how do i solve for this

The length of the rectangle is, (x + 5).

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

We have to given that;

The area of a rectangle is (x² + 4x - 5).

And, The width of rectangle = (x - 1)

Now, We know that;

In a rectangle;

⇒ Area of rectangle = Length × Width

Substitute given values,

⇒ (x² + 4x - 5) = Length × (x - 1)

⇒ (x² + 5x - x - 5) = Length × (x - 1)

⇒ x(x + 5) - 1 (x + 5) = Length × (x - 1)

⇒ (x + 5) (x - 1) = Length × (x - 1)

⇒ (x + 5) (x - 1) / (x - 1) = Length

⇒ Length = (x + 5)

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The outer perimeter of this figure will be;

⇒ 62.84 m

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The figure is shown in image.

Now,

By the figure,

The radius of semicircle = 12/2

                                     = 6 m

Hence, The Perimeter of semicircle = πr

                                                        = 3.14 × 6

                                                        = 18.84 m

Here, The side of square = 12 m

Hence, The Perimeter of square = 12 + 12

                                                  = 2 × 12

                                                  = 24 m

Here, The hypotenuse of triangle = 10 m

Hence, The perimeter = 10 + 10

                                  = 20 m

Thus, The total outer perimeter of this figure is,

⇒ 18.84 + 24 + 20

⇒ 62.84 m

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The percent of the iceberg which is not visible above the water could be 12.5%.

What is percentage ?

percentage can be defined as the  product of ratio of value and total value and 100 .

Given, the captain of a ship must use extreme caution when approaching an iceberg, because only 0.125 of it is above the surface of the water

so the percent of the iceberg which is not visible could be

0.125 * 100 = 12.5 %

Hence , the percent of the iceberg which is not visible above the water could be 12.5%.

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The width of the single slit is 0.00135 mm and the second minimum will be at angle of 69.9º.

To find the width of the single slit, we can use the formula:

w = λL/d * sinθ

where w is the width of the single slit, λ is the wavelength of light, L is the distance from the slit to the screen, d is the distance between the slits and θ is the angle at which the first minimum is observed. By substituting the given values, we get:

w = (633*10^-9 m) (2L) / (d) * sin(28.0º) = 0.00135 mm

The angle of the second minimum can be found by using the formula: θn = sin^-1(nλ/w)

where θn is the angle at which the nth minimum is observed, n is the order of the minimum and λ and w are the wavelength and width of the single slit respectively. Substituting the values we get: θ = sin^-1(2*(633*10^-9 m) / (0.0175 mm)) = 69.9º

It is important to note that the above explanation is based on the assumption that the width of the single slit is much smaller than the distance between the slit and the screen (L) and the distance between the slits (d).

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The probability of a or b will be equal to 0.30769.

What is probability?

Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

The probability of the total sample points in A U B is P(A U B). The probabilities of sample points in A and B are now added together as P(A) + P(B). To get the total of probabilities in (A U B), which is P, we need to subtract once because we added the sample points in (A B) twice (A U B).

Given that p(a)=0.07692, p(b)=0.25, and probability of a and b. =0.01923. The probability will be calculated by using the formula below:-

P(A) = 0.07692

P(B)=0.25

P(AB) = 0.01923

P(AUB) = P(A) + P(B) - P(AB)

P(AUB) = 0.07692 + 0.25 - 0.01923

P(AUB) = 0.30769

Therefore, the probability of a or b will be equal to 0.30769.

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The difference between classical and empirical probability is C. The empirical method obtains an approximate empirical probability of an event by conducting a probability experiment. The classical method of computing probabilities does not require that a probability experiment actually be performed. Rather, it relies on counting techniques, and requires equally likely outcomes. The classical method obtains an approximate em be performed. Rather, it relies on counting techniques, and requires equally likely outcomes.

Classical probability is based on the idea of equally likely outcomes. In classical probability, the probability of an event is determined by counting the number of favorable outcomes and dividing by the total number of possible outcomes.

Empirical probability, on the other hand, is determined by observing the frequency of an event over a period of time or a number of trials. It's based on the relative frequencies of the outcomes of an experiment.

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Nelson has 2+x/3 pears.

Mathematical expressions can be used to depict situations or issues, and algebra is the field of mathematics that does this. For a mathematical expression to have meaning, it needs to include variables like x, y, and z as well as mathematical operations like addition, subtraction, multiplication, and division. Algebra is used in every area of mathematics, including coordinate geometry, calculus, and trigonometry.

In algebra, symbols are used, and operators are used to connecting the symbols to one another. It is more than just a mathematical idea; it is a skill that we all utilize on a regular basis without even being aware of it.

After Donovan gives Mabel 6 pears, she has 6+x pears. If Mabel gives one-third of her pears to Nelson, he gets (1/3) * (6+x) pears = (2+x/3) pears. Therefore, Nelson has 2+x/3 pears.

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There are six possible numbers that can be made by using the digits 2, 5, and 3: 253, 325, 235, 352, 523, and 532.

1. 253: This number is formed by using the digits 2, 5, and 3 in that order.

2. 325: This number is formed by rearranging the digits 2, 5, and 3 to form a new number.

3. 235: This number is formed by rearranging the digits 2, 5, and 3 to form a new number.

4. 352: This number is formed by rearranging the digits 2, 5, and 3 to form a new number.

5. 523: This number is formed by rearranging the digits 2, 5, and 3 to form a new number.

6. 532: This number is formed by rearranging the digits 2, 5, and 3 to form a new number.

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The number of years that Reema took the loan will be 8 years.

A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.

We know that the compound interest is given as

A = P(1 + r)ⁿ

Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.

Reema took out a 10,000 loan at a 10% annual interest rate. Over the course of the loan, she paid a total of 21,200 in interest.

Then the number of years is calculated as,

21,200 = 10,000 × (1 + 0.10)ⁿ

2.12 = (1.10)ⁿ

Take log on both sides, then we have

log 2.12 = n log (1.10)

n = 7.8839

n ≅ 8 years

The number of years that Reema took the loan will be 8 years.

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Answer:

Step-by-step explanation:

You need to do math to solve for the answer.

Work Shown:

[tex]a^2 + b^2 = c^2\\\\a^2 + 23^2 = 30^2\\\\a^2 + 529 = 900\\\\a^2 = 900 - 529\\\\a^2 = 371\\\\a = \sqrt{371}\\\\a \approx 19.26136\\\\a \approx 19.3[/tex]

For more information, search out "pythagorean theorem" to see other examples. The pythagorean theorem only works for right triangles.

The best summarizes for the result is:

O There is a moderate negative correlation between the variables.

A correlation coefficient measures the strength and direction of the relationship between two variables. The coefficient ranges from -1 to 1, with -1 indicating a perfect negative correlation, 0 indicating no correlation, and 1 indicating a perfect positive correlation.

In this case, the correlation coefficient of -0.524 indicates a moderate negative correlation between the variables. This means that as the value of one variable increases, the value of the other variable decreases, and vice versa. The negative sign indicates that the relationship is negative, and the absolute value of the coefficient (0.524) indicates that the relationship is moderate in strength.

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Answer:

256

Step-by-step explanation:

3 What is the sum of the geometric series 4 2,341 256 525 64 2,343 256 ... A: Geometric series are such finite or infinite series where every next term

Representation of the number of items she must sell by inequality is,

⇒ 5x + 350 ≤ $950

Where, x represents the number of items she sells within that month.

A relation by which we can compare two or more mathematical expression is called an inequality.

We have to given that;

Paula total earnings per month are modeled by the expression,

⇒ 5 x + 350

Where, x represents the number of items she sells within that month.

Here, She wants to earn at least $950 this month.

Hence, We can write this situation in inequality as,

⇒ 5x + 350 ≤ $950

Where, x represents the number of items she sells within that month.

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An equilateral triangle has equally long sides.

An equilateral triangle is a special type of triangle where all three sides are equal in length. This means that all three angles of the triangle measure 60 degrees each. This also means that all three sides of the triangle are of equal length, and that the triangle is also an isosceles triangle (since two of the sides are equal). Therefore, the statement "All sides of an equilateral triangle are equal in length" is true for all equilateral triangles.

All equilateral triangles have three sides of equal length, with all three angles measuring 60 degrees each, and they are also isosceles triangles.

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The function is discontinuous at x=-2, x=0, x=2. The correct answer is B.

A function is said to be discontinuous at a point if it does not have a well-defined value at that point or if the left-hand limit and the right-hand limit at that point are not equal. Discontinuity can be classified as removable or non-removable. Without knowing the specific function, it is not possible to determine exactly where it is discontinuous. However, From the options provided B) x=-2, x=0, x=2 is the only option that lists all possible discontinuous points.

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Answer:

[tex] \frac{2}{3} [/tex]

Approx : 0.66

Step-by-step explanation:

[tex]( - 2 + 12 - {2}^{3}) \div {2}^{0} \times 3 \\ (- 2 + 12 - 8) \div 1 \times 3 ( expla \\ ation \: {2}^{3} = 8 \: and \: {2}^{0} = 1 ) \\ = (10 - 8) \div 3 \\ = 2 \div 3 \\ = 0.66[/tex]

A triangular shape is a polygon since it has three sides and three angles. The triangle has a 180 degree overall angle.

Having three sides and three angles, a triangle is a polygon. The triangle's total angle is 180 degrees.

A closed triangle has 3 sides, 3 angles, and 3 vertices. It is a 2-dimensional shape. Polygons include triangles as well. ABC is a triangle that is depicted in the previous illustration.

An equilateral triangle is one that has equal lengths on all three of its sides. A triangle is said to be an isosceles triangle if its two sides are equal.

There is a triangle ABC.

BK is divided at a ratio of 1:1 if BK = 11 and we are aware that the two medians intersect. Then

[tex]$\frac{\mathrm{KQ}}{\mathrm{BK}}=\frac{1}{1}$$\mathrm{KQ}=\frac{\mathrm{BK}}{1}$$\mathrm{KQ}=\frac{11}{1}$$\mathrm{KQ}=11$[/tex]

Therefore, the KQ is 11.

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The required value of KQ for the question is 11.

Having three sides and three angles, a triangle is a polygon. The triangle's total angle is 180 degrees.

A closed triangle has 3 sides, 3 angles, and 3 vertices. It is a 2-dimensional shape. Polygons include triangles as well. ABC is a triangle that is depicted in the previous illustration.

An equilateral triangle is one that has equal lengths on all three of its sides. A triangle is said to be an isosceles triangle if its two sides are equal.

There is a triangle ABC.

BK is divided at a ratio of 1:1 if BK = 11 and we are aware that the two medians intersect. Then

We know that

KQ/BK = 1/1

So,

KQ = 11

Therefore, the KQ is 11.

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The value of ∠ABD is 20°.

In geometry, an angle bisector is a line that divides an angle into two equal angles. The term "bisector" refers to a device that divides an object or a shape into two equal halves. An angle bisector is a ray that divides an angle into two identical segments of the same length.

Given ∠ABC = 40°

and BD is angle bisector,

so ∠ABD  = ∠DBC

∠ABD  = 3x - 1

∠DBC = 34 - 2x

∠ABD  = ∠DBC

3x - 1 = 34 - 2x

3x + 2x = 34 + 1

5x = 35

x =7

∠ABD  = 3x - 1

∠ABD  =  3(7) - 1

∠ABD  = 20°

Hence value of ∠ABD  = 20°.

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Answer:

a = 19

Step-by-step explanation:

IF x-2 is a factor, then x = 2 will make the equation = 0

4 (2^4) - 7(2^3) + 3(2^2) -2a + 18 = 0

64        -  56      +  12     - 2a  + 18 = 0

38 - 2a = 0

a = 19

a) The equation in the form of x is x + x+2 + x+4 = 648.

b) The three consecutive even integers are 214, 216 and 218.

What is an integer?

The number zero (0), a positive natural number (1, 2, 3, etc.), or a negative integer denoted by a minus sign (1, 2, 3, etc.) are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers.

It is given that the sum of three consecutive even integers is 648.

The smallest integer is taken to be x.

Since, the numbers are consecutive and even then the numbers will be x, x+2 and x+4

So, according to the question the equation will be -

x + x+2 + x+4 = 648

Solve the equation to get the value of x -

3x+6 = 648

3x = 648 - 6

3x = 642

x = 214

Hence, the three numbers are x = 214,

x+2 = 214+2 = 216

x+4 = 214+4 = 218.

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Answer:=4

Step-by-step explanation:√(√7)²+3²

                                            √7+9

                                             √16

                                      =4

Using the formula for the surface area of the rectangular prism and with the provided values, The answer is 366 [tex]mm^2[/tex].

A rectangular prism is a three-dimensional geometric shape that has six rectangular faces. It has three pairs of parallel faces, with each pair being a rectangle of the same size and shape. The opposite faces of a rectangular prism are also parallel and congruent. It is also known as a cuboid. In addition to having three pairs of parallel, congruent rectangle faces, a rectangular prism also has three pairs of parallel edges and four pairs of congruent vertices. It can also be defined by its length, width, and height, which are the measurements of the three rectangular faces.

The surface area of a three-dimensional object is the total area of all of its faces or surfaces. It is the sum of the areas of all the faces of an object. For example, the surface area of a rectangular prism is the sum of the areas of all six of its rectangular faces. To find the surface area, you would add up the area of the length x width of each face. In a rectangular prism, the surface area can be calculated by:

Surface Area = 2lw + 2lh + 2wh

Where l is the length, w is the width and h is the height.

Surface Area = 2lw + 2lh + 2wh

l=9mm

w=3mm

h=13mm

surface area = 2·(3·9+13·9+13·3) = 366[tex]mm^2[/tex].

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The story that can be represented by the equation y=x−2/3x is D. Noah bought x pounds of cheese. Clare bought 2/3 less than that.

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

Since Noah bought x pounds of cheese. Clare bought 2/3 less than that. This will be:

x - 2/3x

Therefore, the correct option is D.

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For the given inequality: 2x - 3y ≥ 12.

m = 2

b = -4

Line: Solid

Shade: Below

(0, 2) is not the solution for the given inequality.

(3, 4) is the solution for the given inequality.

(-2, -2) is not the solution for the given inequality.

What is linear inequality?

An inequality is a mathematical statement comparing two values or expressions, usually involving one of the following relational operators: < (less than), > (greater than), <= (less than or equal to), >= (greater than or equal to), or != (not equal to). The solution to inequality is a set of values that make the inequality true.

The given inequality, 2x-3y>=12, is a linear inequality in two variables. The slope of the line represented by this inequality is the coefficient of x, which is 2. The y-intercept of the line is not explicitly given in the inequality, but we can find it by setting x = 0 and solve for y.

To find the y-intercept, we set x = 0 and substitute it into the inequality:

2(0) - 3y >= 12

-3y >= 12

y <= -4

and by observing the graph, we can say that

Line: Solid

Shade: Below

(0, 2) is not the solution for the given inequality.

(3, 4) is the solution for the given inequality.

(-2, -2) is not the solution for the given inequality.

Hence,

For the given inequality: 2x - 3y ≥ 12.

m = 2

b = -4

Line: Solid

Shade: Below

(0, 2) is not the solution for the given inequality.

(3, 4) is the solution for the given inequality.

(-2, -2) is not the solution for the given inequality.

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Table 4 represents a direct variation function.

What is the direct variation?

A pair of variables that are related when one is a constant multiple of the other. For instance, two variables are said to be in proportion when one affects the other. b = ka is the equation if b is directly proportional to a. (where k is a constant).

Here,

We have given a table and we have to determine which table represents a direct variation function.

A function of direct variation fulfills the following form:

y = kx<br/>

Where,

x: independent variable

y: dependent variable

k: proportionality constant (k> 0)

The value of k is given by:

k = (y₂ - y₁)/(x₂ -x₁)<br/>

Now, we substitute value

k = (12.5 - 5)/(5 -2)<br/>

k = 2.5>0

Hence, table 4 represents a direct variation function.

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This means that as x increases, y decreases and vice versa. This means that the ratio of y to x is always constant.

1. Identify the constant of proportionality, k, which represents the ratio of y to x.

2. Determine an equation that shows the relationship between y and x. This equation should include the constant of proportionality, k.

3. Solve for y in terms of x.

4. Use the equation to find the value of y when given the value of x.

Let k be the constant of proportionality.

example

The equation describing the relationship between y and x is y = k/x

Solve for y: y = k/x

Given x = 2 and k = 4,

y = 4/2

y = 2

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Answer: y+2.50

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

This is a right triangle.

To find the value of x we can use Pythagoras theorem:

[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]

a and b are the legs which are given as 3 and √7 respectively and c is the hypotenuse.

[tex] {3}^{2} + ( { \sqrt{7} )}^{2} = {c}^{2} [/tex]

[tex]9 + 7 = {c}^{2} [/tex]

[tex]16 = {c}^{2} [/tex]

4 = c

Answer:

Answer is written in the link

Step-by-step explanation:

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The number of significant figures that the digits given have are;

1) 3

2) 2

3) 4

Significant figures are defined as the number of digits in a value, which is often a measurement, that contributes to the degree of accuracy of the value.

Some of the rules for counting significant figures are;

- All non-zero  digits and any zeros contained between non - zero digits count e.g 300042 has 6 significant digits

- Leading zeros don't count e.g 0.000254 has only 3 significant figures.

- Trailing zeros count if there is a decimal point e.g 0.0002500 has 4 significant figures.

- Trailing zeros will not count if there is no decimal point e.g 180000 has only 2 significant figures.

1) 90500 Kg; This has only 3 significant figures when applying rule 1 and 4 above.

2) 7.1 x 10 ml = 71 ml; This clearly has 2 significant figures.

3) 0.004300; Applying rule 3 above, this has 4 significant figures.

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We set the radicand to be higher than or equal to zero to determine the domain of a radical function with even index. The radicand for an odd index radical can be any real integer. When the radical has an even index, the radicand must be larger than or equal to zero.

Note that an even radical function is a function of the form f(x) = √(g(x)), where g(x) is an even function. That is, the function is defined as the square root of an even function.

In several methods, either algebraically or visually, a function can be defined as even, odd, or neither. An even function is one whose graph remains intact when reflected in the y-axis.

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