Answers
For a function, every element in the domain must have a unique image in the range.
On checking the domain and range provided in the question, we can see that there are two images for the range when the domain equals -2:
[tex](-2,3)\text{ and (}-2,7)[/tex]Therefore, the given domain and range violate the property of a function.
The relation is NOT a function.
Related Questions
system by applications i belive the answer is A can you check?
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Let's use the variable x to represent the cost of a senior ticket and y to represent the cost of a child ticket.
If the cost of 1 senior ticket and 1 child ticket is $18, we have:
[tex]x+y=18[/tex]If 2 senior tickets and 1 child tickets cost $27, we have:
[tex]2x+y=27[/tex]Subtracting the first equation from the second one, we can solve the result for x:
[tex]\begin{gathered} 2x+y-(x+y)=27-18 \\ 2x+y-x-y=9 \\ x=9 \end{gathered}[/tex]Now, solving for y:
[tex]\begin{gathered} x+y=18 \\ 9+y=18 \\ y=18-9 \\ y=9 \end{gathered}[/tex]Therefore the cost of one senior ticket is $9 and the cost of one child ticket is $9.
Correct option: D.
Sioux Falls Christian teacher says that he can drop one of his test score using history to score of 80 185 which one should he drop and white what is his new address
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if he removes his lowest score the average increases, then if we remove 80 the new average is
[tex]\frac{100+85}{2}=92.5[/tex]new average is 92.5
A baker has 85 cups of flour to make bread. She uses 6 1/4 cups of flour for each loaf of bread. How many loaf of bread can she make
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Answer;
The number of loaf of bread she can make is;
[tex]13\text{ loaves}[/tex]Explanation:
Given that a baker has 85 cups of flour to make bread.
[tex]A=85\text{ cups}[/tex]And for each bread she uses 6 1/4 cups of flour.
[tex]r=6\frac{1}{4}\text{ cups}[/tex]The number of loaf of bread she can make can be calculated by dividing the total amount of flour by the amount of flour per bread;
[tex]\begin{gathered} n=\frac{A}{r}=\frac{85}{6\frac{1}{4}}=\frac{85}{6.25} \\ n=13.6 \end{gathered}[/tex]Since it will not complete the 14th loaf of bread.
So, the number of loaf of bread she can make is;
[tex]13\text{ loaves}[/tex]I need help with this question
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A person who watches TV 11.5 hours can do 36 sit-ups.
Define Regression Analysis
Regression analysis is a mathematical measure of the average relationship between two or more variables in terms of the original units of the data
Given,
y = ax +b
a = -1.073
b = 27.069
r² = 0.434281
r = -0.659
No. of hours TV watched = 11.5 hours
we have , y = ax + b
where, a = 1.073 , b = 27.069 and x = 11.5 hours
put this value in given equation,
y = 1.073 * 11.5 + 27.069
After calculating, we get
y = 39.4085 or 39
Therefore, a person who watches TV 11.5 hours can do 36 sit-ups.
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Find the measure of angle CDB. Explain your reasoning, including the theorem or postulate you used. (2 pts.) b) Find the measure of angle. (1 pt.)
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The triangle is isosceles, since two of its sides are equal. Besides, the little triangles ABD and CBD are congruent and this can be concluding using the criterion SSS , since they share one side, and the other sides are equal. Then the angles are congruent, and the angles ADB and CDB are congruent and have the same measure. Then
[tex]\begin{gathered} m\angle ADB+m\angle CDB=m\angle ADC \\ 2m\angle CDB=m\angle ADC \\ m\angle CDB=\frac{72}{2} \\ m\angle CDB=32 \end{gathered}[/tex]Then, the measure of angle CDB is 32 degrees.
why is 10'15 equal to 10'11? explain ur thinking. ___ 10'4
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Exponent rule is the following:
[tex]\frac{x^a}{x^b}=x^{a-b}[/tex][tex]\text{Therefore, if for }\frac{10^{15}}{10^4}\text{ a is 15 and b is 4, therefore:}[/tex][tex]\frac{10^{15}}{10^4}=10^{15-4}[/tex][tex]So,\text{ }10^{\mleft\{15-4\mright\}}=10^{11}[/tex]ocupo encontrar la x con procedimiento
les regalare coronas!!!!
