On a coordinate plane, a curved line, labeled D, with a minimum value of (3, negative 8), labeled C, with x-intercept (1, 0), labeled B, and y-intercept (0, 10), labeled A. Match the letter of the key feature on the graph with its name. x-intercept: y-intercept: Relative minimum: Increasing interval:
Answers
The interval for the graphed function that has a local minimum of 0 is [-2, 0].
To determine the interval for the graphed function that has a local minimum of 0, we need to examine the behavior of the graph around the x-values where it crosses the x-axis.
We know that the graph crosses the x-axis at -2.5, 0, and 3. Since the local minimum occurs at 0, we need to find the interval where the graph is decreasing to the left of 0 and increasing to the right of 0.
From the given information, we can determine the following:
The graph is decreasing between -2.5 and 0 because it crosses the x-axis at -2.5 and 0, and the minimum value is at (-1.56, -6).
The graph is increasing between 0 and 3 because it crosses the x-axis at 3, and the maximum value is at (1.2, 2.9).
The correct option is [–2, 0].
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Question
On a coordinate plane, a curved line with minimum values of (negative 1.56, negative 6) and (3, 0), and a maximum value of (1.2, 2.9), crosses the x-axis at (negative 2.5, 0), (0, 0), and (3, 0), and crosses the y-axis at (0, 0). Which interval for the graphed function has a local minimum of 0? [–3, –2] [–2, 0] [1, 2] [2, 4]
Related Questions
Which type of conic section is defined by the equation:... 100pts
Answers
Answer:
This is an equation of a parabola.
[tex](y+6)^2=4(x+1)[/tex]
Step-by-step explanation:
A conic section is a curve obtained by the intersection of a plane and a cone. The three major conic sections are parabola, hyperbola and ellipse (the circle is a special type of ellipse).
The standard equations for hyperbolas and ellipses all include x² and y² terms. The standard equation for a parabola includes the square of only one of the two variables.
Therefore, the equation y² - 4x + 12y + 32 = 0 represents a parabola, as there is no x² term.
As the y-variable is squared, the parabola is horizontal (sideways), and has an axis of symmetry parallel to the x-axis.
The conic form of a sideways parabola is:
[tex]\boxed{(y-k)^2=4p(x-h)}[/tex]
where:
(h, k) is the vertex.(h+p, k) is the focus.x = h-p is the directrix.To write the given equation in conic form, we need to complete the square for the y-variable.
Rearrange the equation so that the y-terms are on the left side:
[tex]y^2 + 12y = 4x - 32[/tex]
Add the square of half the coefficient of the y-term to both sides of the equation:
[tex]y^2 + 12y+\left(\dfrac{-12}{2}\right)^2 = 4x - 32+\left(\dfrac{-12}{2}\right)^2[/tex]
[tex]y^2 + 12y+\left(-6\right)^2 = 4x - 32+\left(-6\right)^2[/tex]
[tex]y^2 + 12y+36 = 4x - 32+36[/tex]
[tex]y^2 + 12y+36 = 4x +4[/tex]
Factor the perfect square trinomial on the left side of the equation:
[tex](y+6)^2=4x+4[/tex]
Factor out the coefficient of the x-term from the right side of the equation:
[tex](y+6)^2=4(x+1)[/tex]
Therefore, the equation of the given conic section in conic form is:
[tex]\boxed{(y+6)^2=4(x+1)}[/tex]
where:
(-1, -6) is the vertex.(0, -6) is the focus.x = -2 is the directrix.The conic section of the equation y² - 9x + 12y + 32 = 0 is a parabola
Selecting the conic section of the equationThe given equation is
y² - 9x + 12y + 32 = 0
The above equation is an illustration of a parabola equation
The standard form of a parabola is
(x - h)² = 4a(y - k)²
Where
(h, k) is the center
While the general form of the equation is
Ax² + Dx + Ey + F = 0
In this case, the equation y² - 9x + 12y + 32 = 0 takes the general form
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Find the zeros of the function shown below
Answers
Answer:
x = - 5 , x = 2
Step-by-step explanation:
f(x) = x² + 3x - 10
to find the zeros let f(x) = 0 , that is
x² + 3x - 10 = 0
consider the factors of the constant term (- 10) which sum to give the coefficient of the x- term (+ 3)
the factors are + 5 and - 2 , since
5 × - 2 = - 10 and 5 - 2 = + 3 , then
(x + 5)(x - 2) = 0 ← in factored form
equate each factor to zero and solve for x
x + 5 = 0 ( subtract 5 from both sides )
x = - 5
x - 2 = 0 ( add 2 to both sides )
x = 2
the zeros are x = - 5 , x = 2
The sum of negative twenty-nine and twenty-eight is negative seven more than a number. What is the number?
