[tex]\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\stackrel{\textit{"y" varies directly as "x"}}{y = kx}\qquad \textit{we also know that} \begin{cases} y = 540\\ x = 10 \end{cases}\implies 540=k(10) \\\\\\ \cfrac{540}{10}=k\implies 54=k~\hfill \boxed{y=54x} \\\\\\ \textit{when y = 1080, what is "x"?}\qquad 1080=540x\implies \cfrac{1080}{540}=x\implies 2=x[/tex]
The value of x when y = 1080 for the condition when its given that y varies directly as x and that y = 540 when x = 10, is found to be x = 20
Let there are two variables p and q
Then, p and q are said to be directly proportional to each other if
[tex]p = kq[/tex]
where k is some constant number called constant of proportionality.
This directly proportional relationship between p and q is written as
[tex]p \propto q[/tex] where that middle sign is the sign of proportionality.
In a directly proportional relationship, increasing one variable will increase another.
Now let m and n are two variables.
Then m and n are said to be inversely proportional to each other if
[tex]m = \dfrac{c}{n} \\\\ \text{or} \\\\ n = \dfrac{c}{m}[/tex]
(both are equal)
where c is a constant number called constant of proportionality.
This inversely proportional relationship is denoted by
[tex]m \propto \dfrac{1}{n} \\\\ \text{or} \\\\n \propto \dfrac{1}{m}[/tex]
As visible, increasing one variable will decrease the other variable if both are inversely proportional.
For this case, it is specified that y varies directly as x.
That means
[tex]y \propto x\\or\\y = kx[/tex]
At x = 10, y is 540. Putting these values in the equation y = kx as they're related, we get:
[tex]540 = k \times 10\\\\\text{Dividing both the sides by 10}\\\\\dfrac{540}{10} = k\\\\k = 54[/tex]
Thus, the relationship between x and y is: y = 54x
Now, when y = 1080, we get:
[tex]1080 = 54x\\\\\text{Dividing both the sides by 54}\\\\\dfrac{1080}{54} = x\\\\x = 20[/tex]
Thus, the value of x when y = 1080 for this condition is when x = 20.
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What is the solution of X+8/5x-1
-> O?
5
X5-8 or
x>
O x<-8 or x>5
0x
X
col-
0 -85x<5
0 -8 < x < 1 / 3
x - inf - 8 1/5 + inf
x+8 - 0 + +
5x-1 - - 0 +
result + 0 - ║ +
x+8/(5x-1) > 0 if x € ] -inf ; - 8[ U ] 1/5 ; + inf [
=> x < - 8 and x > 1/5
The solution to the inequality (x + 8)/(5x - 1) ≤ 0 is:
x ∈ (-∞, -8] ∪ [1/5, ∞)
We have,
To solve the inequality (x + 8)/(5x - 1) ≤ 0,
We can use the following steps:
Step 1:
Find the critical values of x where the expression (x + 8)/(5x - 1) is equal to zero or undefined.
The expression is undefined when the denominator is equal to zero:
5x - 1 = 0
x = 1/5
The expression is equal to zero when the numerator is equal to zero:
x + 8 = 0
x = -8
Therefore,
The critical values are x = -8 and x = 1/5.
Step 2:
Create a sign chart to determine the sign of the expression (x + 8)/(5x - 1) for each interval between the critical values.
On the interval (-∞, -8), the expression (x + 8)/(5x - 1) is negative if x + 8 is negative, which means x < -8.
On the interval (-8, 1/5), the expression (x + 8)/(5x - 1) is positive if both the numerator and denominator are negative, or if both are positive.
The numerator is negative on this interval, so the expression is positive if the denominator is negative, which means x < 1/5.
On the interval (1/5, ∞), the expression (x + 8)/(5x - 1) is negative if the numerator is negative and the denominator is positive, which means x > 1/5.
Step 3:
Write the solution in interval notation.
Therefore,
The solution to the inequality (x + 8)/(5x - 1) ≤ 0 is:
x ∈ (-∞, -8] ∪ [1/5, ∞)
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Can someone please help me with this? My mind is blank after doing a lot of questions.
Answer:
6 Hours
Step-by-step explanation:
No.of leaflets---no.of people---work hours
1000 ————. 4. - — — — — — — 5
1500 — — — —5 — — — — — ,— —?
If work increase, no.of people needed more
So, the required ratio is 1500/1000
If work men increase, no of hours decrease
So, the required ratio is 4/5
(1500/1000)× (4/5)×5 = 6
No.of hours required to distribute 1500 leaflets by 5 people = 6 hours
What is the measure of angle b?
