[tex]\large\displaystyle\text{$\begin{gathered}\sf \left(\frac{4}{10}\times x\right)-(2 \times x)+\frac{8}{5}=\frac{4}{5} \end{gathered}$}[/tex]
Reduce the fraction 4/10, to its minimum expression, extracting and canceling 2.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \frac{2}{5}x-2x+\frac{8}{5}=\frac{4}{5} \end{gathered}$}[/tex]Combine [tex]\bf{\frac{2}{5}x }[/tex] and -2x to get [tex]\bf{-\frac{8}{5}x}[/tex].
[tex]\large\displaystyle\text{$\begin{gathered}\sf -\frac{8}{5}x+\frac{8}{5}=\frac{4}{5} \ \end{gathered}$}[/tex]Subtract 8/5 from both sides.
[tex]\large\displaystyle\text{$\begin{gathered}\sf -\frac{8}{5}x=\frac{4}{5}-\frac{8}{5} \ \ \end{gathered}$}[/tex]Since 4/5 and 5/8 have the same denominator, join their numerators to subtract them.
[tex]\large\displaystyle\text{$\begin{gathered}\sf -\frac{8}{5}x=\frac{4-8}{5} \end{gathered}$}[/tex]Subtract 8 from 4 to get -4.
[tex]\large\displaystyle\text{$\begin{gathered}\sf -\frac{8}{5}x=-\frac{4}{5} \end{gathered}$}[/tex]Multiply both sides by [tex]\bf{-\frac{5}{8}}[/tex], the reciprocal of [tex]\bf{-\frac{5}{8}}[/tex].
[tex]\large\displaystyle\text{$\begin{gathered}\sf x=-\frac{4}{5}\left(-\frac{5}{8}\right) \end{gathered}$}[/tex]Multiply -4/5 by -5/8 (to do this, multiply the numerator by the numerator and the denominator by the denominator).
[tex]\large\displaystyle\text{$\begin{gathered}\sf x=\frac{-4(-5)}{5\times8} \ \to \ \ Multiply \end{gathered}$}[/tex][tex]\large\displaystyle\text{$\begin{gathered}\sf x=\frac{20}{40} \end{gathered}$}[/tex]Reduce the fraction 20/40 to its lowest expression by extracting and canceling 20.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf x=\frac{1}{2} \end{gathered}$}}[/tex]Good luck in your studiesYou buy 2 shirts and 3 pairs of pants for $50. Your friend buys 3 shirts and 1 pair of pants for $40. What is the cost of
each shirt? of each pair of pants?
Shirts = 10$ Pants = 10$
Step-by-step explanation:
50 / 5 = 10$
3/1 = 10$
In this system of simultaneous equations, the cost of each shirt (x) equals $5 and the cost of each pair of pants (y) is $25.
Explanation:This is a system of simultaneous equation problems in Mathematics. Let's denote the cost of one shirt as x and one pair of pants as y. Based on the problem information, you have these two equations:
1) 2x + 3y = 50
2) 3x + y = 40
To solve for x, you can multiply the second equation by three and subtract the first equation from it:
3*(3x + y) - (2x + 3y) = 50
After simplifying, you find that x (cost of each shirt) equals 5.
In order to find y (cost of each pair of pants), you can now substitute x = 5 into the second original equation: 3*5 + y = 40, which gives you y = $25, the cost of each pair of pants.
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Please solve and show your equation below, happy teachings!
The expected value for the given data set is 1.4.
What is expected value?
The value that will most likely be obtained from the following iteration of a statistical experiment is known as the expected value. In order to calculate the expected value for a random trial of an experiment, the probability of each possible result is taken into account.
From the given table we have to find the expected value.
Since,
Expected value = E(X) = μ = ∑ x*P(x)
E(X) = (0*0.4) + (1*0.05) + (2*0.3) + (3*0.25)
E(X) = 0 + 0.05 + 0.6 + 0.75
E(X) = 1.4
Hence, the expected value for the given data set is 1.4.
