give the geometrical representation of y=3 as an equation in
a) one variable
b) in two variables.

Answer:GCF = 6

Step-by-step explanation=Notice we have these factorizations

12 = 6*2

18 = 6*3

Which shows that 6 is the greatest common factor (GCF)

So,

12+18 = 6*2+6*3 = 6*(2+3)

We use the distributive property which is a(b+c) = ab + ac

I'll leave the 2+3 part un-simplified so that you can see the two original pieces, and how the 6 can multiply with them both to get back to 12+18 again.

original sum rewrites to 6(2+3)

Mean = 295.4

321, 285, 300, 285, 286, 293,298

Solution:

The mean refers to the average of a set of values. The mean can be computed in a number of ways, including the simple arithmetic mean (add up the numbers and divide the total by the number of observations), the geometric mean, and the harmonic mean

or

Mean is nothing but the average of the given set of values. It denotes the equal distribution of values for a given data set. The mean, median and mode are the three commonly used measures of central tendency.

Mean :

Mean is a statistical concept that carries a major significance in finance and is used in various financial fields and business valuation. Mean, median, and mode are the three statistical measures of the central tendency of data.

Let there be "n" number of items in a list.

mean of data = sum of data/number of data

= 321 + 285 + 300 + 285 + 286 + 293 + 298 / 7

= 2098/7

= 295.4

Mean = 295.4

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The Jon's age is 35 years.

We are given the product of ages of both the persons. Also, we are given Jon's age = j years and Laura's age = (j + 3) years. So, representing the given information in mathematical expression form -

j × (j + 3) = 1330

Performing multiplication on Left Hand Side of the equation to find the value of j

j² + 3j = 1330

Shifting 1330 to Left Hand Side of the equation to find the value of j

j² + 3j - 1330 = 0

Solving the mentioned quadratic equation by factorization -

j² + 38j - 35j - 1330 = 0

Further solving the quadratic equation -

j (j + 38) -35 (j + 38) = 0

(j + 38) (j - 35) = 0

j = 35, -38

The age of Jon can not be negative. So, the age of Jon will be 35 years.

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The complete question is -

Jon is 3 years younger than Laura. The product of their ages is 1,330. If j represents Jon's age and j + 3 represents Laura's age, what value of j could be Jon's age?

The real word examples of Symmetric, Transitive, and Substitution properties are {2 = 1 + 1 ⇒ 1 + 1 = 2} , {4 = 2 + 2 and 2 + 2 = 5 - 1 then 4 = 5 - 1} , { if 4 = 2 + 2 then 8×4 = 8(2+2) } respectively there is no non-example.

A decimal number is a very common number that we use frequently.

Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.

Symmetric property states that if a = b  then b = c

For example 2 = 1 + 1 ⇒ 1 + 1 = 2

Transitive property states that if a = b , b = c then a = c

For example 4 = 2 + 2 and 2 + 2 = 5 - 1 then 4 = 5 - 1

Substitution property states that if a = b then we can put b instant of an in any equation.

For example 4 = 2 + 2 then 8×4 = 8(2+2)

Hence "The example of real word on Symmetric, Transitive, and Substitution properties are {2 = 1 + 1 ⇒ 1 + 1 = 2} , {4 = 2 + 2 and 2 + 2 = 5 - 1 then 4 = 5 - 1} , { if 4 = 2 + 2 then 8×4 = 8(2+2) } respectively".

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The value of h is (3fg +5i²) / 3 using the concept of algebraic operations.

Any of the common arithmetic operations, such as addition, subtraction, multiplication, division, raising to a whole number power, and taking roots, are considered basic algebraic operations in mathematics (fractional power).

Given:

fg= h – 5/3 × i²

Add 5/3i² both sides

h= fg+ 5/3i²

h= (3fg +5i²) / 3

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The value of h in the given operation fg= h – 5/3 × i² is (3fg +5i²) / 3.

So, fg= h – 5/3 × i².

Addition of 5/3i² on both sides as follows:

Therefore, the value of h in the given operation is (3fg +5i²) / 3.

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The radius of a circle with an area of π/4 square units is B. 0.5 units

Area is the quantity that expresses the extent of a region on the plane or on a curved surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of the three-dimensional object.

