Draw triangle ABC with vertics at A(1,6), B (1,1) and C (5,1). In this triangle, AB+ BC=AC. Next use the GeoGebra tools to draw triangle DEF such that AB=DE, meausurement of angle E=90 degrees , and EF=BC. Paste a picture of your drawing in the answer box

Answer:

Answer for (a)   -2x^4/3

Answer for (b)  2^5x/4^3x

Answer:

a. [tex]-2x\sqrt[3]{x}[/tex]

b. [tex]\frac{1}{2^x}[/tex]

Step-by-step explanation:

a.

Original equation:

[tex]\frac{(-x)^4}{4x}*\frac{8(-x)^{-3}}{x^{-\frac{4}{3}}}[/tex]

So (-x)^4 can be seen as (-x * -x) * (-x * -x), which becomes x^2 * x^2 = x^4, the negatives cancel out of the degree is even. So it becomes:

[tex]\frac{x^4}{4x}*\frac{8(-x)^{-3}}{x^{-\frac{4}{3}}}[/tex]

Cancel out one of the x's on the left fraction:

[tex]\frac{x^3}{4}*\frac{8(-x)^{-3}}{x^{-\frac{4}{3}}}[/tex]

Rewrite the exponent in the numerator: [tex]a^{-x} = \frac{1}{a^x}[/tex]

[tex]\frac{x^3}{4}*\frac{8*\frac{1}{-x^3}}{x^{-\frac{4}{3}}}[/tex]

Simplify the numerator:

[tex]\frac{x^3}{4}*\frac{\frac{8}{-x^3}}{x^{-\frac{4}{3}}}[/tex]

Keep numerator, change division to multiplication, flip the denominator:

[tex]\frac{x^3}{4}*\frac{8}{-x^3} * \frac{1}{x^{-\frac{4}{3}}}[/tex]

multiply the denominator using the exponent identity: [tex]x^a*x^b=x^{a+b}[/tex]

[tex]\frac{x^3}{4}*\frac{8}{-x^{\frac{5}{3}}}[/tex]

Multiply the numerators and denominators:

[tex]\frac{8x^3}{-4x^{\frac{5}{3}}}[/tex]

Use the fact that: [tex]\frac{x^a}{x^b}=x^{a-b}[/tex] to divide the x^3 and x^(5/3) and divide the 4 by the -8

[tex]-2x^{\frac{4}{3}}[/tex]

Rewrite the exponent using the exponent identity: [tex]x^{\frac{a}{b}} = \sqrt[b]{x^a}=\sqrt[b]{x}^a[/tex]

[tex]-2\sqrt[3]{x^4}[/tex]

Rewrite as two radicals: [tex]\sqrt[n]{a} * \sqrt[n]{b} = \sqrt[n]{ab}[/tex]

[tex]-2\sqrt[3]{x^3} * \sqrt[3]{x}[/tex]

Simplify:

[tex]-2x\sqrt[3]{x}[/tex]

b.

[tex]2^{2x}\div4^{3x}*64^{\frac{x}{2}}[/tex]

Rewrite the 4 as 2^2

[tex]2^{2x}\div(2^2)^{3x}*64^{\frac{x}{2}}[/tex]

Use the exponent identity: [tex](x^a)^b=x^{ab}[/tex]

[tex]2^{2x}\div2^{6x}}*64^{\frac{x}{2}}[/tex]

Use the exponent identity: [tex]\frac{x^a}{x^b}=x^{a-b}[/tex]

[tex]2^{2x-6x} = 2^{-4x}[/tex]

Rewrite this part using the definition of a negative exponent: [tex](\frac{a}{b})^{-x} = \frac{b}{a^x}[/tex].

[tex]\frac{1}{2^{4x}} * 64^{\frac{x}{2}}[/tex]

Multiply:

[tex]\frac{64^{\frac{x}{2}}}{2^{4x}}[/tex]

rewrite 64 as 2^6

[tex]\frac{(2^6)^{\frac{x}{2}}}{2^{4x}}[/tex]

Use the identity: [tex](x^a)^b=x^{ab}[/tex]

[tex]\frac{2^{3x}}{2^{4x}}[/tex]

Use the identity: [tex]\frac{x^a}{x^b}=x^{a-b}[/tex]

[tex]2^{-x}[/tex]

rewrite using the definition of a negative exponent: [tex](\frac{a}{b})^{-x} = \frac{b}{a^x}[/tex]

[tex]\frac{1}{2^x}[/tex]

The difference for both the rhombus and square are as follows;

Therefore, the difference for both the shapes(square and rhombus)are as follows:

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Answer:

680

Step-by-step explanation:

14(-6x +10) - 16x - 100x + 140 for x = -2.

