The first step in evaluating the expression 6 - (4/2 x 5)² is to simplify the expression inside the parentheses first.
What is an expression?An expression is a mathematical phrase that consists of numbers, variables, and operators (such as addition, subtraction, multiplication, and division) that are combined according to certain rules to represent a mathematical calculation.
Following the order of operations or PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction), as shown below:
4/2 = 2, so we can replace 4/2 with 2:
6 - (2 x 5)²
2 x 5 = 10, so we can replace 2 x 5 with 10:
6 - 10²
10² means 10 multiplied by itself, which equals 100:
6 - 100
Therefore, the expression simplifies to -94.
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A slot machine takes only one-dollar and two-dollars coins and contains a total of thirty six coins altogether. The value of the coins in the machine is ????$55. 4.3.1 Model the statement into two linear equations by letting the number of one-dollar coins to be x and the number of two-dollar coins to be y . (4) 4.3.2 Solve the two equations you formed in 4.3.1 using Cramer’s rule to find the number of coins of each value. (6)
There are 17 one-dollar coins and 19 two-dollar coins in the machine.
How did we arrive at these values?4.3.1 Model the statement into two linear equations by letting the number of one-dollar coins to be x and the number of two-dollar coins to be y:
Let x be the number of one-dollar coins and y be the number of two-dollar coins in the machine. Then we can form the following two linear equations:
Equation 1: x + y = 36 (total number of coins)
Equation 2: 1x + 2y = 55 (total value of coins)
4.3.2 Solve the two equations you formed in 4.3.1 using Cramer’s rule to find the number of coins of each value:
To solve the two equations using Cramer's rule, we need to write them in matrix form:
| 1 1 | | x | | 36 |
| | x | | |
| 1 2 | | y | | 55 |
Using Cramer's rule, we first calculate the determinant of the coefficient matrix:
D = | 1 1 |
| 1 2 |
D = (1 x 2) - (1 x 1) = 1
Then we replace the first column of the coefficient matrix with the constants from the right-hand side of the equations:
Dx = | 36 1 |
| 55 2 |
And calculate the determinant of this matrix:
Dx = (36 x 2) - (55 x 1) = 17
Similarly, we replace the second column of the coefficient matrix with the constants from the right-hand side of the equations:
Dy = | 1 36 |
| 1 55 |
And calculate the determinant of this matrix:
Dy = (1 x 55) - (1 x 36) = 19
Finally, we can calculate the values of x and y using the formulas:
x = Dx / D = 17 / 1 = 17
y = Dy / D = 19 / 1 = 19
Therefore, there are 17 one-dollar coins and 19 two-dollar coins in the machine.
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Kusum brought 50 glasses for Rs 1500 out of which 4 were broken. If she sold
the rest of the glasses for Rs 35 each, how much profit or loss precent did she bear?
Answer: 7.33%
Step by step explanation:
CP of 50 glasses = Rs. 1500
4 glasses broken
Glass remaining = 50 - 4 = 46
Selling price of 1 glass = Rs 35
SP of 46 glass = 46 x 35 = Rs 1610
Profit = SP - CP = 1610 - 1500 = 110
Profit percentage,
= Profit/CP x 100%
= 110/1500 x 100%
= 7.33%
The cost price of 50 glasses = Rs.1500
The remaining glasses = 46
The Selling price of remaining glasses = 46 × 35
=Rs. 1610
Now
Profit = 1610 - 1500
= Rs.110
Now
Profit Percent
[tex] \frac{Profit}{CP} \times 100%[/tex]
[tex] \frac{110}{1500} \times 100%[/tex]
= 7.33%
If 3 −2√5 and 6 + ???? are roots of P(x), what other numbers must
also be roots?
There is no one definite answer.
Given information: If 3 −2√5 and 6 + ???? are roots of P(x), what other numbers must also be roots?To find out the other roots of P(x), we have to make use of the Fundamental theorem of algebra which states that every polynomial of degree n has n roots, both real and complex.In order to find out the other roots, we have to divide the polynomial P(x) by its given roots i.e (x-(3-2√5))(x-(6+????)) = 0Let's begin by solving the first root:Since, If 3 −2√5 is the root, thus we can write, x - (3 - 2√5) = 0Or, x - 3 + 2√5 = 0Or, x = 3 - 2√5Similarly, for the second root, 6 + ???? ,
we can write: x - (6 + ???? ) = 0Or, x = 6 + ????Now, Let's combine these two roots and write the polynomial in factored form. Using these two roots, we can write the equation as below: Thus, P(x) = (x - 3 + 2√5)(x - 6 - ???? ) = 0We have found the other roots to be: Other roots = (x - 3 + 2√5)(x - 6 - ???? ) = 0Where ???? can be any value. Therefore, there is no one definite answer.
