Answer:
[tex]x=\dfrac{42}{13}[/tex]
Step-by-step explanation:
Given equation:
[tex]\dfrac{6}{(x^2-3x)}=\dfrac{12}{x}+\dfrac{1}{(x-3)}[/tex]
Factor the denominator on the left side:
[tex]\implies \dfrac{6}{x(x-3)}=\dfrac{12}{x}+\dfrac{1}{(x-3)}[/tex]
Combine the fractions on the right side by multiplying by the LCM:
[tex]\begin{aligned}\implies \dfrac{6}{x(x-3)} & =\dfrac{12}{x} \cdot \dfrac{(x-3)}{(x-3)}+\dfrac{1}{(x-3)} \cdot \dfrac{x}{x}\\\\& =\dfrac{12(x-3)}{x(x-3)}+\dfrac{x}{x(x-3)}\\\\& =\dfrac{12(x-3)+x}{x(x-3)} \end{aligned}[/tex]
As the denominators are now the same on both sides:
[tex]\begin{aligned}\implies \dfrac{6}{x(x-3)} & =\dfrac{12(x-3)+x}{x(x-3)}\\\\ \implies 6 & = 12(x-3)+x\end{aligned}[/tex]
Simplify and solve for x:
[tex]\begin{aligned}\implies 6 & = 12(x-3)+x\\\\6 & =12x-36+x\\\\6 & =13x-36\\\\13x & =42\\\\\implies x & =\dfrac{42}{13}\end{aligned}[/tex]
the graph of y = cos(x) was shifted downwards by 3 units, shrink horizontally by a fourth of a unit, inverted horizontally and shifted 60° to the left. if it has an amplitude of 5 units, write the equation of the resulting graph.
Using translation concepts, it is found that the equation of the resulting graph is given by:
[tex]y = 2.5(\cos{(4x - 60^\circ)} - 3)[/tex]
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
The parent function is given by:
[tex]y = \cos{x}[/tex]
The transformations are as follows:
Shift down of 3 units, hence [tex]y = \cos{x} - 3[/tex].Shrink horizontally by a fourth of a unit, hence [tex]y = \cos{(4x)} - 3[/tex].Inverted horizontally, hence [tex]y = \cos{-4x} - 3 = \cos{(4x)} - 3[/tex], as the cosine function is even.Shifted 60° to the left, hence [tex]y = \cos{(4x - 60^\circ)} - 3[/tex]Amplitude of 5 units, hence the function is multiplied by 5/2 = 2.5, that is, [tex]y = 2.5(\cos{(4x - 60^\circ)} - 3)[/tex].More can be learned about translation concepts at https://brainly.com/question/4521517
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can anyone help me solve this problem?
Answer:
-0.16875 or -27/16
Step-by-step explanation:
multiply whole numbers with denominator and add with numerator then divide
so it turns into (9/2) divided by (-8/3)
then use the keep change flip method
(9/2) x (-3/8)
now multiply
-27/16 or -0.16875
6.10^5 is how many times as large as 3.10^3
(8 kg 300 g 120 mg) − (3 kg 500 g 480 mg) 4 kg 799 g 640 mg
The value of (8 kg 300 g 120 mg) − (3 kg 500 g 480 mg) is; 4 kg 799 g 640 mg
How to carry out Unit Conversions?We want to find the value of;
(8 kg 300 g 120 mg) − (3 kg 500 g 480 mg)
First of all, let us convert all units to kg as;
120 mg = 0.00012 kg
300 g = 0.3 kg
Thus;
8 kg 300 g 120 mg = 8 + 0.3 + 0.00012 = 8.30012 kg
Similarly, converting the second expression;
480 mg = 0.00048 kg
500 g = 0.5 kg
Thus;
3 kg 500 g 480 mg = 3 + 0.5 + 0.00048 = 3.50048 kg
Thus, we have;
8.30012 kg - 3.50048 kg = 4.77964 kg
Breaking down this gives;
4 kg 799 g 640 mg
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Application of percentages
In an examination 25% of the candidates failed to obtain the pass mark The number of candidates who passed were 150 . How many candidates failed
Answer:
The answer is actually 50
Step-by-step explanation:
Based on the given conditions
formulate:
150 × 25% ÷ (1 - 25%)
150 × 0.35 = 37.5
1 - 0.25 0.75
Rewrite the fraction
3750 = 50
75
What is the sum of −4/5 and 2/3?
