Do 1/4 and 4/16 form a proportion

The equations are recorded in slope intercept form as below

equation            slope intercept form

y + x = 3             y = -x + 3

2x + y = x + 4    y = -x + 4

x + y = -3           y = -x - 3

A linear function consists of functions where the variables has exponents of 1.

The graph of linear functions is a straight line graph and the relationship is expressed in the slope intercept form as shown below.

y = mx + b

definition of variable

y = output variable

m = slope

x = input variable

b = y intercept

The equation are written in the form y = mx + b as below

y + x = 3          

rearranging the equation

y = -x + 3

2x + y = x + 4

rearranging the equation

y = -2x + x + 4

y = -x + 4

\

x + y = -3

rearranging the equation

y = -x - 3

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The length of the hypotenuse of a 45 45 90 triangle with one side of length 8 is 8√2.

The length of the hypotenuse of a 45 45 90 triangle can be calculated using the Pythagorean Theorem. The Pythagorean Theorem states that the sum of the squares of the two sides of a right triangle is equal to the square of the hypotenuse. This can be expressed mathematically as a2 + b2 = c2, where a and b represent the lengths of the two sides and c represents the length of the hypotenuse.

In a 45 45 90 triangle, both sides are equal in length. This means that the mathematical equation simplifies to a2 + a2 = c2 or 2a2 = c2. To calculate the length of the hypotenuse, we can solve for c by taking the  square root of both sides, resulting in c = √2a.

In this particular example, if the length of one of the sides is 8, then the length of the hypotenuse can be calculated as c = √2(8) = 8√2. Therefore, the length of the hypotenuse of a 45 45 90 triangle with one side of length 8 is 8√2.

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The length of this hammer is going to be 38cm

Length has the dimension of distance in the International System of Quantities. The majority of measuring systems choose a base unit for length from which all other units are derived.

The formula that we would use to get the length is

r₁ + r₂ = L

Where r₁  is the lenght 9 cm from the head

29 cm is the length from the bottom

When we add these two, we would have the length of the hammer

29 + 9 = 38cm'

Hence the length of the hammer is 38 cm

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Answer:

[tex]\textsf{B)} \quad \dfrac{x^2+3x-4}{2x-1}[/tex]

Step-by-step explanation:

Given rational expression:

[tex]\dfrac{\dfrac{x^2+2x-3}{x-4}}{\dfrac{2x^2+5x-3}{x^2-16}}[/tex]

[tex]\textsf{Factor}\;\;x^2+2x-3:[/tex]

[tex]\implies x^2+3x-x-3[/tex]

[tex]\implies x(x+3)-1(x+3)[/tex]

[tex]\implies (x-1)(x+3)[/tex]

[tex]\textsf{Factor}\;\;2x^2+5x-3:[/tex]

[tex]\implies 2x^2+6x-x-3[/tex]

[tex]\implies 2x(x+3)-1(x+3)[/tex]

[tex]\implies (2x-1)(x+3)[/tex]

[tex]\textsf{Factor}\;\;x^2-16:[/tex]

[tex]\implies x^2-4x+4x-16[/tex]

[tex]\implies x(x-4)+4(x-4)[/tex]

[tex]\implies (x+4)(x-4)[/tex]

Therefore:

[tex]\implies \dfrac{\dfrac{x^2+2x-3}{x-4}}{\dfrac{2x^2+5x-3}{x^2-16}}=\dfrac{\dfrac{(x-1)(x+3)}{x-4}}{\dfrac{(2x-1)(x+3)}{(x+4)(x-4)}}[/tex]

[tex]\textsf{Apply\:the\:fraction\:rule}:\quad \dfrac{\dfrac{a}{b}}{\dfrac{c}{d}}=\dfrac{a\cdot \:d}{b\cdot \:c}[/tex]

[tex]\implies \dfrac{ (x-1)(x+3)(x+4)(x-4)}{(x-4)(2x-1)(x+3)}[/tex]

Cancel the common factors:

[tex]\implies \dfrac{ (x-1)(x+4)}{(2x-1)}[/tex]

Expand the numerator:

[tex]\implies \dfrac{x^2+3x-4}{2x-1}[/tex]

The shaded region composed of triangle and square has an area of 28 in²

An equation is an expression relating two or more numbers and variables.

The area of a rectangle is the amount of space occupied by the rectangle. It is given by:

Area = length * width

From the diagram:

Area of rectangle = length * width = 8 in * 5 in = 40 in²

Area of triangle = (1/2) * base * height = (1/2) * 8 in * 3 in = 12 in²

Area of shaded region = Area of rectangle - Area of triangle = 40 in² - 12 in² = 28 in²

The shaded region area is 28 in²

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Answer: It assigns a unique output to each input.

