Answer:
[tex]The \ two \ numbers \ are \ \frac{1}{6} \ and \ \frac{5}{6}[/tex]
Step-by-step explanation:
Let the two numbers be = x , y
Given:
One of the number is 5 times other number, that is y = 5x ----- ( 1 )
The sum of their reciprocals is 36/5 , that is
[tex]\frac{1}{x} + \frac{1}{y} = \frac{36}{5}[/tex] ------ ( 2 )
Substitute y in the second equation.
[tex]\frac{1}{x} + \frac{1}{5x} = \frac{36}{5}\\\\\frac{1 \times 5}{5 \times x} + \frac{1}{5x} = \frac{36}{5}\\\\\frac{5}{5x} + \frac{1}{5x} = \frac{36}{5}\\\\\frac{5+1}{5x} = \frac{36}{5}\\\\\frac{6}{5x} =\frac{36}{5}\\\\36 \times 5x = 6 \times 5\\\\x = \frac{6 \times 5}{36 \times 5} = \frac{1}{6}[/tex]
Substitute x in first equation.
[tex]y = 5x\\\\y = 5 \times \frac{1}{6} \\\\y = \frac{5}{6}[/tex]
Please tell me how to do it thank you
Answer:
First set: 0.95. Second set: 0.86. Third set: 0.88.
Step-by-step explanation:
Imagine that these are not decimals, they are regular numbers (for example: 0.88 is turned into 88). You would determine which one is the greatest depending on which one is higher (like 44 is higher than 32). Therefor the first set: 0.95 the second set: 0.86 the third set: 0.88.
Find x
x³ + 3x - 14 = 0
x³ + x² - x² - x + 4x + 4 = 18
x²(x + 1) - x(x + 1) + 4(x + 1) = 18
(x + 1)(x² - x + 4) = 18
x² - x + 4 = 18/(x + 1)
x² - x + 4 - 6 = 18/(x + 1) - 6
x² - x - 2 = 18/(x + 1) - 6
(x - 2)(x + 1) = (18 - 6(x + 1))/(x + 1)
(x - 2)(x + 1) = (18 - 6x - 6)/(x + 1)
(x - 2)(x + 1) = (12 - 6x)/(x + 1)
(x - 2)(x + 1) = (-6(x - 2))/(x + 1)
x + 1 = (-6(x - 2))/(x + 1)(x - 2)
x + 1 = -6/(x + 1)
(x + 1)² = -6
x² + 2x + 8 = 0
x = (-b +- √(b² - 4ac))/2a
x = (-2 +- √(4 - 32))/2
x = (-2 +- √(-28)/2
x = (-2 +- i√28)/2
Something's wrong.
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { \: x = - 1 \: + \: i \sqrt{6} \:(or) \: \: x = - 1 \: -\: i \sqrt{6} }}}}}}[/tex]
And[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {x\:=\:2}}}}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
[tex] \: {x}^{3} + 3x - 14 = 0[/tex]
➺[tex] \: {x}^{2} (x + 1) - x(x + 1) + 4(x + 1) = 18[/tex]
➺[tex] \: (x + 1)( {x}^{2} - x + 4) = 18[/tex]
➺[tex] \: {x}^{2} - x + 4 = \frac{18}{(x + 1)} [/tex]
➺[tex] \: {x}^{2} - x + 4 - 6 = \frac{18}{(x + 1)} - 6[/tex]
➺[tex] \: (x - 2)(x + 1) = \frac{18 - 6(x + 1)}{(x + 1)} [/tex]
➺[tex] \: (x - 2)(x + 1) = \frac{18 - 6x - 6}{(x + 1)} [/tex]
➺[tex] \: (x - 2)(x + 1) = \frac{12 - 6x}{(x + 1)} [/tex]
➺[tex] \: (x - 2)(x + 1) = \frac{ - 6(x - 2)}{(x + 1)} [/tex]
➺[tex] \: (x + 1 )² = \frac{ - 6(x - 2)}{(x + 1)(x - 2)} [/tex]
➺[tex] \: (x + 1)² = \frac{ - 6}{(x + 1)} [/tex]
[tex]\sf\pink{Error\:corrected\:here. }[/tex]
