Help please with this maths

Answer:

Step-by-step explanation:

Given that Angie can mow her lawn 4 times using 1/3 gallon of gas, you want to know how much gas is required for each mowing, and how many times Angie can mow on one gallon of gas.

To find the number of gallons required for each mowing of the lawn, divide the number of gallons by the number of mowings:

  (1/3 gal)/(4 mowings) = 1/(3·4) gal/mowing = 1/12 gal/mowing

It takes 1/12 gallon to mow the lawn once.

The reciprocal of this value has the reciprocal units.

  1/(1/12 gal/mowing) = 12 mowings/gal

Angie can mow the lawn 12 times with one gallon of gas.

__

Additional comment

It often proves useful to keep the units with the numbers when working rate problems. This can eliminate a lot of mistakes. The units are treated as you would treat a variable.

Answer: The first and third options are correct.

Step-by-step explanation:

By algebra properties and trigonometric formulas, the roots x₁ = 30° + n · 360° and x₂ = 210° + n · 360° are solutions of trigonometric function tan x - √(1 - 2 · tan² x) = 0. (Correct choice: B)

In this problem we find a given trigonometric function, whose solution must be found by combining algebra properties and trigonometric formulas. First, write the entire expression:

tan x - √(1 - 2 · tan² x) = 0

Second, use algebra and root properties:

tan x = √(1 - 2 · tan² x)

tan² x = 1 - 2 · tan² x

3 · tan² x = 1

Third, clear x by algebra properties and inverse trigonometric properties:

tan² x = 1 / 3

tan x = √(1 / 3)

tan x = 1 / √3

tan x = √3 / 3

x = tan⁻¹ (√3 / 3)

x  = 30° or x = 210°

Since tangent function has a period of 2π (360°), then the solutions of the trigonometric function is:

x₁ = 30° + n · 360°, x₂ = 210° + n · 360°.

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The nature of the roots of the equation x^2 - 5x + 7 = 0 : no real roots

Consider given quadratic equation: x^2 - 5x + 7 = 0

Comparing given quadratic equation with the standard form of quadratic equation i.e., ax^2 + bx + c = 0

a = 1, b = -5, c = 7

First we find the discriminant:

D = b^2 - 4ac

D = (-5)^2 - 4(1)(7)

D = 25 - 4(7)

D = 25 - 28

D = -3

Since, the discriminant D < 0

Therefore, there are no real roots of this equation.

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Retail price of the product will be double its mean will have a prbability of 0.0401.

An example of a continuous probability distribution is the normal distribution, in which the majority of data points cluster in the middle of the range while the remaining ones taper off symmetrically toward either extreme. The distribution's mean is another name for the center of the range.

A probability distribution that is symmetric around the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean. The normal distribution appears as a "bell curve" on a graph.

The value of the product considering = $37*2 = $74(x)

Mean = $37

Standard Deviation (SD)= $20

here z= [tex]\frac{x - mean}{SD}[/tex] = [tex]\frac{74 - 37}{20} = \frac{37}{20} = 1.75[/tex]

P(z>1.75) = 1 - [tex]\phi(1.75)[/tex] = 1 - .9599 = 0.0401

Retail price of the product will be double its mean will have a prbability of 0.0401.

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Answer: 47

Step-by-step explanation:

4.72 / .1= 47

47

90° is the angle between the lines  2x = 3y = -z and 6x = -y = -2z and explained with directions of ratios as below

Direction ratios of line 2x = 3y = -z  which can be mentioned as [tex]\frac{x}{1/2} = \frac{y}{1/3} = \frac{z}{-1}[/tex] hence  [tex](\frac{1}{2} , \frac{1}{3} ,-1 )[/tex]

Direction ratios of line  6x = -y = -2z  which can be mentioned as

[tex]\frac{x}{1/6} = \frac{y}{-1} =\frac{z}{-1/4}[/tex] hence   [tex](\frac{1}{6} , -1 , \frac{-1}{4} )[/tex]

hence the dot product of the direction ratio of two line is

[tex]\frac{1}{2} .\frac{1}{6} + \frac{1}{3} . (-1) + (-1) . \frac{-1}{4}[/tex]  

= [tex]\frac{1}{12} -\frac{1}{3} + \frac{1}{4}[/tex]  

= 0

hence this shows that angle between the given equations is 90°

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Statement A,B is true rest all statement are false about the given function.

Given the function: [tex]2x^3+8[/tex]

Statement A:

The domain of a function is the set of all possible input values (x-values) for which the function produces a valid output (y-value).

