The rate of change of this linear function is -2.
What is slope of a line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The formula to find the slope of a line is slope = (y₂-y₁)/(x₂-x₁)
From the given table, (-2, 15), (-4, 23) and (-5, 27).
Substitute, (x₁, y₁)=(-2, 15) and (x₂, y₂)=(-4, 23) in (y₂-y₁)/(x₂-x₁), we get
Rate of change =(23-15)/(-4+2)
= 8/(-2)
= -4
Therefore, the rate of change of this linear function is -2.
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There are 96 people on board a ship.of them,1/4 were females.how many were there?
Answer:
24 or 25%
Step-by-step explanation:
First you do 96x1/4 and you get 24 then you calculate the per senate of it and then you get your answers.
Inez made 6 cups of a taco salad. She separates the salad into 3/4 cup servings. She sells the servings for $1.50 each. If she sells all the servings, how much money will she make?
Answer:She sells each serving for $1.50, so she will make 8 * $1.50 = $<<8*1.5=12>>12 from selling all the servings.
Step-by-step explanation:Inez made 6 cups of taco salad and separates it into 3/4 cup servings, so she has 6 / (3/4) = <<6/(3/4)=8>>8 servings.
She sells each serving for $1.50, so she will make 8 * $1.50 = $<<8*1.5=12>>12 from selling all the servings.
Cell phone Plan A costs $70 per month and comes with a free $500 phone. Cell phone Plan B costs $50 per month but does not come with a phone. If you buy the $500 phone and choose Plan B, how many months is it until your cost is the same as Plan A's? Use the table or write and solve an equation to justify your answer.
The number of months should be 25.
The calculation is as follows:
Plan A: 70x
Plan B: 50x+500
Now we have to make the equivalent equation
70x=50x+500
70x - 50x = 500
20x = 500
x = 25
Therefore we can conclude that The number of months should be 25.
The answer is 25 months.
step by step explanation:
Plan A: 70x
Plan B: 50x+500
the equivalent equation is :
70x=50x+500
70x - 50x = 500
20x = 500
x = 25
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The amount of shampoo that a pet groomer uses per day is proportional to the number of dogs groomed. The pet groomer uses 26.25 ounces of shampoo per day when 7 dogs need to be groomed.
Write an equation to represent this relationship. Express the constant of proportionality as a decimal.
Answer:
This equation shows that the pet groomer uses 3.75 ounces of shampoo per dog.
The relationship between the amount of shampoo used and the number of dogs groomed is proportional. We can represent this relationship with an equation using the form y = kx, where y is the amount of shampoo used, x is the number of dogs groomed, and k is the constant of proportionality.
Given that the pet groomer uses 26.25 ounces of shampoo per day when 7 dogs need to be groomed, we can use this information to find the value of k.
26.25 = k * 7
Solving for k, we get:
k = 26.25/7
k = 3.75
So the equation representing the relationship between the amount of shampoo used and the number of dogs groomed is y = 3.75x
This equation shows that the pet groomer uses 3.75 ounces of shampoo per dog.
[tex]\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{"s"ampoo varies directly with "d"ogs}}{s = k(d)}\hspace{5em}\textit{we also know that} \begin{cases} d=7\\ s=26.25 \end{cases} \\\\\\ 26.25=k(7)\implies \cfrac{26.25}{7}=k\implies 3.75=k~\hfill \boxed{s=3.75d}[/tex]
ANSWER ASAP PLEASE
An apartment building has nine floors and each floor has four apartments. The building owner wants to install
new carpeting in eight apartments to see how well it wears before she decides whether to replace the carpet in
the entire building.
The figure below shows the floors of apartments in the building with their apartment numbers. Only the
nine apartments indicated with an asterisk (*) have children in the apartment.
(a) For convenience, the apartment building owner wants to use a cluster sampling method, in which the floors
are clusters, to select the eight apartments. Describe a process for randomly selecting eight different
apartments using this method.
(b) An alternative sampling method would be to select a stratified random sample of eight apartments, where the
strata are apartments with children and apartments with no children. A stratified random sample of size eight
might include two randomly selected apartments with children and six randomly selected apartments with no
children. In the context of this situation, give one statistical advantage of selecting such a stratified sample as
opposed to a cluster sample of eight apartments using the floors as clusters.
