Step-by-step explanation:
a/b = 5/6
a + b = 44
a = 44 - b
so, the first equation is
(44 - b)/b = 5/6
44 - b = 5b/6
264 - 6b = 5b
264 = 11b
b = 24
a = 44 - b = 44 - 24 = 20
the fraction is a/b = 20/24.
Also 2+4 as sum of the digits of the denominator = 6 is correct.
Explain the difference between solving an equation with the variables all on one side compared to equations with variables on both sides.
An equation having variables on both sides can be solved by bringing all variables to one side.
An equation with all variables on one side can be solved by simply keeping the variables on the left and simplifying the value on the right. For example,
5x = 6 + 2x;
3x = 6;
x = 2.
For an equation with variables on both sides, just bring all variables on one side. After that, the same process like above is to be followed. For example,
5y - 3 - 3y = 3y + 5 - 3y;
5y - 3y - 3y + 3y = 5 + 3;
2y = 8;
y = 4;
Thus, methods for solving both kinds of equations is similar.
To learn more about equations, refer to this link:
brainly.com/question/27664510
An equation having variables on both sides can be solved by bringing all variables to one side.
An equation with all variables on one side can be solved by simply keeping the variables on the left and simplifying the value on the right. For example,
5x = 6 + 2x;
3x = 6;
x = 2.
For an equation with variables on both sides, just bring all variables on one side. After that, the same process like above is to be followed. For example,
5y - 3 - 3y = 3y + 5 - 3y;
5y - 3y - 3y + 3y = 5 + 3;
2y = 8;
y = 4;
Thus, methods for solving both kinds of equations is similar.
To learn more about equations, refer to this link:
brainly.com/question/27664510
https://brainly.com/question/28502409
#SPJ4
(Precalc) NEED HELP 100PTS: (−2 ≤ x ≤ 2) f(x) = csc(x)
A. Find the intervals on which the graph of y = f(x) is increasing and the intervals on which the graph of y = f(x) is decreasing. Answer in interval notation.
Increasing: ___
Decreasing: ___
B. Find all relative extrema, if any, of the graph of y = f(x).
Relative min: ___
Relative max: ___
Thank youu!! <333
Answer:
Step-by-step explanation:
y=csc(x) x∈ [-2,2]
[tex]A.\\\displaystyle\\Increasing: \ [-2,-\frac{\pi }{2})U(\frac{\pi }{2},2]\\\\Decreasing:\ (-\frac{\pi }{2},0)U(0,\frac{\pi }{2} ) \\\\B.\\\\Relative\ min:\ 1\\\\Relative \ max:\ -1[/tex]
Watching the graph:
Answer:
[tex]\textsf{Increasing}:\left[-2,-\dfrac{\pi}{2}\right) \textsf{ and }\left(\dfrac{\pi}{2},2\right][/tex]
[tex]\textsf{Decreasing}:\left(-\dfrac{\pi}{2}, 0\right) \textsf{ and }\left(0, \dfrac{\pi}{2}\right)[/tex]
[tex]\textsf{Relative min}: \left(\dfrac{\pi}{2},1 \right)[/tex]
[tex]\textsf{Relative max}: \left(-\dfrac{\pi}{2},-1 \right)[/tex]
Step-by-step explanation:
Part A
Given function:
[tex]f(x)=\csc (x), \quad -2\leq x\leq 2[/tex]
[tex]\csc(x)=\dfrac{1}{\sin(x)}[/tex]
Therefore, the function f(x) is undefined when sin(x) = 0, leading to vertical asymptotes at the value of x where sin(x) = 0.
[tex]\sin(x) = 0 \textsf{ at }x = 0\pm 2 \pi n, \pi \pm 2 \pi n[/tex]
Therefore, f(x) has a vertical asymptotes at x = -2π, -π, 0, π, 2π etc.
Where the graph of the sine function increases, the graph of the cosecant function decreases.
