The length of the long leg of a right triangle is 16 inches more than four times of the shorter leg. The length of the hypotenuse is 17 inches more than four times the length of the shorter leg. Find the side lengths of the triangle.

Answer: 12.69 miles approx

Step-by-step explanation:

let x represent the number of miles traveled

1.75 + 0.65x = 10

0.65x  = 8.25

x = 12.69 miles approx

Answer:

The solution for the given expression is [tex]x^{38}[/tex] , i.e option C

Step-by-step explanation:

Given expression as :

[tex](\dfrac{x^{6}\times x^{10}}{x^{-3}})^{2}[/tex]

Now, From the common radix method

∵ In multiplication of radix , if the radix is same , then power is added

I.e [tex]x^{6}\times x^{10[/tex] = [tex]x^{6+10}[/tex]

Or , [tex]x^{6}\times x^{10[/tex] = [tex]x^{16}[/tex]

Now, The expression can be written as

[tex](\frac{x^{16}}{x^{-3}})^{2}[/tex]

And In Division of radix , if the radix is same , then power is subtracted

So, [tex]\frac{x^{16}}{x^{-3}}[/tex]

Or, [tex]x^{16 - (-)3}[/tex]

Or,  [tex]x^{16 + 3}[/tex]

or, [tex]x^{19}[/tex]

∴ The expression is now

[tex](x^{19})[/tex]²

Now, again this is written as

[tex]x^{19}[/tex] × [tex]x^{19}[/tex]

I.e here again the radix is same and in multiple for, so, power is added

∴ [tex]x^{19}[/tex] × [tex]x^{19}[/tex]  = [tex]x^{19+19}[/tex]

I.e [tex]x^{19}[/tex] × [tex]x^{19}[/tex] =  [tex]x^{38}[/tex]

Hence The solution for the given expression is [tex]x^{38}[/tex] , i.e option C  . Answer

Answer:

[tex]d = \frac{1200}{w}[/tex]

Step-by-step explanation:

According to the blueprint, the floor area of the stage in the new auditorium at my college must be rectangular and equal to 1200 sq. feet.

If the width of the stage is w feet and depth of the stage is equal to d feet, then being a rectangle, we can write  

[tex]d \times w = 1200[/tex]

Therefore, the equation that represents the depth d as a function of width w is given by [tex]d = \frac{1200}{w}[/tex] (Answer)

Answer:

the correct answer d=1200[tex]d=1200/w[/tex]

Step-by-step explanation:

The equation of the parallel line in slope-intercept form is;

y = [tex]\frac{5}{2}[/tex] x - [tex]\frac{25}{2}[/tex]

Step-by-step explanation:

Let us revise some facts about parallel lines

The equations of two parallel lines have:

The slope-intercept form of the equation of a line is y = m x + b, where m is the slope of the line and b is the y-intercept

The given line has equation 5x - 2y = 10

Put it in the form of y = m x + b to find its slope

∵ 5x - 2y = 10

- Subtract 5x from both sides

∴ -2y = 10 - 5x

- Divide to sides by -2

∴ y = -5 + [tex]\frac{5}{2}[/tex] x

∴ y =  [tex]\frac{5}{2}[/tex] x - 5

- The value of m is the coefficient of x

∴ m = [tex]\frac{5}{2}[/tex]

∴ The slope of the given line is [tex]\frac{5}{2}[/tex]

∵ Parallel lines have same slopes

∴ The slope of the parallel line is m = [tex]\frac{5}{2}[/tex]

- Substitute the value of m in the form of the equation

∴ The equation of the parallel line is y = [tex]\frac{5}{2}[/tex] x + b

To find b substitute x and y in the equation by the coordinates of any point lies on the line

∵ The parallel line passes through point (3 , -5)

- Substitute x and y by the coordinates of the point (3 , -5)

