The area of a square with a side length √8 represents a rational number, which is equal to 8 square units.
Is the number behind the area of the square a rational number?
Rational numbers are real numbers of the form m / n, where m and n are integers, where n ≠ 0. The rest of real numbers are irrational (i.e. π, √5, ∛7, e) Besides, the area of the square is determined by the following formula:
A = l²
Where l is the side length of the square.
First, substitute the side length of the square in the area formula:
A = (√8)²
Second, use algebraic properties to simplify the expression and find the corresponding result:
A = ([tex]8^{\frac{1}{2} }[/tex])²
A = 8
This number represents a rational number as 8 is equivalent to the rational number 8 / 1.
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Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2
dont know how to do this either if u could feel free to help me
The graph that beast describes the slope of -2/3 passing through points (-1, 0) is in option c
How to determine the graph that matches the slope and the pointsInformation given in the question include
a linear function graph
The data is plotted as a linear function
What is linear function ?A linear function consists of functions where the variables has exponents of 1. The graph of linear functions is a straight line graph and the relationship is expressed in the form.
y = mx + c
The slope is represented as m, The slope by definition is the ratio change of the output values to the input values
the slope, m = -2/3
negative slopes slants from top left to bottom right as in a and c
from the graph, option c has points (-1, 0) and (0, -2/3)
m = (-2/3 - 0) / (0 - -1)
m = (-2/3) / (0 + 1)
m = -2/3
This matches with option C
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What Is a factor?
Hi
A factor is a number that divides another number, leaving no remainder
determine the interval(s) for which the function shown below is decreasing
Answer:
(∞,-3) and (1,-∞)
Step-by-step explanation:
Decreasing means going down or in math terms, going toward the negatives.
When you are talking intervals in math, you only want to use the x-axis for the interval points. We write the interval as if it was a coordinate point though.
Looking at the graph it looks like it is going from infinity to -3 or written as (∞,3) and from 1 to negative infinity or written as (1, -∞)
The interval(s) for which the function shown below is decreasing are (∞,-3) and (1,-∞).
What is a function?A function is a relationship between two sets of values in mathematics where each input value (or "argument") corresponds to a certain output value.
In most cases, the input values come from a set referred to as the function's domain, while the output values come from a set referred to as the function's range.
Declining is the mathematical phrase for decreasing or moving towards the negatives.
Mathematicians only use the x-axis to represent interval points when discussing intervals. Yet, we express the interval as if it were a coordinate point.
If you look at the graph, it appears to be traveling from infinity to -3, which is written as (,3), and from one to negative infinity, which is written as (1, -).
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The flower box is 5 ft long, and its ends are in the shape of a trapezoid. The upper and lower bases of the trapezoid measure 18 in. and 10 in., respectively, and the height is 9 in. Find the volume of the flower box.
The volume of the flower box is 7560 cubic inches
How to determine the volume of the box?The given parameters in the question are:
Length = 5 ft
Upper and lower bases = 18 inches and 10 inches
Height = 9 inches
The volume of the box can be calculated using the following volume equation
Volume = 0.5 * Height * Length * (Sum of the bases)
Substitute the known values in the above equation So, we have the following equation
Volume = 0.5 * 9 inches * 5 feet * (18 inches + 10 inches)
Convert feet to inches
Volume = 0.5 * 9 inches * 60 inches * (18 inches + 10 inches)
Evaluate
Volume = 7560 cubic inches
Hence, the volume is 7560 cubic inches
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find the number that is exactly halfway between 5 and 17
Oliver borrowed $1,500 to purchase a riding lawn mower for his lawn care business. The bank offered him an interest rate of 12% for 6 months. Calculate the simple interest using I = prt. $69 $90 $420 $1,080
The simple interest that Oliver needs to pay is $ 90
Calculating Simple interest:Simple interest is nothing but interest on a loan at a rate. The formula for Simple interest is given below
Simple interest, I = ptr
where p = principal amount
t = time period in years
r = rate of interest in decimals
Here we have
Oliver borrowed $1,500 to purchase a riding lawn mower
The rate of interest r = 12%
=> 12/100 = 0.12 (in decimals )
The time period given = 6 months = 0.5 years [ 6/12 = 0.5 ]
From the above formula,
The simple interest, I = ptr
=> I = $1,500(0.12) (0.5) = $ 90
Therefore,
The simple interest that Oliver needs to pay is $ 90
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Which function is the inverse of f(x) = -5x—4
Answer: f^-1(x)= - 1/5x - 4/5
Step-by-step explanation:
substitute y for f(x): y= -5x-4
interchange x and y: x=-5y-4
swap the sides: -5y-4=x
move the constant -5y=x+4
divide both sides by 5 y= - 1/5x - 4/5
substitute f^-1(x) for y f^-1(x)= - 1/5x - 4/5
Can you answer this question?