Answers
Answer:
8
Step-by-step explanation:
let x be the number,
according to the question,
-29 + 28 = -7 + x
1 + 7 = x
thus, x = 8
Steven earns extra money babysitting. He charges $31.00 for 4 hours and $62.00 for 8 hours.
Enter an equation to represent the relationship. Let x represent the number of hours Steven babysits and y represent the amount he charges.
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The equation is y = 7.75x, where x is the number of hours Steven babysits and y is the amount he charges.
To represent the relationship between the number of hours Steven babysits (x) and the amount he charges (y), we can use a linear equation in the form of y = mx + b, where m is the slope and b is the y-intercept.
From the given information, we can identify two data points:
(4, 31.00) and (8, 62.00)
Using these points, we can calculate the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
m = (62.00 - 31.00) / (8 - 4)
m = 31.00 / 4
m = 7.75
Now, we can substitute one of the points and the slope into the equation to find the y-intercept (b).
Using the point (4, 31.00):
31.00 = 7.75(4) + b
31.00 = 31.00 + b
b = 0
Therefore, the equation that represents the relationship between the number of hours Steven babysits (x) and the amount he charges (y) is:
y = 7.75x
The equation is y = 7.75x, where x is the number of hours Steven babysits and y is the amount he charges.
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40 POINTS: PLEASE HELP!! urgent! using half-angle identities questions
Answers
Answer:
try gauth. math! Take a photo of each question and upload the photo to see if it works
Organizers of an outdoor summer concert in Toronto are concerned about the weather conditions on the day of the concert. They will make a profit of $40,000 on a clear day and $14,000 on a cloudy day. They will make a loss of $5,000 if it rains. The weather channel has predicted a 60% chance of rain on the day of the concert. Calculate the expected profit from the concert if the likelihood is 14% that it will be sunny and 26% that it will be cloudy.
Answers
Answer:
$6240
Step-by-step explanation:
given likelihoods:
sunny day = 14% = 0.14
cloudy day = 26% = 0.26
rainy day = 60% = 0.60
profits:
profit on a sunny day = $40,000
profit on a cloudy day = $14,000
Loss on a rainy day = -$5,000
expected profit = (probability of sunny day * profit on sunny day) + (probability of cloudy day * profit on cloudy day) + (probability of rainy day * loss on rainy)
expected profit = (0.14 * $40,000) + (0.26 * $14,000) + (0.60 * -$5,000)
=6240
NEED HELP
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Next Activity
Answers
The conditions that prove that the triangles ΔABC and ΔXYZ are similar, ΔABC ~ ΔXYZ, based on the order of the lettering are;
BA/YX = BC/YZ = AC/XZ
AC/XZ = BA/YX, ∠A ≅ ∠C
What are similar triangles?Similar triangles are triangles that have the same shape (the same two or all three interior angles in each triangle) but in which may have different sizes.
Triangles are similar if they equivalent ratio for their sides and and if the angles in each triangle are congruent to the angles in the other triangle
Therefore, the conditions that indicates that two triangles are that one triangle is a scaled image of the other triangle, therefore, the ratio of the corresponding sides of the triangles are equivalent, which indicates;
ΔABC is similar to ΔXYZ if we get;
BA/YX = BC/YZ = AC/XZA condition that indicates that two triangle are similar is the Side Angle Side, SAS, similarity postulate, which states that two triangles are congruent if the ratio of two corresponding sides are equivalent and the angle between the two sides in the two triangles are congruent, therefore;
ΔABC is similar to ΔXYZ if we get;
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The volume of this triangular prism is 1,170 cubic feet. What is the value of m?
