Answers
The table represents the direct relationship y = - 3 · x. (Correct choice: C)
How to determine whether a table represents a direct relationship
Two variables have a direct relationship if and only if the following model is observed:
y ∝ x
y = k · x
Where k is the constant of proportionality.
The table may represent a direct relationship if and only if each ordered pair has the same constant of proportionality. Now we proceed to evaluate the table:
k₁ = - 3 / 1
k₁ = - 3
k₂ = - 9 / 3
k₂ = - 3
k₃ = - 15 / 5
k₃ = - 3
As k₁ = k₂ = k₃, then the table represents the direct relationship y = - 3 · x.
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Related Questions
A box of chocolates costs 9.49. Rita bought 4 boxes. How much did she spend?
Answers
Answer:
$37.96
Step-by-step explanation:
$9.49 x 4 = $37.96
work out value please
Answers
Answer:
270
Step-by-step explanation:
(∛9)³ × (√30)²
9 × 30 = 270
I hope this helps!
Answer:
Answer:
270
Step-by-step explanation:
(∛9)³ × (√30)²
9 × 30 = 270
Step-by-step explanation:
3. Every conditional has two parts. The part following if is the
Ohypothesis
O conclusion
O inverse
O converse
(1 point)
Answers
Every conditional has two parts they are hypothesis and conclusion.
What are hypothesis and conclusion ?The hypothesis is the first part of a conditional statement 'if' and conclusion is the last part of a conditional statement 'then'
According to the given statement every conditional has two parts a hypothesis and a conclusion.
Conditional starts with if and ends with then.It is used to express possible situations.
For example-: if the two angles are complementary then their sum is 90°.
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Given: m<4 + m<7 = 180 degrees
Prove: c || d
Answers
1) m∠4 + m∠7 = 180° (given)
2) ∠4 is congruent to ∠6 (vertical angles)
3) m∠4 = m∠6 (definition of congruent angles)
4) m∠6 + m∠7 = 180° (substitution)
5) c is parallel to d (converse of same side interior angles theorem)
The local gym holds two 45-minute workout sessions and four 30-minute sessions each week. Judy attended all of the sessions this week but left 5 minutes early during the 30-minute sessions and 10 minutes early during the 45-minute sessions. How many total minutes did Judy work out for the week?
Answers
Answer:
170 minutes
Step-by-step explanation:
So if there was two 45 min work outs in a week and she left those 10 mins early that was two 35 min work outs and then there was 4, 30min work outs and she left those 5 mins early so 4, 25min workouts so its 35+35+25+25+25+25.
Solve. Check for extraneous solutions. (x-2)¹/₂ -(28-2 x)¹/₄=0
Answers
-4 is an extraneous solution.
The equation is
[tex](x - 2)^{1/2}[/tex] - [tex](28-2x^{1/4}[/tex] = 0
To know whether the given equation has an extraneous solution or not we need to find the value of x.
[tex](x-2^{1/2}[/tex]= [tex](28-2x)^{1/4}[/tex]
Multiply both sides with the power of 4, and we get
[tex](x- 2)^{2}[/tex] = 28-2x
[tex]x^{2}[/tex] - 4x + 4 = 28-2x
[tex]x^{2}[/tex] - 2x - 24= 0
[tex]x^{2}[/tex]- 6x + 4x -24=0
x(x-6) +4(x-6)=0
(x-6)(x+4) = 0
x = 6 , -4
Now put both the value of x in the equation
x=6
[tex](6-2)^{1/2}[/tex]-[tex](28- 2* 6)^{1/4}[/tex]= 0
[tex]4^{1/2}[/tex]- [tex]16^{1/4}[/tex]= 0
2-2=0
0=0
Now
x = -4
[tex](-4-2)^{1/2}[/tex]-[tex](28-2*-4)^{1/4}[/tex]=0
[tex](-6)^{1/2}[/tex] -[tex]36^{1/4}[/tex]=0
[tex](-6)^{2}[/tex] - [tex]6^{1/2}[/tex]=0
Which is not possible and a negative integer is not present in the square root.
Therefore we get the extraneous solution of the equation which is x= -4, and x = 6 is the solution of the equation.
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Find the real and imaginary solutions of each equation.
x⁴-14 x²+49=0
Answers
The given 4th order polynomial equation only has real solutions, x = √7 and x = –√7
The given equation is x⁴-14 x²+49 = 0.
This is a 4th degree polynomial equation.
Let p = x².
Then we can write x⁴-14 x²+49 = 0 as:
p²- 14p +49 = 0
This is a quadratic equation.
There are three ways to find the solutions of a quadratic equation:
By factoringBy completing the squareBy applying the quadratic formulaNotice that p²- 14p +49 = 0 can be written as a perfect square:
(p - 7)² = 0
Hence, it has only single real solution:
p - 7 = 0
p = 7
Substitute p = 7 into p = x², we get:
x² = 7
x = ± √7
The solutions are, therefore, x = √7 and x = –√7
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P
=
2
L
+
2
W
to find the length of a rectangle when the width is
4 1/2
inches and the perimeter is
29 2/5
inches.
Answers
Answer:
10 2/5 inches
Step-by-step explanation:
Since P=2L+2W, we can flip it to find the length. For example, we could minus 2L from both sides to get P-2L=2W.
We already know that W is 4.5, and P is 29.4.
Plugging that in, we get 29.4-2L=9. Again we can flip the perimeter, and -29.4 on both sides. This would make -2L=-20.4.
For our last flip, we divide the -2 from both sides to finally get L=10.2 (or 10 1/5 if you want) inches.
A football team has a win to loss of 5:8. What is the ratio of losses to total games played
Answers
Write the equation of a line parallel to the line: y = − x − 1 that goes through the point (-2, -8).
Answers
The equation of the required line parallel to the given line is y = -x - 10.
What is slope ?Slope can be defined as the rate of change.
According to the given question we have to write an equation of a line parallel to the line y = - x - 1 that goes through the point (-2,-8).
We know that lines are parallel because of the same slope they have.
So, the required line also have a slope(m) = -1.
∴ The equation of the required line in slope intercept form can be written as y = mx + b.
Putting the value of given points (-2, -8) in (x,y) t evaluate y intercept b.
So, - 8 = (-1)(-2) + b.
- 8 = 2 + b.
b = -10.
∴The equation of the required line in slope intercept form is y = -x -10.
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What inscribed polygon is being constructed? Explain how you know.
Answers
With an equilateral triangle, only two circles are formed.
In geometry, what is an inscribed polygon?An inscribed polygon is one whose vertices are circle points. "In" denotes "in" and "scribed" denotes "written." Connect the points in a straight line with segments.What kind of polygon is carved into the circle?
A cyclic polygon is one that is inscribed in a circle, and the circle is its circumscribed circle or circumcircle.So, according to the given figure, we know that an equilateral triangle and only two circles are formed.Therefore, with an equilateral triangle, only two circles are formed.
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An athlete trains for 105 min each day for as many days as possible write an equation that relates the number of days d that the athlete spends training when the athlete trains for 630 min
Answers
• The athlete spends 105 mins training daily
Now, using that information, we can make an equation, with t representing the total:
t = 630d
In this equation, x represents the total, and d represents the amount of minutes each day the athlete trains for.
The ratio of Richard and Ben's speed is 4:5. The ratio of Richard and Kim's speed is 3:2. If it takes Ben 8 minutes to get to a location, it's going to take Kim _____ minute(s) for the same distance. (FILL IN THE BLANK)
Answers
The time it would take Kim running the same distance is 15 minutes.
How long would it take Kim?
Ratio is used to show the relationship between two or more numbers. It shows the frequency that one value is contained within other value(s). The sign that is used to represent ratio is :.
Speed = distance / time
The first step is to determine the time spent by Richard running:
(4 x 1/8) / 5 = 1/10 or 10 minutes
The second step is to determine the time spent by Kim running:
(2 x 1/10) / 3 = 1/15 = 15 minutes
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Use the properties of logarithms to evaluate each expression.
