prove that (n+5)^2(n+3)^2 is a multiply of 4

Answer:

x = 3

y = -1

Step-by-step explanation:

5x + 3y = 12

x - 4y= 7

Times the second equation by -5

5x + 3y = 12

-5x + 20y = -35

23y = -23

y = -1

Now put -1 back in for y and solve for x

x - 4(-1) = 7

x + 4 = 7

x = 3

Let's check

3 - 4(-1)= 7

3 + 4 = 7

7 = 7

So, x = 3 and y = -1 is the correct answer.

The required volume of the composite figure is given as 18,300 cm³.

Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.

Here,
The volume of the composed figure is given as,
Split the figure into two,
So,
Volume = Volume of 1 + Volume of 2

Volume = 15 × 15 × 30 + 35 × 22 × 15
Volume = 6750 + 11550
Volume = 18,300 cm³

Thus, the required volume of the composite figure is given as 18,300 cm³.

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Therefore , the solution of the given problem of expression comes out to be x - 77.

Arithmetic, algebra, and subdivision are required in math. When united, they produce the following: A mathematical function, some data, and an equation A statement of fact contains values, parameters, and mathematical operations like additions, addition and subtraction, matrix multiplication, and divisions. It is possible to analyse and assess various phrases and terms.

Here,

If we let "a number" be represented by the variable x, then the expression "the difference of a number and 7 times 11" can be written as:

x - 7 * 11

Simplifying this expression gives:

x - 77

Therefore , the solution of the given problem of expression comes out to be x - 77.

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the value of  1 mile divided by 2 laps is 0.5 mi/lap.

The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

Given, 1 mile divided by 2 lap

Simplifying the equation in numerical form

=> 1 mile divided by 2 lap

=> 1/ 2  mil/ laps

=> 0.5 mil/lap

Therefore, the value of  1 mile divided by 2 laps is 0.5 mi/lap.

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Option C is correct : y = ±3x + 8, represents a function because it satisfies the vertical line test.

"y = ±3x + 8" represents a function. A function is a mathematical relationship between a set of inputs (in this case, x) and a set of outputs (in this case, y). In this equation, for each value of x there is exactly one corresponding value of y, which means that it represents a function.

"y = ±2x + 3" is not a function because for each value x, there are two possible values y (one positive and one negative). This is not the definition of a function, as a function must have exactly one output value for each input value.

Options B, D, and E do not represent functions because they do not have an equal sign between the x and y variables, which is the defining characteristic of a mathematical function.

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So Lisa and Linda planted 9/6 of the garden altogether. In simplest form, this fraction can be reduced to 3/2, which means that they planted 3/2 of the total garden area.

To find out the total area of the garden that Lisa and Linda planted, we need to add the fraction of the garden that Lisa planted to the fraction of the garden that Linda planted.

Lisa planted 4/7 of the garden, so we can write this as 4/7 of the total area.

Linda planted 1/6 of the garden, so we can write this as 1/6 of the total area.

To add these two fractions, we need to find a common denominator, which is the smallest number that both 7 and 6 can divide into evenly. The smallest common denominator is 6, so we can convert both fractions to have a denominator of 6:

Lisa planted 4/7 of the garden, which can be converted to 8/14 (by multiplying both the numerator and denominator by 2).

Linda planted 1/6 of the garden, which stays the same, since 6 is already the denominator.

Now that both fractions have a denominator of 6, we can add the numerators together to find the total amount of the garden that they planted:

8/14 + 1/6 = (8 + 1)/6 = 9/6

So Lisa and Linda planted 9/6 of the garden altogether.

In simplest form, this fraction can be reduced to 3/2, which means that they planted 3/2 of the total garden area.

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Answer: isosceles, because each side is accurate

Answer:

Scalene, right.

Step-by-step explanation:

Its scalene because all the sides are not equal.

It is a right angled triangle.

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The formula to calculate the measure of each individual exterior angle in any polygon is: Exterior angle measure = 360°/n.