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The length of a rectangle is twice as long as it’s width. it’s perimeter is 18 in. How long and how wide is the rectangle?
Answer: Let's start by using algebra to solve the problem.
Let's call the width of the rectangle "w". Then we know that the length of the rectangle is twice the width, or "2w".
The formula for the perimeter of a rectangle is:
P = 2l + 2w
where P is the perimeter, l is the length, and w is the width.
We know that the perimeter is 18 inches, so we can substitute the values we have:
18 = 2(2w) + 2w
Simplifying:
18 = 4w + 2w
18 = 6w
Dividing both sides by 6:
w = 3
So the width of the rectangle is 3 inches.
To find the length, we can use the fact that it is twice the width:
l = 2w = 2(3) = 6
So the length of the rectangle is 6 inches.
Therefore, the rectangle is 6 inches long and 3 inches wide.
enjoy!
Which of the integers are multiples of 40 ? Select all that apply. A. 10,
B. 160 C. 360
D. 20 E. 580
Answer:
B AND C
Step-by-step explanation:
B AND C ARE THE CORRECT MULTIPLES 40
Find the exact value using the sum/difference formula.
sin 140 degrees cos 50 degrees-cos 140 degrees sin 50 degrees
Apple stock rose from $75 per share on January 1, 2013 to $109 per share on January 1, 2015. During the
same period, Microsoft stock rose from $27 to $47.
(a) What was the absolute change in dollars in the Apple stock price?
(b) What was the absolute change in dollars in the Microsoft stock price?
(c) What was the relative change in the Apple stock price, rounded to the nearest percent? $
(d) What was the relative change in the Microsoft stock price, rounded to the nearest percent?
%
(e) Suppose you invested $5,000 in Apple stock on January 1, 2013. How many whole shares would you have
been able tobuy? (Enter a whole number.)
shares
%
(f) At the end of the two years, if you sold all these shares, what would be the total amount in dollars from
the sale? $
(g) Suppose you invested $5,000 in Microsoft stock on January 1, 2013. How many whole shares would you
have been able to buy? (Enter a whole number.)
shares
(h) At the end of the two years, if you sold all these shares, what would be the total amount from the
sale? $
The stock price of corporation is [tex]45[/tex]%, [tex]34[/tex] and [tex]20[/tex] correspondingly for the absolute change in the dollar and the Ms dollar.
The price of a stock right now.It is the latest trading price for a stock or some other security. Inside an market, the place to start is the current price. It demonstrates the cost that a both parties would be willing to pay for a subsequent deal involving that security.
(a) The absolute change in dollars in the Apple stock price is:
[tex]109 - 75 = 34[/tex]
(b) The absolute change in dollars in the Microsoft stock price is:
[tex]47 - 27 = 20[/tex]
(c) The relative change in the Apple stock price, rounded to the nearest percent is: [tex]((109 - 75)/75) * 100 = 45[/tex]%
(d) The relative change in the Microsoft stock price, rounded to the nearest percent is: [tex]((47 - 27)/27) * 100 = 74[/tex]%
(e) If you invested $[tex]5,000[/tex] in Apple stock on January 1, 2013, and the price per share was $[tex]75[/tex], you could buy: [tex]5,000/75 = 66.67[/tex] shares
Rounded down to the nearest whole number, you would be able to buy [tex]66[/tex] shares.
(f) If you sold all [tex]66[/tex] shares of Apple stock at the price of $[tex]109[/tex] per share at the end of two years, the total amount from the sale would be:
[tex]66 shares * $109/share = 7,194[/tex]
(g) If you invested $[tex]5,000[/tex] in Microsoft stock on January 1, 2013, and the price per share was $[tex]27[/tex], you could buy: [tex]5,000/27 = 185.19[/tex] shares
Rounded down to the nearest whole number, you would be able to buy [tex]185[/tex] shares.
(h) If you sold all [tex]185[/tex] shares of Microsoft stock at the price of $[tex]47[/tex] per share at the end of two years, the total amount from the sale would be:
[tex]185 shares * 47/share = 8,695[/tex]
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NO EXPLANATION JUST ANSWER!
Answer:
405mm^3
Hope this helps!
Brainliest and a like is much appreciated!