Answer:
b=133 and c=47
Step-by-step explanation:
b+47=180
b=180-47=133
b=133
and
c=b+133=180
c=180-133=47
c=47
Help me In this question it’s urgent
Answer:
CD = 13.75
Step-by-step explanation:
Focus on only half of the rectangle as a triangle
We'll use pythagorean theorem to find the unknown side
[tex]10^{2} +CD^{2}=17^{2}\\CD^{2} = (17^{2} - 10^{2})\\CD^{2}=\sqrt{189} \\CD = 13.75[/tex]
Which value, when placed in the box, would result in a system of equations with infinitely many solutions? y = -2x 4 6x 3y =
The missing value is 12 in a system of equations with infinitely many solutions conditions.
It is given that in the system of equations there are two equations given:
[tex]\rm y =n -2x+4\\\rm and \\\rm 6x+3y= ?[/tex]
It is required to find the missing value in the second equation.
What is a linear equation?It is defined as the relation between two variables if we plot the graph of the linear equation we will get a straight line.
We have equations:
[tex]\rm y = -2x+4 ....(1)\\ \\\rm 6x+3y= ? ....(2)[/tex]
Let's suppose the missing value is 'Z'
We know that the two pairs of equations have infinitely many solutions if and if they have the same coefficients of variables and the same constant on both sides.
From equation (1)
[tex]\rm y = -2x+4 \\\\\rm 2x+y=4[/tex](multiply both the sides by 3)
[tex]\rm 6x+3y=12[/tex] ...(3)
By comparing the equation (2) and (3), we get
M = 12
Thus, the missing value is 12 in a system of equations with infinitely many solutions conditions.
Learn more about the linear equation.
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You are designing a large rectangular fish tank for your tropical fish. The length will be 1 yard 3 inches, the width will be 1. 5 feet, and the height will be 20 inches. Part A Find the volume of the fish tank in cubic inches. The volume is cubic inches. Part B Your math teacher tells you that your fish tank will have a capacity of about 976 cups. You have a total of 30 tropical fish. For them to flourish in a fish tank, there needs to be an average of 2 gallons of water for each fish. Convert 976 cups to gallons. 976 cups equals gallons.
Unit conversion is a way of converting some common units into another without changing their real value. 30 fishes can flourish in a fish tank with a capacity of 976 cups.
What is Units conversion?Unit conversion is a way of converting some common units into another without changing their real value. for, example, 1 centimetre is equal to 10 mm, though the real measurement is still the same the units and numerical values have been changed.
As it is given that the length will be 1 yard 3 inches, the width will be 1. 5 feet, and the height will be 20 inches. Therefore, Converting all the dimensions to inches.
Length = 1 yard 3 inches = 36 inches + 3 inches = 39 inches
Width = 1.5 feet = 1.5×12 = 18 inches
Height = 20 inches
A.) The volume of the fish tank can be written as,
[tex]\rm \text{Volume of the Fish Tank} = Length \times Width \times Height[/tex]
[tex]= 39 \times 18 \times 20\\\\= 14,040\rm\ in^3[/tex]
Thus, the volume of the fish tank is 14,040 in³.
B.) As we know that a cup is equal to 0.0625 gallons. Therefore, the capacity of the fish tank in gallons can be written as,
[tex]\rm 1\ cup= 0.0625\ gallons\\\\976\ cup= 976 \times 0.0625\ gallons\\\\976\ cup= 61\ gallons[/tex]
Now, for a total of 30 fish, the water that will be needed is one fish needs 2 gallons of water is,
[tex]\rm Water\ Needed = 30 \times 2 = 60\ gallons[/tex]
As the water needed for the 30 fishes to flourish is 60 gallons while the tank has a capacity of 61 gallons.
Hence, 30 fishes can flourish in a fish tank with a capacity of 976 cups.
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Help!!! 8. Determine whether each pair of functions f and g are inverses. Explain your reasoning.
Answer:
I would say that a is NOT an inverse, however b is.
Step-by-step explanation:
If you look at the two tables for a, you can tell that every pair has swapped places (as they should) except 0 and 9. In which in the second table, what should be the 9 in the x row, is just another 0 in its place.
While if you look at the two tables for b, every single pair has been swapped like it should, meaning the second table is the inverse of the first table.
Hope this helps you btw. I'm sorry if it doesn't though.