This statement is true of all functions, including the function f(x) = 3x - 12.

A function assigns a unique output to each input, meaning that for each value of x that is input into the function, there is a corresponding and unique value of y that is output. This is also called the vertical line test, if for any vertical line cuts the graph of a function at most one time, it is a function.

It does not matter whether it is linear or nonlinear or whether the correlation is positive or negative, the statement that It assigns a unique output to each input is true for all functions.

Step-by-step explanation:

(a) They are no longer independent because they are related and will more than likely have related blood types. (b) A probability area model will give an accurate theoretical probability is they must be independent.

Genetic information is transmitted from parent to kid through inheritance. Members of the same family typically share traits in common because of this. The process of fertilizations occurs during sexual reproduction when the sperm and egg cells join forces to create the first cell of the new organism.

Genetic material from the two parents is present in each of the newborn's cells. If you look at the shared traits of family members, such as average height, nose and ear shape, eye and hair color, and hair and eye color, you can see how genetic material is passed down.

Blood type is affected by genetic inheritance. if they were brothers or father and son then they are no longer independent because they are related and will more than likely have related blood types.

true in order to assume a probability area model will give an accurate theoretical probability is they must be independent.

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Both the triangles are not similar.

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.

Two triangles are comparable if they have two pairs of sides that are in the same ratio and if the included angles are likewise equal.

The square of any ratio between any two matching sides of two comparable triangles is equal to the ratio of their areas. As an illustration, Area of ABC/Area of DEF equals (AB)2/(DE)2 = (BC)2/(EF)2 = (AC)2(DF)2 for any two comparable triangles ABC and DEF.

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The first term of the Geometric Sequence will be 9,312.

It is a sequence in which every term (except the first term, a) is multiplied by a constant number (common ratio, r) to get its next term. i.e., To get the next term in the sequence, we have to multiply with the common ratio, and to find the preceding term, we just have to divide the term by the same common ratio.

[tex]Sum = \frac{a(r^{n} - 1) }{r - 1}[/tex]

where;

Sn = 46560

r = 4

n = 4

[tex]46560 = \frac{a(4^{4} - 1) }{4 - 1}\\46560 = \frac{a(16 - 1) }{3}\\\\46560 = \frac{a(15\\) }{3}\\\\\\46560 = \frac{a(15\\) }{3}\\\\\\[/tex]

46560 = 5a

a = 9,312

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Answer:

A balanced chemical equation is defined as the equation in which total number of individual atoms on the reactant side is equal to the total number of individual atoms on the product side. These equations follow law of conservation of mass.

Answer: 15

Step-by-step explanation:

15 can't be divided by two and make a non-repeating decimal.

Since 8 is at the bottom where 8 equally sized squares of paper have been stacked on top of one another, the sequence is 82543671, therefore 8.

A sequence is an enumerated group of items in mathematics where repetitions are permitted and order is important.

Similar to a set, it has members (also called elements, or terms).

The length of the series is the number of elements (potentially infinite). In contrast to a set, the same items might appear more than once in a sequence at various points, and unlike a set, the order is important.

A sequence can be described formally as a function from natural numbers (the positions of the sequence's elements) to the items at each of those positions.

An indexed family, which is a function from any index set, can be thought of as a generalization of the idea of a sequence.

For instance, the letter combinations (M, A, R, and Y) have the.

According to our question-

It is evident from the figure that 1 is a top.

I must locate Bottom 1.

6 is less than 7

If 3 weren't below 6, then 6 wouldn't be visible.

In the absence of 4, half of 3 would have been covered.

Unless 5 is below 4, 4 would have been covered.

Unless 2 is less than 5, half of 5 would have been covered.

If 8 were above 2, 2 would have been covered.

The sequence is 82543671.

therefore 8 is at the bottom.

Hence, Since 8 is at the bottom where 8 equally sized squares of paper have been stacked on top of one another, the sequence is 82543671, therefore 8.

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2 fingers dilation is normally 2 cm in measurement.

Dilation is the process of increasing an object's size without altering its form. Depending on the scale factor, the object's size may rise or shrink. A square of side 5 units can be widened to a square of side 15 units using dilation math, but the square's form doesn't change.

A dilation is a function f from a metric space M into itself that, for any locations x, y in M, fulfills the identity d=rd, where d is the distance between x and y and r is a positive real integer. Such a dilatation is a resemblance of the space in Euclidean space.

