When two amounts are proportionate, they fluctuate at the same rate, maintaining the constancy of their relationship.
Here x be the proportionality constant its value 5.5.
What is meant by proportionality constant ?The ratio connecting two given numbers in what is known as a proportional relationship is the constant of proportionality. Constant ratio, constant rate, unit rate, constant of variation, and even rate of change are other names for the constant of proportionality.When two amounts are proportionate, they fluctuate at the same rate, maintaining the constancy of their relationship.In mathematics, we use the constant of proportionality to compute the rate of change and identify whether we are working with direct variation or inverse variation.Matthew bought 2 movie tickets for $11,
Rosa bought 7 movie tickets for $38.50.
let the value of per ticket is x
2x = 11 and 7x = 38.5
7x- 2x = 38.5 -11
x = 5.5
here x be the proportionality constant its value 5.5.
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HELP PLEASE!!!!
Simplify −4r(−11r + 2r − 14).
−36r^2 + 56r
−36r^2 − 56r
36r^2 + 56
36r^2 + 56r
Answer:
[tex]36r^2+56r[/tex][tex]36r^2+56r[/tex]
Step-by-step explanation:
First simplify [tex]-4r(-11r+2r-14)[/tex] into [tex]-4r(-9r-14)[/tex] by adding the terms with common variable r together,
then expand into the answer
Answer:
-36r^2 - 56r
Step-by-step explanation:
Kali just started a new sales floor job to save for college. She earns $15.75 per hour plus a flat fee of $50 per week. She wants to earn between $200 and $400 per week. The following inequality represents her earning potential: 200 ≤ 15.75x + 50 ≤ 400 Solve the inequality.
The solution set of the given inequality is:
9.52 ≤ x ≤ 22.22
Or [9.52, 22.22] if we write this as an interval.
How to solve the inequality?Here we have the inequality:
200 ≤ 15.75x + 50 ≤ 400
Which represents Kali's earning potential.
To solve the inequality we need to isolate the variable in the middle, if we subtract 50 in the 3 sides we get:
200 - 50 ≤ 15.75x + 50 - 50 ≤ 400 - 50
150 ≤ 15.75x ≤ 350
Now we need to divide both all by 15.75, so we get:
150/15.75 ≤ 15.75x/15.75 ≤ 350/15.75
9.52 ≤ x ≤ 22.22
This is the solution of the inequality, the solution set written as an interval will be [9.52, 22.22]
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I am a little confused with this.
The roots of the given equation are:
x = i√13 and x = - i√13Where, There are 2 roots for this polynomial function because of the need to find + and - of the radicand i√13.What are the roots of an equation?The values of the variable that satisfy a quadratic equation are known as its roots.The solutions or zeroes of the quadratic equation are other names for them.The x-coordinates of the x-intercepts of a quadratic function are the roots of the function.Solving quadratic equations refers to the process of locating the roots of quadratic equations.Get roots of equation, 2x² + 26 = 0:
2x² + 26 = 02x² = -26Divide both sides by 2:
x² = -13Finding square roots on both sides:
x = √-13x = √13i²x = ±i√13So, the roots of the equation are x = ±i√13.
There are 2 roots for this polynomial function because of the need to find + and - of the radicand i√13.A real number is multiplied by the imaginary unit i that is specified by its property i²-1 to create an imaginary number.Therefore, the roots of the given equation are:
x = i√13 and x = - i√13Where, There are 2 roots for this polynomial function because of the need to find + and - of the radicand i√13.To learn more about the roots of an equation, refer to:
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Each box holds 48 pencils. The chart below shows the number of pencils in 1 box and 5 boxes.
Help ASAP please
Answer: No, 6 boxes will give you 288 penicils.
Step-by-step explanation: 1 box is 48 penicils, so if use this to the other boxes (4x48) we get 192. Now with six boxes (6x48) we get 288.
what is the area of a rectangle wxyz with vertces w(0,1), x(3,4), y(-1,8), z(-4,5)
Answer: I think 43
Step-by-step explanation:
Draw on a graph out the points and then add up the middle of your shape.
Your welcome!
Multiply 3.2x and 4x.
12.8x2
7.2x2
12.8x
7.2x
Answer: 12.8x2
Step-by-step explanation:
Based on the given task content; the solution to the Multiplication of 3.2x and 4x is 12.8x².