An office supply store in Newport purchased a printer at a cost of $175 and marked it up 45%. Later on, Oliver bought the printer. If the sales tax in Newport is 12%, how much did he pay in all?
please help asap would appreciate it ty
Answer: $284.20
Step-by-step explanation:
In the picture
what are the solutions to the equation?
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♪[/tex]
Let's solve ~
[tex]\qquad \sf \dashrightarrow \:f(x) = g(x)[/tex]
[tex]\qquad \sf \dashrightarrow \:x + 2 = - {x}^{2} + 4[/tex]
[tex]\qquad \sf \dashrightarrow \: {x}^{2} + x + 2 - 4 = 0[/tex]
[tex]\qquad \sf \dashrightarrow \: {x}^{2} + x - 2 = 0[/tex]
[tex]\qquad \sf \dashrightarrow \: {x}^{2} + 2x - x - 2 = 0 [/tex]
[tex]\qquad \sf \dashrightarrow \:x(x + 2) - (x + 2) = 0[/tex]
[tex]\qquad \sf \dashrightarrow \:(x + 2)(x - 1) = 0[/tex]
Hence, x = -2 or x = 1
please giv the answer asap. I'll mark brainliest.
Answer:
Step-by-step explanation:
x = 5.4178
10000x = 54178.178
10x = 54.178 Subtract: that gets rid of the repeating decimal.
9990x = 54124 Divide by 9990 on both sides
9990x/9990 = 54124/9990 The Greatest common divisor of these two is 2
x = 27062/ 4995
p/q = 27062 / 4995
solve pls brainliest
Answer:
[tex](\frac{2}{3})^{4}[/tex] written in simplest form is [tex]\frac{16}{81}[/tex]
Step-by-step explanation:
When taking a fraction to a certain power, you can rewrite the expression as the numerator taken to that power over the denominator to that power. In this case, the fraction is [tex]\frac{2}{3}[/tex] and the exponent is 4, so you can write the expression as [tex]\frac{2^{4}}{3^{4}}[/tex]. [tex]2^{4}[/tex] is 16, and [tex]3^{4}[/tex] is 81, so the fraction is [tex]\frac{16}{81}[/tex].
What is the area of a circle with a radius of 10.2 feet? 10.2
yo how you people doing what's -25 - 57 + 35 ?????
Answer:
-47
Step-by-step explanation:
you don't you use the calcaulator
A bag contains 5 red marbles 8 green marbles 6 orange marbles and 11 yellow marbles what is the probability of randomly choosing an orange marble
Answer: 20%
Step-by-step explanation: Add all the marbles together:5 + 8 + 6 +11= 30
Find the probability of orange: 6/30
Now divide 6 by 30= .2
Turn .2 into a decimal: 20%
work out [tex]\frac{1}{5}[/tex] of 80
Answer:
Here we will explain how to calculate one half of 80.
One half of 80 is simply one half times 80, which can be written as follows:
One/half x 80
Furthermore, you can convert "one" to "1" and "half" to "2" and then the equation and answer is:
1/2 x 80 = 40.00
Step-by-step explanation:
Hey there!
In order to find 1/5 of 80, we can just multiply 80 times 1/5:
[tex]\bold{\displaystyle\frac{1}{5} *80}[/tex]
80 can be written as follows:
[tex]\bold{\displaystyle\frac{1}{5} *\frac{80}{1}}[/tex]
In order to multiply fractions, just multiply the top of one fraction times the top of the other fraction; same with the bottom (also called the denominator)
[tex]\bold{\displaystyle\frac{80}{5}}[/tex]
Guess what? Now we can use mental maths to solve it :)
Hence, the answer is
[tex]\boxed{\boxed{\bold{16}}}[/tex]
Hope everything is clear.
Let me know if you have any questions!
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:-)
find the value of a from the following data whose mean is 23 29,33, 27, a, 19, 17, 10
Answer:
a = 26
Step-by-step explanation:
29 + 33 + 27 + a + 19 + 17 + 10 / 7 = 23
135 + a / 7 = 23
135 + a = 161
a = 26
The Venn diagram shows people go to work
Answer:
If B stands alone in the option,B is the answer.But if it doesn't,choose none or neither
Step-by-step explanation:
Mutually exclusive events are events that do not occur at the same time.On the venn diagram,mutually exclusive events do not overlap. Hence, B is a mutually exclusive event because W and T overlap. Since B doesn't stand alone in any option,the answer is none
X+6y=10 x+5y=9
Use elimination to solve the following equations
Answer:
(4, 1 )
Step-by-step explanation:
x + 6y = 10 → (1)
x + 5y = 9 → (2)
subtract (2) from (1) term by term to eliminate x
0 + y = 1
y = 1
substitute y = 1 into either of the 2 equations and solve for x
substituting into (1)
x + 6(1) = 10
x + 6 = 10 ( subtract 6 from both sides )
x = 4
solution is (4, 1 )
surface area of prisms: find it and. fix it
Answer:
Step-by-step explanation:
i can't solve without seeing the prism
1. D=7.4 calculate the area of the circle
2. R=2.2 yd
Calculate the circumference of the circle
3. D=5 cm
Calculate the circumference of the circle
4. D=6 cm
Calculate the circumference of the circle
5. R=2.1 m
Calculate the area of the circle
6. R= 1.3 mm
Calculate the circumference of the circle
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
We need to know two formulas before we start ~
Area of circle = [tex]\sf \pi r² [/tex]Radius (r) = diameter (d) ÷ 2 Circumference = [tex]\sf 2\pi r \:\: or \;\;\pi d [/tex]Taking value of pi as 3.14
Let's solve ~
problem 1[tex]\qquad \sf \dashrightarrow \:d = 7.4[/tex]
[tex]\qquad \sf \dashrightarrow \:r = d \div 2[/tex]
[tex]\qquad \sf \dashrightarrow \:r = 7.4 \div 2[/tex]
[tex]\qquad \sf \dashrightarrow \:r = 3.7 \: \: units[/tex]
now,[tex]\qquad \sf \dashrightarrow \:area = 3.14 \times (3.7) {}^{2} [/tex]
[tex]\qquad \sf \dashrightarrow \:a = 42.9866 \approx43 \: \: unit {}^{2} [/tex]
problem 2[tex]\qquad \sf \dashrightarrow \:r = 2.2 \: yd[/tex]
[tex]\qquad \sf \dashrightarrow \: circumference = 2 \times 3.14 \times 2.2[/tex]
[tex]\qquad \sf \dashrightarrow \: c =13.816 \: yd[/tex]
problem 3[tex]\qquad \sf \dashrightarrow \:d = 5 \: cm[/tex]
[tex]\qquad \sf \dashrightarrow \:circumference = 3.14 \times 5[/tex]
[tex]\qquad \sf \dashrightarrow \:c = 15.7 \: \: cm[/tex]
problem 4[tex]\qquad \sf \dashrightarrow \:d = 6 \: cm[/tex]
[tex]\qquad \sf \dashrightarrow \:circumference = 3.14 \times 6[/tex]
[tex]\qquad \sf \dashrightarrow \:c =18 .84 \: \: cm[/tex]
problem 5[tex]\qquad \sf \dashrightarrow \:r = 2.1 \: m[/tex]
[tex]\qquad \sf \dashrightarrow \:area = 3.14 \times (2.1) {}^{2} [/tex]
[tex]\qquad \sf \dashrightarrow \:a = 3.14 \times 4.41[/tex]
[tex]\qquad \sf \dashrightarrow \:a \approx13.85 \: \: m {}^{2} [/tex]
problem 6[tex]\qquad \sf \dashrightarrow \:r = 1.3 \: mm[/tex]
[tex]\qquad \sf \dashrightarrow \:c = 2 \times 3.14 \times 1.3[/tex]
[tex]\qquad \sf \dashrightarrow \:c = 8.16 \: \: mm[/tex]
Baba Clothing store is a having a 5% off sale on all of its clothing. Which expression represents the discounted price if p is the original price?
Answer:
The total of the prices of all of the baby shirts and sweaters that the store sold during the sale was $420.00. It's possible that 12 sweaters and 8 shirts are sold a bargen
Step-by-step explanation:
The balloon rises vertically so that the distance between the balloon and Student A is 90 feet. How
many feet did the balloon rise? Express your answer to the nearest foot.
Using the Pythagorean Theorem, it is found that the balloon rises 67.08 feet.
What is the Pythagorean Theorem?The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, according to the following equation:
[tex]h^2 = l_1^2 + l_2^2[/tex]
Researching this problem on the internet, it is found that the situation is modeled by a right triangle, in which the horizontal distance between the balloon and the student is of 60 ft, the vertical distance is of h, while the hypotenuse is of 90 ft, hence:
[tex]60^2 + h^2 = 90^2[/tex]
[tex]h = \sqrt{90^2 - 60^2}[/tex]
[tex]h = 67.08[/tex]
The balloon rises 67.08 feet.
