Step-by-step explanation:
To find a system with the same solution as the given system, we can multiply both sides of both equations by a nonzero constant, which will result in a system that is equivalent to the original one.
For example, let's multiply the first equation by 2 and the second equation by 3:
First equation (multiplied by 2):
6x + 4y = -10
Second equation (multiplied by 3):
6x + 9y = 15
The new system of equations is:
6x + 4y = -10
6x + 9y = 15
This system has the same solution as the original system because it's just a scalar multiple of the original system.
If P= (4,2) Find: RX=3 (P)
Answer: 2,2
Step-by-step explanation:
trust me
Using exactly nine bills, how can you make change for $55 that will NOT make change for a twenty dollar bill?
a.
1 twenty, 3 tens, 5 singles
c.
2 twenties, 1 ten, 6 singles
b.
4 tens, 2 fives, 5 singles
d.
2 twenties, 2 fives, 5 singles
The correct combination is option a) 1 twenty, 3 tens, and 5 singles, which allows us to make change for $55 without making change for a twenty dollar bill.
The correct answer is a) 1 twenty, 3 tens, 5 singles.
To make change for $55 using exactly nine bills without making change for a twenty dollar bill, we need to avoid using any combination that includes a twenty dollar bill.
Option a) includes 1 twenty, 3 tens, and 5 singles. The total value of these bills is 20 + 3(10) + 5(1) = $55. This combination allows us to make the exact change for $55 without including a twenty dollar bill.
Option b) includes 4 tens, 2 fives, and 5 singles. The total value of these bills is 4(10) + 2(5) + 5(1) = $55. Although this combination also makes the exact change for $55, it includes four tens, which can be exchanged for a twenty dollar bill.
Option c) includes 2 twenties, 1 ten, and 6 singles. The total value of these bills is 2(20) + 10 + 6(1) = $57. This combination exceeds $55 and also includes two twenty dollar bills, making change for a twenty dollar bill.
Option d) includes 2 twenties, 2 fives, and 5 singles. The total value of these bills is 2(20) + 2(5) + 5(1) = $55. However, this combination includes two twenty dollar bills, making change for a twenty dollar bill.
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A students score is at the 16th percentile. This indicates that:
A. 16% of scores are at his/her score or below
B. 84% of scores are at his/her score or below.
Answer:
A. 16% of scores are at his/her score or below
Step-by-step explanation:
When a student's score is at the 16th percentile, it means that their score is equal to or better than 16% of the scores in the population. In other words, 16% of the scores are at their score or below.
Michelle had 5 paperback books and 3 hardcover books on the shelf by her bed. Write a ratio to represent the ratio of paperback books to hardcover books.
3:5
five over three
3 to 8
5:8
Answer: The correct ratio to represent the ratio of paperback books to hardcover books is 5:3.
GEOMETRY 50POINTS
determine what type of triangle they will form.
BRILLIANT for the best answer
Answer:
acute triangle
Step-by-step explanation:
for the given sides to form a triangle
the sum of any 2 sides must be greater than the third side
given 56 , 90 , 100
56 + 90 = 146 > 100
56 + 100 = 156 > 90
90 + 100 = 190 > 56
the condition is met so the 3 lengths will form a triangle.
let a = 56 , b = 90 and c = 100 , where c represents the longest of the 3 sides , then
• if a² + b² = c² , then triangle is right
• if a² + b² > c² , then triangle is acute
• if a² + b² < c² , then triangle is obtuse
a² + b² = 56² + 90² = 3136 + 8100 = 11,236
c² = 100² = 10, 000
since a² + b² > c² , then triangle is acute
The manager of an ice cream shop found that the probability of a new customer ordering vanilla ice cream is 3/22. What are the odds against a new customer ordering vanilla ice cream?
Answer:
Step-by-step explanation:
[tex]P(\text{not vanilla})=1-\frac{3}{22}=\frac{19}{22}[/tex]
Odds are 19 to 3.
A parabola can be drawn given a focus of... 100 pts
Answer:
[tex](y+1)^2=8(x+3)[/tex]
Step-by-step explanation:
The focus of a parabola is a fixed point located inside the curve. It is equidistant from the vertex and the directrix.
The directrix is a line that is located outside the curve. As the directrix on the given graph is a vertical line, the parabola is horizontal (sideways). The directrix is located to the left of the focus, which means the parabola opens to the right.
The axis of symmetry is perpendicular to the directrix and passes through the focus. So the axis of symmetry in this case is y = -1.
The vertex is the turning point of the parabola. It is located on the axis of symmetry, and is halfway between the focus and the directrix. Therefore, the y-coordinate of the vertex is y = -1. Given the focus is (-1, -1) and the directrix is x = -5, the vertex is (-3, -1).
The standard equation of a sideways parabola is:
[tex]\boxed{(y-k)^2=4p(x-h)}[/tex]
where:
Vertex = (h, k)Focus = (h+p, k)Directrix: x = (h - p)Axis of symmetry: y = kAs the vertex is (-3, -1), then h = -3 and k = -1.
Use the formula for the focus to find the value of p:
[tex]\begin{aligned}(h+p, k)&=(-1,-1)\\(-3+p, -1)&=(-1, -1)\\\implies -3+p&=-1\\p&=2\end{aligned}[/tex]
To write an equation for the parabola based on the given focus and directrix, substitute the values of h, k and p into the standard equation :
[tex](y-(-1))^2=4(2)(x-(-3))[/tex]
[tex](y+1)^2=8(x+3)[/tex]
Therefore, the equation of the parabola is:
[tex]\boxed{(y+1)^2=8(x+3)}[/tex]
The equation of the parabola with focus (-1, -1) and directrix x = -5 is (x + 1)² = 16(y + 1).
What is the equation of the parabola?The equation of a parabola with a focus at (-1, -1) and a directrix of x = -5 can be written in standard form as:
(x - h)² = 4p(y - k)
Where (h, k) represents the vertex of the parabola and p is the distance between the vertex and the focus (or directrix).
In this case, the x-coordinate of the focus (-1, -1) is h = -1, and the y-coordinate is k = -1. The directrix is a vertical line x = -5, which means the parabola opens to the right.
Step 1: Determine the value of p
The distance between the vertex and the directrix is given by the absolute difference of their x-coordinates. In this case, p = |-5 - (-1)| = |-5 + 1| = 4.
Step 2: Write the equation
Substituting the values into the standard form equation, we have:
(x - h)² = 4p(y - k)
(x - (-1))² = 4(4)(y - (-1))
(x + 1)² = 16(y + 1)
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IfmWF = 143° and m/WBF = 117°. find mVL
Answer:
arc VL = 91°
Step-by-step explanation:
the chord- chord angle WBF is half the sum of the arcs intersected by the angle and its vertical angle , that is
[tex]\frac{1}{2}[/tex] (WF + VL) = ∠ WBF
[tex]\frac{1}{2}[/tex] (143 + VL ) = 117° ( multiply both sides by 2 to clear the fraction
143° + VL = 234° ( subtract 143° from both sides )
VL = 91°
at the movie theatre, child admission is $5.20 and adult admission is $9.60 on sunday, 131 tickets were sold for a total sales of $1020.00 how many adult tickets were sold that day
Taking into account the definition of a system of linear equations, on Sunday 77 adult tickets were sold.
Definition of System of linear equationsA system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.
Solving a system of equations consists of finding the value of each unknown with which when replacing, they must give the solution proposed in both equations.
Amount of adult tickets soldIn this case, a system of linear equations must be proposed taking into account that:
"a" is the amount of adult tickets sold."c" is the amount of children tickets sold.You know:
At the movie theatre, child admission is $5.20 and adult admission is $9.60 On sunday, 131 tickets were sold for a total sales of $1020.00So, the system of equations to be solved is
a + c= 131
9.60a + 5.20c= 1020
There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.
In this case, isolating the variable c from the first equation:
c= 131 -a
Substituting the expression in the second equation:
9.60a + 5.20×(131 -a)= 1020
Solving:
9.60a + 5.20×131 -5.20a= 1020
9.60a + 681.2 -5.20a= 1020
9.60a -5.20a= 1020 - 681.2
4.4a= 338.8
a= 338.8÷ 4.4
a= 77
In summary, 77 adult tickets were sold that day.
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GEOMETRY 50POINTS
Find cos Z.
Answer:
cos Z = [tex]\frac{5}{13}[/tex]
Step-by-step explanation:
cos Z = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{YZ}{XZ}[/tex] = [tex]\frac{10}{26}[/tex] = [tex]\frac{5}{13}[/tex]
The exponential growth model y = Ae^rt can be used to calculate the future population of a city. In this model, A is the current population, r is the rate of growth, and y is the future population for a specific time, t, in years.
A certain city's population has a growth rate of r = 0.08. Approximately how long will it take the city's population to grow from 250,000 to 675,000?