14(-6(-2) + 10) - 16(-2) - 100(-2) + 140

14(12 + 10) + 32 + 200 + 140

14(22) + 372

308 + 372

680

Answer:

Proof below

Step-by-step explanation:

A number, p, is divisible by another number, d, if and only if there is some non-negative integer, n, such that n*d=p.

To prove that, 300 is divisible by 10 because, 30 is a non-negative integer, and 10*30=300.

Strategies for Divisibility by a composite number

Note that in the previous example, 10 is a composite number.  This means that both one 2 and one 5 (the full list of 10s factors) had to be factored out of the 300.

In the given problem, we are to prove that the number is divisible by 14.  Observe 14 is composite with factors of 2 and 7.

Since the expression is given with exponents, it will be helpful to recall a few exponent properties to algebraically manipulate the expression.

Recall the following property of exponents:

Original expression...

[tex]8^{10}-2^{27}[/tex]

Recognizing 8 as a power of 2...

[tex](2^3)^{10}-2^{27}[/tex]

Simplifying and rewriting so that both terms are powers of 2...

[tex]2^{30}-2^{27}[/tex]

Observing that both terms have 27 twos as factors...

[tex]2^{27}*2^{3}-2^{27}[/tex]

Factoring out 27 twos...

[tex]2^{27}*(2^{3}-1)[/tex]

Simplifying the expression in the parenthesis:

[tex]2^{27}*(8-1)[/tex]

[tex]2^{27}*(7)[/tex]

Knowing that we also need a factor of 2, use properties of exponents, and associative property of multiplication...

[tex](2^{26}*2^1)*7[/tex]

[tex]2^{26}*(2^1*7)[/tex]

[tex]2^{26}*(2*7)[/tex]

[tex]2^{26}*14[/tex]

Since 2^26 is a non-negative integer, the original expression is divisible by 14.

Answer:

y = 5

Step-by-step explanation:

Step-by-step explanation:

the slope of a line is the ratio "y coordinate change / x coordinate change" when going from one point on the line to another.

when the slope is 0, it means the y coordinate change is 0 for all points. that means y is a constant. and the line is a horizontal line.

to go through (-2, 5) this constant y has to be the y value of the point.

so,

y = 5

that's it. that is the whole equation for that line, because the slope m is 0. what remains is the y-axis intercept (y = 5).

Answer:

X=11

Step-by-step explanation:

Answer:

$17578.13

Step-by-step explanation:

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Answer:

Step-by-step explanation:

Find the price increase in number:

Find the percent increase, relevant to initial price:

Answer:

[tex]\huge\boxed{\sf (f+g)(x) = 4x - 1}[/tex]

Step-by-step explanation:

Add both functions

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

Combine like terms

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

(f+g)(x) = 4x - 1

[tex]\rule[225]{225}{2}[/tex]

Answer:

[tex](f+g)(x)=4x-1[/tex]

Step-by-step explanation:

Functions written in equation form usually have several parts:

So, for instance, [tex]g(x)=x+1[/tex] has a name of "g", has an input of "x", and has a rule that it adds 1 to the input to get the output.

The name of the function should tell what rule to follow (look for the equation with that function name), or it may give some details on what the function does.

Dealing with so many different problems, functions often get a default name of "f", "g", or "h".  

If a function is special and/or used commonly, it will sometimes get a special name (like the natural logarithm function "ln").

In this case, the function is (f+g)(x).  The function name means that the result of each function, f and g, will be added together, while using the same input "x" for both functions.

[tex](f+g)(x)=f(x)+g(x)\\=(3x-2)+(x+1)\\=3x+(-2)+x+1\\=4x+(-1)\\=4x-1[/tex]

So, given these two functions for "f" and "g",  [tex](f+g)(x)=4x-1[/tex]

The complete equation of the polynomial is 2x(x^2 - 11x) + 10x^3 = 3x(4x^2 - 7x) - x^2

The equation is given as:

_x(x^2 - _x) + _x^3 = _x(_x^2 + _x) - x^2

Complete the blanks using alphabets

ax(x^2 - bx) + cx^3 = dx(ex^2 + fx) - x^2

Open the brackets

ax^3 - abx^2 + cx^3 = dex^3 + dfx^2- x^2

Factorize the expression

(a + c)x^3 - abx^2 = dex^3 + (df - 1)x^2

By comparison, we have:

a + c = de

-ab = df - 1

Rewrite the second equation as:

ab + df = 1

So, we have:

a + c = de

ab + df = 1

Set a = 2 and c = 10.

So, we have:

a + c = de ⇒ de = 2 + 10 ⇒ de = 12

ab + df = 1 ⇒2b + df = 1

Express 12 as 3 * 4 in de = 12

de = 3 * 4

By comparison, we have:

d = 3 and e = 4

So, we have:

2b + df = 1

This gives

2b + 3f = 1

Set b = 11.

So, we have:

2 * 11 + 3f = 1

This gives

22 + 3f = 1

Subtract 22 from both sides

3f = -21

Divide by 3

f = -7

Hence, the complete equation is:

2x(x^2 - 11x) + 10x^3 = 3x(4x^2 - 7x) - x^2

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Answer:

The given relation {(5,2),(6,1),(6,2),(4,8)} is not a function.

Step-by-step explanation:

The relation {(5,2),(6,1),(6,2),(4,8)} is given.

It is required to determine whether the given relation is a function.

To determine whether the given function is a relation, identify the domain and range and then check whether the given relation is a function.

Step 1 of 1

The given relation is {(5,2),(6,1),(6,2),(4,8)}.

The set of the first components of each ordered pair is called the domain.

From the relation, the domain is {5,6,6,4}.

The set of the second components of each ordered pair is called the range.

From the relation, the range is {2,1,2,8}.

The domain of the function does not have a unique range. So, the given relation is not a function.

Answer:

785 Remainder 5

Step-by-step explanation:

Answer:

its 1/2 and 8

Step-by-step explanation:

got it right

The graph which represents the relationship between the year and the computers value is; Choice A.

According to the task content, it follows that the computer loses 1/3 of its value every year. Hence, it follows that the value of the computer each year is 2/3 of its previous value.

Hence, the relationship can best be modelled by an exponential function, a decay function to be more specific and can best be represented by Choice A.

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Answer:

[tex]\frac{1}{8}[/tex]

Step-by-step explanation:

2 ( [tex]\frac{1}{4}[/tex] )²

= 2 × [tex]\frac{1}{16}[/tex] ← cancel 2 and 16 by 2

= 1 × [tex]\frac{1}{8}[/tex]

= [tex]\frac{1}{8}[/tex]

Answer:

c is 1

o is q

h is 2

in ch3

c is 2 h is 3

and finally o is 1

Step-by-step explanation:

a11 = 4 × a2

a + 10d = 4 × (a + d)

a + 10d - 4d = 4a

a + 6d = 4a

6d = 4a - a

6d = 3a

(6/3)d = a

2d = a ----- eq. 1

now, sum of 7 terms = s7 = 175

7/2 {2a+6d} = 175

7/2 { (2 × 2d ) + 6d} = 175

7 ( 4d + 6d ) = 175 × 2

7 ( 10d ) = 350

70d = 350

d = 350/70

d = 5

Now from eq. 1,

2d = a

2(5) = a

a = 10, d = 5

THANK YOU........

Answer:

[tex]\huge\boxed{\sf \pm 10i}[/tex]

Step-by-step explanation:

[tex]\pm \sqrt{-100}[/tex]

We can write it as:

[tex]\pm \sqrt{-1 \times 100} \\\\\pm \sqrt{-1} \times \sqrt{100} \\\\\underline{We \ know \ that:}\ i =\sqrt{-1} \\\\\pm i \times 10\\\\\boxed{\pm 10i}\\\\\rule[225]{225}{2}[/tex]

The wholesale cost of the bike is 95.

Wholesale price is the price charged for a product as sold in bulk to large trade or distributor groups as opposed to what is charged to consumers.

The selling price is how much a buyer pays for a product or service.

The profit formula is used to calculate the amount of gain that has been made in a transaction

Profit = Selling Price (S.P.) - Cost Price (C.P.)(here it is the wholesale price)

Given =  

Substituting it in the profit formula we get

0.3 x wholesale price = 123.50 + wholesale price

1.3 x wholesale price = 123.50

Wholesale price = [tex]\frac{123.50}{1.3}[/tex] = 95

Thus the wholesale cost of the bike is 95.

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The smallest positive integer n for which n^2 is divisible by 18 and n^3 is divisible by 640 is 120

The modulo (or "modulus" or "mod") is the remainder after dividing one number by another.

The smallest integer is 120, since:

[tex]120^{2}[/tex] mod 18 = 0, (reminder after dividing [tex]120^{2}[/tex] by 18 is 0) and

[tex]120^{3}[/tex] mod 640 = 0 (reminder after dividing [tex]120^{3}[/tex] by 18 is 0)

Hence, The smallest positive integer n for which n^2 is divisible by 18 and n^3 is divisible by 640 is 120.

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The perimeter of each region is 12 + 1.5π if a circle with an area of 36π is divided into 8 congruent regions

An equation is an expression that shows the relationship between two or more numbers and variables.