Answer: y= 3 times 2 to the power x. Second answer
Step-by-step explanation:
if you plug in 0 for x, y= 3x 1= 3
if you plug in 1 for x y= 3 x 2 = 6
Look at the x values and y values
(0,3) and (1, 6) on the graph. It matches answer number 2. Remember, 2 raised to the power 0 = 1 and 3 times 1 = 3. And 2 raised to the power 1 =2 and 3 times 2 = 6.
Who wants brainliest? First come first serve
Value: 2
In the year 2000, the population of Ohio was 11.03 million people. By the year 2017 the
population of Ohio was 11.66 million people. Create an equation modeling the
population, p, of Ohio given the year, t. Round to the nearest hundredth if necessary.
O a. p=11.1t+232.14
O b. p=11.1t-11.66
O c. p=0.09t+191.93
O d. p=0.04x-68.97
Check Answer
An equation modeling the population, p, of Ohio given the year, t is,
p = 0.04t + 10.98.
What is population?
The term "population" refers to all citizens who are either permanently residing in a country or who are just passing through. This indicator reveals how many people typically reside in a certain area. Growth rates are the population changes that occur each year as a result of births, deaths, and net migration.
Given: In the year 2000, the population of Ohio was 11.03 million people. By the year 2017 the population of Ohio was 11.66 million people.
From this we get, two points (0, 11.03) and (17, 11.66).
First to find the slope using the above two points.
[tex]m=\frac{11.66 - 11.03}{17-0} = \frac{0.63}{17} = 0.04[/tex]
Now to find the equation,
Consider,
p - 11.66 = 0.04(t - 17)
p - 11.66 = 0.04t - 0.68
p = 0.04t - 0.68 + 11.66
p = 0.04t + 10.98
Therefore, the equation modeling the population, p, of Ohio given the year, t is, p = 0.04t + 10.98
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A teacher bought markers at a cost of $3 per set. The teacher had a $2-off coupon to use
toward the total cost of the markers bought.
Which table shows the relationship between , the number of sets of markers bought by the
teacher, and y, the total cost of the markers?
The first table A shows the relationship between the number of sets of markers bought by the teacher and the total cost of the markers.
From given question, the cost per set of markers = $3
The teacher had a $2-off coupon to use toward the total cost of the markers bought.
It is given that the number of sets of markers bought by the teacher is x, and y is the total cost of the markers.
so, we get a linear equation as:
3x - 2 = y
From table A we can see that the data satisfied the given equation,
3x - 2 = y
when x = 3, y = 3(3) - 2 = $7
when x = 9, y = 3(9) - 2 = $25
when x = 12, y = 3(12) - 2 = $34
when x = 24, y = 3(24) - 2 = $70
Therefore, the first table A shows the relationship between the number of sets of markers bought by the teacher and the total cost of the markers.
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The revenue function is given by R(x)=x⋅p(x) dollars where x is the number of units sold and p(x) is the unit price. If p(x)=26(4)−x5, find the revenue if 15 units are sold. Round to two decimal places.
