what's
\( \sqrt{10 {}^{2} - 6 {}^{2} } \)
​

Answer:

A

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

The length of line segment AB in the triangle using the midsegment theorem is 64.

The Midsegment Theorem states that "the segment joining the midpoints of two sides of a triangle is parallel to and half the length of the third side."

From the diagram:

Midsegment = 3x + 5

Third side = 7x + 1

First, we solve for x, using the midsegment theorem:

( 3x + 5 ) = 1/2 × ( 7x + 1 )

Multiply both sides by 2:

2( 3x + 5 ) = ( 7x + 1 )

6x + 10 = 7x + 1

Collect and add like terms:

7x - 6x = 10 - 1

x = 10 - 1

x = 9

Now, we solve for line AB:

Line AB = 7x + 1

Plug in x = 9

Line AB = 7(9) + 1

Line AB = 63 + 1

Line AB = 64

Therefore, the line segment AB is 64.

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Answer:

16

Step-by-step explanation:

Answer:

(2x-5)(3x+1)

Step-by-step explanation:

make brackets:

(    )(    )

(    )(    )

we no that since there is two minuses in the trinomial there will be one - and one +

there are two beacause 6 is 6*1 and 2*3

(2x-   )(3x+  )

(6x+  )(1x-    )

now use some ingenuity to find where 5 and 1 should go to complete

(2x-5)(3x+1)

(2x+5)(3x-1)

(2x-1)(3x+5)

(2x+1)(3x-5)

the first binomial is the answer

2x*3x = 6x^2

-5*+1 = -5

2x*1 = 2x

3x*-5 = -15x

6x^2 +2x - 15x - 5

6x^2 - 13x - 5

Answer:

3.25 Its 3.25 because for every 3.25 seconds a number of color pictures will be printed.

Step-by-step explanation:

Answer:

Step-by-step explanation:

5b-5-9b+8+4b=

=0+3=3

A perfect linear relationship is essential for making accurate inferences in regression analysis. If the relationship between the variables is not linear, the results from the analysis may not be valid or reliable.

Option (a) would have resulted in a violation of the conditions for inference, as it would not be a representative sample of the population. Inference relies on the sample being representative of the population, and selecting the entire sample from one classroom would not be a random selection from the population.

Options (b), (c), (d), and (e) do not necessarily violate the conditions for inference. The sample size of 15 may affect the precision of the estimate, but it does not necessarily violate the conditions for inference.

A perfect linear relationship is essential for making accurate inferences in regression analysis. The scatterplot not showing a perfect linear relationship is expected in most cases, as perfect linear relationships are rare in real-world data. The histogram having an outlier may affect the distribution, but it does not necessarily violate the conditions for inference. And the standard deviation of foot length is different from the standard deviation of height is expected, as they are measuring different variables.

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Answer:

x= -4

Step-by-step explanation:

Subtract 7 from both sides

-5x + 7 - 7 = 27 - 7

-5x =  20

Divide both side by -5

-5x/-5 = 20/-5

x = - 4

Answer:

\(-15\)

Step-by-step explanation:

\(11-(-2)\\11+2\\13\)

Line KL has a range of 13.

Line JK has the same range covered as line KL.

\(-2-13\)

\(-15\)

J is located at -15.

Answer:

-6 33/40

Step-by-step explanation:

\(2\frac{5}{8} = 2.625\\-2\frac{3}{5} = 2.6\\\\2.625 *-2.6 = -6.825\\\\-6.825 = -6\frac{33}{40}\)

Answer:

C

Step-by-step explanation:

Verify, give me brainliest, and rate, and say thank you

Answer:

log ( \(\frac{x^2-2x(x-1)}{(x-1)^2}\) )

Step-by-step explanation:

to find (f ◦ g)(x) , substitute x = g(x) into f(x)

= log ( ( \(\frac{x}{(x-1)^}\) )² - 2(\(\frac{x}{x-1}\) ) )

= log ( \(\frac{x^2}{(x-1)^2}\) - \(\frac{2x}{x-1}\) ) ← express as a single fraction

= log ( \(\frac{x^2-2x(x-1)}{(x-1)^2}\) )

The surface area of the prism in this problem is given as follows:

46 cm².