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La variable x asociada al sistema geométrico con dos ángulos alternos externos es igual a 23.
¿Cómo determinar la variable asociada a dos ángulos alternos externos?
En esta pregunta tenemos un sistema geométrico conformado por dos líneas paralelas atravesadas por una tercera línea. Este conjunto incluye dos ángulos alternos externos, que guardan la siguiente relación según la geometría euclídea:
6 · x - 28 = 4 · x + 18
A continuación, despejamos la variable x:
6 · x - 4 · x = 28 + 18
2 · x = 46
x = 23
El valor de la variable x es 23.
ObservaciónNo existen preguntas en español sobre ángulos alternos externos, por lo que se añade una pregunta en inglés.
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I need help with math. I have a big exam coming up but I do t understand this lesson at all. Can I have help answering all the questions?
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Step 1
Given;
[tex]\begin{gathered} Head\text{ represent male} \\ Tail\text{ represent female} \end{gathered}[/tex]The total number of puppies is 4 represented by 4 coins.
Step 2
Find the experimental probability that exactly 3 of the puppies will be female
[tex]\begin{gathered} From\text{ table we find that THTT, TTHT, HTTT and HTTT are the only outcomes that } \\ \text{show exactly 3 females} \\ Remember\text{ tail\lparen t\rparen is for female puppies} \end{gathered}[/tex]Therefore, the total number of samples/coin tosses=20
The formula for probability is;
[tex]Pr\left(event\right)=\frac{Numberofrequiredevent}{Total\text{ number of events}}[/tex]Total number of events =the total number of samples/coin tosses=20
Number of required events= outcomes with 3 T's from the tab;e=4
Hence.
[tex]=\frac{4}{20}=0.2=0.2\times100=20\text{\%}[/tex]Answer;
[tex]\frac{4}{20}=0.20=20\text{\%}[/tex]In 1980 approximately 4,825 million metric tons of carbon dioxide emissions were recorded for the United States. That number rose to approximately 6,000 million metric tons in the year 2005. Here you have measurements of carbon dioxide emissions for two moments in time. If you treat this information as two ordered pairs (x, y), you can use those two points to create a linear equation that helps you make predictions about the future of carbon dioxide emissions!A) Organize the measurements into ordered pairs. B) Find the slope,C) Set up an equation in point-slope form,D) Show the equation in slope-intercept form,E) Predict emissions for the year 2020,
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ANSWER and EXPLANATION
A) To organize the measurements in ordered pairs implies that we want to put them in the form:
[tex](x_1,y_1);(x_2,y_2)[/tex]Therefore, the measurements in ordered pairs are:
[tex]\begin{gathered} (1980,4825) \\ (2005,6000) \end{gathered}[/tex]Note: 4825 and 6000 are in millions (10⁶) of metric tons
B) To find the slope, apply the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Therefore, the slope is:
[tex]\begin{gathered} m=\frac{6000-4825}{2005-1980} \\ m=\frac{1175}{25} \\ m=47\text{ million metric tons per year} \end{gathered}[/tex]C) To find the in point-slope form, we apply the formula:
[tex]y-y_1=m(x-x_1)_{}[/tex]Therefore, we have:
[tex]y-4825=47(x-1980)[/tex]Note: the unit is in million metric tons
D) To show the equation in point-slope form, we have to put it in the form:
[tex]y=mx+b[/tex]To do that, simplify the point-slope form of the equation:
[tex]\begin{gathered} y-4825=47(x-1980) \\ y=47x-93060+4825 \\ y=47x-88235 \end{gathered}[/tex]E) To predict the emissions for the year 2020, substitute 2020 for x in the equation above:
[tex]\begin{gathered} y=47(2020)-88235 \\ y=94940-88235 \\ y=6705\text{ million metric tons} \end{gathered}[/tex]That is the prediction for the year 2020.
