Natalia and her friends held a bake sale to benefit a local charity. The friends sold 15 cakes on the first day and 22 cakes on the second day of the bake sale. They collected $60 on the first day and $88 on the second day. Write an equation to represent the amount R Natalia and her friends raised after selling c cakes.
The name of the assignment is 5-1 Writing Equations In Slope Intercept Form
Answers
Answer:
✅\( R = 4c \)
Step-by-step explanation:
The equation that will represent the amount raised after selling the cakes to be written in slope-intercept form is given as \( y = mx + b \).
Where,
y = R (amount of cake sold in dollars)
x = c (cakes sold)
m = slope
b = y-intercept.
The equation would look like:
\( R = mc + b \)
We need to find the value of m and b, to get an equation to represent the situation.
The first point we have from the information given is (15, 60) => 15 cakes sold for $60.
The second point is (22, 88) => 22 cakes sold for $88.
\( slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{88 - 60}{22 - 15} = \frac{28}{7} = 4 \)
To find b, substitute c = 15, R = 60 and m = 4, into \( R = mc + b \).
\( 60 = 4(15) + b \)
\( 60 = 60 + b \)
\( 0 = b \)
Since b = 0, this means there is a proportional relationship between R and c.
Substitute m = 4 and b = 0 into \( R = mc + b \) to derive an equation to represent the amount R Natalia and her friends raised after selling c cakes.
\( R = 4c + 0 \)
✅\( R = 4c \)
Related Questions
Given the definitions of f(x) and g(x) below, find the value of (fog)(-3).
f(x) = 3x² - 7x-3
g(x) = -4x - 10
Answers
The value of the composite function (f o g)(3) is 1603
How to evaluate the composite function?The functions are given as
f(x) = 3x² - 7x - 3
g(x) = -4x - 10
Next, calculate (f o g)(x) using
(f o g)(x) = f(g(x))
So, we have
(f o g)(x) = 3(-4x - 10)² - 7(-4x - 10) - 3
Substitute 3 for x.
So, we have
(f o g)(3) = 3(-4 x 3 - 10)² - 7(-4 x 3 - 10) - 3
Evaluate
(f o g)(3) = 1603
Hence, the value of the composite function (f o g)(3) is 1603
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A blueprint used a scale of 1.5 cm = 2 m to
represent a grain silo. If the height of the silo in
the drawing was 33 cm, how tall is the actual grain
silo?
Answers
Answer: The Silo is 44 meters tall
Step-by-step explanation:
To find the height of the silo, first you have to divide the drawing height (33cm) by 1.5 to get the unit rate. Then multiply the 22 by 2 to get 44 meters (The height of the silo)
The heights of women aged 20-29 in the United States are
approximately Normal with mean 64.1 inches and standard
deviation 3.7 inches. Men the same age have mean height
69.4 inches, with standard deviation 3.1 inches.
Cheryl D. Fyar et al., "Anthropometric reference data for children and adults:
United States, 2011-2014, Val and Health Statistics, Series 3, no. 39 (August
2016), at www.ode govchs. This report provides the means of various
anthropometric measurements. Standard deviations were computed from the
sample size and reported standard errors of the mean. Instructions on
measuring upper arm length are in the National Health and Nutrition
Examination Survey: Anthropometry Procedures Manual, January 2007.
M
B
O
Surat pen
What is the z-score for a woman 5.5 feet tall? Give your
answer to two decimal places.
-1.16
Incorrect
N
Sep 8
10:28
Answers
Using the normal distribution, the z-score of the height of a women 5.5 feet tall is 0.51.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean \(\mu\) and standard deviation \(\sigma\) is given by:
\(Z = \frac{X - \mu}{\sigma}\)
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.Considering that each feet has 12 inches, the parameters are given as follows:
\(X = 5.5 \times 12 = 66, \mu = 64.1, \sigma = 3.7\)
Hence the z-score is found as follows:
\(Z = \frac{X - \mu}{\sigma}\)
Z = (66 - 64.1)/3.7
Z = 0.51
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Submit the worksheet with your constructions to your teacher to be graded.
Answers
Answer:
p: (-4)2 > 0
q: An isosceles triangle has two congruent sides.
r: Two angles, whose measure have a sum of 90, are supplements.