Meaning of Dilation in Math. Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is a picture with the same shape as the original. However, there is a variation in the shape's size.

Normally 1 finger dilation represents 1 cm so by unitary methord 2finger dilation is 2 cm

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The extension of two fingers is usually 2 cm.

Dilation is the process of enlarging an object without changing its shape. Depending on the magnification, the size of the object will increase or decrease. A 5 unit square can be expanded to a 1l5 unit square using dilation math, but the shape of the square remains the same. A dilation is a function f from the metric space M to itself, satisfying the identity d=rd for any position x,y in M. where d is the distance between x and y and r is a positive real number. Such an extension resembles the space of Euclidean space.

Stretching Used in Mathematics To change the size of an element, we use a transition called Stretch. Grow is used to enlarge or shrink an object. The result of this transformation is an image with the same shape as the original image. However, there is variation in the size of the shape.

Normally, one finger will stretch 1 cm, so in the unified method, two fingers will stretch 2 cm.

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From linear equation of a line,

y=mx+c or y=mx+b

Slope of a line is m and y-intercept is c (or b).

So first we have to make y the subject in

→8x+y=9

→y= - 8x+9

y = mx + c

Hence slope is (-8) and y-intercept is 9.

for x-intercept, put y=0 and we get

0 = -8x+9

x=-8/-9

x= 8/9

therefore x intercept is 8/9.

The average rate of change is 0.8

It is the average amount by which the function changed per unit throughout that time period. It is calculated using the slope of the line linking the interval's ends on the graph of the function.

Given:

x     f(x)

5       13

10      17

15      21

20     25

As, The rate of change of the function is its gradient or slope.

So, the formula for calculating the gradient of a function is expressed as:

m = [tex](y_2 - y_1)/ (x_2 - x_1)[/tex]

Using the coordinate points from the table (5, 13) and (10, 17)

Substitute the coordinate into the expression:

m = (17- 13)/ (10 - 5)

m = 4 /5

m = 0.8

Hence, the average rate of change is 0.8.

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The minors of the 2 x 3 matrix are -3, -2, -1, 9, -2, -3, 6, and 5. The cofactors are -18, 16, 5, -3, -18, 18, 3, -12, and -5.

Minor of 2: -3

Cofactor of 2: -18

Minor of -8: -2

Cofactor of -8: 16

Minor of 5: -1

Cofactor of 5: 5

Minor of 3: 9

Cofactor of 3: -3

Minor of 9: -2

Cofactor of 9: -18

Minor of 6: -3

Cofactor of 6: 18

Minor of -1: -3

Cofactor of -1: 3

Minor of -2: 6

Cofactor of -2: -12

Minor of -3: 5

Cofactor of -3: -5

The minors of the 2 x 3 matrix are -3, -2, -1, 9, -2, -3, 6, and 5. The cofactors are -18, 16, 5, -3, -18, 18, 3, -12, and -5.

The given 2 x 3 matrix is composed of the values 2, -8, 5, 3, 9, 6, -1, -2, and -3. The minors of the matrix can be found by using the Laplace expansion formula and removing the row and column of the element in question. This yields the minors -3, -2, -1, 9, -2, -3, 6, and 5. The cofactors of the matrix can be calculated by taking the determinant of the minor and multiplying it by the sign of the element in question. This results in the cofactors -18, 16, 5, -3, -18, 18, 3, -12, and -5.

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Answer:

the answer is y = -4x + 5

Step-by-step explanation:

Im dum i cant explain it  :D

The equation of variation is xy = k.

The required values are given below.

A proportional relationship is a relationship between two expressions and where changes in one expression means some constant change in the other expression as well. Generally, it is represented as x/y = k, where x and y are two expressions and k is constant.

Given:

y inversely varies as x.

That means, y ∝ 1/x.

So, y = kx, where k constant of variation.

Then, x × y = k

When y = 8, x = 3.

k = 3 × 8 = 24

So, the equation of variation is xy = 24.

When x = 6,

6y = 24

⇒ y = 4

When y = 9, x = 6.

k = 6 × 9 = 54

So, the equation of variation is xy = 54.

When y = 4,

4x = 54

⇒ x = 27/2

When y = 1.5, x = 14.

k = 1.5 × 14 = 21

So, the equation of variation is xy = 21.

When x = 9,

9y = 21

⇒ y = 7/3

When y = 20, x = 10.

k = 20 × 10 = 200

So, the equation of variation is xy = 200.

When y = 25,

25x = 200

⇒ x = 8

Therefore, the values are given above.

