y =5.5x represents a proportional relationship. What is the constant proportionality?
Answer: 5.5 is the constant proportionality.
Step-by-step explanation:
Since we have given that
y = 5.5x
As we can see that
y is directly proportional to x.
So, mathematically written as
[tex]y\ \alpha\ x\\\\y=kx[/tex]
If we comparing both the expression, we get that
k = 5.5.
Hence, 5.5 is the constant proportionality.
The constant of proportionality of y = 5.5x is 5.5.
A directly proportional relational relationship can be represented below
y ∝ xwhere
∝ = symbol for proportionality
y and x are the variable that are related. Therefore,
y = kx
where
k = constant of proportionality.
The equations y = 5.5x can be modelled as directly proportional relationship using y = kx.
Therefore, k = 5.5 is the constant of proportionality.
The constant of proportionality of y = 5.5x is 5.5.
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write an expression that represents the area of a square with side length 6xy^2 (for any square with side length s, A=s^2=s.s.)
how do you evaluate log2 1/64
Suppose a parabola has an axis of symmetry at x=-1 a maximum height of 6 and passes through point -2,1. Write the equation of the parabola in vertex form
In an isometric transformation, the preimage and image must not __________.
A.
change size
B.
rotate
C.
preserve angle measures
D.
reflect across the -axis
a shopper purchased 8 t-shirts and 5 pair of pants for $220. the next day, he purchased 5 t-shirts and a pair of pants for $112. how much does each t shirt and pair of pants cost
The dimensions of a closed rectangular box are measured as 50 centimeters, 90 centimeters, and 80 centimeters, respectively, with the error in each measurement at most .2 centimeters. Use differentials to estimate the maximum error in calculating the surface area of the box.
The maximum error in calculating the surface area of the box is approximately 176 square centimeters.
What is the surface area of the rectangular box?The surface area of the rectangular box is given by:
S = 2(wh + lh + lw)
where w, h, and l are the width, height, and length of the box, respectively. The differential of S with respect to each dimension can be expressed as:
dS = 2((h+dh)(w+dw) + (l+dl)(h+dh) + (l+dl)(w+dw)) + 2(wh + lh + lw) - 2S
where dw, dh, and dl represent the maximum error in each measurement, which is given as 0.2 cm. We have to find the maximum error in calculating the surface area, so we need to find the maximum value of dS.
Substituting the given values into the differential expression, we get:
dS = [2*(0.2)*80+2*90*(0.2)]+[2*(0.2)*50+2*80*(0.2)]+[2*(0.2)*50+2*90*(0.2)]
≈ 176
Therefore, the maximum error in calculating the surface area of the box is approximately 176 square centimeters.
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Write 98 as the product of prime factors in ascending order
information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f
Degree 4; zeros: i, 14+i
what are the remaining zeros of f
The remaining zeros of the given degree 4 polynomial f(x) with known zeros i and 14+i are -i and 14-i.
In Mathematics, particularly in studying polynomials, if a polynomial has real coefficients, then complex zeros always occur in conjugate pairs.
That is, if a+bi is a zero, then its conjugate, a-bi is also a zero.
Given that f(x) is a polynomial of degree 4 with zeros i and 14+i, then its conjugate zeros are -i and 14-i. Therefore, the four zeros of the polynomial f(x) are i, -i, 14+i and 14-i.
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A pharmacy claims that the average medication costs $32 but it could differ as much as $8. Write and solve an absolute value inequality to determine the range of medication costs at this pharmacy.
|x − 32| ≥ 8; The medication costs range from $24 to $40
|x − 32| ≥ 8; The medications cost less than $24 or greater than $40.
|x − 32| ≤ 8; The medication costs range from $24 to $40
|x − 32| ≤8; The medications cost less than $24 or greater than $40.
the answer is C the third one
A hemispherical dome with radius=20 feet needs 11 coats of paint, which are 1/100 inch thick...need to use linear approximation to get the volume of paint needed for the job.
On average 113,204 aluminum cans are recycled in a minute. Approximately how many cans will be recycled in 16 days? (Express your answer in scientific notation.)
a.
2.61x10^9 cans
b.
4.35x10^7 aluminum cans
c.
1.09x10^8 aluminum cans
d.
1.63x10^8 aluminum can
Answer:
the answer is A
Step-by-step explanation:
Final answer:
The answer is approximately 2.61x10⁹ cans recycled in 16 days, which is option (a).
Explanation:
The student is asking about a mathematical estimation of how many aluminum cans are recycled over a 16-day period, given an average rate of recycling per minute.
