Answer:
Proportional relationship between two quantities x and y means that the quotient y/x stays constant, i.e. that there is a constant c such that y=cx. In our case we have that y=3x+5 which means that x and y are NOT proportional.
Answer:
Check the explanation provided
Step-by-step explanation:
This equation does not represent a proportional relationship because it's graph does not pass through the origin (i.e. 0,0)
[tex]y = mx + c[/tex]
where m = gradient OR slope
= 3
c = y-intercept
= 5
For the equation to have a proportional relationship, the value of c MUST BE '0’
Bisectors of triangles
Find RT
The length of RT is 13 units
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
As T is the centroid of the given triangle.
TN=TP
x+10=4x-17
Now solve for x
27=3x
x=9
Now TP=4(9)-17
TP=36-17
TP=19
Now from pythagoras theorem we find the length of RT
19²=14²+RT²
361-196=RT²
165=RT²
Take square root on both sides
RT=13
Hence, the length of RT is 13 units
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2. A container holds 5 red pens, 4 purple pens and 3 blue pens. Find the
probability P(red pen, purple pen) without replacement. (use the simplest
fraction)
The probability P(red pen, purple pen) without replacement is 10/33.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given that a container holds 5 red pens, 4 purple pens and 3 blue pens.
We need to find the probability P(red pen, purple pen) without replacement.
P(red pen, purple pen) = (number of ways to select a red pen and a purple pen) / (total number of ways to select two pens)
Total number of ways to select two pens=¹²C₂=66 ways.
Number of ways to select a red pen and a purple pen = (number of ways to select a red pen) x (number of ways to select a purple pen from the remaining pens)
Number of ways to select a red pen = 5
Number of ways to select a purple pen from the remaining pens = 4
Therefore, the number of ways to select a red pen and a purple pen without replacement is:
Number of ways to select a red pen and a purple pen = 5 x 4 = 20
P(red pen, purple pen) =20/66
=10/33
Hence, the probability P(red pen, purple pen) without replacement is 10/33.
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What is the cube root of 12 167?
From the given information provided, the cube root of 12,167 by prime factorization method is approximately 23.
You can find the cube root of 12,167 using a calculator or by using the prime factorization method.
Using the prime factorization method, we can express 12,167 as the product of its prime factors:
12,167 = 19 × 641
Since the cube root of a product is equal to the product of the cube roots of the factors, we can find the cube root of 12,167 as follows:
∛12,167 = ∛(19 × 641)
∛12,167 = ∛19 × ∛641
∛12,167 = 2.7144 × 8.0186
∛12,167 = 23.1649 (rounded to four decimal places)
Therefore, the cube root of 12,167 is approximately 23.
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Ann borrowed $8000 at a rate of 15%, compounded annually. Assuming she makes no payments, how much will she owe after 6 years?
Answer:
Ann will owe $15,258.23 after 6 years, assuming she makes no payments.
What is Compound Interest ?
Compound interest is a method of calculating interest on a loan or investment, where interest is earned on both the initial principal amount and on any interest that has already been earned. In other words, interest is added to the principal, and then interest is calculated on the new total amount (the principal plus the previously earned interest). This results in the interest earned growing exponentially over time.
According t o given condition :
To calculate the amount Ann will owe after 6 years, we can use the formula for compound interest:
A = P(1 + r/n)^(n*t)
where:
A = the amount Ann will owe after 6 years
P = the initial principal amount borrowed, which is $8000 in this case
r = the annual interest rate as a decimal, which is 15% or 0.15
n = the number of times interest is compounded per year, which is once annually in this case
t = the number of years, which is 6 in this case
Plugging in these values, we get:
A =
A =
A = $15,258.23
Therefore, Ann will owe $15,258.23 after 6 years, assuming she makes no payments.