To find the measure of each individual exterior angle in any polygon, first, you must understand the Polygon Exterior Angle-Sum Theorem, which states that the exterior angles of any polygon add up to 360 degrees.

With this information, the formula for the measure of an individual exterior angle is simple: Exterior angle measure = 360°/n, where n is the number of sides in the polygon.

By dividing the total sum of the exterior angles (360°) by the number of sides (n) in the polygon, you can determine the measure of each individual exterior angle.

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Answer:

Last option:

x ≤ 217

Step-by-step explanation:

Mean time = Total Time/Number of observations

Mean time = (192 + 206 + 194 + 191 + x)/5 = (783 + x)/5

We want this mean time to be no greater than 200 seconds.

In other words we want mean time ≤ 200 s

We therefore get the inequality:
(783 + x)/5 ≤ 200

Multiplying both sides by 5
=> (783 + x) · 5  ≤ 200 · 5

=> 783 + x ≤ 1000

=> x ≤ 1000 - 783

=> x ≤ 217

Answer:

2n+2

Step-by-step explanation:

The solution to the given algebraic expression is 162.

The process of solving algebraic expressions can sometimes be the process whereby numbers are used as a substitute or to replace a variable(s) in order to get a desired solution.

In the given question,  we have 2x² + 3xy, where x = 6 and y = 5. It means that we are going to replace the value of x with 6 where ever we see x in the expression and y with 5.

Thus, 2x² + 3xy becomes:

= 2(6)² + 3(6)(5)

= 2(36) + 3(30)

= 72 + 90

= 162

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Answer: Let x be the number of hours Tay practices the piano. Then, Omar practices for 2/5 less than that, or x - 2/5x = 3/5x hours.

Step-by-step explanation:

-108 is the depth of the submarine after 9 ​minutes.

An expression is combination of variables, numbers and operators.

The given expression is  -210+ 12m

This expression  represents a submarine that began at a depth of 210 feet below sea level and ascended at a rate of 12 feet per minute.

We need to find the depth of the submarine after 9 ​minutes

m=9

Now put m value in the expression

-210+12(9)

-210+108

-108

Hence, -108 is the depth of the submarine after 9 ​minutes.

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The volume of the cylinder is  538.9 m³.

A cylinder is a three-dimensional solid object with two bases that are identically circular and are connected by a curving surface that is located at a specific height from the center.

Examples of cylinders are toilet paper rolls and cold beverage cans.

The volume of a cylinder is πr²h.

Curved surface area = 2πrh.

Total surface area = 2πr(h + r).

The T.S.A. is equal to 231m² and C.S.A. is equal to 154m².

We know that,

T.S.A - C.S.A = 2πr².

231 - 154 = 2πr².

77 = 2πr².

πr² = 77/2.

πr² = 38.5.

r² = 12.26.

r = 3.5.

2πrh = C.S.A

2πrh = 154.

h = 154/(πr).

h = 14.01

Therefore, The volume is equal to,

π×(3.5)²×14.01.

= 538.9 m³.

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Any real value of x which is greater than 9 inches will make the perimeter of rectangle more than 50 inches

Let us assume that the length of the rectangle is represented by l and the width is represented by w.

Assuing l = 16 inches and width = x inches

Let P represents the perimeter of the rectangle.

We know that the formula for the perimeter of the rectangle is:

P = 2(l + w)

The perimeter should be more than 50.

So, we get an inequality,

P > 50

2(l + w) > 50

l + w > 25

16 + x > 25

16 + x - 16 > 25 - 16

x > 9

Thi means, that for any  x > 9 will make the perimeter greater than 50 in.

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A simple correlation between two variables when there is no obvious third variable that could be causing changes in both a and b.

A measure of the degree to which two variables vary together or the strength of the link between two variables is simple linear correlation. Correlation is frequently misused. You must provide evidence that one variable is really having an impact on another. and when we compare r to the relevant crucial value in the table, the association is statistically significant. The correlation coefficient is significant if it is greater than zero and does not fall between the positive and negative critical values.

the possibility that a reported correlation between two variables may not actually reflect any underlying relationship (in a causal sense) between the two variables, but rather the shared correlation between each of the variables and a third variable.