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Answer:

3/2m^5n

Step-by-step explanation:

9m^8n^5÷6m^3n^4

(9/6)(m^8/m^3)(n^5/n^4)

3/2m^5n

Answer :

F1 and F2 refer to the two principal focal lengths of a lens.

The two main focal lengths of a lens are referred to as f1 and f2 in the field of optics. The first principal focal length, or f1, is the distance from the lens to the point where parallel light rays, which have already passed through the lens, condense into a single point known as the focal point.

The second principal focal length, or f2, is the distance from the lens to the point where light rays diverging from a single point will appear to converge after passing through the lens. The distance from the lens to the point at which the light rays converge or diverge is known as the focal length. The values of f1 and f2, respectively, depend on the shape and type of the lens.

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We must remember to multiply each integer by a power of 10 while subtracting numbers in scientific notation.

A value's accuracy is influenced by the number of significant digits in the value, which is frequently a measurement. Count the significant digits starting with the first non-zero digit. All zeros are permitted in the decimal places to the right of the last non-zero place. Consider the five significant digits in the number 0.0079800. Any zeros to the right of the last non-zero digit, when they come from the measurement, are significant. rounding an integer to 3 significant digits and 3 decimal places is identical. Go up to three and begin counting at the first digit that is not zero. Remove the last digit after that. The final two digits to the right of the decimal point should be increased by zeros.

To make it simple to subtract these integers, they must all be in the same power, as demonstrated in the example below.

5×10^2−3×10^2=

5(100)−3(100)^2×10^2=

(500−300)^2×10^2

=200

However, before continuing, we must restate the numbers in similar powers of ten if the powers of ten for the numbers to be subtracted are not the same.

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Answer:

$1.48

Step-by-step explanation:

Meal cost: $7.24

Coffee cost: $2.65

Total cost: $9.89

Now we need to find 15% of 9.89.

This is a percentage question, we need to first multiply 9.89 with 15% then divide it by 100%:

9.89 × 15 ÷ 100 = 1.48 approximately.

The image of the point (2, 3) in the line y=−x is (-3, -2).

Let there be a point P(2, 3) on the cartesian plane. The image of this point in the line y=−x will lie on a line that is perpendicular to this line and the distance of this point from y=−x will be equal to the distance of the image from this line.

Let Q be the image of p and let the co-ordinate of Q be (h, k)

The slope of line y=−x is −1

Line joining P, Q will be perpendicular to y=−x so, its slope =1.

Let the equation of the line be y=x+c since this passes through points (2,3)

3=2+c⇒c=1

and the equation y=x+1

The point of intersection R lies in the middle of P & Q. Point of the intersection of lines y=−x and y=x+1 is

2y =1 , y= [tex]\frac{1}{2}[/tex] and x = [tex]-\frac{1}{2}[/tex]

Hence, [tex]\frac{h+2}{2} = -\frac{1}{2}[/tex] and [tex]\frac{k+3}{2} = \frac{1}{2}[/tex]

⇒ h=−3 and k =−2

So, the image of the point (2, 3) in the line y=−x is (-3, -2).

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The correct question is:

What is the image of the point (2,3) in the line y= -x?

None of the above. The answer is 10! (10 factorial) which number is 3,628,800.

The number of ways to arrange 10 people in a line is 10! (10 factorial). This is equal to 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 which is 3,628,800.

The answer to the question is 10! (10 factorial). This is because in order to determine the number of ways to arrange 10 people in a line, you must multiply the number of people by every number between that number and 1. In this case, it would be 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 which is 3,628,800.

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Answer:

[tex]\huge\boxed{\sf \$ 2.2}[/tex]

Step-by-step explanation:

5 pounds of flour = $11

5/5 pound of flour = $11 / 5

[tex]\rule[225]{225}{2}[/tex]

Answer:

4.97% is your answer

Step-by-step explanation:

Identify variables

T (time) seconds

Y amount of times per day

T * Y = amount of time you would spend carrying water in a day, 24 hrs

365 * t * y = 365 (amount of days per year, multiplied by the amount of time you carry water per day).

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The confidence interval is given as : 2.379 < u < 3.221

How to solve for the confidence interval

we have the following details to solve the problem with

n = 9 residents

mean = x = 2.8

s = 0.68

significance level ∝ = 1 - c

= 1 - 0.9

= 0.1

the confidence interval is given as:

C.I = x ± t ∝/2 , n - 1 * s/√n

t ∝/2 , n - 1 is the critical value. This is = 1.859

C.I = 2.8 ± 1.859 * 0.68 / √9

C.I = 2.8 ± 0.421

C.I = 2.8 - 0.421,  2.8 + 0.421

C.I = 2.379 < u < 3.221

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