Where the graph of the sine function decreases, the graph of the cosecant function increases.
The sine function increases on the intervals:
[tex]\left(-\dfrac{\pi}{2}\pm 2 \pi n, \dfrac{\pi}{2}\pm 2 \pi n\right)[/tex]
and decreases on the intervals:
[tex]\left(\dfrac{\pi}{2}\pm 2 \pi n, \dfrac{3\pi}{2}\pm 2 \pi n\right)[/tex]
Therefore, for the interval -2 ≤ x ≤ 2, the cosecant function f(x):
Increases on the intervals:
[tex]\left[-2,-\dfrac{\pi}{2}\right) \textsf{ and }\left(\dfrac{\pi}{2},2\right][/tex]
Decreases on the intervals:
[tex]\left(-\dfrac{\pi}{2}, 0\right) \textsf{ and }\left(0, \dfrac{\pi}{2}\right)[/tex]
Part B
The relative minimums of the graph of the sine function are the relative maximums of the graph of the cosecant function.
The relative maximums of the graph of the sine function are the relative minimums of the graph of the cosecant function.
The sine function has a range of -1 ≤ sin(x) ≤ 1.
Therefore, its minimum points are when sin(x) = -1 and its maximum points are when sin(x) = 1.
[tex]\sin(x)=-1 \implies x=\dfrac{3\pi}{2}\pm 2 \pi n \implies \textsf{Minimum points}: \left(\dfrac{3\pi}{2}\pm 2 \pi n ,-1 \right)[/tex]
[tex]\sin(x)=1 \implies x=\dfrac{\pi}{2}\pm 2 \pi n \implies \textsf{Maximum points}: \left(\dfrac{\pi}{2}\pm 2 \pi n,1 \right)[/tex]
Therefore, the minimum and maximum points of the cosecant function in the given interval -2 ≤ x ≤ 2 are:
[tex]\textsf{Relative min}: \left(\dfrac{\pi}{2},1 \right)[/tex]
[tex]\textsf{Relative max}: \left(-\dfrac{\pi}{2},-1 \right)[/tex]
Note in the attached graph:
The given interval -2 ≤ x ≤ 2 is shown shaded in green.Vertical asymptotes are shown as red dashed lines.Function f(x) is the black curve.The sine function is the blue dashed curve.Relative min/max shown as black points.What is the value of the absolute value expression |−134| + |4| − |−35|?
Answer:
174
Step-by-step explanation:
absolute value means the distance from zero. Distance is always measured with a positive number. If you asked me how far I lived from my work, I would never say -12 miles away. If I was going or coming to work, the distance would be the same 12 miles.
134 + 4 + 35 = 174
Multiplying and dividing Decimals.
−6.87(−2.65).
Answer:18.2055
Step-by-step explanation:−6.87(−2.65)=−6.87*−2.65=18.2055
Which of the following options are examples of how you can name the angle?
Answer:
∠T and ∠STP
Step-by-step explanation:
You can name an angle by their middle vertex letter which, in this case, is T.
And you can name an angle using the three letters provided. P, T, and S are the three letters provided. However, the vertex letter always has to be in the middle. So, it could be ∠STP or even ∠PTS.
Let me know if you don't understand or need more explanation.
Help !!! With this please !!!
Answer: $48.17
Step-by-step explanation:$148.68-$24.32= $124.36
$124.36-$37.53= $86.83
$135 -$86.83=$48.17
So he needs forty-eight dollars and 17 cents.
When the relationship between the unit of measurement of a scale (strength) and an outcome (pounds lifted) can be described by a linear equation y = a bx, the scale is said to have what property?
When the relationship between the unit of measurement of a scale (strength) and an outcome (pounds lifted) can be described by a linear equation y = a bx, the scale is said to have a property of equal intervals.
What are equal intervals?Equal intervals denote that the variations between numbers (units) are the same anywhere on the scale (e.g., the difference between 4 and 5 is the same as the difference between 76 and 77). The difference between two successive categories is equal in an equal interval. Temperature measured in Fahrenheit, for example, has equal intervals; that is, the difference between 30 and 31 degrees is one degree, and the difference between 100 and 101 degrees is one degree.When the relationship between a scale's unit of measurement (strength) and a consequence (pounds lifted) can be described by the linear equation y = a bx, the scale is said to possess an equal intervals property.Therefore, when the relationship between the unit of measurement of a scale (strength) and an outcome (pounds lifted) can be described by a linear equation y = a bx, the scale is said to have a property of equal intervals.
Know more about equal intervals here:
https://brainly.com/question/26620085
#SPJ4
Which is an equivalent expression for 4 times d raised to the negative third power all over quantity 22 times d raised to the ninth power end quantity?
really need help pleeease
An equivalent expression for 4 times d raised to the negative third power all over quantity 22 times d raised to the ninth power is 2d⁻³/11d⁻⁹
What is an expression?An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.
What is an exponent?An exponent can be defined as a mathematical operation that is used to raise a quantity to the power of another and it is generally written as bⁿ.
Translating the word problem into an algebraic expression, we have;
4 times d raised to the negative third power = (4 × d)⁻³ = 4d⁻³
22 times d raised to the ninth power = (22 × d)⁻⁹ = 22d⁻⁹
Next, we would write the equation as a quotient:
Expression = 4d⁻³/22d⁻⁹
Expression = 2d⁻³/11d⁻⁹
Read more on expressions here: https://brainly.com/question/28260012
#SPJ1
11. A population of bacteria triples every week in a laboratory. The number of
bacteria is modeled by the expression 900 3*, where x is the number of weeks
after a scientist measures the population size. When x = -2, what does the value
of the expression represent?
Answer:
Step-by-step explanation:
Let x represent the number of weeks a population of the bacteria increases. Then, we have the number of bacteria is molded by the expression of 900*3^x. By, the given expression and when we assigned a value of x=2. Then we have 900*3² .
HELPPPPP PLEASE. PLEASE TELL ME THE BLANKS IN ORDER.
Please help !!! , I have 8 mins left on the clock .
Express the relation below as a set of ordered pairs.
By critically observing the graph shown above, the set of ordered pairs include the following:
(-1, 5)(4, -3)(-5, -3)(0, 5)(-4, 5)What is a graph?A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.
What is an ordered pair?An ordered pair can be defined as a pair of two elements that are typically written in a fixed order within parentheses as (x, y), which represents the x-axis (abscissa) and the y-axis (ordinate) on a coordinate plane.
By critically observing the graph shown above, we can logically deduce that the set of ordered pairs include the following:
(-1, 5)(4, -3)(-5, -3)(0, 5)(-4, 5)Read more on ordered pairs here: https://brainly.com/question/13432927
#SPJ1
please help me, i have a test soon :/
Answer:
-2 <= y <= 4
Step-by-step explanation:
-3 <= 2y + 1 <= 9
-4 <= 2y <= 8
-2 <= y <= 4
Answer:
-2 <= y <= 4
Step-by-step explanation:
-3 <= 2y + 1 <= 9
-4 <= 2y <= 8
-2 <= y <= 4
x^5y^5z^3 =?
A. bases are different, so this can't be done.
B. xy5z3
C. (xy)5z3
To simplify the indices expression x⁵y⁵z³, we can conclude that; A. bases are different, so this can't be done.
How to simplify Indices?We want to simplify the indices given as;
x⁵y⁵z³
Now, we can see that the bases are different and as such it means they cannot be simplified using laws of indices on the exponents.
This is because when the bases are different, the expression cannot be factored with the exponents being added, subtracted, divided or multiplied.
Thus, we will conclude that the bases are different, so this can't be done.
Read more about Indices at; https://brainly.com/question/15361818
#SPJ1
here were 34 bales of hay in the barn. Dan stacked more bales in the bar
today. There are now 64 bales of hay in the barn. How many bales did he store in the barn?
Ella's bait and tackle shop sold 128,107 live worms in april and 102,278 live worms in may to the nearest thousand how many worms did ella's bait and tackle shop sell in april and may together
Ella's bait and tackle shop sells 230,385 in April and May.
Based on the given conditions, formulate:
Bait and tackle sold in 128,278 live worms in April
Bait and tackle sold in 102,278 live worms in May
So the total number of Bait and tackles sold in April and May =
=128,107+102,278
= 230,385
To know more about the sum sold refer to the link given below:
https://brainly.com/question/25586322
#SPJ4
area of a parallelogram find the areas of the parallelograms whose vertices are given in exercises 35–40.
The area of parallelogram ABCD is found to be 2√3 square units.
What is parallelogram?A quadrilateral is known as a parallelogram in geometry. The opposite sides of a parallelogram are parallel & equal in length. Rhombus, rectangle, & square are a few examples of parallelograms.
We know that diagonal of such a parallelogram divides it into two equal triangles.
So, parallelogram area,
ABCD = 2× area of ΔABC (equation 1)
The area pf the triangle is found through the vertices are (x₁,y₁), (x₂,y₂), (x₃,y₃) is;
Area = (1/2)×[x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)]
The vertices of the triangles are given as;
A(2,4), B(2+ √3 ,5) and C(2,6)
Area = (1/2)×[2(5−6) + (2+√3)(6−4) + 2(4−5)]
Area = (1/2)×[−2+2(2+ √3)−2]
Area = √3
When we plug this value into equation (1),
Parallelogram area,
ABCD = 2×the area of ABC
ABCD = 2×√3
ABCD = 2√3
Thus, the area of the parallelogram ABCD id estimated as 2√3 square units.
To now more about the parallelogram, here
https://brainly.com/question/20526916
#SPJ4
The correct question is -
Find the area of a parallelogram ABCD if three of its vertices are A(2,4), B(2+ √3 ,5) and C(2,6)
v/9 - 7 = -8
I'll give brainliest!! please explain
By isolating the variable, we will see that the solution of the linear equation is v = -9
How to solve the linear equation?Here we have the following linear equation:
v/9 - 7 = -8
Where we can see that the variable is v. To solve this, we need to perform operations in both sides of the linear equation in a way such that the variable is isolated in one of the sides.
Adding 7 in both sides we get:
v/9 - 7 + 7 = -8 + 7
v/9 = -1
Now we multiply both sides by 9:
(v/9)*9 = -1*9 = -9
v = -9
We conclude that the solution of the linear equation is v = -9.
Learn more about linear equations:
https://brainly.com/question/1884491
#SPJ1
The granite sample has a
mass of 24. 31 g and a volume
of 9. 35 cm3. What is the
density of the granite?
d = [?] g/cm3
Which number would be found on the number line between 0 and -1
Answer: -.5 OR -.1, -.2, -.3, -.4, -.5, -.6,-.7,-.8,-.9
Step-by-step explanation: The simple answer is -.5, it is right in the middle of 0 and -1. The answer number is everything in between.
Help pleaseeeeeeeeee
Answer:
y2 = m*(x2 - x1) + y1
Step-by-step explanation:
m = (y2 - y1) / (x2 - x1)
y2 - y1 = m*(x2 - x1)
y2 = m*(x2 - x1) + y1
(write each as an algebratic expression) a cubed is equal to 31
Find the median and mean of the data set below:
Median = 1
201
49, 16, 5, 3, 6
Mean =
The mean and the median value of the given data set is 12.62 and 6.
According to the statement
We have to find that the mean and the median of the following data.
So, For this purpose, we know that the
The mean is found by adding all of the numbers together and dividing by the number of items in the set.