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With Mo and Beth splitting £48 in the ratio 3.5 , Beth would get £10.67 with the total ratio of 4.5.

When two people split a sum of money in a certain ratio, it means that they divide the total amount into parts that are proportional to the ratio. In this case, Mo and Beth are splitting £48 in the ratio 3.5. This means that Mo gets 3.5 parts of the total amount, while Beth gets 1 part of the total amount.

To calculate the total ratio, you add up the individual parts of the ratio. In this case, the total ratio is 3.5 + 1 = 4.5. This means that the £48 has to be divided into 4.5 equal parts.

Next, to find the amount that Beth gets, you need to find what portion of the 4.5 parts of the total amount corresponds to her 1 part of the ratio. You do this by dividing £48 by the total ratio, which gives you £48 / 4.5 = £10.67.

Finally, you multiply this amount by 1, which represents Beth's share of the ratio. So, £10.67 * 1 = £10.67. Therefore, Beth would get £10.67.

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Answer:

30

Step-by-step explanation:

this is the explanation

6÷20% = 30

The common region or overlapped region in the graph of both the inequalities represents the number of cats and dogs that can be at the store.

Given is that  Priya’s Pet Store never has more than a combined total of 20 cats and dogs and never more than 8 cats. This is represented by the inequalities x + y ≤ 20 and x ≤ 8.

The number of cats and dogs that can be at the store on a graph can be represented by the common region in the graph of both the inequalities.

Therefore, the common region or overlapped region in the graph of both the inequalities represents the number of cats and dogs that can be at the store.

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Based on the given pictures:

Angle ∠1 has a more than 90° angle, means that it is classified as obtuse angle.

Angle ∠2 has a less than 90° angle, means that it is classified as an acute angle.

∠ABC is a straight angle because it creates a straight line with 180°.

Angle ∠2 can be named as ∠EBD because it was created by lines EB and ED.

∠WXY = 88°

∠WXZ = 4x - 3

∠ZXY = 2x + 1

∠WXY = ∠WXZ + ∠ZXY

88 = (4x - 3) + (2x + 1)

88 = 6x - 2

6x = 90

x = 15

∠HIJ = 108°

IK bisects ∠HIJ

∠HIK = 4x + 2

∠HIJ = 2∠HIK

108 = 2(4x + 2)

108 = 8x + 4

8x = 104

x = 13

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Answer:

15/16

Step-by-step explanation:

The lateral surface area of the rectangular prism is 72 square inches.

All of the sides of the object are the lateral surface of an object, except its base and top (when they exist). The lateral surface area is the lateral surface zone. This is to be distinguished from the overall surface area, which, along with the base and top areas, is the lateral surface area.

Given that, length =7 inches, breadth =5 inches and height =3 inches.

We know that, the lateral surface area of the rectangular prism is 2(l+b)h

Now, the lateral surface area = 2(7+5)×3

= 2×12×3

= 72 square inches

Therefore, the lateral surface area of the rectangular prism is 72 square inches.

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Answer:

21

Step-by-step explanation:

The median is the value separating the higher half of the data from the lower half.

10,11,13,18,19,  21   ,22,25,27,30,32

We see the middle number in this set is 21, so the median is 21

The value of the function W(x) for x=6 is 17,799,730.56 cubic inches.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Given that, the function V(x)=4/3 πx³ represents the volume (in cubic inches) of the sphere.

The function W(x) = V(27x) represents the volume (in cubic inches) of the sphere when x is measured in feet.

W(x) = 4/3 π(27x)³

W(x) = 4/3 π(27x)³

= 4/3 π×19683×x³

= 4π×6561×x³

W(x)= 26244πx³

W(6)= 26244×3.14×(6)³

= 17,799,730.56 cubic inches

Therefore, the value of the function W(x) for x=6 is 17,799,730.56 cubic inches.