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1001₂ = ______ (base 6)
A. 13
B. 14
C. 15
D. 21
E. 23
The binary number will be equal to 14 in base 6
1001₂ = 14 (base 6)
What is a number base?Base is defined as a set of digits used to represent numbers. There are different number systems which make use of different combinations of digits as the base.
One of the most common which is the binary number system uses only 2 digits, i.e., 0 and 1 to represent numbers, while the Octal number system uses 8 digits, i.e., 0 to 7, to represent numbers.
The most common number system that is in use is the decimal number system that uses the base 10, which includes digits from 0 to 9 for writing numbers.
1001₂ = 1 x 2^3 + 0 x 2^2 + 0 x 2^1 + 1 x 2^0
1001₂ = 1 x 8 + 1 x 1
1001₂ = 8 + 1
1001₂ = 9
Converting 9 into base 6
6 9
6 1 r 3
0 r 1
From downwards pointing up
9 = 13 (base 6)
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The population in a small town is increasing annually by 2.8%. What is the quarterly rate of population increase?
Answer:
To find the quarterly rate of population increase, we first need to find the annual rate of population increase in decimal form, which is 2.8% expressed as 0.028.
To find the quarterly rate, we need to divide the annual rate by 4, since there are 4 quarters in a year:
0.028 / 4 = 0.007
Therefore, the quarterly rate of population increase is 0.007 or 0.7%
What is -8/9 divided 2/3??
Answer:
-1.33333333333
Step-by-step explanation:
Answer:
-1 1/3
Step-by-step explanation:
I need some help please
Answer:
32
Step-by-step explanation:
Substitute values given into the expression :
3[2(1)+(3)]-4[((1)-(3)]+(3)²
3[5]-(-8)+9
15+8+9 =
32
Hope this helped and have a good day
Which shape has two pairs of parallel sides
The shape with two pairs of parallel sides is called a parallelogram.
What is a paralellogram?A parallelogram is a shape that has four sides, in which the two opposite lengths are:
Parallel to each other.Have the same measure.As there are four sides, divided two by two, the shape has two pairs of parallel sides, and is called a parallelogram.
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Consider the experiment of rolling a pair of dice. Suppose that we are interested in the sum of the face values showing on the dice. (a) How many sample points are possible?
(b) What is the probability of obtaining a value of 7?
(c) What is the probability of obtaining a value of 8 or greater?
a) There are 36 sample points that are possible.
b) The probability of obtaining a value of 7 is 1/12.
c) The probability of obtaining a value of 8 or greater is 1/6.
(a) When rolling a pair of dice, each die has six possible outcomes: 1, 2, 3, 4, 5, or 6. The possible outcomes for the pair of dice can be represented by the set of all ordered pairs (a, b), where a and b represent the outcomes of the first and second die, respectively.
Since each die has six possible outcomes, there are a total of 6 x 6 = 36 possible outcomes for rolling a pair of dice.
(b) To obtain a sum of 7, we must have one die showing 1 and the other die showing 6, or one die showing 2 and the other die showing 5, or one die showing 3 and the other die showing 4, for a total of three possible outcomes.
Since each die has six possible outcomes, there are a total of 6 x 6 = 36 possible outcomes. Therefore, the probability of obtaining a sum of 7 is 3/36, or 1/12.
(c) We must have one die showing 2 and the other die showing 6, or one die showing 3 and the other die showing 5, or one die showing 4 and the other die showing 4, or one die showing 4 and the other die showing 5, or one die showing 5 and the other die showing 3, or one die showing 6 and the other die showing 2, for a total of 5 + 1 = 6 possible outcomes.
Therefore, the probability of obtaining a sum of 8 or greater is 6/36, or 1/6.
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Write the number
five million four thousand three hundred
in standard form.
The required five million four thousand three hundred in standard form is 5,004,300.
What is a number system?A number system is described as a technique of composing to represent digits. It delivers a special presentation of every digit and describes the arithmetic structure.
Here,
In the question, we are asked to write the word of the number five million four thousand three hundred in standard form.