The correct answer option is option a.
Multiplication of numbersThis is a process of computing the sum of a number with itself in a specified number of times. Multiplication is also called product and it is represented by the sigh ×. The product of a and b means ab.
For instance, from the task which is given above;
3.2x and 4x
= 3.2x × 4x
= 12.8x²
In this answer above,
12.8 is the coefficient and
x² is the variable.
In conclusion, 3.2x × 4x will give the result 12.8x².
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Latisha has $40 in her checking account. She makes a withdrawal of $20 and then writes a check for $40. Then she deposits $30. Use the number line and complete the equation to find her final balance.
The final balance that will be in the account of Latisha is $10.
What is a checking account?A checking account simply means the account that makes use of a check. It is usually used by business owners.
From the information, Latisha has $40 in her checking account, she makes a withdrawal of $20 and then writes a check for $40 and then she deposits $30.
The appropriate operations to find the balance will be:
= 40 - 20 - 40 + 30
= 10
She will have $10 left. Note that a withdrawal is subtraction.
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find the length of the sides indicated round to nearest tenth
BEING TIMED HElp
Which rectangular equation is formed by eliminating the parameter?
y = t3
x = t + 5
A.y = x3 – 125
B. y = x3 + 125
C. y = x3 – 5x2 + 25x – 125>>>>>> WRONG
D.y = x3 – 15x2 + 75x – 125
Answer:
its d i got it right
Step-by-step explanation:
When 12 is subtracted from the square of a number, the result is 4 times the number. Find the negative solution.
When 12 is subtracted from the square of a number and the result is 4 times the number, then the negative solution is -2
Consider the number as x
Square of the number = [tex]x^{2}[/tex]
12 subtracted from the square of a number = [tex]x^{2} -12[/tex]
4 times the number = 4x
Then the equation will be [tex]x^{2} -12=4x[/tex]
Rearrange the terms and it will become a quadratic equation
[tex]x^{2} -4x-12=0[/tex]
Split the middle term and solve the equation
[tex]x^{2} +2x-6x-12=0[/tex]
Take common terms
x(x+2)-6(x+2) = 0
Take common term outside
(x-6)(x+2) = 0
Therefore
x = 6, -2
The negative solution is -2
Hence, when 12 is subtracted from the square of a number and the result is 4 times the number, then the negative solution is -2
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get it down give u more points for the rest of the questions
A contractor purchases 3 dozen pairs of padded work gloves for $43.56 incorrectly calculates the unit price as $14.52 per pair for the expense report. What is the correct unit price?What is the error?
Answer: I think the answer is $1.21
Step-by-step explanation: Instead of 3 pairs it says 3 dozen. A dozen is 12.
3 x 12 = 36
Then you should do 43.56 / 36
For one pair of gloves it should be $1.21
The contractor got $14.52 because he did a dozen (12) divided by 43.56.
I hope that helps! ^^
I no longer need this to be answered
Answer:
oh ok hope you got the answer
Step-by-step explanation:
a forest trail is 607 feet long. a person biked from one end to the other and back again 6 times in the past 5 weeks. how far the person bike over the past 5 weeks
The distance that the person bike over the past 5 weeks is 7284 feet.
How to illustrate the expression?Distance is the sum of an object's movements, regardless of direction. Regardless of an object's starting or ending position, distance can be defined as the amount of ground it has covered. Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively.
From the information, the forest trail is 607 feet long and a person biked from one end to the other and back again 6 times in the past 5 weeks.
Therefore, the distance that the person covered will be:
= 2 × 6 × 607
= 7284 feet.
The distance is 7284 feet.
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Given the equation k over 22.8 equals 6.9, determine the value of k.
3.30
15.9
29.7
157.32
The value of k in the equation, k over 22.8 equals 6.9, is 157.32.
What is the value of k?The given equation is:
k / 22.8 = 6.9
In order to determine the value of k, multiply both sides of the equation by 22.8.
Multiplication is one of the basic mathematical operation. It is the operation that is used to determine the product of two or more numbers by adding a number with another number repeatedly over a number of times. The sign that represents multiplication is ×.
(k / 22.8) x 22.8 = 6.9 x 22.8
k = 157.32.
