the length of the side of square a is 50% of the length of square b

On solving the provided question, we can say that  let the equation be  X =   4ª - 4(2) (-8) => X = -15

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

let the equation be

X =   4ª - 4(2) (-8)

here, a = 0

X = 1 - 8-8

X = -15

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The other side length is √20 after applying the Pythagoras and other two sides are 2 and 2√3.

The square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.

One side length = 2

Other side length = 2√3

Apply Pythagoras

x^2 = 2^2 + (2√3)^2

x^2 = 4 + 12

x = √20

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Answer:

3,744 [tex]cm^{2}[/tex]

Step-by-step explanation:

Front is a trapezoid

a = 1/2([tex]base_{1}[/tex] + [tex]base_{2}[/tex])h

a = 1/2(29 +12)24

a = 492

the back is the same value 492

Bottom

29 x 30 = 870

Right sides

30 x 26 = 780

Left side

25 x 30 = 750

Top

12 x 30 = 360

492 + 492 + 870 + 780 + 750 + 360 = 3744[tex]cm^{2}[/tex]

The option that best describes the pattern of association for the scatterplot graph is; There is a positive nonlinear association.

In statistics, we say that two random variables have a positive correlation if Y tends to increase as X increases.

Meanwhile, we can say that two random variables have a negative correlation if Y tends to decrease as X increases.

Now, when there is a relationship between the x and y variables, we can say that there is some type of association such as linear, quadratic, exponential e.t.c

Now, in this given scatterplot, we can see that y almost certainly increases as x increases and as such this is a positive correlation. Similarly, we see that it is not a linear relationship as it looks like an exponential curve. Thus, it is a non linear association.

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Answer:

The option that best describes the pattern of association for the scatterplot graph is; There is a positive nonlinear association.

Step-by-step explanation:

Answer:

20 per kilogram. then it is necessary to know just what units are being used for the purchase. This information is given under 'Comparative Costs per Unit'.

Step-by-step explanation:

The 10 years continuous growth rate as calculated is 0.9259 % per year and the equation to model the population growth of the United States, and is used it to estimate the population in 2020 is  P = 281.4e^(0.009 259t); 338.6 million  .

Given,

P₀ = 281.4 million

P  = 308.7 million

To calculate the growth rate

t = 2010 - 2000 = 10 yr

P = P₀e^(rt)

308.7 = 281.4e^(10r)

e^(10r) = 1.0970

10r = ln1.0970

r = (ln1.0970)/10 = (0.092 59)/10 = 0.009 259  

r = 0.9259 % per year

To find the equation of population model

P = 281.4e^(0.009 259t)

here , P is in millions and

the number of years passed since 2002 is represented as t.

P = 281.4e^(0.009 259 × 20) = 281.4e^0.1852 = 281.4 × 1.203

P = 338.6 million

Therefore, the population in 2020 is assumed to be 338.6 million.

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The one-third of the job will take md/3n days. The result is obtained by using the concept of inverse proportion.

Inverse proportion is a proportionality relationship when one value increases and the other decreases.

Assuming that the workers are working at the same rate, the more workers will complete the job more quickly. It means the more workers that do the job, the less time needed. We use inverse proportion to solve this problem.

We have workers and time to complete a job. Let's say e is the time for n workers to complete the job.

By the inverse proportion concept, we get

m/n = e/d

e = md/n days

To complete one-third of the job, they need

⅓e = ⅓ (md/n)

⅓e = md/3n

Hence, it will take md/3n days to complete the one-third of the job.

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The answer to the above question is B. Multiply the first equation by -2 and add the second equation.

A mathematical statement that establishes the equality of two mathematical expressions is the definition of an equation in algebra. Consider the equation 3x + 5 = 14, in which the terms 3x + 5 and 14 are separated by the word "equal."

Given,

[tex]2x - 2y = 24\\4x + 7y=-40\-4x +4y = -96\\4x+7y = -40\\11y = -136\\y = -136/11[/tex]

The answer to the above question is B. Multiply the first equation by -2 and add the second equation.

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The radical exponent for five to the three fourths power all raised to the two thirds power is C. the square root of five.

The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.

In this situation, five to the three fourths power all raised to the two thirds power will be:

= 5^3/4(^2/3)

= 5^1/2

The correct option is C

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A cylindrical basin is 2 feet tall and has a diameter of 5 feet, as shown. If the basin is completely filled with water, how much water will it hold? Round the answer to the nearest tenth of a foot.

The basin holds 39.3 cubic feet of water.

The volume of a cylinder is the number of unit cubes (cubes of unit length) that can be fit into it. It is the space occupied by the cylinder as the volume of any three-dimensional shape is the space occupied by it. The volume of a cylinder is measured in cubic units such as cm3, m3, in3, etc. Let us see the formula used to calculate the volume of a cylinder. We know that the base of a right circular cylinder is a circle and the area of a circle of radius 'r' is πr2. Thus, the volume (V) of a right circular cylinder, using the above formula, is,

V = πr²h

Here,

⇒ 'r' is the radius of the base (circle) of the cylinder

⇒ 'h' is the height of the cylinder

⇒ π is a constant whose value is either 22/7 (or) 3.142.

Thus, the volume of cylinder directly varies with its height and directly varies with the square of its radius. i.e., if the radius of the cylinder becomes double, then its volume becomes four times.

We are given that the height of the basin h = 2 ft and the diameter = d = 5 ft.

So, radius r = d/2 = 5/2 = 2.5 ft

The amount of water the basin holds is equal to the volume of cylindrical basin.

Volume =πr²h

=3.1416×2.5²×2

=39.27 cubic feet

= 39.3 cubic feet

Thus, the basin holds 39.3 cubic feet of water.

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The statements which are correct about the equation 3(x - a) = 3x - 6 are;

According to the task content; the equation which is to be considered is;

3(x - a) = 3x - 6

Therefore, it follows from the distributive property that we have;

3x - 3a = 3x - 6

Therefore

On this note, the true statements are as indicated above.

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If the range of X is the set {0,1,2,3,4,5,6,7,8} and P(X=x), then the,

(a) Mean = 3.42544

(b) Variance = 7.91

Given data,

If the range of X is the set {0,1,2,3,4,5,6,7,8} and P(X=x) as defined in the following table:

x              0         1               2                  3          4          5         6        7     8      

P(X=x)    0.06528   0.3870     0.03062       0.0968      0.06913        0.0968      0.04846                0.01252            0.1935

Mean = Σ [tex]x p(x)[/tex]

Mean = (0 * 0.06528) + (1*0.3870) + (2*0.03062) + (3*0.0968) + (4*0.06913) + (5*0.0968) + (6*0.04846) + (7*0.01252) + (8*0.1935)

Mean = 0 + 0.3870 + 0.06124 + 0.2904 + 0.2765 + 0.484 + 0.2907 + 0.0876 + 1.548

Mean = 3.42544

Mean = Σ [tex]x p(x)[/tex] = 3.42544

Σ [tex]x^{2} p(x)[/tex] = (0 * 0.06528) + ([tex]1^{2}[/tex]*0.3870) + ([tex]2^{2}[/tex]*0.03062) + ([tex]3^{2}[/tex]*0.0968) + ([tex]4^{2}[/tex]*0.06913) + ([tex]5^{2}[/tex]*0.0968) + ([tex]6^{2}[/tex]*0.04846) + ([tex]7^{2}[/tex]*0.01252) + ([tex]8^{2}[/tex]*0.1935)

Σ [tex]x^{2} p(x)[/tex] = (0 * 0.06528) + (1*0.3870) + (4*0.03062) + (9*0.0968) + (16*0.06913) + (25*0.0968) + (36*0.04846) + (49*0.01252) + (64*0.1935)

Σ [tex]x^{2} p(x)[/tex] = 0 + 0.3870 + 0.1224 + 0.8712 + 1.106 + 2.42 + 1.744 + 0.613 + 12.38

Σ [tex]x^{2} p(x)[/tex] = 19.6436

Variance = Σ [tex]x^{2} p(x)[/tex] - ( Σ [tex](xp(x))^{2}[/tex])

Variance = 19.6436 - [tex](3.42544)^{2}[/tex]

Variance = 19.6436 - 11.7336

Variance = 7.91

Therefore,

If the range of X is the set {0,1,2,3,4,5,6,7,8} and P(X=x), then the,

(a) Mean = 3.42544

(b) Variance = 7.91

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The value of the expression [(x² + 7x + 10) / (x² + 4x + 4)] · [(x² + 3x + 2) / (x² + 6x + 5)] will be 1.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The expression is given below.

⇒ [(x² + 7x + 10) / (x² + 4x + 4)] · [(x² + 3x + 2) / (x² + 6x + 5)]

Simplify the expression, then we have

⇒ [(x² + 7x + 10) / (x² + 4x + 4)] · [(x² + 3x + 2) / (x² + 6x + 5)]

⇒ [(x + 5)(x + 2) / (x + 2)(x + 2)] · [(x + 2)(x + 1) / (x + 5)(x + 1)]

⇒ 1

The value of the expression [(x² + 7x + 10) / (x² + 4x + 4)] · [(x² + 3x + 2) / (x² + 6x + 5)] will be 1.

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Answer:see photo #4

Step-by-step explanation:

Answer:

-18.66666666666667

Step-by-step explanation:

The Consistent System Of Linear equations have at least one Solution , and the inconsistent system of linear equations have No Solution .

Let the system of two linear equations be given as :  [tex]a_{1}x +b_{1}y =c_{1}[/tex] and [tex]a_{2}x +b_{2}y =c_{2}[/tex] ;

Case(i) If the equations satisfies the condition :  [tex]\frac{a_{1} }{a_{2} } \neq \frac{b_{1} }{b_{2} }[/tex] ,

then linear equations has a unique solution and solutions are called as consistent .

Case(ii) If the equations satisfies the condition :  [tex]\frac{a_{1} }{a_{2} } = \frac{b_{1} }{b_{2} } = \frac{c_{1} }{c_{2} }[/tex]  ,

then linear equations has infinitely many solution and the solutions are called consistent .

Case(iii) If the equations satisfies the condition : [tex]\frac{a_{1} }{a_{2} } = \frac{b_{1} }{b_{2} } \neq \frac{c_{1} }{c_{2} }[/tex]  ,

then the linear equations has No Solution and the solutions are called as inconsistent .

Therefore  , if system has at least one solution , then solutions are consistent .

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The zeros of the quartic equation x⁴ - 2 · x² - 63 are x₁ = √(1 - √62), x₂ = √(1 + √62), x₃ = - √(1 - √62) and x₄ = - √(1 + √62).

In this problem we find a quadratic-like quartic equation, that is, a quadratic equation of the form:

y = a · x⁴ + b · x² + c

Where a, b, c are real coefficients.

From this expression in standard form we must determine its roots by using an application of algebra properties known as completing the square, which is transforming a part of the function into cubic square trinomial.

First, write the expression and equal it to zero:

x⁴ - 2 · x² - 63 = 0

Second, complete the square and simplify:

(x⁴ - 2 · x² + 1) = 63 - 1

(x² - 1)² = 62

x² - 1 = ± √62

x² = 1 ± √62

x = ± √(1 ± √62)

Third, write all the zeros of the quartic equation:

x₁ = √(1 - √62), x₂ = √(1 + √62), x₃ = - √(1 - √62), x₄ = - √(1 + √62)

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Answer: 48°

Step-by-step explanation:

       We know that the angles of a triangle are equal to 180 degrees when added together. Using this logic, we will create an equation to solve for x. Then we will substitute this value of x back into the expression for angle F.

   Given:

E + D + F = 180°

   Substitue:

(8x - 18)° + (6x - 4)° + (5x - 7)° = 180°

   Reorder and combine like terms:

8x° + 6x° + 5x° - 18° - 4° - 7° = 180°

19x° - 29° = 180°

   Add 29 to both sides of the equation:

19x° = 209°

   Divide both sides of the equation by 19:

x = 11

   Substitute this value of x into the expression for angle F:

(5x - 7)°

(5(11) - 7)°

(55 - 7)°

48°

The property of the triangle congruence state that a ≅ B then B ≅ A are:

The triangle is a polygon that has 3 edge and vertices. Triangle is one of the basic shape in the geometric. The area of the triangle is formulated as base of the triangle * height of triangle x 0,5. The value of three triangle edge degree is 180°.

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Third grade class :: 148 books

Fourth grade class :: 175 books

Total :: 323 books

1 box = 9 books.

323/9 =

36 box....

The scale of the map is 1 dm : 25 km

From the question, we have the following parameters that can be used in our computation:

Mathematical statement

The mathematical statement is given as

50 km in real distance is 2dm on a map

The scale is then calculated as

Scale = Map distance :  Actual distance

Substitute the known values in the above equation, so, we have the following representation

Scale = 2 dm : 50 km

Divide by 2

Scale = 1 dm : 25 km

Hence, the scale is 1 dm : 25 km

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All the situation are Exponential relationship accept the last one.

A linear function is modeled by the following rule:

y = mx + b

In which: m is the slope, which is the rate of change, that is, the change in y divided by the change in x. b is the y-intercept, which is the the value of y when the function crosses the x-axis, that is, when x = 0.

Given that "you work as a taxi driver. you earn an average of $75 in tips each day".

That is, 75^x

This is a Exponential equation.

2. The number of visitors to the eiffel tower in paris increases by 1.5% each year.

This is a Exponential equation.

The number of tadpoles in the pond triples each day.

This is a Exponential equation.

Also, every year 39 million cars cross the golden gate bridge in san francisco.

This is a Linear equation.

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Answer:

  (8, 12)

Step-by-step explanation:

You want to solve the system ...

Add the two equations:

  (2x -y) +(y -x) = (4) +(4)

  x = 8 . . . . . . . . . . . . simplify

  y = 4 +x . . . . . . rearrange the second equation

  y = 4 +8 = 12

The solution is (x, y) = (8, 12).

The false statement is that the membership rates are increasing 20% each year.

When the expression of function is such that it involves the input to be present as exponent (power) of some constant, then such function is called exponential function. There usual form is specified below. They are written in several such equivalent forms.

We are given the equation models the number of members, M, of a gym t years after the gym opens.

[tex]M = 1,800 (1.02) ^t[/tex]

Now if the t time is 3 year then;

[tex]M = 1,800 (1.02) ^t\\\\M = 1,800 (1.02) ^3\\\\M = 1910.14[/tex]

So the last option is True.

Now we can see that the model shows exponential growth. so it is true also.

From the equation the inital part is that  1,800 members joined the gym when it first opened. that is also true.

Hence, the statement is false.

•The membership rates are increasing 20% each year.

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The amount of customers  exceed 285 and when there are 47 tables of 4 and 16 tables of 5 the number so new customers is 17.

Given,

The numbers of customers one at a time is 285

At 12 pm it has 216 customers.

Part A :

To check new amount of customers exceeds 285 or not.

Also given 147 new customers.

So by substituting values:

216 x (1 - 1/3) + 147

= 144 + 147

= 291

Since 291 > 285

Therefore the new number of customers exceed 285.

Part B :

To find number of customers in the restaurant  when there are 47 tables of 4 and 16 tables of 5.

47 x 4 + 16 x 5

= 188 + 80

= 268

So, 285 - 268

= 17

Therefore there are  17 new customers in the restaurant.

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Answer:

f⁻¹(x) = [tex]\frac{\sqrt{x}}{2}[/tex] , -[tex]\frac{\sqrt{x} }{2}[/tex]

Step-by-step explanation:

f(x) = 4x²

rewrite as:

y = 4x²

Interchange the variables, then solve for y:

x = 4y²

y² = x/4

y = √x/2, -√x/2

Answer:

f⁻¹(x) = [tex]\frac{\sqrt{x}}{2}[/tex] , -[tex]\frac{\sqrt{x} }{2}[/tex]

The equation of the line passing through the points (1,3) with slope = -4 is

y = -4x + 7

The equation of a line can be formed with the help of the slope of the line and a point on the line. The slope of the line is the inclination of the line with the positive x-axis and is expressed as a numeric integer, fraction, or the tangent of the angle it makes with the positive x-axis. The point refers to a point in the coordinate system with the x coordinate and the y coordinate.

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

where m = -4

y1 = 3

x1 = -1

-4 = (y - 3) / (x - 1)

-4(x - 1) = y - 3

-4x + 4 = y - 3

y = -4x + 7

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1) The next number in the series 99, 33, 11, 11/3, 11/9, . . . is 11/27

The correct answer is an option (c)

2)  In the given group the smallest amount is .18

1.

We have been given a sequence of numbers 99, 33, 11, 11/3, 11/9,. . .

We need to find the next number in given sequence .

We can observe that given series is geometric sequence with the first term a₁ = 99 and the common ratio r = 1/3

We know that the formula for the n-th term of gemetric sequence is:

an = a₁ × r^(n - 1)

For n = 6,

a₆ = 99 × (1/3)⁽⁶ ⁻ ¹⁾

a₆ = 99 × (1/3)⁵

a₆ = 11/27

Hence, the next number in the series is 11/27

2.

If we arrange the numbers in ascending order then it would be,

0.18, 0.59, 0.7, 3, 6, 15

So, the smallest amount is .18

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The plant root is growing at a rate of 3.81 centimeters per month.

To find the number of centimeters that the plant root is growing per month, you need to convert the number of inches to centimeters. One inch is equal to 2.54 centimeters, so to convert from inches to centimeters, you need to multiply the number of inches by 2.54.

In this case, the plant root grows 1.5 inches per month. Multiplying this by 2.54 gives us 3.81 centimeters, which is the correct answer. Therefore, the plant root is growing at a rate of 3.81 centimeters per month.

The other answer choices are not correct because they do not give the correct number of centimeters that the plant root is growing per month.

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A particular plant root grows 1.5 inches per month, then 3.81 centimeters the plant root are growing per month.

In the given question, a particular plant root grows 1.5 inches per month.

We have to find how many centimeters the plant root is growing per month.

As we know that 1 inch = 2.54 centimeters

To convert 1.5 inches in centimeters we multiply 1.5 by 2.54 because in 1 inch has 2.54 centimeters. After multiply we can easily find the answer in centimeters.

So 1.5 inch = 1.5*2.54 centimeters

1.5 inch = 3.81 centimeters

Hence, a particular plant root grows 1.5 inches per month, then 3.81 centimeters the plant root are growing per month.

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McCandless weighed a hundred and forty pounds when he died.

It was apparent that McCandless had been deceased for nineteen days based on a mysterious journal that was discovered among his belongings.

According to a driver's license that was granted eight months before he passed away, he was 24 years old and weighed 140 pounds. After being taken out of the woods, his body underwent an autopsy, which found that it weighed only 66.7 pounds and had no subcutaneous fat that could be seen.

The coroner's findings said that malnutrition was the death's most likely cause.

Thus, McCandless weighed a hundred and forty pounds when he died.

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McCandless weigh when he died is at the amount of sixty-seven pounds.

The term weigh in math is defined as the measure of the force of gravity on an object and the mass of an object will never change, but the weight of an item can change based on its location.

Here we have know that the driver's license issued eight months before he perished indicated that he was twenty-four years old and weighed a hundred and forty pounds. Therefore his body was flown out of the wilderness, and at the time of autopsy determined that it weighed sixty-seven pounds and lacked discernible subcutaneous fat and the cause of death was officially reported as starvation.

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