Step-by-step explanation:
Eastco buys televisions from a manufacturer. The list price of a television is $460.00 with a trade discount of 30 percent. The net price of a television is? A. $422.00. B. $233.00. C. $138.00. D. $322.00.
Answers
Answer: D. $322
Step-by-step explanation:
Answer:
$322.00
Step-by-step explanation:
Net price = list price − trade discount N = L − T
First, figure out the Trade discount by multiplying the list price by the discount. Put the discount into decimal form.
T = $460.00 × 0.3 = $138.00
Next, LP - T
NP= $460.00 - $138.00 = $422.00
In the number 98.48, what will you multiply by to get rid of the decimal?
Answers
Based on the number, 98.48, the number you need to multiply by to get rid of the decimal is 100.
What number should you multiply by to remove the decimal?The number that you multiply a number with if you want to remove the decimal has to be a power of 10. The power of 10 used will depend on the number of figures after the decimal.
If there is a single number after the decimal point, then multiply by 10.
If there are two numbers after the decimal point, multiply by 100.
If there are three numbers after the decimal point, multiply by 1,000.
In the case of 98.48, there are two number after the decimal point so you'll multiply by 100 to get:
= 98.48 x 100
= 9,848
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Please help me with this I will give brainliest. Find the value of x. Round to the nearest tenth
Answers
Answer:
the second option
Step-by-step explanation:
\( \sin(20) = \frac{x}{18} \\ x = 6.15 = 6.2\)
Write the explicit formula for the arithmetic sequence below. 14, 9, 4, -1, ...
Answers
Step-by-step explanation:
To find the next term or number, we'll need to keep subtracting 5. So the formula is: n-5
You deposit $5000 in an account earning 5% interest compounded continuously. How much will you have in the account in 5 years? Round to the nearest cent.
Answers
The diameter of a circle is 34 kilometers. What is the circle's circumference?
Answers
Circumference = π × diameter
where π (pi) is approximately 3.14.
Substituting the given value of diameter (34 kilometers) into the formula, we get:
Circumference = 3.14 × 34 kilometers
Circumference = 106.76 kilometers
Therefore, the circumference of the circle is 106.76 kilometers.
Alice wants to use the stack method to pay down her debts listed in the table below. If she applies an extra $150 a month to her debts, what will be the first debt she targets to pay off and what will be the monthly amount she applies to it?
Answers
Therefore , the solution of the given problem of linear equation comes out to be monthly amount she applies to it is $550.
What exactly is a linear equation?Using the formula y=mx+b, a simple regression curve is constructed. The slope is B, and the y-intercept is m. Even if y or y are separate portions, the foregoing sentence is frequently referred to as a "mathematical formula merging many variables." In bivariate linear equations, there are only two variables. Application problems involving linear equations have no known solutions.
Here,
Given :
=> $150 extra in her debt
her debt be x
y be the amount she already pays
=> amount left
=> x - y - 150
=> x- (y+150)
Let x be 1000
y be 300
=> 1000 -(300+150)
=> 1000 -450 = 550
Thus,
monthly amount she applies to it is $550
Therefore , the solution of the given problem of linear equation comes out to be monthly amount she applies to it is $550.
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A, B, C, D are points on a line.
AB = 1
BC = 2
CD = 4
Find the length of segment AD. Consider all possibilities.
So far, I've only gotten 7, 5, and 1. But I know there is one left. Can you guys help?
Answers
The points A, B, C and D are collinear points
The length of the segment AD is 7 units
How to determine the length AD?The given parameters are:
AB = 1
BC = 2
CD = 4
Because the points are on the same line, then the following is the possible equation
AD = AB + BC + CD
Substitute known values
AD = 1 + 2 + 4
Evaluate the sum
AD = 7
Hence, the length of the segment AD is 7 units
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There are 37 people seated in a cafeteria. Each table holds 2 people. One table is not full. How many fulltables are there?
Answers
We need to find the number of full tables, to do this you must keep in mind three important things.
1. there are 37 people
2. the tables are filled with 2 people
3. One table is not full
If the only way to fill a table is with two people at it, it means that we have to arrange the 37 people at the tables and see how many are filled in total.
i.e. divide the 37 people in 2 which is the capacity of the tables.