If price p(x) =26(4)^{-x/5}, the revenue when 15 units are sold is equal to $6.09.
How to calculate the amount of revenue at p(15)?From the information provided, the amount of revenue with respect to price that's being generated in this scenario can be calculated by using the following function (expression):
R(x) = x × P(x)
Where:
x represents the number of units sold.p(x) represents the unit price.Since the revenue function, we would simply substitute the value of the unit price and evaluate as follows:
Revenue, R(x) = x × 26(4)^{-x/5}
Substituting the given parameters into the formula, we have;
Revenue, R(x) = 15 × 26(4)^{-15/5}
Revenue, R(x) = 15 × 26(4)^{-3} or (15 × 26)/4³
Revenue, R(x) = 15 × 26(0.015625) or 390/64
Revenue, R(x) = 6.09375 ≈ $6.09.
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Complete Question:
The revenue function is given by R(x)=x⋅p(x) dollars where x is the number of units sold and p(x) is the unit price. If p(x)=26(4)^{-x/5}, find the revenue if 15 units are sold. Round to two decimal places.
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Suppose that 12 inches of wire cost 48 cents at the same rate how many inches of wire can be bought for 28 cents
Answer:
7 in
Step-by-step explanation:
If 12 inches of wire can be bought for $0.48, we can set up the following ratio:
[tex]\frac{12\text{ in}}{\$0.48}[/tex]
Then, to determine how many inches of wire can be bought for $0.28, set up equivalent fractions, as such:
[tex]\frac{12\text{ in}}{\$0.48}=\frac{x}{\$0.28}[/tex]
Then, cross-multiply and solve for [tex]x[/tex]:
[tex]\$0.48x=(\$0.28)(12)[/tex]
[tex]\$0.48x=\$3.36[/tex]
[tex]x=\frac{\$3.36}{\$0.48}[/tex]
[tex]x=7[/tex]
can y’all help me please
The slope of the line x = 3 is undefined
How to describe the slope of the line
The slope is defined as the ratio of the vertical change between two points, the rise, to the horizontal change between the same two points, the run.
Mathematically, the slope is the change in y divided by the change in x. That is:
Slope = y2-y1 / x2-x1
Let's pick any two convenient points on the line:
(3, 9) and (3, -9) = > x1 = 3, y1 = -9 and x2 = 3, y2 = 9
Slope = 9-(-9) / 3-3 = 18/0
The denominator here is 0, if you evaluate this using a calculator you will a maths error. So we say the slope is undefined
Notice that: There is no change in x i.e. x1 = x2
Therefore, the slope of x = 3 is undefined because x = 3 is a vertical line
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Use point-slope form to write the equation of a line that passes through the
point (14,-17) with slope -2.
Answer:
[tex]y+17=-2(x-14)[/tex]
Step-by-step explanation:
The equation of the line passing through the point [tex](x_1, y_1)[/tex] and slope [tex]m[/tex] is [tex]y-y_1=m(x-x_1)[/tex].
Find the Smallest number which
being added 28 to
exactly divisable by 32, 36, 48
and 96
Answer:
265 is the snakiest number
Step-by-step explanation:
7 1
The equation y--(x-4) is written in point-slope form. What is the y-intercept of the equation?
11
02
2
92
O
32
Mark this and return
Save and Exit
Next
Submit
The y-intercept of the equation y = (x - 4) is -4
How to determine the y-intercept of the equation?From the question, we have the following equation that can be used in our computation:
y --(x - 4)
Rewrite the equation properly
So, we have the following representation
y = (x - 4)
To calculate the y-intercept, we set x to 0
So, we have the following representation
y = 0 - 4
Evaluate the difference
y = -4
Hence, the y-intercept is -4
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HALPPPPPPPPPPPPPPPP NED QUESTIEON ANSERWDDDDD 1 MILLION POINTS
A business started the year with a net worth of $4,873. During the first six months of the year, the business
recovered and increased its net worth to a value of $15,866. Find the average monthly increase in net worth for the 6-month period.