Answer:
405
Step-by-step explanation:
Answer is above!A group of friends wants to go to the amusement park. They have no more than $125 to spend on parking and admission. Parking is $9, and tickets cost $20 per person, including tax. Write and solve an inequality which can be used to determine
�
p, the number of people who can go to the amusement park.
Answer:
Hello, your answer is 10
Step-by-step explanation:
Have a good day UwU
Solve the equation.
8.88=4.44(x−7)
x = ?
Answer: x=9
Step-by-step explanation:
Simplify the expression
Add 777 to both sides
Simplify the expression
Divide both sides by the same factor
Simplify the expression
What is the range of f(x)? {x | −2 ≤ x < 4} {x | −2 < x ≤ 4} {y | −5 < y < −1} {y | −5 ≤ y ≤ −1}
Option (d) is correct i.e., y | −5 ≤ y ≤ −1 , for this we have to know the concept of range and coordinates.
What is Range?In mathematics, a function's range can refer to one of two closely related ideas: The function's codomain a representation of the action A binary relation f between two sets P and Q is a function if there is exactly one y in Q such that f connects x to y for every x in P .
In geometry, a coordinate system is a method for determining how to place points or other geometrical objects on a manifold, such Euclidean space, uniquely using one or more numbers, or coordinates.
The range of a function is the set of all values that f can produce for all the x-axis in the domain.
If we are given the graph, in order to find the range, we project the graph into the y-axis. Informally, we draw the "shadow" of the graph into the y axis as in the FIGURE attached.
Option (d) is correct i.e., y | −5 ≤ y ≤ −1 .
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1. Evaluate each expression. Give your answer in radians:
i. Without using a calculator: cos^-1(-√2/2)=
ii. Use a calculator: sin^-1(-0.512)=
i. π/4
ii. -0.529
1. Evaluate each expression. Give your answer in radians:
i. Without using a calculator: cos⁻¹(−√2/2)Firstly, let us discuss the meaning of the inverse cosine function. The inverse cosine function is the angle (in radians) that corresponds to the cosine value of the input angle. The inverse cosine function returns values in the range [0, pi].cos⁻¹(−√2/2) can be read as "what angle has a cosine of -√2/2?"In a right-angled triangle with angle θ, adjacent is -1, hypotenuse is √2, and opposite is -1. Therefore, we can write the cosine ratio as adjacent over hypotenuse or -1/√2. Let us now solve for θ using the formula for cosine:cosθ = adjacent/hypotenusecosθ = -1/√2θ = cos⁻¹(-1/√2)The exact value of cos⁻¹(-1/√2) is π/4. Therefore, cos⁻¹(-√2/2) = π/4.
ii. Use a calculator: sin^-1(-0.512)As previously mentioned, the inverse sine function is the angle (in radians) that corresponds to the sine value of the input angle. The inverse sine function returns values in the range [-π/2, π/2].sin⁻¹(-0.512) can be read as "what angle has a sine of -0.512?" To find this value, we use a calculator. First, we press the "sin⁻¹" button or "2nd" + "sin" button. Then, we enter the value we want to find, which is -0.512. The final answer is -0.529. Therefore, sin⁻¹(-0.512) = -0.529.
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Maggie has a bag of different colored marbles the probability of picking an orange marble is 3 out of 10 what is the probability that Maggie will not pick an orange marble is it 3% ,7%, 30%, or 70%
Answer:
70%
Step-by-step explanation:
3 out of the 10 marbles are not orange, so 7/10 chance you don't, and then you can multiply by 10, and then you have 70 percent
I NEED HELP ON THIS ASAP!
please help i will give points
The value of m, n and w are 92, 48 and 88 respectively
What is sum of angle in a triangle?A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices. A triangle is also a polygon( 3sided polygon). The sum of angles In a polygon is 180. i.e A+B +C = 180
In the triangle above, The triangle is divided into two.
42+36+w = 180
88+w = 180
w = 180 - 88
w = 92°
From the law of the law of exterior angle of a triangle which states that; The exterior angle of a triangle is equal to the sum of opposite angles.
