Which law would you use to simplify the expression (p/q) 3
power of a power
power of a quotient
quotient of powers
power of a product

The answer is 6 because you replace c with the 2 (because it says that c equals 2) and add it normally which you get 6

If the observation deck is 871 feet high, the horizontal distance from the base of the skyscraper out to the ship is: 784.25 feet.

Given:

Angle of depression (∅) = 48°

Opposite side = 871 feet

Let x represent the horizontal distance

Hence,

tan 48° =871/x

x = 871/tan 48°

x= 871/ tan(0.8377)

x= 871/ 1.1106125

x =784.25 feet

Therefore If from the observation deck of a skyscraper, Ian measures a 48∘ angle of depression to a ship in the harbor below. If the observation deck is 871 feet high, the horizontal distance from the base of the skyscraper out to the ship is: 784.25 feet.

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the answer is pyramid or cone

After rationalizing the denominator for the expression √3 x / 2y, we get that the result is [√6xy)] / 2y.

The removal of a radical or imaginary number from the denominator of an algebraic fraction is referred to as rationalization. That is, eliminate the radicals from a fraction to leave only a rational integer in the denominator.

Rationalizing the divisor suggests that you get eliminate the novel within the divisor. 

by the rules of radicals, We can rephrase this as √(5x) / √(2y)

The expression will then be multiplied by √(2y) / √(2y).  Keep in mind that this results in 1, and multiplying this by the first expression has no effect on the original issue.

On multiplying we get-

[√(3x) * √(2y)] / [√(2y) * √(2y)]

[√6xy)] / 2y 

Therefore, after rationalizing the denominator for the expression √3 x / 2y, we get that the result is [√6xy)] / 2y.

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Answer:

$2,009

Step-by-step explanation:

Hope this helped! <3 If correct pls mark me as brainliest! Have a great day!

If Mr. Jackson has a circular garden with a diameter of 10 feet surrounded by edging and using the same length of edging, he is going to create a square garden, then the maximum side length of the square is equal to 7.85 feet.

First, we have to find the amount of edging Mr. Jackson has. This can be calculated by finding the circumference.

Circumference can be found by using diameter by the formula;

c = π (diameter)

c = π (10)

c = 3.416 feet

This is the amount of edging on the circular garden. As he has to use the same amount of edging on the square garden, the edging on the square garden is the parameter of the square garden. As the parameter of the square is four times the side length, therefore;

3.416 ÷ 4 = 7.85

Hence, the maximum side length of the square is equal to 7.85 feet.

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According to the question, the given expression is written as below:

The expression is : [tex](\frac{2x^{4} }{10y^{-2} } )(\frac{5y^{3} }{4x^{3} } )[/tex]

Using indices concept, the same variables get cancelled with each other. The divisible numbers get divided by their respective numbers.

And finally, the negative power becomes positive in numerator. Using these concepts the above expression can be re-written as:

Final expression: [tex]\frac{xy^{5} }{y4} =xy[/tex]

Hence, the evaluated expression is [tex]xy[/tex].

What is indices?

In mathematics, the indices are the power or the exponent which is either raised to numbers or variables.

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The simplified expression after solving the given equation is 8.4721 .

The given expression is,

[tex]4\sqrt{7} - \sqrt[3]{7}[/tex]                                                                   equation 1

Name the given expression as equation 1.

To simplify the given expression first we need to solve step wise,

As we know [tex]\sqrt{7}[/tex] = 2.6457 , we can write,

4[tex]\sqrt{7}[/tex] = 4 × (2.6457) = 10.5830

[tex]\sqrt[3]{7}[/tex] = 1.9129

Now, we need to substitute the above solved values in equation 1 and after substituting them we can write as follows:

[tex]4\sqrt{7} - \sqrt[3]{7}[/tex] = 10.5830 - 1.9129

On further simplifying, we will get

[tex]4\sqrt{7} - \sqrt[3]{7}[/tex] = 8.4721

Thus we can write that the simplified expression after solving the given equation is 8.4721.

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[tex]\cfrac{6}{7}\div \left(-\cfrac{11}{2} \right)\implies \cfrac{6}{7}\cdot \left(-\cfrac{2}{11} \right)\implies -\cfrac{12}{77}[/tex]

The error that Eli made is that C. He did not solve the equation completely since there are two positive solutions.

It should be noted that the equation given is g² = 49.

In this case, Eli solved it and got -7. This is incorrect.

It should be noted that the appropriate solution should have been ✓49 = 7.

Therefore, the error that Eli made is that C. He did not solve the equation completely since there are two positive solutions.

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Answer:

here to help!

Step-by-step explanation:

no; Sample answer: If the vertices of ABC are A(1, 2), B(3, 4), and. C(1, 4), then the vertices of the final image are A"(-3, −1), B"(-5, 1), and C"(-3, 1).

Step-by-step explanation:

a ratio of 5:5:6 tells us first that there are 5+5+6 = 16 units in all the sides lengths of the triangle.

we don't know how large a single unit is yet, but we know, we have 16 of them.

we also know that all 3 sides together is 32 cm.

and that is another form to bring all side lengths together.

so, we know now that

32 cm = 16 ratio units.

therefore, one ratio unit is 32/16 = 2cm.

therefore, the sides are actually :

2×5 = 10 cm

2×5 = 10 cm

2×6 = 12 cm

so, we have an isoceles triangle (the 2 legs are equally long : 10 cm) with a baseline of 12 cm.

that means the height to the baseline splits the triangle in half (into 2 equal right-angled triangles).

and the height of the main triangle we get via Pythagoras from these smaller triangles :

c² = a² + b²

with c being the Hypotenuse (the baseline opposite of the 90° angle), a and b are the legs.

10² = (baseline/2)² + height² = 6² + height²

100 = 36 + height²

64 = height²

height = 8

the area of a triangle is

baseline × height / 2

so, in our case the area of the triangle is

12 × 8 / 2 = 12 × 4 = 48 cm²

[tex]\frac{ln(e)}{4}=\frac{1}{4}[/tex], by properties of logarithm.

Now, as we know that ln (e) = 1,

In the given expression, [tex]\frac{ln(e)}{4}[/tex], for ln(e) = 1,

The expression becomes: [tex]\frac{ln(e)}{4}=\frac{1}{4}[/tex]

Hence, [tex]\frac{ln(e)}{4}=\frac{1}{4}[/tex], by properties of logarithm.

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Answer:

Six hundred fifty eight and one hundred twenty nine thousandths

Attributes shared by rhombuses and rectangles:

Both are quadrilaterals.

Both have their opposing sides equal and parallel.

If a rhombus and a rectangle have the same length and width,

The perimeter of the rhombus equals the sum of the diagonals of the rectangle.

The sum of the diagonals of the rhombus equals the semiperimeter of the rectangle.

The angles of the rhombus equal the angles formed by the diagonals of the rectangle.

The angles formed by the diagonals of the rhombus are all right angles, as are the angles of the rectangle.

The area of the rhombus is one half of the area of the rectangle.

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Hans will run additional 9 miles to the 18 miles he has run to complete 27 miles in wants to run for the week.

If Hans is to run 27 miles this week and he has run 18 miles, the additional miles he has to run in the week is t. Meaning that t plus eighteen is equal to 27, which is expressed mathematically below

t + 18 = 27

To solve the equation above, use balancing method. To use balancing method, subtract 18 from both side of the equation.

t +18 -18 = 27-18

t + 0 = 27-8

t = 27 -18

t = 9

Therefore, Hans will run additional 9 miles to complete 27 miles for the week.

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The value of the composite function (g/f)(x) is (x^2 - 5)/(4x + 1)

The definition of the functions are given as

f(x) = 4x + 1

g(x) = x^2 - 5

The composite function is given as

(g/f)(x)

The composite function is calculated using

(g/f)(x) = g(x)/f(x)

Substitute the known values in the above equation

So, we have

(g/f)(x) = (x^2 - 5)/(4x + 1)

Hence, the value of the composite function (g/f)(x) is (x^2 - 5)/(4x + 1)

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The composition of f(x) and g(x) gives:

(f ◦ g) (x) =  x²  + 9x + 20

Here we have the two functions:

f(x) = x² + 5x +6

g(x) = x +2

And we want to find the composition:

(f ◦ g) (x)

The composition means that we need to evaluate f(x) in g(x), so we get:

(f ◦ g) (x) = f( g(x))

Then we will get:

(f ◦ g) (x) = g(x)² + 5*g(x) +6

Now, replacing g(x) we get:

(f ◦ g) (x) = (x + 2)² + 5*(x + 2) + 6

Expanding that, we get:

(x + 2)² + 5*(x + 2) + 6 = x² + 4x + 4 + 5x + 10 + 6 = x²  + 9x + 20

(f ◦ g) (x) =  x²  + 9x + 20

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For line segment CD, we have that:

10. The length is of 5 units.

12. The midpoint is of (0.5,0).

14. The slope is of -4/3.

The endpoints are given as follows:

c(-1,2) and d(2,-2).

The length is given by the distance between the two endpoints, hence:

[tex]CD = \sqrt{(2 - (-1))^2+(-2-2)^2}[/tex]

CD = sqrt(25) = 5.

The length is of 5 units.

The midpoint is the mean of the coordinates, hence:

The midpoint is (0.5,0).

The slope, taking two points, is given by change in y divided by change in x, hence:

m = (-2 - 2)/(2 - (-1)) = -4/3.

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The value of the expression when p =-3 and q =5 is -4

Algebraic expressions are defined as expressions made up of variables, terms, factors, constants and coefficients.

They are also made up of mathematical or arithmetic operations such as:

Given the expression;

p + (-q) -2p

Where:

Now, substitute the values of p as - 3 and q as -5 in the expression, we have:

(-3) + (-5) - 2(-3)

expand the bracket

-3 - 5 + 6

add the values first

-3 - 1

-4

Thus, the value of the expression when p =-3 and q =5 is -4

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The midpoint of the line segment described by the two endpoints; (-3, 8) and (-8, 2) according to the task content is; (-11/2, 5).

It follows from the task content that the midpoint of the line segment joining the two points (-3, 8) and (-8, 2) is to be determined.

Since the midpoint of a line is given by coordinates;

x = (x1 + x2)/2 and y = (y1 + y2)/2.

It follows that we have;

x = (-3+(-8))/2

x = -11/2

while; y = (8+2)/2

y = 10/2

y = 5.

Ultimately, the midpoint of the line segment described by the two endpoints; (-3, 8) and (-8, 2) according to the task content is; (-11/2, 5).

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√3+ √11 is greater than 5 .

We first assume that √3+ √11 is greater than 5. Then we check if our assumption is correct.

So suppose that √3+ √11 > 5

Squaring on both sides and using the identity [tex](a+b)^2=a^2+b^2+2ab[/tex],

⇒ 14 + 2√33 > 25

Subtracting 14 from both sides,

⇒ 2√33 > 11

Again squaring,

⇒ 132 > 121

This is a true statement. So our assumption that √3+ √11 is greater than 5 is right.

Therefore, √3+ √11 > 5

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The LCM of 1250 and 525 is 26,250.

The HCF of 1250 and 525 is 5.

The factors of a number is the number that perfectly divides another number. For example, a factor of 30 is 3. A prime number is a number that is perfectly divisible by 1 and itself. An example of a prime number is 3. The highest common factor is the highest factor that is common to two or more numbers.

A multiple is the product of a number and another number. For example, the multiple of 3 is 15. This is because 3 multiplied by 5 is 15. The lowest common multiple is the smallest multiple that is common to two or more numbers.

Prime factors of 1250 = 2 x 5 x 5 x 5 x 5

Prime factors of 525 = 3 x 5 x 7

HCF = 5

LCM = 2 x 3 x  5 x 5 x 5 x 5 x 7 = 26,250

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The scores from least to greatest is -8. -6, 4, 7

The absolute value of the scores from least to greatest is 4, 6, 7, 8

A negative number is a number that is less than zero. Negative numbers are denoted with a minus sign in front of the number. The further away from zero a negative number is, the smaller the number. Examples of negative numbers are -2, -9.

A positive number is a number that is greater than zero. The further away from zero a positive number is, the greater the number. Examples of negative numbers are 2, 9.

The scores from least to greatest is: -8. -6, 4, 7

The absolute value of a number is when the negative signs from the numbers are removed.

The absolute value of the scores from least to greatest is: 4, 6, 7, 8

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Answer:

1.2115/12 times

7=25.179

2.?????????

The cost spent per gallon of the gas is a $4 and the total money spent on gas is a 20$.

According to the statement

We have to find that the cost of the gas he used.

So, For this purpose, we know that the

A cost function may be a mathematical formula wont to wont to chart how production expenses will change at different output levels.

From the given information:

It costs Kobel $3.50 in tolls to drive to figure and back day after day, plus he uses 5 gallons of gas. It costs him a complete of $23.50 to drive to figure and back daily.

Then

Total money he spent = Toll cost + amount of gas she used

$23.50 = $3.50 + 5 gallons

Then

Cost of the 5 gallons = 23.50 - 3.50

Cost of the 5 gallons = 20

Then

cost of the 1 gallon gas = 20/5

cost of the 1 gallon gas = $4.

So, The cost spent per gallon of the gas is a $4 and the total money spent on gas is a 20$.

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The slope can be found as the quotient or rise/run.

Rise - difference of y-coordinates of two points, run - difference of x-coordinates of same two points.

Find the slope using the first two pairs of coordinates in the table:

The y-intercept is the point of intersection of the line with the y-axis.

This point has x = 0 coordinate. On the table we can see the corresponding y- coordinate is  - 2:

The equation of the line is obtained by substituting the values of m and b into slope-intercept form:

The slope is 1/3 and the y-intercept is -2, so the equation is:

y = (1/3)*x - 2

if we use the first two pairs on the table we get:

(-3, -3) and (0, -2)

Then the slope of the linear relation will be:

a = (-2 - (-3))/(0  - (-3)) = (-2 + 3)/3 = 1/3

The slope is 1/3.

We can see that the point (0, -2) is on the table, so the y-intercept is y = -2

How to write the equation?

The linear equation in the slope-intercept form is:

y = a*x + b

Where a is the slope and b is the y-intercept.

Then we will get:

y = (1/3)*x - 2

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