The average monthly increase in net worth for the 6-month period is $1832.16.
Given:
A business started the year with a net worth of $4,873. During the first six months of the year, the business recovered and increased its net worth to a value of $15,866.
Six months net worth = 15,866 - 4873
= 10,993
Average monthly increase in net worth = six month net worth / 6
= 10,993/6
= $1832.16.
Therefore The average monthly increase in net worth for the 6-month period is $1832.16.
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What is the correct answer
Answer:
given point is (-3,-2)
The rule for a rotation by 270° about the origin is (x,y)→(y,−x).
So,
(-3,-2)==============(-2,3).
there fore,
(-2,3) is the image point of (-3,-2)after the transformation r(x-axis) and rotation 270°.
Any confusion ask in CMT!!what is 4 2/3 - 1 1/3 / 4= because i cant get the right awnser
Step-by-step explanation:
first you have to multiply 4 with 3 and add with 2 and do same as in second .
then do lcm
help, please !!!!!!!! **50points**
Answer:Answer: SAS
Step-by-step explanation:
Una torre de 50 pies está a la orilla de un río. El ángulo de elevación entre la orilla opuesta y la punta de la torre es de 37°. ¿Qué anchura tiene el río?
Usando una relación trigonometrica veremos que la anchura del rio es 66.4 pies.
¿Como encontrar la anchura del rio?
Podemos ver la situación como si trabajaramos con un triangulo rectangulo, donde la torre de 50 pies es un cateto y la anchura del rio es el otro cateto. (la imagen de este triangulo se puede ver en la imagen al final)
Usando la relacion:
tan(a) = (cateto opuesto)/(cateto adjacente)
Podemos escribir:
tan(37°) = 50ft/x
Resolviendo para x, la anchura del rio:
x = 50ft/tan(37°) =66.4 ft
El rio tiene un ancho de 66.4 pies.
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What is the slope of a line that is parallel to the line
−
7
x
−
5
y
=
−
6
? Write your answer as an integer or fraction.
The slope of the line that is parallel to the line -7x-5y=-6 is -7/5
What is the slope of a line?It is possible to determine a line's direction and steepness by looking at its slope. Finding the slope of lines in a coordinate plane can aid in anticipating whether the lines are parallel, perpendicular, or none at all without actually using a compass.
Any two unique places along the line may be used to determine the slope of any line. When two different places on a line are considered, the slope of a line formula compares the vertical change to the horizontal change in each case. We shall comprehend how to discover the slope in this piece, along with some of its uses.
Given, line is -7x-5y=-6
We have to write the given line in slope-intercept form
Then, y= (-7/5)x+(6/5)
The slope-intercept form is y= mx +c
By using the slope-intercept form,
Slope=(-7/5)
The lines that are parallel to y= (-7/5)x+(6/5) have the same slope of -7/5
Therefore, the slope of the line that is parallel to the line -7x-5y=-6 is -7/5
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I need asap thank you
Answer:
33 degrees
Step-by-step explanation:
The square in the corner of these two vectors signifies that this is a right angle, which will always equal 90 degrees, so if you subtract angle 2's value of 57 degrees, you will be left with angle 1 as 33 degrees.
Pls help would really mean a lot
Answer:
Use AAA congurency rule
Step-by-step explanation:
1 angle=52
2 angle=58
3 angle=78
Let f(x)=x/x+1 and g(x)=√x-1
Find the following
i. f(a − 1) + g(a + 1)
ii. f(a² + 1)g(a² + 1)
Answer:
Step-by-step explanation: a square x b square
Jamal has 54 marbles.
Lucas has 70 marbles.
How many more marbles
does Lucas have than
Jamal?
Answer: 16
Step-by-step explanation:
