The cost price of the article, which is sold for Rs. 150 at a gain but if sold for Rs. 135 would have resulted in a loss equal to 50% of the original gain, is Rs. 127.50.
How the cost of the article is determined:The cost price is the difference between the selling price and the profit or gain.
The difference is determined by subtraction.
Selling price of the article = Rs. 150
Loss if sold at Rs. 135 = 50% of the original gain
Original gain = Rs. 15 (Rs. 150 - Rs. 135)
50% of the original gain = Rs. 7.50 (Rs. 15 x 50%)
Cost price of the article = Rs. 127.50 (Rs. 135 - Rs. 7.50)
Thus, the cost price is Rs. 127.50.
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List at least five combinations of nickels and dimes such that the total value of the coins is 80 cents.
Here are five combinations of nickels and dimes that add up to 80 cents:
4 dimes and 4 nickels
3 dimes and 7 nickels
2 dimes and 12 nickels
1 dime and 16 nickels
8 dimes and 4 nickels
3×2×1+3+8+6+7-9-9÷7×0×1=?
Answer:
3 × 2 × 1 + 3 + 8 + 6 + 7 - 9 - 9 ÷ 7 × 0 × 1
= 6 + 3 + 8 + 6 + 7 - 9 - 0
= 31 - 9
= 22
Therefore, the value of the expression is 22
Use the diagram of the right triangle above and round your answer to the nearest hundredth.
If Measure of angle B = 60 degreesº and a = 10 meters, find b.
a.17.32 m
b6.93 m
c.14 m
d.9.99 m
The calculated value of the side length b is 17.32 meters
Finding the side length bFrom the question, we have the following parameters that can be used in our computation:
Angle B = 60 degrees
Length a = 10 meters
The side length b is calculated as
tan(60) = b/a
So, we have
tan(60) = b/10
Make b the subject
b = 10 * tan(60)
Evaluate
b = 17.32
Hence, the side length b is 17.32 meters
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The vertices of a quadrilateral are listed below.
The strongest classification of the quadrilateral with the given vertices is rhombus.
The vertices of the quadrilateral is given as,
E(5, 4), F(9, 2), G(5, 0) and H(1, 2).
Find the adjacent sides EF and FG whether they are equal.
Using the distance formula,
EF = √(9 - 5)² + (2 - 4)² = √(16 + 4) = √20
FG = √(5 - 9)² + (0 - 2)² = √(16 + 4) = √20
Adjacent sides are equal.
So they are either square or rhombus.
Find the lengths of the diagonals whether they are equal.
EG = √(5 - 5)² + (0 - 4)² = √(0 + 16) = 4
FH = √(1 - 9)² + (2 - 2)² = √(64 + 0) = 8
Diagonals are not equal.
So it is a rhombus.
Hence the quadrilateral is a rhombus.
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PLEASE HELP (WILL GIVE BRAINLIEST)
Answer:
[tex] \sqrt{ {13.5}^{2} - {8.6}^{2} } = \sqrt{108.29} = 7 \sqrt{2.21} = \frac{7}{10} \sqrt{221} [/tex]
V = (1/2)(8.6)(.7√221)(22.4) = 1,002.33 square meters
The closest answer is 1,001.73 square meters.
Mitra drives her car 469.8 miles and uses 14.5 gallons of gasoline. Adira drives her car 355 miles and uses 12.5 gallons of gasoline. What is the difference between the gas mileage for Mitra's car (in miles per gallon) and the gas mileage for Adira's car (in miles per gallon)?
A) 2 miles per gallon
B) 4 miles per gallon
C) 8 miles per gallon
D) 9 miles per gallon
Answer:
4 miles per gallon. Answer choice B is correct.
Step-by-step explanation:
To find the gas mileage for each car, we need to divide the distance traveled by the amount of gasoline used.
For Mitra's car, the gas mileage is:
gas mileage = distance traveled / amount of gasoline used
gas mileage = 469.8 / 14.5
gas mileage = 32.4 miles per gallon
For Adira's car, the gas mileage is:
gas mileage = distance traveled / amount of gasoline used
gas mileage = 355 / 12.5
gas mileage = 28.4 miles per gallon
To find the difference in gas mileage, we can subtract the gas mileage for Adira's car from the gas mileage for Mitra's car:
difference = gas mileage for Mitra's car - gas mileage for Adira's car
difference = 32.4 - 28.4
difference = 4 miles per gallon
Therefore, the difference in gas mileage between the two cars is 4 miles per gallon. Answer choice B is correct.
Evaluate 6×[2−(4)×(–8)]
Answer:204
Step-by-step explanation:
pemdas
6x[2--32]=6×[34]=204
Solve equation by using the quadratic formula. 15 x squared + 13 x = 0
Answer:
x= -13/15
Step-by-step explanation:
x(15x +13)
x =0
15x + 13 = 0
15x = -13
x =-13/15
Consider the parabola given by the equation:
f
(
x
)
=
−
2
x
2
−
8
x
+
14
Find the following for this parabola:
A) The value of
f
(
−
5
)
:
B) The vertex = (
,
)
C) The
y
intercept is the point (0,
)
D) Find the two values of
x
that make
f
(
x
)
=
0
. Round your answers to two decimal places. Write the values as a list, separated by commas:
x
=
Answer:
Sure, here are the answers to your questions:
**A) The value of $f(-5)$ is $-2$.**
To find the value of $f(-5)$, we can simply substitute $x=-5$ into the equation $f(x)=-2x^2-8x+14$. This gives us:
$$f(-5)=-2(-5)^2-8(-5)+14=-2(25)+40+14=-50+54=4$$
**B) The vertex of the parabola is $(2,6)$.**
To find the vertex of the parabola, we can complete the square. This involves adding and subtracting $\left(\dfrac{{b}}{2}\right)^2$ to both sides of the equation, where $b$ is the coefficient of the $x$ term. In this case, $b=-8$, so we have:
$$\begin{aligned}f(x)&=-2x^2-8x+14\\\\ f(x)+20&=-2x^2-8x+14+20\\\\ f(x)+20&=-2(x^2+4x)\\\\ f(x)+20&=-2(x^2+4x+4)\\\\ f(x)+20&=-2(x+2)^2\end{aligned}$$
Now, if we subtract 20 from both sides, we get the equation of the parabola in vertex form:
$$f(x)=-2(x+2)^2-20$$
The vertex of a parabola in vertex form is always the point $(h,k)$, where $h$ is the coefficient of the $x$ term and $k$ is the constant term. In this case, $h=-2$ and $k=-20$, so the vertex of the parabola is $(-2,-20)$. We can also see this by graphing the parabola.
[Image of a parabola with vertex at (-2, -20)]
**C) The $y$-intercept is the point $(0,14)$.**
The $y$-intercept of a parabola is the point where the parabola crosses the $y$-axis. This happens when $x=0$, so we can simply substitute $x=0$ into the equation $f(x)=-2x^2-8x+14$ to find the $y$-intercept:
$$f(0)=-2(0)^2-8(0)+14=14$$
Therefore, the $y$-intercept is the point $(0,14)$.
**D) The two values of $x$ that make $f(x)=0$ are $2.5$ and $-3.5$.**
To find the values of $x$ that make $f(x)=0$, we can set the equation $f(x)=-2x^2-8x+14$ equal to zero and solve for $x$. This gives us:
$$-2x^2-8x+14=0$$
We can factor the left-hand side of the equation as follows:
$$-2(x-2)(x-3)=0$$
This means that either $x-2=0$ or $x-3=0$. Solving for $x$ in each case gives us the following values:
$$x=2\text{ or }x=3$$
However, we need to round our answers to two decimal places. To do this, we can use the calculator. Rounding $x=2$ and $x=3$ to two decimal places gives us the following values:
$$x=2.5\text{ and }x=-3.5$$
Therefore, the two values of $x$ that make $f(x)=0$ are $2.5$ and $-3.5$.
Bozo can read at a rate of 300 words every four minutes. what is his rate of reading in words per minute?
Answer:
Bozo's rate of reading in words per minute is 75 (300 words / 4 minutes = 75 words/minute).
Step-by-step explanation:
Mark Brainliest!!
Answer: 75 words per minute
Step-by-step explanation:
We will divide 300 words by 4 to find the rate of words per minute since the original rate is words per four minutes.
300 / 4 = 75 words per minute
Look at the picture
Answer: 84 in
Step-by-step explanation:
A = h(b)/2
h= 7
b= 24
24x7= 168
168/2= 84
Find the equation of a line that passes through the point ( 4 , 2 ) that is perpendicular to the line y = 4 3 x . Show your work.
The equation of the line that passes through the point (4, 2) and is perpendicular to the line y = 43x is y = (-1/43)x + (90/43).
What is the equation of a line that passes through the point ( 4 , 2 ) that is perpendicular to the line y = 43x?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
Given that the line has a slope of 43.
To find the slope of the line perpendicular to it, we use the fact that the product of the slopes of two perpendicular lines is -1.
So, the slope of the perpendicular line is -1/43.
Using the point-slope form of a line, we can write the equation of the line as:
y - y1 = m(x - x1),
where (x1, y1) = (4, 2) and m = -1/43
Plugging in the values, we get:
y - 2 = (-1/43)(x - 4)
y - 2 = (-1/43)x + (4/43)
y = (-1/43)x + (4/43) + 2
y = (-1/43)x + (90/43)
Therefore, the equation of the line is y = (-1/43)x + (90/43).
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-2 square root of 2r +5=6
Evaluating the square root expression -2√(2r + 5) = 6 gives r = 2
Evaluating the square root expressionFrom the question, we have the following expression that can be used in our computation:
-2 square root of 2r +5=6
Express properly
So, we have
-2√(2r + 5) = 6
Divide by -2
√(2r + 5) = -3
So, we have
2r + 5 = 9
Subtract 5 from both sides
2r = 4
Divide
r = 2
Hence, the solution is 2
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The Jackson Hole Aerial Tram takes passengers from an elevation of 6311 ft to an elevation of 10,450 ft up the slope of Rendezvous Mountain in Wyoming. If the tram runs on a cable measuring 12,463 ft in length, what is the angle of incline of the tram to he nearest tenth of a degree?
The angle of incline of the tram is 19.4 degree.
According to the question:
h=(10450-6311)ft
= 4139 ft
We know that, sinθ=Opposite/Hypotenuse
So, sinθ=h/12463
sinθ= 4139/12463
sinθ= 0.3321
Solve the trigonometric equation by isolating the function and then taking the inverse. Use the period to find the full set of all solutions.
θ=19.39
θ≈19.4°
Therefore, the angle of incline of the tram is 19.4 degree.
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How many solutions does this equation have 10+ 6k6k
Answer:
10 + 36k²
Step-by-step explanation:
considering that it is not an equation but an algebraic expression we solve it like this
10 + 6k6k =
10 + 36k²
Round to the nearest whole number, then find the sum. 15.43 + 12.85 + 21.3 = ___ pls i will give 60 points!!!!!!!!!!
Answer:
15.43 + 12.85 + 21.3 = 49.58
Rounding to the nearest whole number, the sum is 50.
Step-by-step explanation:
Answer:
15.43 + 12.85 + 21.3 = 49.58
Step-by-step explanation:
A
Find the measure of each side indicated.
Round to the nearest tenth.
8)
X
5 C
58°
B
The value of the measure of each side indicated are,
⇒ x = 12.48
⇒ BC = 16
We have to given that;
In triangle ABC;
AC = x
AB = 10
Hence, We can formulate;
⇒ tan 58° = BC / AB
⇒ 1.60 = BC / 10
⇒ BC = 16
By using Pythagoras theorem;
⇒ x² + 10² = 16²
⇒ x² = 256 - 100
⇒ x² = 156
⇒ x = 12.48
Thus, The value of the measure of each side indicated are,
⇒ x = 12.48
⇒ BC = 16
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Select the correct answer.
What is √81y6 in simplest form?
A. 3√/9y
B. 9y^4
C.3 √9y^2
D.9y^3
Andrew deposits $40 in a saving account earning5% interest, compounded annually. Which function can be used to determine the amount of money in the savings account after x years
The function that can be used to determine the amount of money is f(x) = 40 * (1.05)^x
Which function can be used to determine the amount of moneyFrom the question, we have the following parameters that can be used in our computation:
Principal = 40
Rate = 5% annually
Time = x
The function that can be used to determine the amount of money is represented as
f(x) = P * (1 + r)^x
Substitute the known values in the above equation, so, we have the following representation
f(x) = 40 * (1 + 5%)^x
Evaluate
f(x) = 40 * (1.05)^x
Hence, the function is f(x) = 40 * (1.05)^x
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The answer…………………..:
Answer:
what?
Step-by-step explanation:
One month Eric rented 3 movies and 5 video games for a total of $34. The next month he rented 9 movies and 7 video games for a total of $56. Find the rental
cost for each movie and each video game.
Rental cost for each movie:
Rental cost for each video game:
G
O
G
movies 1.75 each
games 5.75 each
6. Teachers' Salaries New York and Massachusetts lead the list of average teacher's
salaries. The New York average is $76,409 while teachers in Massachusetts make an
average annual salary of $73,195. Random samples of 45 teachers from each state
yielded the following.
Step-by-step explanation:
Rectangle ABCD is shown on the coordinate plane below. What is the perimeter of rectangle ABCD? If necessary, round your answer to the nearest tenth.
The area of the given rectangle is 34 squared units.
How to find the area of the rectangleDetermining the area of a rectangle with the coordinates
A(-5, 3), B(3, 5), C(4, 1), and D(-4, -1)can be achieved through using the distance formula to calculate the magnitude of its sides and then applying the formula for the area pf rectangle we find the area.
Length of Side AB:
= square root of [(3 - (-5))^2 + (5 - 3)^2]
= square root of 68
Length of Side BC:
= square root of [ (4-3)^2 + (1 - 5)^2]
= square root of 17
Area of this rectangle
= side AB × Side BC
= square root[68] x square root[17]
= square root of [68 times 17]
= square root of 1156
= 34 Square Units
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Use the trapezoid shown to new each statement below as true or false, if false rewrite the statement correctly in the space below the statement.
Note that the perimeter of the trapezoid shown is 23 units. Thus, the statement is false.
How so you arrive at that?To derive the perimeter we must know the following:
a = base = 5
b = base = 8
d = side = 4
c is the hypotenuse" = (h x base of the right triangle) = (4x3)/2 = 6
Thus, Perimeter of the trapezoid = a + b + c + d =
5 + 8 + 4 + 6
= 23 units.
Thus, the statement that the perimeter of the trapezoid shown is 22 units is false.
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Full Question>
Use the trapezoid shown to mark each statement below as true or false. if false, please rewrite the statement correctly in the space below the statement!
Q: The perimeter of the trapezoid shown is 22 units.
True false?
What is the value of x in the equation 4x+2x-3=15?
Answer:
x = 3
Step-by-step explanation:
4x + 2x - 3 = 15 ← collect like terms on left side
6x - 3 = 15 ( add 3 to both sides )
6x = 18 ( divide both sides by 6 )
x = 3
Answer:
x=3
Step-by-step explanation:
You can start of by adding 4x and 2x because they both share the same variable "x". Now you have 6x-3=15. Using the addition property of equality, you can add 3 on both sides of the equation to cancel it out. You are left with 6x=18. Divide both sides by 6 and that leaves you with x=3
Please help with this question I’m stuck brainiest and points will be rewarded
Matching of the statements with their respective linear equations are:
1) The line contains (0, -8) and a slope of 3/2: y = ³/₂x - 8
2) A line that contains the point (0, -2) and (4, 0): 2y - x = -4
3) y-intercept is (0, -2) and slope is -3/4: y = -³/₄x - 2
4) A line that has a slope of 5/3 and a y-intercept of -4: 5x + 3y = -12
How to Identify the linear equation?The formula for the equation of a line in slope intercept form is:
y = mx + c
where:
m is slope
c is y-intercept
1) The line contains (0, -8) and a slope of 3/2
The only option that even has a slope of 3/2 is option B with the equation: y = ³/₂x - 8
2) A line that contains the point (0, -2) and (4, 0)
The only one that fits this is option C with the equation:
2y - x = -4
3) y-intercept is (0, -2) and slope is -3/4.
This means the only equation that matches it is:
y = -³/₄x - 2
4) A line that has a slope of 5/3 and a y-intercept of -4.
This means the only equation that matches it is:
5x + 3y = -12
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an octagonal prism has a surface area of 50mm^2 and a volume of 88 mm^3 Another octagonal prism has a surface area of 450mm^2 and a volume of 792mm^3. Are these two shapes similar ? Explain your answer
The two octagonal prisms are similar because their corresponding sides are proportional.
How do we determine the octagonal prisms are similar?We can find out if two octagonal prisms are similar by checking if they have the same shape but may be different sizes. Two shapes are similar if their corresponding sides are proportional, and their corresponding angles are congruent.
Let's represent the dimensions of octagonal prism1:
Base edge length = a
Height = h
The octagonal prism2 dimensions:
Base edge length = b
Height = k
From the surface area and volume equations of an octagonal prism, we have the following system of equations:
50 = 2a² + 8ah
88 = 2a²h
450 = 2b² + 8bk
792 = 2b²k
We can simplify these equations by dividing the second equation by the first, and the fourth equation by the third, to eliminate h and k:
88/50 = 2a²h / (2a² + 8ah) => 44/25 = h / (a + 2h)
792/450 = 2b²k / (2b² + 8bk) => 44/25 = k / (b + 2k)
Then, we rearrange the equations to obtain expressions for h and k in terms of a and b, respectively:
h = (44/25) * (a + 2h)
k = (44/25) * (b + 2k)
Multiplying both sides of each equation by 25/19, we obtain:
h = (44/19) * a
k = (44/19) * b
We can now check if the corresponding sides are proportional:
Base edge length = a:b = 1:3
Height = h:k = 1:3
Since the corresponding sides are proportional, the two octagonal prisms are similar.
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perimeter of a tabe is 228 inches and the length is 18 inches which is more than twice the width. How do I find the length and width of the worktable
The length of the worktable is 82 inches and the width is 32 inches.
To find the length and width of the worktable, we can use a system of equations. Let's denote the width of the table by w.
Since the length is 18 inches more than twice the width, we can write:
Length = 2w + 18
The perimeter of the table is the sum of all its sides, which in this case is the sum of the length and the width, each multiplied by 2:
Perimeter = 2(length + width)
Perimeter = 2(2w + 18 + w)
Perimeter = 2(3w + 18)
Perimeter = 6w + 36
We know that the perimeter is 228 inches, so we can set up an equation:
6w + 36 = 228
Solving for w, we get:
w = 32
Now that we know the width, we can use the equation for the length to find:
Length = 2w + 18
Length = 2(32) + 18
Length = 82
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Abi takes out a loan that gathers compound interest. The table below shows the value of the loan over time. a) What is the rate of interest per annum? Give your answer as a percentage to 1 d.p. b) Work out the value of the loan 10 years after it starts. Give your answer in pounds (£) to the nearest 1p. Start After 1 year After 2 years £2500.00 £2645.00 £2798.41
Answer:
25000
Step-by-step explanation:
Find the average of 327 and 827
Answer:
577
Step-by-Step Explanation:
577 is right between 327 and 827.
327+827=1,154
1,154/2=577