How do you prove that a triangle is transitive congruent?

Answer:

x = 1

Step-by-step explanation:

x² = x

x² / x = 1

x = 1

Check:

1² = 1

Jack can jump upto 97.5 inches.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have Jack who can long-jump 195% of his height with a running start.

Assume that he can jump a height of [x] inches. So -

x = 195% of 50

x = (195/100) x 50

x = 97.5 inches

Therefore, Jack can jump upto 97.5 inches.

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Answer:

35 x^4  - 5x^3

Step-by-step explanation:

5x^3 (7x−1)

Distribute

5x^3 (7x) +5x^3 *(−1)

35 x^3 *x - 5x^3

35 x^4  - 5x^3

Answer:

Answer:

35 x^4  - 5x^3

Step-by-step explanation:

5x^3 (7x−1)

Distribute

5x^3 (7x) +5x^3 *(−1)

35 x^3 *x - 5x^3

35 x^4  - 5x^3

Step-by-step explanation:

Answer: 4

Answer:

See explanation

Step-by-step explanation:

In most cases, we run into the problem of arranging objects that are repeated. This often occurs when we have a word that has repeated letters.

Let us recall that permutation deals with arrangements which are distinguishable.

Hence, for the word CONCLUSION, the number of distinguishable arrangements are;

10!/2!2!2!

Answer:

coordinates for vertex are (5, -9)

Step-by-step explanation:

Given

\(a=1\\\\b=-10\\\\c=16\)

using the formula for the x coordinate of the vertex which is \(\frac{-b}{2a}\) it yields:

\(x_{vertex}=\frac{-(-10)}{2}=5\)

We now have the x-coordinates of the vertex, by applying the x coordinate in the equation we get:

\(5^2-(10\times 5)+16\\\\=25-50+16\\\\=-9\)

thus the \(y_{vertex}=-9\)

Thus the coordinates of the vertex should be (5, -9)

The set of numbers {6, 8, 14} and the set {11, 14, 22} could represent the three sides of a triangle.

To determine whether a set of numbers could represent the sides of a triangle, we need to check if it satisfies the triangle inequality theorem. According to the theorem, the sum of any two sides of a triangle must be greater than the length of the third side.

Let's evaluate each set of numbers:

1. {6, 8, 14}

  The sum of the two smaller sides is 6 + 8 = 14, which is greater than the third side 14. Therefore, this set could represent the sides of a triangle.

2. {13, 20, 34}

  The sum of the two smaller sides is 13 + 20 = 33, which is less than the third side 34. Hence, this set cannot represent the sides of a triangle.

3. {11, 14, 22}

  The sum of the two smaller sides is 11 + 14 = 25, which is greater than the third side 22. Therefore, this set could represent the sides of a triangle.

4. {13, 20, 35}

  The sum of the two smaller sides is 13 + 20 = 33, which is less than the third side 35. Hence, this set cannot represent the sides of a triangle.

In summary, the sets {6, 8, 14} and {11, 14, 22} could represent the three sides of a triangle.

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well, let's convert the mixed fraction to improper fraction firstly, then let's check their difference.

\(\stackrel{mixed}{15\frac{3}{5}}\implies \cfrac{15\cdot 5+3}{5}\implies \stackrel{improper}{\cfrac{78}{5}}\qquad \impliedby \textit{that's for just 1 day} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{\LARGE after 6 days}}{\cfrac{78}{5} +\cfrac{78}{5} +\cfrac{78}{5} +\cfrac{78}{5} +\cfrac{78}{5} +\cfrac{78}{5} }\implies \cfrac{468}{5} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{change in bushels}}{\cfrac{468}{5}~~ - ~~\cfrac{78}{5}}\implies 78\qquad \impliedby \textit{so 6 days later he's got 78 more bushels}\)

Answer: 33.33

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

no because there is 2 fours in x

Answer:

Step-by-step explanation:

These options are in the middle.

Here are the options verified:

It is a difference of squares, so we can factor this to

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

Then, we can solve for \(x\).

\(x=-2,2\)

Hope this helps.

頑張って!

The 2007 National Survey of Children's Health found that first-generation children had higher rates of some health conditions than second- or third-plus-generation children, but lower rates of other conditions.

The survey looked at weighted and age-standardized percent distributions of health conditions for first-, second-, and third-plus-generation children, by race/ethnicity.

The results showed that first-generation children had higher rates of allergies, asthma, and developmental problems than second- or third-plus-generation children. However, first-generation children had lower rates of overweight and obesity than second- or third-plus-generation children.

