Solve (x – 3)2 = 49. Select the values of x.

Angle C is the biggest.

The longest side in a triangle is opposite the largest angle, and the shortest side is opposite the smallest angle.

It is not possible to construct a triangle with 6cm, 9cm, and 17cm.

The sides measure 6 cm, 9 cm, and 17 cm in length.

Only when the third side is greater than the sum of any two sides can a triangle be drawn. This the condition.

Let's verify the rule now.

6 + 9 > 17        Not true

6 + 17 > 9        True

9 + 17 > 6        True

As 6 + 9 > 17 does not satisfy the condition.

Hence, it is not possible to construct a triangle having 6cm, 9cm, and 17cm in length.

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Answer:

Q = 216 - 0.5P

Step-by-step explanation:

One approach to modeling the demand as a function of the cost is to use a linear demand equation of the form:

Q = a - bP

where Q is the quantity demanded, P is the price, and a and b are constants. To find these constants, we can use the two points given:

When P = $180, Q = 8 portraits, so 8 = a - b * 180

When P = $100, Q = 24 portraits, so 24 = a - b * 100

Solving the system of equations gives us:

a = 216

b = 0.5

So, the demand equation is:

Q = 216 - 0.5P

This represents the demand for portraits as a function of the price, where the demand decreases linearly as the price increases.

Answer:

0.0021645

Step-by-step explanation:

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other

What is an equivalent ratios?

A ratio compares two quantities named as antecedent and consequent, by the means of division. For example, when we cook food, then each ingredient has to be added in a ratio. Thus, we can say, a ratio is used to express one quantity as a fraction of another quantity.

Two ratios are equivalent to each other if one of them can be expressed as the multiple of the other. Hence, to get the equivalent ratio of another ratio, we have to multiply the two quantities (antecedent and consequent) by the same number.

Given ratios are 2:1 and 3:1

we can write it as 2/1 and 3/1.

The lcm of 2 and 3 is 6.

Multiply denominator of both ratio with 6, we get

2/6 and 3/6 And we can see both the ratios are not equal.

Hence, there are not equivalent ratios.

4:1 and 8:3 are equivalent ratios -----> is false, because 4:1 is equivalent to 8:2

11:2 and 2:11 are equivalent ratios------> is false (because, are reciprocal ratios, not equivalent ratios)

3:1 and 9:3 are equivalent ratios ------> is true

because 3:1 multiply both sides by 3 -----> 3*3:1*3=9:3

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To optimize his long-term predicted profit percentage, he should select 20.567%.

Both decimal and fractional forms of the expression are acceptable.

Given, The boat's daily running expense is $2,250.

$1.50 is the minimal amount.

a maximum of $5.50

Most likely value is $3.50. Now, each day's conclusion.

More lobsters mean a lower price per pound which the grocery shop will accept ($3.85 - $0.0005). × y,

Amir's daily haul of lobster has a normally distributed with a mean of 1,500 pounds and a standard deviation of 12,500 pounds.

He should therefore select 20.567% to increase his anticipated profit in the long run.

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Answer:

Step-by-step explanation:

Let the height be h units

then the base is h+3 units

Area = (1/2)(base)(height)

= (1/2)(h)(h+3) or (1/2)(h^2 + 3h)

In this scenario, if a computer was bought for $2350 and is being depreciated over 5 years, the annual depreciation is $470, and its value 3 years later would be $1410.

The straight-line method of depreciation is a method of calculating the decline in value of an asset over time. Using this method, an asset's value is spread evenly over its useful life.

In this scenario, if the computer was bought for $2350 and is being depreciated over 5 years, the annual depreciation is ($2350 / 5) = $470.

Three years later, the computer's value would be $2350 - ($470 x 3) = $1410. This is because the value of the computer is decreasing by $470 per year, and after three years, the total amount of depreciation would be $470 x 3 = $1410.

It's important to note that the straight-line method of depreciation is a simple method and it does not reflect the real-world scenario in which assets may have a higher value of depreciation in the initial years and less in the later years. But it's easy to calculate and use.

In conclusion, if an asset is depreciated using the straight-line method, its value decreases evenly over its useful life. It's important for businesses to understand the various methods of depreciation and choose the one that best suits their needs.

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For the figure shown in the image having TV as the midsegment, the length of TV is 40

When the comparable triangles' angles are congruent and their respective sides are proportionate, this is referred to as similar triangles in geometry.

In light of this, if the triangle's corresponding angles are congruent, then the side should be proportionate.