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Jim is recording the number of points he misses on each math quiz. Here are his results for the last nine quizzes. 8, 3, 8, 6, 3, 3, 3, 6, 7 Find the range and the mode for the data.
Answer:
See below!
Step-by-step explanation:
Data:8, 3, 8, 6, 3, 3, 3, 6, 7
Range:The difference between highest value and lowest value in a data is called range.Here, Range is:
= Highest value - Lowest value
= 8 - 3
= 5
Mode:The most frequently occurring value in a data is called mode.Here, the mode is:
= 3 (occurring 4 times)
[tex]\rule[225]{225}{2}[/tex]
Two angles are complementary to each other. One angle measures 18°, and the other angle measures (8x − 28)°. Determine the value of x.
Value of x = 12.5 that is determined by solving equation.
what is complementary angle?
Two angles are called complementary to each other when the sum of these two angles is equal to 90 degrees.
What is the value of x?given, two angles are complementary two each other.
value of one angle = 18 degrees
the other angle is given by = (8x - 28) degrees
As the above two are complementary so the sum of the two is equal to 90 degrees.
The equation will be.
18 + (8x - 28) = 90
8x - 10 = 90
8x = 100
x= 12.5
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Find the scale length of the following:
actual length is 36 ft
scale is 3 in. : 24 ft
The requried scaled length of the actual length is given as 4 inches.
What is the scale factor?The scale factor is defined as the ratio of the modified change in length to the original length.
here,
In the question,
Scale 3 in = 24ft
Scale factor = modified length / original length
Scale factor = 3 / 24 = 1/8
Now,
For an actual length of 36 ft,
Scaled length is given as = 36 × 1/8 = 4 inches
Thus, the requried scaled length of the actual length is given as 4 inches.
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Can somebody please tell me how do we solve this? Thank you.
The last option which says the roots of the auxiliary equation are √6 and -√6 is the correct one.
What are Auxiliary Equations?Auxiliary equation is the equation of characteristic polynomial which is calculated by substituting the right member of a standard differential equation by zero.
The roots of the equation is helpful in determining the nature of the general solution of the given differential equation.
We have the differential equation given in the question,
d²y / dx² - 6y = 0
Now we can replace d²y / dx² as y''.
y'' - 6y = 0, where y'' is the second derivative of y.
Now we have to find the roots of the auxiliary equation.
Let c = y', then c² = y''
c² - 6 = 0
c² = 6
c = +√6 and -√6
So the roots of the equation are √6 and -√6.
Hence the roots of the auxiliary equation of the differential equation given are +√6 and -√6.
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Considering both dividends paid and capital gains, Dylan's pretax profit from his investment is $
Dylan's pretax return on investment (ROI) is
96.
Type the correct answer in each box. Use numerals instead of words.
Therefore ,the return on investment prior to deducting taxes is known as the net income rate of return.
What distinguishes taxable income from pretax income?The amount a company makes prior to taxes is known as pretax investment gains, on the other hand. Income that is subject to taxation is referred to as taxable income.
Here,
Investment income generally refers to, but is also limited to, earnings, profits, corporate taxes, rental and royalty revenues, non-qualified leases, income from businesses that trade investment products or commodities, and businesses which are passive for such taxpayer.
Pretax rates of return refers to an investment's profit or loss before taxes are taken into account.
The government imposes taxes on investment on any extra money made from buying or selling investments. Capital gains taxes must be paid on securities that are successfully sold.
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Answer: Considering both dividends paid and capital gains, Dylan’s pretax profit from his investment is $30. Dylan’s pretax return on investment (ROI) is 24%.
Step-by-step explanation: To determine Dylan’s profit from his investment, add his dividends of $5 and his capital gains of $25.total profit = $25 + $5= $30Before taxes are applied, Dylan can calculate his return on investment (ROI) by dividing his profit by the cost of his investment:30125 = 0.24, or 24%.