Therefore;
92 = n + 44
n = 92-44
n = 48°
w = 180-92( angles on a straight line)
w = 88°
Therefore the value of m, n, w are 92, 48 and 88 respectively
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Which set of ordered pairs does NOT represent a function?ResponsesA(-4, 2), (-3, 2), (-2, 2), (-1, 2), (0, 2), (1, 2)(-4, 2), (-3, 2), (-2, 2), (-1, 2), (0, 2), (1, 2)
B(0, 1), (2, 2), (4, 8), (-2, 7), (5, 8)(0, 1), (2, 2), (4, 8), (-2, 7), (5, 8)
C(0, 1), (2, 2), (4, 8), (2, 7), (5, 8), (7, 9)(0, 1), (2, 2), (4, 8), (2, 7), (5, 8), (7, 9)
D(1, 4), (3, 7), (5, 8), (4, 9), (6, 2), (7, 8), (2, 5)(1, 4), (3, 7), (5, 8), (4, 9), (6, 2), (7, 8), (2, 5)
E(-3, 6), (2, 7), (0, 5), (1, 5), (4, 9), (5, 4)
The set of ordered pairs in option C does not represent a function.
What is a function?
A function is a mathematical expression, rule, or law that describes the relationship between an independent variable and a dependent variable.
We know that in a function each input has only one output.
So, on evaluating the options, we get
Option A
This represents a function as each input has only one output.
Option B
This represents a function as each input has only one output.
Option C
This does not represent a function as input 2 has two different outputs which are 2 and 7.
Option D
This represents a function as each input has only one output.
Option E
This represents a function as each input has only one output.
Hence, the set of ordered pairs in option C does not represent a function.
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Question: Which set of ordered pairs does NOT represent a function?
A. (-4, 2), (-3, 2), (-2, 2), (-1, 2), (0, 2), (1, 2)
B. (0, 1), (2, 2), (4, 8), (-2, 7), (5, 8)
C. (0, 1), (2, 2), (4, 8), (2, 7), (5, 8), (7, 9)
D. (1, 4), (3, 7), (5, 8), (4, 9), (6, 2), (7, 8), (2, 5)
E. (-3, 6), (2, 7), (0, 5), (1, 5), (4, 9), (5, 4)
a weather ballon ascends at a constant rate. the height of the ballon 8 minutes after beginning to ascend is 2,320 feet. the height 15 minutes after ascending is 4,350 feet. what is the change in the elevation of the ballon per minute
Answer:
290 feet/minute
Step-by-step explanation:
2320/9 = 290
4350/15 = 290
The box plot shows a comparison of the heights of gymnasts and basketball players. The mean absolute deviation for each group is approximately 2.
How many mean absolute deviations describe the difference between the two medians?
See image below:
Please give me an answer, work doesn't have to be shown at all, thank you so much.
Answer:
6.75 in
Analysis:
[tex]\text{The average heights of gymnasts is 60 in, the other is 75 in.}[/tex]
[tex](60+75)\div2=6.75 \ \text{in}[/tex]
In8=2.08 in exponential form
write an equation of the line that passes through (-1,0) and (0,0)
y=
Answer:
y = 0
Step-by-step explanation:
the 2 points (- 1, 0 ) and (0, 0 ) both have the same y- coordinate.
this indicates the line is horizontal with equation
y = c ( c is the value of the y- coordinates the line passes through )
both points have a y- coordinate of 0 , then
y = 0 ← equation of line
simplify 3 c -9 d+7 c+5 d
A shop is having a sale. All items are reduced by 20%. Work out the price of an item that is normally £120
The price of an item that is normally £120 after a 20% discount is £96.
To find the price of an item that is normally £120 after a 20% discount,
Calculate the discount amount: To find the discount amount, multiply the original price (£120) by the discount rate ( 20% ) in decimal form:
Discount amount = Original price x Discount rate
= £120 x 0.2
= £24
Calculate the sale price: To find the sale price, subtract the discount amount from the original price:
Sale price = Original price - Discount amount
= £120 - £24
= £96
Therefore, the sale price is £96
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In the diagram below of circle O, PA is tangent to circle O
at A, and PBC is a secant with points B and C on the circle.
A
4
8
B
C
If PA= 8 and PB = 4, what is the length of BC?
The length of BC is 6 units.
Describe Tangent?In geometry, the tangent is commonly used to describe the relationship between a circle and a straight line. A tangent line to a circle is a line that intersects the circle at exactly one point. This point of intersection is called the point of tangency. The tangent line is perpendicular to the radius of the circle at the point of tangency.
By the tangent-secant theorem, we have:
PB^2 = PA(PA + AB)
where AB is the length of the tangent segment from point A to the point of intersection of the secant with the circle.
