The cost of bill is,
⇒ $24
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
To Calculate the percent of a number , divide the number by whole number and multiply by 100.
Given that;
A 15% tip on a restaurant bill is $3.60.
Now,
Let the cost of bill is, $x
Hence, We can formulate;
⇒ 15% of x = 3.60
⇒ 15x/100 = 3.60
⇒ 15x = 360
⇒ x = 360 / 15
⇒ x = 24
Thus, The cost of bill is, $24
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A group of friends wants to go to the amusement park. They have no more than $160 to spend on parking and admission. Parking is $10.50, and tickets cost $32.50 per person, including tax. Write and solve an inequality which can be used to determine x, the number of people who can go to the amusement park.
Answer:
x=4.6 answer is at most 4 people can go
Step-by-step explanation:
32.50x+10.50=160.00
- 10.50 -10.50
149.50
32.50x = 149.50
Divide 32.50 and 149.50 to find x.
x = 4.6 round down because you cant have a fraction of a person. so 4 people can go.
Which binomial is a factor of f/x )= x³ 6x² +3x 10?
Factor (x+1) is the binomial factor for x³ - 6x²+ 3x + 10 using the rational roots test.
If a polynomial function has integer coefficients, then every rational zero will have the form p/q where p is a factor of the constant and q is a factor of the leading coefficient.
p = ±1, ±10, ±2, ±5
q = ±1
Find every combination of ± p/q . These are the possible roots of the polynomial function.
±1, ±10, ±2, ±5
Substitute −1 and simplify the expression. In this case, the expression is equal to 0 so −1 is a root of the polynomial.
Substitute: −1 into the polynomial.
(−1)3−6(−1)2+3⋅(−1)+10
Raise −1 to the power of 3.−1−6(−1)2+3⋅−1+10
Raise −1 to the power of 2.−1 −6⋅1 + 3⋅−1+ 10
Multiply −6 by 1.−1−6+3⋅−1+10
Subtract 6 from −1.−7+3⋅−1+10
Multiply 3 by −1.−7−310
Subtract 3 from −7.−10+10
Add −10 and 10.0Since −1 is a known root, divide the polynomial by x+1 to find the quotient polynomial. This polynomial can then be used to find the remaining roots.
x³− 6x²+ 3x+ 10x+ 1
Divide
x³−6x²+ 3x+ 10 by x + 1.
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Find an equivalent ratio in simplest terms:
22:36
Answer:
11:18.
Step-by-step explanation:
22:36
We divide each number by their Greatest Common Factor.
The GCF of 22 and 36 is 2.
So, in simplest terms
22:36 = 11:18.
What will be the nature of roots of quadratic equation 2x2 4x 7?
The roots of the quadratic equation 2x2 4x 7 will be two complex conjugate roots.
To determine the nature of roots of a quadratic equation, we can use the formula of the discriminant. The discriminant of a quadratic equation ax2 + bx + c = 0 is given by D = b2 - 4ac.
For the equation 2x2 4x 7, the discriminant is D = (-4)2 - 4(2)(7) = 16 - 56 = -40.
Since the discriminant is negative, the roots will be two complex conjugate roots.
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Is rigid motion congruent?
Yes, rigid motion is congruent?
What is rigid motion congruency?A stiff motion occurs when an object is transported from one place to another while maintaining its original size and shape.
If and only if there is a stiff motion that establishes a correspondence of one figure as the likeness of the other, then two figures are said to be congruent. Interior angles are unchanged, as well as side lengths.
An object is rigidly moved from its initial place to the exact same location in a motion known as an identity motion. It appears as though the thing hasn't changed at all.
According to the Common Core, the "principle of superposition" states that two figures are congruent if there is a rigid motion projecting one onto the other.
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Find the total surface area of the cone in the figure. (Use π = 3.14.)
A) 282.6 cm^2
B) 219.8 cm^2
C) 266.9 cm^2
D) 314.0 cm^2
The total surface area of the cone is calculated to be
A) 282.6 cm²How to find the total surface area of the coneInformation given in the problem
the total surface area of the cone in the figure. (Use π = 3.14.)
A cone is a three-dimensional geometric structure with a smooth transition from a flat, usually circular base to the apex or vertex, a point that creates an axis to the base's center.
The formula of the total surface are of a cone is given by
T = πr(r + l) square units.
calculating for l
l = √(12² + 5²) = 13
= 3.14 * 5 (5 + 13)
= 3.14 * 5 *(18)
= 282.6 cm^2
282.6 cm^2 is the total surface area of the cone
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What are 2 digit multiples of 27?