6x = 18 what does x =
Answer:
x= 3
Step-by-step explanation:
6x =18
divide 6 by both sides.
x=3
help
What is the slope of the line that passes through the points (2, 8) and (-3, 14)?
Write your answer in simplest form.
The slope of the line that passes through the points (2, 8) and (-3, 14) is -6/5 in the simplest form.
Define Slope.A line's steepness may be determined by looking at its slope. Slope is computed mathematically as "rise over run" (change in y divided by change in x).
What are coordinate pairs?An ordered pair in mathematics is a set of two things. The order of the objects in the pair matters because, unless a = b, the ordered pair differs from the ordered pair. Ordered pairs are also known as 2-tuples, or 2-length sequences.
The slope of a line is given by the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are two points on the line.
Plugging in the given points, we get:
m = (14 - 8) / (-3 - 2)
m = 6 / -5
m = -6/5
so the slope of the line that passes through the points (2, 8) and (-3, 14) is -6/5 in the simplest form.
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HELP PLEASE TYYY easy
The angle measure of the circle graph is as follows:
Train = 90 degreesAirplane = 198 degreesBoat = 72 degrees.How to find the angles in a pie chart?A travel magazine surveyed 500 of its adult readers about their favourite ways to travel. The circle graph below shows that 125 people like to travel by train, 275 like to travel airplane and 100 people like to travel by boat.
Therefore, let's use the data to create a pie chart with the measured angles.
Hence,
angle for train travellers = 125 / 500 × 360
angle for train travellers = 45000 / 500
angle for train travellers = 90 degrees
angle for the airplane travellers = 275 / 500 × 360
angle for the airplane travellers = 99000 / 500
angle for the airplane travellers = 198 degrees
Finally,
angle for the boat travellers = 360 - 198 - 90 = 72 degrees.
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Unit 7 geometry homework 8 quadrilaterals.
Math
The data and the image both characterize the object as a rectangle because its length is 12 and its width is 9.
what is rectangle ?A quadrilateral having four right angles, or rectangle, in Euclidean plane geometry. A quadrilateral that is equiangular, or one in which all of the angles are equal, is another way to describe it. Also possible is a straight angle in the parallelogram. With four sides that are of the same size, a square is a rectangle. Four 90-degree vertices and equal parallel sides make up a quadrilateral with a rectangle-like shape. Its equirectangular rectangle moniker derives from this. The term "parallelogram" also refers to a rectangle, which has equal and parallel opposite sides.
given
in 8 th question
The illustration depicts a rectangle with four sides and two opposite sides that are the same length as a square with equal lengths on all four sides.
The data and the image both characterize the object as a rectangle because its length is 12 and its width is 9.
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Let V be the vector space of symmetric 2 Times 2 matrices and W be the subspace W = span{ , }. Find a nonzero element X in W. X = Find an element Y in V that is not in W. Y =
The solutions are - X = [5 5; 5 -2] is a nonzero element in W and Y = [1 1; 1 1] is the element in V that is not in W.
A nonzero element X in W can be any linear combination of the given basis vectors:
X = a[5 5; 5 -2] + b[5 -4; -4 1]
Where a and b are nonzero scalars. For example, X = [5 5; 5 -2] is a nonzero element in W.
An element Y in V that is not in W can be any symmetric 2x2 matrix that cannot be written as a linear combination of the given basis vectors. For example, Y = [1 1; 1 1] is not in W as it cannot be written as a linear combination of [5 5; 5 -2] and [5 -4; -4 1].
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The complete question is -
Let V be the vector space of symmetric 2 Times 2 matrices and W be the subspace W = span{[5 5; 5 -2], [5 -4; -4 1]}. Find a nonzero element X in W. Find an element Y in V that is not in W.