Answers
The calculated value of m in the triangular prism is 13
How to calculate the value of m?From the question, we have the following parameters that can be used in our computation:
The triangular prism
Where, we have
Volume = 1170
The volume of the triangular prism is calculated as
Volume = Base area * Height
So, we have
1/2 * m * 18 * 10 = 1170
Evaluate the products
This gives
90m = 1170
So, we have
m = 13
Hence, the value of m is 13
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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.
Answers
From the Table display of scores and students on a recent exam, The mean of the scores to the nearest 10th is 83.7.
To find the mean of the scores, we need to calculate the sum of the products of each score and its corresponding number of students, and then divide it by the total number of students.
Here's the calculation:
(70 * 6) + (75 * 3) + (80 * 9) + (85 * 5) + (90 * 7) + (95 * 8) = 420 + 225 + 720 + 425 + 630 + 760 = 3180
Total number of students = 6 + 3 + 9 + 5 + 7 + 8 = 38
Mean = Sum of products / Total number of students = 3180 / 38 ≈ 83.7 (rounded to the nearest tenth)
Therefore, the mean of the scores is approximately 83.7.
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Find the limit (if the limit exists). Solve in two different ways.
Answers
The limit of the trigonometric expression is equal to 0.
How to determine the limit of a trigonometric expression
In this problem we find the case of a trigonometric expression, whose limit must be found. This can be done by means of algebra properties, trigonometric formula and known limits. First, write the entire expression below:
[tex]\lim_{\Delta x \to 0} \frac{\cos (\pi + \Delta x) + 1}{\Delta x}[/tex]
Second, use the trigonometric formula cos (π + Δx) = - cos Δx to simplify the resulting formula:
[tex]\lim_{\Delta x \to 0} \frac{1 - \cos \Delta x}{\Delta x}[/tex]
Third, use known limits to determine the result:
0
The limit of the trigonometric function [cos (π + Δx) + 1] / Δx evaluated at Δx → 0 is equal to 0.
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Find the co-vertices of the hyperbola defined by the equation.. 100pts
Answers
Answer:
(-13, -9) and (-5, -9)
Step-by-step explanation:
The given equation of the hyperbola is:
[tex]\dfrac{(y+9)^2}{25}-\dfrac{(x+9)^2}{16}=1[/tex]
As the y²-term of the given equation is positive, the transverse axis is vertical, and so the hyperbola is vertical (opens up and down).
The standard equation for a vertical hyperbola is:
[tex]\boxed{\dfrac{(y-k)^2}{a^2}-\dfrac{(x-h)^2}{b^2}=1}[/tex]
where:
center = (h, k)vertices = (h, k±a)co-vertices = (h±b, k)foci = (h, k±c) where c² = a² + b²Compare the given equation with the standard equation to find the values of h, k, a and b:
h = -9k = -9a² = 25 ⇒ a = 5b² = 16 ⇒ b = 4The formula for the co-vertices of a vertical hyperbola is (h±b, k).
Substitute the values of b, h and k into the formula:
[tex]\begin{aligned}\textsf{Co-vertices}&=(h\pm b,k)\\&=(-9\pm 4, -9)\\&=(-13,-9)\;\;\textsf{and}\;\;(-5, -9)\end{aligned}[/tex]
Therefore, the co-vertices of the given hyperbola are:
(-13, -9) and (-5, -9)The co-vertices of the hyperbola are (-4, -9) and (-14, -9).
What are the co-vertices of the hyperbola?To find the co-vertices of the hyperbola defined by the equation:
[(y + 9)² / 25] - [(x + 9)² / 16] = 1
We can compare the equation to the standard form of a hyperbola:
[(y - h)² / a²] - [(x - k)² / b²] = 1
In this case, we have h = -9 and k = -9.
The co-vertices of a hyperbola lie on the transverse axis, which is the line passing through the center of the hyperbola. The center of the hyperbola is given by (h, k), which in this case is (-9, -9).
For a hyperbola with the equation in this form, the co-vertices are located a units to the right and left of the center. In this case, since the equation is [(y + 9)² / 25] - [(x + 9)² / 16] = 1, we have a = 5.