Which will hold more cake batter; the rectangular pan or two round pans? The volume of the rectangle pan is 234 in 3rd power. Find the volume of the two round pans and choose your decision. Round your answer to the nearest tenth if necessary.
Answers
Solution
Given a rectangular pan and two round pans
The volume, V, of the rectangular pan is 234 in³
A round pan is in the form of a cylinder
To find the volume, V, of the a round pan, the formula is
[tex]V=\pi r^2h[/tex]Where
[tex]\begin{gathered} d=8in \\ r=\frac{d}{2}=\frac{8}{2}=4in \\ r=4in \\ h=2in \end{gathered}[/tex]Substitute the variables into the formula above
[tex]\begin{gathered} V=\pi\left(4\right)^2\left(2\right)=100.53in^3\text{ \lparen two decimal places\rparen} \\ V=100.53in^3\text{ \lparen two decimal places\rparen} \end{gathered}[/tex]Since, there are two round pans, the volume of the two round pans will be
[tex]2\times100.53=201.06in^3[/tex]nce, the volume of the two round pans is 201.06 i³.
Since the volume of the two round pans (201.06in³) is less than the volume of the rectangular pan (234in³), the rectangular pan will hold more.
Hence, the answer is rectangular pan (option a)
In how many different ways can a relation be represented?Give an example of each
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It is to be noted that a relations in math can be represented in 8 different ways. See the examples below.
What are relations in Math?The relation in mathematics is the relationship between two or more sets of values.
The various types of relations and their examples are:
Empty Relation
An empty relation (or void relation) is one in which no set items are related to one another. For instance, if A = 1, 2, 3, one of the empty relations might be R = x, y, where |x - y| = 8. For an empty relationship,
R = φ ⊂ A × A
Universal Relation
A universal (or complete) relation is one in which every member of a set is connected to one another. Consider the set A = a, b, c. R = x, y will now be one of the universal relations, where |x - y| = 0. In terms of universality,
R = A × A
Identity Relation
Every element of a set is solely related to itself via an identity relation. In a set A = a, b, c, for example, the identity relation will be I = a, a, b, b, c, c. In terms of identity, I = {(a, a), a ∈ A}
Inverse Relation
When one set includes items that are inverse pairings of another set, there is an inverse connection. For example, if A = (a, b), (c, d), then the inverse relation is R-1 = (b, a), (d, c). As a result, given an inverse relationship,
R-1 = {(b, a): (a, b) ∈ R}
Reflexive Relation
Every element in a reflexive relationship maps to itself. Consider the set A = 1, 2, for example. R = (1, 1), (2, 2), (1, 2), (2, 1) is an example of a reflexive connection. The reflexive relationship is defined as- (a, a) ∈ R
Symmetric Relation
If a=b is true, then b=a is also true in a symmetric relationship. In other words, a relation R is symmetric if and only if (b, a) R holds when (a,b) R. R = (1, 2), (2, 1) for a set A = 1, 2 is an example of a symmetric relation. As a result, with a symmetric relationship, aRb ⇒ bRa, ∀ a, b ∈ A.
Transitive Relation
For transitive relation, if (x, y) ∈ R, (y, z) ∈ R, then (x, z) ∈ R. For a transitive relation, aRb and bRc ⇒ aRc ∀ a, b, c ∈ A
Equivalence Relation
If a relation is reflexive, symmetric and transitive at the same time, it is known as an equivalence relation.
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It is found that a relations in math can be represented in 8 different ways.
What are relations?The relation in mathematics is defined as the relationship between two or more sets of values.
There various types of relations and their examples:
An empty relation (or void relation) is one in which no set items are related to one another. if A = 1, 2, 3, one of the empty relations might be R = x, y, where |x - y| = 8.
R = φ ⊂ A × A
Universal Relation; It is one in which every member of a set is connected to one another.
R = A × A
Identity Relation; Every element of a set is solely related to itself via an identity .