∵ x = 3 and y = -5

∴ -5 = [tex]\frac{5}{2}[/tex] (3) + b

∴ -5 = [tex]\frac{15}{2}[/tex] + b

- Subtract [tex]\frac{15}{2}[/tex] from both sides

∴ b = [tex]\frac{-25}{2}[/tex]

∴ The equation of the parallel line is y = [tex]\frac{5}{2}[/tex] x + [tex]\frac{-25}{2}[/tex]

∴ The equation of the parallel line is y = [tex]\frac{5}{2}[/tex] x - [tex]\frac{25}{2}[/tex]

The equation of the parallel line in slope-intercept form is;

y = [tex]\frac{5}{2}[/tex] x - [tex]\frac{25}{2}[/tex]

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Answer:

C, because

-32 x seconds since she jumped + 14000

because 14000 would be 14000 units above 0, and -32 represents the seconds she had jumped, which would basically be -32+14000, which is the same as saying 14000 - 32.

Answer:

y = -x + 0

slope intercept: 0

Step-by-step explanation:

You would start at the origin, since your slope intercept is 0. The slope, -1 (since -x is the same as -1x), is telling us the line will be negative, so the line you are graphing will be heading up one space at a time towards the left, up 1 and sideways 1. Rise over Run.

Answer:

17

Step-by-step explanation:

17=15

so this is not equal

5,998.7714 ft

Step-by-step explanation:

Well find x in the illustration;

First To find the opposite side of the right-angled triangle we'll using tangent of the given angle

Tangent Ф = Length of the opposite side / Length of the adjacent side

Tan 43 = h / 6390

h = Tan (43) * 6390

h = 5,958.7714 ft

Then we'll add the height of the beacon which is 40 ft above ground;

x = 5,958.7714 ft + 40 ft

x = 5,998.7714 ft

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Answer:

Yes the mean is greater than the median

Step-by-step explanation:

To find the mean of numbers, you add all of them and divide them by how many there are in total.

75+80+81+96+100= 432

There are five numbers so divide the total by 5.

432÷5= 86.4

That is your mean.

The median is the one in the middle. There are five numbers, so the one in the middle is 81.

The mean is 86.4 and the median is 81.

Answer:

the mean is greater

Step-by-step explanation:

well mean is average so lets do that first

to find the mean, you add all of the percentages up and divide it by the amount of percentage

75 + 80 + 81 + 96 + 100 = 155 + 177 + 100 = 432

and now you divide 432 by 5 to get 86.4

so the mean is 86.4

and the median is the middle:

75 80 81 96 100

           ↑

81 is the median since its in the middle

86.4 > 81

so the mean is greater than the median

Answer:

its a right triangle

Step-by-step explanation:

i just took the test

Answer: Yes, I can confirm it is right triangle!

Let n be the current term and n+1 be the next term

Then the pattern is: n+1 = n * 5

Step-by-step explanation:

Given series is:

0.13, 0.65, 3.25, 16.25

We can find the ratio between consecutive numbers to find the pattern

So,

[tex]Ratio = \frac{0.65}{0.13}\\=5[/tex]

We can see that multiplying the previous term with 5 gives us the next term

0.13 * 5 = 0.65

0.65 * 5 = 3.25

3.25 * 5 = 16.25

Let n be the current term and n+1 be the next term

Then the pattern is: n+1 = n * 5

Keywords: Pattern, Sequence

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Answer:3

Step-by-step explanation:

Answer:

A vector is a quantity having direction as well as magnitude, especially as determining the position of one point in space relative to another.

Answer:

2

Step-by-step explanation:

Because the # ends in a even number, it can be divisible by 2

Answer:

16

Step-by-step explanation:

6-10=-4

4*-4=-16

abs(-16)=16

Answer:

|4(6-10)|

|4(-4)|

|-16|=16

Step-by-step explanation:

the answer is 16 because the distance of a number from zero is positive not negative.

Answer:

No, the two ratios are not the same.

