What are the three types of solution and differentiate each type of solution?

There are 2 types of images namely virtual and real image

The point where light rays from an object meet or appear to contact after reflection or refraction is sometimes referred to as the image. In this concept, a "object" might be anything that light rays are emanating from.

Real images and virtual images are the two types of images. The method by which they are created distinguishes a genuine image from a virtual image. Light beams must converge to create an actual image, whereas they must diverge to create a virtual image.

Real images are those that are created when light rays collide at a specific location after being reflected or refracted by a mirror or lens.

Virtual pictures are those that only seem to form when viewed from behind a mirror. Behind the mirror, the picture is not actually there. When light beams are refracted or reflected, a virtual picture is created.

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Answer:3/8 was left over

Step-by-step explanation: 3/8 plus 1/4 x 2 equals  5/8... remainder 3/8

Answer:

3/8 (this is the answer)

The additive inverse of 8 /- 13 is -8 /+ 13. This means that when you add 8 /- 13 to its additive inverse, the result is 0.

The additive inverse of 8 /- 13 is its opposite number. This means that the sign of the number must be flipped. The inverse of 8 /- 13 is -8 /+ 13. To find the inverse of a number, you must switch the sign of the number from positive to negative or from negative to positive.

When two numbers are added together, the result will be zero if the numbers are opposites. This means that 8 /- 13 and its inverse, -8 /+ 13, when added together, will equal 0. This is because the two numbers have the same value but opposite signs. The positive 8 is cancelled out by the negative 8, and the negative 13 is cancelled out by the positive 13, leaving 0.

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r<15 because I am smart dont doubt me

Answer:

First question:

y intercept = 3

slope = -1/3

y = -1/3x+3

Second Question:

y intercept = -3

slope = -3/2

y = -3/2x=3

Third Question:

y intercept = -1

slope = 3

y = 3x-1

youre welcome buddy :)

Total Seeds required 9.33 kg  and she has 10 kg.so, she has enough grass seed to make a lawn 10m by 14 m.

If you're fortunate enough to have a rectangular lawn, determining the size is straightforward. Multiply the length and breadth measurements together to get the total. You now have your region/area.

So, Maisie knows that she needs 3 kg of grass seed to make a rectangular lawn 5 m by 9m.

Grass seed is sold in 2 kg boxes,

Maisie wants to make a rectangular lawn 10 m by 14 m,

She has 5 boxes of grass seed

To Find, Has Maisie got enough grass seed to make a lawn 10m by 14 m

Solution:

3 kg of grass seed to make a rectangular lawn 5 m by 9m.

=> 3 kg  of grass seed  needed for 5 x 9 = 45 m²

=>  1 m² required  = 3/45  kg seed

a rectangular lawn 10 m by 14 m,

area = 10 x 14 = 140 m²

Hence 140 m² required = 140 x  3/45  =  9.33 kg

Grass seed is sold in 2 kg boxes,

She has 5 boxes of grass seed

Hence total seeds = 5 x 2 = 10 kg

Therefore, total seeds required 9.33 kg  and she has 10 kg.so, she has enough grass seed to make a lawn 10m by 14 m.

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Step-by-step explanation:

well,

y = x²

would give us

y = 5² = 25

(5, 25)

but we have

(5, 18) so, what is the difference ?

we see that y is reduced by 7 units.

so,

y = x² - 7

the whole curve is moved down by 7 units.

The rate at which Jose will swim if there was no current would be = 2 km / hour

Speed is defined as the scalar quantity that is used the express the relationship of the distance of a moving object with respect to its time.

Jose swims with the current of the water and against the current of the water within the same time.

When swimming with the current he covers = 8 km

The rate he used with the current = 1 km / hour

When he is swimming against the current he covers = 16 km

Therefore the rate at which he swims against the current = 16/8 = 2km/hour.

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The length of the rectangle is 25 cm and the width is 10 cm.