In a set A = a, b, c, for example, it is I = a, a, b, b, c, c. I
n terms of identity, I = {(a, a), a ∈ A}
Inverse Relation; When one set of data includes items that are inverse pairings of another set, there is an inverse connection.
For example, if A = (a, b), (c, d), then the inverse is; R-1 = (b, a), (d, c).
R-1 = {(b, a): (a, b) ∈ R}
Equivalence Relation; When a relation is reflexive, symmetric and transitive at the same time, it is calles as an equivalence relation.
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A person has 29 1/2 -yd of material available to make a doll outfit. Each outfit requires 3/4 yd of material. a. How many outfits can be made? b. How much material will be left over?
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Which is the equivalent of 6 14’ 48’’ written in decimal form Round to the nearest thousandth of a degree A. 6.145 B. 6.367 C. 6.247 D. 6.313
Answers
Answer
Step-by-step explanation
First, we need to convert the 48'' into minutes. Using the conversion factor: 1' = 60'', we get:
[tex]\begin{gathered} 48^{\prime}^{\prime}=48^{\prime}^{\prime}\cdot\frac{1^{\prime}}{60^{\prime}^{\prime}} \\ 48^{\prime\prime}=\frac{48}{60}^{\prime} \\ 48^{\prime}^{\prime}=0.8^{\prime} \end{gathered}[/tex]Then, 14 minutes and 48 seconds are equivalent to 14 + 0.8 = 14.8 minutes. To convert this amount of minutes into degrees we need to use the conversion factor 1° = 60', as follows:
[tex]\begin{gathered} 14.8^{\prime}=14.8^{\prime}\cdot\frac{1\degree}{60^{\prime}^{\prime}} \\ 14.8^{\prime}=\frac{14.8}{60}\degree \\ 14.8^{\prime}=0.247\operatorname{\degree} \end{gathered}[/tex]In consequence, 6° 14’ 48’’ is equivalent to 6 + 0.247 = 6.247°
4 Consider the quadratic equation below.[tex]4 {x}^{2} - 5 = 3x + 4[/tex] Determine the correct set-up for solving the equation using the quadratic formula.
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The equation:
4x² - 5 = 3x + 4
First, we need to re-arrange in the form : ax² + bx + c
4x² - 5 = 3x + 4
4x² - 3x -5 -4 = 0
4x² - 3x -9 =0
comparing the above with ax² + bx + c
a= 4 b= -3 c=-9
we will then substitute the values into the quadratic formula:
[tex]x\text{ = }\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex][tex]x=\frac{-(-3)\pm\sqrt[]{(-3)^2-4(4)(-9)}}{2(4)}[/tex]The perimeter of a quarter circle is 3.57 kilometers. What is the quarter circle's radius? Use 3.14 for . kilometers Siubmit explain
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Given:
It is given that the perimeter of a quarter circle is 3.57 km.
To find :
The radius of the quarter circle.
Explanation :
The perimeter of the quarter circle is
[tex]P=\frac{2\pi r}{4}\text{ }+2r[/tex]Substitute the value of perimeter in the above formula
[tex]3.57=\frac{\pi r}{2}+2r[/tex][tex]3.57=(\frac{3.14}{2}+1)r[/tex][tex]3.57=2.57r[/tex][tex]r=1.39[/tex]Answer
Hence the radius of a quarter circle is 1.39 km.
2 dot plots. Both number lines go from 0 to 10. Plot 1 is titled fifth grade. There are 2 dots above 1, 3 above 2, 1 above 3, 4 above 4, 5 above 5, 5 above 6, 2 above 7, 2 above 8, 0 above 9, 0 above 10. Plot 2 is titled seventh grade. There are 2 dots above 0, 2 above 1, 3 above 2, 5 above 3, 5 above 4, 3 above 5, 3 above 6, 1 above 7, and 0 above 8, 9, and 10.
The dot plot shows the number of hours, to the nearest hour, that a sample of 5th graders and 7th graders spend watching television each week. What are the mean and median?
The 5th-grade mean is
.
The 7th-grade mean is
.
The 5th-grade median is
.
The 7th-grade median is
.
Answers
The mean of the 5th grade students is 4.67
The mean of the 7th grade students is 3.46
The median of the 5th grade students is 5
The median of the 7th grade students is 3.5
What are the mean and median?A dot plot is a graph used to represent a dataset. A dot plot is made up of a number line and dots. The dots in the dot plot represent the frequency of the data. The greater the frequency of a data, the greater the number of dots.
Mean is the average of a dataset. It is determined by adding all the numbers in the dataset together and dividing it by the total numbers in the dataset.
Mean = sum of numbers / total numbers in the dataset
Mean of the 5th grade students = ( 1 + 1 + 2 + 2 + 2 + 3 + 4 + 4 + 4 + 4 + 5 + 5 + 5 + 5 + 5 + 6 + 6 + 6 + 6 + 6 + 7 + 7 + 8 + 8 ) / 24
112 / 24 = 4.67
Mean of the 7th grade students = ( 0, 0, 1 + 1 + 2 + 2 + 2 + 3 + 3 + 3 + 3 + 3 + 4 + 4 + 4 + 4 + 4 + 5 + 5 + 5 + 6 + 6 + 6 + 7) / 24
83 / 24 = 3.46
Median is the number that is in the middle of a dataset.
Median = (n + 1) / 2
Median of the 5th grade students = (24 + 1) / 2 = 12.5 terms = 5
Median of the 7th grade students = (24 + 1) / 2 = 12.5 term = (3 + 4) / 2 = 3.5.
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has overdrawn his bank account Jim has overdrawn his bank account and has a balance of -$3.47.he received a paycheck of $292.54 he deposits $163.93 of his paycheck into his account how much does Jim have in his bank account after the deposit is made
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Since Jim deposits $ 163.93 of his paycheck into his account and there has a balance of - $ 3.47, then he has in his account:
[tex]\text{\$}$163.93$-\text{\$}3.47=\text{ \$}160.46[/tex]Therefore, Jim has $ 160.46 in his bank account after the deposit is made.
What is the product of 3√6 and 5√12 in simplest radical form?
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In order to calculate and simplify this product, we need to use the following properties:
[tex]\begin{gathered} \sqrt[]{a}\cdot\sqrt[]{b}=\sqrt[]{a\cdot b} \\ \sqrt[c]{a^b}=a\sqrt[c]{a^{b-c}} \end{gathered}[/tex]So we have that:
[tex]\begin{gathered} 3\sqrt[]{6}\cdot5\sqrt[]{12} \\ =(3\cdot5)\cdot(\sqrt[]{6}\cdot\sqrt[]{2\cdot6}) \\ =15\cdot\sqrt[]{2\cdot6^2} \\ =15\cdot6\cdot\sqrt[]{2} \\ =90\sqrt[]{2} \end{gathered}[/tex]So the result in the simplest radical form is 90√2.
Which statements about the graph of the exponential function f(x) are TRUE?The x-intercept is 1.The y-intercept is 3.The asymptote is y = -3The range is all real numbers greater than -3The domain is all real numbers.f(x) is positive for all x-values greater than 1As x increases, f(x) approaches, but never reaches, -3.
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1 The x-intercept is the value of x where the graph intersects the x-axis. The graph crosses the x-axis at x = 1. This statement is true.
2 The y-intercept is the value of y where the graph intersects the y-axis. The graph crosses the y-axis at y = -2. This statement is false.
3 The horizontal asymptote is the value of y to which the graph approaches but never reaches. This value seems to be y = -3, thus this statement is true.
4 The range is the set of values of y where the function exists. The graph exists only for values of y greater than -3. This statement is true.
5 We can give x any real value and the function exists, i.e., any vertical line would eventually intersect the graph. This statement is true.
To find the domain of a function when we are given the graph, we use the vertical line test. This consists of drawing an imaginary vertical line throughout the x-axis. If the line intersects the graph, that value of x is part of the domain.
This imaginary exercise gives us the centainty that there is no value of x that won't intercept the graph, thus the domain is the set of all the real values.
6 We can see the graph is positive exactly when the function has its x-intercept, thus This statement is true.
7 As x increases, y goes to infinity. The value of -3 is not a number where f(x) approaches when x increases, but when x decreases. This statement is false.
The court ruled that Lox Auto was liable in the death of an employee.The settlement called for the company to pay the employee's widow $60,000 at theend of each year for 20 years. Find the amount the company must set aside today,assuming 5% compounded annually.
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We have to calculate the present value PV of a annuity.
The payment is yearly and it is P=60,000.
The interest rate is 5% (r=0.05), compounded annually (m=1).
The number of periods is n=20 years.
Then, we can use the formula for the present value of a annuity:
[tex]\begin{gathered} PV=P\cdot\frac{1-\frac{1}{(1+r)^n}}{r} \\ PV=60000\cdot\frac{1-\frac{1}{1.05^{20}}}{0.05} \\ PV\approx60000\cdot\frac{1-\frac{1}{2.653}}{0.05} \\ PV\approx60000\cdot\frac{1-0.377}{0.05} \\ PV\approx60000\cdot\frac{0.623}{0.05} \\ PV\approx60000\cdot12.462 \\ PV\approx747720 \end{gathered}[/tex]Answer: the company must set aside $747,720.
help mee pleaseeeeeeeeeeeeee
Answers
Step-by-step explanation:
this simply means to put first 5, then 9 and then 12 in place of the x in the function and calculate the 3 results.
a.
after 5 years it is worth
V(5) = -1500×5 + 21000 = -7500 + 21000 = $13,500
b.
after 9 years it is worth
V(9) = -1500×9 + 21000 = -13500 + 21000 = $7,500
c.
V(12) = $3000
means that after 12 years the car is worth only $3000.
let's check
V(12) = -1500×12 + 21000 = -18000 + 21000 = $3000.
correct.
A newsletter publisher believes that more than 31% of their readers own a Rolls Royce. Is there sufficient evidence at the 0.01 level to substantiate the publisher's claim? State the null and alternative hypotheses for the above scenario. Answer
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The null hypothesis is H0: P = 0.31 and the alternative hypothesis is Ha: P > 0.31.
What is a null hypothesis?The null hypothesis is simply to predict that there is no effect of relationship between the variables.
The alternative hypothesis is to state the research prediction of a relationship or effect. In this case, the newsletter publisher believes that more than 31% of their readers own a Rolls Royce.
The null hypothesis is P = 0.31. while the alternative hypothesis will be that it's greater than 0.31.
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the coldest temperature ever recorded on earth is 135.8 Fahrenheit below zero recording in Antarctica on July 21st 1983 the hottest temperature ever recorded on earth is 134 Fahrenheit recorded in Death Valley California on July 10th 1913 what is the difference between those two temperature
Answers
Let's begin by listing out the information given to us:
The coldest temperature ever recorded on earth (T1) = -135.8 Fahrenheit
The hottest temperature ever recorded on earth (T2) = 134 Fahrenheit
The difference between the two temperature = Hottest - Coldest temperature
[tex]undefined[/tex]Find the slope of the line passing through points -8, 8 and 7,8
Answers
We can calculate the slope of a line using the formula
[tex]m=\frac{y_b-y_a_{}}{x_b-x_a}[/tex]Let's say that
[tex]\begin{gathered} A=(-8,8) \\ B=(7,8) \end{gathered}[/tex]Therefore
[tex]\begin{gathered} x_a=-8,y_a=8 \\ x_b=7,y_b=8 \end{gathered}[/tex]Using the formula
[tex]m=\frac{y_b-y_a}{x_b-x_a}=\frac{8-8}{7-(-8)}=\frac{0}{15}=0[/tex]The slope of the line passing through points (-8, 8) and (7,8) is 0. Which means it's a constant function (horizontal line).
Text-to-Speech 11. Diva wants to make a flower arrangement for her aunt's birthday. She wants 1/3 of the arrangement to be roses. She has 12 roses. How many other flowers does she need to finish the arrangement?
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Which of the following is a correct way to name this angle? B, 2 ACB А, САВ D. BCA C. Z CBA
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The answer is Angle ACB
The angle is form from both line A and C
The expression below is scientificnotation for what number?4.58x10^-2
Answers
Using the exponent rules, 10^-2 can be expressed as follows:
[tex]10^{-2}=\frac{1}{10^2}=\frac{1}{100}[/tex]Substituting into the expression in scientific notation, we get:
[tex]4.58\cdot10^{-2}=4.58\cdot\frac{1}{100}=\frac{4.58}{100}=0.0458[/tex]Jamal buys a water heater online for $861. If shipping and handling area additional 11% of the price, how many shipping and handling will Jamal pay?
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^3square root of 1000
Answers
Given the following question:
[tex]\sqrt[3]{1000}[/tex][tex]\begin{gathered} \sqrt[3]{1000} \\ \sqrt[3]{1000}=\sqrt[3]{10^3} \\ 10^3=1000 \\ \sqrt[3]{10^3} \\ \sqrt[n]{a^n}=a \\ \sqrt[3]{10^3}=10 \\ =10 \end{gathered}[/tex]Your answer is 10.
In a game of cornhole, Sasha tossed a bean bag and it landed at the edge of the hole. The hole can be represented by the equation x^2+ y^2= 5, and the path of the bean bag canbe represented by y = -0.5x^2 -1.5x + 4. To which points could she have tossed her bean bag?(-1,-2) or (-2, 1)(1.-2) or (2,1)(-1,2) or (-2,-1)(1, 2) or (2, -1)
Answers
We have two equations, the first is a circle, which we can identify by the characteristic form of the equation:
[tex]x^2+y^2=5[/tex]The second is a quadratic equation:
[tex]y=-0.5x^2-1.5x+4[/tex]We know that Sasha got the bag to land in the edge of the circle defined by the hole, equation 1.
So, to know the points at which the bag landed, we can look for th eintersection of the two equations, which is the same as solving a system of equations:
[tex]\begin{gathered} x^2+y^2=5 \\ y=-0.5x^2-1.5x+4 \end{gathered}[/tex]Since we have been given alternatives, we can check them to get the correct answer.
The first option is (-1,-2) or (-2,1). Since the sign of the alternatives are the only thing that change and the circle equation doesn't differenciate the signs, the best equation to test first is the second one. Let's try that for (-1,-2).
[tex]\begin{gathered} y=-0.5(-1)^2-1.5(-1)+4 \\ y=-0.5+1.5+4=5 \end{gathered}[/tex]We got y = 5, which is not -2, so this alternative is incorrect.
Let's got for the second alternative, (1.-2) or (2,1):
[tex]y=-0.5(1)^2-1.5\cdot1+4=2[/tex]This is also incorrect.
The third alternative is (-1,2) or (-2,-1), we already saw that for x = -1, y = 5, which makes this alternative also incorrect.
Let's check if the last one will be correct, (1, 2) or (2, -1). We already saw that for x = 1, y = 2 in the second equation, let's check if this is also correct for the first:
[tex]\begin{gathered} (1)^2+y^2=5 \\ y^2=5-1=4 \\ y=\pm2 \end{gathered}[/tex]One of the results is y = 2, so this also checks out.
The other point is (2,-1), let's check in both equations:
[tex]\begin{gathered} (2)^2+y^2=5 \\ 4+y^2=5 \\ y^2=1 \\ y=\pm1 \end{gathered}[/tex]Checks out, and:
[tex]\begin{gathered} y=-0.5(2)^2-1.5\cdot2+4 \\ y=-2-3+4=-1 \end{gathered}[/tex]And the "y" checks out too.
So, the correct alternative is the last one: (1, 2) or (2, -1).