For the function 2x^3 + 8, the domain is all real numbers, which is represented as (-infinity, +infinity).

It is because the expression inside the function, 2x^3, is defined for all real numbers.

so above statement is true.

Statement B:

statement A and B are same so it's also true.

Statement C:

The range of a function is the set of all possible output values (y-values) that the function can produce.

For the function 2x^3 + 8, the range is also all real numbers (-infinity, +infinity)

It is because the function is a polynomial of odd degree (3) and it does not have any restriction on the output value. Since the function does not have any restriction, it can take any real number as an output value and thus the range is all real numbers.

so this statement is false.

Statement D:

The y-intercept of the function 2x^3 + 8 is 8. It is the point at which the graph of the function crosses the y-axis, which occurs when x = 0. So when x = 0, y = 2(0)^3 + 8 = 8.

so this statement if false.

Statement E:

A function has a center of symmetry if it is unchanged (i.e. is symmetric) when reflected across a line or point. The line or point across which the function is symmetric is called the axis of symmetry or center of symmetry.

The function 2x^3 + 8 does not have a center of symmetry. It is because the function is a polynomial of odd degree and it does not have any symmetry. The polynomials of odd degree are not symmetric about any point or line.

So this statement is also false.

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================================================

Explanation:

The x and y are placeholders for numbers.

Think of them as boxes so to speak, and we fill each box with a number.

In this case we will plug in x = 6 and y = 2.

The steps are shown below.

[tex]\frac{3\text{x}+4}{\text{y}}\\\\\frac{3*6+4}{2}\\\\\frac{18+4}{2}\\\\\frac{22}{2}\\\\11\\\\[/tex]

The final answer is choice B

-----------

This means,

[tex]\frac{3\text{x}+4}{\text{y}} = 11 \ \text{when} \ \text{x} = 6 \ \text{and y} = 2 \\\\[/tex]

Put another way

[tex](\text{x},\text{y}) = (6,2) \ \text{ is a solution to } \frac{3\text{x}+4}{\text{y}} = 11[/tex]

In a visual sense, the point (6,2) is on the equation of [tex]\frac{3\text{x}+4}{\text{y}} = 11[/tex]

The cuboidal tank has a volume of [tex]6m^3[/tex] with dimensions of 4 m in length, 2 m in width, and 0.75 m in height.

The total amount of room or volume that a cuboidal tank can hold is known as its capacity. By multiplying the tank's length, width, and height collectively, it is determined.

The tank in this instance measures 4 metres long, 2 metres wide, and 0.75 metres high. We must multiply these three parameters collectively to determine the tank's capacity:

[tex]4m * 2m * 0.75m = 6m^3[/tex]

The tank can therefore hold [tex]6m^3[/tex] of liquid.

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Answer:

6 and 9/16

Step-by-step explanation:

The area of a rectangle can be calculated by multiplying the width and length. So 1 3/4*3 3/4=7/4*15/4=105/16 or 6 and 9/16

The equation  y = x + 0.4x is the retail price y in dollars for an item with the original cost and a markup of 40% .

What is equation ?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used.

So, we choose the first equation.

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Answer:

Step-by-step explanation:

SHOW HIGH CLARITY IMAGE, BUT USE CONGRUENCE OF TRINALGES AND FIND X BY EQUATING THE GIVEN SIDE I GUESS

IF YES MARK ME BRAINLIEST

Answer: I think it's 6816606.576

Step-by-step explanation: Hope this helps?

Answer: The reciprocal of a number is defined as 1 divided by that number. The opposite of a number is the number with the opposite sign. Therefore, the opposite reciprocal of a number is equal to the reciprocal of the opposite of that number.

In this case, the opposite reciprocal of 0/6 is the reciprocal of the opposite of 0/6. The opposite of 0/6 is 0/-6, which is equal to -0/6. The reciprocal of -0/6 is 1/(-0/6) = -6/0.

However, division by 0 is not defined, so it is not possible to find the reciprocal of -0/6. Therefore, the opposite reciprocal of 0/6 is undefined.

Step-by-step explanation:

Answer:

there is no reciprocal for 0/6

Step-by-step explanation:

Logs are a type of mathematical operation used to solve exponential equations.

Logs are written as log boxes, where b is the base. The base is the number that the logarithm is being calculated concerning. The x is the number that the logarithm is calculated. Logarithms allow us to convert multiplication and division problems into addition and subtraction.