We shall represent the length and width of the original rectangle with x and y respectively so that the perimeter is;

2(x + y) = 70 {divide through by 2}

x + y = 35...(1)

length of new rectangle = x - 5

width of new rectangle = y + 5

area of new rectangle:

(x - 5)(y + 5) = xy + 50

xy + 5x - 5y - 25 = xy + 50

xy - xy + 5x - 5y = 50 + 25

5x - 5y = 75 {divide through by 5}

x - y = 15...(2)

add equations (1) and (2) we have;

x + y + x - y = 35 + 15

2x = 50 {divide through by 2}

x = 25

substitute 25 for x in equation (1), we have;

25 + y = 35

y = 35 - 25 {subtract 25 from both sides}

y = 10

Therefore, have the length and width of the original rectangle to be x = 25 cm and y = 10 cm respectively.

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Answer:

Step-by-step explanation:

Question 4 I got something different x= 5, y= -4 (double check my work to make sure i used correct equation and all)

Also for slopes does your teacher want you to include the "x". Cuz when I think of slope its only the "m" part which means it should only be -1, -4 but its your call.

Answer:

One glass of milk: 15 carbs

One snack bar: 13 carbs

Step-by-step explanation:

This problem is an example of systems of linear equations. We can set this problem up by defining variable. I used [tex]m[/tex] for the glass of milk and [tex]b[/tex] for the snack bar.

First, we have: 4 glasses of milk and 2 snacks bar have a total of 86 carbs. We can write this as

[tex]4m+2b=86[/tex]

Next: 2 glasses of milk and 3 snack bars have a total of 69 carbs.

We can write this as

[tex]2m+3b=69[/tex]

Now we set it up.

[tex]4m+2b=86[/tex]

[tex]2m+3b=69[/tex]

By dividing both sides of the first equation by 2, we can use the subtraction method to get rid of the variable [tex]m[/tex]. Now we have

[tex]2m+b=43[/tex]

[tex]2m+3b=69[/tex]

Subtract like terms and solve for [tex]b[/tex]

[tex]-2b=-26[/tex]

[tex]b=13[/tex]

Now we substitute [tex]b[/tex] back into the original equation to find [tex]m[/tex].

[tex]2m+(13)=43[/tex]

[tex]2m=30[/tex]

[tex]m=15[/tex]

There you have it. I hope this helps!

The time taken by the ball to reach the ground is 11.5 seconds.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Suppose a ball was dropped from a TV tower 2120 feet high. The time it takes an object to free-fall from the top of this tower to the ground can be represented by the equation s = -16t² + 2120.

The time will be calculated as,

s = -16t² + 2120

Equate with zero as the ball reaches the ground the height s becomes zero.

-16t² + 2120 = 0

-16t² = -2120

t² = 2120 / 16

t² = 132.5

t = √132.5

t = 11.5 seconds

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The range is found by finding the vertex and noting that it is the minimum or maximum (depending on direction) of the function. You can find the vertex by using -b/2a for the x value and then plugging in to get y value.

What is a function?

A mathematical phrase, rule, or rule that establishes the link between explanatory variables or a dependent variable  In mathematics, curves exist everywhere, and they are crucial for constructing physical links in the sciences.

A Method can be defined by a module, an object, or another function. An internal feature of a class is called a method. Methods are listed inside a base class to make the connections between it class and thus the method clear. A method can be called or invoked using different syntax. We can convert a type into an object before being able to access its methods.

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We have drawn the graph of the given linear inequality.

What is linear inequality?

A linear inequality is a mathematical statement involving a linear function and one of the symbols <, >, ≤, or ≥. The general form of a linear inequality in one variable is:

ax + b <, >, ≤, or ≥ c

where a, b, and c are constants, and x is the variable.

To graph the inequality 2y - 4x < 8, we first need to put it in slope-intercept form, y = mx + b, so we can see the slope and y-intercept of the line. We can do this by adding 4x to both sides:

2y - 4x < 8

2y < 4x + 8

Then we divide both sides by 2 to get y by itself:

y < 2x + 4

Now we have y = 2x + 4 in slope-intercept form, where the slope is 2 and the y-intercept is 4. To graph the line, we can use the y-intercept as a starting point and use the slope to find additional points on the line.

To graph the line, we can follow these steps:

Plot the y-intercept, which is (0,4) on the graph.