➺[tex] \: {x}^{2} + 2x + 1 = - 6[/tex]
➺[tex] \: {x}^{2} + 2x + 7 = 0[/tex]
By quadratic formula, we have
➺[tex] \: x = \frac{ - b± \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]
➺[tex] \: x = \frac{ - 2± \sqrt{ {2}^{2} - 4.1.7} }{2 \times 1} [/tex]
➺[tex]x = \frac{ - 2± \sqrt{ - 24} }{2 } [/tex]
➺[tex] \: x = \frac{ - 2± \sqrt{ - 1 \times 4 \times 6} }{2} [/tex]
➺[tex] \: x = \frac{ - 2± \sqrt{ - 1} \times \sqrt{4} \times \sqrt{6} }{2} [/tex]
➺[tex] \: x = \frac{ - 2 \: ± \: i \times 2 \times \sqrt{6} }{2} [/tex]
➺[tex] \: x = \frac{ - 2 \: ± \:i \: 2 \sqrt{6} }{2} [/tex]
➺[tex] \: x = \frac{ 2 \: ( - 1 \: ± \: i \: \sqrt{6}) }{2} [/tex]
➺[tex] \: x = - 1 \: ± \: i \sqrt{6} [/tex]
Therefore, the two values of [tex]x[/tex] are ([tex] \: - 1 \: + \: i \sqrt{6}[/tex]) and ([tex] \: - 1 \: -\: i \sqrt{6}[/tex]).
Let us look at another method.[tex]x[/tex]³ + 3 [tex]x[/tex] - 14 = 0
➼ [tex]x[/tex]³ + 3 [tex]x[/tex] = 14
➼ [tex]x[/tex] ( [tex]x[/tex]² + 3 ) = 14
Factors of 14 = 1, 2, 7 and 14.
a) Substituting [tex]x\:=\:1[/tex], we have
➼ 1 ( 1 + 3 ) ≠ 14
➼ 1 x 4 ≠ 14
➼ [tex]\boxed{ 4\: ≠ \:14 }[/tex]
b) Substituting [tex]x\:=\:2[/tex], we have
➼ 2 ( 2² + 3 ) = 14
➼ 2 ( 4 + 3 ) = 14
➼ 2 x 7 = 14
➼ [tex]\boxed{ 14 \:= \:14 }[/tex]
c) Substituting [tex]x\:=\:7[/tex], we have
➼ 7 ( 7² + 3 ) ≠ 14
➼ 7 ( 49 + 3 ) ≠ 14
➼ 7 x 52 ≠ 14
➼ [tex]\boxed{ 364\: ≠ \:14 }[/tex]
d) Substituting [tex]x\:=\:14[/tex], we have
➼ 14 ( 14² + 3 ) ≠ 14
➼ 14 x 199 ≠ 14
➼ [tex]\boxed{ 2786\: ≠ \:14 }[/tex]
Hence, our only real solution is 2.
[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]
If P = (7,-4), Find:
(180° (P)
([?], []
Enter
Step-by-step explanation:
the answer is in the above image
Choose the function whose graph is given by: A. y=tan(x+1)-pi B. y=tan(x-pi)-1 C. y=tan(x-pi)+1 D. y=tan(2(x+pi))-1
Aver si le entiendes bro
The graph of the function f(x)=4/5 sqrt x is shown.
What is the domain of the function?
Answer:
All real number greater than equal to zero.
Step-by-step explanation:
The function is given by
[tex]f(x) = \frac{4}{5}\sqrt x[/tex]
The domain is defined as the input values so that the function is well defined.
here, the values of x should be all real number and zero also.
So, the correct option is (d).
Answer:
D
Step-by-step explanation:
ano ang area ng isang maliit na parisukat
Answer:
Area of square = Side²
Step-by-step explanation:
The area of a 2-D region, form, or flattened lamina in the planes is the quantity that represents its extent. On the 2-D surface or 3-D object, surface is its counterpart. A shape's area can be calculated by comparing it to squares of a specific size.
