Using proportional relationships, we have that:
a) They are defined as follows:
Soprano = 0.1 x Students.Trucks = 1/3 x Vehicles.b) The relation is Out of State Team = 1/5 x Residents.
Proportional relationships and graphsA graph represents a proportional relationship if the output variable y in the y-axis is written as a product of the input variable x in the x-axis and the constant of proportionality k, as follows:
y = kx.
Voice instructor notices that only one out of every ten of her students can sing soprano, hence the constant is:
k = 1/10 = 0.1.
Then the relationship is:
Soprano = 0.1 x Students.
Two out of every six vehicles are trucks, hence the constant is:
k = 2/6 = 1/3.
Hence the relationship is:
Trucks = 1/3 x Vehicles.
Then, in item b, we want to write a relation that has a constant between those represented on the previous relations, that is, between 1/10 and 1/3.
One possible constant is of 1/5. Supposing that one out of five New York City residents root for out of state NFL teams, the relation is:
Out of State Team = 1/5 x Residents.
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Write each number as a polynomial and then simplify the sum or difference
Answer:
[tex]90a+10b[/tex]
Step-by-step explanation:
[tex](100a+10b+c)-(10a+c) \\ \\ =100a+10b+c-10a-c \\ \\ =90a+10b[/tex]
Suppose the domain of f is ( -1, 1).
Define the fucnction g by g(x)=f([tex]\frac{x+1}{x-1}[/tex]).
What is the domain of g?
If the domain of f is ( -1, 1), then the function g defined by g(x) = f((x + 1)/(x - 1)) has a domain of; (-2, 0)
What is the domain of the function?The domain of a function refers to the set of all possible intput values that make the function possible.
Now, we are given the function;
g(x) = f((x + 1)/(x - 1))
The domain would be a set of real numbers excluding 1 because at x = 1, the function is undefined.
Since the domain of f(x) is -1 < x < 1 ,
Then the domain of f(x + 1) is -1 < x + 1 < 1 .
domain of -1 < x + 1 < 1 will simplify to -2 < x < 0
Thus, we can say that the domain of f(x + 1) is (-2, 0).
Thus;
g(x) = f(x + 1) and as such, the domain of g(x) is (-2, 0) .
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how do I write this ?
Answer:
1: -⅔
2: -⅓
Step-by-step explanation:
You plug the number into the Equation.
1:
2 = 3x + 4
-2 = 3x
x = -⅔
2:
3 = 3x + 4
-1 = 3x
x = -⅓
DO,K = (9, 6) (3, 2) The scale factor is___ 1/3 6 3
Based on the dilation, the scale factor of dilation of the point is 1/3
What is dilation?Dilation involves enlarging or reducing the side length of a shape to create another shape by a constant scale factor, where the scale factor does not equal one.
How to determine the scale factor of dilation?From the question, we have the following parameters
Dilation rule: Do,k
Point = (9, 6)
Image = (3, 2)
As a general rule of dilation, the following are the properties of a scaled copy of another figure
If the scale factor is greater than 1, the side lengths would be greater than the original figureIf the scale factor is less than 1, the side lengths would be less than the original figureThe side lengths may or may not be whole numbersUsing the above as a guide, the scaled factor is calculated as
Scaled factor = Image/Poins
This gives
Scaled factor, k = (3, 2)/(9, 6)
This gives
Scaled factor, k = 1/3
Hence, the scale factor is 1/3
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Select the correct answer. which situation is best met through long-term saving? a. a broken refrigerator b. retirement c. an unexpected car repair d. an unexpected medical bill
The situation best met through long term saving is retirement (Option B).
In many cases, the retirement fund is taken out of the paychecks at your job and is accumulated over years of your service and job till retirement, it is a long-term saving.
The purpose of long-term saving is the type of saving for long term financial goals. The other options are not long-term financial goals rather unexpected expenses. Hence, a situation best fulfilled through long term saving is retirement.
There are several long-term saving accounts use to save for long term financial goals such as retirement, buying a house, children’s education, or similar one-time, long-term expenses.
Hence, the correct answer is retirement – Option B
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Avani and her children went into a grocery store and will buy peaches and mangos.
Each peach costs $0.75 and each mango costs $1.75. Avani has a total of $15 to spend
on peaches and mangos. Write an inequality that would represent the possible values
for the number of peaches purchased, p, and the number of mangos purchased, m.
The inequality which represents the possible values for the number of peaches and mangos purchased will be;
⇒ $0.75p + $1.75m = $15
What is Inequality?
A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
Avni and her children went into a grocery store and will buy peaches and mangos.
Each peach costs $0.75 and each mango costs $1.75.
And, Avni has a total of $15 to spend on peaches and mangos.
Now,
Let number of peaches purchased = p
And, Number of Mangos purchased = m
Since, Each peach costs $0.75.
Hence, Total cost of peaches purchased = $0.75p
And, Each mango costs $1.75.
Hence, Total cost of mangos purchased = $1.75m
Since, Avani has a total of $15 to spend on peaches and mangos.
So, An inequality that would represent the possible values of peaches and mangos will be;
⇒ $0.75p + $1.75m = $15
Thus, The inequality which represents the possible values for the number of peaches and mangos purchased will be;
⇒ $0.75p + $1.75m = $15
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find the lcm of the numbers 3,6,16 using lists of multiples
Answer:
48
Step-by-step explanation:
3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48
6 12 18 24 30 36 40 48
16 32 48
Simplify 9 3 × 9 2 × 9 4 leaving your answer in index form.
Answer:
804,264
Step-by-step explanation:
Evaluate 93×92×94
We have 1 of the number 93
We have 1 of the number 92
We have 1 of the number 94
Group numbers by powers:
93×92×94 = 93[1]92[1]94[1]
93[1]92[1]94[1] = 804,264
A line has a slope of 1/3 and includes the points (6,1) and (9,j). What is the value of j?
WE WILL USE THE FORMULA OF CALCULATING GRADIENT
[tex]m = \frac{y2 - y1}{x2 - x1} \\ m = \frac{j - 1}{9 - 6} \\ \frac{1}{3} = \frac{j - 1}{3} [/tex]
I WILL USE CROSS MULTIPLICATION
[tex]3(j - 1) = 3 \\ \frac{3(j - 1)}{3} = \frac{3}{3} \\ j - 1 = 1 \\ j = 1 + 1 \\ j = 2[/tex]
ATTACHED IS THE SOLUTION
BE ALERT I INSERTED THE KNOWN VALUES IN THE FORMULA OF FINDING THE GRADIENT.
The school that Brenda goes to is selling tickets to a choral performance. On the first day of
ticket sales the school sold 14 adult tickets and 5 student tickets for a total of $140. The school
took in $190 on the second day by selling 10 adult tickets and 10 student tickets. What is the
price each of one adult ticket and one student ticket?
The price of one adult ticket is $5 and one student ticket is $14
What is algebra ?Mathematical expressions can be used to depict situations or issues, and algebra is the field of mathematics that does this. For a mathematical expression to have meaning, it needs to include variables like x, y, and z as well as mathematical operations like addition, subtraction, multiplication, and division. Algebra is used in every area of mathematics, including coordinate geometry, calculus, and trigonometry. A straightforward algebraic expression is 2x + 4 = 8.
Given that : first day of ticket sales the school sold 14 adult tickets and 5 student tickets for a total of $140. The school took in $190 on the second day by selling 10 adult tickets and 10 student tickets.
Let the price for adult ticket x and for student ticket y
we have ,
14x + 5y =140.....(i)
10x + 10y = 190....(ii)
10 x + 10y = 190
x + y = 19
y = 19-x .....(iii)
put the value of y in equation i
14x + 5(19-x) = 140
14x + 95 - 5x = 140
9x = 45
x = 5
Now put value of x in equation iii
y = 19 - 5
y = 14
The price of one adult ticket is $5 and one student ticket is $14
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What is the radius of a circle with a circumference of 26 69 centimeters
In the rectangle below
is 2y-3>11 a expression equation or inequality
Answer:
Inequality
Step-by-step explanation:
An expression is a mathematical phrase that contains numbers, variables, or both. Expressions never have an equal sign. An equation is a mathematical sentence that says two expressions are equal.
Given the function, [tex]f(x)=-2x-1[/tex] express the value of [tex]\frac{f(x+h)-f(x)}{h}[/tex] in simplest form.
Value of the function [ f(x+ h) - f(x) ] /h in simplest form when f(x) = -2x -1 is equal to -2.
As given,
Given function:
f(x) = -2x -1
Express value of in simplest form:
f( x + h ) = -2 (x + h ) - 1
= -2x -2h -1 ___(1)
Simplify the function by substituting value of f(x +h and f(x),
[f(x + h) - f(x) ] /h
= [ (-2x -2h -1 )- ( -2x -1 ) ] /h
= ( -2x -2h -1 +2x +1 ) /h
= -2h /h
= -2
Therefore, value of the function [ f(x+ h) - f(x) ] /h in simplest form when f(x) = -2x -1 is equal to -2.
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What is the equation of a line that contains the points (5, 0) and (5,-2)?
Ox=5
Ox=0
Oy=0
Oy=5
Answer:
x=5
you're welcome
A car traveled at a constant speed. The graph shows how far the car traveled, in miles, during a given amount of time, in hours.
The point is on the graph. Explain what this means in terms of the car.
Is the point on this graph? Explain how you know.\
The point (1, 60). on the graph how's the speed that the car travels.
How to illustrate the value?It should be noted that car traveled at a constant speed. The distance traveled is 210 miles and the time to travel is 3.5 hours.
Therefore, it should be noted that the point (3.5, 120) shows the distance.
The slope of the like which is the speed will be:
= Distance / Time
= 210 / 3.5
= 60 mph
Therefore, it should be noted that the point B(1, 60) lies on the graph.
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algebra vocabulary question
Answer:
We would describe 7x - 3 > 24 as an inequality
Step-by-step explanation:
The definition of inequality is a relationship between two expressions using one of these inequality symbols:
greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤), and not equal to symbol (≠).
Answer:
Inequality
Step-by-step explanation:
Inequalities are never equal just like the question you have
simplify 2(x - 4) + 9
Answer: 2x + 1
Step-by-step explanation:
We will simplify this expression down to it's lowest terms.
Given:
2(x - 4) + 9
Distribute:
2x - 8 + 9
Combine like terms:
2x + 1
Mr. Lopez travels a distance of 100 miles to work each day, Which of the following graphs best represents the
relationship between the time Mr. Lopez takes to get to
work and the speed at which he drives?
Answer:
Step-by-step explanation:
they left at 12:34
Find three consecutive odd integers such that the sum of three times the smaller and twice the largest is equal to one less than four times the middle. find the integers.
Answer:
-1, 1, 3
Step-by-step explanation:
Let x equal the first odd integer.
The three consecutive odd integers would be represented by x, then x+2, then x+4.
So 3x + 2(x + 4) = 4(x + 2) - 1
Solve for x
3x + 2x + 8 = 4x + 8 -1
5x + 8 = 4x + 7
x = -1
Do the ordered pairs represent a function?
Answer: A.
Step-by-step explanation:
Something is a function if the x value is not repeated. The y value can be repeated however.
Which graph represents the solution to the inequality 2(b + 2) ≥ 24?
number line with open point at 10 with arrow pointing left
number line with closed point at 10 with arrow pointing left
number line with closed point at 10 with arrow pointing right
number line with open point at 10 with arrow pointing right
The graph that represents the solution to inequality 2(b + 2) ≥ 24 is given by the statement "number line with closed point at 10 with arrow pointing right" .
In the question ,
the inequality is given as
2(b + 2) ≥ 24
Solving the inequality further , we get
2b + 2*2 ≥ 24
2b + 4 ≥ 24
Simplifying further we get
2b ≥ 24-4
2b ≥ 20
b ≥ 10 .
Since the inequality has equal to sign, hence number line representing the inequality will have a closed point 10 ,
And on number line as the number increases the value move towards right ,
hence the arrow will point Right .
Therefore , the graph that represents the solution to inequality 2(b + 2) ≥ 24 is given by the statement "number line with closed point at 10 with arrow pointing right" .
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Answer: C number line with closed point at 10 with arrow pointing right
Step-by-step explanation:
I took the test and I got it right. :)
hope this helps
please helpp i am very confused on finding the answer
Answer:
C. Lines l and m appear to be skew--they are not parallel, and they are not intersecting each other.
Guadalupe quiere saber la longitud de un túnel construido a través de una montaña. Para ello, ella toma las medidas indicadas en la figura a continuación. Utilizar estas medidas para hallar la longitud del túnel.
Llevar a cabo los cálculos intermedios usando al menos cuatro posiciones decimales.
Redondear la respuesta a la décima de metro más cercana.
A line is drawn through (-7, 11) and (8,-9). The equation
y-11 = -4/3(x + 7) is written to represent the line. Which
equations also represent the line? Check all that apply.
Answer:
[tex]\textsf{Slope-intercept form}: \quad y=-\dfrac{4}{3}x+\dfrac{5}{3}[/tex]
[tex]\textsf{Standard form}: \quad 4x+3y=5[/tex]
Step-by-step explanation:
Given linear equation:
[tex]y-11=-\dfrac{4}{3}(x+7)[/tex]
The given linear equation is point-slope form.
[tex]\boxed{\begin{minipage}{3.7cm}\underline{Slope-intercept form}\\\\$y=mx+b$\\\\where $m$ is the slope\\ and $b$ is the $y$-intercept.\\\end{minipage}}[/tex]
To write the equation in slope-intercept form, isolate y:
[tex]\implies y-11=-\dfrac{4}{3}(x+7)[/tex]
[tex]\implies y-11=-\dfrac{4}{3}x-\dfrac{28}{3}[/tex]
[tex]\implies y-11+11=-\dfrac{4}{3}x-\dfrac{28}{3}+11[/tex]
[tex]\implies y=-\dfrac{4}{3}x+\dfrac{5}{3}[/tex]
[tex]\boxed{\begin{minipage}{5.4 cm}\underline{Standard form}\\\\$Ax+By=C$\\\\where $A, B$ and $C$ are constants and $A$ must be positive.\\\end{minipage}}[/tex]
To write the equation in standard form, eliminate the fraction, bring the terms in x and y to the left of the equation, and the constants to the right:
[tex]\implies y-11=-\dfrac{4}{3}(x+7)[/tex]
[tex]\implies (y-11) \cdot 3=-\dfrac{4}{3}(x+7) \cdot 3[/tex]
[tex]\implies 3y-33=-4(x+7)[/tex]
[tex]\implies 3y-33=-4x-28[/tex]
[tex]\implies 3y-33+4x=-4x-28+4x[/tex]
[tex]\implies 3y-33+4x=-28[/tex]
[tex]\implies 3y-33+4x+33=-28+33[/tex]
[tex]\implies 4x+3y=5[/tex]
the 5ft tall person casts a shadow that is 4 ft long. how tall is the flagpole if it 28 foot shadow?
The flagpole is 35ft tall.
How to find the shadow's height?Given,
A 5ft tall person casts a shadow that is 4 ft long.
Flagpole has a 28-foot shadow.
Solution:
Let x be the height of the flagpole.
5/x = 4/28
x = 35ft
The flagpole is 35ft tall.
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If GI and JL are parallel lines and mZJKH = 70°, what is m<LKM
WILL GIVE BRAINLIEST
Answer:
70°
Step-by-step explanation:
Since m∠JKH and m∠LKM are verticle angles, they are equal to each other.
What is the slope of a line that goes through the points (1,-5) and (-3, 2)?
O
O
O
7
4
3
3
Answer:
[tex]\sf -\dfrac{7}{4}[/tex]
Step-by-step explanation:
Finding the slope of a line:(1, -5) ⇒ x₁ = 1 ; y₁ = -5
(-3, 2) ⇒ x₂ = -3 ; y₂ = 2
[tex]\sf \boxed{\bf Slope = \dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\sf =\dfrac{2-[-5]}{-3-1}\\\\= \dfrac{2+5}{-4}\\\\=\dfrac{7}{-4}\\\\= -\dfrac{7}{4}[/tex]
Write an equation of the line that passes through each pair of points
[tex](\stackrel{x_1}{-10}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{-5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-5}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-10)}}} \implies \cfrac{-9}{2 +10} \implies \cfrac{ -9 }{ 12 }\implies -\cfrac{3}{4}[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{-\cfrac{3}{4}}(x-\stackrel{x_1}{(-10)}) \implies y -4= -\cfrac{3}{4} (x +10) \\\\\\ y-4=-\cfrac{3}{4}x-\cfrac{15}{2}\implies y=-\cfrac{3}{4}x-\cfrac{15}{2}+4\implies {\Large \begin{array}{llll} y=-\cfrac{3}{4}x-\cfrac{7}{2} \end{array}}[/tex]
A number, c, rounded to 1 d.p. is 47.3
Another number, d, rounded to 1 d.p. is 4.6
What are the lower and upper bounds of c- d?
The lower and upper bounds of c- d are 42.0 and 43.0 respectively.
What is termed as the rounding off?Rounding off merely refers to an estimate. Rounding off is the process of estimating this same actual number to a nearby number.Examine this same unit place digit:If indeed the unit place digit is a little less than 5, keep a tens place digit unchanged and replace it with 0.Whereas if unit place is 5 or greater, replace the tens digit with its successor and place 0 just at unit place.For the given question;
A number, c, rounded to 1 decimal place is 47.3
Another number, d, rounded to 1 decimal place is 4.6
c- d = 47.3 - 4.6
c- d = 42.7
Lower bound = 42.0
Upper bound = 43.0.
Thus, the lower and upper bounds of c- d are 42.0 and 43.0 respectively.
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