Equivalent fractions are those that, despite their visual differences, reflect the same value. we consumed half of a cake, for instance, if you have one, divide it into two equal pieces, and then eat one of the pieces.
what is fraction?Any number of equal portions, or parts of a whole, are described by fractions. Fractions in standard English indicate the number of pieces of a specific size. 8, 3/4 of .Part of an entire is a fraction. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. When a fraction is true, its numerator is smaller than its denominator.
If the denominators differ, similar fractions with a common denominator must be used. This requires figuring out the LCM of the two denominators. To be used as a denominator in fractions with various denominators, rename the fractions with a similar denominator.
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Simplify the following: (3 + 10i) - (-9 - 4i)
*PLEASE INCLUDE EXPLANATION
Answer:
12+14i
Step-by-step explanation:
For -(-9-4i), you need to clean up the parentheses so you would distribute. -1 times -9 and -1 times -4i.
You will get 9+4i
Now you have 3+10i+9+4i. You will now add like terms. 10i+4i= 14i. 9+3= 12.
12+14i
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Ron's car uses 12 L of gasoline per 100 km of highway driving. Asma's car as 5/6 as much fuel. How much fuel does Asma's car use per 100 km of highway driving?
10L fuel does Asma's car use per 100 km of highway driving
In this question, we have to use the unitary method
The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
What is a unitary in math?
a unitary state. (mathematics, of an algebra) That contains an identity element. (mathematics, linear algebra, mathematical analysis, of a matrix or operator) Whose inverse is equal to its adjoint.
So from the unitary method, we can solve it
12 L of gasoline per 100 km
so for 5/6
12 L * 5/6
= 10 L
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Select all expressions that are equivalent to 8.5x + 0.5 +3.5x - 2x
12x - 2x 10x
10x + 0.5
12-2x
9x + 3.5 - 2x
12x - 2x + 0.5
To see if it makes more sense… I added a photo of the problem on my hw
All expressions that are equivalent to 8.5x + 0.5 +3.5x - 2x are (12x - 2x + 0.5) and (10x + 0.5).
What are Equivalent expressions:Expressions that are equivalent perform the same thing even when they have distinct appearances.
When we enter the same value for the variable, two algebraic expressions that are equivalent have the same value.
By combining like terms, we can create expressions that are equivalent to a given expression. Terms with the same variables raised to the same powers are said to be "like terms".
Here we have
8.5x + 0.5 +3.5x - 2x
The above expression can be simplified as given below
=> 8.5x + 0.5 +3.5x - 2x
Add and subtract like terms
=> 8.5x +3.5x - 2x + 0.5
=> 12x - 2x + 0.5
=> 10x + 0.5
Therefore,
All expressions that are equivalent to 8.5x + 0.5 +3.5x - 2x are (12x - 2x + 0.5) and (10x + 0.5).
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Please help fast
a rock is thrown off a bridge 40 feet above a river at an initial velocity of 96 feet per second. The height h, in feet, of the rock t seconds after it was thrown can be modeled by the function h(t)=-16t^2 +96t+40. Find the height of rock 4 seconds after it was thrown.
The height of rock 4 seconds after it was thrown is 168 ft.
What is speed?Speed is measured as distance moved over time.
Speed = Distance/ Time.
Here, given that,
we have
a rock is thrown off a bridge 40 feet above a river at an initial velocity of 96 feet per second.
The height h, in feet, of the rock
t seconds after it was thrown can be modeled by the function
h(t)=-16t^2 +96t+40.
where
h -----> is the height in feet of the rock
t -----> the time in seconds
For , t=4, we get,
substitute the value of t in the function and find the value of h
h(4)=-16×4^2 +96×4+40.
So, h= 168
Hence, the height of rock 4 seconds after it was thrown is 168 ft.
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EKA MATH²
6 M2 TD Lesson
▸
A trainer at a gym earns $2,456.75 every month. She earns an extra $4.75 every time she sells
a gym membership. Last month, the trainer sold 32 gym memberships. What is the total amount
of money the trainer earned last month?
Answer: We know that the trainer earns $2,456.75 every month, and she earns an extra $4.75 every time she sells a gym membership.
And last month she sold 32 gym memberships
We can calculate the total amount of money the trainer earned from selling gym memberships by multiplying the number of memberships sold by the amount earned per membership:
32 memberships * $4.75 per membership = $152.00
To find the total amount of money the trainer earned last month, we can add the amount earned from selling gym memberships to the amount earned from her salary:
$2,456.75 + $152.00 = $2,608.75
So, the total amount of money the trainer earned last month is $2,608.75
Step-by-step explanation:
the total cost of the airline ticket is $432, including an 8% tax. What was the cost of the ticket before the tax was added?