Question 1 Complete the following addition exercises. 3 + 7 = 2 + 9 = 4 + 6 = 5 + 9 = 12 + 5 = 6 + 3 = 8 + 3 = 10 + 0 = 9 + 8 = 1 + 9 = 7 + 6 = 9 + 3 = 6 + 8 = 0 + 3 = 3 + 6 = 7 + 1 = 4 + 2 = 4 + 7 = 11 + 3 = 7 + 7 = 9 + 7 = 12 + 9 =
On performing addition exercises we get 10 , 11 , 10 , 14 , 17 , 9 , 11 , 10 , 17, 10 , 13 , 12 , 14 , 3 , 9 , 8 , 6 , 11 , 14 , 14 , 16 , 21 .
What is Addition ?
Addition can be defined as the performing addition operation by using operand + between two operators.
3 + 7 = 10
2 + 9 = 11
4 + 6 =10
5 + 9 =14
12 + 5 =17
6 + 3 =9
8 + 3 =11
10 + 0 = 10
9 + 8 = 17
1 + 9 = 10
7 + 6 = 13
9 + 3 =12
6 + 8 = 14
0 + 3 = 3
3 + 6 = 9
7 + 1 = 8
4 + 2 =6
4 + 7 = 11
11 + 3 = 14
7 + 7 = 14
9 + 7 = 16
12 + 9 =21
Hence, On performing addition exercises we get 10 , 11 , 10 , 14 , 17 , 9 , 11 , 10 , 17, 10 , 13 , 12 , 14 , 3 , 9 , 8 , 6 , 11 , 14 , 14 , 16 , 21 .
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BRAINLIEST HEEEEEELLLLLLLPPPPPPPPPPPPPPPPPPP
X and y are both 20 degrees because all triangles = 180 degrees and 140 + 20+20= 180
Answer:
Step-by-step explanation:
if you may, try finding 180 degrees, which y is 40 and x is 0
Airplane A flies 300 miles due east of an airport and then flies 200 miles at 15° north of east. Airplane B flies 200 miles due north and then flies 300 miles at 20° west of north. Which airplane is closer to the airport? Explain how you know.
Answer:
It is not possible to determine which airplane is closer to the airport without additional information. The distance and direction of each airplane's flight are given, but the starting point for each airplane is not specified. If we knew the starting point of each airplane, we could use the information provided to calculate the final position of each airplane and determine which one is closer to the airport.
Step-by-step explanation:
Find the solution to the system of equations.
You can use the interactive graph below to find the solution.
\begin{cases} y=2x+3 \\\\ y=-3x+3 \end{cases}
y=2x+3
y=−3x+3
x=x=x, equals
y=y=y, equals
The solution to the system of equation y = 2x + 3 and y = -3x + 3 is (0, 3)
What is an equation?An equation is an expression that shows the relationship between variables and numbers.
The linear equation is in the form:
y = mx + b
where m is the rate of change and b is the y intercept.
Given the equation:
y = 2x + 3 (1)
y = -3x + 3 (2)
To solve by elimination method, subtract equation 2 from 1:
0 = 5x + 0
x = 0
substitute x = 0 in equation 1:
y = 2(0) + 3 = 3
The solution to the equation is (0, 3)
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Thomas swam 5 laps in two and one-half minutes. At this rate, how many laps would he swim in 8 minutes?
5 laps
8 laps
14 laps
16 laps
At this rate, how will swim 16 laps in 8 minutes.
What is rate?A rate is a ratio in which the two terms being compared have different units.
Instead of using the "to" form for ratios (for example, 3 red ball to 2 blue balls), rates often use the word per. Rate is a ratio that compares two different quantities which have different units.
When two quantities of different units are compared and expressed as a ratio, we refer to it as 'Rate'.
5:2 1/2
x:8
x = (5 x 8) /5/2
x = (40) / 5/2
x = 16laps
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Put the numbers in order from least to greatest.
Answer:
0.6 > 0.49 > 0 > -0.2 > -0.32
Step-by-step explanation:
-0.32 is the smallest number because it is farthest to the left of 0.-1/5 is the same thing as -0.2. Therefore it is the second smallest number because it is greater than -0.32 but smaller than zero. 0 belongs in the middle because it has no value and is a neutral number. 0.49 is greater than 0 so it should go to the right of zero. 6/10 is the same thing as 0.6. 0.6 is the greatest number of all these numbers so it should be the farthest to the right from 0.Please let me know if this helped!!!
Which term describes a system with no solution? A consistent B dependent C inconsistent D independent
the answer is inconsistent i think
Can anyone explain to me how to solve this for h? I was given the volume and radius and I still got it wrong. My incorrect answer is in red, and the coreect one was filled in, but I still don't understand how to solve it for h.
What is the 8[tex]\pi[/tex]mean? does it mean 8 times pi?
I need the minimum interval on [-10,6]
The minimum of the function is at x = -10. The minimum on the interval [-10,6] is -2.67.
What is a function?
A function from a set X to a set Y allocates exactly one element of Y to each element of X. The set X is known as the function's domain, while the set Y is known as the function's codomain.
Given function is f(x) = ³√(x-9)
The graph of the given function increases with the increase of the value of x and decreases with the decrease of the value of x.
Thus the minimum value of f(x)on the interval [-10,6] is at x = -10
Putting x = -10 in the given function.
f(-10) = ³√(-10-9)
f(-10) = ³√(-19)
f(-10) = -2.668
f(-10) = -2.67 (rounded to 2 decimal places).
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The physician orders Mylanta 0.5 oz how many milliliters would you give
Answer: 14.7868
Step-by-step explanation: There are 29.5734 milliliters in a US fluid ounce. Since we need .5 oz, we multiply this number by .5.
Solve this you won't.
Step-by-step explanation:
It would be 4w=36
÷4 on both sides
W=9
what is the direct answer to this equation?
13 + n-26 < 38
[tex]13 + n-26 < 38[/tex]
Simplify:
[tex]n-13 < 38[/tex]
Add 13 to both sides:
[tex]n-13+13 < 38+13[/tex]
[tex]\fbox{n} < \fbox{51}[/tex]
Answer:
n<51 but what I got was n+25
An apple in a dessert contributes one-thirtieth the number of fat grams that the cup of cottage cheese contributes. If the total number of fat grams in the dessert is 4.03 g, how many fat grams are in the apple and how many are in the cup of cottage cheese?
The cottage cheese contains 3.9 g of fat and the apple has 0.13 g, making a total of 4.03 g of fat in the dessert.
what is proportionality ?Relationships that always have the same ratio are said to be proportional. For instance, the number of trees in an orchard and the number of apples in a harvest of apples are determined by the average number of apples per tree. A linear relationship between two numbers or variables is referred to as proportional in mathematics. When the first quantity doubles, the other number does as well. When one of the variables is reduced to 1/100th of its previous value, the other also decreases. If two quantities are proportional, it means that when one rises, the other rises as well, and the ratio between the two quantities remains constant throughout all values. The diameter and circumference of a circle serve as an example.
given
fat grams from the apple, where a
a +30a = 4.03g
31a/31 = 4.03 / 31
a = 0.13
The cottage cheese has 30(0.13) = 3.9 g fat, compared to the apple's 0.13 g.
The cottage cheese contains 3.9 g of fat and the apple has 0.13 g, making a total of 4.03 g of fat in the dessert.
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[tex]y=sin (3x + \pi ) for -\frac{\pi }{3} \leq x\leq \frac{\pi }{3}[/tex]
The trigonometric function y = sin(3x + π) = 0 for -π/3 ≤ x ≤ π/3.
What is a trigonometric function?A trigonometric function is a function that uses one of the trigonometric ratios.
How to find the possible values of the trigonometric function?Given that we have the trigonometric function y = sin(3x + π) for -π/3 ≤ x ≤ π/3.
To find the range of output values for the range of input values given, we insert the given values of the input into the equation.
So, for the minimum value of y, we substitute x = -π/3 into the equation.
So, y = sin(3x + π)
y = sin(3(-π/3) + π)
y = sin(-π + π)
y = sin(0)
y = 0
For the maximum value of y, we substitute x = π/3 into the equation.
So, y = sin(3x + π)
y = sin(3(π/3) + π)
y = sin(π + π)
y = sin(2π)
y = sin2π
y = 0
So, y = 0 for -π/3 ≤ x ≤ π/3.
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K
X
If the price of gasoline increased by 0.3% per month, which
equation models the future cost of gasoline?
X
Ay=1.19(z)1.03
Ix B
By=1.19(z) 1.003
C y = 1.19(1.03)"
D
y = 1.19(1.003)
The equation that models the future cost of gasoline, if the price increases by 0.3% per month, is option D: y = 1.19(1.003)
In this equation, y represents the cost of gasoline at a certain time (measured in months) in the future. The initial cost of gasoline is represented by 1.19 (since this is the base value we are starting with), and the increase in price over time is represented by (1.003)^z where z represents the number of months in the future.
The equation 1.19(1.003)^z to model the future cost of gasoline is correct, the base cost multiplied by a number representing an increase in the price each month (1.003) raised to the power of the number of month. Each time z increases by 1, the price increases by 0.3%
Therefore, increasing z by 1 increases the price of gasoline by 0.3%. If you want to calculate the price for a certain number of months in the future, you can plug in that number for z in the equation and calculate the result.
Answer:y=1.19(1.003)x
Step-by-step explanation:
Please help I’m struggling
Answer:
The answer to both parts is (C)
In the first 9/3.9 = 2.31 half lives elapsed
(1/2)^2.31 = .5^2.31 = .202 pressure at 9 mi above sea level
P = .202 * 31 = 6.26 mi
In the second:
19/5 = 3.8 half-lives
.5^3.8 = .072 left after 3.8 half lives
635.8 * .072 = 45.6
Work out the value of 10 squared takeaway 4 cubed
Give your answer as a power of 6
Answer:
[tex]6^2=36[/tex]
Step-by-step explanation:
[tex]10^2-4^3=100-64=36=6^2[/tex]
20 pairs of atletics shoes and 10 pair of casual shoes are 750. how much is each shoe
Each pair of athletic shoe cost $20 and each pair of athletic shoe cost $35, in the given arithmetic problem.
What is arithmetic?By doing addition, subtraction, multiplication, and division on numbers, arithmetic is defined as the study of numbers.
Let 20x be the cost of manufacturing 20 athletic shoes and 10y be the cost of manufacturing 10 casual shoes, then
20x + 10y = 750
10y = 750 - 20x
y = 75 -2x
Let 25x be the cost of manufacturing 25 athletic shoes and 20y be the cost of manufacturing 20 casual shoes, then
25x + 20y = 1200
20y = 1200 - 25x
y = 60 - 25x/20
y = 60 - 1.25x
Equalise the y terms
75 -2x = 60 - 1.25x
75 - 60 = -1.25x + 2x
15 = 0.75x
x = 15/ 0.75
x = 20
Substitute the value of x in y = 75 -2x
y = 75 -2(20)
y = 75 - 40
y = 35
Thus, each pair of athletic shoe cost $20 and each pair of athletic shoe cost $35.
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Full question:-
Ranger Shoe Company manufactures two types of shoes, athletic shoes and casual shoes. The cost of manufacturing 20 pairs of athletic shoes and 10 pairs of casual shoes is $750. If 25 pairs of athletic shoes and 20 pairs of casual shoes were manufactured, the cost would be $1200. How much does it cost to manufacture each type of shoe?