So,
five million four thousand three hundred = 5,004,300
Since
1 million = 1000, 000
1 thousand = 1000
1 hundred = 100
Thus, the required five million four thousand three hundred in standard form is 5,004,300.
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If the numerator of a fraction is multiplied by 4 and the denominator is reduced by 2,the result is 4 . If the numerator of the fraction is increased by 15 and 2 subtracted from the double of the denominator, the result is 5/4. Find the fraction.
The original fraction described in the question is; 25/31
How to simplify fractions?Let the numerator be x and let the denominator be y.
We are told that the numerator of a fraction is multiplied by 4 and the denominator is reduced by 2,the result is 4. Thus;
4x/(y - 2) = 4
4x = 4y - 8
4x - 4y = -8 -----(1)
The numerator of the fraction is increased by 15 and 2 subtracted from the double of the denominator, the result is 5/4. Thus;
(x + 15)/(2y - 2) = 5/4
4x + 60 = 10y - 10
4x - 10y = - 70 ----(2)
Subtract eq 2 from eq 1 to get;
6y = 62
y = 31/3
Thus;
4x - 4(31/3) = -8
Multiply through by 3 to get;
12x - 124 = -24
12x = 100
x = 25/3
Thus, the fraction is;
(25/3)/(31/3) = 25/31
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2/ac + 1/ab + 3/bc = ?
Answer:
Abc
Step-by-step explanation:
2b + c + 3a = Abc
to find the value of a numerical or algebraic expression is called?
The process of finding the value of a numerical or algebraic expression is called evaluation.
Evaluation involves substituting the given values of the variables in the expression and then simplifying the expression using the order of operations (PEMDAS).
For example, if we are asked to evaluate the expression 3x + 2y when x=4 and y=5, we would substitute these values to get 3(4) + 2(5), which simplifies to 12 + 10 = 22. Therefore, the value of the expression 3x + 2y when x=4 and y=5 is 22.
In algebra, evaluation is an important process because it allows us to find the value of an expression for specific values of the variables, which can help us to solve equations or inequalities, and to simplify expressions.
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Which function has a range limited to only negative numbers?
Answer:
F (x)=-x^2
Step-by-step explanation:
The measure of an angle is 71.6°. What is the measure of its complementary angle
Answer:
18.4 degrees
Step-by-step explanation:
a complementary angle is 90 degrees and 90 - 71.6 is 18.4. So, the answer is 18.4 degrees.
The rectangular floor of a classroom is 22 feet in length and 24 feet in width. A scale drawing of the floor has a length of 11 inches. What is the perimeter, in inches, of the floor in the scale drawing?
The scale floor's perimeter is 34 inches.
What is meant by perimeter?The overall length of a form's boundary is referred to as the perimeter of that shape. Adding the lengths of all the sides and edges that surround a form yields its perimeter. It is calculated using linear length units such centimeters, meters, inches, and feet. The perimeter is the space surrounding a shape's edge. Get the perimeter of various forms by multiplying their side lengths.The circumference of an object is known as its perimeter. For instance, your home has a yard that is enclosed. The length of the fence is the perimeter. The length of your fence is 200 feet if the yard is 50 feet by 50 feet.To solve, we can set up fractions:
21/7 = 30/x
Cross multiply and you get:
21x = 210
Divide each side by 21:
x = 10
You can apply the following equation since you're attempting to determine the floor's perimeter:
2w + 2l = p
Substitute to solve:
2 ( width = 10 )
2 ( length = 7 )
2 (7) + 2 (10) = p
14 + 20 = p
34 = p
The complete question is:
The rectangular floor of a classroom is 21 feet in length and 30 feet in width. A scale drawing of the floor has a length of 7 inches. What is the perimeter, in inches, of the floor in the scale drawing?
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Find the y-Intercept and x-intercept of the line.
