Answers
The following relationships between linear equations are shown below:
12 - (1 / 2) · r → [13 - (3 / 2) · r] - (1 - r) r - 13 / 6 → (7 · r - 3 / 2) - (2 / 3 + 6 · r) 13 · r + 20 → (6 · r + 7) + (13 + 7 · r) - 12 + r → (- 8 - r) + (2 · r - 4)How to match an expression with its simplified form
In this problem we find four cases of linear equations whose relationship with simplified forms, that is, linear equations of the a · r + b, where a, b are constants, must be found. Each relationship can be determined by using algebra properties. Now we proceed to present the conclusion for each case:
Choice A
(6 · r + 7) + (13 + 7 · r)
(6 · r + 7 · r) + (7 + 13)
(6 + 7) · r + 20
13 · r + 20
Choice B
[13 - (3 / 2) · r] - (1 - r)
[13 - (3 / 2) · r] + (- 1 + r)
[- (3 / 2) · r + r] + (13 - 1)
[- (3 / 2) + 1] · r + 12
(- 1 / 2) · r + 12
12 - (1 / 2) · r
Choice C
(- 8 - r) + (2 · r - 4)
(- r + 2 · r) + (- 8 - 4)
(- 1 + 2) · r - 12
r - 12
- 12 + r
Choice D
(7 · r - 3 / 2) - (2 / 3 + 6 · r)
(7 · r - 3 / 2) + (- 2 / 3 - 6 · r)
(7 · r - 6 · r) + (- 3 / 2 - 2 / 3)
r + [- (9 + 4)] / 6
r + [- 13] / 6
r - 13 / 6
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Related Questions
The leg of a right triangle is 3 units and the hypotenuse is 11 units. What is the length, in units, of the other leg of the triangle? HURRY PLEASE!!!
a
112 units
b
square root 112 units
c
130 units
d
square root 130 units
Answers
The correct option is (b) square root 112 units
Step-by-step explanation:By using Pythagoras theorem,
a² + b² = c²where a & b = legs of triangle and c = hypotenuse
Hence:
3² + b² = 11²9 + b² = 121b² = 121 - 9b² = 112b = √112Un coche tarda 9hrs en recorrer un trayecto siendo su velocidad de 85km/h, ¿Cuánto tardará en recorrer el mismo trayecto a 70km/h?
Answers
The time taken to travel the distance 70 Km/h is 11 hours.
What is speed distance formula?Speed tells us how fast something or someone is travelling. You can find the average speed of an object if you know the distance travelled and the time it took.
The formula can be rearranged in three ways:
speed = distance ÷ timedistance = speed × timetime = distance ÷ speedGiven:
time = 9 hours
speed = 85 Km/h
Now, distance
=speed * time
=85 * 9
= 765 km
As, the speed is 70 km/h
time = distance/ speed
time = 765 / 70
time = 10.92
time= 11 hours
Hence, the time taken to travel the distance 70 Km/h is 11 hours.
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The translation of the question is:
A car takes 9 hours to travel a distance with a speed of 85km/h, how long will it take to travel the same distance at 70km/h?
2. Plot two numbers that are 5 units from zero on the number line.
Answers
Answer:
5 and -5
This is because these 2 spots are exactly 5 spaces from 0.
Find the degree measure of the indicated angle.
Answers
Answer:
75 degree
Step-by-step explanation:
35+70+75=180 degree
Is 4/8 equivalent to 7/8
Answers
Answer:
is 7 more than 4 or 4 more than 7?
Step-by-step explanation:
JUST USE YOUR BRAIN!
Answer:
no
Step-by-step explanation:
of course not. since the denominators are the same, the numerators have to be equal. since the numerators aren't equal, the answer is no
In a survey, respondents were asked which type of activity they enjoyed most while on vacation. The bar graph shows the responses of males and females.
How many more males than females said that bike riding was their favorite activity?