Which expression is equivalent to (-3) × (-3)²?
Answer:
[tex] \sf \: (-3) × {( - 3)}^{2} = - 27[/tex]
Step-by-step explanation:
Given expression,
→ (-3) × (-3)²
Let's simplify the expression,
→ (-3) × (-3)²
→ (-3) × ((-3) × (-3))
→ (-3) × 9
→ (-3 × 9) = -27
Hence, the answer is -27.
Given g(x) = -x + 5, find g(-6).
Answer:
g(- 6) = 11
Step-by-step explanation:
substitute x = - 6 into g(x) , that is
g(- 6) = - (- 6) + 5 = 6 + 5 = 11
Answer:
11
Step-by-step explanation:
g(x) = -x + 5
Let x = -6
g(-6) = -(-6) + 5
=6+5
=11
Identifying Characteristics of an Exponential Function
Consider the function f(x) = (6). What is the value of the growth factor of the function?
02
06
O 18
The function be f(x) = (6) then growth factor for the given equation (b) = 6.
What is meant by exponential growth function?Quantity grows exponentially over time. It happens when a quantity's instantaneous rate of change with regard to time is proportional to the quantity itself.
A function called exponential growth illustrates an expansion within a population that happens at the same pace across time. When a population's per capita growth rate remains constant across time, regardless of population size, exponential growth occurs, causing the population to grow exponentially as the population increases.
The general exponential growth function is given by :-
[tex]$f(t)=A b^t$[/tex] , where A is the initial amount , b is the growth factor and t is the time period.
The given function : [tex]$f(x)=(6)^x$[/tex]
When we compare it to the general exponential equation , we get
The growth factor for the given equation (b) = 6.
The complete question is:
Consider the function f(x) = (6)x. What is the value of the growth factor of the function?
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The function be f(x) = (6) then growth factor for the given equation (b) = 6.
What is meant by exponential growth function?Quantity grows exponentially over time. It happens when a quantity's instantaneous rate of change with regard to time is proportional to the quantity itself.
A function called exponential growth illustrates an expansion within a population that happens at the same pace across time. When a population's per capita growth rate remains constant across time, regardless of population size, exponential growth occurs, causing the population to grow exponentially as the population increases.
The general exponential growth function is given by :-
F(t) = AB^t, where A is the initial amount , b is the growth factor and t is the time period.
The given function : f(t) = (6)^x
When we compare it to the general exponential equation , we get
The growth factor for the given equation (b) = 6.
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The complete question is:
Consider the function f(x) = (6)x. What is the value of the growth factor of the function?
Plot the remaining data point. 1
2
, 1 , 1
1
4
, 1
1
4
, 1
3
4
, 3 , 3
3
The information you gave was presented as a table with three columns: value, x-coordinate, and y-coordinate.
You would need to make a graph with the x-coordinate acting as the horizontal axis and the y-coordinate acting as the vertical axis in order to plot this data point. The size or colour of the data point would serve as a representation of the value.
Here is an illustration of a data point plot:
[tex]x | 12 | 14 | 14 | 34 \\ y | 1 | 1 | 3 | 3 \\ v | 1 | 1 | 3 | 3[/tex]
The value at the position (12,1) will be 1, the value at the point (14,1) will be 1, the value at the point (14,3) will be 3, and the value at the point (34,3) will be 3. It's vital to remember that the values on the graph can be depicted by many colours or shapes.
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It takes 52 yards of fabric to make 8 costumes for the dance recital. How many yards are needed to make one costume?
Make a Ratio Table
(MUST INCLUDE THE TABLE!!)
Total 6.5 yards , fabaric are needed to make one costume for the dance recital.
We have , Total lengths of fabaric present for making costumes = 52 yards
Total number of costumes for the dance recital made from 52 yards = 8
we have to calculate the length of fabaric in yards are used for make one constume .
Let the " x yards " be the fabric length used to make one constume.
Now, total fabric length used to make 8 conatumes = 8x yards
but it will be equals to 52 yards . So, we get a simple linear equation with one variable, i.e
=> 8x = 52
=> x = 52/8
=> x = 6.5
So, the required fabric length is 6.5 yards .
