If two triangles are congruent, then the six ___ parts are congruent.

The value of x to solve the given equation is 16.

The given equation is:

[tex]log_2x=4[/tex]

A logarithm function is a special style to write an exponential function.

For example, If [tex]a^x=b[/tex] then we write it as [tex]log_ab=x[/tex].

So, [tex]log_2x=4[/tex] can be written as:

[tex]2^4=x[/tex]

Or, [tex]x=2^4[/tex]

[tex]x=16[/tex]

So, the value of x =16.

Hence, the value of x to solve the given equation is 16.

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Answer:

it's true

Step-by-step explanation:

The triangles made by diagonal parallelograms will be congruent so we can prove statements so will be True.

A basic quadrilateral with two sets of parallel sides is known as a parallelogram.

A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size.

As per the parallelogram drawn.

ΔABC ≅ ΔADC (By SAS postulute of congruency)

So we can make the statement that the two triangles made by the diagonal of a parallelogram will be congruent.

Hence "The triangles made by diagonal parallelograms will be congruent so we can prove statements so will be True".

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Factoring  x2-13x+40 

The first term is,  x2  its coefficient is  1 .
The middle term is,  -13x  its coefficient is  -13 .
The last term, "the constant", is  +40 

Step-1 : Multiply the coefficient of the first term by the constant   1 • 40 = 40 

Step-2 : Find two factors of  40  whose sum equals the coefficient of the middle term, which is   -13 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -8  and  -5 
                     x2 - 8x - 5x - 40

Step-4 : Add up the first 2 terms, pulling out like factors :
                    x • (x-8)
              Add up the last 2 terms, pulling out common factors :
                    5 • (x-8)
Step-5 : Add up the four terms of step 4 :
                    (x-5)  •  (x-8)
             Which is the desired factorization

1. The quantity of fuel left in the tank when the plane lands will be 3,375 gallons.

2. The total distance of the flight is 6,325 miles.

The quantities are computed using basic mathematical operations, including subtraction, division, addition, and multiplication.

Full tank of the airplane = 40,000 gallons

Average speed = 550 miles per hour

Number of hours on first flight = 8 hours

The quantity of fuel left = 14,000

The quantity of fuel consumed in 8 hours = 26,000 (40,000 - 14,000)

The quantity of fuel consumed per hour or per 550 miles = 3,250 miles (26,000 ÷ 8)

Additional hours on the final flight = 3.5 hours

The quantity of fuel consumed during the final flight = 11,375 gallons (3.5 x 3,250)

The total quantity of fuel consumed for the flight = 37,375 gallons (26,000 + 11,375)

The quantity of fuel left after the flight = 2,625 gallons (40,000 - 37,375)

The total hours for the flight = 11.5 hours (8 + 3.5)

The total distance of the flight = 6,325 miles (550 x 11.5)

Mathematically, after flying 11.5 hours or 6,325 miles, the airplane consumed 37,375 gallons of fuel, leaving only 2,625 gallons in its tank.

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I think the answer is $216.99 ?

Answer:

The amount of interest on the loan was of $214.57.

Step-by-step explanation:

Slingerland borrowed $8,000 at an 11% interest rate, thus having to pay $880 after a year.

As the loan was due on October 17, and the difference between July 20 and October 17 is of 89 days, using the exact interest method we can affirm that:

880 / 365 x 89 = X

2.41 x 89 = X

$214.57 = X

The amount of interest on the loan was of $214.57.

The percent error in Mark's estimate to the nearest tenth of a percent is 6.9%.

Percentage is the ratio such that it can be expressed as a fraction of 100. Percentage is calculated by dividing the number with the whole and then multiplying by 100.

The symbol used to denote percentage is '%'.

Percent error is the absolute value calculated by finding the difference of the estimated value and the actual value and then dividing by the actual value followed by multiplication with 100.

Percent Error = [(Estimated value - Actual value) / Actual value] × 100

                      = [(15.5 - 14.5) / 14.5] × 100

                      = (1 / 14.5) × 100

                      = 6.897%

                      ≈ 6.9%

Hence, there is a 6.9% percent error in Mark's estimate if his estimated distance from his house to the school is 15.5 m and the actual distance is 14.5 m.

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The percent error in Mark's estimate is 6.9%.

To calculate the percent error, we use the formula:

[tex]\[ \text{Percent Error} = \left( \frac{\text{Estimated Value} - \text{Actual Value}}{\text{Actual Value}} \right) \times 100\% \][/tex]

Given the estimated distance is 15.5 mi and the actual distance is 14.5 mi, we can plug these values into the formula:

[tex]\[ \text{Percent Error} = \left( \frac{15.5 \text{ mi} - 14.5 \text{ mi}}{14.5 \text{ mi}} \right) \times 100\% \][/tex]

[tex]\[ \text{Percent Error} = \left( \frac{1 \text{ mi}}{14.5 \text{ mi}} \right) \times 100\% \][/tex]

[tex]\[ \text{Percent Error} \approx \left( \frac{1}{14.5} \right) \times 100\% \][/tex]

[tex]\[ \text{Percent Error} \approx 0.069 \times 100\% \][/tex]

[tex]\[ \text{Percent Error} \approx 6.9\% \][/tex]

Therefore, the percent error in Mark's estimate is approximately 6.9%.

Answer:

commutative property

Step-by-step explanation:

Given equation: [tex]\pi+10=10+\pi[/tex]

The property of real number used in this equation is Commutative property

Commutative property : A binary operation [tex]{\displaystyle *}[/tex] on a set   is commutative if  [tex]a {\displaystyle *}b= b{\displaystyle *}a[/tex]

Following this property  [tex]\pi+10=10+\pi[/tex]

Answer:

D.[tex]f(n)=3n+27[/tex]

Step-by-step explanation:

Total number of pages in a book=f(n)

Jason has already read pages=27

He plans to read pages of the book everyday=3

He takes times to complete reading the book=n days

He read pages in n days=3n

We have to find the function which represents the relationship between f(n) and n.

According to question information

[tex]f(n)=3n+27[/tex]

This is required relation between f(n) and n.

Answer:D.[tex]f(n)=3n+27[/tex]

D.) Quadrant lll or Quadrant IV

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To find a line parallel to a given line and passing through a certain point, determine the slope of the given line, rearrange it to slope-intercept form, then substitute the point's coordinates to find the y-intercept of the parallel line.

To find a line parallel to the given line, we need the same slope of 3. Start by rearranging the given equation 3x - 4y = 7 to slope-intercept form: y = (3/4)x - 7/4. Since the parallel line passes through (-4,-2), substitute these values into the slope-intercept form to find the y-intercept. The equation of the line parallel to 3x - 4y = 7 that passes through (-4,-2) is y = (3/4)x + 2.

The half life of an element which decays 3.401% is 20 days.

The time required for a radioactive substance (or one-half of its atoms) to decay or change into a new substance is commonly characterised as its half-life. Ernest Rutherford discovered the idea for the first time in 1907. It is commonly denoted by the symbols Ug or t1/2.

To help you comprehend the notion, consider a radioactive element with a half-life of one hour. In this example, one half would decay in an hour and the other half would decay in another hour.

We are given;

y = a[tex]b^{(t)}[/tex]

Where t is the half life

y = a/2 is the amount of substance remaining after decay

So, b = 100% - 3.401%

b = 96.599%

b = 0.96599

Now, a/2 = a[tex](0.96599)^t[/tex]

and, 0.5=  [tex](0.96599)^t[/tex]

Now, taking log on both side we get

ln (0.5) = t(ln 0.96599)

t = ln(0.5)/ln(0.96589)

t = 20.032 days

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Final answer:

The total number of miles Trip and Lindsey travel to and from school each week is 68 miles, determined by using the greatest common factor of 12 and 56, which is 4, and the distributive property to group and multiply the sum of the unit contributions by 4.

Explanation:

To find the total number of miles Trip and Lindsey travel to and from school each week using the greatest common factor (GCF) and the distributive property, we first identify the GCF of the two numbers. The GCF of 12 and 56 is 4. We can then apply the distributive property to factor out the GCF and write the equation as follows:

(3 + 14) × 4 = total number of miles traveled to and from school each week.

Trip contributes '3' units of the GCF and Lindsey contributes '14' units of the GCF. To find the total, we add 3 and 14 to get 17, and then multiply by the GCF:

17 × 4 = 68

Therefore, Trip and Lindsey travel a total of 68 miles to and from school each week.

Answer:

Option A is correct.

Step-by-step explanation:

Selecting eight members randomly and recording whether each member is wearing a blue shirt.

A binomial experiment is defined as a statistical experiment which consists of n repeated trials. Only two possible outcomes are possible in each trial- either its a success or a failure. Here the probability of success remains the same on every trial.

Here, in 8 members the person wearing blue will be a success others will be a failure outcome.

Answer:

The value of the car is 0.94 times the value of the car the previous year.