Answers
Answer: 1
Step-by-step explanation:
Answer:
1
Step-by-step explanation:
Classify each number as rational or irrational
Answers
11/3 [rational]
Sqrt 3/16 [irrational]
Sqrt 48 [irrational]
0.01045 [rational]
Sqrt 16/81 [rational]
16pi [irrational]
0.42 [rational]
Identify rise over run (please!)
Answers
2- 3/1
3- 5/3
4- -3/2
5- 3/2
6- 3/1
The first three are the top row and 4,5, and 6 are the bottom row
2/3p - 11 = 1/3p -15
p=_
Answers
Answer:
p = - 12
Step-by-step explanation:
[tex]\frac{2}{3}[/tex] p - 11 = [tex]\frac{1}{3}[/tex] p - 15
multiply through by 3 to clear the fractions
2p - 33 = p - 45 ( subtract p from both sides )
p - 33 = - 45 ( add 33 to both sides )
p = - 12
Answer:
-12
Step-by-step explanation:
(sorry its a bit messy - hope it helps though!)
A manufacturer makes bags of popcorn and bags of potato chips. The average weight of a bag of popcorn is supposed to be 3.03 ounces with an allowable deviation of 0.02 ounces. The average weight of a bag of potato chips is supposed to be 5.08 ounces with an allowable deviation of 0.05 ounces. A factory worker randomly selects a bag of popcorn from the assembly line and it has a weight of 3.06 ounces. Then the worker randomly selects a bag of potato chips from the assembly line and it has a weight of 5.03 ounces. Which description closely matches the findings on the assembly line?
Answers
Answer:
The weight of the popcorn is off but the potato chips are safe. Simply determine whether each value is within the limit of deviation from eachother.
0.3596 is considered a rational number. What makes this number rational
Answers
Answer:
see explanation
Step-by-step explanation:
a rational number has the form
[tex]\frac{a}{b}[/tex] , where a and b are integers
given
0.3596 ← with 6 in the [tex]\frac{1}{10000}[/tex] place
= [tex]\frac{3596}{10000}[/tex] = [tex]\frac{899}{2500}[/tex] ← a rational number
how do you divide 1/2 by -4
Answers
Answer:
Step-by-step explanation:
1/2÷4 = 1/8 = 0.125.
[tex]\cfrac{1}{2}\div -4\implies \cfrac{1}{2}\div \cfrac{-4}{1}\implies \cfrac{1}{2}\cdot \cfrac{1}{-4}\implies {\LARGE \begin{array}{llll} -\cfrac{1}{8} \end{array}}[/tex]
What is the value of x that makes the given equation true?
4x 3-12x13
—
A. 0x = -3
B. O x = 0
C. O x = 1
D. O x = 16
Answers
The value of the x is 1 in the linear equation. Thus, option C is correct.
According to the statement
We have to find that the value of the x.
So, For this purpose, we know that the
The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line.
From the given information:
The equation is:
4x−3=−12x+13
Then
we have to solve it
4x−3=−12x+13
4x+12x = 3+13
16x = 16
x = 16/16
x =1.
When we put x =1 in the given equation and then i satisfy the equation and give same values after calculation.
So, The value of the x is 1 in the linear equation. Thus, option C is correct.
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PLEASE HELP and explain in the answer
Answers
The missing numbers are 17,66,13, 9 3 and 15 respectively .
The rules given to us are-
first row consist of a number which is the sum of two numbers of middle row
Third row consist of a number which is the product of two numbers of middle row
The first part
The sum of 6 and 11 is 17 and the product of 6 and 11 is 66
17
6 11
66
The second part
To find the second number of middle row we need to divide 36 by 4 and we get 9 and the sum of 4 and 9 is 13
13
4 9
36
The third part
To find the numbers of middle row we need to find the factors of 45 that sum up to 18
The factors of 45 are 3*3*5
The factor 15 and 3 satisfy both the requirements
18
3 15
45
Hence, The missing numbers are 17,66,13, 9 3 and 15 respectively
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4 metode la 381-(x+y)=15
Answers
Answer:
codec log 8x + y =15
Step-by-step explanation:
have a good day!
Solve each equation.
2x=8
Answers
Solution of this polynomial equation is x = 4
What are polynomial equations ?In mathematics, polynomial equation can be defined as the equation which consist of coefficient, variables and exponents. A polynomial equation has positive numbers as their exponent which is also known as its degree. All the equations such as quadratic equation, cubic equation which has non negative number as their powers are part of polynomial equation.
Types of polynomial equations :
Monomial equationBinomial equationCubic EquationsLinear Polynomial Quadratic PolynomialSome examples of polynomial equation are :
2x+53x = 93x² + 5x+19(x-3)³According to question,
2x = 8
=> 2x / 2 = 8 /2
=> x = 4
Thus solution for given equation is x = 4.
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Cadence baked 45 cupcakes on Tuesday. This was 3 more than twice the number of cupcakes she baked on Monday. How many cupcakes did Cadence bake on Monday?
Group of answer choices
25
21
24
14
Answers
Considering the definition of an equation and the way to solve it, the correct answer is the third option: Cadence baked 21 cupcakes on Monday.
Definition of equationAn equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns.
The members of an equation are each of the expressions that appear on both sides of the equal sign.
The solution of a equation means determining the value that satisfies it. To solve an equation, keep in mind:
When a value that is adding, when passing to the other member of the equation, it will subtract.If a value you are subtracting goes to the other side of the equation by adding.When a value you are dividing goes to another side of the equation, it will multiply whatever is on the other side.If a value is multiplying it passes to the other side of the equation, it will pass by dividing everything on the other side.Cupcakes baked on MondayBeing "x" the number of cupcakes baked by Cadence on Monday, and knowing that:
Cadence baked 45 cupcakes on Tuesday. The number of cupcakes baked on Tuesday was 3 more than twice the number of cupcakes she baked on Monday.the equation in this case is:
3 + 2x= 45
Solving:
2x= 45 -3
2x= 42
x= 42 ÷ 2
x= 21
Finally, the correct answer is the third option: Cadence baked 21 cupcakes on Monday.
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Multiply. State any restrictions on the variables.
8 y-4 / 10 y-5 . 5 y-15 / 3 y-9
Answers
The required product of two rational numbers is 8y² - 28y + 4) / (6y² - 21y + 9).
What is a rational number?
Any real number that can be represented in the form of p/q, where q is not equal to 0 is called a rational number. The decimal expansion of rational numbers is terminating and repeating.
Calculation of the product of two rational numbers
Given two rational numbers,
8y - 4 / 10y - 5 and 5y -15 / 3y - 9
We need to multiply both the numbers i.e.
= (8y - 4 / 10y - 5) × (5y -15 / 3y - 9)
= (8y -4) × (5y - 15) / (10y - 5) × (3y - 9)
= (40y² - 140y + 20) / (30y² - 105y + 45)
= (8y² - 28y + 4) / (6y² - 21y + 9)
= (8y² - 28y + 4) / (6y² - 21y + 9)
The restriction is that the denominator, 6y² - 21y + 9 should not be 0.
Hence, the required product of two rational numbers is 8y2 - 28y + 4) / (6y2 - 21y + 9).
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Are there any values of x that you cannot substitute into the equation? If so what are they? Same question for y
Answers
Answer: The problem asks to solve for x. Equation B gives you the value of y, y = 2, so you can substitute 2 into Equation A for y.
Step-by-step explanation:
Data points are considered to be unusual if they are more than two standard deviations
away from the mean. Which data points in each distribution are considered to be unusual?
Show all work.
Answers
Answer:
Step-by-step explanation:
30 and 20
“Solve the equations”3x*3-9x^2-54x=0
Answers
x = 0
x = −5
Answer:x=6 x=-3
Step-by-step explanation:
3x(x^2-3x-18)=0
(X-6)(x+3)=0
X-6=0. X+3=0
+6=+6. -3=-3
X=6. X= -3
Given t(x)=4x−7,what is t(x)when x=3
Answers
Answer:
The correct answer is 4(x-7)²-(x-7)+3.
Step-by-step explanation:
When we have captured (t*s)(x), that is as equivalent as t(s(x)). To solve this, we take the important role of s(x), x-7, and call in an alternative for it in for every x in t(x). Instead of 4x², we have 4(x-7)²; instead of -x, we have -(x-7). This gives us 4(x-7)²-(x-7)+3.
Evaluate each logarithm.
log₃9
Answers
The value of the expression log₃9 is 2.
The logarithmic function is the inverse of the exponential function. This means that the logarithm of a given number, say x, is the exponent to which another fixed number that is the base b, must be raised, so as to produce that number x.
Log a to the base b can be written as- log a/ log b.
Moreover, log [tex]a^{k}[/tex]= k log a, for all non negative values of a
Here, we are given a logarithmic expression- log₃9
We can expand this as-
log₃9 = log 9/ log 3
= log [tex]3^{2}[/tex]/ log 3
= 2 log 3/ log 3
= 2
Thus, the value of log₃9 is 2.
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Read each question. Then write the letter of the correct answer on your paper.What is an equivalent form of 5/2+2 i ?
(F) 5/4i (H) 5+5 i / 4 (G) 10-10i / 4-4i (I) 5-5i / 4
Answers
An equivalent form of 5 / ( 2 + 2 i ) is ( 5 -5 i ) / 4 [ option I ]
Given,
5 / ( 2 + 2 i )
To find its equivalent form we need to simplify the term by using the concept of conjugates.
Conjugate of a term results in opposite power of the imaginary part.
The conjugate of 2 + 2 i = 2 - 2 i
Multiply and divide the term with the conjugate
=> 5 * ( 2 - 2 i ) / ( 2 + 2 i ) * ( 2 - 2 i )
=> 10 - 10 i / 2 ² - ( 2 i ) ² [ ( a + b ) ( a - b ) = a ² - b ² ]
=> 10 - 10 i / 4 - (-4) [ i ² = - 1 ]
=> 10 - 10 i / 8
=> 5 - 5 i / 4
This matches with option I
Therefore, we get an equivalent form of 5 / ( 2 + 2 i ) as ( 5 -5 i ) / 4
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The product of two factors is 1. One of the factors is 1. Can you tell what the other factor is? A. Yes; the other factor is 0 since 0 × 1 = 1. B. Yes; the other factor is 1 since 1 × 1 = 1. C. No; any number times 0 is 0, so there is no way to know what the other factor is. D. No; any number times 1 is 1, so there is no way to know what the other factor is.
Please help I have to turn in my homework by tonight at 11:00 PM!
Answers
The product of two factors is 1. One of the factors is 1. B. Yes; the other factor is 1 since 1 × 1 = 1.
How to calculate the value?From the information given, the product of two factors is 1 and one of the factors is 1.
Let the other number = y
The other number will be:
1 × y = 1
y = 1
Therefore, the other number is 1
In conclusion, the correct option is B.
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necesito hacer la recta numerica con números negativos y positivos, alguien me ayuda
Answers
De acuerdo a la información se puede inferir que su hijo nació en el año 22 antes de Cristo.
¿Qué es una recta numérica?Una recta numérica es una herramienta gráfica de las matemáticas que nos sirve para ubicar números positivos y negativos en un gráfico con el objetivo de organizarlos con respecto al número cero.
¿Cómo funcionan las líneas de tiempo con años Antes de Cristo y Después de Cristo?Las líneas de tiempo con fechas Antes y Después de Cristo se pueden asociar a una recta numérica debido a que los años Antes de Cristo se ubican en la parte negativa de la gráfica (a la izquierda del cero) y los número Después de Cristo se ubican en la parte positiva (a la derecha del cero).
¿Cuál es el año de nacimiento de su hijo?Para identificar el año de nacimiento del hijo debemos tener en cuenta que las fechas que se ubican en la zona negativa de la recta numérica aumentan de forma invertida, es decir que si su hijo nació 28 años después de ella se debe restar este número a su fecha de nacimiento como se muestra a continuación:
50 - 28 = 22
Entonces, el año de nacimiento de su hijo sería el año 22 Antes de Cristo.
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Solve each equation. If necessary, round to the nearest ten-thousandth.1/2log x+log 4=2
Answers
For logarithmic equation 1/2 log x + log 4 = 2, the value of x is 34,040.25
How can a logarithmic equation be solved?Step 1: Using exponentiation principles, isolate a logarithmic expression (with the same base) on both sides of the equation.
Step 2: balance the arguments.
Step 3: Solve the resultant equation.
Step 4: Double-check your answers.
Given,
1/2 log x + log 4 = 2
log x^(1/2) + log 4 = 2
using logₐ(m.n) = logₐ(m) + logₐ(n)
log e (4 (x^1/2)) = 2
e² = 4x^(1/2)
7.38 = 4√x
Squaring on both sides -
54.4644 = 16x
x = 54.4644 / 16
x = 34,040.25
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Carson wants to divide 128 by 3.2. What is the place value of the first digit in his answer?
tenths
ones
tens
hundreds
Answers
Answer:Tenths
Step-by-step explanation:Hope it helps
mile
long. You walk 3 laps around the lake in the morning
and 2 laps in the evening. Your friend walks the same
1
total distance as you on a 1--mile track. How many
2
laps does your friend walk?
Answers
The sidewalk around a lake is 9/10 mile long. You walk 3 laps Around the lake in the morning and 2 laps in the evening. Your friend walks the same total distance as you on a 3/2 mile track.
The total laps of our friend runs is 3laps.Given that
The sidewalk around a lake is 9/10 mile long.You walk 3 laps around the lake in the morning and 2 laps in the evening.Your friend walks the same total distance as you on a 3/2 mile track.To find
How many laps does your friend walks?So, according to the question
we have,
The length of sidewalk around the lake = 9/10 miles.Total distance walk by you = 9/10 (3+2)= (9 ×5)/10
= 4.5 miles.
Now, from question
Your friend walk same distance travel by you on 3/2 mile track.So, Total laps walk by your friend
= ( Total distance walk by you)/(Total length of your friends track)
= [tex]\frac{4.5}{(\frac{3}{2}) }[/tex]
= [tex]\frac{4.5\times 2}{3}[/tex]
= 9/3 = 3
Answer:
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Question 6(Multiple Choice Worth 2 points)
(Linear Relationships MC)
At a restaurant, hot chocolate can be purchased in three different cup sizes. A 12-ounce cup costs $1.97, a 16-ounce cup costs $2.62, and a 20-ounce cup costs $3.27.
Which statement is true based on the given description?
O The description shows a linear relationship, but not a proportional relationship.
O The description shows a linear relationship and a proportional relationship.
O The description does not show a linear relationship or a proportional relationship.
O The description shows a proportional relationship, but not a linear relationship
Answers
We need to know about linear and proportional relationship to solve this problem. Statement 2 is true, the description shows a linear relationship and a proportional relationship.
Linear relationship is a relationship between two variables where if one increases the other increases or if one decreases the other decreases. The varibales in a linear relationship form a straight line on graph. Proportional relationship is the relationship between two variables where the ratio between pairs of different data always remains constant. In the given question, a 12 ounce cup costs $1.97, a 16 ounce cup costs $2.62 and a 20 ounce cup costs $3.27. The price of each cup increases with increase in capacity of the cup, so we can say that the cup capacity and price have a linear relationship. The ratio between each pair can be given by
12/1.97=6.10
16/2.62=6.10
20/3.27=6.10
The ratios between every pair is same, so it is a proportional relationship.
Thus we found that the description shows a linear relationship and a proportional relationship between the cup capacity and it's price, statement 2 is the right option.
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