\(\frac{37}{2}=18.5\)since you can't have 18.5 tables full we approximate 18, this is accurate since it also tells us that there is one table that is not full.
In conclusion, the cafeteria has 18 full tables
Of all the species in the world,4 out of every 5 are insects.
What percentage of species are insects?
Answers
Answer:
80%
Step-by-step explanation:
It has long been recognized and documented that insects are the most diverse group of organisms, meaning that the numbers of species of insects are more than any other group. In the world, some 900 thousand different kinds of living insects are known. This representation approximates 80 percent of the world's species.
Millilitre are used to measure the large amount of volume
Answers
Answer:
false
Step-by-step explanation:
Plot each point that is a horizontal distance of 6 and a vertical distance of 2 from the origin.
Answers
The points that are a horizontal distance of 6 and a vertical distance of 2 from the origin are (6, 2), (-6, 2), (6, -2), (-6, -2)
What are points?Points are undefined terms in geometry, however they are used to represent the coordinate or location of items in a coordinate plane
How to plot the point?The features of the point are given as:
Horizontal distance = 6
Vertical distance = 2
The above means that:
x = 6
y = 2
The points are then represented as:
(x, y) = ±(x. y)
So, we have
(x, y) = ±(6, 2)
When the above equation is expanded, we have
(x, y) = (6, 2), (-6, 2), (6, -2), (-6, -2)
Next, we plot the points on a coordinate plane
See attachment for the graph of the plane
Hence. the points that are a horizontal distance of 6 and a vertical distance of 2 from the origin are (6, 2), (-6, 2), (6, -2), (-6, -2)
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True or False: If the discriminant is less than zero, then the graph will never cross the x-axis.
False
True
Answers
Answer:
True
Step-by-step explanation:
If the discriminant \(D=b^2-4ac < 0\), then there are two complex roots
If the discriminant \(D=b^2-4ac > 0\), then there are two real roots
If the discriminant \(D=b^2-4ac=0\), then there is only one real root
Which graph represents function g if g(x)=f(2x)
Answers
The new function g(x) which is equal to f(2x) will be stretched or compressed by the factor 2.
What is a function?It is defined as a special type of relationship and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a function f(x) shown in the coordinate plane.
The function g(x) = f(2x)
As we can see in the new function g(x) it is the transformation of the f(x).
Transformation is applied as below:
x → 2x (x is replaced by the twice of it)
= f(x)
= f(2x)
= g(x)
When the function is multiplied by a positive number it will be stretched or compressed according to that factor vertically and in the given function the factor is 2 which means the g(x) will be stretched or compressed according to that factor.
Thus, the new function g(x) which is equal to f(2x) will be stretched or compressed by the factor 2.
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Solve for x.
Your Answer:
Question 3 options:
Answer
Answers
Will someone help me with this basic geometry?
Answers
The value of x in the right angle placed is equal to 16
Right AnglesA right angle is an angle that measures 90 degrees. It is the most commonly seen angle in our day-to-day life. It can be seen in the corners of a room, the edges of boxes, the screen of a mobile phone, and so on. The sides of a square and a rectangle always form a right angle with each other. In radians, it is represented as π/2. Let us discuss more about a right angle in this article.
A right angle is an angle of 90°. When two rays intersect and form a 90˚ angle or are perpendicular to each other at the intersection, they are said to form a right angle.
In the given question, we can set an equation and find the value of x
90 = 26 + 4x
Lets solve for x
4x = 90 -26
4x = 64
x = 16
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Selina is remodeling her home. She installed a low-flow toilet in her home that flushes 0.8 gallon each time. She replaced her showerhead with a low-flow showerhead that releases 1.5 gal/min. She flushes 12 times a day and showers for 10 minutes a day. On average, her appliances use 40.2 gal/day. Assuming no other appliance use, how much less water will she use than the average U.S. citizen?
Answers
The average U.S. citizen uses approximately 88 gallons of water a day.
What is Frequency?
Frequency is a measure of how often an event occurs within a given period of time. It is typically expressed as the number of occurrences of a given event per unit of time. Frequency can be used to measure a variety of phenomena such as the frequency of sound in a given environment or the frequency of a particular chemical element in a given sample.
Selina's low-flow toilet and showerhead will reduce her total water use to just 48.4 gallons per day, a savings of 39.6 gallons of water each day. This is a 44.8% reduction in her water consumption, saving her almost 40 gallons of water per day.
By making these improvements, Selina is helping to conserve a precious resource and limit her environmental impact. Not only is she helping to conserve water, but she is also saving money on her water bill. It is estimated that a typical household can expect to save about $170 annually by making these simple changes.
In addition to her low-flow fixtures, Selina can take additional steps to reduce her water consumption. She can install a water-efficient dishwasher, reduce the frequency of her laundry loads, and install a rain barrel to collect rainwater for gardening. By making these changes, she can reduce her water consumption even further and save even more money.
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1. Prove ~ (Pvq) <=> (~P^~9).
Algebra of propositional variables
2. P^ q = q^q
P v q = q v p
show that both are commutative
Answers
Based on the information, both ∧ (conjunction) and ∨ (disjunction) satisfy the commutative property.
How to explain the commutative property.It should be noted that to prove the commutativity of the logical connectives ∧ (conjunction) and ∨ (disjunction), we need to show that they satisfy the commutative property
From the truth table, both P ∧ Q and Q ∧ P have the same truth values for all combinations of truth values of P and Q. Therefore, we can conclude that P ∧ Q ≡ Q ∧ P, and ∧ (conjunction) is commutative.
In order to prove P ∨ Q ≡ Q ∨ P, we construct a truth table for both expressions. Both P ∨ Q and Q ∨ P have the same truth values for all combinations of truth values of P and Q. Therefore, we can conclude that P ∨ Q ≡ Q ∨ P, and ∨ (disjunction) is commutative.
Hence, both ∧ (conjunction) and ∨ (disjunction) satisfy the commutative property.
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pls answer the top one need a naswer fast
Answers
The polynomial expression that represents the perimeter is (3x^3 +3x -148)ft and the value is 182ft
what is a polynomial?Polynomials are algebraic expressions that consist of variables and coefficients. Variables are also sometimes called indeterminates. We can perform arithmetic operations such as addition, subtraction, multiplication, and also positive integer exponents for polynomial expressions but not division by variable.
Perimeter of the triangle is the sum of the sides of the triangle which is = 2x^2 -120 + x^2 -5x +8x -28
Perimeter = (3x^2 +3x -148)ft
when x = 10
Perimeter = 3(10)^2 +3(10) -148 = 182ft
In conclusion the expression (3x^2 +3x -148)ft is the expression for the perimeter of the triangle and the value is 182ft
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If a store marks up merchandise by 40% on cost, what is the markup in dollars on an item costing $80?
Answers
Graph the solution to the inequality on the number line.
q<69.5
Answers
The graph of the solution to the given inequality on the number line plotted is attached.
Inequalities are the mathematical expressions in which both sides are not equal.
In inequality, unlike in equations, we compare two values.
The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
The given inequality is q < 69.5.
The result can be shown in multiple forms.
Inequality Form:q<69.5
Interval Notation:(−∞,69.5)
Therefore, the graph the solution to the given inequality on the number line plotted below.
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May someone please help me my work is do tomorrow 1/4x - 3 = 1/2x + 12
Answers
X/4-3=1/2x+12
X/4+4(-3)/4=1/2x+12
X+4(-3)/4=1/2x+12
X-12/4=1/2x+12
Solve the polynomial inequality.
(x-16)4^ > 0
Answers
Whats the number thats above 4?
Answer:
B on edug
(-infinty , 0) U (0 , infinty )
What is the diffrence between 7/8 and 1/2?
Answers
Answer:
3/8
Step-by-step explanation:
1. Find common denominators, which is 7/8 and 4/8
2. 7/8 - 4/8 = 3/8
Answer:
7/4 or 1 3/4
Step-by-step explanation:
The water park charges a $10 entry fee per person and a $3 parking fee per family vehicle. What is the total cost in tepeople ride in the same vehicle? what is the dependent variable
Answers
100+3=103
The answer is＄103
Is it ten people
math question plzz help i’ll give you brainliest
Answers
Answer:
C: 3^0 = 1
Step-by-step explanation:
When dividing two exponents with the same bases, you subtract them
2-2 = 0
so: 3^0 which equals 1
For this specific question there's an even easier way
dividing a number by itself is always gives 1 so it has to be C