The differences in health conditions between the three generations of children were not consistent across all race/ethnic groups. For example, first-generation black children had higher rates of overweight and obesity than second- or third-plus-generation black children.

However, first-generation Hispanic children had lower rates of overweight and obesity than second- or third-plus-generation Hispanic children.

The reasons for the differences in health conditions between the three generations of children are not fully understood. However, some possible explanations include differences in access to healthcare, differences in cultural beliefs about health, and differences in socioeconomic status.

The findings of the National Survey of Children's Health suggest that it is important to consider the generation of a child when assessing their health needs.

Children from different generations may have different risk factors for certain health conditions, and they may also have different access to healthcare. It is important to provide culturally-sensitive care to all children, regardless of their generation.

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Answer:

£334.40

Step-by-step explanation:

12% of 5700

= \(\frac{$(12\times 5700)/100$}\)

= 684

=  the deposit

5700 - 684 = 5016

this is the amount that needs to be paid after the deposit.

5016 / 15 = 334.40

= £334.40

When determining the size of a fact table, estimating the number of possible values for each dimension associated with the fact table is equivalent to: determining the number of possible values for each foreign key in the fact table.

The measures, metrics, or facts of a business process are contained in a fact table in data warehousing. In a star or snowflake schema, it sits in the middle, surrounded by dimension tables.

When several fact tables are employed, they are organized according to a fact constellation schema. The two types of columns that make up a fact table are typically those that hold facts and those that serve as a foreign key to dimension tables.

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Answer:

2.848 pound

Step-by-step explanation:

On 5 pizzas = 14.24 pound cheese

On 1 pizza = 14.24/5 pound

=2.848 pound

Polynomials are algebraic expressions consisting of terms that include real numbers, variables, and positive integer exponents. Each term in a polynomial has a variable raised to a non-negative integer power, and the coefficient of each term is a real number. Polynomials are classified by the degree of their highest power. If two or more terms in a polynomial have the same variable raised to the same power, they can be combined into a single term.

1. -x² + x - x² + 1

Combine like terms: -x² + x - x² + 1 = -2x² + x + 1

This polynomial has degree 2 because the highest power of the variable is 2.

2. x² + x + 2x³ - x

Rearrange terms: 2x³ + x² + x - x = 2x³ + x²

This polynomial has degree 3 because the highest power of the variable is 3.

3. 4x + x + x - 2

Combine like terms: 4x + x + x - 2 = 6x - 2

This polynomial has degree 1 because the highest power of the variable is 1.

4. 3x² + 4 - 3x² - 1

Combine like terms: 3x² - 3x² + 4 - 1 = 3

This polynomial has degree 0 because there is no variable term.

Therefore, the four given polynomials have degrees 2, 3, 1, and 0, respectively.

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The difference quotient evaluated in x = 2 gives:

[ f(2 + h) - f(2)]/h = h + 9

So the last option is the correct one.

Here we know the function:

f(x) = x^2 + 5x + 6

And we want to find the difference quotient:

[ f(2 + h) - f(2)]/h

Let's evaluate the function:

f(2 + h) = (2 + h)^2 + 5*(2 + h) + 6

            = 2^2 + h^2 + 4h + 10 + 5h + 6

            = h^2 + 9h + 20

f(2) = 2^2 + 5*2 + 6

f(2) = 4 + 10 +  6 = 20

Then we have:

[ f(2 + h) - f(2)]/h

[h^2 + 9h + 20 - 20]/h

[h^2 + 9h ]/h

Taking the quotient we get:

[h^2 + 9h ]/h = h + 9

So the correct option is the last one.

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Isolate the variable term on one side of the equation by using equality's multiplication property. Then the correct option is A.

Given information:

\(\dfrac{2}{5} \left ( \dfrac{1}{2} y + 20 \right) - \dfrac{4}{5} = \dfrac{9}{20} \left ( 2y-1 \right)\)

The distributive property is often expressed as:

a(b + c) = ab + ac

a(b - c) = ab - ac

Where "a" is a coefficient (or factor) and "b" and "c" are terms.

The equation is simplified as,

\(\dfrac{1}{5} y + 8 - \dfrac{4}{5} = \dfrac{9}{10} y- \dfrac{9}{20}\)

Isolate the variable term on one side of the equation by using equality's multiplication property. Then the correct option is A.