Therefore, the co-vertices are located at (-9 ± a, -9), which gives us:
(-9 + 5, -9) = (-4, -9)
(-9 - 5, -9) = (-14, -9)
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The length of a rectangle is 4 ft longer than its width. If the perimeter of the rectangle is 32 ft, find its area.
Answers
To find the area of a rectangle, we need to know its length and width. Let's solve the problem step by step:
Let's assume that the width of the rectangle is represented by "w" (in feet).
According to the given information, the length of the rectangle is 4 feet longer than its width, which means the length can be represented as "w + 4" (in feet).
The perimeter of a rectangle is calculated by adding up all the sides. In this case, the perimeter is given as 32 feet.
Since a rectangle has two pairs of equal sides (length and width), we can express the perimeter equation as the following:
2(length + width) = perimeter
Substituting the values into the equation, we get:
2(w + (w + 4)) = 32
Simplifying the equation, we have:
2(2w + 4) = 32
4w + 8 = 32
4w = 24
w = 6
Now we know that the width of the rectangle is 6 feet. To find the length, we can substitute this value back into the equation for the length:
Length = w + 4 = 6 + 4 = 10 feet
The width is 6 feet, and the length is 10 feet. Now we can calculate the area of the rectangle:
Area = Length × Width = 10 × 6 = 60 square feet
Answer: The area of the rectangle is 60 square feet.
Use the 2021 marginal tax rates in the table to compute the tax owed by the person with the given filing status and taxable income.
Single with a taxable income of $61,000
The tax owed is $_____.
(Type an integer or a decimal. Round to the nearest cent as needed.)
Answers
The amount of tax owed is $13,420
How to determine the amount of tax owedFrom the question, we have the following parameters that can be used in our computation:
Single with a taxable income of $61,000
Using the table of marginal tax, we have
Tax = 22%
So, we have
Tax = 22% * 61000
Evaluate
Tax = 13420
Hence, the amount of tax owed is $13,420
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simplify each expression 4(x+2)+(8+2x)
Answers
The simplified form of the expression for 4( x + 2 ) + ( 8 + 2x ) is 6x + 16.
What is the simplified form of the expression?Given the expresion in the equestion:
4( x + 2 ) + ( 8 + 2x )
To simplify the expression 4( x + 2 ) + ( 8 + 2x ), first, apply distributive property by distributing 4 to the terms ( x + 2 ):
4( x + 2 ) + ( 8 + 2x )
4 × x + 4 × 2 + 8 + 2x
4x + 8 + 8 + 2x
Collect and add like terms:
4x + 2x + 8 + 8
Add 4x and 2x
6x + 8 + 8
Add the constants 8 + 8
6x + 16
Therefore, the simplified form is 6x + 16.
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Analyzing Wages-Plus-Commission Pay
Maybelle works in the shoe department for a high-end
store. She earns $15 per hour for at least 40 hours per
week. On top of that, she earns 10% commission for each
pair of shoes she sells. She is expected to sell $2,500
worth of shoes every week.
What will Maybelle earn in wages in a typical week?
How much commission will Maybelle earn if she sells
$3,000 of shoes in one week?
v
The next week, customers return $1,000 worth of
shoes. How much money will be deducted from
Maybelle's paycheck?
With an economic downturn, sales slump. As a result,
Maybelle will likely
Answers
a)In a typical week, Maybelle will earn a total of: $600 + $250 = $850
b) Her total earnings for the week would be: $600 + $300 = $900
c) Her paycheck will be reduced by $100.
d) Her wage earnings should remain the same assuming she still works at least 40 hours per week.
To calculate Maybelle's earnings in a typical week, we first need to determine the minimum number of hours she works. Since she earns $15 per hour for at least 40 hours per week, her minimum wage earnings are:
$15 x 40 = $600
In addition to her wage earnings, Maybelle earns a commission of 10% for each pair of shoes she sells. Since she is expected to sell $2,500 worth of shoes every week, her commission earnings are:
$2,500 x 0.10 = $250
b) If Maybelle sells $3,000 worth of shoes in one week, her commission earnings would be:
$3,000 x 0.10 = $300
On top of her wage earnings of $600 (based on working at least 40 hours at $15 per hour)
c) If customers return $1,000 worth of shoes the next week, Maybelle's commission earnings will not be affected. However, her wage earnings will be reduced by the amount of the returned shoes, which is $1,000 x 0.10 = $100.
d) With an economic downturn and sales slump, Maybelle's earnings from commission will likely decrease since she will sell fewer shoes. However, her total earnings will likely decrease due to the decrease in commission earnings.