Using the slope of 2, find a second point by going up 2 units and over 1 unit. This point is (1,6)

Draw a line through these two points.

Hence, we have drawn the graph of the given linear inequality.

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The equation of the line passing through the point (-6, 5) and (8, -2) in point-slope form is y - 5 = -0.5(x + 6).

The point-slope form of a line is

y - y1 = m(x - x1)

where (x1, y1) is a point on the line, and m is the slope of the line.

To find the equation of a line given two points, we can use either point and find the slope of the line using the formula:

m = (y2 - y1) / (x2 - x1)

So, we can use the point (-6, 5) and (8, -2)

m = (y2 - y1) / (x2 - x1) = (-2 - 5) / (8 - (-6))

m = -7/14

m = -1/2

Now we can use this slope and the point (–6,5) to find the equation of the line in point-slope form:

y - 5 = -1/2(x - (-6))

y - 5 = -0.5(x + 6)

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The correct dot plot for the given data would be option A. Number of Errors for the Week for Workstations.

A dot plot is a graph that displays the frequency of a data set by plotting a dot above the number for each occurrence of that number. The x-axis represents the data values and the y-axis represents the frequency of each data value.

In this case, the data represents the number of errors each workstation makes during the week, so the correct way to display the data in a dot plot would be to have the x-axis represent the number of errors and the y-axis represents the frequency of each error. Each dot on the dot plot would be above the number of errors for each workstation.

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Light and emotional variables are affected by eye dilation. Under typical conditions, pupils are meant to dilate as a result of changes in lighting and psychological factors.

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So on solving the provided question we can say that coefficient of x^2 in  x³ +4x² -7x -2 is 1.

A coefficient in mathematics is a polynomial, a series, or the multiplicative coefficient of a particular term in an expression. Typically numeric, however any expression is permitted. The term "parameter" can also refer to the coefficients themselves if they are variables. A number times a variable equals a coefficient. Coefficient examples include:  The coefficient is 14 in phrase 14c 14c 14c. The coefficient is 1 for word g. multiplies the variable by this amount. example  Given that "z" is a variable and that 6z is the definition of the term, the coefficient is 6. One is the coefficient of the square of x.

here,

coefficient of x^2 in  x³ +4x² -7x -2 is 1

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The volume of a sphere, to the nearest cubic meter is; 44 cubic meter

We are given that the formula for the volume of a sphere is;

V = [1/(6√π)]S^(3/2)

where;

V is volume

S is the surface area of the sphere

π = 3.14

We are given that  surface area is 60 square meters. Thus, we will now have;

V = [1/(6√3.14)]60^(3/2)

V = 43.713 m³

Approximating to the nearest cubic meter gives;

V = 44 cubic meter

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The value of x in the given equation x² = 9 is x = ± 3.

In x² = 9, we need to remove the power of 2 in order to separate just x.

This implies finding the square root √x² which is equal to x.

However, there are 2 possible answers to any square root, a positive or a negative answer.

x = √9

x = ± 3

0r we can solve this equation by the splitting method.

Rearrange the equation

x² = 9

(x - 3)(x + 3) = 0

On solving, we get

x = +3 and x = -3

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In the word problem ,the total cost for cruise for total family is $5475.

What is word problem?

Word problems are often described verbally as instances where a problem exists and one or more questions are posed, the solutions to which can be found by applying mathematical operations to the numerical information provided in the problem statement. Determining whether two provided statements are equal with respect to a collection of rewritings is known as a word problem in computational mathematics.

Here the Total members of the Harrison family = 3

Cost of cruise per person = $1825

Now, Total cost for cruise of Harrison family is,

=> Total members × Cost per person

=> 3 × 1825

=> $5475

Hence the total cost for cruise for total family is $5475.

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The null hypothesis is: H0: p ≤ 0.31

The alternative hypothesis is : H1: p > 0.31

A common statistical theory called the null hypothesis asserts that there is no statistical link or significance between two sets of observed data and measurable events for a given single observed variable.

The null states that the probability of the readers have the personal computers have to be lower than or equal to 31 percent.

What is the alternative hypothesis?

An alternate hypothesis is a claim that the two variables have some kind of statistical relationship.

