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The equation to solve the missing the side length is x² + 10² = 26²

What is right-angled triangle ?

A right triangle is a triangle with one angle at a right angle, meaning that two of its sides are perpendicular. It is also known as a right-angled triangle, an orthogonal triangle, or more commonly as a rectangled triangle. Trigonometry's foundation is the right triangle's relationship between its sides and other angles.

If one of the triangle's angles is 90 degrees, the triangle is said to be right-angled. 90 degrees is the sum of the other two angles. Perpendicular and the triangle's base make up the sides that the right angle is formed from. The hypotenuse, or third side, is the longest of the three. It is also known as the hypotenuse.

Lets take the missing side be x

The equation be

x² + 10² = 26²

x² = 26² - 10²

x² = (26 + 10)(26 - 10)

x² = 36*16

x² = 576

x = √576

  = 24

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The critical points of the function f are x = 1 or x = - 2

The critical point of a function is the value at which the function changes direction.

It is also the value at which the first derivative of the function equals zero.

To find the critical points of the function f, since we have the derivative of the function F'(x) = (x - 1)(x + 2).

At the critical point, the derivative of the function F'(x) equals zero.

So, we have that F'(x) = 0.

So, equating the function F'(x) to zero, we have that

F'(x) = 0

(x - 1)(x + 2) = 0

x - 1 = 0 or x + 2 = 0

x = 1 or x = - 2

So, the critical points are x = 1 or x = - 2

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Answer:

To determine which cream cheese is a better buy, we need to compare the price per unit of volume for each brand.

For Brand Y cream cheese:

Price per unit = 44 AED / 220 ml = 0.2 AED/ml

For Brand Z cream cheese:

Price per unit = 100 AED / 470 ml = 0.2127 AED/ml

Since the price per unit of volume for Brand Y cream cheese is 0.2 AED/ml and the price per unit of volume for Brand Z cream cheese is 0.2127 AED/ml, Brand Y cream cheese is cheaper per unit of volume. Therefore, Brand Y cream cheese is a better buy.

Step-by-step explanation:

The amount of heat released in the given situation would be as follows:

-66.2 KJ−66.2KJ

Given that,

Weight of H2OH2O = 27g=27g

The Temperature of the Liquid = 314 k=314k

The Temperature of the Solid = 263 K=263K

Melting point of H2O = 273 KH2O=273K

To find,

The amount of heat released = [Q[Q × C_{p}lC

p

l ×(T_{final} - T_{Initial} ) +(T

final

−T

Initial

)+ Δ Hfusion + [mHfusion+[m × C_{p}sC

p

s × T_{final} - T_{Initial} ]T

final

−T

Initial

]

By putting the values in the above formula,

∵ Heat released = -66.2 KJ−66.2KJ

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The total number of gallons of oil consumed during the first 14 days of the month is (b) 13.739

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

F (t) = 0.3 + 0.1t — 0.85 cos(2pi/15 (t+ 5))

The question is asking for the total number of gallons of oil consumed by the furnace during the first 14 days of the month,

This can be found by integrating the function F(t) with respect to t from 0 to 14

Using a graphing calculator, we have the integrated function to be

f(t) =  0.3t + 0.05t^2 - 0.85(2/15)sin(2π/15(t+5))

Also, we have

f(14) - f(0) = 13.739

Hence, the solution is 13.739

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The percentage of the people surveyed that had a cell phone will be 38.9%.

A percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100.

The percentage of the people surveyed that had a cell phone will be;

= 236 / (317 + 236 + 263) × 100

= 236 / 816

= 28.9%

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Answer:

-9

Step-by-step explanation:

The constant doesn't have a letter attached to it

Answer:

Step-by-step explanation:

the answer is:

5y^10

_____

7x^4

If this isnt the simplified version, you want im sorry

Answer:

[tex]\frac{5y^{10} }{7x^{4} }[/tex]

Step-by-step explanation:

[tex]\frac{30x^{3}y^{2} }{42x^{7} y^{-8} }[/tex]  to make [tex]y^{-8}[/tex] positive we need to put it in the numerator (top)

[tex]\frac{30x^{3}y^{2}y^{8} }{42x^{7} }[/tex]  Now I am going to write it in expanded form

[tex]\frac{2x3x5xxxyyyyyyyyyyyy}{2x3x7xxxxxxx}[/tex]  If we cross out what we have on the bottom and the top, we will be left with our answer simplified.