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Aschalew is able to do apiece of work in 15 days and Abay can do the same work in 20 daya. if they can work together for 4 days, what is the fraction of the work left?
Answers
Answer:
8/15
Step-by-step explanation:
1/15(4 + 1/20(4)
4/15 + 4/20 I can reduce 4/20 to 1/5
4/15 + 1/5
4/15 + 3/15 = 7/15
Together they can get 7/15 of the job done. 15/15 - 7/15 is 8/15.
That means that they have 8/15 left to do.
Helping in the name of Jesus.
graph the equation y = 2x + 2
Answers
Answer:
Step-by-step explanation:
When the equation is in the slope intercept form of y = mx + b, you know that the m is the slope and the b is the y-intercept (0, b)
By looking at the equation y=2x + 2, you can determine that the y-intercept will be at the point (0, 2) and the slope is 2.
To graph, start with the point of (0, 2) then go up 2 units and to the right 1 unit. So the next point will be at (1, 4)
You can also, substitute and number in for the x and calculate the y value. For example, if x is 3, then y=2(3)+2; y = 8 so the point (3, 8) is on the line.
8.4.4. Define sets. How many kinds of sets Also list the operation of sets. Give the short activites for teaching Learning Union of sets. 2+2+2+4=10)
Answers
In mathematics, a set is a well-defined collection of distinct objects, called elements or members of the set. These objects can be anything: numbers, letters, people, or even other sets.
he concept of sets is fundamental in various branches of mathematics, including set theory, algebra, and statistics.There are different kinds of sets based on their properties:
Finite set: A set with a specific number of elements, which can be counted.Infinite set: A set with an endless number of elements.Empty set: A set with no elements. It is denoted by the symbol Ø or {}.
Singleton set: A set with only one element.Subset: A set whose elements are all contained within another set.Universal set: A set that includes all the possible elements of interest in a particular context.Operations on sets involve various ways of combining or manipulating sets:
Union: The union of two sets A and B is the set that contains all the elements from both sets. It is denoted by A ∪ B.Intersection: The intersection of two sets A and B is the set of elements that are common to both sets. It is denoted by A ∩ B.
Complement: The complement of a set A, denoted by A', is the set of all elements that are not in A but are in the universal set.Difference: The difference between two sets A and B is the set of elements that are in A but not in B. It is denoted by A - B.
Cartesian Product: The Cartesian product of two sets A and B is the set of all possible ordered pairs, where the first element is from set A and the second element is from set B. It is denoted by A × B.
For teaching the concept of the union of sets, you can use the following activity:
Activity: Venn Diagrams
Draw two overlapping circles on the board or use physical cut-out circles.Label one circle as Set A and the other as Set B.
Ask the students to suggest elements for each set and write them inside the circles.Discuss the elements that are common to both sets and write them in the overlapping region.Explain that the union of sets A and B represents all the elements in both sets.
Combine the elements from sets A and B, including the elements in the overlapping region, and write them in a new circle labeled as A ∪ B.Emphasize that the union includes all the distinct elements from both sets without repetition.
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Find a, b,c, and d, such that the cubic f(x)=ax^3+bx^2+cx+d has a relative maximum at (-7, 163); has a relative minimum at (5, -125); and has a point of inflection at (-1, 19).
Answers
The cubic function with the desired properties is:
f(x) = (-3/4)x³ - (9/4)x² - (113/4)x + 63/4
To find the values of a, b, c, and d, we can use the given information about the relative maximum, relative minimum, and point of inflection.