5x - 2y = 10
The x-intercept and the y-intercept of the line 5x - 2y = 10 include the following ordered pairs:
x-intercept = (2, 0).
y-intercept = (0, -5).
What is the x-intercept?In Mathematics, the x-intercept can be defined as the point at which the graph of a function crosses the x-coordinate (x-axis) and the value of "y" or y-value is equal to zero (0).
What is y-intercept?In Mathematics, the y-intercept is sometimes referred to as an initial value (base value) and the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).
In this exercise, we would use an online graphing calculator to plot the linear function in order to determine the x-intercepts and y-intercepts as shown in the image attached below.
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-12x3^2+36 please ty
Answer:
-72
Step-by-step explanation:
Answer:
-72
Step-by-step explanation:
multiply-12 x3^2 and then add 36
Help pleaseee
Solve for g
Answer:
g=4f-k+h
Step-by-step explanation:
f=g-h+k
4
4f=g-h+k
4f-k=g-h
4f-k+h=g
Please answer both questions in the photo!!! (20p)
Answer:
(2.4, 2)
(4, -3.4)
Step-by-step explanation:
Brainliest Please
During a seven-year period, the average housing prices (in thousands of dollars) for a year in Miami $M$M and Gainesville cap g$G$G are modeled by the equations
cap m is equal to 1 point 7 t cubed minus 6 point 5 t squared plus 212$M=1.7t^3-6.5t^2+212$M=1.7t3−6.5t2+212 and
cap g is equal to 1 point 6 t squared minus 14 t plus 165$G=1.6t^2-14t+165$G=1.6t2−14t+165 ,
where t is equal to 1$t=1$t=1 represents the first year.
a. Write a polynomial that represents the difference in housing prices.
Polynomial:
Question 2
b. What is the difference in housing prices in the fifth year?
$
The difference in housing prices in the fifth year is $7,125.
What is price?Price is the amount of money one has to pay for goods or services. It is also the return on an investment or the cost of borrowing money. Price is determined by the supply and demand of a product or service. It is also influenced by market forces such as competition, production costs, and availability of resources. Price is a key factor in determining the success of a business, as it can affect consumers' buying decisions and profitability.
$M(5) - G(5) = (1.7(5)³- 6.5(5)²+ 212) - (1.6(5)²- 14(5) + 165) = $7,125
Therefore, the difference in housing prices in the fifth year is $7,125.
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How many solutions does the equation have?
4x + 3 = 4x + 3
Answer:
Infinitely Many
Step-by-step explanation:
Both answer are equal to each other
Shana wants to use all 62 feet of the fencing she has to make a rectangular run for her dog. She decides to make the length of the run 20 feet. She writes and solves the equation 2 l plus 2 w equals 62 to find the width of the run.
Which statements are true of the solution? Check all that apply.
The value of w is 10 feet.
The value of w can be zero.
The value of w cannot be a negative number.
Substitution is used to replace the variable l with a value of 20.
The subtraction property of equality is used to isolate the term with the variable w
Answer:
11 feet long
Step-by-step explanation:
20+20=40
62-40=22
22÷2=11
check
11+11+20+20=62
4. A line segment has two end-points M(3, 7) and N(11, -6). Find the coordinates of the point W that lies on the y-axis such that W is equidistant from M and from N.
would appreciate a step by step answer (quickly please)
The coordinates of point W which is equidistant from M and N ( 7, 1 / 2).
What is coordinate geometry?A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.
Given that the points are M(3, 7) and N(11, -6). The coordinates of the midpoints are,
W = ( x₁ + x₂ ) / 2, ( y₁ + y₂ ) / 2
W = ( 3 + 11 ) / 2, ( 7 - 6 ) / 2
W = 14 / 2, 1 / 2
W = 7, 1 / 2
Hence, the value of the coordinate of the midpoint is ( 7, 1 / 2 ).
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How do you solve verifying identity with calculator?