1/2 log₅15 - log₅√75
Answers
Using the properties of logarithm the value of the expression is [tex]\frac{1}{2}log_{5} 15 - log_{5} \sqrt{75} = -\frac{1}{2}[/tex]
According to the question the expression that we have been given is
= [tex]\frac{1}{2}log_{5} 15 - log_{5} \sqrt{75}[/tex]
Now solving it step by step using the properties of logarithm which are
[tex]log a^{m} = m*loga[/tex] , [tex]log \frac{x}{y} = logx - logy[/tex] and [tex]log_{a} a = 1[/tex]
As √75 is also equal to [tex](75)^{1/2}[/tex]. Thus equating in the equation we get
Therefore ,
[tex]= \frac{1}{2}log_{5} 15 - log_{5} 75^{\frac{1}{2} } \\= \frac{1}{2}log_{5} 15 - \frac{1}{2} log_{5}{75} \\[/tex]
As we can see that 1/2 is common in both the terms we will take out 1/2 common from both terms, by which we get
[tex]= \frac{1}{2} [log_{5} 15 - log_{5}{75} ] \\= \frac{1}{2} [log_{5} \frac{15}{75} ] \\\= \frac{1}{2} [log_{5} \frac{1}{5} ] \\= \frac{1}{2} [log_{5} 1 - log_{5}{5} ]\\= \frac{1}{2} [0 - 1]\\= -\frac{1}{2}[/tex]
Hence using the properties of logarithm the value of the expression is [tex]\frac{1}{2}log_{5} 15 - log_{5} \sqrt{75} = -\frac{1}{2}[/tex]
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A line passing through point (-6, 1) and has a slope of -3
Write an equation in Ax+By=C
Use integers A, B and C
Answers
Answer:
y=-3x-17
Step-by-step explanation:
y=mx+b (slope-intercept form) b=y-intercept= (0,?) m=slope
y=-3x+b substitute values
y+3x=b isolate b to find b
1+3(-6)=b substitute given ordered pair
-17=b
y=-3x-17
x+2−0.5x=1+.0.5x+1 solve for x
Answers
Answer:
x = 0
Step-by-step explanation:
x + 2 - 0.5x = 1 + 0.5x +1
2 - 0.5x = 2 + 0.5x
-0.5 - 0.5x = 2 - 2
-1x = 0
-1x/-1 = 0/-1
x = 0
Answer:
Step-by-step explanation:
Solve X + 2 - 0.5 x = 1 + 0.5 x + 1 : The answer is: X = 2X
Write each logarithmic expression as a single logarithm.
1/4 log₃2+ 1/4 log₃x
Answers
For the logarithm expression 1 / 4 log₃ 2 + 1 / 4 log₃ x, we get the single expression as 1 / 4 log₃ 2 x.
We are given the logarithm expression as:
1 / 4 log₃ 2 + 1 / 4 log₃ x
Now, take 1 / 4 common from the expression:
1 / 4 ( log₃ 2 + log₃ x)
Now, we know that log₃ a + log₃ b = log₃ ( a b)
So, we get that:
1 / 4 ( log₃ ( 2 x) )
1 / 4 log₃ 2 x
Therefore, for the logarithm expression 1 / 4 log₃ 2 + 1 / 4 log₃ x, we get the single expression as 1 / 4 log₃ 2 x.
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The product of any integer and –1 is always
Answers
What are the domain and points of discontinuity of the rational function? Are the points of discontinuity removable or non-removable? What are the x - and y -intercepts of the rational function?
c. y=x+1/x²+3 x+2}
Answers
The domain of given points are :
IR x ≠ -1 , -2
Points of discontinuity - x = -2 ( non removable / asymptote )
x = -1 ( removable / hole)
x - intercept = -1 , y - intercept = 1/2
What is rational functions ?Any function that can be expressed as a polynomial divided by a polynomial is said to be rational. The domain of a rational function is the set of all numbers except the zeros of the denominator since polynomials are defined everywhere. First example: f(x) = x/ (x - 3).
CALCULATIONy=x+1/x²+3 x+2
= x+1/x²+2x+x+2
= x+1/(x+2)(x+1)
The domain of given points are :
IR x ≠ -1,-2
Points of discontinuity - x = -2 ( non removable / asymptote)
x = -1 ( removable / hole)
x-intercept :
0 = x + 1
x = -1
y - intercept :
0+1 / (0+1)(0+2) = 1/2
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Sandy is training for a triathlon. Between running and bicycling, she covers a
distance of 200 miles every week. Her average speed on a bicycle ride is 20
mph. Her average speed running is 8 mph. If she spends 16 hours per week
training, how many hours does she spend on each sport?
Answers
Answer:
Step-by-step explanation:
Each ordered pair is from an inverse variation. Find the constant of variation. (6,3)
Answers
The value of constant variation is 18.
Constant is what?A key integer with a stable value determined by a clear specification is referred to as a mathematical constant.
Inverse variation: what is it?connection in mathematics between two variables that may be described by an equation in which the sum of their products equals a constant
Inverse variation is y = k. 1/x
given y = 3
x = 6
So, 3 = k. 1/6
So, the value of k = 18.
