A car travels 50 miles per hour, h. What expression
represents the total distance you've traveled m?

Note that it is correct to state that LN ≅ MN and Nk ⊥ LM, so NK is the perpendicular bisector of LM and P is on NK. See attached image.

A perpendicular bisector is a line that cuts another line segment across the junction point at a straight angle. As a result, a perpendicular bisector always cuts a line segment through its midway. The phrase bisect implies dividing evenly or uniformly.

A simple technique to determine a perpendicular bisector is to measure the line segment you need to bisect. Then, divide the measured length by two to determine the midway. Draw a line at a 90-degree angle out from this middle.

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Full Question:

Tell whether the information in the diagram allows you to conclude that point P lies on the perpendicular bisector of LM. Explain your reasoning. See attached image.

A) No. You would need to know that LK ⊥ MK

B) No. You would need to know that KP ⊥ LM
C) Yes, t LN ≅ MN and Nk ⊥ LM, so NK is the perpendicular bisector of LM and P is on NK
D) Yes, NK ⊥ LM, so NK is the perpendicular bisector of LM and P is on NK

$105 is higher than $100, the minimum Payment due on Josiah's credit card is $105.

The minimum payment due on Josiah's credit card 3% of his outstanding balance and compare it to the minimum payment of $100. The higher amount between the two will be the minimum payment.

1. Calculate 3% of $3,500:

3% * $3,500 = 0.03 * $3,500 = $105

2. Compare the calculated amount with the minimum payment of $100:

Minimum payment = max($105, $100)

Since $105 is higher than $100, the minimum payment due on Josiah's credit card is $105.

The credit card company sets a minimum payment to ensure that the cardholder makes regular payments towards their outstanding balance. The minimum payment is usually a percentage of the balance or a fixed amount, whichever is higher. In this case, the minimum payment is calculated as 3% of the outstanding balance or $100, whichever amount is greater.

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Answer:

D

Step-by-step explanation:

The value of tan (A-pi/4) is  (-√(15)- 1) / 1 -√(15).

One of the trigonometric identities for compound angles is the tan(a-b) identity. When the angle for which the tangent function value is to be determined is supplied in the form of the difference of any two angles, it is used. The compound angle is denoted by the angle (a-b) in the formula for tan(a-b).

Given:

tanA = -square root 15

tanA = -√(15)

To find the value of tan (A-pi/4):

Use the formula,

Tan(a - b) Identity

tan(A-B) = (tanA - tanB) / 1 + (tanAtanB)

Substituting the values,

tan(A-π/4) = (tanA - tanπ/4) / 1 + (tanAtanπ/4)

tan(A-π/4) = (-√(15)- 1) / 1 + (-√(15)

tan(A-π/4) = (-√(15)- 1) / 1 + (-√(15)

tan(A-π/4) = (-√(15)- 1) / 1 -√(15)

Therefore, the value is tan(A-π/4) = (-√(15)- 1) / 1 -√(15)

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Answer:

Step-by-step explanation:

- Because the domain refers to the set of possible input values, the domain on the graph consists of all the input values shown on the x-axis.

- The range is the set of possible output values, shown on the y-axis

SOLUTION

For f and g to be inverses, then

Now

Also

Since we got x in both cases, hence f and g are inverses of each other

The answer is YES

Answer:

112 km/h

125 km/hr

Step-by-step explanation:

Distance = time * speed

Distance  = distance train 1 + distance train 2

474 = 2(s) + 2(s + 13)

Distribute

474 = 2s + 2s + 26

Combine like terms

474 = 4s + 26

Subtract 26 from both sides

448 = 4s

Divide both sides by 4

112 = s

s = 112 km/h

s + 13 = 125 km/hr

Answer:

179.6 (Estimated)

Step-by-step explanation:

5,924 ÷ 33 = 179.6 (Estimated)

Hoped this helped.

Answer:

5,924 ÷ 33 = 179.6 (in estimated form)

Step-by-step explanation:

5,924 divided by 33 equals 179.515151515.