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The height of the tree, given the angle from the ground and the distance from the base of the tree, is 64. 94 feet.

Assuming that this situation was modelled as a right angled triangle, then the angle from the ground to the top of the tree would be such that the distance from the base of the tree would be the adjacent measure and the height of the tree would be the opposite measure.

This means that the relevant operation to use would be Tan.

Using the Tan operation, and assuming the height of the tree was x, the formula would be:

Tan (33 degrees ) = x / Distance from base

Tan (33 degrees ) x / 100

x = 64. 94 ft

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Therefore 128 ways that Peter can make 8 steps and land back at vertex A.

There are two possible directions for each step that Peter can take, either clockwise or counter-clockwise.

Therefore, for 8 steps, there are 2^8 = 256 possible ways that Peter can make the steps. However, only half of these ways will end with Peter back at vertex A, since the other half will have him end at the opposite vertex.

Therefore, there are 256/2 = 128 ways that Peter can make 8 steps and land back at vertex A.

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The solution to this ¾ divided by 4 is 0.1875.

To visualize the question we are trying to solve, let's put 3/4 and 4 side-by-side so it's easier to see:

3/4÷4

The numbers in 3/4 divided by 4 are labeled below:

3 = numerator

4 = denominator

4 = whole number

All we need to do here is keep the numerator exactly the same (3) and multiply the denominator by the whole number:

3/4 x4= 3/16.

Once you have your final fraction, just divide the numerator by the denominator to get your answer in decimal form:

3/16=0.1875

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Answer: 2/5, 4/5, -4/5, 8/5, -16/5

I dunno that's what I got I could be wrong

When we multiply any number by zero, the outcome is always a zero, according to the definition of the zero property of multiplication, examples as 8 x 0 = 0.

When we multiply any number by zero, the end result is always a zero, according to the definition of the zero property of multiplication. Zero need not always be the first or second number. When multiplied by another number, it could be anywhere. This indicates that the outcome of the multiplication is unaffected by the placement of the digit zero.

All different kinds of numbers fall under the umbrella of this property. They could be fractional, decimal, or integer numbers. Thus, the results of some such numbers will be as follows:

10 x 0 = 0         6.4 x 0 = 0

½ x 0 = 0         1 x 2 x 3  = 0

A non-example of property 0 is: 5 × 1 = 5, the number is not multiplied by 0, therefore, it does not denote the zero property of multiplication.

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Compete question is: Give non-example of the property 0.

X for type 1 cabinets = 30

Y for type 2 cabinets = 80

And that proven that type 2 cabinets (Y) produced exceeded more than twice the number of type 1 cabinets (X)

As per the equations stated

X + Y = 110  ……….. (1)

Y = 2x + 20  …...... (2)

We substitute Y at equation (1) with equation (2), to find X

X + Y = 110

X + (2X + 20) = 110

3X + 20 = 110

3X = 110 – 20

3X = 90

X = 90 / 3

X = 30

Then, We substitute value X at equation (1 ) with the value that we have discovered before

X + Y = 110

30 + Y = 110

Y = 110 – 30

Y = 80

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The solutions of x² + 4x > 77 is x < –11 or x > 7

An equation is a mathematical expression that states that two algebraic expressions must be equal in nature. Finding the value of a variable in an equation indicates the process of solving an equation. The solution of the equation is the value that was determined while solving the equation.

Here we have

x² + 4x > 77  

Subtract -77 from both sides

=> x² + 4x - 77 > 77 - 77  

=> x² + 4x - 77 > 0

The above expression can be factorized as follows

=>  x² + 11x - 7x - 77 > 0     [ Split middle term ]

=> x(x + 11) - 7(x + 11) > 0  

=> (x + 11) (x - 7) > 0

=> (x + 11) > 0              (x - 7) > 0

=> x < -11                       x > 0

Therefore,

The solutions of x² + 4x > 77 is x < –11 or x > 7

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Answer: triangle 1's 1/2 length* triangle 1's width+triangle 2's 1/2 length* triangle 2's width+triangle 3's 1/2 length* triangle 3's width

Step-by-step explanation: triangle 1/2 length* triangle width=triangle area.