The equation 2y=3x-1 does not represent a direct variation in its strict definition, as it includes a y-intercept. If the y-intercept is ignored, the constant of variation would be k = 3/2.
The equation 2y=3x-1 represents a direct variation if it can be written in the form y = kx, where k is the constant of variation. To determine if this equation represents a direct variation, we can solve it for y:
Divide both sides of the equation by 2 to isolate y:
y = (3/2)x - 1/2.
Since we can express y as an equation of the form y = kx + b, with b being a constant, it does not represent a pure direct variation, as direct variation should have a form y = kx without the constant term.
However, if the question is interpreted to include such linear relationships as direct variations despite the y-intercept, then the constant of variation would be k = 3/2.
given the equation -2x-13=8x+7, which order of operations completely solves for x
Which is equivalent to 243 2/5 ? 3 6 9 12
Answer:
The answer is [tex]9[/tex]
Step-by-step explanation:
we have
[tex](243)^{\frac{2}{5}}[/tex]
we know that
[tex]a^{\frac{n}{m}}=\sqrt[m]{a^{n}}[/tex]
so
[tex](243)^{\frac{2}{5}}=\sqrt[5]{243^{2}}[/tex]
Remember that
[tex]243=3^{5}[/tex]
Substitute
[tex]\sqrt[5]{243^{2}}=\sqrt[5]{(3^{5})^{2}}\\ \\= \sqrt[5]{(3^{10})}\\ \\=3^{\frac{10}{5}}\\ \\= 3^{2} \\ \\=9[/tex]
Twice the sum of a number and 2 is equal to three times the difference of the number and 8. find the number please help
Answer:
28
Step-by-step explanation:
Let n represent the number.
Twice the sum of the number and 2 is ...
2(n +2)
Three times the difference of the number and 8 is ...
3(n -8)
The problem statement tells us these quantities are equal, so ...
2(n +2) = 3(n -8) . . . . the given quantities are equal
2n +4 = 3n -24 . . . . . use the distributive property to eliminate parentheses
2n +28 = 3n . . . . . . . add 24
28 = n . . . . . . . . . . . . subtract 2n
The number is 28.
_____
Check
The sum of the number and 2 is 30; twice that is 60.
The difference of the number and 8 is 20; three times that is 60--the same number.
Write an expression for the quantity 506 000 cm in which it is clear that all zeros are significant
The distributive property to express 48+72
Answer:
24(2+3)=24.2+24.3=48+72
Step-by-step explanation:
Given form of number is 48+72.
we have to apply the distributive property to express the above number.
The distributive property is
a(b+c)=ab+ac
Multiply the common term with the term inside the parentheses
So to express 48+72 we have to take the highest factor outside
Let us take 24 outside, we get
24(2+3)=24.2+24.3=48+72
Hence applied
The required expression is [tex]24(2+3)[/tex] by using the distributive property.
Given:
The given expression is [tex]48+72[/tex].
To find:
The equivalent expression by using the distributive property.
Explanation:
According to the distributive property:
[tex]a(b+c)=ab+ac[/tex]
We have,
[tex]48+72[/tex]
It can be rewritten as:
[tex]48+72=24\times 2+24\times 3[/tex]
Using the distributive property, we get
[tex]48+72=24(2+3)[/tex]
Therefore, the required expression is [tex]24(2+3)[/tex].
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The graphs of the equations 2x+5y=3 and 2x+5y=7 are parallel lines. Find the equation of the line that is parallel to both lines and lies midway between them.
A lamp manufacturer uses 714 meters of electrical cord each week. The cord comes on spools that hold 12 meters each. How many spools of electrical cord does the manufacturer use each week?
divide 714 by 12
714 / 12 = 59.5 spools per week
Simplify. Express your answer as a single term, without a denominator. t0u/tu
He ages of mark and adam add up to 28 years total. mark is 20 years older than adam. how many years old is adam
The measures of two complementary angles are 3x+1 and 5x-y. Find x
A: 8
B: 12
C: 14
D: 23
Find the Least Common Multiple of these two monomials:
16jk^8m^5 and 20j^9k^4m^6
36j^9k^8m^6
80j^9k^8m^6
4jk^4m^5
80j^10k^12m^11
lcm 16 & 10 = 80
lcm j^8 & j^9 = j^9
lcm k^8 & k^4 = k^8
lcm m^5 & m^6 = m^6
answer is: 80j^9k^8m^6
How many 12ths are equivalent to 1/3?
Decide which of the two points lies on the graph of the line
6x-2y= -4
A, -1, -1
B, -3,-2
Bill earns $87.50 per week and Jack earns $70.00 per week. What percent of Bill's salary is Jack's?
Answer:
80%
Step-by-step explanation:
Let us suppose x percent of Bill's salary is equal to Jacks's salary.
Thus, we can write
x% of 87.50 = 70
Mathematically, we can write this as
[tex]0.0x\times87.50=70[/tex]
Solve the equation for x
[tex]0.0x=\frac{70}{87.50}\\\\x=\frac{70}{87.50}\times100\\\\x=80[/tex]
Therefore, Jack's salary is 80% of Bill's salary
The sum of the squares of two consecutive even integers is 452. find the integers.
MATH HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
1. less than ( I gave x a number and did both equations )
2. the equation = 400 which is greater than 35
Need the calculations please
What is the missing term in the factorization? 18x2−32=2(3x+?)(3x−4)
Answer:
4.
Step-by-step explanation:
[tex]18x^{2} -32 = 2(9x^{2} -16)[/tex]
we apply difference of squares
2(3x-4)(3x+4)
So, the missing term is 4.
The missing term in the factorization 18x² − 32 = 2(3x + ?)(3x − 4) is 4.
What is Factorization ?Factorization is the method of breaking a number into smaller numbers that multiplied together will give that original form. Factorization is expressing a mathematical quantity in terms of multiples of smaller units of similar quantities.
For an integer, Factorization is decomposition of that integer in terms of smaller integers; when multiplied with each other give back that considered number. Those composing integers are called factors of that considered integers.
WE have given an expression as;
18x² − 32 = 2(3x + ?)(3x − 4)
Now we apply difference of squares;
2(9x² - 16)
2(3x + 4)(3x - 4)
OR
2(3x-4)(3x+4)
Therefore, the missing term is 4.
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Which is an x-intercept of the graphed function?
The x-intercepts of the graphed function are -2, -1, 1, and 2
How to determine the x-intercept?The x-intercept is the point where the graph crosses the x-axis
This means that the point on the x-axis where y = 0
From the graph, we have:
x = -2, -1, 1, and 2 when y = 0
Hence, the x-intercepts of the graphed function are -2, -1, 1, and 2
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What is the equation of a line that passes through the point (2, 7) and is perpendicular to the line whose equation is y=x/4+5 ?
How does doubling the side lengths of a triangle affect its area?
PLEASE HELP ASAP!! Will give brainliest!
50 POINTS!!
What are the missing parts that correctly complete the proof?
Answer:- 2. ∠JKM≅∠LKM
5. MK≅MK
6. AAS congruence postulate.
7. Corresponding parts of congruent triangles are congruent.
8. Definition of equidistant.
Therefore the complete proof will be
Proof :- 1. KM is the line bisector of ∠JKL. [Given]
2. ∠JKM≅∠LKM [Definition of bisector]
3. ∠KXM and ∠KYM are right angles [Given]
4. ∠KXM ≅ ∠KYM [All right angles are congruent]
5. MK≅MK [reflexive property of congruence]
6. ΔKXM ≅ ΔKYM [AAS congruence postulate]
7. MX≅MY [Corresponding parts of congruent triangles are congruent]
8. Point M is equidistant from the sides of ∠JKL [Definition of equidistant]
Hence proved.
Donald baked 77 cookies in the morning and 83 cookies in the afternoon for 14 days how many total cookies did he bake
in the graph below, point D is reflected across the y axis. what are the coordinates of its image ?
Generally, whenever a point (x,y) is reflected across the y axis, the y coordinate stays the same and the sign of x coordinate changes.
So [tex](x,y)[/tex] changes to [tex](-x,y)[/tex].
Point D in the diagram shown has coordinates [tex](3,-1)[/tex]. According to the rule, the x-coordinate, 3, will change to -3 and the y-coordinate, -1, would stay the same.
Hence, our image of D after the reflection about y-axis would have coordinates [tex](-3,-1)[/tex].
ANSWER: [tex](-3,-1)[/tex]
Answer:
(-3, -1)
Step-by-step explanation:
. Catie is 3 years older than her brother. The sum of their ages is no more than 31. Write an inequality that can be used to represent this situation, where x represents Catie's brother's age. Don’t combine like terms.
Answer: So, the required inequality that can be used to represent this situation is [tex]2x+3\leq 31[/tex]
Step-by-step explanation:
Let the age of Catie's brother be 'x'.
Let the age of Catie be 'x+3'.
According to question, the sum of their ages is no more than 31.
So, it becomes,
[tex]x+x+3\leq 31\\\\2x+3\leq 31[/tex]
So, the required inequality that can be used to represent this situation is
[tex]2x+3\leq 31[/tex]
If i run 5 miles in 38 minutes how many miles can i run in 57
The sides of a square are 5 2/5 inches long. what is the area of the square?
a. 5 4/5 square inches
b. 5 4/25 square inches
c. 25 4/5 square inches
d. 25 4/25 square inches
Answer:
29 4/25 square inches (not given in the options)
Step-by-step explanation:
A square is a plain 4 sided shape with equal sides. As such, all sides of a square are equal. If the length o a side of a square is s, the area of the square will be s² while the perimeter will be 4s.
Area of square = (5 2/5 inches)²
= (27/5 inches)²
= 729/25 square inches
= 29 4/25 square inches
A basketball team played 14 games. the team's mean score was 66 points. how many total points did they score in the 14 games?
Type an equation of the line that passes through the origin with the slope 3
The required equation of the line is y = 3x which passes through the origin with the slope 3.
What is the slope of the line?The slope of the line is defined as the gradient of the line. It is denoted by m
Slope m = (y₂ - y₁)/(x₂ -x₁ )
We have to determine the equation of the line that passes through the origin with slope 3.
Let's assume slope-intercept form:
So required line in the slope-intercept form is:
y = mx + b
where m is the slope and b is the y-intercept.
In this case, the slope of line m = 3, and the line passes through the origin
So, therefore equation will be:
y = 3x + 0 or
y = 3x
Thus, the required equation of the line is y = 3x which passes through the origin with the slope 3.
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