Relative Maximum:
The point (-7, 163) is a relative maximum. At this point, the derivative of the cubic function is equal to zero. Taking the derivative of the cubic function, we have:
f'(x) = 3ax² + 2bx + c
Setting x = -7 and f'(-7) = 0, we get:
49a - 14b + c = 0
Relative Minimum:
The point (5, -125) is a relative minimum. At this point, the derivative of the cubic function is equal to zero. Taking the derivative of the cubic function, we have:
f'(x) = 3ax² + 2bx + c
Setting x = 5 and f'(5) = 0, we get:
75a + 10b + c = 0
Point of Inflection:
The point (-1, 19) is a point of inflection. At this point, the second derivative of the cubic function changes sign. Taking the second derivative of the cubic function, we have:
f''(x) = 6ax + 2b
Setting x = -1, we get:
-6a + 2b = 0
Solving the system of equations formed by the above three equations, we can find the values of a, b, c, and d.
49a - 14b + c = 0
75a + 10b + c = 0
-6a + 2b = 0
Solving these equations, we find:
a = -3/4
b = -9/4
c = -113/4
d = 63/4
Therefore, the cubic function with the desired properties is:
f(x) = (-3/4)x³ - (9/4)x² - (113/4)x + 63/4
Consider the transformation.
2 trapezoids have identical angle measures but different side lengths. The first trapezoid has side lengths of 4, 2, 6, 2 and the second trapezoid has side lengths of 8, 4, 12, 4.
Which statement about the transformation is true?
Answers
The true statement about the transformation is that the second trapezoid is a dilation of the first trapezoid with a scale factor of 2.
The given transformation involves two trapezoids with identical angle measures but different side lengths. Let's analyze the two trapezoids and determine the statement that is true about the transformation.
First Trapezoid:
Side lengths: 4, 2, 6, 2
Second Trapezoid:
Side lengths: 8, 4, 12, 4
To determine the relationship between the side lengths of the two trapezoids, we can compare the corresponding sides.
Comparing the corresponding sides:
4 / 8 = 2 / 4 = 6 / 12 = 2 / 4
We can observe that the corresponding sides of the two trapezoids have the same ratio. This indicates that the side lengths of the second trapezoid are twice the lengths of the corresponding sides of the first trapezoid. Therefore, the statement that is true about the transformation is:
The second trapezoid is a dilation of the first trapezoid with a scale factor of 2.
A dilation is a type of transformation that produces an image that is the same shape as the original figure but a different size. In this case, the second trapezoid is obtained by scaling up the first trapezoid by a factor of 2 in all directions.
This transformation preserves the shape and angle measures of the trapezoid but changes its size. The corresponding sides of the second trapezoid are twice as long as the corresponding sides of the first trapezoid.
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The sum of the measures of the angles is 180. The sum of the measures of the second and third angles is two times the measure of the first angle. The third angle is 20 more than the second. Let x, y, and z represent the measures of the first, second, and third angles, respectively. Find the measures of the three angles.
Answers
Let's assign variables to the measures of the angles:
Measure of the first angle: X
Measure of the second angle: Y
Measure of the third angle: Z
According to the problem, the sum of the measures of the angles is 180. Therefore, we can write the equation:
X + Y + Z = 180
The problem also states that the sum of the measures of the second and third angles is two times the measure of the first angle. We can express this as an equation:
Y + Z = 2X
Additionally, it is given that the third angle is 20 more than the second angle. This can be expressed as an equation:
Z = Y + 20
Now, we have a system of three equations:
Equation 1: X + Y + Z = 180
Equation 2: Y + Z = 2X
Equation 3: Z = Y + 20
To solve this system, we can substitute Equation 3 into Equation 2 to eliminate Z:
Y + (Y + 20) = 2X
2Y + 20 = 2X
2Y = 2X - 20
Y = X - 10
Now, we have an expression for Y in terms of X. We can substitute this expression into Equation 1 to eliminate Y:
X + (X - 10) + Z = 180
2X - 10 + Z = 180
Z = 190 - 2X
So, we have expressions for Y and Z in terms of X:
Y = X - 10
Z = 190 - 2X
Now, we can substitute these expressions into the original equation for the sum of the measures of the angles to solve for X:
X + (X - 10) + (190 - 2X) = 180
X + X - 10 + 190 - 2X = 180
2X - 2X + X = 180 - 190 + 10
X = 0
Substituting X = 0 back into the expressions for Y and Z, we get:
Y = 0 - 10 = -10
Z = 190 - 2(0) = 190
Therefore, the measures of the angles are:
First angle (X): 0 degrees
Second angle (Y): -10 degrees
Third angle (Z): 190 degrees
Note: It is unusual to have negative angles in a geometric context. Please double-check the problem statement to ensure there are no errors or inconsistencies in the given information.