Since 179.515151515 is not in estimated form, this can't be the correct answer.

Since we see that 51 is repeating, this allows us to determine whether we can round this up or not.. And we can!

179.515151515 → 179.6

Since 51 was repeating, we could round it up.

Therefore, 179.6 is your final answer.

Hope this helps! :D

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Answer: x=14

Step-by-step explanation:

Since it’s a rectangle, there are two pairs. In this case 6 and across from it are a pair both being 6, and 14 and above it are the same, 14

Answer:14

Step-by-step explanation: x=14 because both the top and bottom are parallel.

Proved that, sin⁴x-cos⁴x/ sin²x-cos²x = 1​.

Here, we have,

given that,

the LHS is:

sin⁴x-cos⁴x/ sin²x-cos²x

now, we know that,

sin²x+cos²x = 1

and, we know that,

a² - b² = (a+b) (a-b)

so, we get,

sin⁴x-cos⁴x/ sin²x-cos²x

= (sin²x+cos²x) (sin²x-cos²x ) / sin²x-cos²x

=(sin²x+cos²x)

=1

= RHS

Hence, Proved that, sin⁴x-cos⁴x/ sin²x-cos²x = 1​

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Answer:

16

Step-by-step explanation:

3^x +1 = f(X)

2x-4 = g(x)

find f(2)-g(-1)

we substitute in function f(X) by value (2), and in function g(X) by value (-1)

1. 3^x +1 becomes 3^2+1 =9+1=10

2. 2(-1)-4= -2-4=-6

then f(2)-g(-1)

= 10-(-6) =10+6=16

Answer:

15 sheets

Explanation:

The wall is rectangular; thereofre, its area is the product of its height and length.

The area of the wall is

Now the area of one sheet of drywall is

Now we ask ourselves: how many sheets of drywall fit into an area of 450 square ft?

The answer is found by dividing the area of the wall by the area of one sheet:

This means that 15 sheets are needed to cover the wall.

If you have previous taxable wages of $102,000 and your current taxable wages are $1,100, your Social Security tax would be $6,324 for the previous wages and $68.20 for the current wages.

To calculate the Social Security tax, we need to know the tax rate for Social Security and the taxable wages. Let's assume the Social Security tax rate is 6.2% for both the employee and the employer.

Given that your taxable wages for Social Security purposes are $1,100, and your previous taxable wages are $102,000, we can determine the Social Security tax amount.

First, we need to calculate the Social Security tax on the previous taxable wages of $102,000. Multiply $102,000 by 6.2% (0.062) to find the Social Security tax for that amount:

Social Security tax = $102,000 x 0.062 = $6,324

Next, we calculate the Social Security tax on the current taxable wages of $1,100. Multiply $1,100 by 6.2% to find the tax amount:

Social Security tax = $1,100 x 0.062 = $68.20

Therefore, if you have previous taxable wages of $102,000 and your current taxable wages are $1,100, your Social Security tax would be $6,324 for the previous wages and $68.20 for the current wages.

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Answer:

Irrational.

Step by step explanation:

\(\sqrt 6 + \dfrac{2}{3}\\\\\\=\dfrac{3\sqrt 6 +2}{3}\\\\\text{The sum of the these two numbers cannot be expressed as the the ratio of two integers,}\\\\\text{So the sum is not rational.}\)

To find the mean of a set of numbers, you need to add up all the numbers and then divide by the number of numbers in the set.

In this case, the mean of the four numbers is 12, which means the sum of those four numbers is 4 × 12 = 48. The mean of the other six numbers is 22, which means the sum of those six numbers is 6 × 22 = 132. The sum of all ten numbers is therefore 48 + 132 = 180.

To find the mean of all ten numbers, we need to divide the sum by the number of numbers, which is \(\frac{180}{10}\) = 18. Therefore, the mean of all ten numbers is 18.

Answer:

Given that 1minute =3/7of the vessel

let the time taken in minutes to fill the whole of the vessel be' x' minute.

1min =3/7

xmin =whole vessel =1=7/7

=3x/7=1=x=7/3=2.3min=2min.3sec

In the given problem, solving the problem systematically, the greatest number of groups the teacher can make is 6.

To form groups with the same combination of sopranos and altos, we need to find the greatest common divisor (GCD) of the numbers of sopranos and altos. Then, we can divide the total number of singers by the GCD to find the maximum number of groups.

The GCD of 36 and 30 is 6 (you can find it by listing the factors and finding the greatest one that they have in common: 36=2x2x3x3 and 30=2x3x5, so GCD=2x3=6).

So, we can form groups of 6 sopranos and 5 altos. Each group would have 6 + 5 = 11 singers.

To find the maximum number of groups, we divide the total number of singers by the number of singers per group:

(36 + 30) / 11 = 66 / 11 = 6

Therefore, the greatest number of groups the teacher can make is 6.

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The similarity statement is completed as below

Triangle MTA ~ triangle HTM ~ triangle HMA

A similarity statement is a statement in mathematics that expresses the affinity between two or more figures.

These figures are similar, meaning they have corresponding angles that are identical and sides that are equivalent in size ratio. The same shape is shared by them, although their sizes may be different.

The similar triangles are

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After making payments for 15 years, the amount still owed on the mortgage would be approximately $145052.36.

To determine how much will still be owed after making payments for 15 years, we can use the formula for the remaining balance on a mortgage:

Remaining balance = P ((1 + r)ⁿ - (1 + r)ᵇ) / ((1 + r)ⁿ - 1)

where:

P = the initial loan amount (in this case, $219,000)

r = the monthly interest rate (which is the annual interest rate divided by 12)

n = the total number of monthly payments (which is 30 years times 12 months per year, or 360 months)

b = the number of monthly payments made so far (which is 15 years times 12 months per year, or 180 months)

First, we need to calculate the monthly interest rate:

r = 4.5% / 12 = 0.00375 = 0.375%

Next, we can plug in the values to get:

Remaining balance = $219,000 ((1 + 0.00375)³⁶⁰- (1 + 0.00375)¹⁸⁰) / ((1 + 0.00375)³⁶⁰ - 1)

= $145052.36

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The probability that a randomly selected female is taller than 67 inches is 0.8133, or approximately 81%.

To calculate this probability, we need to standardize the height of 67 inches using the formula:

z = (x - mu) / sigma

where x is the height we're interested in, mu is the mean, and sigma is the standard deviation.

z = (67 - 64.5) / 2.8 = 0.8929.

Then, we can look up the area to the right of z = 0.8929 in the standard normal distribution table, which is 0.1867.

Finally, we subtract this value from 1 to get the probability that a randomly selected female is taller than 67 inches:

P(X > 67) = 1 - 0.1867

P(X > 67) = 0.8133

So, the probability that a randomly selected female is taller than 67 inches is 0.8133, or approximately 81%.

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Answer:

∠E = tan

∠D = tan

Step-by-step explanation:

Common sense, only perpendicular and base is present.

The group of rotations and symmetries of a geometric configuration is the group of isometries.

According to the above paragraph, "the group of rotations and symmetries of the configuration" refers to the group of isometries of a geometric configuration that preserve the configuration itself, without involving any translations. This group consists of rotations about a fixed point and symmetries about a straight line that pass through that point.

This group is formed by combining isometries of the configuration through the operation of composition, and it satisfies certain properties, such as closure, associativity, identity, and inverses. It is a useful tool for studying the symmetries and transformations of the configuration, and it is used in fields such as crystallography and quantum mechanics.

In summary, the group of rotations and symmetries of a geometric configuration is the group of isometries that preserve the configuration and can be composed with each other to obtain new isometries.

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Answer:

$140

Step-by-step explanation:

Rent alone = 400

Rent with roommate = (400 + 30%) / 2
= (400 + 120) / 2

= 520 / 2

Rent with roommate = 260

400 - 260 = 140

Their house will be worth approximately $240,154.57 in 8 years.

Non of the options is correct.