Answer:
-0.33333 (3 is repeating )
Step-by-step explanation:
jason was surveying students about their use of the new software lab in a school. Which question in the survey is a statistical question? How many hours do you spend developing software in the software lab? What is the number of learning stations at the software lab? Where is the software lab located in the school? What are the times the software lab is open?
HELP 10 MIN/ 66 points!
hope you can understand
Given g(x)=^3√x+6, on what interval is the function negative?
A (-∞, -6)
B (-∞, 6)
C (-6, ∞)
D (6, ∞)
The interval which the function is negative is (-∞, -6)
How to determine the interval?The equation of the function is given as:
[tex]g(x) = \sqrt[3]{x + 6}[/tex]
When the function is negative.
It means that g(x) is less than 0
i.e. g(x) < 0
So, we have:
[tex]\sqrt[3]{x + 6} < 0[/tex]
Take the cube of both sides
x + 6 < 0
Subtract 6 from both sides
x < -6
The above represents a value from negative infinity to -6
i.e. (-∞, -6)
Hence, the interval which the function is negative is (-∞, -6)
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Which equation represents a line that passes through (4, left-parenthesis 4, StartFraction one-third EndFractin right-parenthesis.) and has a slope of StartFraction 3 Over 4 EndFraction.?
y – y minus StartFraction one-third EndFraction equals StartFraction 3 Over 4 EndFraction left-parenthesis x minus 4 right-parenthesis. = y minus StartFraction 3 Over 4 EndFraction equals StartFraction one-third EndFraction left-parenthesis x minus 4 right-parenthesis.(x – 4)
y – y minus StartFraction one-third EndFraction equals 4 left-parenthesis x minus StartFraction 3 Over 4 EndFraction right-parenthesis. = y minus StartFraction one-third EndFraction equals StartFraction 3 Over 4 EndFraction left-parenthesis x minus 4 right-parenthesis.(x – 4)
y – y minus StartFraction one-third EndFraction equals 4 left-parenthesis x minus StartFraction 3 Over 4 EndFraction right-parenthesis. = 4(x – )
y – 4 = y minus 4 equals StartFraction 3 Over 4 EndFraction left-parenthesis x minus StartFraction one-third EndFraction right-parenthesis.(x – )
The equation represents a line that passes through(4, 1/3) and has a slope of 3/4 option A; y - 1/3 = 3/4 ( x - 4).
What is the Point-slope form?
The equation of the straight line has its slope and given point.
If we have a non-vertical line that passes through any point(x1, y1) has gradient m. then general point (x, y) must satisfy the equation
y-y₁ = m(x-x₁)
Which is the required equation of a line in a point-slope form.
we know that
The equation of the line into point-slope form is equal to
y-y₁ = m(x-x₁)
we have
(x₁, y₁) = (4, 1/3)
m = 3/4
substitute the given values
y-y₁ = m(x-x₁)
y - 1/3 = 3/4 ( x - 4)
therefore,
y minus StartFraction one-third EndFraction equals StartFraction 3 Over 4 EndFraction left-parenthesis x minus 4 right-parenthesis.(x – 4)
Thus, option A is correct.
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What is the value of x? 2 3 6 7
Answer:
The answer is 2 or A
sorry if wrong
what is 3+7, i got 346 but i dont know if its right
Answer:
10
Step-by-step explanation: The sum of 3+7 is 10
Answer:
10
Step-by-step explanation:
3+7 is 10
if you add 1 on to 7 three times, we get
8,9,10
(i know this is a troll question lol)
hope this helps!
give brainliest :)
Two sides of an acute triangle meaure 5 inches and 8 inches. The length of the longest side is unknown. What is the greatest possible whole-number length of the unknown side?
The greatest whole possible whole number length of the unknown side is 9 inches.
How to identify if a triangle is acute?Let us have:
H = biggest side of the triangle
And let we get A and B as rest of the two sides.
Then we get:
If
[tex]A^2 + B^2 < C^2[/tex]
then the triangle is acute
Two sides of an acute triangle measure as 5 inches and 8 inches
The length of the longest side is unknown.
We have to find the length of the unknown side
WE know that the longest side of any triangle is a hypotenuse
For an acute triangle we know:
[tex]A^2 + B^2 < C^2[/tex]
Here in this sum,
a = 5 inches
b = 8 inches
c = ?
Substituting we get,
[tex]A^2 + B^2 < C^2\\\\5^2 + 8^2 < C^2\\\\25 + 64= C^2[/tex]
c < 9
Hence, The greatest whole possible whole number length of the unknown side is 9 inches.
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Will’s meal of grilled chicken strips and carrots contained a total of 333 calories. The bag of grilled chicken strips contained x servings of 110 calories each. The bag of carrots contained y servings of 29 calories each. Which equation written in standard form represents the number of servings of chicken strips and carrots that Will may have eaten?
The equation written in standard form represents the number of servings of chicken strips and carrots that Will may have eaten is:
x*110 + y*29 = 333
Which equation written in standard form represents the number of servings Will may have eaten?
We know that he consumed a total of 333 calories.
Chicken strips have 110 calories.Each carrot contains 29 calories.There are x chicken strips and y carrots, so we must have that:
x*110 + y*29 = 333
That is the equation in standard form that we must solve to find how many carrots and how many chicken strips he ate.
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a rectangle with a perimeter of 30 centimeters is twice as long as it is wide. what is the area of the rectangle in square centimenters?
Answer:
50cm squared
Step-by-step explanation:
Imagine the width is 'a'
Then the length will be 2a as it's twice as wide as it's long.
The formula for perimeter is 2(L+W)
If we subsitute the algebra/numbers in we get
P = 2(L+W)
30 = 2(2a+a)
30 = 2(3a)
30 = 6a
5 = a
a = 5cm
Then the area is the following
A = LW
A = 2a(a)
A = (2(5))(5)
A = 10(5)
A = 50cm squared
If two variables have a correlation coefficient of r=0.625 which statement below best represents the relationship?
Answer:
There is a moderate positive linear association between the variables
Step-by-step explanation:
Since 0.5<r<0.7, there is a moderate positive linear association between the variables. The closer r is to 1, the stronger the positive linear association.
A point has been translated left and down. Based on the graph, which could be true? Check all that apply. A is the image of C. A is the image of D. B is the image of D. B is the image of E C is the image of A. C is the image of D. D is the image of E. please please hurry with the answers.
From the image that we have here, the translation of the image would be:
B is the image of D. B is the image of E.C is the image of D.What is translation in mathematics?In the field of mathematics, this is the type of transformation which would take points in an image and move it in similar distance and direction.
It has to do with the movement of points in an horizontal manner or in a vertical manner.
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A population of sea turtles decreases by 25% per year. The population size is currently 1,024. Which expression calculates the population x years From now?
The expression calculates the population x years from now will be given as y = 1024 (0.75)ˣ.
What is an exponent?Consider the function:
y = a (1 ± r) ˣ
Where x is the number of times this growth/decay occurs, a = initial amount, and r = fraction by which this growth/decay occurs.
If there is a plus sign, then there is exponential growth happening by r fraction or 100r %
If there is a minus sign, then there is exponential decay happening by r fraction or 100r %
The population of sea turtles decreases by 25% per year. The population size is currently 1,024.
Let y be the population of sea turtles and x be the number of years.
Then we have
y = 1024 (1 - 0.25) ˣ
y = 1024 (0.75) ˣ
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Please help!!
Explain the difference between using the cosine ratio to solve for a missing angle in a right
triangle versus using the secant ratio. You must use complete sentences and any evidence
needed (such as an example) to prove your point of view.
In trigonometry, secant in a right triangle, is the reciprocal of the cosine of an angle symbol: sec while cosine is in a right triangle, is the ratio of the length of the side adjacent to an acute angle to the length of the hypotenuse.
The cosine of an angle is the ratio of the length of the side adjacent to the angle divided by the length of the hypotenuse of the triangle. The cosine of ∠A will be abbreviated as cos ∠A
The secant of x is 1 divided by the cosine of x: sec x = 1 cos x , and the cosecant of x is defined to be 1 divided by the sine of x: csc x = 1 sin x .
Answer:
Step-by-step explanation:
Suppose a right triangle ABC in which
BC=3 units and AC=5 unit and angle B=90 degree
Let x be the missing angle of right triangle
We know that
Hence, there is no difference between using cosine ratio to solve for a missing angle in a right triangle versus using the secant ratio.
quadratic formula
[tex] {4v}^{2} - 16v + 7 = 0[/tex]
Please help
[tex]~~~~~~~~~~~~\textit{quadratic formula} \\\\ \stackrel{\stackrel{a}{\downarrow }}{4}v^2\stackrel{\stackrel{b}{\downarrow }}{-16}v\stackrel{\stackrel{c}{\downarrow }}{+7}=0 \qquad \qquad v= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a} \\\\\\ v= \cfrac{ - (-16) \pm \sqrt { (-16)^2 -4(4)(7)}}{2(4)} \implies v= \cfrac{ 16 \pm \sqrt { 256 -112}}{ 8 } \\\\\\ v=\cfrac{16\pm\sqrt{144}}{8}\implies v=\cfrac{16\pm 12}{8}\implies v= \begin{cases} \frac{7}{2}\\[1em] \frac{1}{2} \end{cases}[/tex]
Points ABC forms a right triangle.
A: (-2,4) B: (5,0) C: (2,6)
The sum of the squares of the lengths of the legs of the triangle is?
The square of the length of the hypotenuse of the triangle is?
The sum of squares of the lengths of the triangle is 130 and the square of the length of the hypotenuse is 65
What is a right-angled triangle?This is a triangle with 3 sides and one side is called the hypotenuse which faces one of the angles 90°
Analysis:
distance between two points = [tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2} }[/tex]
distance AB with coordinates A(-2,4) B(5,0) = [tex]\sqrt{(5 - -2)^{2} + (0 - 4)^{2} }[/tex] = [tex]\sqrt{65}[/tex]
distance AC with coordinates A ( -2,4) C(2,6) = [tex]\sqrt{(2--2)^{2} + (6-4)^{2} }[/tex] = [tex]\sqrt{20}[/tex]
distance BC with coordinates B(5,0) C(2,6) = [tex]\sqrt{(2-5)^{2} + (6-0)^{2} }[/tex] = [tex]\sqrt{45}[/tex]
sum of squares of the lengths = [tex](\sqrt{45} )^{2}[/tex] + [tex](\sqrt{65}) ^{2}[/tex] + [tex](\sqrt{20}) ^{2}[/tex] = 65 + 45 + 20 = 130
the square of the length of the hypotenuse = 65
In conclusion, the sum of the squares of the three length is 130 and the square of the hypotenuse is 65
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Write a power function representing the verbal statement. (Let k represent the constant of proportionality)
A quantity W is inversely proportional to the square root of a quantity n.
W(n)=
Answer:
W = k·n^(-1/2)
Step-by-step explanation:
When two quantities are proportional, their relationship can be described by the linear equation y = kx, where k is the constant of proportionality.
Saying two quantities are inversely proportional is the same as saying one is proportional to the inverse of the other. Then "inversely proportional to the square root" is the same as "proportional to the inverse of the square root."
__
W is inversely proportional to the square root of n, so we have ...
[tex]W=k\cdot\dfrac{1}{\sqrt{n}} = \dfrac{k}{n^{\frac{1}{2}}}\\\\\boxed{W=kn^{-\frac{1}{2}}}[/tex]
_____
Additional comment
The rules of exponents let us write the square root as a fractional power, and the inverse as a negative power. Thus our power function ends up with a negative fractional power.
The Power function representing the verbal statement is W = k.[tex]n^{1/2}[/tex].
What is the Power function?A power function is in the form of f(x) = kxⁿ, where k = all real numbers and n = all real numbers. You can change the way the graph of a power function looks by changing the values of k and n.
When two quantities are proportional, their relationship can be described by the linear equation y = kx, where k is the constant of proportionality.
Now "inversely proportional to the square root" is the same as "proportional to the inverse of the square root."
According to question,
W α 1/√n
W = k/√n
W = k.[tex]n^{-1/2}[/tex]
Thus, the Power function representing the verbal statement is W = k
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Simplify:
-11√21-11√/21
Step-by-step explanation:
by using the radical and suds rule
Which is true about the functional relationship shown in the graph?
