An electric utility worker wants to anchor a guy wire from the top of a 20.4 ​-foot utility pole to a spot that is ​ 8.5 feet from the base of the pole on level ground. How long does the guy wire need to be? Round your answer to one decimal place.

Answer:

x = 140

Step-by-step explanation:

Using the exterior angle rule ( an exterior angle of a triangle is equal to the opposite interior angles of a triangle )

x is the interior angle and the given angles ( 50 and 90 ) are the opposite interior angles

So

x = 50 + 90

50 + 90 = 140

x = 140

Note: there is a right angle ( indicated by the little square. A right angle has a measure of 90 degrees so that's where the 90 came from)

Answer:

Step-by-step explanation:

First we compute \(9^n\), for \(n = 0,1,2,3,4,5\)

\(9^0=1,9^1=9,9^2=81,9^3=729,9^4=6561,9^5=59049\)

We have the unit digit of \(9^n\), is either 1 or 9

Therefore, the conjecture can be state as follows

Conjecture; the unit of digit of \(9^n\), is 1, when n is even and 9 when n is odd

Let the property p(n) be the formula;

"The unit digit of \(9^n\), is 1 when n is even and 9 when n is odd"↔ P(n)

To show p(n) is true , we will use strong mathematical inductive

Show tgat p(0) and p(1) are true

We have  to show the unit digit of \(9^0\) is 1 and \(9^1\) is 9

Since any integer with zero power is one and hence

\(9^0=1\) and \(9^1 = 9\)

Therefore, p(0) and p(1) are true

Show that for al integer \(k\geq 1\), if  p(i) is true for all integer i from o through k, then p(k+1) is also true

let k be any integer with \(k \geq 1\) and suppose that for all integer i with \(0 \leq i \leq \leq k\)

the unit digit of \(9^i\) is 1 when is even and 9 when n is odd

we must show that \(9^{k +1}\) equals 1 when n is even and 9 when n is odd

Case I; (k +1 is odd)

in this case k is even and so, by inductive hypothesis, the unit digit of \(9^k\) is 1 and hence there is some non negative integer q such that

\(9^k = 10q + 1\)

now, \(9^{k+1}=9^k(9)\)

= (10q + 1)9

= 90q + 9

= 10.9q + 9

Note that for any non negative integer q , 9q is also an integer and this implies the unit digit of \(9^{k+1}\) is 9

Case II

(k +1 is even)

in this case k is odd and so, by inductive hypothesis, the unit digit of \(9^k\) is 9 and hence there is some non negative integer q such that

\(9^k=10q+9\)

Now,

\(9^{k+1}=9^k.9\\=(10q+9)9\\=90q+81\\=10(9q+8)+1\)

Note that any non negative integer q, 9q + 8 is also an integer and this implies the unit of \(9^{k+1}\) is 1

Since we have proved both the basis and the inductive step of the strong mathematical induction, we conclude that the given statement is true

Answer:

The two whole numbers that are between the square root of 99 is, 9 and 10.

Step-by-step explanation:

        Because 9 x 9 = 81       and        10 x 10 = 100

             so 91 is between those two numbers.

and the square root of 81 is 9 and the square root of 100 is 10.

Answer:

yes it is

Step-by-step explanation:

90,040/8 is 11222

Answer:

38

Step-by-step explanation:

38+38+38= 114

Answer: C

Step-by-step explanation: The layers of rocks implies superposition and changes in species implies evolution

Each person used the computer for \(\frac{3}{2}\) hours.

A fraction is a number that is a component of a whole. By breaking a whole into a number of parts, it is evaluated. For instance, the symbol for half of a complete number or item is 12. The components of a whole or group of items are represented by fractions. A fraction consists of two components. The numerator is the figure at the top of the line. It details the number of equal portions that were taken from the total or collection. The denominator is the figure that appears below the line. A fractional equation is one in which one or more of its terms have the unknown as their denominator.

Given Data

They worked on their homework for 3 hours, and agreed to share the computer equally for that time.

They share computer equally, so

\(\frac{time}{2}\)

Fraction - \(\frac{3}{2}\)

Each person used the computer for \(\frac{3}{2}\) hours.

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Answer:

-0.33333333333 in other word it o.3 with line over 3

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

Here m = - 13 and (a, b ) = (5, 7 ) , then

y - 7 = - 13(x - 5) → A

Answer:

85

Step-by-step explanation:

Answer:

Decimal: 0.1

Percent: 10%

Step-by-step explanation:

Answer:

0.1 as decimal or 10% as percentage

Answer:

680

Step-by-step explanation:

The number of thousands in the number 680,000 will be 680.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

The expanded form of a number is given by separating the number into its place.

The number is given below.

⇒ 680,000

Write the number 680,000 in the expanded form, then we have

680,000 = six hundred and eighty thousand

The number of thousands in the number 680,000 will be 680.

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LStep-by-step explanation:

(a) To proof this statement choose m = 4 and n = -1, from here we have 2(4) + 7(-1) = 1 as required. Hence th statement is true.

(b) To proof this statement choose m = 1 and n = -1, from here we have 15(1) + 12(-1) = 3 as required. Hence the statement is true.

(c) To proof this statement, suppose m and n are integers, since integers are closed under addition and multiplication then 2m, 4n and 2m + 4n are all integers. Obviously 2m and 4n are even integers, therefore their sum is also an even integer. This contradicts the equation 2m + 4m = 7, hence there do not exist integers m and n that satisfy the statement.

(d) To proof this statement, suppose m and n are integers, then 12m, 15n and 12m + 15n are all integers, since integers are closed under addition and multiplication. Factoring out 3 from the sum, we have: 3(4m + 5n). Therefore 3(4m + 5n) = 1 is a contradiction, because it will give 4m + 5n = 1/3 and addition of two integers can never give a fraction.

(e) To proof this statement, suppose m and n are integers, then 15m + 16n = t can be rewritten as 3(5m) + 8(2n) = t. Since integers are closed under multiplication, then 5m and 2n are integers. Let 5m = r and 2n = s, then we have: 3r + 8s = t as required.

(f) To proof this statement, suppose that m and n are both negative integers, we see that 12m + 15n = 1 is clearly impossible because the sum would be less than 0. Therefore, if there exist integers m and n such that 12m + 15n = 1, then they must be positive.

(g) To proof this statement, suppose m is an integer and has the form 4k + 1 for some integer k, then m + 2 = 4k + 1 + 2 = 4k + 3 = 4k + 4 - 1 = 4(k + 1) - 1. Since k is an integer then k + 1 is an integer because integers are closed under addition. Therefore, put j = k + 1. Hence we have 4j - 1.

(h) suppose that m is odd, then there is an n such that m = 2n + 1, therefore m² = (2n + 1)² = 4n² + 4n + 1 = 4(n² + n) + 1. Here, we need a lemma that says: suppose k is an integer, k(k + 1) is an even integer. This can be proven intuitively, when k is odd, the term in the bracket becomes even, and the whole expression is even. If k is even, then automatically the whole expression becomes even. Hence, our lemma is proven intuitively. This implies that n² + n is an even integer and can be replaced by 2k for some k that is an integer. Therefore, we have 4(2k) + 1 = 8k + 1 as required.

(i) suppose that m and n are odd integers such that mn = 4k - 1 for some k that is an integer. If we assume that neither m nor is in the for 4j - 1, then:

mn = (4a + 1)(4b + 1) for some a and b that are integers. Expanding that we have mn = 4(4ab + a + b) + 1 which is not in the form 4k - 1 for some k that is an integer as assumed. Therefore, if m and n are odd integers such that mn is in the form 4k - 1 for some k that is an integer, then m and n are in the form 4j - 1 for some j that is an integer.

Answer:

x^2

Step-by-step explanation:

1^2=1

2^2=4

3^2=9

Answer: \(6\sqrt{6}\)

Step-by-step explanation:

\(\sqrt{12}=2\sqrt{3}\\\\\sqrt{18}=3\sqrt{2}\\\\\implies \sqrt{12} \sqrt{18}=2\sqrt{3}(3\sqrt{2}=\boxed{6\sqrt{6}}\)

The product of square root of 12 i.e.,√12 and square root of 18 i.e.,√18 is 6√6.

When two numbers has equal power then we can multiply the the numbers and the power remains same. The number in the power is called exponent and the number is called as base. In \(a^m\), \(m\) is the exponent and \(a\) is the base of the number \(a^m\).

Step-by-step explanation:

\(\sqrt{12}\)\(=\sqrt{4}\)×\(\sqrt{3}\)\(=2\)×\(\sqrt{3}\) , since the square root of 4 is 2

\(\sqrt{18}=\sqrt{2}\)×\(\sqrt{9}\)\(=\sqrt{2}\)×\(3\) , since the square root of 9 is 3

Now, \(\sqrt{12} \sqrt{18} = 2\)×\(3\)×\(\sqrt{2}\)×\(\sqrt{3}\) from above.

                       \(=6\sqrt{6}\)

Hence the product of √12 and √18  is √12√18=6√6

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Answer:

6 x a number - 9 = factored

In this case, since the number is not declared as a specific number, this is the key to us factoring.

Like the number could be 6. ↓

Factoring:

\(6*6-9=27\\6*3-9=9\\6*9-9=45\)

bonus even factor:

\(6*2-9=3\)

These are factors and Least common multiples of 6 and 9.

Because 9 and 3 show up during half of the problem, and these are related to 6 and 9, the parents, we could measure this on a mathematical scale that this proves the factors correct.

There are other ways to factor this. See comments.

Mode of the stated data set is 5.

The given data set is;

5, 10, 12, 4, 6, 11, 13, 5.

Arrange the data in increasing order.

4, 5, 5, 6, 10, 11, 12, 13.

The maximum frequency is called mode.

thus,

mode = 5.

Therefore, mode of the given data set is 5.

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The composite function f·g(x) is 4x⁴+24x³.

The given functions are f(x)=x²+6x and g(x)=4x².

We need to find f·g(x).

We know that, f·g(x)=f(x)×g(x)

Here, f·g(x)=(x²+6x)×4x²

= x²×4x²+6x×4x²

= 4x⁴+24x³

Therefore, the composite function f·g(x) is 4x⁴+24x³.

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Answer:

41.93 degrees

Step-by-step explanation:

A ordered pair is a solution to the system if it satisfies all the equations of the system.

We have to check each equation for each pair.

We start with (-9,-6):

As one of the equation is not satisfied, (-9,-6) is not a solution.

For (7,7) we have:

As one of the equation is not satisfied, (7,7) is not a solution.

For (0,-2) we have:

As this equation is satisfied, we test the second equation:

As one of the equations is false, (0,-2) is not a solution.

Now, we test (4,5):

As this equation is satisfied, we test the second equation:

The ordered pair (4,5) is a solution to the system.

Answer:

The only pair that is a solution is (4,5)

Nominal categorical data is a categorical variable with two or more values, with no order. The examples of nominal categorical data here are the issue type, country, city.

Categorical data can be divided as two as per the variables. They are nominal and ordinal. In nominal categorical data, there will be two or more data points, but they are not ranked. The hair color can be red/blond/brown/black etc. But these cannot be ranked by taking one over the other.

In ordinal categorical data, there we can assign an order on the data points. Like grading system in marks of students, size comparison like large, medium, small. Here we could rank these in order.

Year can sometimes be nominal and sometimes ordinal. It is as per the context. If we are using it to calculate time it is ordinal.

So here we could not rank of variables in country, issue type, city. So all are nominal categorical data.

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Answer:

x=4

Step-by-step explanation:

x=4 because when you have 3x+2=14 Subtract 2 from both sides. Then 3x+2−2=14−23x=12. Divide both sides by 3.3x3=123

The value of x in the figure having 3 angles on a line as shown in the image attached below is 28.

The angle is formed by two rays and a common point.

To calculate the value of x using the diagram attached below:

∠AOC+∠COD+∠BOD = 180° because the sum of all the angles on a line is 180°

On substituting the values from the figure,

∠AOC=3x-7

∠COD=55

∠BOD=x+20

∠AOC+∠COD+∠BOD =3x-7+55+x+20

3x-7+55+x+20=180

4x+68=180

4x=112

x=28

Thus, the value of x is 28 for the figure attached below.

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Step-by-step explanation:

the scale factor is 1/1

both triangles are similar, and the scale factor is 1/1

Sukhir should buy life insurance with a coverage amount of at least $898,652.

To get amount of life insurance Sukhir should buy, we need to consider the followings:

Sukhir's total income for 10 years is:

= 12 months x $4,966 x 10 years

= $595,920

We will add to amount needed to pay off the mortgage and other debt. The total amount needed is:

= $595,920 + $198,620 + $4,112

= $798,652

We will now add estimated cost of the children's education. Assuming each child will need $50,000 for their education. The total amount needed is:

= $798,652 + $50,000*2 child

= $798,652 + $100,000

= $898,652.

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-0.8+1.875+100%

1.05+100%

0.1

Answer:

0.00212

Step-by-step explanation:

Option B, 0.212 represents two hundred twelve thousandths.

One of the number types in algebra that has a whole integer and a fractional portion separated by a decimal point is a decimal. The decimal point is the dot that appears between the parts of a whole number and a fraction.

Given a phrase two hundred twelve thousandths,

for the phrase tenth digit is 2,

the hundredth digit is 1 and the thousandth digit is 2

so the digit is 0.212

here 2 is in tenth place, 1 is at the hundredth place and 2 is on thousandth place,

Hence option B is correct.

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Answer:

The surface area of the triangular prism is approximately 16.222 square feet, and the volume of the triangular prism is 12 cubic feet.

Step-by-step explanation:

formulas:

Surface Area = 2B + Ph

Volume = Bh

where B is the area of the triangular base, P is the perimeter of the base, h is the height of the prism, and B and h are both in the same units (inches, feet, etc.).

Given:

Height of the triangular prism = 1 foot

Base of the triangular prism = 6 inches

Height of the triangular base = 4 inches

Length of the other two sides of the triangular base = 5 inches

First, we need to find the area of the triangular base (B):

B = (1/2) x base x height

B = (1/2) x 6 inches x 4 inches

B = 12 square inches

Next, we need to find the perimeter of the triangular base (P):

P = sum of all three sides

P = 6 inches + 5 inches + 5 inches

P = 16 inches

Now, we can use the formulas to find the surface area and volume:

Surface Area = 2B + Ph

Surface Area = 2(12 square inches) + (16 inches)(1 foot)

Surface Area = 24 square inches + 16 square feet

Surface Area = 16.222 square feet (rounded to three decimal places)

Volume = Bh

Volume = 12 square inches x 1 foot

Volume = 12 cubic feet

Therefore, the surface area of the triangular prism is approximately 16.222 square feet, and the volume of the triangular prism is 12 cubic feet.