For example, log2 (8) can be calculated by taking the logarithm of 2, which is 0.301029996, and then multiplying it by 8, which is 2.408239965. This means that log2 (8) is equal to 2.408239965.

Another example is log10 (100). This can be calculated by taking the logarithm of 10, which is 1 and then multiplying it by 100, which is 100.

This means that log10 (100) is equal to 100. Logs are an important tool in mathematics and are used in a variety of fields, such as chemistry, engineering, and economics.

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The likelihood event:

Player 1 is more likely to hit the ball than Player 2 because P (Player 1) > P (Player 2).

The correct option is A.

Least Common Multiple is the meaning of the acronym LCM. The lowest number that may be divided by both numbers is known as the least common multiple (LCM) of two numbers. It may also be computed using two or more real numbers.

Given:

Three softball players discussed their batting averages after a game.

Probability:

Player 1 = six tenths = 6/10

Player 2 = five ninths = 5/9

Player 3 = four sevenths = 4/7

To find better batting averages:

LCM of 10, 9 and 7.

10 = 2 x 5. 9 = 3 x 3, 7 = 7

So, the LCM (10, 9, 7) = 630

Now we have the number of chances are equal for each of the three players.

So, the P(Player 1) = 6/10 = 378/630

P(Player 2)= 5/9 = 350/630

P(Player 3)= 4/7 = 360/630

The Player 1 has better batting average than Player 2 and Player 3.

Therefore, Player 1 is more likely to hit the ball than Player 2 because P (Player 1) > P (Player 2).

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Answer:

Step-by-step explanation:

slope is the coefficient of x when the coeficient of y is 1.

we need change the form.

2y=x+8

y=[tex]\frac{1}{2}[/tex]x+4

so, the slope of a line parallel to the line is 1/2

Answer:

Step-by-step explanation:

WX≅VY

VY = 7

CD≅BE

BE = 13

Answer: x= 8+ x over 2 = x over 2 + 8

Step-by-step explanation:

The length of the line is 5 units.

The distance between two points is the length of the line joining the two points.

Formula: distance= √(x_2-x_1)²+(y_2-y_1)²

Given that, endpoints are (-1,4) and (2,0) of the line segment.

The length= √(2+1)²+(0-4)²

                 =5units

Hence, The length of the line is 5 units.

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To verify the inverse we can use Horizontal Line Test.

Suppose F is a function.

F does not have an inverse if any horizontal line crosses the graph of f more than once. If no horizontal line crosses the graph of F more than once, then F does have an inverse. In mathematics, having an inverse is a very significant quality, and it has a name.

If and only if a function f has an inverse, then it is one-to-one. The following definition, which is also the one that is most frequently used, is equivalent. If f(a) = f(b) implies a = b for all a and b in its domain, then a function f is one-to-one.

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A pentagonal prism have 35 diagonals.

We know tha in a polygon or polyhedron the formula for finding the number of diagonals is: n(n-3)/2,

where n= the number of sides

We find the number of diagonals of a pentagonal prism.

As we know a pentagonal prism has two pentagonal bases like top and bottom and five rectangular sides.

For a pentagonal prism n = 10

So, using above formula the total number of diagonals would be,

d = [10 × (10 - 3)] / 2

d = (10 × 7) / 2

d = 70/2

d = 35

Therefore, the total number of diagonals would be = 35

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The midpoint for zero is (0,0).

The midpoint can be zero. This is dependent on the value of the two points. For two points on a number line on points with values -4, and 4, the midpoint is 0. And for two points such as (-2, 5), and (2, -5), the midpoint is equal to (0, 0).

The midpoint of a line segment is known as the midpoint in geometry. It is the centroid of the segment and of the ends, and it is equally distant from both of them. It cuts the section in half.

A compass and straightedge setup can be used to locate the midpoint of the line segment they determine given two points of interest. By initially building a lens out of circular arcs with equal radii centered at the two endpoints and joining the cusps of the lens, one can determine the midpoint of a line segment immersed in a plane. The midpoint of the segment is then the place where the line joining the cusps intersects the segment.

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Therefore , the solution of the given problem of triangle comes out to be  ΔA"B"C "≅ ΔABC is congruent.

The fact that a triangle has sides or vertices qualifies it as a polygon. It is an elementary geometric form. The name given to a triangle with vertices A, B, & C is Triangle ABC. A singular planes and triangle are obtained in Euclidean geometry when the vertices are not collinear. Any triangle that has three sides and three corners is a polygon.

