Number 75: Find the length of side x.

With some give information, we need to solve some algebraic problems that involve a change of units, lets see step by step how we do that:

A) First, we know that:

The bridge was constructed in 2.5 years

Knowing that 1 year =  12 months, we can rewrite:

2.5 years = (2.5)*(12 montsh) = 28 months

The two crews built, together, 12,513 ft of the bridge.

Now, we know that the South Padre Island crew built an average of 208.5 per month.

Then in the 28 months for the whole construction, they built 28 times that amount:

D = (28 months)*(208.5 per month)  = 5,838 ft

Then the rest was constructed by the Port Isabel Crew.

They constructed 12,513 ft -  5,838 ft = 6,675ft

So that crew constructed 6,675 ft in 28 months, then the average number of feet built per month (the quotient between the total amount built and the number of months in which that was built) is:

6,675 ft/28 months = 238.39 ft per month.

b)

South Padre Island crew constructed  5,838 ft

Port Isabel Crew constructed 6,675ft

Now we want to transform these to miles.

Remember that;

1 mille = 5280 ft.

Then to transform from ft to miles, we just need to divide our measures by 5280 ft

Then:

South Padre Island crew constructed  5,838 ft = (5,838ft/5280ft) mi = 1.11 mi

Port Isabel Crew constructed 6,675ft = (6,675ft/5280ft) mi = 1.26 mi

c) Is this answer reasonable?

Mathematically, yes, both crews constructed about the same in about the same time, with a small difference that may be related to the sizes of each crew or something like that.

We could conclude that this would not be reasonable if the monthly rates were dramatically different.

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Answer:

0

Step-by-step explanation:

Any nonzero number to 0 power results in 1.

This implies m is simply 0 since it would give

(x^8/yz^5)^0 which is 1.

Answer:

the value of "m" is 0

Step-by-step explanation:

the entire fraction is equal to 1, the fraction is raised to a power of 0, non-zero

raised to the power of 0 is always equal to 1 so then its  

(\frac{x^{8}}{yz^{5}})^0 =1

now then this gives us the value of "m" = 0

hope that helps>3

Answer:

39

Step-by-step explanation:

G is the midpoint of the line FH, FH=2*GH. 9x+15=10x+8, x=7, FG=39

Answer:

Read explanation

Step-by-step explanation:

The two operations that you will get the same answer for no matter what order you do it is addition and multiplication.

Bonus: Technically, if you had something like 1-2-3 you could rewrite it as 1 + (-2) + (-3) and now it won't matter the order and for something like 1/2/3 you could rewrite as 1 * (1/2) * (1/3) and not it wont matter the order too!

This propetie is called the associative property of addition and multiplication.

In the second question since its addition the order you do it in does not matter.

Why: If you think of it logically adding in a diffrent order than the question does not matter since in the end your still adding the same ammount.

Remember: You can only swap the orders if everything is addition or multiplication and remember your order of operations when using this propety in the years to come.

Hoped this helped, Eddie K.W.

Hey there! I'm happy to help!

We see that all of our y-values go negative and our x-values stay the same. It isn't a rotation because then our x-values will switch, but they haven't switched in our problem, so A and D are incorrect.

Reflecting over the line y=x is just reflecting over a diagonal line, and that will switch the x-value as well.

The correct answer is B. reflect over the x-axis. All of the x-values stay the same here, but the y-values are all on the other side of the x-axis, so they are all negative now, and this matches the change we see with our points.

Have a wonderful day and keep on learning! :D

Answer:

6v+16

Step-by-step explanation:

2(2v+13) + 2(v-5) > 4v+26+2v-10 > 6v+16

Answer:

Perimeter is 6v + 16

Step-by-step explanation:

Perimeter formular of rectangle:

[tex]{ \sf{perimeter = 2(length + width)}} \\ { \sf{p = 2(l + w)}}[/tex]

length is (2v + 13)

width is v - 5

[tex]{ \sf{p = 2 \{(2v + 13) + (v - 5) \}}} \\ { \sf{p = 2 \{(2v + v) + (13 - 5) \}}} \\ { \sf{p = 2(3v + 8)}} \\ { \sf{p = 6v + 16}}[/tex]

Use the co‐interior rule, corresponding angle rule, alternate angle rule and vertical opposite angle rule to solve the question above.

angle G5 = angle K1 reason : corresponding angles

angle J1 = angle H3 reason: vertical opposite angles

angle J2 = angle K4 reason: vertical opposite angles

angle G5 = angle K4 reason: co‐ interior angles

angle F6 = angle K4 reason: alternate angle

The answer would be 98/5

Answer:

[tex] \sqrt{12} \times \sqrt{27} \\ = 2 \sqrt{3} \times 3 \sqrt{3} \\ 6 \sqrt{3 } \times \sqrt{3} \\ = 6 \times 3 \\ = 18 \\ thank \: u[/tex]

Answer:

18

Step-by-step explanation:

Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.

its correct i solved it by paper im lazy typing it here lol, anyways 18 has to be the correct answer.

hope i helped

Step-by-step explanation:

2f - 3(4f - 5g) + 5g +7fg

multiply the 3 in

2f - 12f - 15g + 5g + 7fg

add or subtract common terms

-10f -10g +7fg will be your final answer

Answer:

Step-by-step explanation:

As the question did not say how to 'solve the question', I would assume it will be to simplify the equation, as there is no way of solving an expression without an answer.

Simplify:

2f - 3(4f-5g) + 5g +7fg

Get rid of the parentheses

2f - 12f - 15g + 5g +7fg

Simplify similar expressions

-10f - 10g + 7fg

Therefore, 2f - 3(4f-5g) + 5g +7fg simplified is equal to -10f - 10g + 7fg.

Answer:

gauth math

got it perfect answer

Answer:

x=30

Step-by-step explanation:

Subtract 5 from both sides of the equ

. is written as ×

Step-by-step explanation:

6 ÷ 2 × 3 - 6² ÷ 2² - 3²

6 ÷ 2 × 3 - 36 ÷ 4 - 9

3 × 3 - 9 - 9

9 - 9 - 9

0 - 9

- 9

Answer:

Enter the expression you want to simplify into the editor.

The simplification calculator allows you to take a simple or complex expression and simplify and reduce the expression to it's simplest form. The calculator works for both numbers and expressions containing variables.

Step-by-step explanation:

Answer: 855 is the answer

Answer:

120 + z = 180 (linear pair)

=> z = 180 - 120

=> z = 60

130 + y = 180 (linear pair)

=> y = 180 - 130

=> y = 50

50 + 60 + x = 180 (Angle sum property of a triangle = 180)

=> 110 + x = 180

=> x = 180 - 110

=> x = 70

Answer:

q/b = r/c

Step-by-step explanation:

We can determine which equation is correct by looking at the similar angles

A ~ P and B ~ Q so the side length that is between these angles would be proportional which are :

r/c

Next up

C ~ R and again B ~ Q and the side length that is between these angles:

q/b

so the answer is

q/b = r/c as given in last option

Answer: a/b=r/c

Step-by-step explanation: i did the

Answer:

see explanation

Step-by-step explanation:

The inverse of a matrix A = [tex]\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right][/tex] is

[tex]A^{-1}[/tex] = [tex]\frac{1}{ad-bc}[/tex] [tex]\left[\begin{array}{ccc}d&-b\\-c&a\\\end{array}\right][/tex]

If ad - bc = 0 then the matrix has no inverse

A = [tex]\left[\begin{array}{ccc}11&-5\\3&-1\\\end{array}\right][/tex]

ad - bc = (11 × - 1) - (- 5 × 3) = - 11 - (- 15) = - 11 + 15 = 4 , then

[tex]A^{-1}[/tex] = [tex]\frac{1}{4}[/tex] [tex]\left[\begin{array}{ccc}-1&3\\-5&11\\\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}-0.25&0.75\\-1.25&2.75\\\end{array}\right][/tex]

Answer:

Step-by-step explanation:

[tex]A=\begin{bmatrix}11&-5\\3&-1\end{bmatrix}\\det(A)=11*(-1)-3*(-5)=-11+15=4\\minor=\begin{bmatrix}-1&3\\-5&11\end{bmatrix}\\cofactor=\begin{bmatrix}-1&-3\\5&11\end{bmatrix}\\Transposed\ cofactor=\begin{bmatrix}-1&5\\-3&11\end{bmatrix}\\A^{-1}=\dfrac{Transposed\ cofactorx}{det(A)} =\begin{bmatrix}\dfrac{-1}{4} &\dfrac{5}{4} \\\\ \dfrac{-3}{4} &\dfrac{11}{4}\end{bmatrix}\\[/tex]

[tex]Proof:\\A*A^{-1}=\begin{bmatrix}11&-5\\\\3&-1\end{bmatrix}*\begin{bmatrix}\dfrac{-1}{4} &\dfrac{5}{4}\\\\ \dfrac{-3}{4}&\dfrac{11}{4}\end{bmatrix}\\\\\\=\begin{bmatrix}\dfrac{-11+15}{4} &\dfrac{55-55}{4}\\\\ \dfrac{-3+3}{4}&\dfrac{15-11}{4}\end{bmatrix}\\\\\\=\begin{bmatrix}1&0\\\\ 0&1\end{bmatrix}\\[/tex]

Bonus: method of Gauss 's pivot jointed

Answer:

The height is 11/2

Step-by-step explanation:

We know SA = 30n

and r = 2

We are solving for h. So plug in our values

30n = 2n(2)^2 + 2n(2)h

Multiply and square on the right side terms

30n = 8n + 4nh

Divide everything by n

30 = 8 + 4h

Subtract 8 on both sides

22 = 4h

Divide by 4 on both sides

h = 22/4 = 11/2

Check:

30n = 2n(2)^2 + 2n(2)(11/2)

30n = 8n + 22n

30n = 30n

Step-by-step explanation:

[tex]sum \: of \: angles \: in \: a \: circle = 360 \\ so \\ 5a + 2a + 2a + 5a + 4a = 360 \\ 18a = 360 \\ a = \frac{360}{18} \\ a = 20 \\ thank \: you[/tex]

Answer:

[tex]x2+x+xy+y+zx+z \\ =x(x+1+y+y+z)+z \\ =x(x+2y+z+1)+z

[/tex]

Step-by-step explanation:

take like terms together..

x²+x+zx+xy+y+z

x(x+z+y)+y(x+y+z)

(x+y)(x+y+z)

hope it helps

Answer:

sandwich and drink only (no dessert)

so 4 x 6 = 24

you have 24 different combinations you can do

hope this helps

Step-by-step explanation:

Answer:

[tex]\frac{12}{3} - 5 +16 : 4 = 3[/tex]

Step-by-step explanation:

[tex]\sqrt{144} = 12\\\sqrt[5]{243} = 3\\\\\sqrt[3]{64}= 4[/tex]

Answer:

$14.50

Step-by-step explanation:

Is the answer because we don't put a decimmel pint after the number

The property of real numbers demonstrated in the given statement is the "Reflexive Property of Equality."

The Reflexive Property of Equality is one of the fundamental properties of real numbers, stating that any real number is always equal to itself. In mathematical terms, for any real number 'a,' the Reflexive Property is expressed as:

a = a

This property is self-evident, as it simply means that any quantity or value is identical to itself. In the provided statement, the cost of one item sold for $14.50 is precisely $14.50, showing that the item's cost is equal to itself.

To further illustrate this concept, consider any real number 'x.' According to the Reflexive Property, we have:

x = x

This applies to all real numbers, whether they are whole numbers, decimals, fractions, negative numbers, or irrational numbers. For example:

1 = 1

5.3 = 5.3

-2 = -2

π = π (pi)

No matter what value 'x' represents, the Reflexive Property holds true for all real numbers. It is a fundamental principle that underpins many mathematical operations and proofs.

In summary, the Reflexive Property of Equality states that any real number is equal to itself. The given statement, "The cost of one item sold for $14.50 is $14.50," exemplifies this property, showing that $14.50 is indeed equal to $14.50, thus reaffirming the reflexive nature of real numbers.

To know more about Property here

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Answer:

B) Associative Property of Multiplication

Step-by-step explanation:

The associative property states you can change where the parentheses (grouping terms) are in a multiplication statement, and you'll get the same product.

More generally:

(a * b) * c = a * (b * c)

Answer:

B) Associative Property Of Multiplication

Step-by-step explanation:

The associative property is a math rule that says that the way in which factors are grouped in a multiplication problem does not change the product.

Therefore, changing the grouping of (8x3) or (3x4) does not change the product.