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Answer:

The problem has a mistake in it. The mistake is found in line 3. The person who solved the problem subtracted 6 from both sides when they should have added 6.

x = 1

Step-by-step explanation:

4x-2=8-6x

10x-2=8

10x=10

x= 1

Answer:-

B

I hope it helps.

Question 3: True

Question 4: False

Question 5: True

If the derivative of a function, f'(x), is positive for values of x less than c and negative for values of x greater than c, then it indicates a change in the slope of the function. This change from positive slope to negative slope suggests that the function has a maximum value at x = c.

This is because the function is increasing before x = c and decreasing after x = c, indicating a peak or maximum at x = c.

Question 3: If f'(c) < 0 then f(x) is decreasing and the graph of f(x) is concave down when x = c.

True

When the derivative of a function, f'(x), is negative at a point c, it indicates that the function is decreasing at that point. Additionally, if the second derivative, f''(x), exists and is negative at x = c, it implies that the graph of f(x) is concave down at that point.

Question 4: A local extreme point of a polynomial function f(x) can only occur when f'(x) = 0.

False

A local extreme point of a polynomial function can occur when f'(x) = 0, but it is not the only condition. A local extreme point can also occur when f'(x) does not exist (such as at a sharp corner or cusp) or when f'(x) is undefined. Therefore, f'(x) being equal to zero is not the sole requirement for a local extreme point to exist.

Question 5: If f'(x) > 0 when x < c and f'(x) < 0 when x > c, then f(x) has a maximum value when x = c.

True

If the derivative of a function, f'(x), is positive for values of x less than c and negative for values of x greater than c, then it indicates a change in the slope of the function. This change from positive slope to negative slope suggests that the function has a maximum value at x = c. This is because the function is increasing before x = c and decreasing after x = c, indicating a peak or maximum at x = c.

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The percent of coal with sulfur content exceeding 2.25 is approximately 21.35%. If the target sulfur value is changed to 1.45, the effect on the percent of coal accepted by the utility company will be explained in Step 2.

To determine the percent of coal with sulfur content exceeding 2.25, we need to calculate the z-score for the target sulfur value of 1.65 using the formula:

z = (x - μ) / σ

where x is the target sulfur value, μ is the mean sulfur value, and σ is the standard deviation.

Given that the target sulfur value is 1.65, the standard deviation is 0.617, and assuming the mean sulfur value is 2.25 (as the utility company will not use coal with sulfur content above this value), we can calculate the z-score:

z = (1.65 - 2.25) / 0.617

 ≈ -0.972

Using a standard normal distribution table or calculator, we can find the area to the left of this z-score, which represents the percentage of coal with sulfur content below 2.25. In this case, the area to the left of -0.972 is approximately 0.1667.

To find the percent of coal in the category with sulfur content exceeding 2.25, we subtract the above value from 1 (since the total percentage must add up to 100):

Percent = 1 - 0.1667

       ≈ 0.8333 or 83.33%

Now, if the target sulfur value is changed to 1.45, we repeat the same calculations. Using the new target value, the z-score can be calculated as:

z = (1.45 - 2.25) / 0.617

 ≈ -1.297

Again, finding the area to the left of -1.297 in the standard normal distribution, we obtain approximately 0.0968. Subtracting this value from 1 gives us the new percent of coal in the category with sulfur content exceeding 2.25:

New Percent = 1 - 0.0968

          ≈ 0.9032 or 90.32%

Therefore, changing the target sulfur value to 1.45 increases the percent of coal accepted by the utility company to approximately 90.32%.

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The equation of the line is y = one-third x + 2. Option C

To determine the equation of a line, we need to know that the general equation of a line is expressed as;

y = mx + c

This is so such as the parameters are;

From the information given, we have;

Slope, m = y₂- y₁/x₂- x₁

Substitute the values

m = 4 - 2/6 - 0

m = 2/-6

m = -1/3

Then, for c, we have;

2 = 0(-1/3) + c

expand the bracket

c = 0

Equation of line ; y = -1/3x + 2

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Answer:

Step-by-step explanation:

C-10,20,-40,80,...\( u_{n+1}=(-2)*u_{n}\). is geometric1

Answer:

B-SAS

Step-by-step explanation:

Was right on acellus

Answer:

We can conclude that the room temperature on Saturday was 24°C

Step-by-step explanation:

For a set of N values:

{x₁, x₂, ..., xₙ}

The mean of the set is calculated as:

\(M = \frac{x_1 + x_2 + ... + x_n}{N}\)

In this case, our set is the temperature of 7 days (so we have 7 elements)

{T₁, T₂, T₃, T₄, T₅, T₆, T₇}

Such that:

T₆ = temperature on Saturday

T₇ = temperature on Sunday.