Now it is given that,

Area of circle =  π/4 square units

Since we know that,

Area of circle =  πr²

where r is the radius of circle.

⇒ r² =  Area of circle / π

Put the values we get,

⇒ r² = (π/4)/ π

⇒ r² = 1/4

Taking square root both the side we get,

⇒ r = 1/2 units

or,  r = 0.5 units

Thus, the radius of a circle with an area of π/4 square units is B. 0.5 units

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The coordinate of point I is such that ΔI K L is a right-angle triangle that will be either (0,y) or (2a,y).

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.

Given the ΔI K L right angle triangle.

The possible coordinate of the point I will be either  (0,y) if IJ is perpendicular to JK and IK is perpendicular to JK.

Hence "The coordinate of the point I is such that ΔI K L is a right-angle triangle that will be either (0,y) or (2a,y)".

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The  probability that a randomly chosen dog is a female or over 5 years old is 0.68 .

 Age                       Male             Female  

Under 1 year            6                        5

1 to5 year                  8                         7

6 to10 years              4                         6

Over 10 years            3                         5

From the table, we can estimate that there are 23  f_emale dogs, 18 are over 5 years old,  and there are 11 f_emale dogs who are over 5 years old.

Therefore,  the total number of dogs which are f_emale and over 5 years old =  23 + 18 – 11 = 30

This means there total of 44 dogs in total.

A be the event the  randomly chosen dog is f_emale and  over 5 years old, The probability of the event will be, P(A)=  30/44 = 0.68.

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In other words, the triangles are consistent if the hypotenuse and one of the legs of one right triangle agree with the hypotenuse and one of the legs of another right triangle.

Congruent triangles are two triangles that are the same size and shape. Two congruent triangles remain congruent even if we flip, turn, or rotate one of them. Two triangles must have the same angles and, as a result, must be congruent if their sides are the same.

Two right triangles are supposed to be consistent on the off chance that they are of a similar shape and size. All in all, two right triangles are supposed to be consistent in the event that the proportion of the length of their comparing sides and their relating points is equivalent.

Right triangles are harmonious in the event that both the hypotenuse and one leg are a similar length. These triangles are harmonious by HL or hypotenuse leg.

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The slope is 23, from x>=1 , the domain is (1,∞) and the range is {f: A→B; f(x) = 23x}.

Given,

Cost for first day = $39

Cost for each additional day = $23

Let x denote the number if days

Y denote the total cost

(a) As the cost for the first day to rent a zoom $39, so its domain is from (x=0 to x=1)

i.e., (0,1] and Range is $39 --> for the first day

For each additional day, the cost increases by $ 23.

Therefore, slope is 23, from x>=1.

(b) For the first day = $39

Therefore, cost is fixed for the first day its domain is (0,1] and Range is $39

For each additional day, cost increases by $ 23

Therefore, slope after x=1 is 23

Domain = (1,∞)

Ranges = {f: A→B; f(x) = 23x}

Ranges will be set of positive integers of multiple of 23

i.e., {23,46,69…….}

(c) Set of equations to model the relationship.

Hence the equation is,

[tex]\mathrm{y}=\mathrm{f}(\mathrm{x})=\left\{\begin{array}{c}\$ 39,0 \leq x \leq 1 \\39+23 x, x > 1\end{array}\right.[/tex].

Hence, the slope is 23, from x>=1 , the domain is (1,∞) and the range is {f: A→B; f(x) = 23x} can be used to model relationship between the price of renting a car and the number of days you rent it.

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Answer:

f = - [tex]\frac{g}{x-1}[/tex]

Step-by-step explanation:

fx = f - g ( subtract f from both sides )

fx - f = - g ( factor out f from each term on the left side )

f(x - 1) = - g ( divide both sides by (x - 1) )

f = - [tex]\frac{g}{x-1}[/tex]

Answer:

16/39

Step-by-step explanation:

1/3=13/39

1/13=3/39

13/39+3/39=16/39

Answer:

a) 3⁴

b)7⁵

c)10²

d)5⁷

Step-by-step explanation:

a) 3²*3², add the exponents if multiplying(subtract if division)

b) add the other 7, cause 7⁴ is 7*7*7*7 and since you're doing another *7 just add a number to the exponent

c)10⁹/10⁷ is 9-7, and take that and use it as the exponent

d)since there is no exponent but it is basically the same as b, but switched. Instead of adding an exponent you take one away