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I need help with this question please
The average rate of change is the ratio of the difference between the y coordinates of two points to the x coordinate of the same point.
It can be found by using two points on the graph and substitute into the formula: (y₀ - y₁) / (x₀ - x₁)
The square brackets [] is used to mean the end points as shown is inclusive
What is average rate of change in quadratic equation?A quadratic equation is a polynomial of degree two
The average rate of change here is not constant and is usually specified by the two points to which it is measured
For instance using points (-3, 0) and (0, -1) we have
= (y₀ - y₁) / (x₀ - x₁)
= (-1 - 0) / (0 - (-3))
= -1/3
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The sixth-grade class is holding a week long fund-raiser. The class set a goal of raising $700. 0. So far they have raised $176. 95. Write an equation that can be used to solve for x, the amount of money the class still must raise to meet their goal
An equation that can be used to find the value of,x=$700.0 - $176.95.
What is an equation ?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
We have LHS = RHS (left hand side = right hand side) in every mathematical equation.
To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.
The statement is not an equation if there is no "equal to" sign in it.
According to our question-
x= $700.0 - $176.95
523.05
Hence, An equation that can be used to find the value of,x=$700.0 - $176.95.
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The function w (t) = 29 + 0.0674t gives the estimated weight, in pounds, of a beaver t days
after June 1, where t < 90. Which of the following is the best interpretation of 29 in this context?
1)The estimated weight, in pounds, of the beaver 90 days after June 1
2)The estimated weight, in pounds, of the beaver on June 1
3)The estimated number of pounds by which the beaver's weight increased each day after June 1
4)The estimated number of pounds by which the beaver's weight increased in the 90 days after
June 1
Answer:
2) The estimated weight, in pounds, of the beaver on June 1.
Step-by-step explanation:
Given function:
[tex]w(t) = 29 + 0.0674t \quad t < 90[/tex]
where:
w = weight of a beaver (in pounds)t = time after June 1 (in days)When t = 0:
[tex]\begin{aligned}\implies w(0)&=29+0.0674(0)\\&=29+0\\&=29\end{aligned}[/tex]
Therefore, the constant of the equation (29) is the estimated weight of the beaver, in pounds, when t = 0.
As t = 0 is June 1:
29 is the estimated weight, in pounds, of the beaver on June 1.Required:
a. For the balance sheet, identify how each transaction affects total assets, total liabilities, and total equity. For the income statement, identify how each transaction affects net income.
b. For the statement of cash flows, identify how each transaction affects cash flows from operating activities, cash flows from investing activities, and cash flows from financing activities.
WHAT AM I MISSING?!?!
The answers for the two questions is described below:
a. The balance sheet is a financial statement that shows a company's assets, liabilities, and equity at a specific point in time. Each transaction will affect one or more of these categories in different ways:
An increase in assets will increase total assets.
An increase in liabilities will increase total liabilities.
An increase in equity will increase total equity.
The income statement is a financial statement that shows a company's revenues, expenses, and net income over a specific period of time. Each transaction will affect net income in different ways:
An increase in revenues will increase net income.
An increase in expenses will decrease net income.
b. The statement of cash flows is a financial statement that shows the cash flows from operating activities, investing activities, and financing activities over a specific period of time. Each transaction will affect one or more of these categories in different ways:
An increase in cash from operating activities will increase cash flows from operating activities.
An increase in cash from investing activities will increase cash flows from investing activities.
An increase in cash from financing activities will increase cash flows from financing activities.
It is important to note that it can be complex to classify some transactions into one category or another, and it may require more context of the specific transaction and the company's operations.
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What is the additive inverse of 6 /- 5 of Class 8?
The additive inverse of 6 /- 5 is 6/5
We know that for any real number 'a' an additive inverse is a number 'b' such that a + b = 0
i.e., b = -a
An additive inverse of 'a' is -a.
The means, an additive inverse is nothing but changing sign + to - OR - to +
Here we have been given a rational number 6/(-5)
Let m be the additive inverse of number 6/(-5)
From the definition of additive inverse,
6/(-5) + m = 0
[6/(-5) + m] - 6/(-5) = -6/(-5)
[6/(-5) - 6/(-5)] + m= -6/(-5) ...........(associative property of addition)
0 + m = 6/5
m = 6/5
Hence, the additive inverse is 6/5
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Pleas help me with #2, thanks
what is 8 1/4 divided by d=2/11
When 8[tex]\frac{1}{4}[/tex] is divided by 2/11, we get 45[tex]\frac{3}{8}[/tex].