Verifying Identity with a calculator requires an individual to enter specific numerical values into a calculator and then solve a given equation. This can be used to prove the validity of an equation, or the accuracy of a given answer.
The equation is typically written in algebraic form and includes numerical values.Verifying Identity with a calculator requires an individual to enter specific numerical values into a calculator and then solve a given equation. This can be used to prove the validity of an equation, or the accuracy of a given answer. For example, if an individual is asked to verify the identity [tex]sin^2x + cos^2x[/tex]= 1, they will be given numerical values to plug into the equation. For example, if they are given x = 60, they would enter[tex](sin60)^2 + (cos60)^2[/tex] into the calculator and solve. This should result in an answer of 1, proving the equation is accurate.
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An architect is drawing a floor plan for the basement of a house. He has drawn the
plans as shown. On the plan, 1/4 inch represents 4 feet in length in the house.
What is the area of the basement?
The area of the basement will be 576 square feet.
What is an area?The area is defined as the space covered by the object in a two-dimensional plane. The area of the rectangle is calculated by the multiplication of the length and the width.
Given that a basement floor plan for a house is being created by an architect. He drew the plans as they are seen. On the plan, one-fourth of an inch corresponds to four feet in the house.
The area of the basement will be calculated as:-
Area = 12 x 6
Area = 72 square inches
Area = 72 x 8 feet
Area = 576 square feet
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You can work at most 20 hours next week. You need to earn at least $90 to cover
you weekly expenses. Your dog-walking job pays $7.50 per hour and your job as a
car wash attendant pays $6 per hour. Write and graph a system of linear
inequalities to model the situation. Use the graph to list 3 solutions
The system of inequalities is.
x + y ≤ 20
x*7.5 + y*6 ≥ 90
And some solutions can be:
(10, 5)
(11, 5)
(12, 6)
How to write the system of inequalities?Let's define the variables we will be using:
x = number of hours dog-waling
y = number of hours at the car wash.
We know that you can work at most 20 hours, then:
x + y ≥ 20
And you need toearn at least $90, then wecan write:
x*7.5 + y*6 ≥ 90
The system of inequlities is:
x + y ≤ 20
x*7.5 + y*6 ≥ 90
And the graph is the one below. The solutions are all the points in the dark blue region, some solutions we can see there are:
(10, 5)
(11, 5)
(12, 6)
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Solve for x
A. Solve using the change of base formula.
Logby= log y/log b
B. Solve using a different method.
C. verify your solutions by substituting your value back into the original equation.
A) By using the change of base formula, the solution of the expression is,
⇒ x = - 2/3
B) The solution of the expression is,
⇒ x = - 2/3
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ 5³ˣ⁻² = 125²ˣ
Now, We have the change of base formula,
⇒ [tex]log_{b} y = \frac{log y}{log b}[/tex]
Here, The expression is,
⇒ 5³ˣ⁻² = 125²ˣ
⇒ 5³ˣ⁻² = 5⁶ˣ
Take log on both side,
⇒ log 5³ˣ⁻² = log 5⁶ˣ
⇒ (3x - 2) log 5 = 6x log 5
⇒ 3x - 2 = 6x
⇒ - 2 = 6x - 3x
⇒ 3x = - 2
⇒ x = - 2/3
B) By using another method as;
The expression is,
⇒ 5³ˣ⁻² = 125²ˣ
⇒ 5³ˣ⁻² = 5⁶ˣ
By comparing we get;
⇒ 3x - 2 = 6x
⇒ - 2 = 6x - 3x
⇒ 3x = - 2
⇒ x = - 2/3
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find missing value
i rlly need help thanks
The missing value using concept of similar triangle ratio is; 35
How to find the length of similar triangles ?Similar triangles are defined as triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.
Using the concept of similar triangles on the given diagram, we have;
p/(30 + 20) = 14/20
p = (14 * 50)/20
p = 35
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