Answer:

A) 27

Step-by-step explanation:

3 x 3 = 3²

3 x 3 = 9

9 x 9

27

Using the summation notation, the series 5+8+11+ . . . . . . +38 can be written as

[tex]\sum\limits^{12}_{n=1} {(3n+2)}[/tex]    or    [tex]24+3\sum\limits^{12}_{n=1} {n}[/tex]

Given an arithmetic series:

     5+8+11+ . . . . . . +38

The common difference (d) of each term is:

d = 8 - 5 = 3

The first term, a(1) = 5.

Hence, using the formula for the nth term of an arithmetic sequence:

a(n) = a(1) + (n-1) . d

a(n) = 5 + (n-1) . 3

a(n) = 3n + 2

Let us find n that result in a(n) = 38

a(n) = 3n + 2

38 = 3n + 2

3n = 36

n = 12

We can, then, conclude that the series  5+8+11+ . . . . . . +38 has 12 terms.

Therefore, the summation notation is:

[tex]\sum\limits^{12}_{n=1} {a(n)} = \sum\limits^{12}_{n=1} {(3n+2)}[/tex]

[tex]= \sum\limits^{12}_{n=1} {3n}+ \sum\limits^{12}_{n=1} {2}[/tex]

[tex]= 3\sum\limits^{12}_{n=1} {n}+ 2\times 12[/tex]

[tex]= 24+3\sum\limits^{12}_{n=1} {n}[/tex]

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The coordinate of point J on the number line is -9

The given parameters are

JK = KL

K = 7

L = 23

The above means that:

K = 1/2 * (J + L)

So, we have

7 = 1/2 * (J + 23)

Multiply both sides by 2

14 = J + 23

Subtract 23 from both sides of the equation

J = -9

Hence, the coordinate of point J on the number line is -9

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Hello,

[tex]2(x - 3) + 2x = 22[/tex]

[tex]2x - 6 + 2x = 22[/tex]

[tex]4x - 6 = 22[/tex]

[tex]4x = 22 + 6[/tex]

[tex]4x = 28[/tex]

[tex]x = \frac{28}{4} = 7[/tex]

Answer: 82

Step-by-step explanation:

Answer:

48°

Step-by-step explanation:

The sum of interior angles in a triangle is equal to 180°.

We can use this information to find the value of third angle, represented with x.

70 + 62 + x = 180 add like terms

132 + x = 180 subtract 132 from both sides

x = 48°

The equation of the line in point-slope form, which passes through the pair of points located at (0 , 1/2) and (5/7 , 0), is y - 1/2 = -7/10 x

The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).

Getting the slope of the two points: (0 , 1/2) and (5/7 , 0).

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

m = (0 - 1/2)/(5/7 - 0)

m = (-1/2)/(5/7)

m = -7/10

Using the point slope form, plug in the values of the slope and one point to set up the equation.

(y - y1) = m(x - x1)

where m = -7/10 and (x1 , y1) = (0 , 1/2)

(y - 1/2) = -7/10(x - 0)

y - 1/2 = -7/10 x

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According to the given data" the arithmetic mean of 6 x, 3 x , and 27 is 18" the value of x = 3.

The arithmetic mean or average, or simply the mean or average, is indeed the sum of a set of numbers multiplied by the number of numbers in the set.

One approach is to compute the arithmetic mean. To do this, add all of the values together and divide the total by the number pf values. For example, if you have a set of "n" numbers, add them together as follows: a + b + c + d, and so on. Then divide the total by "n."

If the arithmetic mean of 6 + x, 3 + x ,  27  =  18

So value of x will be as follows:

(6x + 3x + 27)

(6x + 3x + 27)/3 = 18

9x+27/3 = 18

9x +27 = 54

x = (54-27)/9

x  = 27/9

x = 3

According to the given data the value of x = 3.

