
Answer:
The actual length of 60 cm is modeled as 1 cm length.
Step-by-step explanation:
The diameter of the sweep of the main rotor of the helicopter is 18.6 meters i.e. 1860 cm.
Now, the toy model of the helicopter has a sweep of 31 cm.
Therefore, the scale in which the model is made is 1860 : 31 i.e. 60 : 1 ratio.
So, the actual length of 60 cm is modeled as 1 cm length. (Answer)
Answer:
The scale of the model to the actual is 1:60
Step-by-step explanation:
The scale of the model may be computes as the ratio of the diameter of the original sweep to the diameter of the model. Given that the diameter of the sweep of the main rotor of the eh101 helicopter is 18.6 meters and that of the model is 31 cm, the scale of the model
= 31cm to 18.6m
since 100cm = 1m,
18.6m = 18.6 * 100cm
= 1860 m
31cm to 18.6m = 31cm to 1860cm
= 1 to 60
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:
Which of the following lines is parallel to x = 4
O 1) 3y = 9
O 2) y = 4
O 3) x = 2
O4) x = y
Answer:
O4) x = y
Step-by-step explanation:
I took this before
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 graph shows how many apples Erin can pick if she maintains a constant rate. What is the linear equation for this relationship? How many apples can she pick per hour?
An equation that represents the relationship between the x and y-values is y = 75x.
Erin can pick 75 apples per hour.
What is a proportional relationship?In Mathematics and Geometry, a proportional relationship is a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical equation:
y = kx
Where:
y represents the y-variable.x represents the x-variable.k is the constant of proportionality.Next, we would determine the constant of proportionality (k) by using various data points as follows:
Constant of proportionality, k = y/x
Constant of proportionality, k = 75/1 = 150/2
Constant of proportionality, k = 75.
Therefore, the required linear equation that models the graph can be written as follows;
y = kx
y = 75x
Read more on proportional relationship here: brainly.com/question/28350476
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Find the equation of the linear function represented by the table below in slope-intercept form.
x
0
1
2
3
4
y
2
7
12
17
22
The equation of the function represented by the table is y = 5 x + 2
Step-by-step explanation:
The equation of the linear function in the slope-intercept form is
y = m x + b, where
m is the slope of the lineThe formula of the slope is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] , where [tex](x_{1},y_{1})[/tex] and [tex](x_{1},y_{1})[/tex] are any two points lie on the lineb is the y-intercept, means the line intersects the y-axis at point (0 , b)The table:
→ x : 0 : 1 : 2 : 3 : 4
→ y : 2 : 7 : 12 : 17 : 22
Let us chose any two points from the table to calculate the slope
∵ Points (1 , 7) and (2 , 12) lie on the line
∴ [tex]x_{1}[/tex] = 1 and [tex]x_{2}[/tex] = 2
∴ [tex]y_{1}[/tex] = 7 and [tex]y_{2}[/tex] = 12
- Substitute these values in the formula of the slope
∵ [tex]m=\frac{12-7}{2-1}=\frac{5}{1}[/tex]
∴ m = 5
Substitute the value of m in the form of the equation
∵ y = m x + b
∴ y = 5 x + b
∵ The line intersects the y-axis at point (0 , b)
∵ From the table point (0 , 2) lies on the line
∴ b = 2
∴ y = 5 x + 2
The equation of the function represented by the table is y = 5 x + 2
Learn more:
You can learn more about linear function in brainly.com/question/9801816
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write 2 formulas you use for finding the circumference of a circle
Answer: the 2 equations are 2(pi)r and (pi)d.
Step-by-step explanation: the radius is from the center of the circle to the edge. And the diameter is double that. R is radius and d is diameter since the diameter is double the radius, you don’t need to multiply it by 2. Hope this helps!
The local Orchestra has been invited to play at a festival. There are 111 members of the orchestra and six are licensed to drive large multiple passenger vehicles. Busses 25 people but are much more expensive to rent passenger vans for 12 people. Create a system of equations to find the small list number of buses there orchestra can rent.
Answer:
Small list number of buses [tex]=3[/tex],the orchestra can rent.
Step-by-step explanation:
Form an equation representing the number of vehicles needed.
Let the number of buses be [tex]x[/tex] and the number of vans be [tex]y[/tex]
We have six drivers so,
[tex]x + y\leq 6[/tex] for both vehicles.
And it's an inequality,where we can equate with by removing the inequality to close in our answer.
[tex]x + y = 6[/tex]
Then form an equation representing the total number of seats [tex]K[/tex] in vehicles for the orchestra members.
[tex]25[/tex] people for bus and [tex]12[/tex] people for vans can be written in terms of seats.
So,[tex]K = 25x + 12y[/tex]
In terms of an inequality it can be written as,
[tex]25x + 12y\geq111[/tex],[tex]111[/tex] is the maximum numbers of the orchestra.
Solving the system of inequality.
We have
[tex]x + y = 6[/tex]
Re-arranging y.
[tex]y = 6 - x[/tex]
Plugging the values in [tex]25x + 12y\geq111[/tex] by removing the inequality and considering it as an equation.
[tex]111 = 25x + 12y = 25x + 12(6-x)[/tex]
[tex]111 = 25x + 72 - 12x[/tex]
[tex]111 - 72 = 13 x[/tex]
[tex]39 = 13 x[/tex]
[tex]x = 3[/tex]
So small list number of buses are [tex]3[/tex] there orchestra can rent.