Point N is the midpoint of FG. If FN = 2x, what expression represents FG?

the angles are the same as their pair

the pairs are

1 and 5

2 and 6

4 and 8

3 and 7

Answer:

a=25

b=40

Step-by-step explanation:

We can get two equations from these statements

1.a+b=65

2.a<b

therefore 2a=10+b

and 2a-10=b

substitute into original equation

a+(2a-10)=65

3a=75

a=25

b=65-25

=40

Answer:

$30.75

Step-by-step explanation:

Since the sale was 20% off, the tennis racket is 80% of its original price.

[tex].8p = 24.60[/tex]

[tex]p = 30.75[/tex]

The final answer in scientific notation is 4 × 10⁰.

Firstly writing both dividend and divisor in scientific notation.

Dividend = 32 × 10⁻²²

Divisor = 8 × 10⁻²²

Now  performing division to find the quotient.

Quotient = Dividend ÷ Divisor

Quotient = 32 × 10⁻²² ÷ 8 × 10⁻²²

As per the known rule of exponents, aˣ ÷ aⁿ = aˣ⁻ⁿ

Quotient = (32 ÷ 8) × 10⁻²² ⁻ ⁽⁻²²⁾

Dividing the base numbers

Quotient = 4 × 10⁻²²⁺²²

Performing subtraction on exponents

Quotient = 4 × 10⁰

Also, as per the known fact, a⁰ = 1. So, the final answer is 4 and in scientific notation the final answer is 4 × 10⁰.

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Common ratio= 1/2, Next two term= 1/16, 1/32

This is a geometric sequence since there is a common ratio between each term.

i.e.,

the common ratio (r) = [tex]\frac{1/2}{1}[/tex] = [tex]\frac{1/4}{1/2}[/tex]

                                  = 1/2

We can write the formula for general term of the series as

[tex]a_{n}[/tex] = a[tex](\frac{1}{2})^{n-1}[/tex]

If the further sequence does continue in the same way then the whole infinite sequence indicated is a geometric series.

So we have

[tex]a_{2}[/tex] =(1) [tex](\frac{1}{2} )^{2-1}[/tex]= 1/2

[tex]a_{3}[/tex] = 1× [tex](\frac{1}{2} )^{3-1}[/tex]= 1/4

[tex]a_{4}[/tex] = 1× [tex](\frac{1}{2} )^{4-1}[/tex]= 1/8

[tex]a_{5}[/tex] = 1× [tex](\frac{1}{2} )^{5-1}[/tex]= 1/16

[tex]a_{6}[/tex] = 1× [tex](\frac{1}{2} )^{6-1}[/tex]= 1/32

......

Therefore the sequence is in the same series, and we get the next two terms of the sequence which are 1/16, 1/32

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The function f(x)=1+|2x-5| in piecewise form without using absolute values will be f₁ = 4, f₂ = 2 and  a = 5/2.

Given that,

f(x) = 1 + |2x - 5|

And,

f(x) = {f₁       x < a

         {f₂      x ≥ a

Now,

We have,

f(x) = 1 + |2x - 5|

And,

By definition of absolute value,

|x| = {x        x ≥ 0

       {-x       x < 0

And,

Given the absolute value,

|2x - 5|

Solve for x,

i.e.

2x - 5 = 0

We get,

x = 5/2 = 2.5

i.e.

a = 5/2

i.e.

For all values greater than x = 5/2, 2x - 5 is positive,

And,

For all values less than x = 5/2, 2x - 5 is negative.

So,

|x| = {x        x ≥ 5/2

       {-x       x < 5/2

i.e.

|2x - 5| = {2x - 5        x ≥ 5/2

              {-(2x - 5)       x < 5/2

Now,

f(1) = 1 + |2(1) - 5|

We get,

f₁ = 4

And,

f(2) = 1 + |2(2) - 5|

We get,

f₂ = 2

Hence we can say that the function f(x)=1+|2x-5| in piecewise form without using absolute values will be f₁ = 4, f₂ = 2 and  a = 5/2.

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Answer:

b) 9

Step-by-step explanation:

Given that,

→ A = -3

Then the value of A² will be,

→ (-3)² = 9

Hence, option (b) is correct.

Answer:

You have to use the distance formula

d=√(x2-x1)^2 + (y2-y1)^2

replace the points and get 10

The inequality given by (x/3) + 5 ≥ 1/6 has the solution x ≥ -29/2 or [-29/2 , +∞).

Inequality refers to the relationship between two non-equal expressions. It can be denoted by > for greater than, < for less than, >/= for greater than and equal to, and </= for less than and equal to.

To solve an inequality is to find the values of x such that when we substitute that number for x we have a true statement.

Given the inequality (x/3) + 5 ≥ 1/6, subtract 5 from both sides.

(x/3) + 5 - 5 ≥ 1/6 - 5

x/3 ≥ -29/6

Multiply both sides by 3.

3(x/3) ≥ 3(-29/6)

x ≥ -29/2

To check, let x = -29/2

x = -29/2 ≥ -29/2

Substitute this value to the inequality.

(x/3) + 5 ≥ 1/6

(-29/2)/3 + 5 ≥ 1/6

1/6 ≥ 1/6

let x = -14,

x = -14 ≥ -29/2

Substitute this value to the inequality.

(x/3) + 5 ≥ 1/6

-14/3 + 5 ≥ 1/6

1/3 ≥ 1/6

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The numerical length of line segment AC is 25.

A line segment refers to a straight line connecting two points.

If point B is on line segment AC, then point B divides the line segment into segments AB and BC.

AB + BC = AC

Given that AB =2x + 10, BC = x, and AC = 5x, substitute these expressions in the equation AB + BC = AC.

AB + BC = AC

2x + 10 + x = 5x

3x + 10 = 5x

5x - 3x = 10

2x = 10

x = 5

To determine the numerical length of line segment AC, substitute the value of x in the equation AC = 5x.

AC = 5x

AC = 5(5)

AC = 25

Hence, the numerical length of line segment AC is 25.

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Answer:

-4/3

Step-by-step explanation:

[tex] \frac{6 - ( - 2)}{ - 2 - 4} = - \frac{8}{6} = - \frac{4}{3} [/tex]

For given data set, The value of mean is 6.02.

The sum of a set of numbers divided by the total number of numbers in the set is known as the arithmetic mean or arithmetic average in mathematics and statistics.

The formula to calculate mean is = sum of all observations / total number of observations

x = 4     5    6    7    8  

f = 12     1     8   18   4        ∑f = 43

fx = 48  5   48  126  32    ∑fx = 259

The formula of mean = ∑fx /  ∑f

= 6.02

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Answer:

She could have planted 250 seeds on Wednesday

The value of the given expression (5/3)(3x - 6) - (6 - 4x) at x = 5 is 29.

According to the given question.

We have an expression (5/3)(3x - 6) - (6 - 4x).

So, the value of the given expression (5/3)(3x - 6) - (6 - 4x) at x = 5 is given by

(5/3)(3x - 6) - (6 - 4x)

= 5x - 10 - (6 - 4x)               (by distributive rule)

= 5x - 10 - 6 + 4x

= 9x - 16

= 9(5) - 16                 (at x = 5)

= 29

Hence, the value of the given expression (5/3)(3x - 6) - (6 - 4x) at x = 5 is 29.

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The inequality that models the situation is:

$50 + $25*x < $175

Where x is the number of lessons that the student can take.

We know that Mr. Bass charges $25 per class plus a fixed fee of $50.

Then if a student takes x classes, the cost is given by the expression:

$50 + $25*x

And we know that this needs to be smaller than $175, then we can write the inequality:

$50 + $25*x < $175

Now we can solve this for x:

$25*x < $175 - $50

$25*x < $125

x < $125/$25

x < 5

So the student needs to take less than 5 classes.

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Answer:

x=2/7 - 6y/7

Step-by- explanation:

The length of the line segment XY which was bisected at point M is;

1) 32

2) 6

1) From the given line segments, it is clear that XM is congruent to YM since M bisects XY. Thus;

XM = YM and XM + YM = XY

We are given that;

XM = 3x + 1

YM = 8x - 24

Thus;

3x + 1 = 8x - 24

8x - 3x = 1 + 24

5x = 25

x = 25/5

x = 5

Thus;

XM = 3(5) + 1 = 16

YM = 8(5) - 24 = 16

XY = 16 + 16 = 32

2) From the given line segments, it is clear that XM is congruent to YM since M bisects XY. Thus;

XM = YM and XM + YM = XY

We are given that;

XM = 5x + 8

YM = 9x + 12

Thus;

5x + 8 = 9x + 12

9x - 5x = 8 - 12

4x = -4

x = -1

XM = 5(-1) + 8 = 3

YM = 9(-1) + 12 = 3

XY = 6

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The statement "Line t is called the transversal for lines p and q" is true

Given,

The statement "Line t is called the transversal for lines p and q"

In the figure we can see that line t cut two parallel line p and q

So the line t is transversal for lines p and q

So the given statement "Line t is called the transversal for lines p and q" is true

Hence, the The statement "Line t is called the transversal for lines p and q" is true

The complete question is:

State whether the sentence is true or false. If false, replace the underlined word or number to make a true sentence.

Line t is called the transversal for lines p and q .

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Answer:

x

2

−4x−5=0

All equations of the form ax

2

+bx+c=0 can be solved using the quadratic formula:  

2a

−b±

b

2

−4ac

​

​

. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

x

2

−4x−5=0

This equation is in standard form: ax

2

+bx+c=0. Substitute 1 for a, −4 for b, and −5 for c in the quadratic formula,  

2a

−b±

b

2

−4ac

​

​

.

x=

2

−(−4)±

(−4)

2

−4(−5)

​

​

Square −4.

x=

2

−(−4)±

16−4(−5)

​

​

Multiply −4 times −5.

x=

2

−(−4)±

16+20

​

​

Add 16 to 20.

x=

2

−(−4)±

36

​

​

Take the square root of 36.

x=

2

−(−4)±6

​

The opposite of −4 is 4.

x=

2

4±6

​

Now solve the equation x=

2

4±6

​

 when ± is plus. Add 4 to 6.

x=

2

10

​

Divide 10 by 2.

x=5

Now solve the equation x=

2

4±6

​

 when ± is minus. Subtract 6 from 4.

x=

2

−2

​

Divide −2 by 2.

x=−1

The equation is now solved.

x=5

x=−1

Answer:

$26.22

Step-by-step explanation:

Stuart's bank account balance (before) : $ - 51.41

Profit/Loss : + $ 77.63

Therefore:

-  $  5  1  .  4  1

+

   $ 7  7  .  6  3

_____________

  $ 2  6  .  2  2

Therefore, Stuart has $26.22 in his bank account at the end of the month assuming there are no other other transactions.

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The total percentage they travelled when Jai fell asleep is 35%.

In mathematics, a percentage is a ratio or value that is expressed as a fraction of 100. The Latin term "per centum," which means "by a hundred," is the source of the English word "percent." The sign "%" stands for percentage. We apply the percentage method to determine the portion of a whole expressed in terms of 100. Use the percentage formula to convert a number to a fraction of 100.

The total length of trip was 740 miles.

Jai travelled before they fell asleep  = 259 miles

Therefore the percentage of total trip travelled before Jai fell asleep =

= [tex]\frac{259}{740}\times100[/tex]

= 35 %

So by 35% of the total trip, they travelled when Jai fell asleep.

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Answer:

55 minutes

Step-by-step explanation:

→ Work out long it will take to get to 7:00

7:00 - 6:10 = 50 minutes

→ Work out how much extra time after 7:00

7:05 - 7:00 = 5 minutes

→ Add the 2 answers together

50 + 5 = 55 minutes

According to the question, the given expression can be simplified with the help of factors.

Given expression = [tex]-2\sqrt{-45}-3\sqrt{125}[/tex]

Do the factors of 45 as well as 125 and take the common things out from the square root:

Required expression = [tex]-2(3)\sqrt{-5}-3(5)\sqrt{-5}= -21i\sqrt{5}[/tex]

In the theory of complex number, [tex]i^{2} = -1[/tex] is already defined.

Hence, the answer for the given expression is [tex]-21i\sqrt{5}[/tex].

What is simplification?

Simplification is the process to make the expression as simple for the calculation. That means, to calculate the solution of a complex expression.

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By elimination, the solution of the system of equations, x + y = 12 and x - y = 2, is (7 , 5).

A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.

There are three methods that can be used to solve system of equations.

1. Elimination

2. Substitution

3. Graphing

Using the elimination method, given two equations in x and y, a variable should be eliminated by adding/subtracting the two equations.

Adding the two equations will eliminate the variable y.

x + y = 12     (equation 1)

x  - y = 2    (equation 2)

2x + 0y = 14

x = 7

Substitute the value of x to any of the two equation and solve for y.

x + y = 12     (equation 1)

7 + y = 12

y = 12 - 7

y = 5

Hence, the solution of the system of equations is (7 , 5).

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The floating-point literal that correctly represents the scientific notation value: 2.3 x 10^7 will be A. 2.3e^7.

It should be noted that scientific notation simply means. way that's used to express numbers that are either too large or too small to be written in decimal form.

Therefore, it should be noted that the floating-point literal that correctly represents the scientific notation value: 2.3 x 10^7 will be:

= 2.3 × 20^7

= 2.3 × e^7

= 2.3e7

The correct option is A.

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Which floating-point literal correctly represents the scientific notation value: 2.3 x 10^7?

a. 2.3e^7

b. 2.3 × 10e^7

c. 2.3e × 10^7

d. 2.3 × e^7

To evaluate anything is to determine its monetary value. Finding all of the values of a variable or collection of variables necessary to make a statement true is what it means to solve something.

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Answer:(x+3)(x-5)

Step-by-step explanation:(x^2-5x)+(3x-15)

x(x-5)+3(x-5)

(x+3)(x-5)

Answer:

11, 15, 19, 23 = An+4

23,19,15,11=An-4

Answer:

Hope this helps :)

All of these are the answers, the final answer is the simplified one, and the explanation is below.

9/6 (improper fraction)

1 3/6 (mixed number)

1 1/2 (simplified)

Step-by-step explanation:

1. Common denominators which is 6.

7/6 + 1/3

1/3 × 2/2 = 2/6

2. Add the numerators since they already have common denominators.

7/6 + 2/6 = 9/6

3. Change into mixed number and simplify if needed.

9/6 = 1 3/6 = 1 1/2