Use Pythagoras' theorem to work out the height of the equilateral
triangle below.
Give your answer in centimetres (cm) to 1 d.p.
N
10 cm
allowed
M
10 cm
10 cm

[tex]3^x=(-27)^{-6} \\ \\ 3^x=(-3^3)^{-6} \\ \\ 3^x=(3^3)^{-6} \\ \\ 3^x=3^{-18} \\ \\ \boxed{x=-18}[/tex]

Answer:

8x4=32

Step-by-step explanation:

I hope I helped you

Hi,

I hope you and your family are doing well!

An angle is coterminal with another angle if it has the same terminal side as the other angle, but may have a different degree measure. In other words, coterminal angles are angles that are measured around the same point on the unit circle, but may start at different points.

To find the angle between 0 and 2π in radians that is coterminal with the angle -25π/6, we can add or subtract multiples of 2π to -25π/6 until we get an angle between 0 and 2π.

For example, adding 2π to -25π/6 gives us:

-25π/6 + 2π = -π/6 + 2π = 7π/6

This angle is between 0 and 2π, so it is coterminal with -25π/6.

Alternatively, subtracting 4π from -25π/6 gives us:

-25π/6 - 4π = -29π/6 = -π/2

This angle is also between 0 and 2π, so it is coterminal with -25π/6.

Therefore, the angle between 0 and 2π in radians that is coterminal with -25π/6 is either 7π/6 or -π/2.

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The value equivalent to   [tex](64)^{1/4}[/tex] is [tex]2\sqrt[4]{4}[/tex].

An expression or mathematical expression is a finite arrangement of symbols that are well-formed in line with context-dependent criteria. To help define the logical grammar and order of operations, mathematical symbols can be used to represent variables, operations, functions, brackets, punctuation, and grouping.

A formula and an expression are often distinguished by authors, with the former designating a mathematical entity and the latter a statement about such a thing.

But in contemporary mathematics, and particularly in computer algebra, formulas are seen as expressions that can be evaluated as true or false, depending on the values given to the variables present in the expressions.

Given expression is  [tex](64)^{1/4}[/tex]

The number 64 can be written as 2 × 2 × 2 × 2 × 2× 2 =2⁶

So, the above given expression becomes,

[tex](64)^{1/4}[/tex]=[tex](2^{6}) ^{1/4}[/tex]

2⁶=2⁴.2²

So,

[tex](2^{6}) ^{1/4}[/tex]=[tex](2^{4} 2^{2})^{1/4}[/tex]

By simplifying we get,

[tex](64)^{1/4}[/tex]=[tex]2\sqrt[4]{4}[/tex]

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The median cost of the market research surveys is $900 so option (a) is correct.

Mode is the highest frequency number while the median is the middle value of a data set after writing in either an increasing or decreasing manner.

As per the given surveys,

Survey 1: $725 Survey 2: $850, Survey 3: $1,250, Survey 4: $1,350, Survey 5: $900.

Write the surveys in the increasing format as

$175,$850,$900,$1250,$1350

The median will be the middle value thus $900 will be correct.

Hence "The median price of the surveys for market research is $900".

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The optimal binary search tree for the given frequency is attached below.

Binary search tree:

Binary search tree refers the value of left node must be smaller than the parent node, and the value of right node must be greater than the parent node.

Given,

Here we have to plot  the optimal binary search tree for the following words, where the frequency of occurrence is in parentheses: a (0.18), and (0.19), I (0.23), it (0.21), or (0.19).

In order to plot the binary search tree, we have to do the following steps,

Then we get the binary search tree like the following.

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A linearization at a suitably chosen integer near a at which the given function and its derivative are easy to evaluate is L(x)=-6 -4x .

What is function ?

A function is a type of rule that produces one output for a single input. Source of the image: Alex Federspiel. This is illustrated by the equation y=x2. Any input for x results in a single output for y. Considering that x is the input value, we would state that y is a function of x.

Nearest integer is x =-1

Centre of linearization as x =-1

f(x)=3x2 +2x -3

f(-1)=3(-1)2 +2(-1) -3

f(-1)=-2

f(x)=3x2 +2x -3

f '(x)=6x +2

f '(-1)=6(-1) +2

f '(-1)= -4

L(x)=f(-1) + f '(-1) (x-(-1))

L(x)=-2 -4(x+1)

L(x)=-2 -4x -4

L(x)=-6 -4x

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a. Using linear equations in one variable we get the number of songs at which both companies would charge the same amount is 100 songs.

b. Company B would be a better choice as the total charges for 150 songs would be $127.5.

Explain linear equations in one variable.

A straight line with only one variable is a linear equation. the single variable's power is 1. Simple algebraic methods are used to solve these equations, which have the form ax+b=0.

a) Assume the number of songs downloaded is 'x'.

Now according to the question,

Total charges by company A is 15+0.75x

Total charges by company B is 0.90x

For equal charges, both must be equal,

Hence equating the 2 expressions we get,

15+0.75x=0.90x

15=0.15x

x=100

Hence total number of songs to reach the charge of the same amount is 100.

b)Let us take 150 songs from company A, we get the total charge to be

15+0.75*150=$127.5

Taking for company B, we get

0.90*150=$135.

We see that for 150 songs, the charges of company A is less compared to company B. Therefore I would choose company B over company A.

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Answer:

Step-by-step explanation:

First, you will multiply 2 times 4,374 and get 8,748 then you will divide 8748 by 7 which is a week, and get 1249.7 then you will divide it by 356 which is a year approximate, and get 10.51 days.

Answer:

x=1   y=6

Step-by-step explanation:

???

Answer:

Where, if anywhere, does h(x) = m(x) when h(x) = (x+2)^2-9 and m(x) = x-10

wut do i have to find

Step-by-step explanation:

Answer:

4/5

Step-by-step explanation:

5/6q-1/3q=2/5

We change the coefficient’s denominators to 6 so we can subtract them

5/6q-2/6q=2/5

3/6q=2/5

1/2q=2/5

Now divide both sides by 1/2 or multiply both sides by 2

1/2q=2/5

/1/2.  /1/2

q=2/5/1/2

q=2/5*2/1

q=4/5

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It's a right angle as 13² is the addition of 5² and 12².

A right triangle or right-angled triangle, or more formally an orthogonal triangle, formerly known as a rectangled triangle, is a triangle with one right angle, i.e. two perpendicular sides. Trigonometry is founded on the relationship between the sides and other angles of a right triangle.

In this case, the values given are 5, 12 and 13. This will be illustrated thus:

5² + 12² = 13²

25 + 144 = 169

169 = 169

This was done based on Pythagoras theorem.

Therefore, it's a right angle.

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Answer:

x>9

Step-by-step explanation:

2x-5>13

2x>13+5

2x>18

x>18/2

x>9

Answer:

x > 9

Step-by-step explanation:

To find the solution to this inequality we need to follow these steps:

2x - 5 > 13

2x > 18 (-5 will be eliminated by +5 on the left side while 13 will be 18 when 5 added to it)

x > 9

Answer:

The answer is 62 and 86

Step-by-step explanation:

Mean

(50 + 70 + 58 + 62 + 66 + 53 + 76) ÷ 7

435/7 = 62.1 ≈ 62

Variance

(50 - 62)² + (70 - 62)² + (58 - 62)² + (62 - 62)² + (66 - 62)² + (53 - 62)² + (76 - 62)²

(144 + 64 + 16 + 0 + 16 + 81 + 196)/(7 - 1)

517/6 = 86

Thus, The mean of the given data is 62 and Variance is 86

Answer:

1.25 es la respuesta

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given:

Each picture costs $7.50

One time shipping cost = $3.25

Total cost of the order = $85.75

To FInd:

An equation to determine the number of pictures ordered.

Solution:

Define x:

Let x be the number of pictures bought.

Let y be the total amount of money collected.

Form the equation:

The $3.25 one time shipping cost is a fixed cost.

The $7.50 is a variable cost depending on the number of pictures ordered.

Therefore the equation:

⇒ y = 3.25 + 7.5x

Find the number of pictures bought.

The total cost is $85.75

3.25 + 7.5x = 85.75

7.5x = 82.50

x = 11

Answer: The equation is y = 3.25 + 7.5x and Todd bought 11 pictures.

The upper and lower sums for f(x) = 1 + cos - SXST, with n = 3, 4, and 6 is 10.1913798 and 10.19913798.

What is upper and lower sums?

Using rectangles that are both enscribed in and circumscribed by a curve, we may approximate the area under a curve. The total area of the rectangles that are inscribed is the lower sum, while the total area of the rectangles that are circumscribed is the higher sum.

[tex]$n=6: \quad \Delta x=\frac{2 \pi}{6}$[/tex]

[tex]\begin{aligned}& \text { Lower sum }=\frac{2 \pi}{6}\left[f(-\overline{4})+f\left(-\frac{2 \pi}{3}\right)+f\left(-\frac{\pi}{3}\right)+f(0)+f\left(\frac{\pi}{3}\right)+f\left(\frac{2 \pi}{3}\right)\right] \\& c_6=\frac{2 \pi}{6}[1+1.5+1.8660256+2+1.8660254+1.5] \\& c_6=10.1913798\end{aligned}[/tex]

upper sum:

[tex]\begin{aligned}& =\frac{2 \pi}{6}\left[f\left(-\frac{2 \pi}{3}\right)+f\left(-\frac{\pi}{3}\right)+f(0)+f\left(\frac{\pi}{3}\right)+f\left(\frac{2 \pi}{3}\right)+f(\pi)\right] \\R_6 & =\frac{2 \pi}{6}[1.5+1.8660254+2+1.8660254+1.5+1] \\R_6 & =10.1913798]\end{aligned}[/tex]

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By using the concept of factorization and compound interest, it can be calculated that-

1a) f(2) = 0

 b) f(x) = (x - 2)(x + 6)(x + 3)

2)   Miguel must initially invest 497118.23

What is factorization and compound interest?

Factorization is the reduction of an algebraic expression into two or more algebraic expressions of smaller degree

If the interest on a certain principal at a certain rate over a certain period of time increases exponentially rather than linearly, the interest earned is called compound interest.

1) a) f(x) = x³+7 x²-36

      f(2) =  2³+7(2)²-36

      f(2) = 36 - 36 = 0

  b) Since f(2) = 0, (x - 2) is a factor of f(x)

      f(x) =  x²(x - 2) + 9x(x - 2) + 18(x - 2)

      f(x) = (x - 2)(x² + 9x + 18)

      f(x) = (x - 2)(x² + 6x + 3x + 18)

      f(x) = (x - 2){x(x + 6) + 3(x + 6)}

      f(x) = (x - 2)(x + 6)(x + 3)

  c) Let the principal be $p

      Rate = 3%

      Time = 4 years

      [tex]560000 = p(1 + \frac{3}{200})^{4 \times 2}\\\\560000 = p(\frac{203}{200})^8\\\\\\p = 560000 \times (\frac{200}{203})^8\\\\p = 497118.23[/tex]

      Miguel must initially invest 497118.23

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Answer:

(23x+4.2)

Step-by-step explanation:

If P is the minimum number of tests to achieve full statement coverage for f(x) and Q is the minimum number of tests to achieve full branch coverage for f(x), then (P,Q) =(3, 4)

Branch coverage: During program testing, every branch in a statement must be run at least once.

Coverage of the statement:

This means that during testing, every statement in the computer code must be run at least once.

All of the statements must be executed in order to obtain complete statement coverage.

Statement coverage is calculated as (statement executions divided by total statement executions).

To obtain complete statement coverage in the code above, two test cases are necessary.

Case 1: If the if condition is satisfied,

{

int res=0;

if(m<0) {res=n-m;}

return res;

}

These commands will be carried out.

Case 2: All remaining statements will also be put into effect when the other two cases of else do. Full statement coverage is attained after three tests.

Branch coverage: It includes both true and false situations and is decision-based.

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Using trigonometric relations we will see that:

a =  5*√3

b = 5

The correct option is the one you marked.

For a right triangle with a known hypotenuse H and a known angle x, we can use the trigonometric relations:

cos(x)= (adjacent cathetus)/h

sin(x) = (opposite cathetus)/h

Here the hypotenuse measures 10 units, and the known angle is x = 30°.

The adjacent cathetus to that angle is a, so we can write:

cos(30°) = a/10

a = cos(30°)*10  = 10*√3/2 = 5*√3

And b is the opposite cathetus:

sin(30°) = b/10

b = 10*sin(30°) = 5

Then the correct option is the one you marked.

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(a) Minimum payment to be paid is $22

(b) Minimum payment to be paid is $35

Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan.The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest. Although some mortgages employ this calculation approach, this kind of interest typically relates to auto loans or short-term loans.

The formula for simple interest is:

Simple Interest=P×R×T

where:

P=Principal Amount

R=Daily interest rate

T=Number of days between payments​

(a)The minimum monthly payment is calculated by taking 1.5 percent of the outstanding principle

(0.015) ×$ (677+452+139+141) = $21.135

as there is no additional interest due.

The minimum monthly payment required on December 1 is $22, rounded up to the nearest whole dollar.

(b) The minimum monthly payment will be equal to 1.5 percent of the outstanding principle plus the new interest charges.

We will apply the simple interest formula, S.I = p×r×t, to get his new interest costs.

Because Dec contains 31 days, the

Principle amount, p = (677+452+139+141) - 300 = 1109,

the rate, r = 0.05163% each day

Time, t = 31 days.

S.I =p×r×t=1109×0.0005163×31= $17.75

0.015×1109 = 16.64, which is 1.5 percent of the outstanding amount.

To reach $17.75 + $16.64 = $34.39, we must now add the additional interest to 1.5 percent of the outstanding principal.

The minimum monthly payment required on January 1 is $35, rounded up to the next whole dollar.

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The equation of the line that passes through the point (3,4) and has an undefined slope is y = 3

An undefined slope is an infinite slope. This is the slope of a vertical line. The x values never changes no matter the changes in the y values.

The equation of a line in slope intercept form can be represented as follows:

y = mx + c

where

m = slope

c = y-intercept

Since the slope, m is undefined, the expression that has an undefined slope is a vertical line

Therefore,

y = 3

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Answer:

B. x = 0 and x = 5

Step-by-step explanation:

The zeros of this function are x = 0 and x=5

_________________

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In 11.61 years the given principal amount of $ 900 will be double.

Compound interest is interest charged on a loan and is determined by both the principal amount and the rate of interest compounding per year.

The formula for the Amount when compound interest is calculated is given by

P = Principal amount

r = Rate of interest

n = Number of compounds

t = Time period in years

Here from the given data,

Principal amount = $ 900

Rate of interest = 6% = 6/100 = 0.06

Number of compounds = 12    [ ∵ compounded monthly]

Here we need to find the time period

Assume that after 't' years the amount will be doubled

From the given data and formula,

Amount, A = 900(1+0.06/12)^12t        

= 900(1+0.06/12)^12t

= 900(1 + 0.005)^12t

= 900 (1.005)^12t  

As we assumed after 't' years the amount is double

=> 900 (1.005)^12t  = 2 × 900

=> (1.005)^12t  = 2    

Applying log on both sides

=> log (1.005)^12t  = log 2

=> 12t log(1.005) = log 2

=> 12t = log 2/log(1.005)

[ we can use a calculator for log (1.005) and log 2]

=> 12t = 0.30108/ 0.00216  

=> 12t = 139.888

=>  t =  11.61

Therefore,

In 11.61 years the given principal amount of $ 900 will be double.

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The roots of the quadratic equation 3y² + 3(4y² - 2) is ± √(1/7).

A quadratic equation is an algebraic expression in the form of variables and constants.

A quadratic equation has two roots as its degree is two.

Given, 3y² + 3(4y² - 2).

3y² + 12y² - 2.

14y² - 2.

Let 14y² - 2 = 0.

14y² = 2.

y² = (2/14).

y = ± √(2/14) Or ± √(2/2×7) Or ± √(1/7).

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By using the concept of algebraic expression, it can be calculated that

The number that makes the expressions equivalent is -0.7

What is algebraic expression?

Algebraic expression consist of variables and numbers connected with addition, subtraction, multiplication and division.

The given algebraic expression is

−1.1−1.4m + 0.4

On simplifying −1.1−1.4m + 0.4

−1.1−1.4m + 0.4

-0.7 - 1.4m

So the number that makes the expressions equivalent is -0.7

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The expression that is a factor of the polynomial x³ + 2x² - 9x - 18 is (x + 2).

Factoring of a polynomial is the method of breaking the polynomial into a product of its factors.

For example x² - 4 can be broken as (x - 2) and (x + 2).

Therefore, the expression that factor the polynomial x³ + 2x² - 9x - 18 is as follows:

Therefore,

x³ + 2x² - 9x - 18 = (x - 3)(x² + 5x + 6)

Let's break (x² + 5x + 6) down

x² + 5x + 6

x² + 2x + 3x + 6

x(x + 2) + 3(x + 2)

(x + 3)(x + 2)

Therefore, the factors are (x + 3)(x + 2) and (x - 3)

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Answer:

The answer is C, (x+2).