Let r represent the area of the circle, hence:

Area = πr²

36π = πr²

r = 6 units

Perimeter = 2πr = 2π(6) = 12π

The circle has 8 congruent regions, hence:

Perimeter of each region = 6 + 6 + 12π/8 = 12 + 1.5π

The perimeter of each region is 12 + 1.5π if a circle with an area of 36π is divided into 8 congruent regions

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Answer:

x = i, -i

Explanation:

p(x) = x² + 1

To set a polynomial to zero, p(x) = 0.

⇒ x² + 1 = 0

relocate variable

⇒ x² = -1

square root both sides

⇒ x = ±√-1

breakdown

⇒ x = √-1, -√-1

simplify if x = √-a then √a i

⇒ x = i, -i

Answer:

+i , -i

Step-by-step explanation:

   p(x) =0

x² + 1 = 0

      x² = -1

     Take square root both sides,

      [tex]\sf x = \sqrt{-1}\\\\x =\sqrt{i^2}\\[/tex]

     x = ± i

Zeros of the polynomial:

   x = +i , -i

Answer:

C. Infinitely many

Step-by-step explanation:

First, find x.

3(x-2)=22-x

Use distributive property.

3x-6=22-x

Add x to both sides.

4x-6=22

Add 6 to both sides.

4x=28

Divide 4 from both sides.

x=7

Plug in 7 for x into the original equation.

3(7-2)=22-7

3(5)=22-7

15=15

Since 15 does equal 15, the answer has infinitely many solutions.

Hope this helps!

If not, I am sorry.

Pak Hamid has worked more than 15 years. The correct premise and conclusion is B.

Determining the proper option, acquiring evidence, and exploring various options are all steps in the decision-making process.

Premise: The 20 numbers that were randomly chosen from a box that contains 25 cards labeled with prime numbers of less than 100 are odd numbers.

Conclusion: All prime numbers are odd numbers.

Both premise and conclusion are incorrect because 2 is an even prime number.

Premise 1: All the employees that have worked at least 15 years and above in Syarikat LMN will receive the excellent service rewards.

Premise 2: Pak Hamid has worked in the LMN Company for 23 years.

Conclusion: Pak Hamid will be awarded an excellent service.

Both premise and conclusion are correct. Because Pak Hamid has worked more than 15 years.

Premise: Faisal had consecutively scored 'A' for his Mathematics subject for the last three examinations.

Conclusion: Faizal will also score 'A' during the next term examination.​

The conclusion is incorrect because all the exams are independent to each other.

Then the correct premise and conclusion is B.

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Answer:

25

Step-by-step explanation:

sin © =36/(35+x)=21/35

36/(35+x)=21/35

x=(36*35/21)-35

x=25

Step-by-step explanation:

SOLUTION::

please watch the image for explanation

Answer:

The solution of the given set in interval form is [tex]$(-\infty,-4] \cup[12, \infty)$[/tex].

Step-by-step explanation:

It is given in the question an inequality as [tex]$|x-4| \geq 8$[/tex].

It is required to determine the solution of the inequality.

To determine the solution of the inequality, solve the inequality [tex]$x-4 \geq 8$[/tex] and, [tex]$x-4 \leq-8$[/tex]

Step 1 of 2

Solve the inequality [tex]$x-4 \geq 8$[/tex]

[tex]$$\begin{aligned}&x-4 \geq 8 \\&x-4+4 \geq 8+4 \\&x \geq 12\end{aligned}$$[/tex]

Solve the inequality [tex]$x-4 \leq-8$[/tex].

[tex]$$\begin{aligned}&x-4 \leq-8 \\&x-4+4 \leq-8+4 \\&x \leq-4\end{aligned}$$[/tex]

Step 2 of 2

The common solution from the above two solutions is x less than -4 and [tex]$x \geq 12$[/tex].

The solution set in terms of interval is [tex]$(-\infty,-4] \cup[12, \infty)$[/tex].

Answer:

Sophie.

Step-by-step explanation:

15. 30 in Italian minus 15 in German.

Answer:

Hey! I am gona help you.

BC ≅ EF

DE ≅ AB

Angle C ≅ Angle F

Angle D ≅ Angle A

Hope it might help!

2,3 can't be solved as there is no figure given here.

Answer:

35

Step-by-step explanation:

2x9+12+5=35

The given study is observational study

To gauge how strongly two variables are related to one another, correlation coefficients are used.

A statistical indicator of the strength of the association between the relative movements of two variables is the correlation coefficient. The values are in the -1.0 to 1.0 range. There was a measurement error in the correlation if the estimated value was larger than 1.0 or lower than -1.0. Perfect negative correlation is shown by a correlation of -1.0, and perfect positive correlation is shown by a correlation of 1.0. A correlation of 0.0 indicates that there is no linear link between the two variables' movements. Finance and investing can benefit from the usage of correlation statistics.

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