Cost of Apples
0
2
3
Weight (pounds)
A. The cost of the apples is a function of their weight.
B. The weight of the apples is a function of the number of apples.
C. The cost of the apples is a function of the type of apples.
D. The weight of the apples is a function of their cost.
Cost ($)
28882889882
110
100
90
80
70
50
40
30
20
10
its b Answer:
Step-by-step explanation:
The cost of the apples is a function of their weight option (A) is correct because the independent variable (x) is the weight of the apples.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
The options are:
A. The cost of the apples is a function of their weight.B. The weight of the apples is a function of the number of apples.C. The cost of the apples is a function of the type of apples.D. The weight of the apples is a function of their cost.From the graph:
The y-axis is representing the cost(c) of the apples in dollars and
The x-axis is representing the weight(w) of the apples in pounds.
c = f(w)
The independent variable (w) is the weight of the apples
The dependent variable (c) is the cost of the apples
Thus, the cost of the apples is a function of their weight option (A) is correct because the independent variable (w) is the weight of the apples.
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What is it asking me to do?
A landscaping company charges $44 per cubic yard of mulch plus a delivery charge of $22. Find a linear function which computes the total cost C (in dollars) to deliver x cubic yards of mulch
c(x)=
The linear function which computes the total cost C (in dollars) to deliver x cubic yards of mulch is C(x) = 44x + 22
How to find a linear function?Charges per cubic yard = $44Delivery charge = $22cubic yards of mulch = xUsing the slope-intercept form (y = mx +b),
The delivery charge of $22 is a constant and will represent the y-intercept.
The $44 per cubic yard of mulch will represent the slope.
Therefore,
C(x) = 44x + 22
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Question 9 of 13
Which of the following scatterplots represents the data shown below?
(1,31), (2,8), (3, 38), (4, 14), (5, 22), (6, 31), (7, 27), (8, 47),
(9,34), (10,3), (11, 33), (12, 35)
The attached graph represents the scatter plot of the points
How to determine the scatter plot?The lists of options are not given. So, I will plot the points and upload the scatter plot as an attachment.
The points are given as:
(1,31), (2,8), (3, 38), (4, 14), (5, 22), (6, 31), (7, 27), (8, 47), (9,34), (10,3), (11, 33), (12, 35)
The above points would be plotted using the following scale:
x: axis -> 1 interval = 10 unitsy: axis -> 1 interval = 10 unitsSee attachment for the scatter plot
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Mission Company is preparing its annual profit plan. As part of its analysis of the profitability of individual products, the controller estimates the amount of overhead that should be allocated to the individual product lines from the information provided below. (CMA based)
Wall Mirrors Specialty Windows
Units Produced 40 20
Material moves per product line 5 15
Direct labor hours per product line 200 300
Budgeted material handling costs: $50,000
Under a traditional costing system that allocates overhead on the basis of direct labor hours, the materials handling costs allocated to one unit of Specialty Windows would be:
Answer:
Arrange the following number in descendig otder
write an article for publication into the school's magazine on three effects of indiscipline and suggest about three ways of arresting the menace
Answer:
East West Point E.W English School's effects and solutions of indiscipline Effects.peer influence.Teacher's immoral relationship.Poor attitude of teachers to work Solutions .Review children's act to incorporate emerging issues.Indiscipline students be absorbed into correctional schools.That student involved in criminal activities be treated as criminals and dealt with in accordance with lawStep-by-step explanation:.......Question 8
Select the solution to the following system of equations:
3x+2y=0
-x-y=1
Answer:
-x-y=1
-x= 1+y
x= -1-y
3x+2y=0
3(-1-y) +2y=0
-3-3y+2y=0
-3-y=0
y= -3
x= -1-(-3)
x= -1+3
x= 2
Therefore, x= 2 and y= -3
A number is divided in the ratio 5:9. If the first part is 35, find the number.
A number is divided in the ratio of 5:9. If the first part is 35, the number will be 7.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
A number is divided in the ratio of 5:9. If the first part is 35, then we need to find the number.
By unitary method
5x = 35
x = 7
Then the other number will be
9x = 9(7)
= 63
Thus, A number is divided in the ratio of 5:9. If the first part is 35, the number will be 7.
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Please help!!! Whats 7/9 x 5 2/5
Answer:
[tex] \frac{7}{9} \times 5 \frac{2}{5} = \frac{21}{5} \\ [/tex]
Step-by-step explanation:
[tex]5 \frac{2}{5} = \frac{5 \times 5 + 2}{5} = \frac{27}{5} \\ [/tex]
[tex] \frac{7}{9} \times \frac{27}{5} \\ [/tex]
[tex] \frac{7 \times 27}{9 \times 5} \\ [/tex]
[tex] \frac{7 \times 3}{5} = \frac{21}{5} \\ [/tex]