pls help with this
Find the length of side x in simplest radical form with a rational denominator.

Answer:

See below for solution steps for parts (a) and (c)

Step-by-step explanation:

The trick here is to get all the roots to have the same radical. Each of the lowest radical is the square root pf a prime so cannot be reduced further

For example, in a, the lowest is [tex]\sqrt{3}[/tex]

So get all the others to this level a[tex]\sqrt{3}[/tex]  and then you can just add up the non-radicals and use the radical as the common expression

I will solve a couple and that will give you a general idea of solving the rest

Let's do a.
[tex]5\sqrt{3} , \sqrt{3}[/tex] are already at the lowest radical level of [tex]\sqrt{3}[/tex] so let's reduce 108 to have [tex]\sqrt{108}[/tex] to have [tex]\sqrt{3}[/tex] as one of its components

We can factor 108 as follows;

108/3 = 36

So 108 = 36 x 3

√108 = √36 × √3 = 6√3

Therefore the original expression becomes

[tex]5\sqrt{3} - 6\sqrt{3} + \sqrt{3} = (5 - 6 + 1)\sqrt{3} = 0 \sqrt{3} = 0[/tex]

[tex]-------------------------------[/tex]

c.
[tex]2\sqrt{20} - 7\sqrt{5} + \sqrt{45}[/tex]

Lowest radical is [tex]\sqrt{5}[/tex] whose coefficient is 7

Factor 20 = 4 x 5

[tex]2\sqrt{20} = 2\sqrt{4 \times 5} = 2\sqrt{4} \times \sqrt{5} = 2\times 2 \times \sqrt{5}\\= \bold{4\sqrt{5}}[/tex]

Factor 45:
45 = 9 x 5

[tex]\sqrt{45} = \sqrt{9} \times \sqrt{5} = \bold{3\sqrt{5}}[/tex]

Original expression becomes:
[tex]4\sqrt{5} - 7\sqrt{5} + 3\sqrt{5}\\\\=(4 - 7 + 3)\sqrt{5}\\\\= 0 \sqrt{5}\\\\= 0\\----------------------------[/tex]

I am sure you can do the rest. If not post them as another question. Maybe someone else will answer a few of the ones I did not.

All the best

1. Area of the figure = 702 square feet.

Perimeter = 114 feet

2. Area of the figure = 20 square inches.

Perimeter = 24 inches.

Area of a rectangle = length * width

Perimeter of a shape = length of all the surrounding of a figure.

1. Area = area of rectangle 1 + area of rectangle 2 = 27 * 24 + 9 * 6

= 702 square feet.

Perimeter = 30 + 27 + 24 + 18 + 6 + 9 = 114 feet

2. Area = area of rectangle 1 + area of rectangle 2 = 7 * 2 + 3 * 2

= 20 square inches.

Perimeter = 7 + 2 + 3 + 3 + 2 + 3 + 2 + 2

= 24 inches.

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The statement "the sum of a two-digit number is less than the value of the original two-digit number" can be rewritten as conditional statement. If the sum of two digits of a two-digit number is less than the value of the original two-digit number, the number is valid.

A conditional statement, "if p, then q," with p representing the hypothesis and q representing the conclusion. We can identify the hypothesis and conclusion by rewriting the statement "the sum of the digits of a two-digit number is less than the value of the original two-digit number" as an if-then conditional statement.

The hypothesis is the condition that must be satisfied in order to valid the conclusion. In this case, the hypothesis is "the sum of the digits of a two-digit number is less than the value of the original two-digit number".

By combining these, we can rewrite the statement as follows:

If the sum of a two-digit number's digits is less than the value of the original two-digit number, the number is valid.

The hypothesis (the sum of the digits of a two-digit number is less than the value of the original two-digit number) is a sufficient condition for the conclusion, according to this conditional statement (the number is valid). In other words, if the hypothesis is correct, we can be certain that the conclusion is correct as well.

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Answer:B

Step-by-step explanation:

The area of circle that is needed to be filled with concrete is 509 m².

What is the definition of a circle?

A circle is a kind of ellipse with zero eccentricity and two coinciding foci. The locus of points drawn at equal distances from the centre is also known as a circle. A circle's radius is the distance between its centre and its outer line. A circle's diameter is the line that divides it into two equal halves and is equal to twice its radius.

A circle in the plane has the following equation:

(x-h)^²+ (y-k)² = r²

When the coordinate points are aligned (x, y)

(h, k) is the centre of a circle's coordinate.

r denotes the radius of a circle.

where 2πr is the circumference of the circle

πr²=circle's area

Now,

Given that circumference of the area=80 m

2πr=180

2*22/7*r=80

r=80*7/44

r=140/11 m

then area of the circular pad=πr²

=22/7*140/11*140/11

=2*20*140/11

=5600/11

=509 m²

hence,

              The area of circle that is needed to be filled with concrete is 509 m².        

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The graph of the quadratic function is on the image at the end.

Here we want to graph the quadratic function:

f(x) = -x² - 2

To do so, we can complete the table of values by evaluating the function.

if x = ±2 then:

f(±2) = -(±2)² - 2 = -4 - 2 = -6

if x =  ±1

f(±1) = -(±1)² - 2 = -1 - 2 = -3

if x = 0

f(0) = -(0)² - 2 =  - 2 = -2

Then we have the points:

(-2, -6), (-1, -3), (0, -2), (1, -3), (2, -6)

Now just graph these points and connect them with a curve. The graph of the parabola is below.

The average rate of change over the interval (-1, 2) of the function is 3.

A parabola is a curve drawn in a plane. Where any point is at an equal distance from a fixed point (the focus) and a fixed straight line (the directrix).

A graph of the parabola is given.

The vertex is (-1, -4).

And the y-intercept is -3.

So, the equation of the parabola is,

y = (x + 1)² - 4.

The average rate of change over the interval (-1, 2):

= f(-1) - f(2)/(-1 - 2)

= (-4 - 5)/-3

= 3

Hence, 3 is the average rate of change.

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Answer:

A nonlinear function is a function in which the rate of change of the output (y) is not proportional to the rate of change of the input (x). In other words, a nonlinear function is a function where the graph of the function is not a straight line.

Here are a few examples of equations that represent nonlinear functions:

y = x^2: This is the equation for a parabolic function, which is a classic example of a nonlinear function.

y = sin(x): This is the equation for the sine function, which is periodic and nonlinear.

y = |x|: This is the equation for the absolute value function, which is nonlinear and has a "kink" at x = 0.

y = log(x): This is the equation for the natural logarithmic function, which is also nonlinear.

These are just a few examples of nonlinear functions. There are many other types of nonlinear functions, including polynomial, exponential, and trigonometric functions.

The value of x from the given triangle is 17.5 units.

The sides and angles of a right-angled triangle are dealt with in Trigonometry. The ratios of acute angles are called trigonometric ratios of angles. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

We know that, sinθ= Opposite/Hypotenuse

Here, sin31°=9/x

0.515=9/x

x=9/0.515

x=17.5

Therefore, the value of x is 17.5 units.

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The expression that represents the area of each section is 14z-9

The expression to denote the area of each section would be: 14z -9

Given that,

The expression for the area of plot  area 84z -54

The number of equal sections in which it is divided 6

To find,

The expression for each section = ?

The area of each section = (total area of the garden(/number of equal sections

= (84x-54)/6

= 6(14z-9)/6

=14z - 9

Thus,  is the expression that would represent every section's area.

Answer:

Step-by-step explanation:

Cross-price elasticity of demand is a measure of the relationship between the prices of two goods and the quantity demanded of each. It is used to determine how changes in the price of one good affect the demand for another good.

In this scenario, Janet is shopping for formula and bottles for her baby. The price of her favorite brand of formula has increased by 20%, causing her to buy 50% fewer new bottles. The cross-price elasticity for the new bottles calculated using the cross-price elasticity formula is -2.5.

A negative cross-price elasticity value of -2.5 means that the two goods, formula and bottles, are complements. This indicates that an increase in the price of one good (the formula) leads to a decrease in the demand for the other good (the bottles). In other words, when the price of formula increases, Janet is less likely to buy as many new bottles because she is spending more on formula.

On the other hand, if the cross-price elasticity were positive, it would indicate that the two goods are substitutes. In that case, an increase in the price of one good (the formula) would lead to an increase in the demand for the other good (the bottles) as people switch to the cheaper alternative.

In summary, cross-price elasticity of demand is a useful tool for understanding the relationship between the prices of two goods and the quantity demanded of each, and can help businesses make informed decisions about pricing and product strategy.

The cross-price elasticity is -3.66., complements.

A demand that is elastic experiences a significant shift in quantity demanded as a result of a price adjustment. When the amount sought changes little as a result of a price adjustment, the demand is said to be inelastic.

The percentage change in the quantity demanded for one good has an impact on the percentage change in the price of another good, which is measured by the cross elasticity of demand.

Based on the values given above, the cross elasticity of demand will be:

= [(3 - 6) / (18 - 15)] × [(15 + 18) / (6 + 3)]

= (-3/3) × (33/9)

= -1 × 3.66

= -3.66%

Since it's a negative value, the goods are complement.

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The relative minimum's coordinates are (1, -5).

The first derivative test can be used to determine if a continuous function's critical point is a relative minimum or maximum. Simply put, the first derivative is a relative minimum if it is negative to the left of the critical point and positive to the right of it.

The parabola's equation takes the following form because its vertex is at (1, -5).

y = a(x - 1)² - 5

where "a" is a constant that determines the shape of the parabola. Since the parabola crosses the y-axis at (0, -3), we can substitute these coordinates into the equation and solve for "a" as follows:

-3 = a(0 - 1)² - 5

-3 = a - 5

a = 2

Thus, the equation of the parabola is:

y = 2(x - 1)² - 5

The x-coordinate of the vertex is given by x = 1

find the corresponding y-coordinate by substituting x = 1 into the equation:

y = 2(1 - 1)²- 5 = -5

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Answer:

oranges

Step-by-step explanation:

20% of 460 = 92

30% of 340 = 102

Answer:yo no se come ablar ingles

Step-by-step explanation:

The amount after 35% off on a 85 dollar item will be $55.25

Percentage is a way to express a number as a fraction of hundred. It is often used to represent proportions  and  ratios in a more convenient and understandable form, especially in financial  statistical and financial  contexts. For example, 50% means 50 per 100, or half of a given quantity. It is denoted using the symbol "%".

To find the sale price of an item that has a discount, you can use the following formula:

Sale price = Original price - (Discount percent × Original price)

In this case, the discount is 35% off of an $85 item. So we have:

Discount percent = 35%

Original price = $85

Substituting these values into the formula, we get:

Sale price = $85 - (35% × $85)

Sale price = $85 - $29.75

Sale price = $55.25

Therefore, the sale price of the item after a 35% discount is $55.25.

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The y-coordinate for the solution to the system of equations is 6.

In mathematics, the value that is equally divided by the two supplied numbers is known as the LCM of any two. Least Common Multiple is its full name. Another name for it is the Least Common Divisor (LCD).

When the fractions' denominators differ, LCM can also be used to add or subtract any two fractions. LCM is used to make the denominators common when doing any arithmetic operations using fractions, such as addition and subtraction. The simplifying process is facilitated by this procedure.

The system of equation is given as:

−x + 3y = 9

y = 2/3x

The second equation can be written as:

x = 3/2y

Substituting the value of x in equation 1:

-3/2y + 3y = 9

Take the LCM:

-3y + 6y / 2 = 9

-3y + 6y = 18

3y = 18

y = 6

Hence, the y-coordinate for the solution to the system of equations is 6.

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Based on the rating information of 10.2, a total of 1,800,000 households watched the show that week is 18360000 household.

An evaluation of something's quality or appeal is given a rating. a 10 out of 10 value-for-money rating, as an illustration. The president's standing among the public is at its lowest point since assuming office.

Position is synonymous with ranking, evaluation, appraisal, and categorisation. Additional Ratings

Since 1 rating point is given = 1,800,000

Rating point = 1,800,000 household

Rating point = 10.2 × 1,800,000 household.

Rating point =18360000 household.

Therefore, correct to state that the number of households that watched the show that week are 18360000 household.

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Answer:

x² + 23x + 49

Step-by-step explanation:

area of rectangle = length × width

Area of outer rectangle:

(x + 10) × (2x + 5) = 2x² + 5x + 20x + 50 = 2x² + 25x + 50

Area of unshaded square:

(x + 1)² = x² + 2x + 1

shaded area = area of outer rectangle - area of square

shaded area = 2x² + 25x + 50 - (x² + 2x + 1) =

= 2x² + 25x + 50 - x² - 2x - 1

= x² + 23x + 49

Answer: A. 6

Step-by-step explanation:

Answer: I think D.

Step-by-step explanation: why not pick D…..

Hope this helps^^

For the information provided the x- and y-components of the vector are 1.5 km and 2.6 km, respectively.

To find the x- and y-components of the vector, we can use trigonometry.

The x-component of vector is given by:

d_x = d × cos(θ)

where d is the magnitude of the vector and θ is the angle between the vector and the x-axis.

In this case, d = 3.0 km and θ = 60 degrees (since the vector is 30 degrees to the left of the y-axis).

So, d_x = 3.0 km × cos(60°) = 1.5 km.

The y-component of vector is given by:

d_y = d × sin(θ)

In this case, d_y = 3.0 km × sin(60°) = 2.6 km.

Expressing the answer using two significant figures gives:

d_x = 1.5 km, d_y = 2.6 km.

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Answer:

where’s the options??

Step-by-step explanation:

The temperature on the surface of the planet, based on the equation for the temperature, is 47 degrees Celsius.

The equation given of y = 47 - 5x, is such that every one kilometer that we go from the surface of the planet, the temperature reduces by 5 degrees Celsius.

What this means is that at the surface of the planet the temperature is 47 degrees Celsius because this is the temperature when we have not gone a single kilometer above the surface.

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The rest of the question is:

Note that a change can be an increase or a decrease.

For an increase, use a positive number. For a decrease, use a negative number.

What is the temperature on the surface of the planet?

the  solution of the given equation will be x =1

What is a System of Equations?

A system of equations in algebra is made up of two or more equations that are solved together. "A group of equations satisfied by the same set of variables are called a system of linear equations. Finding the values of the variables employed in the system of equations is the first step towards solving it. While maintaining the balance of the equations on both sides, we compute the values of the unknown variables. Finding a variable whose value makes the condition of all the given equations true is the primary goal of solving an equation system.

The given equation x -5 = -4

add +5 in both side we get

x = -4+5

x=1.

Hence the solution of the given equation will be x =1

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Answer:

this is the answer ................................

The perimeter of the pentagon PQRST will be equal to the perimeter of the pentagon ABCDE.

The regular polygon's edges are all identical to one another. The relationship between the number of sides to the mean distance determines the regular polygon's perimeter when it has n sides.

Then the perimeter of the pentagon ABCDE is given as,

P = AB + BC + CD + DE + EA

And the perimeter of the pentagon PQRST is given as,

P = PQ + QR + RS + ST + TP

Regular pentagons ABCDE and PQRST are congruent with each other.  Then the perimeter of the pentagons will be identical to each other.

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