NEED ASAP
Step-by-step explanation:
in the formula
y = Ae^rt
y is 675,000
A is 250,000
r is 0.08
to get the value of t
y = Ae^rt
y/A = e^rt
ln(y/A) = rt
[ln(y/A)]/r = t
Given that g(x)=2x^2 - 2x + 9 , find each of the following.
a) g(0)
b) g(- 1)
c) g(2)
d) g( - x)
e) g(1 - t)
Answer:
Step-by-step explanation:
To find the values of the given expressions using the function g(x) = 2x^2 - 2x + 9, we substitute the given values into the function and simplify the expression. Let's calculate each of the following:
a) g(0)
To find g(0), substitute x = 0 into the function:
g(0) = 2(0)^2 - 2(0) + 9
g(0) = 0 - 0 + 9
g(0) = 9
b) g(-1)
To find g(-1), substitute x = -1 into the function:
g(-1) = 2(-1)^2 - 2(-1) + 9
g(-1) = 2(1) + 2 + 9
g(-1) = 2 + 2 + 9
g(-1) = 13
c) g(2)
To find g(2), substitute x = 2 into the function:
g(2) = 2(2)^2 - 2(2) + 9
g(2) = 2(4) - 4 + 9
g(2) = 8 - 4 + 9
g(2) = 13
d) g(-x)
To find g(-x), substitute x = -x into the function:
g(-x) = 2(-x)^2 - 2(-x) + 9
g(-x) = 2x^2 + 2x + 9
e) g(1 - t)
To find g(1 - t), substitute x = 1 - t into the function:
g(1 - t) = 2(1 - t)^2 - 2(1 - t) + 9
g(1 - t) = 2(1 - 2t + t^2) - 2 + 2t + 9
g(1 - t) = 2 - 4t + 2t^2 - 2 + 2t + 9
g(1 - t) = 2t^2 - 2t + 9
Therefore:
a) g(0) = 9
b) g(-1) = 13
c) g(2) = 13
d) g(-x) = 2x^2 + 2x + 9
e) g(1 - t) = 2t^2 - 2t + 9
In random sampling, the probability of selecting an item from the population is:
Select one:
a. Un-Known
b. One
c. known
d. undefined
e. Un-decided
Note: Answer D is NOT the correct answer. Please find the correct answer. Any answer without justification will be rejected automatically.
Answer: c. known
Step-by-step explanation:
In random sampling, the probability of selecting an item from the population is known. This probability can be calculated based on the sampling method and the characteristics of the population being sampled. Random sampling ensures that each item in the population has an equal chance of being selected, making the probability of selection known and calculable.
Given that p(x)=2(5−x)2+1 , what is the value of p(-4)? Responses
Answer:
37
Step-by-step explanation:
x=-4
=2(5-(-4)2+1
=2(5+4)2+1
=2(9)2+1
=18(2)+1
=36+1
=37
Write an inequality and solve.
Negative one hundred eighty three is at least nine more than 24 times a number.
Answer: -8 ≥ x
Step-by-step explanation:
Let x be the number, we set up an inequality:
-183 ≥ 9 + 24x [we use ≥ to present "at least"]
-192 ≥ 24x
-8 ≥ x
help needed fast pleaseeeeeeee. Identify the solution of the system graphed below.
The solution to the system of equations is (a) (1, 0)
Identifying the solutions to the system of equationsFrom the question, we have the following parameters that can be used in our computation:
The graph
The point of intersection of the lines of the graph represent the solution to the system graphed
From the graph, we have the intersection point to be
(x, y) = (1, 0)
This means that
x = 1 and y = 0
Hence, the solution to the system of equations is (a) (1, 0)
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The table displays the scores of students on a recent exam. Find the mean of the
scores to the nearest 10th.
Score Number of Students
70
6
75
80
85
90
95
3
9
5
7
8
2
The mean of the scores to the nearest tenth is 83.7.
What is the mean?Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.
Given the question above, we need to find the mean of the scores to the nearest tenth.
We can find the mean by using the formula below:
[tex]\text{Mean} = \dfrac{\text{Sum of all the observations}}{\text{Total number of observations}}[/tex]
Now,
[tex]\text{Mean} = \dfrac{70(6)+75(3)+80(9)+85(5)+90(7)+95(8)}{6+3+9+5+7+8}[/tex]
[tex]\text{Mean} = \dfrac{420+225+720+425+630+760}{38}[/tex]
[tex]\text{Mean} = \dfrac{3180}{38}[/tex]
[tex]\text{Mean} = 83.7[/tex]
Therefore, the mean of the scores to the nearest tenth is 83.7.
