The required value of constant of variation, k does not exist for which x and y vary directly..
What is the constant of proportion?
A constant of proportion is illustrated as the ratio which relates two given quantities with each other in the relationship of proportion. Constant of proportion is also called constant variation, rate of change, and constant ratio.
Solving for the value of constant of variation
When a quantity varies directly with others, then we have a relation, y = kx, where k is the constant of the proportion —-- 1
Given relation is y + 3 = -3 x
y = -3 x - 3
y = -3(x + 1)
Comparing with equation 1, we get that y does not vary directly for any value of k.
Hence, the required value of constant of variation is does not exist.
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Determine whether each series is arithmetic or geometric. Then evaluate the finite series for the specified term number. 5000+1000+200+. . . . . . ; n=5
The given series is geometric series. The sum of its first 5 terms is 6248.
To determine whether the series is an arithmetic or geometric one, we need to check how the consecutive terms relate to each other.
If it is an arithmetic series, then:
a(n) = a(n-1) + d
where d is the common difference.
If it is a geometric series, then:
a(n) = a(n-1) . r
where r is the common ratio.
The given series is:
5000 + 1000 + 200 +. . . .
and the number of terms is 5.
In the given series:
a(1) = 5000
a(2) = 1000
a(3) = 200
Notice that
a(2)/a(1) = 1000/5000 = 0.2
a(3)/a(2) = 200/1000 = 0.2
Since the ratio of consecutive terms are constant, then the given series is a geometric series. Furthermore, its ratio, r = 0.2
Sum formula for the first n term of a geometric series is:
S(n) = a(1) . (1 - rⁿ)/(1 -r)
Substitute n = 5, a(1) = 5000, and r = 0.2
S(5) = 5000 . (1 - (0.2)⁵)/(1 - 0.2)
S(5) = 5000. (0.99968) / 0.8
= 6248
Since the number of terms is not much we can also evaluate the sum directly. Write all the terms until n = 5.
a(4) = 200 . (0.2) = 40
a(5) = 40 . (0.2) = 8
Hence, the series is:
5000+1000+200+40+8 = 6248.
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A school is studying Math for Data and Financial Literacy standardized test scores. Which of the following displays could be used to represent the data, and why?
Bar chart, because test scores are numerical
Box plot, because test scores are categorical
Circle graph, because test scores are categorical
Stem-and-leaf-plot, because test scores are numerical
its stem and leaf just took the test
Stem-and-leaf-plot displays could be used to represent the data because test scores are numerical. Then the correct option is D.
What is the Stem and leaf plot?In order to help visualize the shape of a distribution, a stem-and-leaf presentation or stem-and-leaf plot is a tool for displaying quantitative data in a graphical manner, comparable to a histogram. They are helpful tools for exploratory data analysis and developed from Arthur Bowley's work in the early 1900s.
This is simply accomplished by creating a draft of the unsorted leaves before arranging them in the final stem-leaf display. On the Undergraduate and graduate levels, you may find a number of examples that have been solved and even obtain expert assistance to learn the subject of stem and leaf plots.
A school is studying Math for Data and Financial Literacy standardized test scores.
Stem-and-leaf-plot displays could be used to represent the data because test scores are numerical. Then the correct option is D.
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Write an equation of the line through the pair of points in slope-intercept form. (Lesson 3-4 )
(-1,8) and (5,-4)
y = -2x + 6 is the equation of the line in slope-intercept form passing through points (-1 , 8) and (5 , -4).
An equation of a line in slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept.
Given two points passed through by the line, you can use them to write the equation of the line in slope-intercept form.
1. Find the slope of the line using the two given points.
let Point 1(-1 , 8) and Point 2(5 , -4)
slope = m = (y2 - y1) / (x2 -x1)
m = (-4 - 8) / (5 - -1)
m = -12 / 6
m = -2
2. Use the value of the slope and one of the points to find the value of the y-intercept, b. Plug in these values in the formula for slope-intercept form.
y = mx+ b
y = -2x + b
Using Point 1,
8 = -2(-1) + b
8 = 2 + b
b = 6
3. Write the equation of the line in slope-intercept form.
y = mx+ b
where m = -2 and b = 6
y = -2x + 6
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from
3. Error Analysis A student claims the
sequence 0,1,3, 6, ... is an arithmetic
sequence, and the next number is 10. What
error did the student make?
The given sequence 0,1,3,6,10 ......is not an arithmetic sequence because students make the error of common difference
What is an arithmetic sequence?
An arithmetic progression or arithmetic sequence ( AP ) is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 5, 7, 9, 11, 13, 15, . . . is an arithmetic progression with a common difference of 2.
here the given sequence is 0,1,3,6,10,......is an arithmetic sequence
then the common difference between the consecutive terms is constant
lets check take two consecutive terms as 0 and 1 then the difference is 1
take 1 and 3 then common difference is 3-1 =2
take 3 and 6 then common difference is 6-3 =3
take 6 and 10 then common difference is 10-6=4
.............in the same way we check for other terms also
and found that the common difference is not same
Hence the given sequence 0,1,3,6,10 ......is not an arithmetic sequence because students make the error of common difference
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LCM of 21, 56
I really need help it’s due today
Answer: the answer is 168
The mean of a distribution of test scores is 80. The standard deviation of the scores is 10. If every
score is doubled and 15 is added to each score, what would the new mean and standard deviation be?
The new mean of a distribution of tests would be 175 and the new standard deviation of a distribution of tests would be 10 which is unchanged.
We have been given that in the question:
Mean of data = 80
Standard deviation = 10.
Then, every score is doubled and 15 is added to each score.
What is the mean of a distribution?The mean of a distribution is defined as the ratio of the sum of observations to the total number of observations. It can be referred to as the average of a specific set of data or the arithmetic mean.
a) Mean of new data
The mean of the data rises by the same amount when a constant value is applied to each observation.
Mean of new score =
μ' = 2μ + 15 = 2(80) + 15 = 175
b) Standard deviation of new data
Every observation has a constant value added to it, therefore the standard deviation stays constant.
The standard deviation of the new score =
σ' = σ = 10
Therefore, the new mean and standard deviation would be 175 and 10 respectively.
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two non-zero real numbers, a and b, satisfy ab=a-b. Find a possible value of [tex]a/b +b/a -ab[/tex]
100 points
Answer:
2
Step-by-step explanation:
Given equations:
[tex]\begin{cases}ab=a-b\\\\\dfrac{a}{b}+\dfrac{b}{a}-ab\end{cases}[/tex]
Rewrite the second equation as a rational expression:
[tex]\begin{aligned}\implies \dfrac{a}{b}+\dfrac{b}{a}-ab & = \dfrac{a}{b} \cdot \dfrac{a}{a}+\dfrac{b}{a} \cdot \dfrac{b}{b}-ab\cdot \dfrac{ab}{ab} \\\\&=\dfrac{a^2}{ab}+\dfrac{b^2}{ab}-\dfrac{(ab)^2}{ab}\\\\&=\dfrac{a^2+b^2-(ab)^2}{ab}\\\\\end{aligned}[/tex]
Substitute the first equation [tex]ab=a-b[/tex] into the rational expression:
[tex]\begin{aligned}\implies \dfrac{a^2+b^2-(a-b)^2}{ab}&=\dfrac{a^2+b^2-(a^2-2ab+b^2)}{ab}\\\\&=\dfrac{a^2+b^2-a^2+2ab-b^2}{ab}\\\\&=\dfrac{2ab}{ab}\\\\&=2\end{aligned}[/tex]
Therefore, the possible value of the given expression is 2.
An equilateral triangle has
sides of 4x + 10. Write an
expression for the perimeter of
the triangle.
Determine the value of x when the perimeter is 42.
Answer:
x = 1 if the perimeter is 42
Step-by-step explanation:
Given
s = 4x + 10
when Perimeter = 42, what is x?
Solution
Perimeter = 3s
Perimeter = 3(4x +10) Remove the brackets
Perimeter = 12x + 30
Let the Perimeter = 42
42 = 12x + 30 Subtract 30 from both sides
42-30 = 12x + 30-30 Combine
12 = 12x Divide by 12
12/12 = 12x/12
x = 1
Determine whether each sequence is geometric. If so, find the common ratio. -1,1,-1,1, . . . . .
The given sequence is geometric, with common ratio = -1.
What is a geometric progression?A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.Now, Given: -1, 1, -1, 1, ...
Here, a₁ = -1, r = [tex]\frac{1}{-1}=\frac{-1}{1} = \frac{1}{-1} = -1[/tex]
Hence, it is a geometric sequence, with common ratio = -1.
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Use the table below to complete the following statements.
The value of m • n (8) is
The value of n • m (-4) is
Answer:
Step-by-step explanation:
What can we use to represent repeated multiplication
Answer:
This expression can be written in a shorter way using something called exponents. An expression that represents repeated multiplication of the same factor is called a power.
Answer:
Step-by-step explanation:
This formula can be written shorter using so-called exponents. Expressions representing repeated multiplications of the same factor are called exponentiations. 5 is called the base and 2 is called the exponent.
Use the graphs of f and g to graph h(x)=(f+g)(x). I need help with #4.
Answer:
My teacher helped
Step-by-step explanation:
By first rounding each number to 1 significant figure, estimate the answer to 527 +389
Answer:
900
Step-by-step explanation:
527 to 1sf is 500
389 to 1sf is 400
400+500=900
Answer:
900
Step-by-step explanation:
527 to 500
389 to 400
500+400=900
Find the slope of the line passing through the points (-5, 2) and (3, -9).
Answer: -8/11
Step-by-step explanation:
apply the formula
x sub 2- x sub 1
over
y sub 2 - y sub 1
yw
Which of the following domain restrictions would allow the inverse of f(x) = (x + 4)^2 - 1 graphed below to also be a function? Select the THREE (3) that apply!
The domain restrictions that would allow the inverse of f(x) to also be a function are given as follows:
x ≤ -4.x ≥ 1.x > -3.When does a graph represents an one to one function?The function is one to one if there are no horizontally aligned points, that is, each value of y is also related to only one value of x. A function will have an inverse in the part of the domain of the function that is one to one.
For this problem, the relation is symmetric at x = -4, hence the domains x <= -4 and x >= -4 must not intersect for the inverse to be a function, and the restrictions are given by:
x ≤ -4. (no horizontally aligned points considering only x ≤ -4).x ≥ 1. (same).x > -3(same).More can be learned about one to one functions at brainly.com/question/10853542
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What is 50+50 and explain how you got the anwer
Answer:
50+50=100
How I got answer there are two 50 so if I multiply 50×2 I will get 100
and answer will come
Answer:
100
Step-by-step explanation:
Columnar addition
50
+50
____
100
The section of a window consists of a rectangle surmounted by and equilateral triangle. If the perimeters be given as 10ft, find the dimensions of the window in order that the maximum amount of light may be admitted.
100 POINTS PLEASE
Answer:
Solution
verified
Verified by Toppr
Correct option is C)
Perimeter of window P=2y+3x=16
⇒y=
2
16−3x
....(1)
Area A=xy+
4
3
x
2
=
4
3
x
2
+x(
2
16−3x
)
A=8x+(
4
3
−
2
3
)x
2
dx
dA
=8+(
4
3
−
2
3
)2x
For maxima or minima,
dx
dA
=0
⇒4−
4
(6−
3
)
x=0.
∴x=
6−
(3)
16
=
36−3
16(6+
3
)
=
33
16(6+1.73)
=
33
16(7.73)
=
33
123.68
⇒x=3.75 nearly.
Now,
dx
2
d
2
A
=2(
4
3
−
2
3
)<0
Hence A is maximum.
By (1),
y=2.375
Step-by-step explanation:
9xy-22
Term(s):
Coefficient(s):
Variable(s):
Constant(s):
Answer:
Coefficient(s):9
Variable(s):x,y
Constant(s):-22
Step-by-step explanation:
Write the function rule for each function reflected in the given axis.
f(x)=4+x ; x -axis
Functions can be reflected on the x-axis, the y-axis, or both axes. For example, function reflection y= f(x) can be written as y= -f(x) or y= f(-x) even y= -f(-x). There are four types of function or graph transformations: reflection, rotation, translation, and dilation. In mathematics, especially geometry, mirror or mirroring means flipping, so basically, the mirroring of a function is the mirror image of a given function or graph. Hence the reflection function is commonly known as the reflection function.
The reflection of the given function should be similar in size and shape to the original function.
f(x)=4+x; x -axis
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A scientist measures 4.62 ml of a chemical into a beaker. \with a pipette, he carefully takes out 0.67 of the chemical. finally, he adds 1.25 ml of water into the beaker. how much liquid is in the beaker now?
Using basic mathematical operations such as addition and subtraction, the beaker now has 5.2 ml of liquid.
Basic mathematical operations include addition, subtraction, multiplication, and division.
Addition is combining two or more values to come up with a total or sum. On the other hand, subtraction, the opposite of addition, is removing a value from another resulting to their difference.
If a scientist measures 4.62 ml of a chemical into a beaker, then takes out 0.67 ml of the chemical, and finally adds 1.25 ml of water into the beaker, subtracting the amount of chemical taken out from the initial amount of chemical and adding the amount of water, we can solve how much liquid is in the beaker.
4.62 ml - 0.67 ml + 1.25 ml = 5.2 ml
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Divide. State any restrictions on the variables.
3 y-12 / 2y+4 ÷ 6y-24 / 8+4 y
The restrictions on the variables x and y of the equation
(3y-12)/(2y+4) ÷ (6y-24)/(8+4y) be y ≠ 4 and y ≠ -2
What is meant by expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure exists as pursues: Expression: (Math Operator, Number/Variable, Math Operator)
Let the equation be (3y-12)/(2y+4) ÷ (6y-24)/(8+4y)
simplifying the equation, we get
(3y-12)/(2y+4) × (8+4y)/(6y-24)
⇒ (3y-12)/(2y+4) × 2(4+2y)/2(3y-12)
⇒ 2/2 = 1
What are the restrictions on the variables?If y = 4 ⇒ denominator (6 × 4 - 24) = 0 = ∞
Similarly, If y = -2 ⇒ denominator ((2 × -2) + 4) =0 = ∞
So, y ≠ 4, y ≠ -2
How to find restrictions on the variables?
The denominator determines the restrictions of a rational expression's domain.Find those limitations without regard to the numerator.Set the denominator to 0 and solve the provided expression to discover the domain restrictions.To learn more about restrictions on the variables, refer:
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If a student picked is 10 years old, what
are the chances that they skip breakfast?
Answer:
There are 29% chance that they will skip their breakfast
Step-by-step explanation:
40 / 14 x 10 = the percentage of the kid skipping his breakfast
40 / 14 x 10 = 28.5%
28.5 = (rounded off) = 29%
The kid has a 29% chance of skipping the breakfast
Solve for x.
33 ÷ x = 3
Will mark brainlest
=================================
[tex]\\[/tex]
[tex]33\div x=3\\[/tex]
multiplying both sides by x
[tex]33=3x\\3x=33[/tex]
dividing by 3 both sides
[tex]x=11[/tex] {SOLUTION}===================================
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[tex]\textcopyright ELIZA[/tex]
Answer:
x = 11
Step-by-step explanation:
33/x = 3
33 = 3x
x = 33/3
x = 11
Hope it helps!!!
Expand and simplify (2x+5) (2x-5) (3x+7)
Answer:
yall i tried
Step-by-step explanation:
bring it to the formula first then gotta multiply
Which graph shows a set of ordered pairs that represent a function?
3
2
1 .
5-4-3-2-11. 2.3
-2-
3+
Mark this and return
3-2.
3-
2-
4
+2+
-3-
O
123
5
34
2+
1+
4-3-2-1₁- 1 2 3 4 5
.
Save and Exit
+24
-3-
4
O
4
3-
2
44
54-3-2-11-
•
1 2 3 4 5 X
Next
Submit
The second graph shows a set of ordered pairs that represent a function.
What is function?Functions are an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
here, we have,
A relation is a function in which every x value will have different y values, this represents "every input will have unique output" part of the definition of the function,
When we observe the graphs (attached), we will notice in graph 1) there are two ordered pairs with same x value and different y values, (2, -1) and (2, -3), which is making them out of the list of being a function,
In graph 2) we have, (-2, 2), (1, 1), (5, 4), (-4, -4), (2, -5) and (4, -3), in this all the order pairs have different x-y values, therefore, this set of ordered pairs that represent a function.
Hence, the second graph shows a set of ordered pairs that represent a function.
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The question do not have graph, so, the question is solved for the graph attached.
solve the equation for the indicated variable
A = 1/2(pi)(r)^2 solve for pi
Answer:
(2A)/(r^2)=pi
Step-by-step explanation:
The goal is to get pi by itself, so you have to move all the other elements over
2A=pir^2
(2A)/(r^2)=pi
Determine whether the quadrilateral can always, sometimes, or never be inscribed in a circle. Explain your reasoning.kite
A pair of opposite angles is supplementary, a quadrilateral ABCD can be inscribed in a circle.
What can be inscribed in a circle?
Every circle has an inscribed triangle with any three given angle measurements (summing to 180°, of course), and every triangle can be inscribed in any circle (which is called its circumscribed circle or circumcircle). Every triangle has an incircle, which is a circle that has been inscribed.
A cyclic quadrilateral is one that can be encircled by a circle. If and only if a pair of opposite angles is supplementary, a quadrilateral ABCD can be inscribed in a circle. Because the sum of all the angles is 360 degrees, it is true that one pair of supplementary angles is supplementary if and only if both pairs are supplementary.
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Squere root
Find the using division methos
15384
The square root of the 15384 by division method is a 124.032.
According to the statement
We have to find that the square root with the division method.
So, For this purpose, we know that the
The long division is the mathematical method for dividing large numbers into smaller groups or parts
And
A generalised version of this method called polynomial long division is also used for dividing polynomials
From the given information:
The number is a 15384.
And then
Firstly in this number by the squaring of the same number and by this method after going down until the remainder is zero.
And after solving the square root of 15384
The answer will become 124.032.
So, The square root of the 15384 by division method is a 124.032.
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Which of the following numbers is between -3/4 and 5/8
-1
-1/2
7/8
0.9
Answer:
7/8 if you divide you will get your answer
891.8 ÷ 5.2 = pls with the work out to
The answer to your question would be, 171.5
