Find the perimeter of hexagon ABCDEF plotted below.

By using the equation of the line and properties of perpendicular lines, we find that the equation of the line is equal to y = - 2 · x - 6.

Herein we need to find a line that passes through point (- 5, 4) and is perpendicular to a given line in implicit form: x - 2 · y = - 4. The complete procedure is shown below. First, rewrite the equation of the perpendicular line into explicit form:

x - 2 · y = - 4

2 · y = x + 4

y = (1 / 2) · x + 2

Second, determine the slope of the new line:

m · m' = - 1

(1 / 2) · m' = - 1

m' = - 2

Third, calculate the intercept of the new line:

b = y - m · x

b = 4 - (- 2) · (- 5)

b = 4 - 10

b = - 6

Fourth, complete the new equation of the line:

y = - 2 · x - 6

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Answer:

168.28

Step-by-step explanation:

1) To find the scale factor for these triangles, we need to write a pair of ratios and then solve for x:

Now, we can plug x=8 into those:

Answer:

1 hour, 28 minutes, 15 seconds

Step-by-step explanation:

======================================================

Explanation:

x = width

2x = length, since it is twice as long as it is wide

area = length*width = 2x*x = 2x^2

Set this equal to the area of 450 sq ft and solve for x

2x^2 = 450

x^2 = 450/2

x^2 = 225

x = sqrt(225)

x = 15 feet is the width

2x = 2*15 = 30 feet is the length

Check:

area = length*width = 30*15 = 450

The answers are confirmed.

Answer:

Answer is - 4  1/15

Step-by-step explanation:

-6 2/5 = -32/5

-32/5   + 7/3       to add fractions they must have the same denominator

- 96/15   + 35/15   =  ( -96 + 35) / 15 = - 61/15  = - 4  1/15

Answer:

n=2.4

Step-by-step explanation:

The value of n is ∛14.

An equation is a mathematical statement that asserts the equality of two expressions. It consists of two sides, known as the left-hand side (LHS) and the right-hand side (RHS), connected by an equal sign (=).

To solve the equation −8 + n³= 6

Add 8 to both sides of the equation to isolate the term with n:

−8 + n³ + 8 = 6 + 8.

Simplifying the equation gives: n³ = 14.

Take the cube root of both sides to solve for n.

Taking the cube root of n³ = 14

∛(n^3) = ∛14.

Therefore, n = ∛14.

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The fraction of counters Lesley get if Adam gives 10 counters out of 18 counters is 5/9.

The fraction of counters Adam have now is 4/9.

This is an expression which consists of a numerator and a denominator

A numerator is the upper of top value of a fraction

A denominator is the lower or bottom value of a fraction

Number of counters Adam has left = Number of counters Adam has - Number of counters Adam gave to Lesley

= 18 - 10

= 8

Fraction of the 18 counters Lesley get = Number of counters Adam gave to Lesley / Number of counters Adam has

= 10/18

= 5/9

Fraction of the 18 counters Adam have now = Number of counters Adam has left / Number of counters Adam has

= 8 / 18

= 4/9

In conclusion, the fraction of counters Adam have now after giving out 10 counters to Lesley is 4/9

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2.5% of 8 = .2

5/8 + .2/8 = 5.2/8

5.2/8 = .65 x 100 = 65%

65% of games cost 1 or 2 dollars

100% - 65% = 35%

!! after doing it i did realize I could've just converted 5/8 into a percent than added it.

or

5/8 = .625 + .025 = .65 x 100 = 65%; 100% - 65% = 35%

A total of 8 cups of mix is needed for a Gatorade recipe calls for 2 cups of mix for every 4 cups of water if you have a total of 16 cups of water.

The unitary technique in actuality involves first determining the actual value of a single unit, alongside followed by the value of the necessary number of units.

The unitary approach is a kind of a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

2 mix for 4 cups of water

⇒ 1 mix for 2 cups

⇒ for 1 cup = 1/2 mix

so for 16 cups = 8 mix

A single or distinct unit is referred to by the word unitary. Therefore, the goal of this strategy is to establish values in reference to a single unit.

The unitary technique, for instance, can be used to calculate how many kilometers a car will go on one liter of gas if it travels 44 km on two liters of fuel.

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Answer: 6 blue, 6 yellow, 6 red

Step-by-step explanation:

A fair stack of cards is an equal amount of cards.

3 colors, 18 total

18 / 3 = 6

Therefore 6 of each

The ball reaches a maximum height of 96 feet and it spent 0 seconds in the air

Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k

The quadratic equation is given as

h(t) = -16t^2 + 96

Differentiate the equation of the function

So, we have

h'(t) = -32t

Set the differentiated function to 0

So, we have

-32t = 0

Divide both sides by -32

So, we have

t = 0

Substitute t = 0 in the equation h(t) = -16t^2 + 96

So, we have

h(0) = -16(0)^2 + 96

Evaluate

h(0) = 96

This means that the maximum height of the ball is 96 feet

Recall that the quadratic equation is given as

h(t) = -16t^2 + 96

Next, we differentiate the equation of the function

So, we have

h'(t) = -32t

Set the differentiated function to 0

So, we have

-32t = 0

Divide both sides by -32

So, we have

t = 0

Hence, the ball spent a total of 0 seconds in the air

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The technique of altering an existing graph or graphed equation to create a different version of the following graph is known as graph transformation.

Numerous different coordinate systems can be used to describe geometrical figures.

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64 ^ (-2/3)

Rewrite 64 as 4^3

(4^3) ^ (-2/3)

Using the power rule a^b^c = a^(b*c)

4 ^(3*-2/3)

4^ -2

We know that a^ -b = 1/ a^b

1 / 4^2

1/16

So,

The temperature was -10 degrees in the morning. Given that it dropped 15 degrees by midnight, we could substract 15 to -10 to find the temperature at midnight:

The temperature at midnight was -25 degrees.

b. Clearly,

c. The absolute value of the morning temperature is:

That's because:

i think 16? 1/2+1/2=1 so 8*2=16

The logarithms in terms of a and b are:

a) log 72 = 3a + 2b

b) log √27 =  [tex]\frac{3}{2} b[/tex]

c) log 360 = 3a + 2b + log 5

         nˣ = a ⇔ logₙ a = x , log stands for logarithm here.

       Where,

         Two positive real numbers are a and n. x is a real number.

Given:

log 2 = a

log 3 = b

a) log 72

= log (2³ × 3²)

= log 2³ + log 3²   [ By product rule of logarithms, log mn = log m + log n]

= 3log 2 + 2log 3   [By power rule of logarithms, log mⁿ = nlog m]

Replacing with the values of log 2 and log 3.

= 3a + 2b

b) log √27

= [tex]\frac{1}{2}[/tex] log 27    [By power rule of logarithms, log mⁿ = nlog m]

=  [tex]\frac{1}{2}[/tex] log 3³

= [tex]\frac{1}{2} *3 log3[/tex]

= [tex]\frac{3}{2} log 3[/tex]

= [tex]\frac{3}{2} b[/tex]

c) log 360

= log (2³ × 3² × 5)  

= log 2³ + log 3² + log 5 [By product rule of logarithms,log mn = log m +  log n]

= 3log 2 + 2log 3 + log 5  [By power rule of logarithms, log mⁿ = nlog m]

= 3a + 2b + log 5

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we have that

the distance city B to city C is equal to

405+401=806 miles4

therefore

the answer is

The account would be worth more after 6 years if calculating interest compounded daily versus calculating simple interest by $62.46

Compound interest:

A = P(1 + r/n)^nt

= 2,000(1 + 0.04/365)^(365×6)

= 2,000.00(1 + 0.000109589041095)^(2190)

= 2000(1.0.000109589041095)^2190

= 2000 (0.00010958904109589)

= $2,542.46 to the nearest cent

Simple interest:

S.I = principal × rate × time

= 2,000 × 0.04 × 6

= $480

Total = Principal + simple interest

= $2,000 + $480

= $2,480

To find the amount more would the account would be worth after 6 years by calculating interest compounded daily versus calculating simple interest

= Compound interest - Simple interest

= $2,542.46 - $2,480

= $62.46

In conclusion, the account would be worth $62.46 more if compounded daily than simple interest.

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When you're reading a study that reports selecting a random sample of hospitals and estimating admission delay times, it's an example of C. probability sampling.

Probability sampling is the process of selecting a sample from a population when the selection is based on the randomization principle, often known as chance or random selection. In general, probability sampling is more difficult, time-consuming, and expensive than non-probability sampling.

Using a method based on probability theory, probability sampling is a strategy in which the researcher selects samples from a larger population.

Researchers can produce a sample that accurately represents the relevant real-world population by using probability sampling.

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You are reading a study that reports selecting a random sample of hospitals and estimating admission delay times. You know this is an example of:

a. Quota sampling

b. Convenience Sampling

c. Probability sampling

d. Sampling bias

We are going to evaluate for the giving values

x | y | x + 3y

0 | 4 | 0 + 3(4) = 3(4) = 12

2 | 3 | 2 + 3(3) = 2 + 9 = 11

4 | 2 | 4 + 3(2) = 4 + 6 = 10

3 | 6 | 3 + 3(6) = 3 + 18 = 21

The powers can be used in the following manner using multiplicative identity.

Powers are mathematical expressions of the kind where x is the base and n is the exponent. In powers, the exponent specifies how many times to multiply the base by itself whereas the base is the integer or variable that is continuously multiplied.

The quotient rule states that exponents should be subtracted when dividing powers by the same base. For instance, h(6-2) Equals h when h(6) is divided by h(2) (4). Subtracting the exponents is a quick and easy way to simplify the issue.

When separating similar words with exponents, using the Quotient of Powers Rule to minimize the number of terms. This rule states that when dividing words with the same base, the exponents should be removed in order to find the result. When separating similar words with exponents, using the Quotient of Powers Rule to minimize the number of terms. This rule states that when dividing words with the same base, the exponents should be removed in order to find the result. The trick is to eliminate only exponents with compatible bases.

Since the multiplicative identity, or one, is the simple outcome of no numbers at all, it follows that every integer raised to the power of zero equals one.

Thus, we came to the logical conclusions.

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It should be noted that the z-score for the sample mean that's given is 0.5.

A Z-score is a metric that quantifies how closely a value relates to the mean of a set of values. Standard deviations from the mean are used to measure Z-score. A Z-score of zero means the data point's score is the same as the mean score.

The following can be seen from the information illustrated:

Mean ( u ) =55

Standard Deviation ( sd )=12

Number ( n ) = 4

Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)

Z = (58-55)/12/ Sqrt ( 4 )

Z = 3/6= 0.5

Therefore, the z score is 0.5.

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The verdict on whether the frequency distribution given appears to be normal is; No, the distribution is not symmetric.

It follows from the task content that it is required to determine if the frequency distribution as given appears to be normal.

On this note, since a major distinctive feature of a normal distribution is that; there is a concentration of frequency in the middle and additionally, a normal distribution infers symmetry in the frequency distribution.

Therefore, since none of the data values (speed) can be chosen as the middle value, and the distribution is not symmetric, it follows that;

The frequency distribution in discuss is not a normal distribution because the distribution is not symmetric.

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Answer:

She will have 23.1 gallons left after 3 days.

Step-by-step explanation:

We know Margaret uses an average of 1.3 gallons of gas every day and her car holds 27 gallons total. In three days, she would use 3 times her daily average, or 3 * 1.3 = 3.9 gallons consumed in 3 days. To find how many gallons are left in her tank after 3 days, we would subtract 3.9 gallons from 27 gallons. This equals exactly 23.1 gallons of gas.

Answer:

[tex]y = \frac{3}{5} x + \frac{13}{5} [/tex]

Step-by-step explanation:

The equation of a line can be written in the slope-intercept form y= mx +c, where m is the slope and c is the y-intercept.

Let's rewrite the given equation into the slope-intercept form, so that we can identify its slope.

5x +3y= 15

3y= -5x +15

Divide both sides by 3:

[tex]y = - \frac{ 5}{3} x + 5[/tex]

Thus, the slope of the given line is [tex] - \frac{5}{3} [/tex]

The slope of a perpendicular line is the negative reciprocal of the given line. In simpler terms, the slope of the perpendicular line can be found by flipping the denominator and numerator, and by multiplying -1 afterwards.

Slope of perpendicular line= [tex] \frac{3}{5} [/tex]

Substitute the value of the slope into the equation:

[tex]y = \frac{3}{5} x + c[/tex]

To find the value of c, substitute a pair of coordinates the line passes through.

When x= -1, y= 2,

[tex]2 = \frac{3}{5} ( - 1) + c[/tex]

Solve for c:

[tex]c = 2 + \frac{3}{5} [/tex]

[tex]c = \frac{13}{5} [/tex]

Thus, the equation of the line described is [tex]y = \frac{3}{5} x + \frac{13}{5} [/tex].

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The inequality in vertex form represents the region containing the results of the year is y < -2(x - 25)² + 200 option (D) is correct.

It is defined as the graph of a quadratic function that has something bowl-shaped.

(x - h)² = 4a(y - k)

(h, k) is the vertex of the parabola:

a = √[(c-h)² + (d-k²]

(c, d) is the focus of the parabola:

From the graph:

The vertex is:

(25, 200)

The vertex form of the parabola:

y = a(x - h)² + k

y = a(x - 25)² + 200

Plug x = 30 and y = 150

a = --2

y = -2(x - 25)² + 200

The inequality will be:

y < -2(x - 25)² + 200

Thus, the inequality in vertex form represents the region containing the results of the year is y < -2(x - 25)² + 200 option (D) is correct.

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