We can conclude that the value of constant variation is 18.
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3 identical circles inside a rectangle each circle touches the other two circles and sides of a rectangle
the radius of each circle is 2mmworkout the exact area of the rectangle
give your answer in the form a√ 3+b
where a and b are integers
Answers
The area of the rectangle having three identical circles inside is calculated as: (16√3 + 32) mm².
What is the Area of a Rectangle?Area of rectangle = (length)(width)
The image of the three identical circles in the rectangle has been labelled as shown in the diagram attached below.
We need to find the measure of the length and width of the rectangle.
Radius = AB = BD = DF = FG = CD = HI = 2 mm
Length of the rectangle = AB + BD + DF + FG = 2 + 2 + 2 + 2
Length of the rectangle = 8 mm
Width of the rectangle = CD + DH + HI
CD = 2 mm
HI = 2 mm
Use the Pythagorean theorem to find the measure of DH
DH = √(FH² - DF²)
FH = 2 + 2 = 4 mm
DF = 2 mm
Substitute
DH = √(4² - 2²)
DH = √(16 - 4)
DH = √12 = 2√3 mm
Width of the rectangle = CD + DH + HI = 2 + 2√3 + 2
Width of the rectangle = 2√3 + 4
Area = (2√3 + 4)(8)
Area = (16√3 + 32) mm²
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the sum of a number and two thirds the number is the same as 4 less than twice the number
Answers
12
Step-by-step explanation:
n + (2/3)n = 2n - 4
(5/3)n = 2n - 4
(5/3)n - 2n = -4
(-1/3)n = -4
n = 12
Grapes are selling for $0.26 a pound. Ashley spent $3.77 on grapes. How many pounds of grapes did Ashley buy?
Answers
can someone help me really quick
Answers
Answer:
2 2/4 because i just know the answer
(a +11)(11a +1)
Simplify
Answers
Answer:
11a^2 + 122a + 11
Step-by-step explanation:
First, multiply a by 11a, which gives you 11a^2. Then you multiply 11 to 11a, which gives you 122a, then last just multiply 11 to 1 and you get 11. Hope this helps.
Factor the expression. 25-40 x+16 x²
Answers
Factor the expression 25-40 x+16 x² is [tex](4x-5)^2[/tex]
In mathematics, factorization is defined as breaking down or decomposing an entity (such as a number, matrix, or polynomial) into another entity or product of coefficients. Splitting the mean term means that the mean term of the quadratic must be rewritten as the sum or difference of two terms. The middle term should be split into two parts in terms of the sum or difference of the terms. The general form of the quadratic equation is [tex]ax^2+ bx +c=0[/tex]On rearranging the equation , we get
[tex]16x^2-40x+25=0[/tex] ...(1)
To split the middle term of the quadratic equation, we need to look at the middle term of the quadratic equation under consideration.
Midterm is 40 x , to split the middle term, use the sum-and-product form which is
" The sum-product form is the product of intermediate terms after splitting and must equal a × c and the sum must equal b "
[tex]f(x)=16x^2-40x+25[/tex]
here a = 16 , b = -40 and c = 25
We need to divide into 40x in two parts
40x = 20x + 20x
The product of the terms is [tex]16\times25=400[/tex]
Now we can rewrite 40x as 20x + 20x
Putting in equation (1) , we get
[tex]16x^2-(20+20)x+25=0\\\\(16x^2-20x)-(20x-25)=0\\\\4x(4x-5)-5(4x-5)=0\\\\(4x-5)(4x-5)=0[/tex]
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23
−
1/9
= ?????
I really need help please help me...
Answers
Answer: 22.8888888889 but rounded 22.9
Step-by-step explanation: This is so because when you turn 23 to ninths you get 207/9 - 1/9 then put into decimal form, 22.8888888889 or 2.9
HELP ASAP I DONT WANT TO FAIL
Answers
Answer:
16.3p + (-10)
Step-by-step explanation:
Find all the real square roots of each number. 0.49
Answers
The real square root of the number 0.49 is 0.7
0.49 can also be presented as, 49* [tex]10^{-4}[/tex]
The square root of 49* [tex]10^{-2}[/tex]
= [tex]\sqrt{49}[/tex] * [tex]\sqrt{10} ^{-2}[/tex]
= 7 * [tex]10^{-2}[/tex]
=0.7
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