For the given figure, the proportionate sides are

UV and TV, UW and WX

Calculating for s

UV / TV = UW / WX

1 / (-2s + 42) = 2 / (3s + 77)

cross multiplying

3s + 77= 2(-2s + 42)

3s + 77= -4s + 84

collecting like terms

3s + 4s = 84 - 77

7s = 7

s = 1

solving for TV

= -2s + 42

= -2 * 1 + 42

= 40

the value of TV is 40

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Para calcular el 18% menos de un número, se puede utilizar la fórmula: número original x (1 - porcentaje en decimal). En este caso, para calcular el 18% menos de 41, se puede utilizar la fórmula: 41 x (1 - 0.18) = 41 x 0.82 = 33.62. Entonces, el 18% menos de 41 es 33.62.

Espero que esto ayude :)

Answer:

El número es:

50

Step-by-step explanation:

Porcentaje significa "por cada cien"

18% = 18/100 = 0.18

El número buscado corresponde al 100%

Si es el 18% menos quiere decir que corresponde a:

100 - 18 = 82%

Entonces:

Por regla de tres:

41 es a 82%

A es a 100%

A = 41 * 100 / 82

A = 4100 / 82

A = 50

Comoprobación:

50 - (50*0.18) = 50 - 9 = 41

The possible values of the given expression are defined by the inequality below.

1/5 < b/2a < 1/2

Here we want to get the possible values of the expression below:

b/2a

Where we have the restrictions:

4 < a < 5

2 < b < 4

The minimum value of the expression is when a takes it maximum value, and b takes its minimum value, it gives:

2/(2*5) = 2/10 = 1/5

The maximum value of the expression is what we get when a takes its minimum value, and b takes its maximum value:

4/(2*4) = 4/8 = 1/2

These are the bound of the expression, we can write:

1/5 < b/2a < 1/2

These are all the possible values of the expression.

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The total milliliters of punch is 2x + y.

To find the total amount of milliliters of punch, we need to add together the amount of water, apple juice, and grape juice used to make it. Since the punch is made up of "water by volume" and "the rest is grape juice," we know that the ratio of water to grape juice is 1 : 1. If we know the amount of grape juice used in milliliters, we can use that to find the amount of water and apple juice used, and then add all three amounts together to find the total amount of milliliters of punch.

Let's say that "x" milliliters of grape juice were used to make the punch. Since the ratio of water to grape juice is 1 : 1, we know that the same amount of water, "x" milliliters, were used. To find the total amount of milliliters of water and grape juice, we add x + x = 2x milliliters.

However, the prompt also mention "apple juice" is also included in the punch, so we need to add the amount of apple juice used in the punch to find the total milliliters of punch. If the amount of apple juice used is "y" milliliters, then the total milliliters of punch is 2x + y.

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[tex]1\frac{3}{4}[/tex] hours Jada took to put the puzzle together.

A fraction represents a part of a whole.

Given that Jada's aunt took 3/4  hour to put a puzzle together.

Jada took [tex]2\frac{1}{3}[/tex]  times as long as her aunt to put the puzzle together.

Convert the mixed fraction [tex]2\frac{1}{3}[/tex]  to improper fraction

[tex]2\frac{1}{3}[/tex] =7/3

As there is given Jada took [tex]2\frac{1}{3}[/tex]  times as long as her aunt to put the puzzle together we have to multiply 7/3 with 3/4

7/3×3/4

7/4

This can be written as mixed fraction

[tex]1\frac{3}{4}[/tex]

Hence, [tex]1\frac{3}{4}[/tex] hours Jada took to put the puzzle together.

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The turning point of the function is x = 1 and it is a local minima.

The curve of a function has peaks and troughs called maxima and minima. A function may have any number of peaks and minima. Calculus allows us to determine any function's maximum and lowest values without ever consulting the function's graph. Maxima will be the curve's highest point within the specified range, while minima will be its lowest.

Extrema is the result of maxima and minima combined. The graph in the graphic below shows several peaks and falls. We obtain the function's maximum and lowest values at x = a and 0 respectively, and at x = b and c respectively. The valleys are the minima and all the peaks are the maximum.

In a function, maxima and minima can be of two different types:

Local Maxima and Minima

Global or Absolute Maxima and Minima

The function is

y = [tex](x-1)^{2}[/tex] for -3 ≤ x ≤ 3

differentiating both side with respect to x we get

[tex]\frac{dy}{dx} = 2(x-1)[/tex]

for maxima and minima [tex]\frac{dy}{dx} = 0[/tex]

or, 2(x-1) = 0

or x = 1

Now, for x > 1 [tex]\frac{dy}{dx} > 0[/tex]

So, the function's turning point is a minima.

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As per the concept of integration, the value of the function [tex].\int_{5}^{x}u^{3} du[/tex] is [(x⁴/4) - (625/4)]

The term integration in math is defined as the method of adding or summing up the parts to find the whole and the reverse process of differentiation that is we reduce the functions into parts.

Here we have given that [tex].\int_{5}^{x}u^{3} du[/tex]

And now we have to perform the integration operation on it and then we have to find the simplified version of the function.

As we all know the formula of the integration concept, that is written as,

=> [tex]\int {x^{n}} \, dx =\frac{x^{n+1}}{n+1}[/tex]

Based on these details, we have simplify the expression as,

[tex]= > \mathrm{[\frac{u^{4}}{4}]}_{5}^{x}[/tex]

Now, we have to apply the value of u with the given limit values, then we get the expression like the following,

=> [(x⁴/4) - (5⁴/4)]

When we simplify this one then we get,

=> [(x⁴/4) - (625/4)]

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The empirical probability that there are more than 5 left-handed students  in a class of 30 is 0.06.

Empirical probability is a sort of experimental probability that is based on historical data. Empirical probability is, then, an illustration of  the likelihood of an occurrence occurring based on prior data.

The formula of the empirical probability is:

Experimental probability  = number of times an event occurs / total number of outcomes.

In the problem, total number of classes = 50

From the graph, we can read that:

- number of classes with 6 left-handed students = 2

- number of classes with 7 left-handed students = 1

Hence, the empirical probability that there are more 5 left-handed students in a class of 30 is:

Empirical probability = 3/50 = 0.06

Your question is incomplete. Most likely it was:

Casey read a report that said the probability that a randomly selected America is left handed is 14%. she was curious how many left handed students to expect in a class of 30 seconds. she simulated 50 classes of 30 students where each student had a 0.14 probability of being left handed. Casey counted how many left handed students were in each simulated class. here are her results: use her results to estimate the probability that there are more than 5 left handed students in a class of 30 students. (The graph is attached)

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So, (3/10) ∫(0 to t) sin(2πt/5) dt would find the volume of inhaled air in the lungs at time t.

The function f(t) = (3/10)(sin(2πt/5)) is often used to model the rate of air flow into the lungs because it is cyclic, with a period of 5 seconds, and has a maximum value of 0.3 L/s. This function represents the rate of air flow into the lungs at any given time t.

To find the volume of inhaled air in the lungs at time t, we can integrate the function f(t) with respect to time. The volume of air inhaled at time t is the definite integral of f(t) from the start of inhalation (t = 0) to time t.

∫(0 to t) f(t) dt = (3/10) ∫(0 to t) sin(2πt/5) dt

The definite integral can be solved with proper limits, but the result is not in a closed form that can be expressed in terms of elementary functions.

In order to get the volume of inhaled air in the lungs at time t, we need to know the specific values of t and solve the definite integral with proper limits.

It's worth noting that this model is a simplified one and many other factors like breathing rate, lung capacity, and lung compliance could affect the actual volume of inhaled air in the lungs.

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To find the amount of gold needed for gold plating a brick, total surface area of the brick would be needed to be calculated, assuming the brick is cuboid or cube shaped.

While dealing with cubes and cuboids, we should know how to find the surface areas and volumes of the two objects. When we either fill these or talk about all the three dimensions of an object, we talk about the volume of the said object. And, when we paint or talk about just the exterior or interior walls of an object, we talk about the surface area of the said object.

When all the six faces of a cube or a cuboid are used, we calculate surface area for all the faces and this is called the total surface area.

Let us look at the different formulas to calculate volume and total surface area of a cube and a cuboid,

Total surface area of a cube (side [tex]a[/tex]) =  6 × (area of each face)  

                                                          = 6 × [tex]a^{2}[/tex]  

Volume of a cube (side [tex]a[/tex]) = [tex]a^{3}[/tex]

Total surface area of a cuboid (length [tex]l[/tex], breadth [tex]b[/tex], height [tex]h[/tex]) = [tex]2 ( lb + lh + bh)\\[/tex]

Volume of a cuboid (length [tex]l[/tex], breadth [tex]b[/tex], height [tex]h[/tex]) = [tex]lbh[/tex]

For plating the brick with anything, gold for instance, total surface area of the brick would be calculated to determine the amount of gold needed as all the walls or faces of the brick would be plated but not the interior volume.

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The price of the widgets for which it should be sold to make the maximum profit is $25.4   .

A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is  ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

We know that the quadratic equation ax² + bx + c ,

If a < 0; then the maximum value of the quadratic equation will be at x = -b/2a .

Given;

a company is selling a widget;

the selling price of each widget is = x

the profit made by the company = y

the equation of profit is given as y = −3x² + 152x − 1150 ,

here a = -3 , b = 152 and c = -1150

In the given quadratic equation we can see that;

a < 0 , so , the maximum will be at;

x = -b/2a

x = -152/2(-3)

x = 152/6

x = 25.333

x ≈ 25.4

Hence, the price of the widget will be $25.4  

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The actual perimeter is 2934. The perimeter of a rectangle is calculated as P = length + breadth + length + breadth. Alternatively, P = 2(length + breadth).

Perimeter=2(l + b)

=2[6.3cm +10cm) = 2x16.3 cm 32.6cm

Scale 1 cm = Actual 90m.

32.6cm 32.6x90m

= 2934 m

We sum the lengths of all four sides to determine the perimeter of a rectangle. Because opposing sides of a rectangle are always equal, we must obtain the length and breadth measurements to calculate the perimeter of a rectangle. The perimeter of a rectangle is equal to double the sum of its length and breadth.

To calculate the perimeter, or distance around the rectangle, sum all four side lengths. This may be done quickly by adding the length and breadth and then multiplying the total by two because each side length has two lengths. The perimeter formula is perimeter = (length + width)2.

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The midsegment linking the cartesian coordinates of two of a triangle's sides is parallel to the fourth aspect of the triangle, and its length is half that of the third side, according to the midsegment theorem.

The assertions that the Greek mathematician Pythagoras discovered the properties of right-angled triangles in the fifth century BC just did not match up, according to many. Some people think following commentary shows it was a joint effort among his disciples, the Pythagoreans.

Equilateral: equal angles and all three sides. Acute isosceles: two identical sides and angles, both of which are only about 90 degrees. Acute scalene has irregular sides and angles, all of which are under 90 degrees. Obtuse isosceles: two identical sides and angles, one of which is more than 90 degrees.

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Answer:

Step-by-step explanation:

true

Answer:

The measure of the third angle of the triangle is 45°.

Step-by-step explanation:

What is a triangle?

A triangle is a polygon with 3 sides.

Given that, the measures of the two angles of a triangle are 50° and 85°.

Let the measure of the third angle be x.

Since the sum of the interior of a triangle is 180°, it follows,

50°+85°+x=180°

135° +x = 180°

x = 180° - 135°

x = 45°

Hence, the measure of the third angle of the triangle is 45°.

Answer: Parallel

Step-by-step explanation:

To solve this question, we need to find the slopes of both lines q and r.

First, let's find the slope of line q.

Δx/Δy=-7/-6 = 7/6

Next, the slope of line r.

Δx/Δy=-7/-6 = 7/6

Both lines have the same slope.

Therefore, they are parallel.

Step-by-step explanation:

6x-2y = 26 ---(1)

x+y = 3 -------(2)

so, (y = 3-x)

put in equation 1st.,

6x-2(3-x) = 26

6x-6+2x = 26

8x = 32

(x = 4)

so, put x value in equation 2nd,

4+y = 3

(y = -1 ) Answer

Answer:

x = 4

y = -1

Step-by-step explanation:

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Given:

6x-2y=26

-y+3=x  

Flip the equation around:

x = 3 - y

6(3-y) - 2y = 26  << Distribute property

18 -6y -2y = 26  << Add liked term

18 -8y = 26

-8y/-8 = 8/-8   << Divide both sides by -8

y = -1

Now, substitute y into the equation also known as -1.

6x - 2(-1) = 26

6x + 2 = 26  << Subtract 2 from 2 and 26 from 2

6x = 24

6x/6 = 24/6  << Divide both sides by 6.

x = 4

Hence, x = 4 and y = -1.

RevyBreeze

Answer: 9

Step-by-step explanation: It's 9 because both can be divided by 9, as the largest time without going over. As you can see, 81 divided by 9 is 9, and 72 divided by 9 is 8. 8 and 9 are the closest they can be without going over 81 and 72, so it's 9. I hope this helps!

The GCF of the numbers 81 and 72 is 3², which equals 9.

To find the greatest common factor (GCF) of 81 and 72, we can use several methods.

One common approach is to factorize both numbers and identify the common factors.

The prime factorization of 81 is 3⁴, and the prime factorization of 72 is 2³×3².

To find the GCF, we look for the highest power of common prime factors in both numbers.

The highest power of the common prime factor (3) is 3², since it appears as a factor in both numbers.

Therefore, the GCF of 81 and 72 is 3², which equals 9.

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Receipt of May is 835

Net cash flow of April is 210

Cumulative balance of March is 240

Explanation

Net cash flow = Receipt - Expense

Receipts amount = Expenses+Net cash flow

Cumulative balance amount =Cumulative amount for April-Net cash flow for April

The value of the stock after the increase of 1/4(fraction) using the addition expression is equal to $11.75. 

In Mathematics, a fraction is defined as the portion/part of the whole thing. A fraction consists of two parts, numerator and denominator. The number on the top is known as the numerator, and the number on the bottom is known as the denominator.

Given,

         The initial value of stock = $11.50

         Increase in stock ( in fraction) = 1/4

We know that earlier in the stock market the changes in values were indicated by fractions which represent portions of $1

Therefore,

               Increase in value of stock = 1/4 * $1

                                                         =  $0.25

Hence, 

          Value of stock after increase = $11.50 + $0.25

                                                        = $11.75

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