Area of square = Side²
The table shows a linear relationship between x and y.
х
у
-20
96
-12
60
-6
33
-2
15
What is the rate of change of y with respect to x?
Answer:
[tex] -\frac{9}{2} [/tex]
Step-by-step explanation:
Rate of change of x and y can be calculated using the following formula and using any two given pair of values from the table:
Rate of change = [tex] \frac{y_2 - y_1}{x_2 - x_1} [/tex]
Using (-12, 60) and (-6, 33).
Where,
[tex] (-12, 60) = (x_1, y_1) [/tex]
[tex] (-6, 33) = (x_2, y_2) [/tex]
Plug is the values
Rate of change = [tex] \frac{33 - 60}{-6 -(-12)} [/tex]
Rate of change = [tex] \frac{-27}{6} [/tex]
Simplify
Rate of change = [tex] \frac{-9}{2} [/tex]
Rate of change = [tex] -\frac{9}{2} [/tex]
order of operation problem who two operations inside parentheses and two ex outside ( using all add, subtract, multiply and divide)
PLEASE SHOW ALL WORK
Answer:
17 + 123 (4 - 1) + (36 / 18) 52 =
17 + 123 x 3 + 2 x 52 =
17 + 369 + 104 =
17 + 473 =
490
Step-by-step explanation:
hope this helps! i made up everything so i hope its okay!
If the distance from D to D' is 10 and the distance from A to D is 2 what is the scale factor?
Answer:
5
Step-by-step explanation:
10/2=5
The scale factor of the given case that the distance from D to D' is 10 and the distance from A to D is 2 will be 5.
What is the scale factor?
The ratio between comparable measurements of an object and a representation of that object is known as a scale factor in mathematics.
The scale factor is the ratio between two big and small figures and the ratio is called a scale for the given geometry.
For example, if we have a triangle with a side of 10 meters and another triangle with a side of 5 then the scale ratio will be 10/5 = 2.
Given that
distance from D to D' is 10
distance from A to D is 2
So the scale ratio will be
DD'/AD = 10/2 = 5 hence scale ratio will be 5 for the given
geometry.
For more about scale ratio,
https://brainly.com/question/13770371
#SPJ2
Which function is shown in the graph below?
Answer:y=log1x
Step-by-step explanation:
2x – 3(X + 8) = -21
Solve for x step by step
Please answer quickly
Answer:
x = -3
Step-by-step explanation:
2x – 3(x + 8) = -21
Distribute
2x - 3x - 24 = -21
Combine like terms
-x - 24 = -21
Add 24 to both sides
-x = 3
Multiply both sides by -1
x = -3
3.7 pounds of meat costs $20.35. What is the price per pound?
Answer:
$5.5 per pound of meat
Step-by-step explanation:
$20.35 ÷ 3.7 = $5.50
Hope this is helpful
Which shows the following expression after the negative exponents have been eliminated?
Step-by-step explanation:
The given expression is :
[tex]\dfrac{a^3b^{-2}}{ab^{-4}}[/tex]
We need to simplify the above expression.
a³ is in numerator and a is in denominator. It gts cancelled.
[tex]\dfrac{a^3b^{-2}}{ab^{-4}}=\dfrac{a\times a\times a\times b\times b\times b\times b}{a\times b \times b}\\\\=\dfrac{a^2\times b^{-2}\times b^4}{1}\\\\=\dfrac{a^2}{b^{-2}}[/tex]
Hence, this is the required solution.
Convert the following improper fraction to a whole number or a mixed number: 41/6
Answer:
6 and 5 over 6
6 5/6
Step-by-step explanation:
it would be a mixed fraction because 6 can't go into 41 evenly
Answer:
6
Hope that this helps!
Write the expression. Then, complete the statements.
twice the difference of a number and seven
The word "twice" means multiplication by 2 v
The words "the difference of indicate
Rationalize the denominator of the fraction and enter the new denominator below.
Answer:
7/19
Step-by-step explanation:
7/19=square root of 11=22-3 19
Find an equation for the line with the given property. (a) It passes through the point (2, −6) and is parallel to the line 4x + y − 10 = 0.
It has x-intercept 6 and y-intercept 4.
Answer:
[tex]y = -4x + 2[/tex]
Step-by-step explanation:
Required
Determine the equation
From the question, we understand that, it is parallel to:
[tex]4x + y -10 = 0[/tex]
This means that they have the same slope.
Make y the subject to calculate the slope of: [tex]4x + y -10 = 0[/tex]
[tex]y = -4x + 10[/tex]
The slope of a line with equation [tex]y =mx + c[/tex] is m
By comparison:
[tex]m = -4[/tex]
So, the slope of the required equation is -4.
The equation is then calculated as:
[tex]y = m(x - x_1) + y_1[/tex]
Where:
[tex](x_1.y_1) = (2,-6)[/tex]
So, we have:
[tex]y = -4(x - 2) -6[/tex]
Open bracket
[tex]y = -4x + 8 -6[/tex]
[tex]y = -4x + 2[/tex]
what if cars did not exist plz be original
Answer:
If cars did not exist people could do as the did before they were invented. Such as walk to where they need to go or use a horse and buggy or carriage.
Step-by-step explanation:
Help please!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
From Left (earliest) to Right (most recent)
First Pharaoh 3100 BC
First Babylon 1830 BC
First Mali 1235 CE
First US President 1789 CE
There are 750 identical plastic chips numbered 1 through 750 in a box. What is the probability of reaching into the box and randomly drawing a chip number that is smaller than 627
Answer:
0.8358 = 83.58% probability of reaching into the box and randomly drawing a chip number that is smaller than 627
Step-by-step explanation:
Uniform probability distribution:
An uniform distribution has two bounds, a and b.
The probability of finding a value of at lower than x is:
[tex]P(X < x) = \frac{x - a}{b - a}[/tex]
There are 750 identical plastic chips numbered 1 through 750 in a box
This means that [tex]a = 1, b = 750[/tex]
What is the probability of reaching into the box and randomly drawing a chip number that is smaller than 627?
[tex]P(X < x) = \frac{627 - 1}{750 - 1} = 0.8358[/tex]
0.8358 = 83.58% probability of reaching into the box and randomly drawing a chip number that is smaller than 627
peter bought 3 suits and 3 pairs of jeans and paid $2397. James bought 8 suits and 11 pairs of jeans and paid $6989. What is the price of each?
Answer:
Therefore each suit cost $600 and each jean cost $199
Step-by-step explanation:
Let x represent the price of each suit and let y represent the price of each jeans.
Since 3 suits and 3 pairs of jeans cost $2397, this can be represented by the equation:
3x + 3y = 2397
Dividing through by 3:
3x/3 + 3y.3 = 2397/3
x + y = 799 (1)
Also, 8 suits and 11 pairs of jeans cost $6989, this can be represented by the equation:
8x + 11y = 6989 (2)
To find x and y, solve equation 1 and 2 simultaneously. Multiply equation 1 by 8 and subtract from equation 2 to get y:
3y = 597
y = $199
Put y = $199 in equation 1:
x + 199 = 799
x = $600
Therefore each suit cost $600 and each jean cost $199.
If a normal distribution has a mean of 154 and a standard deviation of 15,
what is the value that has a z-score of 1.6?
Answer:
The correct answer is - 178.
Step-by-step explanation:
The standard deviation is a measure of the amount of dispersion in a set of values.
Given:
Mean of a normal distribution (m) = 154
Standard deviation (s) = 15
z-score = 1.6
Solution:
To find: value (x) that has a z-score of 1.6
z-score is given by = x-u/15
1.6*15 = x-154
=> 154+24 = x
x = 178
In a bread recipe, the ratio of milk
to flour is 5 to 4. If 7 cups of flour
are used, how many cups of milk
are used?
What is the slope of the line that passes through the points (10, 5) and (15,20)? Write your answer in simplest form.
Answer:
3
Step-by-step explanation:
(10, 5) and (15,20)
m = rise/run
m = ∆y/∆x
m = (y₂ - y₁) / (x₂ - x₁)
m = (20 - 5) /(15 - 10)
m = 15/5
m = 3
It costs $21.50 to enter an amusement park and $0.50 to ride a ride. You have $24. Write an equation that represents the number r of rides you can ride.
Answer:
$24.00=$21.50+r*$.50
Step-by-step explanation:
total cost= entrance fee + r (number of rides) * $0.50 (cost of rides)
$24.00=$21.50+r*$.50
2.50=r*.50
2.5/.5=r
r=5
Need help on this question been stuck on it
Answer:
Exponential Function
Step-by-step explanation:
y values increase by x4
Answer:
exponential function
the ans is b
A parallelogram has sides 8 ft and 6 ft and an area of 54 ft 2. What is the length of the
altitude to the 8-ft base?
Step-by-step explanation:
there is something wrong with your question.
there is no parallelogram with 8 and 6 ft side lengths that has an area of 54 ft².
the maximum area of a parallelogram with 8 and 6 ft side lengths is 48 ft². and that is a rectangle 8×6 as a special form of a parallelogram.
the area of any parallelogram is calculated
Ap = base length × height
and height is the length of the line perpendicular to the base line to one of the corners on the opposite side (as long as the base line).
if Ap = 54, and the base length is 8, this means
54 = 8 × height
height = 54/8 = 6.75 ft
but the height can only be the length of a side connected to the base line or less. not longer.
and in our example here, this connected side is 6. so, the height can only be 6 or less. not 6.75.
so, there must be something wrong with your numbers.
once you get the actual numbers, use my approach above with them (replace whatever number is wrong here by the true value).
In the questions below suppose the variable x represents students and represents courses, and:
•M(y): y is a math course F(x): x is a freshman
•B(x): x is a full-time student T(x,y): x is taking
•Write the statement in good English without using variables in your answers.
Answer:
Here the answer is given as follows,
Step-by-step explanation:
The last three parts are coming with a question mark, so can't answer those parts. post the image or write it properly
a) Every student is taking at least one course.
[tex]\forall x \exists y T(x,y)[/tex]
So for all x, there is a y such that T(x,y) is a true will be given by the above statement
b) There is a part-time student who is not taking any math courses.
[tex]\exists x \forall y [A(x) \Lambda (M(y) \rightarrow ~T(x,y))][/tex]
can anyone help please??
A concession stand at an athletic event is trying to determine how much to sell cola and iced tea for in order to maximize revenue. Let x be the price per cola and y the price per iced tea. Demand for cola is 100 – 34x + 5y colas per game and iced tea is 50 + 3x – 16y iced teas per game The concession stand should charge: dollars per cola, dollars per iced tea, in order to maximize revenue. The maximum revenue for one game is: dollars.
Solution :
Demand for cola : 100 – 34x + 5y
Demand for cola : 50 + 3x – 16y
Therefore, total revenue :
x(100 – 34x + 5y) + y(50 + 3x – 16y)
R(x,y) = [tex]$100x-34x^2+5xy+50y+3xy-16y^2$[/tex]
[tex]$R(x,y) = 100x-34x^2+8xy+50y-16y^2$[/tex]
In order to maximize the revenue, set
[tex]$R_x=0, \ \ \ R_y=0$[/tex]
[tex]$R_x=\frac{dR }{dx} = 100-68x+8y$[/tex]
[tex]$R_x=0$[/tex]
[tex]$68x-8y=100$[/tex] .............(i)
[tex]$R_y=\frac{dR }{dx} = 50-32x+8y$[/tex]
[tex]$R_y=0$[/tex]
[tex]$8x-32y=-50$[/tex] .............(ii)
Solving (i) and (ii),
4 x (i) ⇒ 272x - 32y = 400
(ii) ⇒ (-) 8x - 32y = -50
264x = 450
∴ [tex]$x=\frac{450}{264}=\frac{75}{44}$[/tex]
[tex]$y=\frac{175}{88}$[/tex]
So, x ≈ $ 1.70 and y = $ 1.99
R(1.70, 1.99) = $ 134.94
Thus, 1.70 dollars per cola
1.99 dollars per iced ted to maximize the revenue.
Maximum revenue = $ 134.94