The first 20 multiples of 27 are as follows:
27, 54, 81, 108, 135, 162, 189, 216, 243, 270, 297, 324, 351, 378, 405, 432, 459, 486, 513, and 540.
What are multiples?A multiple in mathematics is created by multiplying any number by an integer.
In other words, if b = na for some integer n, known as the multiplier, it can be said that b is a multiple of a given two numbers, a and b.
This is equivalent to stating that b/a is an integer if an is not zero.
A is known as a divisor of b when a and b are both integers and b is a multiple of a.
First 20 multiples of 27:
27, 54, 81, 108, 135, 162, 189, 216, 243, 270, 297, 324, 351, 378, 405, 432, 459, 486, 513, and 540.
Therefore, the first 20 multiples of 27 are as follows:
27, 54, 81, 108, 135, 162, 189, 216, 243, 270, 297, 324, 351, 378, 405, 432, 459, 486, 513, and 540.
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Correct question:
What are the first 20 multiples of 27?
Multiply pls
a
1. (a + b)(a + b) =
2. (3a-2b) (3a - 2b) =
3. (x - 4y)(-3x - 2y) =
4.(-y-2z)(y-2z) =
Answer: FOIL method
1. (a + b)(a + b) =
= a² + ab + b² + ab
= a² + 2ab + b²
2. (3a-2b) (3a - 2b) =
= 9a² - 6ab - 6ab + 4b²
= 9a² -12ab + 4b²
3. (x - 4y)(-3x - 2y) =
= -3x² -2xy +12xy +8y²
= -3x² + 10xy + 8y²
4.(-y-2z)(y-2z) =
= -y² + 2yz -2yz + 4z²
= -y² + 4z²
Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-What is a linear graph formula?
Linear graph equations are one-degree equations. It is a straight-line equation. A linear equation with parameters a and b equal to zero has the conventional form ax + by + c = 0.
How do one express the standard form of a linear equation?
A linear equation has the following standard form: ax + by + c = 0.
Here, variables x and y and constants a, b, and c are used.
Also, a ≠ 0, and b ≠ 0.
For linear equations, the slope-intercept formula is: y=mx+b
Where m stands for the line's slope and b represents the y-intercept.
The three types of linear equations are point-slope, slope-intercept, and standard form.
When an algebraic equation is graphed, it always produces a straight line since each term has an exponent of 1 or 0. This type of equation is known as a linear equation.
Steps of drawing linear graphs are described below:
Step 1: Using the provided linear equation, determine the value of y with respect to x.
Step 2: Arrange these data in a table format.
Step 3: Create a graph using the points from the database.
Step 4: Connect the points to form a straight line.
So, ax + by + c = 0 is a linear graph formula.
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Find the curl and the divergence of the vector field.F(x, y, z) = ‹ex, exy, exyz›
The curl and the divergence of the vector field is illustrated below.
The term vector in math contains both position and magnitude.
Here we need to find the curl and the divergence of the vector field.
While we looking into the given question, we have the function
=> F(x, y, z) = <ex, exy, exyz>
AS per the concept of convergence, here we have consider that F=⟨P,Q,R⟩ is a vector field in R3 and Px, Qy, and Rz all exist here then the divergence of F is defined by as,
=> div F = Px + Qy + Rz
=> div F = ∂P/∂x + ∂Q/∂y + ∂R/∂z.
The term curl in vector field is defined as a vector operator that describes the infinitesimal circulation of a vector field in three-dimensional Euclidean space
And the curl of the vector field is calculated as,
=> curl F = (Ry−Qz)i + (Pz−Rx)j + (Qx−Py)k
=> curl F = (∂R/∂y−∂Q/∂z)i + (∂P/∂z−∂R/∂x)j + (∂Q/∂x−∂P/∂y)k.
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-8/19+(-2)/57 solve.
[tex] \frac{ - 8}{19} + \frac{ - 2}{57} \\ \\ [/tex]
LCM of 19 and 57 is 57
so,
[tex] \frac{ - 8 \times 3}{19 \times 3} \\ + \\ \frac{ - 2 \times 1}{57 \times 1} [/tex]
[tex] \frac{ - 24}{57} + \frac{ - 2}{57} \\ [/tex]
as negative negative cancel out each other.