[tex]\frac{5y^{10} }{7x^{4} }[/tex]

The cost for a consumption of 15 cubic meters of water is 23.85 dollars

The cost for a consumption of 30 cubic meters of water is 67.8 dollars

The cost for a consumption of 50 cubic meters of water is 113 dollars

The cost for a consumption of 70 cubic meters of water is 404.6 dollars

A piecewise-defined function is a function that is defined by multiple sub-functions, each of which applies to a certain range of the input (or domain) values.

We have the  piece-wise cost function for different number of "X" cubic meters of water consumed:

          { 1.59x ,si 0< x ≤ 20

C(x) =  { 2.26x ,si 20 < x ≤ 50

          {5.78x ,si            50< x

The cost in dollars, for a consumption of 15 cubic meters of water:

Use C(x) = 1.59x and x = 15

C(15) = 1.59 × 15 = 23.85 dollars

The cost in dollars, for a consumption of 30 cubic meters of water:

Use C(x) = 2.26x and x = 30

C(30) = 2.26 × 30 = 67.8 dollars

The cost in dollars, for a consumption of 50 cubic meters of water:

Use C(x) = 2.26x and x = 50

C(50) = 2.26 × 50 = 113 dollars

The cost in dollars, for a consumption of 70 cubic meters of water.

Use C(x) = 5.78x and x = 70

C(70) = 5.78 × 70 = 404.6 dollars

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Answer:

amazon

Step-by-step explanation:

let's find the price per pack to solve

best buy:

7 packs = 28 dollars

divide both sides by 7 to get 1 pack = something

1 pack = 4 dollars

amazon:

12 packs = 38 dollars

divide both sides by 12 to get 1 pack = something

1 pack = 38/12 dollars = 3.16666666667 dollars which is less than 4 dollars, so amazon is cheaper in terms of price per pack

Anderson's mistake in solving the rational expression, is he cancelled out variable and numbers without taking them in common.

A rational expression is the ratio of two polynomials. If f is a rational expression, then f can be written in the form p/q where p and q are polynomials.

Given that, Anderson multiplies two rational expressions with the following results.

The given expression is  [tex]\frac{x^{2} -16}{x^{2} -8x+16} . \frac{x+1}{x^{2} +2x+1} = \frac{-1}{-8x(x^{2} +2)}[/tex]

His error is, he cancelled out the variables and numbers without taking them common, we can not cancel variables and numbers if they are in addition or subtraction with other variables and numbers.

Hence, the correct solution is;

[tex]\frac{x^{2} -16}{x^{2} -8x+16} . \frac{x+1}{x^{2} +2x+1}\\\\= \frac{(x+4)(x-4)}{x^{2} -4x-4x+16} . \frac{x+1}{x^{2} +x+x+1} \\= \frac{(x+4)(x-4)}{(x-4)(x-4)} .\frac{x+1}{(x+1)(x+1)} \\=\frac{x+4}{(x-4)(x+1)}[/tex]

Hence, the correct solution is [tex]=\frac{x+4}{(x-4)(x+1)}[/tex]

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Answer: 1000%

Step-by-step explanation:

Suppose the newborn mass is 100%. 4000 is 10 times that, which is 1000%.

Answer: %1000

What is a percentage?

A percentage is a ratio, or a number expressed in the form of a fraction of 100. Percentages are often used to express a part of a total.

If we know that the newborn cat's weight is equivalent to 400g, and when it is fully grown it is equal to 4000 grams, we need to know how many times more is the full-grown cats' mass is compared to the newborn.

400 × 10 = 4000

We now know that the adult cat is 10 times larger than the newborn cat, meaning that it is %1000 of the newborn cat's size.

Answer:I don’t know

Step-by-step explanation:

The area under the standard normal curve to the right of Z (3.15) = 0.0008

The total area under the standard normal curve happens to be 1 which is divided between two parts having an area under the curve = 0.5 on each side.

I.e. from 0 to the right side, the area under the curve = 0.5

Similarly, from 0 to the left side, the area under the curve = 0.5

Now, from the standard normal table,                                  

                                                          {the table is given in the attachment}

The area under the curve for the value of Z (3.15) = 0.4992

                                                                         {This value is the area under the curve from 0 to Z (=3.15)}

Hence, the Area under the curve to the right of Z (3.15) = 0.5 – 0.4992

                                                                                            = 0.0008

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For z = 3.15, the area under the standard normal curve is 0.99918365.

Normal distributions are symmetrical, bell-shaped distributions that are useful in describing real-world data.

The standard normal distribution, represented by the letter Z, is the normal distribution having a mean of 0 and a standard deviation of 1.

If {X} is a random variable from a normal distribution with mean {μ} and standard deviation {σ}, its Z-score may be calculated from X by subtracting μ and dividing by the standard deviation :

[tex]${\displaystyle Z={\frac {X-\mu }{\sigma }}}[/tex]

If {X} is the mean of a sample of size {n} from some population in which the mean is {μ} and the standard deviation is {σ}, the standard error is σ/√n :

[tex]${\displaystyle Z={\frac {{\overline {X}}-\mu }{\sigma /{\sqrt {n}}}}}[/tex]

If [tex]{\textstyle \sum X}[/tex] is the total of a sample of size {n} from some population in which the mean is {μ} and the standard deviation is {σ}, the expected total is nμ and the standard error is σ √n :

[tex]${\displaystyle Z={\frac {\sum {X}-n\mu }{\sigma {\sqrt {n}}}}}[/tex]

Given is the value of z = 3.15.

For z = 3.15, the area under the standard normal curve is 0.99918365.

Therefore, for z = 3.15, the area under the standard normal curve is 0.99918365.

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The required factors of the polynomial by grouping are  (x-3)(x^2 + 2).

To factor polynomial equations, a specialized approach is called grouping. It can be applied to polynomials with four terms as well as quadratic equations. Although they differ significantly, the two approaches are comparable.The first two terms and the final two terms are combined: p(x)=(x3 - 4x2) + (3x - 12), and we then identify the shared

factors as follows: p(x) = x2(x - 4) + 3(x - 4). (x - 4).

x^3 - 3x^2 + 2x -6

(x-3)(x^2 + 2)

Thus, required factors are (x-3)(x^2 + 2).

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the  parallelogram JKLM is a square.

What is square?

Having four equal sides, a square is a quadrilateral. There are numerous square-shaped objects in our immediate environment. Each square form may be recognized by its equal sides and 90° inner angles. A square is a closed form with four equal sides and interior angles that are both 90 degrees. Numerous different qualities can be found in a square.

We are given that rajiv wishes to make a cube without lid with cardboard.

JM = -5² = 25

KL =  -5² = 25

JK = -4²=16

LM =-4²=16

So, the parallelogram JKLM is a square.

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Answer:Angle

Step-by-step explanation:

A 140-pound person will typically burn 4 calories per mile of walking at a rate of 3 miles per hour.

Walking at a pace of 3 miles per hour results in an average calorie burn of 4 for a 140-pound person. This person would therefore burn around 112 calories in a period of 30 minutes. On the other hand, a 200-pound person burns roughly 5 calories per minute, or 159 calories every 30 minutes.

An average walking speed of 3 miles per hour (or 120 steps per minute) is recommended for health reasons. That is a mile that takes 20 minutes. You must increase your pace to 4 miles per hour (135 steps per minute), or a 15-minute mile, to walk for weight loss.

Walking and running have about equal calorie burn rates per minute. Walking at 3.5 mph for 40 minutes for a 160-pound person would take 40 minutes.

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Answer: 103

Step-by-step explanation: 309/3 = 103

The height of the house with the ladder is 10.9 feet

Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base and Hypotenuse.

The hypotenuse = 12

adjascent = 5

opp = x

hyp² = opp² + adj²

12² = 5² + x²

x² = 12² - 5²

x² = 144 - 25

x² =119

x² = √119

x= 10.9 feet

therefore the height of the house from the ladder is 10.9 feet

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Here, two sides of the triangle are equal.

Therefore, perimeter of the triangle

= p - 5 + p - 5 + 2p + 8

= 4p - 2

= 2(2p - 1)

Answer:

2(2p - 1)

Hope it helps.

Answer: 4p - 2

Step-by-step explanation:

Sum of all sides is the perimeter.

According to the figure, the two sides are equal.

therefore, perimeter = p - 5 + p - 5 + 2p + 8

= 4p - 2

Answer:

1,2,3,4,6,12,18

Step-by-step explanation:

uh

Answer:

Step-by-step explanation:

put the 2x and make it 2

y = 1/2x + 1 is the line's equation in slope-intercept form.

The equation of a line in slope intercept form is expressed as y = mx + b where:

m is the slope

b is the y-intercept

Given the following coordinate points (4, 3) and (0, 1), the slope is calculated as:

Slope = 1-3/0-4
Slope = -2/-4
Slope = 1/2

For the y-intercept, it is the point where the x-coordinate is zero, hence the y-intercept if (0, 1)

Determine the required equation
y = mx + b

y = 1/2x + 1

Hence the equation of the line in slope-intercept form is y = 1/2x +1

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Answer: 3u⋅(9u−9v) = 285

Step-by-step explanation:

We can start by using the distributive property for the dot product:

3u⋅(9u−9v) = 3u⋅9u - 3u⋅9v

We also know that the dot product of two vectors u and v is u⋅v = ∥u∥∥v∥cos(θ), where θ is the angle between vectors u and v. Therefore,

u⋅v = 5 = 107cos(θ)

So we can write:

cos(θ) = 5/(10*7) = 1/14

Then we can use this value to find the dot product of u and v.

3u⋅9u = 3 * (10^2) = 300

3u⋅9v = 3 * (10)(7)(1/14) = 15

So the final answer is:

3u⋅(9u−9v) = 300 - 15 = 285

Explanation: By using the distributive property and the dot product definition, it was possible to find the dot product of 3u⋅9u and 3u⋅9v. By subtracting the latter from the former, we obtained the final answer of 285.

The value of x, given the angle measures in Triangle ABC, can be found to be 22.

Triangle ABC is a right angled triangle which means that ACB has the angle measure of 90 degrees. This means that the angle measures left will add up to :

= Sum of interior angles in triangle - Angle ACB

= 180 - 90

= 90 degrees

If the sum of 2 x and ( 3 x - 20 ) adds up to 90 degrees, the value of x would then be:

90 = 2 x + ( 3 x - 20 )

2 x + 3 x - 20 = 90

2 x + 3 x = 90 + 20

5 x = 110

x = 110 / 5

x = 22

In conclusion, the value of x is 22.

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The question is:

What is the value of x?

The required correct product is (x + 4)/(x - 4)(x  + 1) for the rational expressions.

Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.

Anderson multiplies two rational expressions with the given results.

His error is the inequivalent can't be canceled out.

The two rational expressions are given in the question, as follows:

(x² - 16)/(x² - 8x + 16) × (x + 1)/(x² + 2x + 1)

(x² - 4²)/(x² - 2 × 4 × x + 4² ) × (x + 1)/(x² + 2 × 1 × x + 1²)

(x + 4)(x - 4)/(x - 4)² × (x + 1)/(x + 1)²

(x + 4)/(x - 4)(x  + 1)

Thus, the required correct product is (x + 4)/(x - 4)(x  + 1).

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An exponential decay function to model the situation is f(x) = 49(0.7)^x.

The average rate of change over 1 ≤ x ≤ 4 is -7.5.

The average rate of change over 5 ≤ x ≤ 7 is -1.4.

The rate of change decreases as x increases.

In Mathematics, an exponential function can be modeled by using this mathematical expression:

f(x) = ab^x

Where:

Since the initial value is 49 and the decay factor is 0.7, an exponential function that models the situation is given by:

f(x) = ab^x

f(x) = 49(0.7)^x

When x = 1, the value of f(x) is:

f(1) = 49(0.7)^1

f(1) = 34.3.

When x = 4, the value of f(x) is:

f(4) = 49(0.7)^4

f(4) = 11.7649.

For the average rate of change over 1 ≤ x ≤ 4, we have:

Average rate of change = [f(b) - f(a)]/(b - a)

Average rate of change = [11.7649 - 34.3]/(4 - 1)

Average rate of change = -22.5351/3

Average rate of change = -7.5

For the average rate of change over 5 ≤ x ≤ 7, we have:

Average rate of change = [f(b) - f(a)]/(b - a)

Average rate of change = [49(0.7)^7 - 49(0.7)^5]/(7 - 5)

Average rate of change = [4.0354 - 8.2354]/2

Average rate of change = -4.2/3

Average rate of change = -1.4.

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The measure of side FG for the triangle FGH is equal to 18 using a scale factor of 1/3 to dilate it.

Scale factor is the ratio between the scale of a given original object and a new object, which is its representation but of a different size either bigger or smaller.

The dilation if the triangle FGH implies it is expanded to the bigger triangle F'G'H' with a scale factor 1/3

side F'G' = 6

side FG = 6 ÷ 1/3

side FG = 6 × 3/1 {change division to multiplication}

side FG = 18.

Therefore, the triangle FGH have the measure of its side FG equal to 18 using a scale factor 1/3.

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