We know that:

"The mean room temperature from Monday to Saturday is 25°C"

Then:

\(\frac{T_1 + T_2 + T_3 + T_4 + T_5 + T_6}{6} = 25 C\)

"the mean room temperature of Saturday and Sunday is 28°C"

\(\frac{T_6 + T_7}{2} = 28C\)

"The mean room temperature from Monday to Sunday is 26°C"

\(\frac{T_1 + T_2 + T_3 + T_4 + T_5 + T_6 + T_7}{7} = 26 C\)

So we have 3 equations.

Let's rewrite:

T₁ + T₂ + T₃ + T₄ + T₅ = A

Then we can rewrite our equations as:

\(\frac{A+ T_6}{6} = 25 C\)

\(\frac{T_6 + T_7}{2} = 28C\)

\(\frac{A + T_6 + T_7}{7} = 26 C\)

Removing the "Celcius" and multiplying in the 3 equations by the denominator on both sides, we get:

A + T₆ = 6*25

T₆ + T₇ = 2*28

A + T₆ + T₇ = 7*26

We now need to solve that system for T₆

The first step is to isolate one of the variables in one of the equations, (because we want to solve this for T₆ , let's not isolate that one). Let's isolate A in the first one:

A = 6*25 -  T₆

A = 150 -  T₆

Now we can replace this on the other two equations:

T₆ + T₇ = 2*28

(150 -  T₆ ) + T₆ + T₇ = 7*26

Now, let's isolate T₇  in the top equation to get:

T₇  = 2*28 - T₆

T₇  = 56 - T₆

Now we can replace this in the last equation to get:

(150 -  T₆ ) + T₆ + (56 - T₆)  = 7*26

Now, we can solve this for T₆

150 - T₆ + T₆ + 56 - T₆ = 182

-T₆ = 182 - 150 - 56

-T₆ = -24

T₆ = 24

We can conclude that the room temperature on Saturday was 24°C

The graph of the model is illustrated below and  the resistance when x = 85 is 1.12

The resistance of a conductor (such as a wire) is a measure of the opposition it presents to the flow of electric current. The resistance of a wire is dependent on various factors such as its length, cross-sectional area, and material. In this case, we are looking at the resistance of 1000 feet of solid copper wire, where the diameter of the wire is given in mils (0.001 inches).

The resistance of the wire can be approximated using the mathematical model:

=> y = 10,770/x² - 0.375,

where x is the diameter of the wire in mils and y is the resistance in ohms. The model is valid for values of x ranging from 5 to 100.

To complete the table, you need to plug in different values of x into the model and solve for y. For example, when x = 10,

=> y = 10,770/(10²) - 0.375 = 106.975 ohms.

The graph of the model can then be plotted by plotting the points (x,y) from the table and connecting them with a smooth curve. The graph can be used to estimate the resistance of the wire when x = 85.5 mils by finding the y-coordinate of the corresponding point on the graph.

Finally, you can use the model to algebraically confirm the estimate you found from the graph by plugging in the value x = 85.5 into the model and solving for y then we get the value as 1.12. This should give you the same answer as you found from the graph.

In conclusion, the resistance of a wire can be estimated using the mathematical model and can be used to make predictions about the resistance for different wire diameters.

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The sales tax for a box of cereal that costs $3.8 is $0.228 and the total cost for this box of cereal at the checkout register is $4.028, given that sales tax is 6% of the price of the item. This can be obtained by using sales tax formula.

The Sales tax formula is given by,

⇒ Sales tax = Total sales × sales tax rate

⇒ Sales tax = item price × 6%  

⇒ Sales tax = 0.06 × item price

Here in the question it is given that,  

a box of cereal costs $3.8, that is, item price = $3.8

By using sales tax formula we get that,

⇒ Sales tax = 0.06 × item price

⇒ Sales tax = 0.06 × $3.8

⇒ Sales tax = $0.228

The total cost for this box of cereal at the checkout register can be obtained using the following formula,

⇒ Total cost = item price + sales tax

⇒ Total cost = $3.8 + $0.228

⇒ Total cost = $4.028

Hence the sales tax for a box of cereal that costs $3.8 is $0.228 and the total cost for this box of cereal at the checkout register is $4.028, given that sales tax is 6% of the price of the item.

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Answer:

{5 x = f(x) + 6, x = g(x) + 4}

Step-by-step explanation: