The coordinate points of x and Y of the given system of equations is x= -1 and Y = 1.
The system of equations are,
Y= -3x-2 _____ (1)
Y= -6x-5 _____ (2)
Solving the given system of equations by applying elimination method,
Multiplying equation (1) by 2 and equation (2) by 1, we get,
2Y= -6x-4 _____ (3)
Y= -6x-5 _____ (4)
Subtracting equation (4) from equation (3), we get,
2Y - Y = ( -6x-4 ) - ( -6x-5)
⇒Y = -6x - 4 + 6x + 5
⇒Y = 1
Putting Y= 1 in equation (1), we get,
1 = -3x - 2
⇒ -3x = 1 +2
⇒ -3x = 3
⇒ x = -3/3
⇒ x = -1
Hence the coordinate points of x and Y are -1 and 1 respectively.
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the equation that describes how the dependent variable (y) is related to the independent variable (x) is called . a. the correlation model b. correlation analysis c. the least squares criterion d. the regression model
The equation that describes how the dependent variable (y) is related to the independent variable (x) is called the regression model (option d).
How to identify the equation?Regression is a statistical method used to analyze the relationship between a dependent variable and one or more independent variables. The regression model estimates the relationship between the dependent variable and the independent variable(s) and can be used to predict the value of the dependent variable for a given value of the independent variable(s).
The regression model is based on the least squares criterion (option c), which is a method used to find the best-fit line through a set of data points. The best-fit line is the one that minimizes the sum of the squared differences between the observed values of the dependent variable and the predicted values from the regression model.
Correlation analysis (option b) is a method used to measure the strength and direction of the relationship between two variables. Correlation analysis does not provide information about the nature of the relationship or allow for prediction.
The correlation model (option a) is not a commonly used term in statistics. However, it could refer to a model that estimates the correlation between two variables or a model that uses correlation as a predictor variable.
In summary, the equation that describes how the dependent variable (y) is related to the independent variable (x) is called the regression model, which is based on the least squares criterion.
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1. In Design 2, what is the radius of the larger
grassy area?
Answer: 5 m
Step-by-step explanation:
A radius is half of the diameter which is the black line. Hope this helps!
Answer:
The radius of the larger grass area is 5m
Step-by-step explanation:
d=2r
r=d/2
r=10/2
r=5m
Write an equation to match this graph.
The equation that matches the given graph can be represented by y = x + 7 , on the basis of coordinates of five different points on cartesian-plane.
What is a cartesian-plane?
A two-dimensional coordinate plane known as the cartesian plane is created when the x- and y-axes connect. The origin is the point at where the x- and y-axes cross perpendicularly. The x-coordinate and y-coordinate are the coordinates for each point on this plane. The ordinate and abcissa are other names for the x- and y-coordinates, respectively.
The points through which the given graph passes are:
(2,9) ; (3,10) ; (4,11) ; (5,12) and (6,13)
In (2,9): x=2 and y=9
y-x=7
In (3,10): x=3 and y=10
y-x=7
In (4,11): x=4 and y=11
y-x=7
In (5,12): x=5 and y=12
y-x=7
In (6,13): x=6 and y=13
y-x=7
∴ we can say that the difference of x and y coordinates in each point is 7
y-x=7
y=7+x
The required equation of the graph: y = x + 7
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what is the simplified product of 2/9 x 3/8
A. 6/72. B. 5/17. C. 3/36. D.1/12
Answer:
[tex] \frac{2}{9} \times \frac{3}{8} = \frac{6}{72} = \frac{1}{12} [/tex]
D is the correct answer.
r^{2} =8 solving equations using square roots
Answer:
[tex]r=\pm\,2\sqrt2[/tex]
Step-by-step explanation:
Given the equation:
[tex]r^2=8[/tex],
we can solve for [tex]r[/tex] by taking the square root of both sides.
[tex]\sqrt{r^2}=\pm\sqrt{8}[/tex]
But, we must remember the even root property, which states that if [tex]x^2 = a[/tex], where [tex]a[/tex] is a non-negative real number, then [tex]x = \pm \sqrt a[/tex], because both [tex](-a)^2[/tex] and [tex]a^2[/tex] result in [tex]a[/tex].
______________
For example, if you want to find the square root of 25, you know that 5 × 5 = 25, so [tex]\sqrt{25}[/tex] = 5. However, (-5) × (-5) also equals 25, so (-5) is also a valid solution for [tex]\sqrt{25}[/tex].
‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾
[tex]r=\pm\sqrt{8}[/tex]
Now, we can simplify the square root by prime factoring it.
[tex]r=\pm\sqrt{2 \cdot 2\cdot2}[/tex]
We can see that there is one complete pair of 2's, so we can take those out of the square root.
[tex]\boxed{r=\pm\, 2\sqrt2}[/tex]
Sally invested some money into a savings account that earns 7.2%
annual simple interest. At the end of 9 years, she earned $745.20 in
interest. How much money did she put into the account initially?
Round to the nearest dollar.
Sally would have invested $1150 initially in the savings account to satisfy the conditions in the question.
What is a savings account?A savings account is a type of bank account that helps people save money over time. It offers a safe and secure way to store money while earning interest on the balance. Unlike checking accounts, savings accounts are intended for long-term storage of funds, with a higher interest rate and regular compounding to help the balance grow. Savings accounts offer flexibility in terms of access to funds and usually allow withdrawals at any time with limits on the number of withdrawals without incurring a fee.
To determine how much money Sally initially invested in a savings account that earns 7.2% annual simple interest, we can use the formula for simple interest: I = Prt. Here, I represents the interest earned, P is the initial principal, r is the annual interest rate as a decimal, and t is the time in years.
Given that Sally earned $745.20 in interest over a period of 9 years with an annual interest rate of 7.2%, we can substitute the values into the formula and solve for P:
I = $745.20
r = 7.2% = 0.072 (decimal)
t = 9 years
Now, P = I / (rt)
P = 745.20 / (0.072 * 9)
P = $1150
Therefore, Sally initially invested $1150 in the savings account.
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Please help this is homework the answers currently in it are wrong it’s also wrong if you round them to the tenth place
Check the picture below.
minimum of [tex]\frac{a}{b+c} + \frac{b}{c+a} + \sqrt{} \frac{2c}{a+b}[/tex]
The minimum of the given expression can be found to be 3 x ∛(√2).
How to find the minimum ?Use these inequalities to find the minimum of the given expression:
(a / (b + c)) + (b / (c + a)) + √(2c / (a + b)) ≥ (a / (√(bc))) + (b / (√(ac))) + √(2c / (√(ab)))
Now, simplify the expression:
(a / (√(bc))) + (b / (√(ac))) + √(2c / (√(ab))) = (√(a²/bc)) + (√(b²/ac)) + (√(2c²/ab))
Apply AM-GM inequality to the terms (√(a²/bc)), (√(b²/ac)), and (√(2c²/ab)):
AM = [(√(a²/bc)) + (√(b²/ac)) + (√(2c²/ab))] / 3 ≥ GM = ∛[(√(a²/bc)) * (√(b²/ac)) * (√(2c²/ab))]
The geometric mean (GM) is:
GM = ∛[(√(a²/bc)) x (√(b²/ac)) x (√(2c²/ab))]
GM = ∛(√(2a²b²c² / a²b²c²))
GM = ∛(√2)
Thus, the minimum of the given expression is:
= 3 x ∛(√2)
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all probabilities can be expressed as decimal values ranging from 0.00 to 1.00.
The answer to the given question after considering the two options is true under the condition all probabilities can be expressed as decimal values ranging from 0.00 to 1.00.
Probability is also known as the estimation of possible changes of a particular event taking place. Furthermore, it is important while dealing with calculations in the branch of science and mathematics. It is useful in eliminating the total changes of systematic errors, which are hampering the research population.
Some examples of probability
The probability on the event of rolling a 4 with a die is 1/6.
The probability of getting a tails while tossing a coin is 1/2.
The probability of getting one joker from a deck of cards is 1/51.
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The complete question is
All probabilities can be expressed as decimal values ranging from 0.00 to 1.00. True or False
Yes, it is true that all probabilities can be expressed as decimal values ranging from 0.00 to 1.00.
This is because probabilities represent the likelihood of an event occurring, and the probability of an event can range from impossible (0.00) to certain (1.00). Therefore, probabilities are expressed as decimal values between these two extremes.
Hi! Yes, all probabilities can be expressed as decimal values ranging from 0.00 to 1.00. A probability of 0.00 represents an impossible event, while a probability of 1.00 represents a certain event. Values between these two extremes indicate varying levels of likelihood for the event to occur.
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6) What is the measure of angle bpc?
if 76x−11=72x 1, what is the value of x?
Answer:
The answer that you're looking for is x = 3
Step-by-step explanation:
You start with the equation:
76x-11=72x+1
You then want to separate the variables and constants so you do the inverse of positive 72 which is to subtract 72x from each side.
(76x-72x)-11=(72x-72x)+1
4x-11=1
After that, you add the inverse of -11 which is adding 11 to both sides to leave 4x by itself.
4x(-11+11)=(1+11)
4x=12
You then finally divide 4 by both sides giving you x = 3 as the final answer.
4x/4=12/4
x = 3
ANSWER ASAP
Question 11
The number of carbohydrates from 10 different tortilla sandwich wraps sold in a grocery store was collected.
Which graphical representation would be most appropriate for the data, and why?
Circle chart, because the data is categorical
Line plot, because there is a large set of data
Histogram, because you can see each individual data point
Stem-and-leaf plot, because you can see each individual data point
Question 12
The line plots represent data collected on the travel times to school from two groups of 15 students.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 10, 16, 20, and 28. There are two dots above 8 and 14. There are three dots above 18. There are four dots above 12. The graph is titled Bus 14 Travel Times.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 8, 9, 18, 20, and 22. There are two dots above 6, 10, 12, 14, and 16. The graph is titled Bus 18 Travel Times.
Compare the data and use the correct measure of center to determine which bus typically has the faster travel time. Round your answer to the nearest whole number, if necessary, and explain your answer.
Bus 14, with a median of 14
Bus 18, with a mean of 12
Bus 14, with a mean of 14
Bus 18, with a median of 12
Question 13
The line plot displays the number of roses purchased per day at a grocery store.
A horizontal line starting at 1 with tick marks every one unit up to 10. The line is labeled Number of Rose Bouquets, and the graph is titled Roses Purchased Per Day. There is one dot above 1 and 2. There are two dots above 8. There are three dots above 6, 7, and 9.
Which of the following is the best measure of variability for the data, and what is its value?
The range is the best measure of variability, and it equals 8.
The range is the best measure of variability, and it equals 2.5.
The IQR is the best measure of variability, and it equals 8.
The IQR is the best measure of variability, and it equals 2.5.
Question 14
Chipwich Summer Camp surveyed 100 campers to determine which lake activity was their favorite. The results are given in the table.
Lake Activity Number of Campers
Kayaking 15
Wakeboarding 11
Windsurfing 7
Waterskiing 13
Paddleboarding 54
If a circle graph was constructed from the results, which lake activity has a central angle of 39.6°?
Kayaking
Wakeboarding
Waterskiing
Paddleboarding
A histogram would be the most appropriate graphical representation for the data, as it shows the frequency distribution of continuous numerical data. It would allow for the visualization of the distribution of the number of carbohydrates in the tortilla sandwich wraps, including the range and frequency of the data.
How to explain the informationIt should be noted that to determine which bus typically has the faster travel time, we need to compare the measures of center (mean and median) for each bus. The median of Bus 14 is 14, and the median of Bus 18 is 12. Therefore, Bus 14 typically has the faster travel time.
The best measure of variability for the data is the range, which is the difference between the highest and lowest values. In this case, the range is 8 (9-1), as the highest value is 9 and the lowest value is 1.
To determine which lake activity has a central angle of 39.6°, we need to convert the number of campers for each activity into a percentage of the total number of campers (100). Then, we can calculate the central angle for each activity using the formula: central angle = percentage/100 * 360.
The percentages and central angles for each activity are:
Kayaking: 15% (54 degrees)
Wakeboarding: 11% (39.6 degrees)
Windsurfing: 7% (25.2 degrees)
Waterskiing: 13% (46.8 degrees)
Paddleboarding: 54% (194.4 degrees)
Therefore, the lake activity with a central angle of 39.6° is Wakeboarding.
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Find the value of $x$ .
Two chords of a circle intersect each other. In first chord, the length of longer segment is 18 units and shorter segment is 10 units. In second chord, the length of shorter segment is 9 units and longer segment is labeled x minus 3.
$x\ =\ $
The value of x for the given chords is 23.
What is a chord?A circle's chord is the line segment that connects any two locations on the circle's circumference. It should be remembered that a circle's diameter is defined as the lengthiest chord that runs across the centre of the circle. In the illustration below, a circle and its chord are shown. At the circle's centre, chords with identical lengths subtend equal angles.
We know that, the product of the lengths of the segments of one chord, when two chords cross inside a circle, equals the product of the lengths of the segments of the other chord.
Thus,
(18)(10) = (9)(x - 3)
180 = 9x - 27
9x = 207
x = 23
Hence, the value of x for the given chords is 23.
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2. when conducting a hypothesis test, the hypothesis that illustrates what we really think is going on in the population is called the hypothesis. an. analytical b. hypothetical c. null d. theoretical e. alternative
Select the correct answer from the drop-down menu. The value from the set {10, 11, 12, 13} that makes the equation 2(x − 5) = 12 true is .
Answer:your answer is 11
Step-by-step explanation:
Rewrite the fraction in the sentence below as a percentage.
In a certain class, 13/50 of the students got problem 10 wrong on Friday's math test.
What's the percent notation?
Answer:
[tex] \frac{13}{50} = \frac{26}{100} = 26\%[/tex]
the list shows the weight in pounds of 6 puppies at birth. 3, 1.6, 2.8, 2.5, 1.7, 2.8 what is the mean absolute deviation of these numbers?
Si un editor pone un precio de $16 a un libro, se venderán 10,000 copias. Por cada dólar que aumente al precio se dejarán de vender 300 libros. ¿Cuál debe ser el precio al que se debe vender cada libro para generar un ingreso total por las ventas de $124,875?
The price of each book must be either $38.53 or $10.8 to generate a total sales revenue of $1,24,875.
If the prices of a book is $16 then 10000 copies will be sold.
For every dollar that increase in price, 300 books will not be sold.
So if the price of a book increases $x then the total price of sold books is given by,
y = (16 + x)*(10000-300x)
Now total sales revenue of the books is $124875, that is, y = 124875.
So, (16+x)*(10000-300x) = 124875
160000 + 10000x - 4800x - 300x² = 124875
35125 + 5200x - 300x² = 0
25 (1405 + 208x - 12x²) = 0
12x² - 208x - 1405 = 0
Solving the above quadratic equation we get,
x = 22.53 or x = -5.20 (Rounding to two decimal places)
So the amount will be either (16+22.53) = $38.53 or (16-5.20) = $ 10.8.
Hence the price must be either $38.53 or $10.8.
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The translation of the question is -
"If a publisher prices a book at $16, 10,000 copies will be sold. For every dollar that increases in price, 300 books will not be sold. What must be the price each book must sell for to generate a total sales revenue of $124,875?"
Aidan wants to find the mass of a
bowling ball.Which unit should he use
Answer:
Aiden should use the Standard unit of Mass
Kilogram.
Step-by-step explanation:
He can use other unit also like gram, pound, ounce, tone etc
2 out of 7 questions. PLEASE help me.
The measure of arc angle KL is determined as 128⁰.
The measure of angle KJL is 26⁰
What is the measure of arc KL?The measure of arc angle KL is calculated by applying the following formula.
The intersecting chord theorem, also known as the intersecting chords inside and outside theorem, is a geometric property that applies to chords (line segments that connect two points on the circumference of a circle) that intersect inside or outside a circle.
Based on the angle of intersecting chord theorem, we will have the following equation.
m∠KML = ¹/₂( arc angle KL )
64 = ¹/₂ KL
KL = 2 x 64
KL = 128⁰
The measure of angle KJL is calculated as follows;
m∠KJL = ¹/₂ (180 - 128) = 26⁰
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1. The temperature during a blizzard is -12°F.
Which scenario would combine to make zero?
A) The weather drops another 12°F
The weather rises 12°F
The weather drops another -12°F
The weather rises another -12°F
B)
C)
()
Answer:
The answer is Rises 12F
Step-by-step explanation:
-12 degrees is 12 below zero. To reach zero, you have to go up an equal amount. -12 + 12 = 0
a card is selected from a deck of 52 cards. what is the probability that it is a queen? what are the odds in favor
Step-by-step explanation:
There are FOUR queens in a deck of 52 cards
4/52 chance of selecting a queen = 1/13 chance = .07692 chance
Michael draws a straight line on a graph that passes through the point (0,
3).
Choose the equation that best fits Michael's line.
B.
A
y = x - 3
C. y = 3x
D.
y = x + 3
y = 3x +1
its b so please mark me as a brainliest
Write the log equation as an exponential equation. You do not need to solve for x.
ln(4x+8)=x+5
^ equation you need to rewrite
Answer: 3x=-3
Step-by-step explanation:
a customer spends 21.50 on cupcakes and muffins. the numbet of muffins purchased is 1 few than number of cupcakes. each cupcake costs $2, and each muffin cost $1.25 create a system of equations
Answer: Let's use the following variables to represent the unknown quantities in the problem:
x: the number of cupcakes purchased
y: the number of muffins purchased
From the problem statement, we can write two equations:
The total amount spent on cupcakes and muffins is $21.50:
2x + 1.25y = 21.50
The number of muffins purchased is one fewer than the number of cupcakes:
y = x - 1
These two equations form a system of equations that can be solved simultaneously to find the values of x and y.
Substituting equation 2 into equation 1, we get:
2x + 1.25(x - 1) = 21.50
Simplifying and solving for x:
2x + 1.25x - 1.25 = 21.50
3.25x = 22.75
x = 7
Now that we know x, we can use equation 2 to find y:
y = x - 1 = 7 - 1 = 6
Therefore, the customer purchased 7 cupcakes and 6 muffins, spending a total of $21.50.
Step-by-step explanation:
The eigenvalues of a matrix A are the same as the eigenvalues of the reduced row echelon form of A.TRUE/FALSE
False, The eigenvalues of a matrix A are not same as the eigenvalues of the reduced row echelon form of A.
A matrix's eigenvalues are not the same as those of the matrix's reduced row echelon form, contrary to what is claimed.
This is due to the fact that when a matrix is reduced to its echelon form via row operations, its eigenvalues may not always stay the same. The eigenvalues of a matrix may be different in the reduced row echelon form than they are in the original matrix as a result.
Think about these matrices as an illustration:
Likewise, B's reduced row echelon form is B, and B's eigenvalues are both 1.
A = [1 2; 2 1]
and
B = [1 0; 0 1].
The eigenvalues of a matrix and its reduced row echelon form are thus typically not the same.
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FALSE. The eigenvalues of a matrix A are NOT the same as the eigenvalues of the reduced row echelon form of A.
Explanation:
Eigenvalues are scalar values that, when multiplied by an eigenvector, produce the same effect as the original matrix A on that eigenvector. Mathematically, for a matrix A and its eigenvector v, Av = λv, where λ is the eigenvalue.
Row echelon form is a matrix transformation using elementary row operations to obtain a triangular form. The reduced row echelon form (RREF) is a further simplified version of the row echelon form.
However, transforming a matrix A to its RREF changes the properties of the matrix, and therefore the eigenvalues of matrix A and its RREF are generally not the same. The eigenvalues are preserved only under specific matrix transformations, such as similarity transformations, which row echelon form is not one of them.
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Simplify. 11 3/4-8 1/2
Therefore, 11 3/4 - 8 1/2 = 13/4, or 3 1/4 as a mixed number.
What is mixed number?A mixed number is a type of number that represents a whole number and a fraction together. It is written in the form of a whole number followed by a fraction, such as 3 1/2. The whole number represents the number of whole units, while the fraction represents the part of a unit.
For example, the mixed number 3 1/2 can be interpreted as three whole units and one half of a unit. Another example of a mixed number is 2 3/4, which represents two whole units and three-quarters of a unit. Mixed numbers are commonly used in everyday life, such as in cooking and measuring, and in mathematical calculations involving fractions.
To subtract mixed numbers like these, we need to convert them to improper fractions first:
[tex]11 3/4 = (4 * 11 + 3)/4 = 47/4[/tex]
[tex]8 1/2 = (2 * 8 + 1)/2 = 17/2[/tex]
Now, we can subtract the fractions:
[tex]47/4 - 17/2[/tex]
To subtract these fractions, we need to find a common denominator. The least common multiple of 4 and 2 is 4 × 2 = 8. We can convert both fractions to have a denominator of 8:
[tex]47/4 = (47/4) * (2/2) = 94/8[/tex]
[tex]17/2 = (17/2) * (4/4) = 68/8[/tex]
Now, we can subtract the numerators:
[tex]94/8 - 68/8 = 26/8[/tex]
Finally, we can simplify the result by dividing both numerator and denominator by their greatest common factor, which is 2:
[tex]26/8 = (2 * 13)/(2 * 4) = 13/4[/tex]
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The orbital period, P, of a planet and the planet’s distance from the sun, a, in astronomical units is related by the formula P = a Superscript three-halves. If Saturn’s orbital period is 29. 5 years, what is its distance from the sun?
9. 5 AU
19. 7 AU
44. 3 AU
160. 2 AU
If the orbital period of Saturn is 29.5 years then the distance of Saturn from the sun is 9.5 AU .
The orbital period of a planet is denoted as P.
A planet's distance from the sun in astronomical units is denoted as a.
The relation between orbital period of a planet and it's distance from the sun is given as,
P = a superscript three halves
or, P = a^3/2
The Saturn's orbital period is P= 29.5 years
Thus from the equation showing the relation between orbital period of a planet and it's distance from the sun in AU (astronomical units ) we get,
29.5 = a^3/2
or, a^3/2 = 29.5
⇒ [tex]\sqrt{a^3}[/tex] = 29.5
Squaring both sides, we get,
⇒ [tex]a^{3}[/tex] = 870.25
⇒ a = 9.5473
⇒ a = 9.5 (approximately)
Thus, the distance between Saturn and the sun is 9.5 AU (approximately) when the orbital period of Saturn is 29.5 years.
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Identify the graph of g(x)=3x^2-24x+45
The graph of an equation can be identified by looking at the characteristics of the equation, such as the order.
Quadratics
The equation given is quadratic because the highest exponent is 2; this means the equation has an order of 2. All equations with an order of 2 are quadratic equations. Quadratic equations form parabolas, which look like a U. Additionally, the leading coefficient is positive. This means that the parabola will open upwards, with the vertex being the minimum of the graph.
Other Characteristics
We can find more information from the equation to help us find the graph. Specifically, we can find the y-intercept. To find the y-intercept, simply plug 0 in for x and solve.
g(0) = 3(0)² - 24(0) + 45g(0) = 45This means that the y-intercept is 45.
Additionally, to find the x-coordinate of the vertex, we can use the equation -b/(2a).
[tex]\frac{-b}{2a}[/tex] = [tex]\frac{24}{6}[/tex] = 4The x-value of the vertex is 4. With all of this information, we can identify what the graph will look like. However, if you need to find the full graph, you can plug x-values into the equation, solve for y, and then plot the coordinate pairs. Below is a picture of the graph.
at a coffee shop, they offer 10 different drinks and four different desserts. how many ways can two people order the same drink but a different dessert. Show your work
Answer:
So if theres two people who can have a drink thats the same and a dessert thats different, then there are 40 different ways you can have one drink with a different dessert.
Step-by-step explanation:
Drinks: 4
Desserts: 10
There are ten desserts for every drink.
10*4, or 10 times 4, equals 40.