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select the correct answer from the drop -down menu . A=[-9,0,3,-1] b= [0,4,-6,2] the order of matrix A+B is ?
If A=[-9,0,3,-1] b=[0,4,-6,2] , so the order of matrix A+B is 4x1(4 rows and 1 column).
What is matrix ?Matrix, a set of number arranged in rows and column so as to form a rectangular array. The number are called the elements, or entries, of the matrix .
What does the matrix serve as?Both data and mathematical equations can be represented by the numbers in a matrix. Multiplying matrices can provide quick but accurate approximations of considerably more complex calculations in many time-sensitive engineering applications.
The elements of the matrix are nothing but the entries of the matrix.
So according, To the question we are adding matrix A which is 4 rows and 1 column to matrix B which is also of 4 rows and one column obtaining a third matrix that has also 4 rows and 1 column :
[-9,0,3,-1]+[0,4,-6,2]=[-9,4,-3,1]
The resultant A+B is also of 4 rows and 1 column
Hence the order of matrix A+B is 4x1 (4 rows and 1 column)
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Translate this phrase into an algebraic expression.
Nine less than the product of 18 and Jose's age
Use the variable j to represent Jose's age.
Answer:
J(18)-9
Step-by-step explanation:
j times 18 minus 9
which two values or x are roots of the polynomial below? x2 - 11x + 13
The two values or x of roots of the polynomial are
[tex]x=\frac{11+\sqrt{69}}{2}, \frac{11-\sqrt{69}}{2}[/tex]
This is further explained below.
What is a polynomial?An expression that consists of variables, constants, and exponents that are combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.
Generally, the equation for polynomial the is mathematically given as
x^2 - 11x + 13
Therefore
We know that,
[tex]x=\frac{-b \pm \sqrt{b^2-4 a c}}{2 a}[/tex]
Here,
a=1
b=-11
c=13
Putting the values,
[tex]x=\frac{-(-11) \pm \sqrt{(-11)^2-4 \times 1 \times 13}}{2 \times 1} \\[/tex]
[tex]&=\frac{11 \pm \sqrt{121-52}}{2} \\\\&=\frac{11 \pm \sqrt{69}}{2} \\[/tex]
Therefore
[tex]x=\frac{11+\sqrt{69}}{2}, \frac{11-\sqrt{69}}{2}[/tex]
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(3, 9), (1, 1) write in standard form
Factorización prima de 162
If x+y =8 and x^2+y^2=36 find x-y
If A intersects B, B intersects C, C is parallel to D, and D intersects E, which is not true?
Following the descriptions of the relationship existing between the lines the option that is not true is the last option which is b || d which is read as b is parallel to d
What are parallel lines?Some set of lines are said to be parallel if the lines are equally spaced apart. This ensures that such line will never meet . Parallel lines is very useful in the field of geometry as it the foundation of many postulates and theorem.
Also, when two lines are being connected by a line. Say line x and line y and the connecting line is z. If the lines x and y makes similar angle with line z then line x and line y is said to be parallel.
Considering the descriptions given in the question. line b is tether perpendicular to line d. Hence saying that line b is parallel to line d is not true and the correct answer to the question.
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Determine if 0.68
0.68 is rational or irrational and give a reason for your answer.
choices for explanation-
it is a decimal that repeats
it is the square root of a non perfect square
it is the square root of a perfect square
it is a decimal that does not repeat or terminate
it is a decimal that terminates
(urgent pls help)
0.68 is a rational number and the reason is because:
It is a decimal that terminatesWhy is 0.68 a rational number?0.68 can be regarded as a rational number because it is a finite number that is also a fraction of two whole integers. In this case, the integers are 68 and 10. Another feature by which rational numbers are known is the fact that they are repeating in nature.
However, it is important to note that the decimal here is terminating in nature because it has a finite number of zeros behind the number 8. So, the reason for selecting 0.68 as a rational number is that it terminates.
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5. Below is a model of the infield of a baseballstadium. How long is each side of the infield?oth a perfectquare rootnumbers?A= 81 in.?
We have that the area of the infield is 81 in2.
This area is a square, which means it has equal sides, and its area is:
[tex]\text{Area}=side^2[/tex]If the area of the square is 81 in2, we have that:
[tex]\begin{gathered} \text{side}^2=81 \\ \text{side}=\sqrt{81} \\ \text{side}=9\text{ in} \end{gathered}[/tex]So the side of the infield is 9 inches.
Sorry for all the questions i'm askin i'm a slow learner so thank you guys for ya help!
50 points will b giving
Answer:
D. [tex]\sqrt{27}[/tex]
Step-by-step explanation:
A, B, and C are all perfect squares being square rooted. This means that they will all result in whole numbers.
For example: A. [tex]\sqrt{9}=3[/tex]
However, D. [tex]\sqrt{27}=3\sqrt{3}[/tex], which is not rational because it contains an unsimplifiable square root (sqrt 3)
Answer:
√27
Step-by-step explanation:
√9 = 3
√81 = 9
√36 = 6
√27 = not whole number
brunette college offers 444 math classes, 222 science classes, 333 language classes, and 555 art classes. sylvia needs to sign up for exactly one class in each subject. how many different combinations of classes does sylvia have to choose from?
The total number of different combinations is 120.
What is combination and permutation?
Combination and permutation are two alternative strategies in mathematics to divide up a collection of components into subsets. The subset's components can be listed in any order when combined. The components of the subset are listed in a permutation in a certain order.We are to find the number of different combinations of classes does Sylvia have to choose from.
We will be using the following formula for number of combinations of n elements taken r (r is less than or equal to n) at a time:
nCr = n!/r!( n - r )!
Since Sylvia needs to sign up for exactly one class in each subject, so the total number of different combinations from which she has to choose will be
⁴C₁ * ²C₁ * ³C₁ * ⁵C₁
= 4!/1!( 4 - 1 )! × 2!/1! ( 2 - 1 )! × 3!/1! ( 3 -1)! × 5!/1! ( 5 - 1 )!
= 4 × 2 × 3 × 5
= 120
Thus, the total number of different combinations is 120.
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If the vertical component of velocity for a projectile is 7.3 meters/second, find its hang time. a. 1.5 seconds b. 2.5 seconds c. 5.6 seconds d. 6.7 seconds e. 7.1 seconds
The hang time is calculated to be a. 1.5 seconds if the vertical component of velocity for the projectile is 7.3 meters/second.
The formula for the height of the projectile can be used to calculate the hang time as follows;
h = ut - 0.5at²
here;
h is the height of the projectile
u is the velocity = 7.3 m/s
a is the acceleration due to gravity
The standard value of acceleration due to gravity is equal to 9.81 m/s²
The height will be zero both the times when t=0 and when the journey has been completed
Now adding these values to the formula;
h = ut - 0.5at²
0 = 7.3t - 0.5(9.81)t²
Solving for t;
4.905t² = 7.3t
4.905t² / t = 7.3
4.905t = 7.3
t = 7.3 / 4.905
t = 1.49 ≈ 1.5
Therefore; the hang time is calculated to be 1.5 seconds.
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Find 3 decimals x such that : 4.1 < x < 4.2
Answer:
There are many numbers, but here are three
4.11, 4.12, 4.13
Step-by-step explanation:
In the diagram below, isosceles triangle ABC is drawn with AB is congruent AC and side BC extended through point D. If
m/ACB=2x+16 and m angle ACD=5x+24, find the measure of angle A.
Answer:
32°
Step-by-step explanation:
Angle A + angle B = angle ACD
Since it is an isosceles triangle angle a = angel b
2(2x + 16) = 5x +24 distribute the 2
4x + 32 = 5x + 24 Subtract 4x from both sides
32 = x + 24 Subtract 24 from both sides
8 = x
Now plug in 8 for x in 2x + 16
2(8) + 16
16+ 16 = 32
What is the sum of the first 11 prime numbers?
Considering the definition of prime numbers, the sum of the first 11 prime numbers is 129.
Definition of prime numbersPrime numbers are those that are only divisible (when divided by another gives an integer) between themselves and 1. That is, prime numbers are those numbers, greater than 1, that only admit themselves and the number as divisors. number 1.
Sum of the first 11 prime numbersThe first 11 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, and 31.
So their sum is:
sum= 2 +3 +5 +7 +11 +13 +17 +19 +23 +29
sum= 129
Finally, their sum is 129.
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