To choose 8 flats at random using the cluster sampling approach, there are thus 36 possible options.
What is random sampling ?(a) Given that there are nine stories in the building, N = nine clusters are assumed. 4 units are found on each floor. 8 flats will be chosen using the cluster sampling technique. By using the cluster sampling approach, a sample of any size n = 2 floors (clusters) will be chosen from the population of N = 9 clusters. To choose 8 flats at random using the cluster sampling approach, there are thus 36 possible options.
(b) In contrast, there is no guarantee that a sample using the cluster sampling method will include both of the characteristics—flats with children and apartments without children—in a representative manner. In the course of this operation, we occasionally obtain floors 3, 4, 6, or 3, 4, which do not contain any of the sample's apartments with children. As a result, the sample will not accurately reflect the population.
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What is the probability range that your data fit the expected 1:1:1:1 ratio of phenotypes?a. p < 0.70b.1.42 < p < 2.37c. p = 0.50d. 0.50 < p < 0.70
The probability range that the data fit the expected 1:1:1:1 ratio of phenotypes is between 0.50 and 0.70.
1. Calculate the observed ratio of phenotypes in the data.
2. Calculate the expected ratio of phenotypes for the data.
3. Calculate the probability of the observed ratio being equal to the expected ratio using the Chi-square test.
4. Calculate the probability range that the data fit the expected 1:1:1:1 ratio of phenotypes.
To calculate the probability range that the data fit the expected 1:1:1:1 ratio of phenotypes, first calculate the observed ratio of phenotypes in the data. Then calculate the expected ratio of phenotypes for the data. Next, calculate the probability of the observed ratio being equal to the expected ratio using the Chi-square test. Finally, calculate the probability range that the data fit the expected 1:1:1:1 ratio of phenotypes, which is between 0.50 and 0.70. This is a measure of how likely it is that the data fit the expected ratio.
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Find the 12th term of the geometric sequence 5, 15, 45, ...
Answer:
Therefore, the 12th term of the geometric sequence 5, 15, 45, ... is 885735.
Step-by-step explanation:
The 12th term of the geometric sequence 5, 15, 45, ... can be found using the general formula for the nth term of a geometric sequence:
an = a1 * r^(n-1)
where:
a1 is the first term of the sequence,
r is the common ratio, and
n is the position of the term that you're trying to find.
In this case,
a1 = 5
r = 15/5 = 3
n = 12
so:
a12 = 5 * 3^(12-1) = 5 * 3^11 = 5 * 177147 = 885735
Therefore, the 12th term of the geometric sequence 5, 15, 45, ... is 885735.
Answer:
12th term = 885735
Step-by-step explanation:
Meaning: A geometric sequence is an ordered set of numbers that progresses by multiplying or dividing each term by the same number.
5 x 3 = 15
15 x 3 = 45
The number we multiply the terms by in this sequence is 3.
4th term = 45 x 3 = 135
5th term = 135 x 3 = 405
6th term = 405 x 3 = 1215
7th term = 1215 x 3 = 3645
8th term = 3645 x 3 = 10935
9th term = 10935 x 3 = 32805
10th term = 32805 x 3 = 98415
11th term = 98415 x 3 = 295245
12th term = 295245 x 3 = 885735
5, 15, 45, 135, 405, 1215, 3645, 10935, 32805, 98415, 295245, 885735
hope this helps :)
You go on a 4-day vacation and bring $84 for spending money. You spend $16 each of the first 3 days. Write a linear function that describes the amount of money, a, that you have after d days. On the last day, you want to buy a sweatshirt that costs $38. Do you have enough money to buy the sweatshirt?
The linear function that describes the amount of money left is f(a) = $84 - $48 . You would not have enough money to buy the sweatshirt.
Will you have enough money to buy the sweatshirt?A linear function is a function that has a single variable raised to the power of 1. An example of a linear function is x + 2. The variable x is raised to the power of 1. 2 is the constant terms
The form of the linear function is : a = amount taken on vacation - (amount spent each day x number of days)
f(a) = $84 - (3 x 16)
f(a) = $84 - $48
f(a) = $36
You would not have enough money to buy the sweatshirt because the sweatshirt costs more than the amount have left.
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A Type II error is committed when
A. we reject a null hypothesis that is true
B. we don't reject a null hypothesis that is false
C. we reject a null hypothesis that is false
D. we don't reject a null hypothesis that is true
Type II error is committed option B. we don't reject a null hypothesis that is false.
What is Null Hypothesis?When we are testing a hypothesis, we first assume that there is no difference in the means or there is no relationship between the population. This assumption is called null hypothesis.
There is also another hypothesis paired to null hypothesis which is called alternative hypothesis which is the assumption opposite to the null hypothesis.
There are two types of errors for hypothesis testing, which are Type I error and Type II error.
Type I error happens when you reject a null hypothesis that is true. That is, you get false positive results.
Type II error happens when you don't reject a null hypothesis that is false. That is, you get false negative results.
Hence Type II error is formed when you don't reject a null hypothesis that is false.
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What type of discontinuity is an asymptote?
A removable discontinuity is a type of discontinuity in a graph that results in a break in the graph and can be fixed by filling in a single point of the graph.
A removable discontinuity is a type of discontinuity in a graph that results in a break in the graph and can be fixed by filling in a single point of the graph. An asymptote is a type of removable discontinuity where the graph approaches, but does not reach, a set value or line. The equation of the asymptote can be determined by setting the denominator of the function to zero and solving for the x-value. Once the equation of the asymptote is known, it can be used to fill in the break in the graph, thus removing the discontinuity.
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Vertical type of discontinuity is an asymptote.
The term discontinuity in math is defined as the function of the graph which is not connected with each other
Here we have to identify the type of discontinuity is an asymptote
While we looking into the definition of discontinuity, we have identified that this is a special type of discontinuity where the function is still undefined, but here we use instead of a hole in the graph or jump discontinuity, and the function that approaches positive or negative infinity.
This type of asymptote is also know as essential discontinuity occurs when the curve has a vertical asymptote and this is also called an infinite discontinuity.
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To rent movies from the store,a person has to pay an annual membership fee of 20 dollars plus 2.50 dollars for each movie rented
Answer:
See below
Step-by-step explanation:
Are you asking for the equation?
y = 2.5x + 20
y = the total cost
x = number of movies.
what is the function type ?
explain your reasoning
help please
the proportions are the same the function is linear.
What is a function?
A function is a special form of relation where each input has exactly one output. In other words, for each input value, the function returns exactly one value. A relation rather than a function is depicted in the above graph since one is mapped to two different values. However, if one were instead mapped to a single value, the relationship described above would change into a function. Furthermore, output values could match input values exactly.
The function machine receives the x-values as input. After finishing its operations, the function machine produces the y-values. Any function may be the one within.
Given table of data x and f(x)
the proportion -3/1, -3/1, -3/1...
As the proportions are the same the function is linear.
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How do you find the relationship in a scatter plot?
If the points cluster in a band running from lower left to upper right, there is a positive correlation (if x increases, y increases).
A scatterplot is a type of data display that shows the relationship between two numerical variables and a graphical representation of individual scores on two variables.
Each member of the dataset gets plotted as a point whose (x, y) left parenthesis, x, comma, y, and right parenthesis coordinates relate to its values for the two variables.
The values of one variable appear on the horizontal axis and the values of the other variable appear on the vertical axis.
There are some objectives to construct a scatter plot:
• First we have to construct and interpret a scatter plot or line graph for two quantitative variables
• Next, recognize linear relationships, non-linear relationships, or independence between two quantitative variables
• After that decide whether a linear relationship is negative or positive and whether the linear relationship appears strong or weak
• To construct and interpret a line graph for displaying changes over time of a quantitative variable
• finally, describe changes over time of a quantitative variable with an index number.
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2 3
When selecting a conference, identify a key factor to help make your decision.
a. dates
c.
b. people
d.
Please select the best answer from the choices provided
OA
B
OD
climate
all of the above
Mark this and return
Save and Exit
Next
57:51
Submit
Answer:
Step-by-step explanation:
B people
Engineers and architects often use transformed shapes to design objects or structures. Analyze a building or structure around you, and describe the transformations that you see using geometric vocabulary. How does the transformed shape contribute to the design of the object?
Transformed shapes contribute to the design of objects by making them more efficient to get the most out of their characteristics.
What is architecture?Architecture is a term to refer to the technique of projecting, designing and building, modifying the human habitat based on the proper use and function of spaces.
Engineering is a term for the use of scientific principles to design and create machines, structures, and other objects.
These two disciplines use modified shapes to design and build objects and structures, that is, they take geometric shapes and make modifications to them to get the most out of an element as needed.
For example, engineers and architects who design and build a house must modify the geometric figures of the square, rectangle and triangle to make their spaces with:
Appropriate amplitude, The most efficient lighting and Their roof is inclined so that on days of rain the water rolls to the sides of the house.
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ray insisted on buying a fancy new sports car, even though the day after he purchased it, the car lost 25% of its value. months later, when the center for auto safety reported that ray's car model had a "sudden acceleration defect", his car's value went down by another 50%. If Ray's car is now worth $18750, how much did he pay for it
The amount Ray paid for the car is at a value of $50000
What is percentage decrease in value?Percentage decrease is the difference between starting and ending values. It shows a loss of value from the original expressed as a percentage regardless of units. The amount of decrease is the original amount minus the final amount.
Let's represent the price ray bought the car by x
It loses its value by 25% firstly. This means that 25/100 × x = 25x/100
the new value of the car = x - 25x/100 = 75x/100
It later losses 50% of its value. This means that 50/100× 75x/100 = 75x/200
The new value of the car = 75x/100 - 75x/200
= $18750
multiply all terms by 200
150x - 75x = 3750000
75x = 3750000
divide both sides by 75
x = 3750000/75
x = $50000.
Therefore Ray bought the car at $50000
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Use the distributive property to re-write the expression to make it simpler to solve. Then solve the expression. 1. 18-9 + 18-91
Answer:
Using the distributive property to re-write the expression, 18 - 9 + 18 - 91 = 18 - (9 + 91) = 18 - 100 = -82 Therefore, the solution to the expression is -82.
You are traveling from Milwaukee (9, 17) to St. Louis (7, 10). Each unit on the map is 50 miles. How many miles did you travel? Round your answer to the nearest tenth.
Answer:
364 miles
Step-by-step explanation:
You want to know the distance from (9, 17) to (7, 10) if each unit on the map represents 50 miles.
DistanceThe map distance can be found using the distance formula:
d = √((x1 -x1)² +(y2 -y1)²)
d = √((7 -9)² +(10 -17)²) = √((-2)² +(-7)²) = √53 ≈ 7.28011
Ground DistanceThe distance on the ground is 50 miles for each map unit, so is ...
(50 mi)(7.28011) = 364.0055 ≈ 364.0
You travel about 364.0 miles.
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Which equation is a slope-intercept form equation for the line AB?
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The equation y = -2/3x + 1/2 is in slope-intercept form.
What is the slope intercept?
The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line. An example of a linear equation is y=mx + b.
A relationship that when graphed produces a straight line. Equation. A mathematical sentence that sets 2 expressions equal to each other.
It has the variable y on one side of the equation and the slope (-2/3) and y-intercept (1/2) are easily identifiable.
This is the equation of line AB.
Hence, the equation y = -2/3x + 1/2 is in slope-intercept form.
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Which decimal below is equivalent to
5/9?
Answer: I do not see the answers but a correct decimal would be 0.5555555555555556
Step-by-step explanation: using a calculator you can put in 5 divided by 9 and it will give you the decimal
Answer:
The answer to your question is 0.56
Solution: 5/9 as a decimal is 0.56.
Step-by-step explanation:
I hope this helps and have a wonderful day!
PLEASE I NEED HELP NOW!!! WHICH LINEAR GRAPH REPRESENTS A PERPORTINAL RELATIONSHIP? A graph of a straight line that passes through the points 0 comma 1 and 3 comma 0. A graph of a straight line that passes through the points 0 comma 0 and 1 comma 2. A graph of a straight line that passes through the points 0 comma negative 4 and 1 comma negative 4. A graph of a straight line that passes through the points 1 comma 0 and 1 comma 1.
A linear graph represents a proportional relationship include the following: C. A graph of a straight line that passes through the points 0 comma negative 4 and 1 comma negative 4.
What is a graph?In Mathematics, a graph can be defined as a type of chart that is typically used to graphically represent data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis (x-coordinate) and y-axis (y-coordinate) respectively.
Generally speaking, the graph of any proportional relationship is always characterized by a straight line with the data points starting from the origin (0, 0) and passes through other unique data points on the cartesian coordinate.
In this context, we can reasonably infer and logically deduce that a graph of a straight line that passes through the data points (0, -4) and (1, -4) represents a proportional relationship because it would go through the origin (0, 0).
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Please help me finish this question
Answer:
Step-by-step explanation:
You need to look carefully at the inequality signs in the first question. Thew amount of pillowcases she buys needs to be AT LEAST 10, but the maximum amount of money she can spend is 100. So I think C would be the best answer.
Answer:
C and then D
Step-by-step explanation:
s = number of small pillow cases
l = number of large pillow cases
s + l >= 10 (but at least 10 cases)
8s + 12l <= 100 (cannot spend more than $100)
remember, every small pillow case costs $8, every large $12.
so, answer C.
8×12 + 3×8 = $120
so, that's not possible.
4×12 + 7×8 = 48 + 56 = $104
so, that's not possible.
6×12 + 3×8 = 72 + 24 = $96
that would work but
6 + 3 = 9 which is not >= 10
so, that's not possible.
2×12 + 9×8 = 24 + 72 = $96
2 + 9 = 11
so, that (D) is a valid solution.
Lines X and Y are parellel lines cut by transversal , A.In 1-5 identify the type of angle relationship shown in the following pairs of angles
1. Angles and Angle 8
2. Angle 6 and Angle 7
3. Angle 8 and angle 4
4. Angle 3 and angle 5
5. Angle 1 and angle 5
Question 2
Using the picture above identify whether the following pairs of angles are congruent or supplementary
1. < 1 and <5
2. <4 and <5
3. <3 and <5
The type of angle relationship shown in the given pairs of angles are,
1. ∠1 and ∠8 - alternate exterior angles
2. ∠6 and ∠7 - alternate exterior angles
3. ∠8 and ∠4 - corresponding angles
4. ∠3 and ∠5 - same side interior angles
5. ∠1 and ∠5 - corresponding angles
What is transversal?
A line that crosses two lines in the same plane at two different geometric locations is referred to as a transversal. The angles that result from a transversal intersection of two lines in pairs can be consecutive interior angles, corresponding angles, or alternate angles.
From the given figure we have to find the type of angle relationship.
1. ∠1 and ∠8
∠1 and ∠8 are the alternate exterior angles, lie on the opposite sides of the transversal A, between lines X and Y.
2. ∠6 and ∠7
∠6 and ∠7 are also alternate exterior angles.
3. ∠8 and ∠4
∠8 and ∠4 are corresponding angles, lie on the same side of the transversal A, on the same sides of lines X and Y.
4. ∠3 and ∠5
∠3 and ∠5 are same side interior angles, or consecutive interior angles lie on the same side of the transversal A, between lines X and Y.
5. ∠1 and ∠5
∠1 and ∠5 are corresponding angles, lie on the same side of the transversal A, on the same sides of lines X and Y.
Hence, the type of angle relationship shown in the given pairs of angles are,
1. ∠1 and ∠8 - alternate exterior angles
2. ∠6 and ∠7 - alternate exterior angles
3. ∠8 and ∠4 - corresponding angles
4. ∠3 and ∠5 - same side interior angles
5. ∠1 and ∠5 - corresponding angles
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To find the total amount that has to be paid back after interest is charged what operation do you use?
To find the total amount to be paid back after interest, we use the operation A = P+I
What is amount ?Simple Interest (S.I.) is the method of calculating the interest amount for a particular principal amount of money at some rate of interest.
For example if a company borrows a loan of $50,000,000 at 10% per annum. The simple interest per year is calculated as : S.I = (P×R×T)/100.
Where R is the rate
P is the principal
and T is the duration
The Interest paid by the company = 50,000,000×10×1/100 =$ 5,000,000
The total amount of money the company will refund = Principal + interest
= 50,000,000+5,000,000
= 55,000,000
Therefore the total amount is calculated as A = P+I
Where A is the total amount
I is the interest and P is the principal.
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Tina earned $60 baby sitting over the weekend for a total of 5 hours. What was her average rate per hour?
Tina's average rate per hour was $12.
the critical value of t for a two-tailed test with 6 degrees of freedom using α = .05 is
a. 1.943
b. 2.447
c. 1.985
d. 2.365
The critical value of t for a two-tailed test with 6 degrees of freedom using α = .05 is b. 2.447.
How to find the critical value ?The critical value of t for a two-tailed test with 6 degrees of freedom using a significance level (α) of .05 can be found using a t-distribution table. In this case, the critical value of t would be approximately 2.447.
This means that if the calculated t-value from your experiment is greater than 2.447 in either direction (positive or negative), it would indicate that the null hypothesis can be rejected and that there is a statistically significant difference between the means of the groups being compared.
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A p-chart is used to monitor A) average shrinkage. B) dispersion in sample data. C) the fraction defective. D) the number of defects per unit. E) the range of values.
A p-chart is used to monitor the fraction defective.
A p-chart is a type of control chart used to monitor the proportion of nonconforming units in a sample. It is used when the sample size is constant and the process is in statistical control.
It plots the proportion of nonconforming units in each sample on the y-axis and the sample number on the x-axis.
The chart can be used to detect changes in the process and to determine if the process is in control. It can also be used to estimate the process capability and to identify the causes of nonconformities.
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Could someone please help. please help asap I need it. see picture...
find the x- and y-intercepts
and write The equation in standard form with integer coefficients
The x-intercept is 5 and the y-intercept is 2.
The standard form of the line is 2x + 5y = 10.
How to find the x-intercept, y-intercept and equation in standard form?The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis. In other words, the x -intercept is the value of x when y = 0 and the y-intercept is the value of y when x = 0.
Hence, the x-intercept is 5 and the y-intercept is 2.
Let's find the equation in standard form.
Ax + By = C
where
A, B and C are constantUsing slope intercept form,
y = mx + b
where
m = slopeb = y-interceptHence, using (5, 0) and (0, 2)
m = 2 - 0 / 0 - 5
m = - 2 / 5
Therefore.
y = - 2 / 5x + 2
Hence, let's multiply through by 5 to eliminate the fraction
5y = -2x + 10
Therefore, the standard form is as follows:
2x + 5y = 10
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Mr.Brown is throwing the entire class a pizza party (not really, keep reading)! When he places the order from Tony's pizza across the street, he learns that each medium pizza has 6 slices, and each large pizza has 8 slices. If Mr.Brown orders 9 total pizzas with a total of 66 slices, how many of each size pizza did he buy? Let x represent the number of medium pieces and let y represent the number of large pizzas.
The number of medium and large pieces of pizza Mr Brown ordered is 3 and 6 respectively.
How to solve simultaneous equation?Let
number of medium pieces = x
number of large pizzas = y
Number of slices in a medium pizza = 6
Number of slices in a large pizza = 8
Total pizzas ordered = 9
Total number of slices = 66
The simultaneous equation can be written as follows;
x + y = 9
6x + 8y = 66
From (1)
x = 9 - y
Substitute into (2)
6x + 8y = 66
6(9 - y) + 8y = 66
54 - 6y + 8y = 66
2y = 66 - 54
2y = 12
divide both sides by 2
y = 12/2
y = 6
Substitute y = 6 into (1)
x + y = 9
x + 6 = 9
x = 9 - 6
x = 3
In conclusion, Mr Brown ordered 3 pieces of medium and 6 pieces of large pizza.
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The postage for a first class letter weighing 1 ounce or less is $.47 each additional ounce is $.21 the maximum weight of a first class letter is 3 1/2 ounces write a function to represent the situation
f(x) = 0.47x + 0.21(x-1), where x ≤ 3.5