[tex] \frac{24}{57} + \frac{2}{57} \\ [/tex]
now simply add this
[tex] \frac{24 + 2}{57} = \\ \frac{26}{57} [/tex]
Now the answer is :: 26/57
Simplify the expression a^2(m-7a^3)-m(a^2-10)
Answer:
the answer it's-7a^5+10m
2x + 3y = 12
what is the slope
answer : slope is -2/3
line should look like
y = mx + b
slope is m or the number next to x
slope refers to the rate or speed of something
make 2x + 3y = 12 look like y = mx + b
2x + 3y = 12
3y = -2x + 12
y = (-2x + 12)/3
y = -2/3x + 12/3
y = -2/3x + 4
slope is -2/3
b is called the y intercept
b is +4 which is where the line passes thru in the y axis at (0,4)
when x is 0 but y is not then that means the graph is not proportional
Determine the range of the following graph:
Answer:
[-9,0]
Step-by-step explanation:
Look along the y inercept and find where the lines end
plus they are solid circles so it'd be closed
Answer: see below
Step-by-step explanation:
The range is the set of possible output values shown on the y-axis.
This graph's maximum y value, or the highest y value, is 0. The lowest y value is -9
R:yE[-9,0]
please help draw line segment AB and find its axis of symmetry
The figure is attached.
What is axis of symmetry?The axis of symmetry is a straight line that makes the shape of the object symmetrical. The axis of symmetry creates the exact reflections on each of its sides.
Given that, draw line segment AB and find its axis of symmetry
Let's first draw a line segment of length 7.3 cm.
1) Draw a line l, mark point A on it.
2) Since length is 7.3 cm, we measure 7.3 cm using ruler and compass.
3) Now, keeping compass opened the same length, we keep pointed end at point A and draw an arc on line l.
So, the required line segment is AB = 7.3 cm.
Now, we need to find its axis of symmetry.
1) Given a line segment AB.
2) Now with A as centre, and radius more than half AB, draw an arc on top and bottom of AB.
3) Now with B as centre, and same radius, draw an arc on top and bottom of AB.
4) Where the two arcs intersect above AB is point C and where the two arcs intersect below AB is point D.
Join CD.
CD is the line of symmetry of line segment AB.
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How do you identify a quadrilateral?
We can identify quadrilateral because a regular polygon must have four equal sides in order to be called a quadrilateral.
Describe the quadrilateral.
Having four sides, four vertices, and four angles, a closed quadrilateral is a type of polygon. It consists of four connected non-collinear points. Quadrilaterals' internal angles always add up to 360 degrees.
According to the given question:
In a quadrilateral -
Four vertices make up each of them.Four sides comprise each side.All interior angles add up to 360 degrees.There are 2 diagonals.Both regular and irregular quadrilaterals exist.In order to be considered a quadrilateral, it must have four sides, four angles.
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How is the literal equation y = a( bx + c) similar to the equation for converting °F to °C?
How would you solve this equation for the variable x ?
ans is 4 I don't really know how to explain it
In the figure below OZ perpendicular OX and OY perpendicular OW. If a= 50, what is the value of C? A.50 B.45 C.40 D.35 E.30
Answer:
A. 50
Step-by-step explanation:
a + b = 90
b = 90-50 = 40
b + c = 90
c = 90-40 = 50
What is SSS rule in maths?
According to the SSS rule, two triangles are said to be congruent if all three sides of one triangle are equal to the corresponding three sides of the second triangle.
What is the SSS condition?According to the SSS rule, two triangles are considered to be congruent if the corresponding three sides of each triangle are equal to each other.
The triangles are congruent if all three sets of comparable sides are present.
The side-side-side shortcut is a congruence technique (SSS).
Side-angle-side (SAS), which uses two sets of sides and an angle between them that is known to be congruent, is another shortcut.
Therefore, according to the SSS rule, two triangles are said to be congruent if all three sides of one triangle are equal to the corresponding three sides of the second triangle.
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Identify the graph of f(x)=2|x+3|.
Answer:
The graph f(x)=2×+3 will have y-intercepts of (0,3) and a slope of 2.
reasoning suppose le ol i and fe o gi. what else must you know in order to prove kfde and kghi are congruent by asa? by aas?
In order to prove that KFDE and KGHI are congruent by ASA, you need to know that KFDE and KGHI have two congruent angles (angle F and angle H) and a congruent side (side DE and side HI).