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the statement -
"8[tex]\frac{1}{4}[/tex] divided by 2/11"
We can write it as -
x = {8[tex]\frac{1}{4}[/tex]} ÷ {2/11}
x = 33/4 x 11/2
x = 363/8
x = 45[tex]\frac{3}{8}[/tex]
Therefore, when 8[tex]\frac{1}{4}[/tex] is divided by 2/11, we get 45[tex]\frac{3}{8}[/tex].
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What are the values for the coefficients and constant term of 0 2 3x² 5x?
The coefficient of the expression 3x² is the number 3 and constant term is 20
What are the coefficients?
The coefficients are the numbers on the left side or before each variable.
What is an algebraic expression?
Is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.
If the expression of a single term is:. 3x²
Then the only coefficient will be the number that is placed before it and it is:
Number 3
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Write an equation of the line that passes through the points (-7,-3) and (8, -3)
y=
Answer:
y = - 3
Step-by-step explanation:
Call the line y = a + bx (d)
Since d go through (-7;-3) so -7 = a - 3b (1)
Since d go through (8;-3) so 8 = a - 3b (2)
From (1) and (2), we have equations: [tex]\left \{ {{a - 3b = -7} \atop {a - 3b = 8}} \right.[/tex]
Solve the equations, we have [tex]\left \{ {{a = 0} \atop {b = -3}} \right.[/tex]
The graph shows the cost of grapes at a grocery store. What is the slope of the line?
The slope of the line that passes through the graph is 3
How to calculate the slope of the line?From the graph, the points are given as
(0, 0) and (1, 3)
Rewrite the above points properly
So, we have the following ordered pairs
(x, y) = (0, 0) and (1, 3)
The slope of the line is then calculated using the following slope equation
Slope = (y₂ - y₁)/(x₂ - x₁)
Where
(x, y) = (0, 0) and (1, 3)
Substitute the known values in the above equation
So, we have the following equation
Slope = (3 - 0)/(1 - 0)
Evaluate
Slope = 3
Hence, the slope of the line is 3
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Can u please help.............
The rotation about the center that can map an equilateral triangle onto itself is C. 120 degrees.
What angle rotates an equilateral triangle onto itself ?There are three equal sides and angles in an equilateral triangle which is 60 degrees each. This means that an equilateral triangle can be divided into three-axis of symmetry such that there are three lines dividing the triangle.
Should this happen, then the angle to rotate the triangle and map it onto itself would be 120 degrees as each of these axes of symmetry measure 120 degrees.
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Data on the fuel consumption y of a car at various speeds x is given. Fuel consumption is measured in mpg, and speed is measured in miles per hour. Software tells us that the equation of the least‑squares regression line is ^ y = 55. 3286 − 0. 02286 x
Fuel consumption is 53.957 miles per gallon for a car moving at a speed of 60 miles per hour using least square Regression .
What is Regression ?A statistical word for models that evaluate the connections between variables is regression. A single dependent variable Y and one or more independent variables X are studied using a linear regression model.
A technique for employing a goodness-of-fit criterion to fit a curve—not necessarily a straight line—through a collection of points. Regression that is most frequently used is linear regression. Recursion is occasionally used interchangeably with the word regression.
Y = mX + b, where X is the predictor (independent) variable, m is the estimated slope, and b is the expected intercept, is the formula for simple linear regression.
Calculation of Fuel Consumption in 60 miles per hour.
given the least square regression line is
y = 55.3286 - 0.02286x
so, y = 55.3286 - 0.02286 * 60 = 53.957 miles per gallon.
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if x+3=9 whats the answer:)
enjoy
Answer:
x=6
Step-by-step explanation:
then x=6 because replacing x 6+3=9
Need answer for b)iii)
Answer:
3.23, -1.23
Step-by-step explanation:
Draw the line y=1
See where it intersects x^2-2x-3
The x coordinates of the intersections are your answer
What is the length of the short side of one of the 30 60 90 triangles?
Remembering the ratio of 1: 3: 2 and understanding that the smallest side length is always opposite the shortest angle (30°) and the longest side length is always opposing the greatest angle (90°) can help you recall the 30-60-90 triangle principles.
According to the 30-60-90 triangle theorem, the hypotenuse is twice as long as the shorter leg. Additionally, the sides of this particular triangle have a ratio of 1:2: [tex]\sqrt{3}[/tex].
