Using a linear function, it is found that:
a. The table is completed as follows: Month 2, Stamps 144; Month 3, Stamps 156; Month 4, Stamps 168; Month 5, Stamps 180.
b. She will have 264 stamps after one year.
c. The function is given by: t(n) = 120 + 12n.
What is a linear function?A linear function, in slope-intercept format, is modeled according to the following rule:
y = mx + b
In which:
m is the slope of the function, which is the rate of change of the function, that is, the change in y divided by the change in x.b is the y-intercept of the function, which is the the value of y when the function crosses the x-axis(x = 0).For the function in this problem, we have that:
The intercept is of 120, as the initial value is of 120 stamps.The slope is of 12, as 12 stamps are added each month to the collection.Hence the function is given by:
t(n) = 120 + 12n.
To complete the table, we find the numeric values are follows:
t = 2, t(2) = 120 + 12(2) = 144.t = 3, t(3) = 120 + 12(3) = 156.t = 4, t(4) = 120 + 12(4) = 168.t = 5, t(5) = 120 + 12(5) = 180.One year from now is 12 months, hence:
t(12) = 120 + 12(12) = 264.
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Trigonometry please help
Radius = 12 cm
Central angle = 30°
Length of circular arc = 2πr(θ/360)
⇒ Length of circular arc = 2π x 12 (30/360)
⇒ Length of circular arc = 2π x 1
⇒ Length of circular arc = 2π = 2 x 3.14 = 6.283 cm
What is a Circular arc?A section of curvature or a circle is referred to as an arc in mathematics. The chord of the circle is the line that forms the connection between the arc's ends. A semicircular is exactly half the length of the circle.If the two points are not exactly opposite one another, the major arc will subtend an angle larger than radians at the circle's center whereas the minor arc will subtend an angle less than radians (180 degrees).Plotting two lines from the arc's ends to the circle's center, measuring the angle at which the two lines intersect, and solving for L by cross-multiplying the resulting statement are useful methods for calculating an arc's length.To learn more about Circular arcs, refer to:
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Write a paragraph proof to prove that if P, Q, R, and S are collinear, PQRS, and O is the midpoint of PR, then R is the midpoint
of QS.
Because PQ RS and congruent segments have ___ lengths, PQ = ___ Because Q is the midpoint of PR, ___ so R is the midpoint of QS. PQ ___ By the Select Choice Property of Equality. QR
The Addition of AnglesABD + DBC = ABC, according to the postulate formula, if D is within of ABC.The formula is applicable to adjacent angles' angle measurements.The greater angle that the two adjacent angles combine to generate will equal the total of the two adjacent angles.
Write a paragraph proof to prove that if P, Q, R, and S are collinear, PQRS, and O is the midpoint of PR, then R is the midpointof QS.
demonstrating PR = QS
Given: Q is PR's halfway point.
A segment's midpoint:
PQ = QR
Given: QS's midpoint is R.
A segment's midpoint:
PQ = QR
The equality's addition property is: QR + RS = PQ + QR.
Consequently, PR = QS.
The seven seven-statement proof below provides evidence that "PQO" and "RSO" are true.
I have provided the triangles image since it is missing.
The following is a step-by-step statement proof that "PQO" and "RSO" are true:
First statement; P R
the first; given
2. O is the midway of PR and QS
second; provided
Indicator 3; PO OR ; QO OS
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The points on this graph represent a relationship between
x
- and
y
-values. Which statement about the relationship is true?
Since the points on this graph represent a relationship between x- and y-values, the statement which is true about the relationship is that: 4. It cannot be proportional because a straight line through the points does not go through the origin.
What is a graph?A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.
In Mathematics, the graph of any proportional relationship is characterized by a straight line with the points passing through the origin (0, 0) because as the values on the x-axis (x-coordinate) increases or decreases, the values on the y-axis (y-coordinate) increases or decreases simultaneously.
In this context, we can reasonably infer and logically deduce that the relationship between x-values and y-values in this graph is not proportional.
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Complete Question:
The points on this graph represent a relationship between x- and y-values. Which statement about the relationship is true?
1. It must be proportional because the points lie on the same line.
2. It must be proportional because each time x increases by 2, y stays the same.
3. It cannot be proportional because the y-values are not whole numbers.
4. It cannot be proportional because a straight line through the points does not go through the origin.
4x-y=3 in slope intercept form
Answer:
y=4x-3
Step-by-step explanation:
Answer: the slope for y is y=-3+4x
the slope for x is x=[tex]3/4 +y/4[/tex]
Step-by-step explanation:.
Suppose PQ has one endpoint at P (4, 6) and a midpoint coordinate of (-5, 9).
The coordinate for Point Q is
Answer:
(-14,12)
Step-by-step explanation:
Way 1: (little more complicated)
we know two things,
The two halves of the line have the same slope, and that the length from the endpoint to the midpoint is equal to the length from the midpoint to the other end point.
The slope is equal to: (6-9)/(4-(-5)) = -3/9 = -1/3
The length is equal to (using the Pythagorean theorem):
height = delta y = 9 - 6 = 3
length = delta x = 4 - (-5) = 9
3^2+9^2=hypotenuse^2
9+81 = h^2
h = sqrt(90)
So, the let's say point Q has the coordinate (a, b).
The formula of the slope would give us (b-9)/(a-(-5)) = -1/3
The formula of the hypotenuse would give us (b-9)^2+(a-(-5))^2 = 90
solving the system of equations, we would get that a = -14 and b = 12, so the point is (-14,12)
Make sure to be careful, however, because you will get two points with this system of equations. Only one works
Way 2:
since from point P to the midpoint we went to the left by 9 and up by 3, from the midpoint to point Q, we would go left by 9, and up by 3.
from the midpoint (-5,9), go left by 9, so x decreases by 9 to get (-14, 9).
go up by 3, so y increases by 3 to get (-14,12). This agrees with our other answer
Can Someone please help!!
1) The slope of line that goes through the points (12, 13) and (-8, 8) is; 5/28
2) Using the point (12, 13) and the slope 5/28, the equation of the line is;
y - 13 = (5/28)(x - 12)
3) The equation of the line in slope intercept form is; y = (5/28)x - 76/7
Write the equation of the Line in slope intercept form?We are told that a line goes through the points; (12, 13) and (-8, 8)
1) The slope is gotten from the formula;
m = (y2 - y1)/(x2 - x1)
m = (8 - 13)/(-8 - 20)
m = -5/-28
m = 5/28
2) Using the point (12, 13) and the slope 5/28, the equation of the line is;
y - 13 = (5/28)(x - 12)
3) Expanding the equation in answer 2 above, we have;
y - 13 = (5/28)x - (60/28)
y - 13 = (5/28)x - 15/7
y = (5/28)x - 15/7 + 13
y = (5/28)x - 76/7
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Drag and drop the range of each data set into the boxes.
PLS HELP! ITZ MY LAST QUESTION
Answer:
Team 1 is 7, team 2 is 6
Step-by-step explanation:
Upper Extreme-Lower Extreme
Order the numbers from least to greatest:
-8/9, 7/8, 1.7, -10/7, 0.3
Answer: -10/7 < -8/9 < 0.3 < 7/8 < 1.7
Step-by-step explanation:
Sofia and Zara join a queue to get tickets for the school disco. There are 51 people in front of them. What are Sofia and Zara's positions in the queue?
The position of Zara and Sofia will be 52nd and 53rd.
According to the question, the persons standing in front of Sofia and Zara are 51. After 51 people, Sofia and Zara came and stood in line due to which they will be counted as the next persons.
The individual position of Zara and Sofia can't be determined as it is not given that between Zara and Sofia who came earlier.
This question is related to order and ranking. It means the process of knowing the position of a person, a thing, or a place in comparison to the position of other persons, or things.
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The equation shown has a missing value.
-2(2x - _) + 1 = 17 - 4x
For what missing value(s), if any, does the equation have exactly one solution?
There is no value for which the missing place should be filled in order to have exactly one solution.
A Linear equation may be defined as the one which can be represented in the form ax + b = 0 where a, b are coefficients and x is the independent variable. Since the equation only has one variable that is x then the linear equation will be rightly called as linear equation in one variable. We are given the equation -2(2x - _) + 1 = 17 - 4x. We solve the equation further which results as
-4x - _ + 1 = 17 - 4x
As we can see that there is -4 in both the right-hand side as well as the left-hand side both of them gets cancelled out.
- _ +1 = 17
As we can see that there is no variable left in order to find the value so any value of missing space will not be able to give any solution.
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Solve the equation.
-7(x-2)-28 - 14
(Simplify your answer.)
Answer:
[tex]-7x-28[/tex]
Step-by-step explanation
[tex]-7(x-2)-28-14[/tex]
To solve this, we must first solve what is inside the parenthesis by the distributive property. We will multiply -7 by x and -2.
[tex]-7(x)=-7x\\-7(-2)=14[/tex]
So then we have:
[tex]-7x+14-28-14[/tex]
From here, we combine like terms.
7x does not have any like terms, so we just combine 14, -28, and -14.
[tex]14+(-28)+(-14)\\=-28[/tex]
So, the final answer would be:
[tex]-7x-28[/tex]
If you have any questions, please feel free to ask!
Parallel lines are in the same ____? , but they do not____?
Answer: parallel lines are in the same slope? , but they do not intersect.
Step-by-step explanation:
because
Answer: slope, intersect
Step-by-step explanation:
As parallel lines never intersect
Draw the graph and find the equation of the hyperbola if the asymptotes are y=0.5x and y = −4−0.5x, and one of the vertices is (−4, 0).
The equation of the hyperbola is -(1/16) (x +4)² + (1/4) (y +2)² = 1
What is Hyperbola?
A hyperbola is a particular kind of smooth curve that lies in a plane and is classified by its geometric characteristics or by equations for which it is the solution set. A hyperbola is made up of two mirror images of one another that resemble two infinite bows. These two sections are known as connected components or branches.
The intersection of the two asymptotes is where the hyperbola's center is located. This is the key idea (-4,-2)
We have y orientation because the vertex at (-4,0) is above this location. The equation will take the form as a result.
-a (x + 4)
2 + b (y + 2)
In the case of certain a and b, 2 Equals 1.
Inputting (-4,0) reveals that b = 1/4.
Finally, requiring that y = x/2 be an asymptote reveals that a = 1/16.
-(1/16) (x +4)² + (1/4) (y +2)² = 1
Hence, The equation of hyperbola is -(1/16) (x +4)² + (1/4) (y +2)² = 1
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HELP ASAP I NEED THIS DONE BEFORE TONIGHT
PARALLEL LINES HAVE EQUAL GRADIENTS...MEANING THE GRADIENT OF THE NEW LINE IS ALSO
[tex] \frac{5}{6} [/tex]
I WILL USE THE GIVEN POINTS RO FIND THE VALUE OF c
[tex] 6= \frac{5}{6} ( - 1) + c \\ 6 = - \frac{5}{6} + c \\ c = 6 + \frac{5}{6} \\ c = \frac{41}{6} [/tex]
The equation now is
[tex]y = \frac{5}{6} x + \frac{41}{6} [/tex]
ATTACHED IS THE SOLUTION
Hello!
A line that is parallel to another line:
⇒ has the same slope
Thus the line: has a slope of 5/6
However, the line passes through (-1, 6):
==> let's set up the equation in point-slope form
[tex]y - y_1=m(x-x_1)[/tex]
m: slope(x₁, y₁): point on the line[tex]y - 6 = \dfrac{5}{6} (x -(-1))\\\\y -6 = \dfrac{5}{6} x + \dfrac{5}{6} \\\\y = \dfrac{5}{6} x +\dfrac{5}{6}+6\\\\ y=\dfrac{5}{6} x + \dfrac{5}{6} +\dfrac{36}{6} \\\\y=\dfrac{5}{6} x + \dfrac{41}{6}[/tex]<== Answer:
Hope that helps!
Order the following numbers from least to greatest.
√19 3√64 4.2
Answer: 4.2; √19; 3√64
Step-by-step explanation: 4.2; 4.35889894354; 24
in 1980 the population of mexico was about 67.38 million. for the years 1980 through 1985, the population grew at a rate of about 2.6% per year. (a) find a formula for an exponential function that gives the population of mexico. (let n be the population in millions and t be the number of year since 1980.) n(t)
∀Answer: keed
Step-by-step explanation: L trash
Select all ratios equivalent to 1:3.
7:21
Submit
6:18
2:9
Mell is twice as old as jerrey. if you subtract 16 from mells age, and 16 is added to jerreys age, their ages will be equal. what are their present ages
Answer: 32 year
Step-by-step explanation:
Let Jerrey age is 'y' year
Mell age = 2y
Now,
2y – 16 = y + 16
y = 32
∴ Mells age = 64 year
& Jerrey age = 32 year
Find the equation of the line.
Use exact numbers.
y=____x+
Answer:
y= 1/2 x - 3
Step-by-step explanation:
because -3 is the y-intercept, it is where the graph crosses the y-axis
the line is increasing at a rate of 1 unit up, and 2 units to the right. meaning that the slope is 1/2
Is this a linear equation if so please explain!
The equation f(-4) = (x - 2)/2 has a constant slope; so it is linear
What are linear equations?As a general rule, these are equations with constant rate of change.
How to determine the equation type?The equation is given as
f(-4) = (x - 2)/2
Rewrite as
f(x) = (x - 2)/2
Simplify
f(x) = x/2 - 2/2
Divide
f(x) = x/2 - 1
A linear equation is represented as
f(x) = mx + c
Where m represents the slope and c represents the intercept
This means that
m = 1/2
c = -1
Hence, the equation is a linear equation
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Find the slope and the y-Intercept of the line.
y=2x-9
Last week, Ellen bought 4 apples for $2.40. This week she bought 9 apples for $5.40. If the cost per apple remains the same, how many apples could she buy next week? Select two that apply.
A.
1 apple for $1.20
B.
3 apples for $1.80
C.
6 apples for $3.40
D.
10 apples for $6.00
E.
13 apples for $8.20
F.
14 apples for $9.00
Answer:
B & D
Step-by-step explanation:
If it’s 60 cents per apple, you will be able to buy 3 apples for $1.80, and 10 apples for $6.00.
0.60 x 3 = 1.80
0.60 x 10 = 6
Hope this helps! <3
Please help! Write without using rational exponents.
[tex](m^3n^5)^\frac{1}{4}[/tex]
Please show all work.
I will give brainliest!!!
The expression without the rational exponents is ⁴√(m^3n^5)
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to rewrite the expression?The expression is given as
(m^3n^5)^1/4
The exponents of the above expression cannot be simplified
This means that, we simply rewrite the expression using the fourth root expression
So, we have
(m^3n^5)^1/4 = ⁴√(m^3n^5)
Hence. the equivalent expression is ⁴√(m^3n^5)
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the diagnostic
Solve for n.
n+4≤5
The value of the inequality given as n ≤ 5 - 4 is n ≤ 1.
How to illustrate the information?It should be noted that an inequality is simony used to how the relationship between the expressions that aren't equal.
In this case, it should be noted that the inequality given is expressed as n + 4 ≤ 5. This will be solved accordingly:
n + 4 ≤ 5.
Collect like terms
n ≤ 5 - 4
n ≤ 1.
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Vector v = <3, 1>. Describe how you would use a graphical method to add vector v to vector u (shown in the graph below). Then, write the resultant vector in component form.
The component form of the resulting vector is <5, -4>
Vector:
Vector means the objects which have both, magnitude and direction. Magnitude defines the size of the vector. It is represented by a line with an arrow, where the length of the line is the magnitude of the vector and the arrow shows the direction.
Given,
Vector v = <3, 1>.
Here we need to find the value of u through the given graph and we have to perform the addition operation in order to find the component form of the resulting vector.
Here we have the value of vector v = <3,1>
While observing the graph we have identified as the value of vector u is,
x value = 2
y value = -5
So, the component from of vector u = <2, -5>
Now the addition of u + v is equal to,
=> u + v
=> <3,1> + <2, -5>
=> < (3 + 2) , (1 + (-5))>
=> < 5, -4>
Therefore, the component form of the resulting vector is <5, -4>.
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Answer:
Draw vector v in standard position. To add v to u, shift v 2 units to the right and 5 units down so its initial point coincides with the terminal point of u. Use a dotted line to depict the shifted vector v.
Now there are three sides of a parallelogram. To complete the parallelogram, draw a dotted line from the tip of vector v in the standard position to the tip of the shifted vector v.
Finally, draw the vector represented by the diagonal of the parallelogram with its initial point at the origin. The resultant vector, u + v, is this diagonal of the parallelogram in which the two vectors, u and v, are adjacent sides. The components of u + v are <5, -4>.
Step-by-step explanation:
Plato/Edmentum
C is in the interior of LABD. m/ABC=
(2x+12)°, m/CBD = (3x + 10)°, and
m/ABD = 72°. Find m/ABC.
Answer:
32°
Step-by-step explanation:
Using the angle addition postulate,
[tex]3x+10+2x+12=72 \\ \\ 5x+22=72 \\ \\ 5x=50 \\ \\ x=10 \\ \\ \implies m\angle ABC=2(10)+12=32^{\circ}[/tex]
the area of lake Okeechobee is 7.3 * 10 to the second power square miles. how many square miles is the area of lake Okeechobee?
Lake Okeechobee has a surface area of 5329 square miles, as determined by solving the given values.
How do you compute a square mile?The area of a square unit, such as a square mile, is calculated by multiplying two lengths. Each length in the case of square miles is measured in miles.
Given: The Okeechobee lake is 7.3 * 10 to the second power square miles in area.
We need to figure out how many square miles Lake Okeechobee covers.
Area covered in square miles = (7.3 × 10)²
= 73²
= 5329 square miles
Therefore, Lake Okeechobee covers an area of 5329 square miles which was calculated by solving the given values.
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A math quiz has 3 multiple choice questions and 2 true/false questions. Each multiple choice questions has 4 answer options: A, B, C, D. Find the number of possible outcomes.
The total number of possible outcomes for the math quiz is 16
How to solve for the number of possible outcomes3 multiple choice questions and each has 4 options. The total number of options here is
= number of question * number of options
= 4 * 3
= 12
2 true/false questions. The total number of options here is
= number of question * number of options
= 2 * 2
= 4
The number of possible outcomes
= outcome from the multiple choice question + outcome from the true/false question
= 12 + 4
= 16
Therefore the total number of outcomes from the quiz in this question is is 16
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Evaluate the expression when r is -7 and s is 2.
rs^3
When r is -7 and s is 2, rs^3 is [ ]
(Simplify your answer)
Answer:
-56
Step-by-step explanation:
Given that,
r => -7
s => 2
To solve this given expression, replace r & s with -7 & 2 respectively.
Let us solve it now.
[tex] \sf \: r {s}^{3} \\ \sf - 7 \times {2}^{3} \\ \sf- 7 \times 8 \\ - 56[/tex]
Can you please help me? Thank you!
The volume of the figure shown in the reference attachment, provided hereby with the question statement will be 6786 ft³.
As per the question statement and the reference attachment, we are provided with a figure and its dimensions.
We are required to calculate the volume of the concerned figure using the dimensional values provided.
To solve this question, we need to calculate the volumes of the bottom cuboidal part, and the top pyramidal part separately, and then add these volumes, to obtain our final desired answer.
Given, the dimensions of the bottom cuboidal part is (21ft by 18ft by 13ft).
We know that, volume of a cuboid = (length * breadth * height).
Therefore, volume of our concerned bottom cuboidal part
= (21 * 18 * 13) ft³
= 4914 ft³.
Also given, the dimensions of the top pyramidal part are as follows,
Base of the triangle = 18 ft,
Altitude of the triangle = 16 ft,
and length of the pyramid = 13 ft.
Therefore, Volume of the concerned pyramid
= [(1/2) * base * altitude * length]
= [(1/2) * 18 * 16 * 13] ft³
= (9 * 16 * 13) ft³
= 1872 ft³.
Therefore, Total volume of the concerned figure shown in the reference attachment, provided hereby with the question statement will be
(4914 + 1872) ft³ = 6786 ft³
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