In order to prove that KFDE and KGHI are congruent by AAS, you need to know that KFDE and KGHI have three congruent angles (angle F, angle G, and angle H). This means that the angles in the triangle are equal, which implies that the sides in the triangle are also equal. Thus, for AAS, KFDE and KGHI must have two congruent sides (side DE and side HI).
Therefore, in order to prove that KFDE and KGHI are congruent by ASA or AAS, you must know that both triangles have two congruent angles and a congruent side (for ASA) or three congruent angles and two congruent sides (for AAS).
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Which entence i correct?
A. -3 > 2
B. -3 < -6
C. -3 > - 8
D. -3 > -2
The correct sentence is C, "-3 > -8."
Here's how you can determine which sentence is correct:
In sentence A, -3 is not greater than 2, so sentence A is incorrect.
In sentence B, -3 is not less than -6, so sentence B is incorrect.
In sentence C, -3 is indeed greater than -8, so sentence C is correct.
In sentence D, -3 is not greater than -2, so sentence D is incorrect.
Remember that when comparing two negative numbers, the one with the smaller absolute value is the larger negative number. For example, -8 is a larger negative number than -3 because -8 is closer to 0 (which is the smallest possible number). Similarly, -2 is a larger negative number than -3 because -2 is closer to 0.
Hence, The correct sentence is C, "-3 > -8."
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The base of a triangular prism is a right triangle with a base of 20 feet and a height of 120 inches. The height of the prism is 5 feet. What is the volume of the prism, in cubic feet? Enter your answer as a number, like this: 42 Do not enter units.
750 cubic feet is the volume of the prism and Therefore, the volume of Jake's box is 8 times larger than Havana's box.
What are a right triangle's three sides?A right right triangle hypotenuse is its longest side, its "across" side is the one that faces a certain angle, and its "adjacent" side is the one that faces the angle in question. To describe both sides of right triangles, we utilize specific terminology. The side opposing its right angle is always the tangent of a right triangle.
Briefing:Dimensions of the Right Triangular Base
Base = 20 feet
Height= 120 inches = 10 feet
Base Area of the Prism
1/2 * 20 * 10
= 150 sq.feet
Height of the Prism = 5 feet
Volume of the Prism = Base Area X Height
= 150 X 5
=750 cubic feet
Jake's Box
Length: 12 inches
Width: 4 inches
Height: 8 inches
Volume = 12 X 4 X 8 =384 cubic inches
Havana's box
Jake's shipment crate is comparable to the one in Havana, except it is only half as long overall.
Therefore:
Length: 12/2=6 inches
Width: 4/2=2 inches
Height: 8/2=4 inches
Volume = 6 X 2 X 4 =48 cubic inches
Now:
384/48=8
Therefore, Jake's box has an 8-times higher volume than Havana's box.
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What is the slope if it is perpendicular?
The slope if it is perpendicular is [tex]-\frac{1}{m}[/tex].
What is slope ?
The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).
What is perpendicular ?
The word perpendicular means at right angles and this is because when two lines meet, they form right angles. Perpendicular lines can face in any direction such as up and down, crossways, and side-to-side.
Let y = 3x + 1 is perpendicular ,
differentiate respect of x
[tex]\frac{dy}{dx} = 3[/tex] , m = 3
Thus , [tex]-\frac{1}{m}[/tex]
then [tex]-\frac{1}{3}[/tex]
The slope if it is perpendicular is [tex]-\frac{1}{m}[/tex].
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Is 7 is a polynomial?
7 is a constant value and it is a polynomial of degree 0.
7 is a polynomial.
What is a polynomial?Polynomial is an equation written as the sum of terms of the form kx^n.
where k and n are positive integers.
We have,
7
This can be assumed as 0x³ + 0x² + 0x + 7.
This is a polynomial.
Thus,
7 is a polynomial.
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Mr. Harrell has 64 feet of fencing that he will use to build a rectangular enclosement for chickens and he will use his barn as one of of the sides of the rectangle as seen in the image. Write a function A (x) relating the area of the enclosement A and the width of the rectangle x. Then, find the width that maximizes the area. Then state the maximum area.
Answer:
A = x(64 -x)/2x = 32 ft512 ft²Step-by-step explanation:
Given 64 feet of fencing that can be used for three sides of a rectangular enclosure next to a barn wall, you want a function for area in terms of enclosure width, the width that maximizes area, and the maximum area.
(a) FunctionIf we define the width (x) as the dimension parallel to the barn wall, then the fence available for the "height" (out from the barn wall) is (64-x) in length. Half that is used on either end of the enclosure, so the area is ...