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02.05 MC)
What additional information would you need to prove that ΔABC ≅ ΔDEF by SAS?
Triangle ABC is drawn with a single hash mark between A and B and triangle DEF is marked with a single hash mark between D and
(4 points)
Group of answer choices
segment AC≅segment EF
segment BC ≅ segment FE
segment AC ≅ segment FE
segment BC ≅ segment EF
Having the information that segment AC ≅ segment EF, angle B ≅ angle E, and segment BC ≅ segment FE is sufficient to prove that triangles ΔABC and ΔDEF are congruent by the Side-Angle-Side (SAS) criterion.
To prove that triangles ΔABC and ΔDEF are congruent using the Side-Angle-Side (SAS) criterion, we need the following additional information:
The length of segment AC is equal to the length of segment EF: This establishes that one pair of corresponding sides is congruent.
The measure of angle B is equal to the measure of angle E: This provides the congruent angle between the corresponding sides.
The length of segment BC is equal to the length of segment FE: This establishes that the other pair of corresponding sides are congruent.
By having this information, we can apply the SAS congruence criterion. The SAS criterion states that if two triangles have a pair of corresponding sides that are congruent, and the included angles are congruent, then the triangles are congruent.
In this case, having segments AC ≅ EF, angle B ≅ angle E, and segment BC ≅ FE would be sufficient to prove that ΔABC ≅ ΔDEF by SAS.
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Simplify the expression to a polynomial in standard form (x^2+3x+3) (-2x^2-x+6)
The polynomial [tex](x^2 + 3x + 3) * (-2x^2 - x + 6)[/tex] simplifies to [tex]-2x^4 - 7x^3 - 3x^2 + 33x + 18.[/tex]
A polynomial is a mathematical expression consisting of variables, coefficients, and exponents, combined using addition, subtraction, and multiplication operations. It is defined as a sum of terms, where each term consists of a variable raised to a non-negative integer exponent, multiplied by a coefficient.
The general form of a polynomial is:
P(x) = aₙxⁿ + aₙ₋₁xⁿ⁻¹ + ... + a₂x² + a₁x + a₀
To simplify the expression[tex](x^2 + 3x + 3) * (-2x^2 - x + 6)[/tex], we need to perform the multiplication and combine like terms.
First, we multiply each term in the first polynomial by each term in the second polynomial:
[tex](x^2 + 3x + 3) * (-2x^2 - x + 6) = x^2 * (-2x^2 - x + 6) + 3x * (-2x^2 - x + 6) + 3 * (-2x^2 - x + 6)[/tex]
Expanding each term, we get:
=[tex](-2x^4 - x^3 + 6x^2) + (-6x^3 - 3x^2 + 18x) + (-6x^2 - 3x + 18)[/tex]
Now, we combine like terms:
=[tex]-2x^4 + (-x^3 - 6x^3) + (6x^2 - 3x^2 - 6x^2) + (18x + 18x - 3x) + 18[/tex]
Simplifying further:
=[tex]-2x^4 - 7x^3 - 3x^2 + 33x + 18[/tex]
The simplified expression in polynomial standard form is:
-2x^4 - 7x^3 - 3x^2 + 33x + 18
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14x^(2n+1)+7x^(n+3)-21^(n+2)
100 points will be awarded
Answer:
Step-by-step explanation:
The given expression is: 14x^(2n+1) + 7x^(n+3) - 21^(n+2)
Unfortunately, it seems there is a missing exponent for the term "21" in the expression. Please provide the correct exponent for 21, and I'll be happy to help you further simplify the expression.
GEOMETRY 50POINTS
find x to the nearest hundredth.
TYSM
Answer:
It's 18.37
Step-by-step explanation:
I'm smart trust me.
please help I'm losing braincells
Answer:h equals 12
Step-by-step explanation:
The pyramid and prism above have the same triangular base and height. The volume of the pyramid is 18 cubic inches. What is the volume of the prism?
A. 36 cubic inches
B. 72 cubic inches
C. 6 cubic inches
D. 54 cubic inches
Tenía unas matas en el vivero.
Sembré 23 el lunes, 28 el
martes, 29 el miércoles. Si el
jueves tenía 90, ¿con cuántas
matas empecé?
If 23 plants were planted on Monday, 28 plants on Tuesday and 29 plants on Wednesday, and 90 plants were planted on Thursday, we can determine that we started with 10 plants initially.
To determine how many plants to start with initially, we need to perform a series of calculations based on the information provided.
On Monday 23 plants were planted, on Tuesday 28 plants were planted and on Wednesday 29 plants were planted. If on Thursday there were a total of 90 plants, we can add all the plants planted until Thursday and then subtract them from the total to obtain the initial amount.
Adding the plants planted:
23 + 28 + 29 = 80
Then, we subtract this amount from Thursday's total:
90 - 80 = 10
Therefore, we started with 10 plants initially.
In summary, if 23 plants were planted on Monday, 28 plants on Tuesday and 29 plants on Wednesday, and 90 plants were planted on Thursday, we can determine that we started with 10 plants initially. This is obtained by adding the plants planted until Thursday and then subtracting that amount from the total for Thursday.
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Hungry Harry is a giant ogre with an even bigger appetite. After Harry wakes up from hibernation, his daily hunger � ( � ) H(t)H, left parenthesis, t, right parenthesis (in kg kgstart text, k, g, end text of pigs) as a function of time � tt (in hours) can be modeled by a sinusoidal expression of the form � ⋅ cos ( � ⋅ � ) + � a⋅cos(b⋅t)+da, dot, cosine, left parenthesis, b, dot, t, right parenthesis, plus, d. When Harry wakes up at � = 0 t=0t, equals, 0, his hunger is at a maximum, and he desires 30 kg 30 kg30, start text, space, k, g, end text of pigs. Within 2 22 hours, his hunger subsides to its minimum, when he only desires 15 kg 15 kg15, start text, space, k, g, end text of pigs. Find � ( � ) H(t)H, left parenthesis, t, right parenthesis.
The equation for Harry's hunger in terms of time can be written as,H(t) = 7.5.cos(π.t) + 22.5
Given:Hunger of Harry as a function of time,H(t)H(t) can be modeled by a sinusoidal expression of the form,a⋅cos(b⋅t)+da⋅cos(b⋅t)+d, where Harry wakes up at t=0t=0t=0, his hunger is at a maximum, and he desires 30 kg 30 kg30, start text, space, k, g, end text of pigs.
Within 2 22 hours, his hunger subsides to its minimum, when he only desires 15 kg 15 kg15, start text, space, k, g, end text of pigs.
Therefore, the equation of the form for H(t)H(t) will be,H(t) = A.cos(B.t) + C where, A is the amplitude B is the frequency (number of cycles per unit time)C is the vertical shift (or phase shift)
Thus, the maximum and minimum hunger of Harry can be represented as,When t=0t=0t=0, Harry's hunger is at maximum, i.e., H(0)=30kgH(0)=30kg30, start text, space, k, g, end text.
When t=2t=2t=2, Harry's hunger is at the minimum, i.e., H(2)=15kgH(2)=15kg15, start text, space, k, g, end text.
According to the given formula,
H(t) = a.cos(b.t) + d ------(1)Where a is the amplitude, b is the angular frequency, d is the vertical shift.To find the value of a, subtract the minimum value from the maximum value.a = (Hmax - Hmin)/2= (30 - 15)/2= 15/2 = 7.5To find the value of b, we will use the formula,b = 2π/period = 2π/(time for one cycle)The time for one cycle is (2 - 0) = 2 hours.
As Harry's hunger cycle is a sinusoidal wave, it is periodic over a cycle of 2 hours.
Therefore, the angular frequency,b = 2π/2= π
Therefore, the equation for Harry's hunger in terms of time can be written as,H(t) = 7.5.cos(π.t) + 22.5
Answer: H(t) = 7.5.cos(π.t) + 22.5.
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At which points is the function continuous?
The function is continuous in the domain x ≥ 3/4
At which points is the function continuous?Here we have a root function:
f(x) = ⁴√(4x - 3)
This is an even degree root function, so we have problems when the argument is negative.
Then the allowed values (where the function is defined, and thus, continuous) are:
4x - 3 ≥ 0
4x ≥ 3
x ≥ 3/4
There the function is continuous.
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Similar Triangles
Determine whether the triangles are similar. If so, write a similarity statement. If not, what would be sufficient to
prove the triangles similar? Explain your reasoning.
I need help on number 1 and 2
The equivalent ratio of the corresponding sides and the triangle proportionality theorem indicates that the similar triangles are;
1. ΔAJK ~ ΔSWY according to the SAS similarity postulate
2. ΔLMN ~ ΔLPQ according to the AA similarity postulate
3. ΔPQN ~ ΔLMN
LM = 12, QP = 8
4. ΔLMK~ΔLNJ
NL = 21, ML = 14
What are similar triangles?
Similar triangles are triangles that have the same shape but may have different sizes.
1. The ratio of corresponding sides between the two triangles circumscribing the congruent included angle are;
24/16 = 3/2
18/12 = 3/2
The ratio of each of the two sides in the triangle ΔAJK to the corresponding sides in the triangle ΔSWY are equivalent and the included angle, therefore, the triangles ΔAJK and ΔSWY are similar according to the SAS similarity rule.
2. The ratio of the corresponding sides in each of the triangles are;
MN/LN = 8/10 = 4/5
PQ/LQ = 12/(10 + 5) = 12/15 = 4/5
The triangle proportionality theorem indicates that the side MN and PQ are parallel, therefore, the angles ∠LMN ≅ ∠LPQ and ∠LNM ≅ ∠LQP, which indicates that the triangles ΔLMN and ΔLPQ are similar according to the Angle-Angle AA similarity rule
3. The alternate interior angles theorem indicates;
Angles ∠PQN ≅ ∠LMN and ∠MLN ≅ ∠NPQ, therefore;
ΔPQN ~ ΔLMN by the AA similarity postulate
LM/QP = (x + 3)/(x - 1) = 18/12
12·x + 36 = 18·x - 18
18·x - 12·x = 36 + 18 = 54
6·x = 54
x = 54/6 = 9
LM = 9 + 3 = 12
QP = x - 1
QP = 9 - 1 = 8
4. The similar triangles are; ΔLMK and ΔLNJ
ΔLMK ~ ΔLNJ by AA similarity postulate
ML/NL = (6·x + 2)/(6·x + 2 + (x + 5)) = (6·x + 2)/((7·x + 7)
ML/NL = LK/LJ = (24 - 8)/24
(24 - 8)/24 = (6·x + 2)/((7·x + 7)
16/24 = (6·x + 2)/(7·x + 7)
16 × (7·x + 7) = 24 × (6·x + 2)
112·x + 112 = 144·x + 48
144·x - 112·x = 32·x = 112 - 48 = 64
x = 64/32 = 2
ML = 6 × 2 + 2 = 14
NL = 7 × 2 + 7 = 21
MN = 2 + 5 = 7
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debbie wants tp compare the simple interest to compound interest on 60,000 investment
Answer:
this question is incomplete
The midpoint of AB is M(-4,2). If the coordinates of A are (-7,3), what are the
coordinates of B?
The midpoint of AB is M(-4,2). If the coordinates of A are (-7,3), and the coordinates of B is (-1, 1).
To find the coordinates of point B, we can use the midpoint formula, which states that the coordinates of the midpoint between two points (A and B) can be found by averaging the corresponding coordinates.
Let's denote the coordinates of point A as (x1, y1) and the coordinates of point B as (x2, y2). The midpoint M is given as (-4, 2).
Using the midpoint formula, we can set up the following equations:
(x1 + x2) / 2 = -4
(y1 + y2) / 2 = 2
Substituting the coordinates of point A (-7, 3), we have:
(-7 + x2) / 2 = -4
(3 + y2) / 2 = 2
Simplifying the equations:
-7 + x2 = -8
3 + y2 = 4
Solving for x2 and y2:
x2 = -8 + 7 = -1
y2 = 4 - 3 = 1
Therefore, the coordinates of point B are (-1, 1).
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Answer:
(a) 10, $2088.81
(b) see attached
(c) B. increases at a slower rate
Step-by-step explanation:
Given the cost function g(x) = -1736.7 +1661.4·ln(x) for the average dollar cost of health insurance in year x after 2000, you want the cost in 2010, a graph for the years 2006 to 2015, and a description of the shape of the curve.
(a) Cost in 2010The value of x is years after 2000, so for the year 2010, the value of x is ...
x = 2010 -2000 = 10
Substituting 10 for x in the function will give the cost in 2010. That is ...
g(10) = -1736.7 +1661.4·ln(10) ≈ 2088.81
The cost in 2010 is about $2088.81.
(b) GraphThe second attachment shows a graphing calculator's rendition of the graph. We note it has positive slope everywhere, but does not intersect the lines y=1000 or y=3000. This eliminates choices A, C, and D, leaving choice B for the graph.
(c) ShapeThe logarithm function has positive and decreasing slope. The function here is a scaled and shifted version of the logarithm function, but it still has positive and decreasing slope. That is, ...
the average cost increases at a slower rate as time goes on
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