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The exact value of the expression is -1/2

Given the following trigonometry value

sin 5π/3

Since the value of π is 180 degrees, hence;

sin 5(180)/3

sin 5(60)

sin 300

This can be written as;

sin(360 - 30) = -sin30

sin(360 - 30) = -(1/2)

Hence exact value of the expression is -1/2

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The proving of the trigonometric function [tex]\frac{1+\cos A}{\sin A}+\frac{\sin A}{1+\cos A} = 2 cosec A[/tex] that LHS = RHS is shown.

So, [tex]\frac{1+\cos A}{\sin A}+\frac{\sin A}{1+\cos A} = 2 cosec A[/tex]:

LHS = [tex]\frac{1+\cos \mathrm{A}}{\sin \mathrm{A}}+\frac{\sin \mathrm{A}}{1+\cos \mathrm{A}}[/tex]

[tex]=\frac{(1+\cos \mathrm{A})(1+\cos \mathrm{A})+\sin \mathrm{A} \sin \mathrm{A}}{\sin \mathrm{A}(1+\cos \mathrm{A})}\\\begin{aligned}&=\frac{(1+\cos \mathrm{A})^2+\sin ^2 \mathrm{~A}}{(1+\cos \mathrm{A}) \sin \mathrm{A}} \\&=\frac{1+\cos ^2 \mathrm{~A}+2 \cos \mathrm{A}+\sin ^2 \mathrm{~A}}{(1+\cos \mathrm{A}) \sin \mathrm{A}}\end{aligned}\\[/tex]

[tex]\begin{aligned}&=\frac{1+2 \cos A+1}{(1+\cos A) \sin A} \\&=\frac{2+2 \cos A}{(1+\cos A) \sin A}\end{aligned}\\\begin{aligned}&=\frac{2(1+\cos A)}{(1+\cos A) \sin A} \\&=2 \frac{1}{\sin A}\end{aligned}\\=2cosecA[/tex]

= RHS

Hence Proved.

Therefore, the proving of the trignometric function [tex]\frac{1+\cos A}{\sin A}+\frac{\sin A}{1+\cos A} = 2 cosec A[/tex] is shown.

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The correct question is given below:
Prove that:  [tex]\frac{1+\cos A}{\sin A}+\frac{\sin A}{1+\cos A} = 2 cosec A[/tex]

Answer:

It seems right to me maybe sign change?

Answer: r=6

Step-by-step explanation:

-8(4-r) =16

-32 +8r =16

8r = 16+32

8r =48

r= 48/8

r=6

Answer:

Similarities: They both are polynomials of degree 2, both of their graphs is a parabola, both have either 2 or 0 real solutions, they are both continuous functions over R

(DOS= difference of two squares, PST=perfect square trinomial

Differences: PST has three terms, whereas the difference of squares has 2. PST's factors are both the same, whereas DOS's elements are conjugates of each other. DOS can always be factored into two distinct polynomials with rational coefficients, whereas PST has two same polynomial factors.

Step-by-step explanation:

The sets to which the numbers belong are given as follows:

32. Rational.

34. Irrational.

For this problem, we have that:

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A glide reflection is a translation followed by a reflection in a line parallel to the translation vector.

A glide translation is what?

when a figure is subjected to one transformation before another is applied?

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The missing second term of the given arithmetic sequence is: 2.5.

A series of numbers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms.

given: -3, __, 8 is an arithmetic sequence, where a₁ = -3 and a₃ = 8

Now, as [tex]a_n=a_1+(n-1)d[/tex], for the nth term of an arithmetic sequence,

For n = 3, a₃ = -3 + (3 - 1)d

=> 8 = -3 + 2d

=> 11/2 = d

=> d = 5.5

Hence, a₂ will be given as n = 2, in the above formula

=> a₂ = -3 + (2 - 1) (5.5)

=> a₂ = -3 + 5.5

=> a₂ = 2.5

Hence, The missing second term of the given arithmetic sequence is: 2.5.

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Answer:

35 pennies

Step-by-step explanation:

Savannah started with 5 pennies. You gave her 3 pennies each day for 10 days. The first day you gave her 3 pennies she now has 8. Now the for the second day you add 3 to 8 which 11. You keep adding 3 each day for 10 days.

Easiest way: 10×3=30 30+5=35

She will have 35 pennis after 10 days.

I answered the first question where it asked: "How much money will Savannah have after 10 days."