Answer:

Option C is correct

The value of the car is 0.94 times the value of the car the previous year.

Step-by-step explanation:

Given the function:

[tex]p(t) = 24,525(0.94)^t[/tex]

where,

p(t) represents the value of a new car

t is the number of years.

We have to find  the value 0.94 represent in this situation.

For t =0 years.

Initial value of car p(0) is 24,525

For t = 1 years

[tex]p(1) =24,525 \cdot 0.94[/tex]

For t = 2 years

[tex]p(2) =24,525 \cdot (0.94)^2[/tex] and so on...

Since;

[tex]\frac{p(2)}{p(1)} = 0.94[/tex]

⇒[tex]p(2) = 0.94 \cdot p(1)[/tex]

In general:

[tex]p(t) = 0.94 \cdot p(t-1)[/tex] where, t is the number of years.

⇒the value of the car is 0.94 times the value of the car the previous year.

Answer:

A. (1,-4)

Step-by-step explanation:

L= (-1, 2)

(x,y)>(x+2, y-6)

(x,y)>(-1+2, 2-6)

(x,y)>(1, -4)

Answer:

The correct option is C) 7/3.

Step-by-step explanation:

Consider the provided numbers.

If the rational number can be written in the form of [tex]\frac{p}{2^n\times 5^m}[/tex] then the rational number will be a terminating decimal.

Now consider the provided options:

Option A) 7/5 can be written as: [tex]\frac{7}{2^0\times 5^1}[/tex]

Thus it is a terminating decimal.

Option B) 7/4 can be written as: [tex]\frac{7}{2^2\times 5^0}[/tex]

Thus it is a terminating decimal.

Option C) 7/3 can be written as: [tex]\frac{7}{2^0\times 5^0\times 3^1}[/tex]

Thus it is not a terminating decimal.

Option D) 7/2 can be written as: [tex]\frac{7}{2^1\times 5^0}[/tex]

Thus it is a terminating decimal.

Hence the only fraction that must be represented by a non terminating decimal is 7/3.

The correct option is C) 7/3.

The edge that is skew to edge AD is edge GC

In geometry, skew edges refer to edges that are not in the same plane and do not intersect. They belong to non-coplanar lines or segments, implying that they extend in different directions. Skew lines, and consequently their edges, never meet and remain at a constant distance from each other.

From the figure

line AD and GC are Skew since they can never meet yet they are not parallel to each other.

Skew lines are non-intersecting, non-coplanar lines in three-dimensional space. They neither share common points nor lie in the same plane, demonstrating their distinct orientation and lack of intersection in a three-dimensional geometric context.

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Answer:

Szymborska's overall opinion of humanity in "A Contribution to Statistics" is overall positive

Step-by-step explanation:

Szymborska is a poet who likes to comment on society with irony and sarcasm.One example of this is when she splits people into categories in her poem “A Contribution to Statistics”. Here Szymborska’s overall opinion of humanity may seem negative due to her bluntness and dry humor. For example, she says in the tenth stanza, “cruel when forced by circumstances -better not to know even ballpark figures.” It’s implied in this line that most people (maybe even all)are cruel or can be. She also says, “taking only things from life -thirty”which comments how lots of people are selfish. However, this seemingly cynical poem takes a sweeter turn near the end with statistics like, “worthy of compassion - ninety-nine” and “mortal- a hundred out of a hundred.” These lines reveal that even though Szymborska believes that humanity is extremely flawed the mass majority of us deserve and are worthy of love. Plus the fact that we’re all mortal may seem dark but the fact remains that both the righteous and the sinners will all end up in the same place. The fact that no one can escape

death gives humans equality in a way. Szymborska’s overall opinion of humanity turned out to be more optimistic after all.

After removing 600 litres from a tank that was half full, it became one-third full. By setting up an equation, we determine that every 600 litres represents one-sixth of the tank's full capacity. Multiplying 600 litres by 6, we find the tank's full capacity is 3600 litres.

The question involves determining the total capacity of a tank based on information given about volume reductions and proportions of fullness. Initially, the tank is half full, but after removing 600 litres, it becomes one-third full. We can set up an equation to find out the total capacity of the tank (T).

Since removing 600 litres takes the tank from being half full to one-third full, that means 600 litres correspond to one-sixth of the tank's capacity because one half minus one-third equals one-sixth.

Now we set up our equation: 600 litres = T/6. To solve for T, we multiply both sides of the equation by 6:

Therefore, the full capacity of the tank is 3600 litres.