Substituting the given values, we get:
4^2 = 8(8 + AB)
Simplifying and solving for AB, we get:
16 = 64 + 8AB
8AB = -48
AB = -6
Since AB is a length, it must be positive, so we take the absolute value:
AB = 6
Now we can use the secant-tangent theorem to find the length of BC:
PC(PC + BC) = PB^2
Substituting the given values and using the fact that PC = PA = 8, we get:
8(8 + BC) = 4^2
64 + 8BC = 16
8BC = -48
BC = -6
Again, since BC is a length, it must be positive, so we take the absolute value:
BC = 6
Therefore, the length of BC is 6 units.
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Which of the following is a rational number?
Answer:
-77
Step-by-step explanation:
What is Radical? The radical of a number is the same as the root of a number. The root can be a square root, cube root, or in general, nth root. Thus, any number or expression that uses a root is known as a radical. The term radical is derived from the Latin word Radix which means root.
(Taken from Online)
Which pair of angles are corresponding?
A. <1 and <3
B. <3 and <4
C. <1 and <8
D. <2 and <6
Answer:
2 and 6
Step-by-step explanation:
2 and 6 is the correct option
Please help ASAP!
Filipe bought a classic car, originally valued at $60,000, in 2012. He believes that the value of the car depreciates exponentially at a rate of 4% each year.
Round the expected value of Filipe's car after 6 years to the nearest cent.
Click “show your work” and show your steps to solve this problem.
(Hint: You need to use the exponential decay formula)
In a case whereby Filipe bought a classic car, originally valued at $60,000, in 2012. whee the value of the car depreciates exponentially at a rate of 4% the expected value of Filipe's car after 6 years is $46970
How can the expected value of Filipe's carbe calculated?Based on the given information, the future value when there is a depreciation can be calculated using the formular below:
FV =[ P (1 - r)^n]
where the
R represent the rate of depreciation =4% = 0.04
N represent the number of years = 6 years
FV represent the Future value
P represent the Present value
From the formula we can input the values as :
$60,000 x ( 1 - 0.04)^6 = $42,890
=$46965.5
=$46970 (rounded up)
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The sum of the areas of the two squares on the legs ( a and b ) equals the area of the square on the hypotenuse ( c )?
Answer: A^2 + B^2 = C^2
Step-by-step explanation:
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Step-by-step explanation:
A square has all the sides equal
If AD which is a side is 11, all other sides are 1
BC is 11
AC is a diagonal that divides the square and forms a triangle
AD =11
CD =11
Use Pythagoras theorem to find AC which is hypotenuse
AC² = AD² + CD²
= 121 + 121
=242
If AC² = 242, then AC is square root of 242
AC = 15.56 (approximate if required) 15.6 to 1d.p if required
BD = AC = 15.56
EC is half of BD and AC = 15.56/2
EC = 7.78 (check the decimal place required) 7.8 to 1d.p if required
Angle DAB is 90
Angle AEB is 90
Angle CBD is 45
Angle BAC is 45
(Add the units)
Quadrilateral C with 4 congruent sides is a square, all opposite sides are congruent
Quad L is a parallelogram, consecutive angles are supplementary and opposite angles are congruent
The width of a box is two-third of it's length and height is one-third of it's length. If the volume of the box is 384 cubic meter, find the dimensions of the box.
Answer:
Length - 12 m, width - 8m, height - 4 m
--------------------------------------
The relation between dimensions of the box:
w = (2/3)l;h = (1/3)l;V = 384 m³.Use volume equation and find the value of l:
V = lwh384 = l*(2/3)l*(1/3)l384 = 2/9l³l³ = 384*9/2l³ = 1728l = ∛1728l = 12 mFind the width and height:
w = (2/3)*12 = 8 mh = (1/3)*12 = 4 mThe radius of a quarter circle is 1 yard. What is the quarter circle's perimeter?
The perimeter of the quarter circle with radius 1 yard is approximately 2.57 yards.
To find the perimeter of a quarter circle, we need to add up the lengths of its curved edge and its straight edge.
In this case, the curved edge is a quarter of a circle with radius 1 yard. The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle. Since we only need a quarter of the circumference, we can divide the formula by 4:
C = (2πr)/4
Substituting r = 1, we get:
C = (2π(1))/4
C = π/2
Therefore, the curved edge of the quarter circle has a length of π/2 yards. The straight edge of the quarter circle is simply the radius, which is also 1 yard.
So the perimeter of the quarter circle is the sum of the curved edge and the straight edge:
Perimeter = (π/2) + 1
Using 3.14 for π and adding the two terms, we get:
Perimeter ≈ 2.57 yards
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