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Answer:

[tex]\textsf{B.} \quad \dfrac{2 +\sqrt{12}}{2}[/tex]

[tex]\textsf{C.} \quad 1[/tex]

[tex]\textsf{E.} \quad \dfrac{2-\sqrt{12}}{2}[/tex]

Step-by-step explanation:

If f(x) is a polynomial, and f(a) = 0, then (x – a) is a factor of f(x).

If the coefficients in a polynomial add up to 0, then (x - 1) is a factor.

Given polynomial function:

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

Sum the coefficients:

[tex]\implies 1-3+2=0[/tex]

As the sum of the coefficients equals one, (x - 1) is a factor the polynomial.

Find the other factor by dividing the polynomial by (x - 1):

[tex]\large \begin{array}{r}x^2-2x-2\phantom{)}\\x-1{\overline{\smash{\big)}\,x^3-3x^2+2\phantom{)}}}\\{-~\phantom{(}\underline{(x^3-x^2)\phantom{-)..)}}\\-2x^2+2\phantom{)}\\-~\phantom{()}\underline{(-2x^2+2x)\phantom{}}\\-2x+2\phantom{)}\\\phantom{)}-~\phantom{()}(-2x+2)\\\end{array}[/tex]

Therefore, the factored form of the polynomial is:

[tex]f(x)=(x-1)(x^2-2x-2)[/tex]

To find the roots, set the function to zero and solve for x.

Set the first factor to zero and solve for x:

[tex]\implies (x-1)=0 \implies x=1[/tex]

Set the second factor to zero and solve for x using the quadratic formula:

[tex]\implies x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]

[tex]\implies x=\dfrac{-(-2) \pm \sqrt{(-2)^2-4(1)(-2)}}{2(1)}[/tex]

[tex]\implies x=\dfrac{2 \pm \sqrt{12}}{2}[/tex]

Answer: Let's call the length of one side of the equilateral triangle x.

Then, the height of the triangle can be represented as √3/2.

By the Pythagorean theorem, we have:

(x/2)^2 + (√3/2)^2 = (x/2)^2 + 3/4 = x^2/4 + 3/4 = x^2/4 + 3/4 = x^2/4

So:

x^2 = 4 * (x^2/4 + 3/4) = 4x^2/4 + 4 * 3/4 = 4x^2/4 + 3

Solving for x:

3x^2/4 = 3

x^2 = 4

x = 2

So the length of one side of the equilateral triangle is 2 feet.

Step-by-step explanation:

Step-by-step explanation:

To find the possible rational roots of a polynomial function, you can use the Rational Root Theorem. According to this theorem, if a rational number "p/q" is a root of a polynomial function, where p and q are integers, and q ≠ 0, then p must div ide the constant term of the polynomial and q must divide the leading coefficient of the polynomial.

To test if one of the possible rational roots is indeed a root (zero) of the polynomial, you can use the Synthetic Division method. In this method, you divide the polynomial by the linear factor (x - p/q) corresponding to the test root, and check if the remainder is zero. If the remainder is zero, then the test root is a zero (root) of the polynomial.

The transformation rule (x, y) → (-y, x) describes a 270* rotation about the origin for a triangle on the coordinate grid.

A transformation in mathematics is a process of mapping or changing one figure into another while preserving its shape, size and orientation. The coordinate grid is a tool used to plot points and study transformations in a two-dimensional plane.

The transformation rule that describes this rotation is (x, y) → (-y, x). This rule means that for every point (x, y) in the triangle STU, the new point (x', y') in the triangle S'T'U' is obtained by swapping the x and y coordinates and negating the y-coordinate. In other words, the x-coordinate remains unchanged, while the y-coordinate is negated.

For example, if the point (3, 4) is in the triangle STU, the new point (x', y') in the triangle S'T'U' would be (4, -3).

This rule applies to all points in the triangle, and the result is a rotation of the original triangle by 270* in a counterclockwise direction about the origin.

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