To find the answer, we'll first calculate the number of minutes in 16 days:
16 days × 24 hours/day × 60 minutes/hour = 23,040 minutes.
Now, we multiply this by the average number of cans recycled per minute:
23,040 minutes × 113,204 cans/minute = 2.61x10⁹ cans.
Expressing this value in scientific notation gives us:
About 2.61x10⁹ aluminum cans recycled in 16 days, which corresponds to option (a) in the multiple-choice provided by the student.
Find the value of a in the diagram of the right triangle. Round to the nearest tenth.
the options are
A) 21.6 in.
B) 24.2 in.
C) 5.0 in.
D) 12.3 in.
Answer:
The answer is the option B
[tex]a=24.2\ in[/tex]
Step-by-step explanation:
we know that
In the right triangle of the figure
[tex]sin(27\°)=\frac{11}{a}[/tex]
Solve for a
[tex]a=\frac{11}{sin(27\°)}[/tex]
[tex]a=24.2\ in[/tex]
the graph of a line goes up and to the right when:
a) the coefficent of x is 0
b) the coffecient of x is negative
c) the coffecient of x is positive
d) there is no coffecient of x
Option: C is the correct answer.
c) the coefficient of x is positive
Step-by-step explanation:We know that graph of a line goes up and to the right when the coefficient of x is positive.
Since we know that when a line goes up and to the right this means that the line is increasing and hence we will get a positive slope of the line and we know that the slope intercept of a line is given as:
[tex]y=mx+c[/tex]
as m is positive this means that:
the coefficient of x is positive.
Hence, the correct answer is:
c) the coefficient of x is positive
The graph of a line goes up and to the right when the coefficient of x is positive, indicating it has an upward slope. This occurs when 'b' in the equation 'y = a + bx' is greater than zero.
The graph of a line wil go up and to the right when the coefficient of x is positive. In other words, when we have an equation like y = a + bx and b is greater than zero, the line has an upward slope. This means that for each step we move to the right on the x-axis, the value of y increases. Therefore, the correct answer to the question is (c) the coefficient of x is positive.
As a reference:
When the slope coefficient b is zero (b = 0), the line is horizontal.If b is negative (b < 0), the line slopes downward to the right.An increase in the slope will cause the line to rotate counter-clockwise around the y-intercept, indicating an increase in its steepness if the slope was positive or a decrease in its negativity if the slope was negative.Remember, the term positive slope indicates the line rises as it moves from left to right, while a negative slope indicates a line that falls as it moves from left to right.
Find the values of x and y that satisfy the equation. 3x+6i=27+yi
The values that satisfy the equation 3x + 6i = 27 + yi are x = 9 and y = 6, which are found by equating real and imaginary parts separately.
To find the values of x and y that satisfy the equation 3x + 6i = 27 + yi, we must equate the real parts and the imaginary parts separately. The real part of the equation gives us x, and the imaginary part gives us y.
From the real part, we have:
3x = 27
x = 27 / 3
x = 9
From the imaginary part, we have:
6i = yi
y = 6
Therefore, the values x = 9 and y = 6 satisfy the given equation.
A geneticist is studying a population of fruit flies. Of the 1278 flies, 467 are wingless and 446 have red eyes. There are 210 flies that are wingless whose eyes are not red. What is the approximate probability that a fly is wingless or has red eyes?
0.49
0.51
0.71
0.88
The approximate probability that a fly is wingless or has red eyes is 0.49.
A geneticist is studying a population of fruit flies. Of the 1278 flies, 467 are wingless and 446 have red eyes.
What is the probability?Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
There are 210 flies that are wingless and whose eyes are not red.
We have determined the approximate probability that a fly is wingless or has red eyes.
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A carpenter makes chairs with slats that run across the chair as shown. each chair uses 7 slats. he needs to make 24 chairs.how many slats must he make?
Write a justification for each step.
which is bigger, half of 30 or one third of 75
please explain for brainlist
what is the inverse of the following statement: if he speaks arabic, he can act as the interpreter.
...?
Answer:
If he can not speak Arabic, he can not act as the interpreter.
Step-by-step explanation:
Negating both the hypothesis and conclusion of a conditional statement. For example, the inverse of "If it is raining then the grass is wet" is "If it is not raining then the grass is not wet".
Janelle practices basketball every afternoon in her driveway. Each day, her goal is to make 4 more baskets than she made the day before. If she makes 10 basket the first day and meets her goal for 2 weeks, how many baskets will Janelle makes on the 14th day
Ari has a total of 22 coins consisting of pennies and nickels. The total value of the coins is $0.54.