Step-by-step explanation:

When we are saying "apples to oranges", mathematically it means:

[tex]\frac{Apples}{Oranges}[/tex],

Which could be 2:3 or 3:2, which in fractional from are written as [tex]\frac{2}{3}[/tex] and [tex]\frac{3}{2}[/tex] respectively.

We see that

[tex]\frac{2}{3} \neq \frac{3}{20}.[/tex]

In words the ratio 2:3  says "for every two apples there are three oranges", and 3:2 says "for every three apples there are two oranges". Again we see that  the two sentences are not saying the same thing, therefore the ratio 2:3 is not same as 3:2.  

Final answer:

The ratio 2:3 is not the same as 3:2 because they represent different relationships between the quantities of apples and oranges in a comparative scenario or barter trade. These ratios suggest different terms of trade and would result in different exchange outcomes.

Explanation:

The question is whether the ratio 2:3 is the same as 3:2 when comparing apples to oranges. To understand this, we must recognize that a ratio represents a relationship between two quantities, expressing how many times one value contains the other or is contained within it. In the context of a fruit bowl, a ratio of 2:3 would mean for every 2 apples, there are 3 oranges, while the ratio 3:2 means for every 3 apples, there are 2 oranges. Therefore, these two ratios are not the same as they represent different relationships between the quantities of apples and oranges.

Considering ratio comparisons like in barter trading, the terms of trade are critical. If 2 bushels of apples can be traded for 3 bushels of oranges, that is a 2:3 apple-to-orange trade ratio. On the other hand, if we reverse the ratio to 3:2, it would mean something quite different for trade or value comparisons. Specifically, you'd need 3 bushels of apples to get 2 bushels of oranges.

It's essential to compare apples to apples; comparative statistics are only useful when the comparison is logical and applicable. The ratios 2:3 and 3:2 convey different terms and thus would yield different outcomes in any exchange or comparative scenario.

Answer:

9

Step-by-step explanation:

It saying 3 times to the power of 2

or

3 squared

so basically it's saying

3^3=9

Answer:

The monthly payment for the loan amount for 20 years is $806.167

Step-by-step explanation:

The principal loan amount= $ 50,000

The rate of interest = 7 %

the time period of loan = 20 years = 20 × 12 = 240 months

let the amount after 20 years = $ A

From Compounded method

Amount = Principal × [tex](1+\dfrac{\textrm rate}{100})^{\textrm Time}[/tex]

or, A = 50,000 × [tex](1+\dfrac{\textrm 7}{100})^{\textrm 20}[/tex]

or, A = 50,000 × [tex](1.07)^{20}[/tex]

Or, A = 50,000 × 3.8696

∴ Amount = $ 193,480

So, The amount after 20 years = $ 193,480

The monthly payment amount = $ [tex]\frac{193480}{240}[/tex] = $ 806.167

Hence The monthly payment for the loan amount for 20 years is $806.167 Answer

Simplifying

4(0.2x + -5) = 12

Reorder the terms:

4(-5 + 0.2x) = 12

(-5 * 4 + 0.2x * 4) = 12

(-20 + 0.8x) = 12

Solving

-20 + 0.8x = 12

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '20' to each side of the equation.

-20 + 20 + 0.8x = 12 + 20

Combine like terms: -20 + 20 = 0

0 + 0.8x = 12 + 20

0.8x = 12 + 20

Combine like terms: 12 + 20 = 32

0.8x = 32

Divide each side by '0.8'.

x = 40

Simplifying

x = 40

Answer:

[tex] {4}^{3} [/tex]

Step-by-step explanation:

your are taking 4 and multiplying it by itself three times hence 4 to the third power

Answer:

4³

Step-by-step explanation:

Answer:14 and 5

Step-by-step explanation:

Area of a regular pentagon with a side of 10in  is 172

Step-by-step explanation:

Given:

Side of the regular pentagon = 10in

To Find:

Area of the regular pentagon=?