Al bought a CD player for $100, then sold it for $125. He then bought it back for $150. Later he sold it for $175. Did he make money, lose money, or break even? Explain.
Answers
His total expenditure is $100. After that, he sold the CD player for $125. As a result, he earned $25.
Al initially bought a CD player for $100 and then sold it for $125. After that, he bought it back for $150 and later sold it for $175. The question is whether Al made money, lost money, or broke even.
Let's examine the transactions in more detail to determine the answer.
Initially, Al bought the CD player for $100.
Now his total income is $25 and his expenditure remains at $100. Next, he purchased the same CD player again for $150. This adds to his expenditure, which is now $250.
Later, he sold the CD player for $175, which means he earned another $25, bringing his total income to $50 (i.e., $25 from the first sale and $25 from the second sale).
Since Al's total expenditure was $250 and his total income was $50, he lost money. He spent more than he earned.
He sold the CD player twice and earned a total of $50, which is less than what he spent on the CD player, which was $250. Al had a net loss of $200 ($250 - $50). Therefore, he lost money.
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The data set shows the ages of everyone in a dance class.
4, 17, 17, 17, 17, 17, 18, 18, 18
Select the statement that correctly describes the data.
3 of 5 QUESTIONS
The typical value is 9 because that is the total number of people.
The typical value is 18 because it is the maximum.
The typical value is 4 because it is the minimum.
The typical value is 17. Most values are close to 17, except 4, which is an
extreme value.
Answers
Answer: The statement that correctly describes the data is:
The typical value is 17. Most values are close to 17, except 4, which is an extreme value.
This is because the value 17 appears most frequently in the data set, making it the mode or the typical value. The value 4 is an extreme value as it is the minimum value in the data set. The maximum value of 18 is not the typical value because it is not as representative of the overall distribution of ages in the data set as the mode, which is 17.
Step-by-step explanation:
Assume that at the current exchange rate, the British pound is worth $1.65 in American dollars. You have some dollar bills and several British pound coins. There are 17 items altogether, which have a total value of $20.25 in American dollars. How many American dollars and how many British pound coins do you have?
Answers
Answer:
So we have $11.64 in American dollars and £5 in British pound coin
Step-by-step explanation:
To solve this problem, we can use a system of equations. Let x be the number of American dollars and y be the number of British pound coins. Then we have:
x + y/1.65 = 20.25 (since each British pound coin is worth 1.65 American dollars)
x = 17 - y (since there are 17 items altogether)
Substituting the second equation into the first, we get:
(17 - y) + y/1.65 = 20.25
Multiplying both sides by 1.65, we get:
28.05 - y + y = 33.4125
y = 33.4125 - 28.05
y = 5.3625
Therefore, we have 5 British pound coins and:
x = 17 - y = 17 - 5.3625 = 11.6375
please answer ASAP I will brainlist
Answers
(a) The average cost in 2010 is $2088.82.
(b) A graph of the function g for the period 2006 to 2015 is: D. graph D.
(c) Assuming that the graph remains accurate, its shape suggest that: B. the average cost increases at a slower rate as time goes on.
How to estimate the average cost in 2011?Based on the information provided, we can logically deduce that the average annual cost (in dollars) for health insurance in this country can be approximately represented by the following function:
g(x) = -1736.7 + 1661.4lnx
where:
x = 6 corresponds to the year 2006.
For the year 2011, the average cost (in dollars) is given by;
x = (2010 - 2006) + 6
x = 4 + 6
x = 10 years.
Next, we would substitute 10 for x in the function:
g(10) = -1736.7 + 1661.4ln(10)
g(10) = $2088.82
Part b.
In order to plot the graph of this function, we would make use of an online graphing tool. Additionally, the years would be plotted on the x-axis while the average annual cost would be plotted on the x-axis of the cartesian coordinate as shown below.
Part c.