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Find x. Perimeter.
What is the value of x?
What is the perimeter of this triangle?
Step-by-step explanation:
the distance of a vertex on the 2 outgoing sides to the touching points with the inscribed circle is the same for both sides.
and that applies to all 3 vertexes.
so, we know for the top left vertex the distance to both touching points is 4.
that means the distance to the touching points from the bottom left vertex is 7-4 = 3.
and that means that the distance to the touching points from the bottom right vertex is 16-3 = 13.
so, x = 13
it is the distance to one of the touching points for the bottom right vertex.
and the perimeter of the triangle is therefore
7 + 16 + (13 + 4) = 40
The exponential function f is given by f(x) = 3x. by what factor does f increase when the exponent x increases by 2? explain how you know. a 3 b 6 c 9 d 12
The exponential function f(x) = 3^x, when x has a value of 2 increases by 9.
What is an exponential function?An exponential function is a function that is in the form: m = ab^x
Where:
a = initial value b = rate of increase x = number of yearsF(x) = 3^x
3^2 = 9
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What is the slope of the original line?
simplify and expand 5(m+2) -3(m-2)
thank you
Answer:
2(m+8)
Step-by-step explanation:
5(m+2) -3(m-2)
= 5m+10-3m+6
= 2m+16
= 2(m+8)
Answer:
2m +16Step-by-step explanation:
[tex]\begin{aligned}& 5(m+2)-3(m-2) \\\\=& 5 m+5 \times 2-(3 m-6) \\\\=& 5 m+10-3 m+6 \\\\=&(5 m-3 m)+(10+6) \\\\=& 2 m+16\end{aligned}[/tex]
HELP
Manny kept track of the number of home runs he hit every year in high school.
{11, 10, 17, 18)
What is the mean absolute deviation (MAD) of the data set?
Enter your answer in the box. Round to the nearest tenth, if necessary.
Answer:
Ok, to find MAD, you have to add up all of the decimals in the set, and then divide by how much decimals there are in the set.
Adding them all up...
The final result of the adding is 56.7
Now, we have to divide by how much decimals.
We now have. 56.7 / 6
Do the division.
56.7 / 6 ===> 9.45
No need to round, the final answer is 9.4
Andrea thought that x = 15 would be a good guess to solve 6x + 19 = 150. Should her second guess be higher or lower? Why?
Answer:
higher
Step-by-step explanation:
should be higher since 6 x 15 is 90, which is far away from 150
Answer:
should be higher
Step-by-step explanation:
because 6×15=90 and 90+19 is lower than 150
Elaine is buying materials for draperies. If the smaller panel costs 79$ for the 24 square feet shown, what should Elaine expect to pay for the larger panel after the dimensions are doubled
more questions!!! he
Answer:
[tex] - 3 \frac{1}{6} \div ( - 1 \frac{4}{9} ) \\ \\ - \frac{19}{6} \div ( - \frac{13}{9} ) \\ \\ - \frac{19}{6} \times ( - \frac{9}{13} ) \\ \\ - \frac{19}{2} \times ( - \frac{3}{13} ) \\ \\ = \frac{57}{26} = 2 \frac{5}{26} = 2.1923[/tex]
Answer:
2 5/26
Step-by-step explanation:
1) convert 3 1/6 to improper fraction. Use this rule: a b/c = ac+b/c
- 3 * 6 + 1/ 6 ÷ -1 4/9
2) Simplify 3*6 to 18.
-18+1/6 ÷ -1 4/9
3) Simplify 18 + 1 to 19.
-19/6 ÷ -1 4/9
4) convert 1 4/9 to improper fraction. Use this rule: a b/c = ac+b/c
-19/6 ÷ -1*9+4/4
5) Simplify 1 * 9 to 9
-19/6 ÷ -9+4/9
6) Simplify 9 + 4 to 13.
-19/6 ÷ -13/9
7) Use this rule: a ÷ b/c = a × c/b
-19/6 × 9/-13
8) Use this rule: a × c/d = ac/bd
- 19*9/6*-13
9) Simplify 19 * 9to 171
-171/6*-13
10) Simplify 6 * -13 to -78
-171/-78
11) Move the negative sign to the left.
-(-171/78)
12) simplify 171/78 to 57/26
-(-57/26)
13) Remove parentheses.
57/26
14) Convert to mixed fraction.
2 5/26