Solution:

We know that ,

[tex]Area of Pentagon = 5\times\text{ Area of triangle}[/tex]................(1)

Step 1: Finding the Area of the triangle

we know that in a right angle triangle, there are base, height and hypotenuse  [tex]tan(\frac{\pi}{5}) =\frac{ height}{hypotenuse }[/tex]

So, from the above equation,  

[tex]height=\frac{(base/2)}{tan(36^{\circ})}[/tex]

[tex]height=\frac{5}{tan(36)}=6.88[/tex]

area of right angle triangle

=> [tex]\frac{1}{2}\times base \times height[/tex]

=> [tex]=\frac{1}{2} \times 5\times 6.88[/tex]

=> 17.20

Area of the triangle =2 x area of right angle triangle

Area of the triangle =2 x  17.20

Area of the triangle= 34.40

Step 2: Finding the Area of the pentagon

Substituting the values in (1)

[tex]Area of Pentagon = 5\times 34.40 [/tex]

Area of Pentagon= 172

Answer:

x= -3 and x= -2

Step-by-step explanation:

(x+3)(x+2)

Hence, the zeroes are:

-3 and -2

Hoep this helps!

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p - 62%p = %=$159.60

p - 62p/100 = $159.60

100p - 62p = $15960

38p = $15960

p = $15960/38

p = $420

Answer:

A

Step-by-step explanation:

The transformation performed on triangle 1 to create triangle 2 is a translation by the vector (-4, -4), which means each point was moved 4 units to the left and 4 units down.

The transformation used can be determined by observing the differences between corresponding coordinates in the two triangles. If we subtract the coordinates of A′(2,2) from A(6,6), for instance, we get a change of -4 in the x-direction and -4 in the y-direction. Similarly, subtracting B′(4,3) from B(12,9) and C′(3,2) from C(9,6) results in changes of -8 and -6 in the x-direction and -6 and -4 in the y-direction, respectively.

This means that every point on triangle 1 was moved 4 units to the left and 4 units down to create triangle 2. Thus, the transformation that took place is called a translation by the vector (-4, -4).

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Answer:

-13/6 or (in mixed number form) -2 1/6

Step-by-step explanation:

Rewriting our equation with parts separated

=10+512−12−712

Solving the whole number parts

10−12=−2

Solving the fraction parts

512−712=−212

Reducing the fraction part, 2/12,

−212=−16

Combining the whole and fraction parts

−2−16=−216

Another way to do it:

Convert any mixed numbers to fractions.

Then your initial equation becomes:

125/12−151/12

Applying the fractions formula for subtraction,

=(125×12)−(151×12) / 12×12

=1500 − 1812/ 144

=−312/144

Simplifying -312/144, the answer is

=−2 1/6

Answer:

x=-12

Step-by-step explanation:

-18=x-6

-18+6=x--6+6

-12=x

Answer:

44

Step-by-step explanation:

20 percent less than 220

Answer:

The answer to this question is S=44

Step-by-step explanation:

Answer:

C. Parallel

D. Segment

F. Ray

Explaination:

Answers A, E, & G (line, point, & plane) are undefined terms.

Answer:

I believe it's 15 days

Answer:

The maximum number of days that she can skip crocheting is s = 57

Step-by-step explanation:

Darcie wants to crochet a minimum of 3 blankets.

She can crochet at a rate of a blanket per day, so she makes 1 blanket in one day.

She has a total of 60 days to work.

If X is the number of days that she works, we can write it as:

X ≥ 3

This means that she works at least 3 days, so she makes at least 3 blankets.

X < 60

This means that she not can work 60 days or more, in this way she has at least one day to do another volunteer job.

then

3 ≤ X < 60

then we have:

1 ≤ s ≤ 60 - 3 = 57

where s is the days that she can skip, where the less or equal sign is used because we have a bigger or equal sign previously.

The maximum number of days that she can skip

The maximum number of days that she can skip crocheting is when the right equality is true, so s = 57.