Here,

Triangle A'B'C' is created by reflecting triangle ABC across the y-axis.

Afterward, it was dilated by a ratio of 1/3 to create triangle A "B"C".

Find the right answer for the triangles ABC and A"B"C."

So,

We are aware that reflection undergoes a rigorous transformation, meaning the shape and size of the original object do not change.

As a result, after reflection, figures always match their pictures.

"ABC," "A'B'C," etc (i)

The process of dilation is flexible. Although the size is changed, the shape is still the same.

Figures after dilatation therefore always resemble their photographs.

ΔA'B'C' ≅ ΔA "B"C" ... (ii)

With I and (ii), we obtain

ΔA"B"C "≅ ΔABC

Similar triangles include ABC and ABC.

As a result, choice A is the right one.

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Answer:

22

Step-by-step explanation:

I timesed 11 by 12 which is 132 and then timesed 10 with 11 which then gave me 110. I then subtracted 132 with 110 which gave me the answer 22. if we remove 11 from the 22 books we then end up with 11. then times it by 12 = 132. then if you subtract 10 of the 22 books then we end up with 12. then times it by 11 which is 132 as well.

Answer:

48cm^2

Step-by-step explanation:

Rectangle=LxW

Triangle=bh/2

Rectangle: 10x4=40cm^2

Triangle: 4x4=16/2=8cm^2

40+8=48cm^2

Hope this helps :)

The total amount withheld from the student's pay last year in federal tax, state tax, and FICA is $667.50 + $201.25 = $868.75

Percentage is a way of expressing a number as a fraction of 100. It is often denoted using the symbol "%" (percent sign). Percentages are used to express how much of something there is in relation to the whole. For example, if a student answers 80% of the questions correctly on a test, it means they answered 80 out of 100 questions correctly.

A tax is a financial charge imposed by a government on individuals, businesses, or other entities to raise revenue for government spending. Taxes are typically based on a percentage of income or sales, and can be levied on various forms of income, including wages, salaries, and profits. The purpose of taxation is to fund government programs and services, such as roads, schools, and national defense. Taxes can also be used to redistribute wealth and influence economic behavior.

The amount withheld from the student's pay last year in federal tax is $6675 x 0.1 = $667.50

The amount withheld from the student's pay last year in state tax is $6675 x 0.03 = $201.25

The total amount withheld from the student's pay last year in federal tax, state tax, and FICA is $667.50 + $201.25 = $868.75

So the answer is A. 867.75

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(A) There is only one solution to the given system.

(B) There is no solution to the given system

(C) There are infinite solutions to the system.

What is solution of the system?

A set of values for a variable that simultaneously satisfy each equation is the solution to a system of equations. A system of equations must be solved by identifying all possible sets of variable values that make up the system's solutions.

Given:

3(- n + 4) + 5n = 2n ← distribute and simplify left side

- 3n + 12 + 5n = 2n

2n + 12 = 2n ( subtract 12 from both sides )

2n = 2n - 12 ( subtract 2n from both sides )

0 = - 12 ← not possible

This indicates the equation has no solution

Comparing the types of solutions

A n = 3

Indicates that there is only one unique solution to the equation.

B no solutions

This is indicated when you solve and obtain a ridiculous statement, similar to the one obtained in part A, that is

0 = 12

C infinite solutions

This is indicated when you solve the equation and obtain

4 = 4 or - 3 = - 3

Hence,

(A) There is only one solution to the given system.

(B) There is no solution to the given system

(C) There are infinite solutions to the system.

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The equation to determine the length and the width of the rug is

21 = W² - 4W.

A rectangle is a quadrilateral with four right angles in the Euclidean plane. It may alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal. A square is a rectangle with four equally long sides.

A quadrilateral is a rectangle.

A rectangle's opposing sides are equal and parallel to one another.

Each vertex of a rectangle has a 90° internal angle.

360° is the total of all interior angles.

The diagonals cut each other in half.

The diagonals are all the same length.

The Pythagorean theorem may be used to determine the length of the diagonals.

A rectangle is also referred to as a parallelogram since its sides are parallel.

While all parallelograms are rectangles, not all rectangles are parallelograms.

The length of the rug is l ft

Then the width of the rug will be l-4 ft

So the are will be l*(l-4) = [tex]l\x^{2} - 4l[/tex]

We know area is 21

so the equation is 21 = [tex]l\x^{2} - 4l[/tex]  (Option a)

And after solving the equation the lenght is7m and breadth is 3 m.

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