A 30-60-90 triangle can have three sides, and if you only know one, you can use shortcuts to discover the other two. The three scenarios you encounter when performing these computations are as follows:
You are aware of the short leg (the side across from the 30-degree angle). To find the hypotenuse, multiply the length by two. The long leg can be calculated by multiplying the short side by the square root of 3.You are aware of the hypotenuse. To get the short side, divide the hypotenuse by two. To determine the long leg, multiply this response by the square root of 3.You are aware of the long leg (the side across from the 60-degree angle). To determine the short side, divide this side by the square root of 3. To find the hypotenuse, multiply that amount by two.To know more about the 30 60 90 triangles on brainly : brainly.com/question/11751274
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the monthly cost for 43 min is $17.96 and the monthly cost for 94 min is $24.72 what is the monthly cost for 88 min
Therefore , the solution to this problem of equation is y = 16.95 cost for 94 minutes.
Explain the equation.A mathematical equation is a formula that links two statements by indicating their equivalence with the equal sign (=). A mathematical statement that proves the equality of two mathematical expressions is known as an equation in algebra. For instance, the components 3x + 5 and 14 in the equation 3x + 5 = 14 are separated by an equal sign. The relationship between two sentences on either side of a letter is expressed mathematically. There is frequently only one variable, which doubles as the symbol. say that 2x - 4 Equals 2.
Here,
y = mx + b
(50,13.98)(78,17.06)
slope = (17.06 - 13.98) / (78 - 50) = 3.08 / 28 = 0.11
slope(m) = 0.11
use either of ur points...(50,13.98)...x = 50 and y = 13.98
now sub into the formula and find b, the y int
13.98 = 0.11(50) + b
13.98 = 5.5 + b
13.98 - 5.5 = b
8.48 = b
so our equation is : y = 0.11x + 8.48.......for 94 minutes...sub in 77 for x
y = 0.11(94) + 8.48
y = 8.47 + 8.48
y = 16.95 <=== this is the cost for 94 minutes
Therefore , the solution to this problem of equation is y = 16.95 cost for 94 minutes.
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Examine the graph of the function. The graph of a line that contains points (negative 1, 7), (0, 5), and (2, 1). © 2017 StrongMind. Created using GeoGebra. What is the initial value of the function? Enter your answer as a number, like this: 42
The initial value of the function is equal to 5.
How to determine the initial value of the function?In order to determine the initial value of the function, we would have to find the slope from line graph and then write the required equation based on the data points contained in the table by using the slope-intercept form.
Mathematically, the slope-intercept form of a line is modeled by this mathematical equation:
y = mx + c
Where:
m represents the slope.x and y are the data points.c represents the y-intercept or initial value.Next, we would determine the slope of the data points as follows;
Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope, m = (y₂ - y₁)/(x₂ - x₁)
Slope, m = (5 - 7)/(0 + 1)
Slope, m = -2/1
Slope, m = -2.
At point (0, 5), an equation of this line can be calculated in slope-intercept form as follows:
Note: The y-intercept or initial value is equal to 5.
y = mx + c
y = -2x + 5
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What is the domain of exponential function f/x )= BX?
The domain of an exponential function is all real numbers. In the interval notation is (-∞, ∞).
What is interval notation?
A set of real numbers known as an interval in mathematics contains all real numbers falling inside any two of the set's numbers. For instance, the interval containing 0, 1, and all integers in between is the set of values x satisfying 0 ≤ x ≤ 1 .
Given exponential function is f(x) = B^x.
A function with an exponent as the independent variable is called an exponential function. The general form of an exponential function is y = f (x) = B^x, where B > 0 and a > 1, and x is any real number. The function is undefined for -1 < x < 1 if an is negative, which is why a > 0 is true. The function can have a domain that includes all real numbers by limiting a to positive values.
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When treated with an anabiotic, 97% of all the dolphins are cured of an ear infection. if 6 dolphins are treated find the probability that exactly 3 are cured.
The probability is _____
(Round your answer to 4 decimal places.)
Answer:
0.0005
Step-by-step explanation:
this is a binomial experiment -- they are either cured or not, and the outcome is random
probability = n choose r * p^r * q^(n-r)
here, n = number of trials, r = number of successes desired, p = probability event occurs, and q = probability event doesn't occur
probability = n choose r * p^r * q^(n-r) = 6 choose 3 * 0.97^3 * 0.03^(6-3)
= 0.00049284342 rounding to 0.0005