And
The median is the middle number in a sorted, ascending or descending list of numbers
From the given information:
The data set are:
1,20,1, 49, 16, 5, 3, 6
Then
According mean definition,
Mean = 1+20+1+ 49+ 16+ 5+ 3+6/8
Mean = 101/8
Mean = 12.625
Then
The data set is 1,3,5,6,16,20,49.
Median = 8 terms /2
Median = 4th term
Median = 6.
So, The mean and the median value of the given data set is 12.62 and 6.
Learn more about mean and the median here
https://brainly.com/question/2689808
#SPJ9
Which scales of data measurement are associated with quantitative data? interval and ratio ratio and nominal ordinal and interval nominal and ordinal
Interval and ratio scales of data measurement are associated with quantitative data.
Data measurement:- Data measurement is the way in which data can be subcategorized to analyze the data properly. Data can be classified into two types-
Quantitative data:- The data, which can be measured with numbers is called as quantitative data. Ex: duration, speed etc. This kind of data can be again subcategorized into two types-Discrete:- The data, which is of whole number, that can't be broken. Ex: a number of items.Continuous:- The data, which can be broken. Ex: height, weight etc. This type of data can be measured using interval and ratio measurement scales.Qualitative data:- The data, which is non-numerical value and categorical is called as qualitative data. Ex: yes, no responses or eye color etc. This type of data can be measured using nominal and ordinal measurement scales.Thus we can conclude that, Interval and ratio scales of data measurement are associated with quantitative data.
To know more about data measurement refer below link:
https://brainly.com/question/23894295
#SPJ4
11. The following describes the United States nuclear stockpile from
1944 to 1974. From 1944 to 1958, there was a gradual increase in the
number of warheads from 0 to about 5000. From 1958 to 1966, there
was a rapid increase in the number of warheads to a maximum of
about 32,000. From 1966 to 1970, there was a decrease in the number
of warheads to about 26,000. Finally, from 1970 to 1974, there was
a small increase to about 28,000 warheads. Sketch a graph of the
function.
10.
nxhudkdodisuhaiioavsbos
write the non-teerminating decimal as fraction 0.555555555...
Answer:
111111111/200000000
on the next play, the team gained 5 yards and then lost 6 yards. what is the total change in yards? 5- blank
= 5 + blank
= blank
help me schools tomorrow
Solve for x in the diagram below.
X =
хо
100°
3x°
Answer:
20
Step-by-step explanation:
the line equals 180 degrees total.
so subtract the angle we already know from the total...
180- 100=80
then, make an equation with the last two variables since we know both of them added together should equal 80
80=x +3x
Combine like terms
80=4x
Divide by 4
20=x
Kyle found the product of two rational expressions and identified the excluded values of the expression. However, he made a mistake in his work and included an extra number in his list of excluded values. His work is shown below.
Select the step where Kyle made his first mistake. Then select the number that should not be included in the list of excluded values.
Answer:
Step-by-step explanation:
Mistake in step 3 the (2x+1) and the (x-1) both cancel out but the other binomials (x + 3) and (x - 3) are different so don't cancel out.
Step 3 should be 3(x-3) / 4(x+3)
3 should not be an excluded value.
3. What is an equation of the line in slope intercept form? (1 point)
A.y=2x-2
B.y=-2x-2
C.y=-2x+2
D.y=2x+2
Answer:
C. y = 2x + 2
Step-by-step explanation:
There are 2 points on the line (0,2) and (-3,-4)
from (-3,-4) to (0,2), rise over run is 6/3 so slope is 2
You can calculate it too
m = (y2-y1)/(x2-x1)
m = (-4 - 2)/(-3 - 0) = -6/-3 = 2
Using m = 2, x = 0, y = 2
y = mx + b
2 = 2(0) + b
b = 2
therefore
y = 2x + 2
Multiply:
-2x(3x - 4)
Enter the correct answer
Answer:
- 6x² + 8x
Step-by-step explanation:
- 2x(3x - 4) ← multiply each term in the parenthesis by - 2x
= - 6x² + 8x