A surface area is given by the sum of all the areas that compose the figure.

The prism in this problem is composed as follows:

The area of the square is given by the side squared, hence:

As = 2² = 4 cm².

The area of a right triangle is given by half the multiplication of the side lengths, hence:

At = 2 x 0.5 x 2 x 7 = 14 cm².

The area of a rectangle is given by the multiplication of the dimensions, hence:

Ar = 2 x 2 x 7 = 28 cm².

Hence the surface area of the prism is then obtained as follows:

S = As + At + Ar

S = 4 + 14 + 28

S = 46 cm².

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Answer:

21 yards

Step-by-step explanation:

4*21/4

84/4

21

Answer:

21yards multiplication

Step-by-step explanation:

Given parameters:

Number of curtains  = 4

Amount of fabric needed = \(5\frac{1}{4}\)yards

Unknown:

How much of fabric is needed  = ?

Solution:

   A curtain requires \(5\frac{1}{4}\)yards  = \(\frac{21}{4}\)yards

  Now to make 4 curtains, we would need  \(\frac{21}{4}\) x 4 = 21yards.

lim x→4 2x x − 4 − 8 x − 4 = lim x→4 2x x − 4 − lim x→4 8 x − 4, If lim x→5 f(x) = 0 and lim x→5 g(x) = 0, then lim x→5 f(x) g(x) does not exist,  If f(3) = 2 and lim x→3+ f(x) = 2, then lim x→3− f(x) = 2, If lim t→0 h(t) does not exist, then h(0) cannot exist all these Limits statement are False

A limit in mathematics is a value that a function approaches when the input gets closer to a certain value. Limits are used to find a function's derivative and integral as well as to characterize how a function behaves around particular places.

lim x -> c f(x) = L

(a) False.

According to the rules of limits, if both limits are present, the limit of a sum of two functions is equal to the total of their limits. The assertion, however, cannot be valid if one or both of the boundaries do not exist.

(b) False.

According to the limit laws, if the sum of two functions approaches 0, then the sum of their limits also does. The opposite of this statement is untrue, though.

In this instance, even if x approaches 5 and both f(x) and g(x) approach 0, the product of their limits, f(x)g(x), may not exist at all or may approach a non-zero value.

(c) False.

A function's limit as x gets closer to a number from the right is not always the same as the limit as x gets closer to the same number from the left.

Although f(3) = 2 in this instance and lim x3+ f(x) = 2, the limit of f(x) as x approaches 3 from the left may not be 2.

(d) False.

The absence of a limit does not imply the existence of the function's value at that time.

In this instance, the value of h(0) may still exist even though the limit of h(t) as t approaches 0 does not exist.

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All these given Limit statement are False.

(a) lim x→4 2x x − 4 − 8 x − 4 = lim x→4 2x x − 4 − lim x→4 8 x − 4

(b) If lim x→5 f(x) = 0 and lim x→5 g(x) = 0, then lim x→5 f(x) g(x) does not exist

(c) If f(3) = 2 and lim x→3+ f(x) = 2, then lim x→3− f(x) = 2

(d) If lim t→0 h(t) does not exist, then h(0) cannot exist.

A limit in mathematics is a value that a function approaches when the input gets closer to a certain value. Limits are used to find a function's derivative and integral as well as to characterize how a function behaves around particular places.

lim x -> c f(x) = L

(a) False.

According to the rules of limits, if both limits are present, the limit of a sum of two functions is equal to the total of their limits. The assertion, however, cannot be valid if one or both of the boundaries do not exist.

(b) False.

According to the limit laws, if the sum of two functions approaches 0, then the sum of their limits also does. The opposite of this statement is untrue, though.

In this instance, even if x approaches 5 and both f(x) and g(x) approach 0, the product of their limits, f(x)g(x), may not exist at all or may approach a non-zero value.

(c) False.

A function's limit as x gets closer to a number from the right is not always the same as the limit as x gets closer to the same number from the left.

Although f(3) = 2 in this instance and lim x3+ f(x) = 2, the limit of f(x) as x approaches 3 from the left may not be 2.

(d) False.

The absence of a limit does not imply the existence of the function's value at that time.

In this instance, the value of h(0) may still exist even though the limit of h(t) as t approaches 0 does not exist.

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You can use the fact that when coefficient of x variable are of equal magnitude but opposite sign, then adding them will make the coefficient 0, thus, making the x variable eliminated.

The numbers that can be multiplied by each equation so that when the two equations are added together, the x term is eliminated is given by

Option A: –10 times the first equation and 3 times the second equation

This method is actually called method of elimination to solve a system of linear equations.

We make one specific variable's coefficients of equal magnitude so that we can subtract or add the equations and eliminate that variable to make it easy to get the value of the other variable which will then help in getting the value of the first variable (if working in dual variable system).

If we have equations:

\(a_1x + b_1y = c_1\\a_2x + b_2y = c_2\)

then, if we want to eliminate variable x, then we have to multiply equation 1 with

\(- \dfrac{a_2}{a_1}\)

which will make coefficient of x in first equation as

\(a_1 \times - \dfrac{a_2}{a_1} = -a_1\)

Then adding both equation will eliminate the variable x.

We could've skipped that -ve sign and at then end, instead of adding, we could've subtracted the equations.

5 has 5 as magnitude, and sign isn't present which means its of positive (+) sign.

-5 has 5 as magnitude and sign is negative(-).

For this case, we're multiplying both the equations but the core concept or aim is same, ie, making the coefficients of equal magnitude but with opposite sign.

The given system of equations is

\(\dfrac{1}{5}x + \dfrac{3}{4}y = 9\\\\\dfrac{2}{3}x - \dfrac{5}{6}y = 8\)

Let two numbers be p,and q who multiply equation first and second respectively to make coefficient of x of equal magnitude but opposite sign.

We have

\(\text{Coefficient of x in first equation}= a_1 = \dfrac{1}{5}\\\\\text{Coefficient of x in second equation} = a_2 = \dfrac{2}{3}\)

Multiplying with p and q will give us

\(p\times a_1 = \dfrac{p}{5}\\\\q \times a_2 = \dfrac{2q}{3}\)

We need both resultant coefficient to add up to 0, or

\(p/5 + 2q/3 = 0\\p = -10q/3\\q = -3p/10\)

Now in options, we see first equation is either getting multiplied with -10, 10, or -3,3

If we put q = 3, we get p =  -10q/3=  -10

If we put q = -3, we get p = 10

If we put q = 5, we get p = -50/3

Thus only first choice is matching the correct pairs.

Thus,

The numbers that can be multiplied by each equation so that when the two equations are added together, the x term is eliminated is given by

Option A: –10 times the first equation and 3 times the second equation

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I know i am 2 weeks late but the answer is B, Have a good day :))

 The equation (4/7) * (7/4) = 1 demonstrates the multiplicative identity property, which states that multiplying any real number by 1 results in the original number.

The multiplicative identity property is a fundamental property of multiplication. It states that for any real number a, the product of a and 1 is equal to a. In the given equation, (4/7) * (7/4) = 1, the product of the two fractions simplifies to 1.
To understand why this equation illustrates the multiplicative identity property, we can evaluate it step by step. By multiplying the numerators and denominators, we have (4 * 7) / (7 * 4) = 28 / 28 = 1. We can see that the product of the fractions on the left side equals 1, which aligns with the multiplicative identity property.
This demonstrates that when we multiply (4/7) by (7/4), the result is 1. This illustrates the multiplicative identity property, as the product preserves the value of 1 and showcases how multiplying any real number by 1 does not change its value.

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The results are different because the simulated data is based on random numbers and may not perfectly match the probability distribution.

To simulate the emergency calls for 3 days, we need to use a cumulative hourly clock and generate random numbers to determine when the calls will occur. Let's use the following table of random numbers:

Random Number Call Time

57 1 hour

23 2 hours

89 3 hours

12 4 hours

45 5 hours

76 6 hours

Starting at 12:00 AM on the first day, we can generate the following sequence of emergency calls:

Day 1:

12:00 AM - Call

1:00 AM - No Call

3:00 AM - Call

5:00 AM - No Call

5:00 PM - Call

Day 2:

1:00 AM - No Call

2:00 AM - Call

4:00 AM - No Call

7:00 AM - Call

8:00 AM - No Call

11:00 PM - Call

Day 3:

12:00 AM - No Call

1:00 AM - Call

2:00 AM - No Call

4:00 AM - No Call

7:00 AM - Call

9:00 AM - Call

10:00 PM - Call

The average time between calls can be calculated by adding up the times between each call and dividing by the total number of calls. Using the simulated data from part a, we get:

Average time between calls = ((2+10+10+12)+(1+2+3)) / 7 = 5.57 hours

The expected value of the time between calls can be calculated using the probability distribution:

Expected value = (1/6)x1 + (1/6)x2 + (1/6)x3 + (1/6)x4 + (1/6)x5 + (1/6)x6 = 3.5 hours

The results are different because the simulated data is based on random numbers and may not perfectly match the probability distribution. As more data is generated and averaged, the simulated results should approach the expected value.

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Given,

At x=-2, f(x) is,

At x=4, f(x) has value,

The rate of change of f(x) on the interval [-2,4] is,

Therefore, the rate of change of f(x) on the interval [-2,4] is 2.

Answer:

b

Step-by-step explanation:

rude people delete meh answers

rude the answer is b

thank u very much now i must b on my way

Answer:

Its B

Step-by-step explanation:

Because the first one is correct give the credit to her.

The annual growth rate is 4.73 %

The continuous growth rate is 4.62 %

What is exponential growth function ?

A process called exponential growth sees a rise in quantity over time. When a quantity's derivative, or instantaneous rate of change with respect to time, is proportionate to the quantity itself, this phenomenon takes place.

Let us assume:

The initial amount of 1, so results are 2.

Let x be the  percent in decimal form

Growth rate per year:

\(1(1+x)^{15} = 2\)

Take ln on both the sides

\(ln((1+x)^{15}) = ln(2)\)

15*ln(1+x) =0 .693

ln(x+1) = 0.693/15

ln(x+1) = 0.04621

Take anti ln on both the sides

x+1 = 1.0473

x = 1.0473 - 1

x = .0473

x =4.73 % annual growth rate

Continuous growth rate:

\(1*e^{15x} = 2\)

\(ln(e^{15x}) = ln(2)\)

15x*ln(e) = ln(2)

ln(e) = 1

15x =0.693

x =0 .693/15

x = .0462

x = 4.62 %

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Therefore, H(t) is increasing on the intervals (-∞, -1/\(\sqrt7\)) and (\(1/\sqrt7\), ∞) and decreasing on the interval (\(-1/\sqrt7\), \(1/\sqrt7\)).and There are no local or absolute maximum values for H(t).

To find the intervals on which the function H(t) is increasing or decreasing, we need to take the first derivative of H(t) and find its critical points.

a.) First derivative of H(t):

\(H'(t) = 12t^11 - 84/7t^13\)

\(= 12t^11(1 - 7t^2)/7t^2\)

The critical points are where H'(t) = 0 or H'(t) is undefined.

So, setting H'(t) = 0, we get:

\(12t^11(1 - 7t^2)/7t^2 = 0\)

\(t = 0\) or t = ±(\(1/\sqrt7\))

H'(t) is undefined at t = 0.

Now, we can use the first derivative test to determine the intervals on which H(t) is increasing or decreasing. We can do this by choosing test points between the critical points and checking whether the derivative is positive or negative at those points.

Test point: -1

\(H'(-1) = 12(-1)^11(1 - 7(-1)^2)/7(-1)^2 = -12/7 < 0\)

Test point: (-1/√7)

\(H'(-1/\sqrt7) = 12(-1/\sqrt7)^11(1 - 7(-1/\sqrt7)^2)/7(-1/\sqrt7)^2 = 12/7\sqrt7 > 0\)

Test point: (1/√7)

\(H'(1/\sqrt7) = 12(1/\sqrt7)^11(1 - 7(1/\sqrt7)^2)/7(1/\sqrt7)^2 = -12/7\sqrt7 < 0\)

Test point: 1

\(H'(1) = 12(1)^11(1 - 7(1)^2)/7(1)^2 = 5/7 > 0\)

Therefore, H(t) is increasing on the intervals (-∞, -1/√7) and (1/√7, ∞) and decreasing on the interval (-1/√7, 1/√7).

b.) To find the local and absolute extreme values of H(t), we need to check the critical points and the endpoints of the intervals.

Critical points:

\(H(-1/\sqrt7) \approx -0.3497\)

\(H(0) = 0\)

\(H(1/\sqrt7) \approx-0.3497\)

Endpoints:

H (-∞) = -∞

H (∞) = ∞

Since H (-∞) is negative and H (∞) is positive, there must be a global minimum at some point between -1/√7 and 1/√7. The function is symmetric about the y-axis, so the global minimum occurs at t = 0, which is also a local minimum. Therefore, the absolute minimum of H(t) is 0, which occurs at t = 0.

There are no local or absolute maximum values for H(t).

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Answer:

0.027

Step-by-step explanation:

The upper bound of the 95% confidence interval for the average age in the U.S. is 48.29 years.

To determine the upper bound of the 95% confidence interval for the average age in the U.S., we can use the sample data from the survey. The sample size is 1072 people, randomly selected from the U.S. population, with a minimum age of 12. By calculating the average age of the respondents, we can estimate the average age of the entire U.S. population.

Using the given information that the average age of the respondents is 43.56 years, and assuming that the sample is representative of the population, we can calculate the standard error. The standard error measures the variability of the sample mean and indicates how much the sample mean might deviate from the population mean.

Using statistical methods, we can calculate the standard error and construct a confidence interval around the sample mean. The upper bound of the 95% confidence interval represents the highest plausible value for the population average age based on the sample data.

Therefore, based on the provided information and calculations, the upper bound of the 95% confidence interval for the average age in the U.S. is 48.29 years.

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The two column proof is completed by

Statement                                            Justification

1. DE || KL                                        1. Given

2. < DFE ≅ < LF-K                            2. Vertical Angles Theorem

3. < DEF ≅ < LKF                            3. Alternate Interior Angles Theorem

4. Δ FDE ≅ Δ FLK                           4. AAS postulate

According to the AAS Postulate, triangles are congruent if two angles and the non-included side of one triangle are congruent with two angles and the non-included side of another triangle.

In the given problem the side is non included and the angels are congruent and hence completes the proof

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Answer:

the solution is (5,5)

Step-by-step explanation:

if you plug in (5,5) where the x and y are you will find that the equation will balance out.

Answer:

50mm

Hope that helps!

Step-by-step explanation:

Answer:

EG=55

Step-by-step explanation:

EF+FG=EG

(6x+12)+(13x+5)=29x-3

19x+17=29x-3

20=10x

2=x

29x-3

29(2)-3

58-3

55

Check

(6x+12)+(13x+5)

((6(2)+12))+((13(2)+5))

(12+12)+(26+5)

24+31

55