To determine how much their house will be worth in 8 years, we can substitute the value of t = 8 into the exponential equation:

y = 150,000(1.004)^(12t)

y = 150,000(1.004)^(12*8)

y = 150,000(1.004)^96

Using a calculator or computer software to evaluate the exponential expression, we find:

y ≈ 150,000 * 1.601030475

y ≈ 240,154.57

None of the provided answer choices match the calculated value. However, we can examine the available options and make an estimation:

A) $240,000: This option is very close to the calculated value of $240,154.57 and is a reasonable estimate.

B) $220,000: This option is significantly lower than the calculated value and is not a close estimate.

C) $1,258,884: This option is significantly higher than the calculated value and is not a close estimate.

D) $14,457,600: This option is extremely higher than the calculated value and is not a realistic estimate.

Based on the provided answer choices, option A) $240,000 is the closest estimate to the calculated value of $240,154.57. However, please note that the actual value may vary depending on the specific calculations and rounding methods used.

Non of the options is correct.

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Answer:

\(h^{-1}(x)=\{(3,-2),(4,0),(6,1),(9,2)\}\)

Step-by-step explanation:

Given: \(h(x)=\{(-2,3),(0,4),(1,6),(2,9)\}\)

To find: \(h^{-1}(x)\)

Solution:

A relation is said to be a function if each and every element of the domain has a unique image in the co-domain.

Inverse of a function exist if it is both one to one and onto.

\(h(x)=\{(-2,3),(0,4),(1,6),(2,9)\}\)

\(h^{-1}(x)=\{(3,-2),(4,0),(6,1),(9,2)\}\)

The sentence indicates that the increase in the value of a coin collection was exponential as such increase was continuous and constant in time. (Correct choice: A)

Exponential functions are trascendent expressions, these are, expressions that cannot be described algebraically, that are defined by the following expressions:

\(f(x) = a \cdot \left(1+ \frac {r}{100}\right)^{x}\)     (1)

Where:

Exponential functions are used to represent constant continuous increases or decreases in terms of the independent variable. The sentence indicates that the increase in the value of a coin collection was exponential as such increase was continuous and constant in time. (Correct choice: A)

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Answer:

12

Step-by-step explanation:

4, 16, 7, 10, 15, 11, 13, 20

Arrange the data from smallest to largest

4, 7, 10 , 11, 13,15, 16, 20

The median is the middle number

There are 8 data points so the middle number is between the 4th and 5th

4, 7, 10 , 11,       13,15, 16, 20

Add the 4th and 5th and divide by 2

(11+13)/2

24/2 = 12

Answer:

\(median = 12\)

Step-by-step explanation:

Arrange the numbers from smallest to largest

\(4 \: , \: 16 \: , \: 7 \:, \:10 \: ,\: 15 \: , \: 11 \:, \: 13 \: ,\: 20\)

Arrange now,

\(4 \: , \: 7 \:, \: 10 \:, \: 11 \: ,\: 13 \: , \: 15 \:, \: 16 \: ,\: 20\)

We know that median means the middle number in the set.

According to that, there are 8 numbers in this set, so, there are two middle numbers.

First let's find what are that middle numbers.

\(4 \: \: 7 \: \: 10 \: \: 11 \: \: \: \: \: \: \: 13 \: \: 15 \: \: 16 \: \: 20\)

Now it's clear that 11 and 13 the two middle numbers in this set.

Now, we have to add both middle numbers and divide them by 2.

\( \frac{11 + 13}{2} \\ = \frac{24}{2} \\ = 12\)

MEDIAN = 12

hope this helps

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Answer:

a1 = 4

a2= -2

a3 = -8

a4= -14

a5= -20

Step-by-step explanation:

a12= a1 + 11d

-62 = 4 + 11d

-62-4 = 11d

-66= 11d

d = \(\frac{-66}{11}\\\)

  = -6

a1 = 4

a2 = 4 - 6 = -2

a3 = 4 - (6×2) = -8

a4 = 4 - (6×3) = -14

a5 = 4 - (6×4) = -20