Assuming the graph remains accurate, the shape of the graph suggest that the average cost of health insurance increases at a slower rate as time goes on.
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The endpoints of AB are A (-7, -14) and B (5,10) . Into which ratio will each point divide AB ?
Answers
The point A divides the line segment AB into the ratio 3:1, while the point B divides it into the ratio 1:3.
1. To find the ratio in which each point divides AB, we need to calculate the distances from each endpoint to the dividing point.
2. Let's calculate the distance from point A to the dividing point. The x-coordinate of point A is -7, and the y-coordinate is -14. Similarly, the x-coordinate of point B is 5, and the y-coordinate is 10.
3. We'll use the distance formula, which states that the distance between two points (x1, y1) and (x2, y2) is given by:
distance = sqrt((x2 - [tex]x1)^2 + (y2 - y1)^2)[/tex]
4. Applying the distance formula, we find the distance from point A to the dividing point:
[tex]distance_A[/tex] = sqrt((5 -[tex](-7))^2 + (10 - (-14))^2)[/tex]
= sqrt((5 + [tex]7)^2 + (10 + 14)^2)[/tex]
= sqrt([tex]12^2[/tex] + [tex]24^2[/tex])
= sqrt(144 + 576)
= sqrt(720)
= 12√5
5. Similarly, let's calculate the distance from point B to the dividing point:
[tex]distance_B[/tex] = sqrt((-7 - [tex]5)^2 + (-14 - 10)^2)[/tex]
= sqrt((-[tex]12)^2 + (-24)^2)[/tex]
= sqrt(144 + 576)
= sqrt(720)
= 12√5
6. The dividing ratio can be determined by comparing the distances from each endpoint to the dividing point. Since distance_A:distance_B = 3:1, we conclude that point A divides the line segment AB into the ratio 3:1, and point B divides it into the ratio 1:3.
Thus, the endpoints A and B divide the line segment AB into the ratios 3:1 and 1:3, respectively.
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Answer:
the ratio for point C is 1 : 2.
the ratio for point D is 3 : 1.
the ratio for point E is 2 : 1.
Step-by-step explanation:
I just got it right on the test
NEED NOW PLEASE HELP OUT
Answers
Answer:
x=50
Step-by-step explanation:
Make this equal to 180.
x+3x-35+x-35 = 180
5x = 180 + 70
5x=250
x=50
Ki Tae uses 54 meters of fencing to make a 6-sided outdoor dog pen. Two of the sides of the dog pen are each 15 meters long. The remaining 4 sides each have the same length.
Answers
Ki Tae used 54 meters of fencing to construct a 6-sided outdoor dog pen. Two of the sides are each 15 meters long, while the remaining four sides are each 6 meters long.
Let's solve the problem step by step. We know that Ki Tae used a total of 54 meters of fencing to construct a 6-sided outdoor dog pen. Two of the sides have a length of 15 meters each.
Let's denote the length of the remaining four sides as "x."
Since the dog pen has six sides, we can set up an equation based on the total length of the fencing:
15 + 15 + x + x + x + x = 54
Simplifying the equation, we have:
30 + 4x = 54
Subtracting 30 from both sides, we get:
4x = 24
Dividing both sides by 4, we find:
x = 6
Therefore, each of the remaining four sides has a length of 6 meters.
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solve this system of equations by using the elimination method x-5y=16 4x-2y=-8
Answers
Answer:
(- 4, - 4 )
Step-by-step explanation:
x - 5y = 16 → (1)
4x - 2y = - 8 → (2)
multiplying (1) by - 4 and adding to (2) will eliminate x
- 4x + 20y = - 64 → (3)
add (2) and (3) term by term to eliminate x
(4x - 4x) + (- 2y + 20y) = - 8 - 64
0 + 18y = - 72
18y = - 72 ( divide both sides by 18 )
y = - 4
substitute y = - 4 into either of the 2 equations and solve for x
substituting into (1)
x - 5(- 4) = 16
x + 20 = 16 ( subtract 20 from both sides )
x = - 4
solution is (- 4, - 4 )
"Twice the difference of M and 14 equals 64."
Answers
Answer:
2(M - 14) = 64
M - 14 = 32
M = 46