A = WH
A(x) = x(64 -x)/2
(b) Best widthWe notice this function describes a parabola that opens downward, with zeros at x=0 and x=64. The vertex (maximum) is on the line of symmetry, halfway between the zeros:
x = (0 +64)/2 = 32
The width that maximizes area is x = 32 ft.
(c) Maximum areaUsing x=32 in the area formula, we find the maximum area to be ...
A(32) = 32(64 -32)/2 = 1024/2 = 512 . . . . square feet
The maximum area is 512 square feet.
__
Additional comment
Perhaps you can see that the best width is half the length of the available fence. The other half of the fence is used for the ends of the enclosure. This is the generic solution to this kind of problem.
Why binomial theorem is used?
Binomial theorem is used to calculate the roots of the equations with highest degree in advance mathematical calculation in any subject.
Binomial theorem is represented by :
( a + b )ⁿ = ⁿC₀aⁿb⁰ + ⁿC₁aⁿ⁻¹b¹ + ⁿC₂aⁿ⁻²b² +..............+ ⁿCₙa⁰bⁿ
When the value of n is higher it helps us to calculate the value of the given expression easily and accurately.I t helps us to calculate the roots of the equation with higher degree in advance mathematics.It also help us to prove many mathematical and Physics equations.It help us to determine the Weather forecast , in architecture calculations , and cost estimation in many engineering projects.Therefore, the binomial theorem help us to calculate the roots of the equations with highest degree in advance mathematical calculations in many subjects.
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Sakhi old a watch at a profit of 15%. Had he bought it at 10% le and old for R. 28 le, he would have gained 20%. Find the cot of the watch
Based on the calculation, we get that the cost of the watch is Rs 22.50.
Cost is the amount of resources, time, money, or effort that must be expended to achieve a goal or achieve something. It can refer to the financial or monetary expense of something, but it can also refer to other types of resources or effort that must be invested.
Let C be the cost of the watch.
The profit that Sakhi made on the watch was 15% of C. We can express this as:
Profit = (15/100) * C
If Sakhi had bought the watch at 10% less than the price at which he sold it and sold it for Rs. 28 le, he would have gained 20% on the sale. We can express this as:
Profit = (20/100) * (C - (10/100) * C)
We can set these two expressions for profit equal to each other and solve for C:
(15/100) * C = (20/100) * (C - (10/100) * C)
This simplifies to:
15/100 = 20/100 - (10/100)^2
Which simplifies to:
15 = 20 - (10/100)
Solving for C, we find that the cost of the watch is:
C = Rs. 22.50
Therefore, the cost of the watch is Rs. 22.50.
The missing part in the question is shown below.
Sakhi sold a watch at a profit of 15%. Had he bought it at 10% le and sold for Rs. 28 le, he would have gained 20%. Find the cost of the watch
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What is the formula for three consecutive odd numbers?
The formula to determine the consecutive odd numbers of a specific value "x" is:
x + 2n
What are consecutive numbers?Consecutive numbers are those numerical values that are found just after a specific number or value, for example consecutive numbers from 5 will be 6 onwards.
If we want to know the consecutive numbers immediately we add +1, +2 and so on.
But as we only want the odd numbers we will add +2, +4 and +6, having as a result the following numbers:
x + 2 x + 4 x + 6If we generalize an equation we have
x + 2n
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a linear function has an x-intercept of −8 − 8 and a y-intercept of 4 4 . which of these is an equation of the linear function?
So, y = (1/2)(x + 8) is the equation of the linear function.
To write the equation of a linear function with a given x-intercept and y-intercept, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
In this case, we are given that the x-intercept is (-8, 0) and the y-intercept is (0, 4). We can use the coordinates of the x-intercept as (x1, y1) and the slope of the line as m to write the equation:
y - 0 = m(x - (-8))
y = m(x + 8)
We can then substitute the y-intercept into this equation to find the value of m:
4 = m(0 + 8)
4 = 8m
m = 1/2
Substituting the value of m back into the equation, we get:
y = (1/2)(x + 8)
This is the equation of the linear function.
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y - y1 = m(x - x1)
y - 0 = m(x - (-8))
y = m(x + 8)
We can then substitute the y-intercept into this equation to find the value of m:
4 = m(0 + 8)
4 = 8m
m = 1/2
Substituting the value of m back into the equation, we get:
y = (1/2)(x + 8)