Answer:

(-2,4)

Step-by-step explanation:

From qsn

x + y = 2

or, x = 2-y .... (i)

And,

y = (x/2) + 5 (one half x)

or 2y = x + 10

or x = 2y - 10 .... (ii)

From eqn i and ii we get

2-y = 2y-10

or 12 = 3y

or y = 4

putting the value of y in eqn (i) we get

x = 2-4

or, x = -2

Answer:

0.002 = x/10

x = 0.002 × 10

0.02 is ans

Answer:

Step-by-step explanation:

Stop doing it

Answer:

Let the integers are p and q.

In case both integers are positive or negative, you add the numbers up and apply their sign to the sum.

Examples:

In case one of the integers is negative and one positive.

Use absolute value in this case.

Subtract the numbers and apply the sign of the number with the greater absolute value.

Examples:

Step-by-step explanation:

Let the numbers be x and y

If both are of same signs then

|x + y| = x + y

-|x + y| = -(x + y) = -x - y

If one is negative and one is positive

-|x + (-y)| = -|x - y| = -x + y

-|y + (-x)| = -|y - x| = -y + x

Answer:

2. ☑ A [tex]\displaystyle f(x) = tan\:\frac{1}{2}x[/tex]

☐ B [tex]\displaystyle f(x) = tan\:2x[/tex]

☐ C x = [tex]\displaystyle 2tan\:x[/tex]

1. ☐ A [tex]\displaystyle \frac{\pi}{2}[/tex]

☐ B [tex]\displaystyle \pi[/tex]

☑ C [tex]\displaystyle 2\pi[/tex]

Explanation:

[tex]\displaystyle \boxed{f(x) = -cot\:(\frac{1}{2}x - \frac{\pi}{2})} \\ \\ y = Acot(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{\pi}{B} \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{\pi} \hookrightarrow \frac{\frac{\pi}{2}}{\frac{1}{2}} \\ Wavelength\:[Period] \hookrightarrow \frac{\pi}{B} \hookrightarrow \boxed{2\pi} \hookrightarrow \frac{\pi}{\frac{1}{2}} \\ Amplitude \hookrightarrow N/A[/tex]

OR

[tex]\displaystyle y = Atan(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{\pi}{B} \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{\pi}{B} \hookrightarrow \boxed{2\pi} \hookrightarrow \frac{\pi}{\frac{1}{2}} \\ Amplitude \hookrightarrow N/A[/tex]

Here is all the information you will need. Now, what you need to know is that ALL tangent, secant, cosecant, and cotangent functions have NO amplitudes. Also, keep in mind that although this IS the tangent graph, if you plan on writing your equation as a function of cotangent, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = cot\:\frac{1}{2}x,[/tex] in which you need to replase "tangent" with "cotangent", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the tangent graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the cotangent graph [photograph on the right] is shifted [tex]\displaystyle \pi\:units[/tex] to the left, which means that in order to match the tangent graph [photograph on the left], we need to shift the graph FORWARD [tex]\displaystyle \pi\:units,[/tex] which means the C-term will be positive, and perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{\pi} = \frac{\frac{\pi}{2}}{\frac{1}{2}},[/tex] but we are NOT YET DONE. Although we shifted the graph back into position, remember, cotangent is graphed in REVERCE, so we need to insert a negative in front of the amplitude term, and with that, the cotangent graph of the tangent graph, accourding to the horisontal shift, is [tex]\displaystyle y = -cot\:(\frac{1}{2}x - \frac{\pi}{2}).[/tex] Now, with all that being said, we can move forward. To find the period in this case, you need to take a look at the distanse between each vertical asymptote. Now, accourding to this graph, the vertical asymptotes are [tex]\displaystyle -\pi = x\:and\:\pi = x.[/tex] From here, you will then find the distanse between these asymptotes by simply perfourming the operation of Deduction, and doing that will give you [tex]\displaystyle \boxed{2\pi} = \pi + \pi.[/tex] So, the period of this function is [tex]\displaystyle 2\pi.[/tex] Now, you will instantly get the jist of the horisontal shift by looking at the above formula. Just keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must pay cloce attention to what is given to you inside those parentheses. Finally, the midline is the centre of your graph, also known as the vertical shift, which in this case is at [tex]\displaystyle y = 0.[/tex]

Well, that just about wraps it up. Now that everything has been explained, you should understand it better. If you still have questions, do not hesitate to comment any you have.

I am delighted to assist you at any time.