How many of each type of coin does Ari have?
Answer:
Let n = the number of nickels that Ari has.
Let p = the number of pennies that Ari has.
The total number of coins she has is 22.
n + p = 22
We have our first equation... But we another one to solve this.
Each penny is going to be $0.01 and a nickel is work $0.05.
And the total is $0.54
Our second equation. 0.05n + 0.01p = 0.54
n + p = 22
0.05n + 0.01p = 0.54
Multiply the top by -0.05
-0.05n - 0.05p = -1.1
0.05n + 0.01p = 0.54
The n terms cancel out.
-0.04p = -0.56
p = 14
Step-by-step explanation:
Which figure shows a reflection of pre-image QRS over the line t?
A.
90° clockwise rotation around point B
B.
180° clockwise rotation around point B
C.
reflection over line a
D.
translation 4 units up
Alex buys 24 apples and when he opens it 6 apples are bad whats the perecentage of the bad apples
Derive the equation of the parabola with a focus at (−5, −5) and a directrix of y = 7
Answer: -1/24(x+5)^2+1
A drawer contains 8 red shirts, 6 blue shirts, and 7 white shirts. If a shirt is drawn at random, what is the probability that the shirt will be blue?
Answer:
The Probability of drawing shirt is blue is [tex]\frac{2}{7}[/tex]
Step-by-step explanation:
Given : A drawer contains 8 red shirts, 6 blue shirts, and 7 white shirts.
We have to find the probability if a shirt is drawn at random, then the shirt will be blue.
Total number of shirt in drawer = 8 + 6 + 7 = 21
Number of blue shirts = 6
Probability of an event = [tex]\dfrac{\text{number of possible outcomes}}{\text{number of total outcomes}}[/tex]
Event (E) : shirt drawn is blue.
number of possible outcomes = 6
number of total outcomes = 21
Thus, the Probability of drawing shirt is blue is [tex]\frac{6}{21}[/tex]
Simplifying , we get,
The Probability of drawing shirt is blue is [tex]\frac{2}{7}[/tex]
Which conditional and its converse form a true biconditional?
A) If x>0, then lxl >0
B) If x=3, then x2^2=9
C) If x^2 =4, Then x=2
D) If x=19, then 2x-3=35
Answer: D) If x=19, then 2x-3=35
Step-by-step explanation:
A) If x > 0, then lxl >0,
L.H.S. x > 0,
R.H.S. lxl >0 ⇒ ± x > 0
⇒ L.H.S. ≠ R.H.S.
B) If x = 3 then [tex]x^2 = 9[/tex]
L.H.S. x = 3,
R.H.S. [tex]x^2 = 9[/tex] ⇒ x = ± 3
⇒ L.H.S. ≠ R.H.S.
C) If [tex]x^2 =4[/tex], Then x=2
L.H.S. [tex]x^2 =4[/tex] ⇒ x = ± 2,
R.H.S. x = 2,
L.H.S. ≠ R.H.S.
D) If x=19, then 2x-3=35
L.H.S. x = 19,
R.H.S. 2x-3=35 ⇒ 2x = 38 ⇒ x = 19
⇒ L.H.S. = R.H.S.
⇒ Option D is correct.
What isthe answer to 3/5 ❌ 20
The area of the square is 144 square cm length of each side of the square is
Which input value produces the same output value for the two functions on the graph?
x = -3
x = -2
x = -1
x = 3
The input value produces the same output value for the two functions on the graph is [tex]\boxed{x = - 2}[/tex]. Option (b) is correct.
Further explanation:
Given:
The options are as follows,
(a). [tex]x = - 3[/tex]
(b). [tex]x = - 2[/tex]
(c). [tex]x = - 1[/tex]
(d). [tex]x = 3[/tex]
Explanation:
The output values of the function are known as range and the input values on which function is defined is known as the domain of the function.
The one-to-one function is a function in which every value of the range has exactly one pre-image in the domain.
The functions are [tex]f\left( x \right){\text{ and }}g\left( x \right).[/tex]
From the graph it has been observed that the line of the function intersects each other at [tex]x=- 2.[/tex]
The input value produces the same output value for the two functions on the graph is [tex]\boxed{x = - 2}[/tex]. Option (b) is correct.
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Answer details:
Grade: High School
Subject: Mathematics
Chapter: Relation and Function
Keywords: relations, functions, all relation are functions, all functions are relations, no relations are functions, no functions are relation, one-to-one, onto, graph representation, paired, y-value, x-values, origin.